%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW371+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 18:08:39 EDT 2024 % Result : Theorem 169.19s 169.64s % Output : CNFRefutation 169.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWW371+1 : TPTP v8.2.0. Released v5.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n007.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Wed Jun 19 06:10:39 EDT 2024 % 0.11/0.33 % CPUTime : % 0.46/0.56 start to proof:theBenchmark % 168.80/169.47 %------------------------------------------- % 168.80/169.47 % File :CSE---1.7 % 168.80/169.47 % Problem :theBenchmark % 168.80/169.47 % Transform :cnf % 168.80/169.47 % Format :tptp:raw % 168.80/169.47 % Command :java -jar mcs_scs.jar %d %s % 168.80/169.47 % 168.80/169.47 % Result :Theorem 154.380000s % 168.80/169.47 % Output :CNFRefutation 154.380000s % 168.80/169.47 %------------------------------------------- % 168.80/169.47 %------------------------------------------------------------------------------ % 168.80/169.47 % File : SWW371+1 : TPTP v8.2.0. Released v5.2.0. % 168.80/169.47 % Domain : Software Verification % 168.80/169.47 % Problem : Hoare's Logic with Procedures 435513, 5000 axioms selected % 168.80/169.47 % Version : Especial. % 168.80/169.48 % English : % 168.80/169.48 % 168.80/169.48 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 168.80/169.48 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 168.80/169.48 % Source : [Bla11] % 168.80/169.48 % Names : hoare_435513.5000.p [Bla11] % 168.80/169.48 % 168.80/169.48 % Status : ContradictoryAxioms % 168.80/169.48 % Rating : 0.83 v8.2.0, 0.78 v7.4.0, 0.87 v7.3.0, 0.83 v7.1.0, 0.78 v7.0.0, 0.83 v6.4.0, 0.81 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0, 1.00 v5.2.0 % 168.80/169.48 % Syntax : Number of formulae : 5249 (1762 unt; 0 def) % 168.80/169.48 % Number of atoms : 12561 (4567 equ) % 168.80/169.48 % Maximal formula atoms : 13 ( 2 avg) % 168.80/169.48 % Number of connectives : 8321 (1009 ~; 149 |; 707 &) % 168.80/169.48 % ( 887 <=>;5569 =>; 0 <=; 0 <~>) % 168.80/169.48 % Maximal formula depth : 22 ( 6 avg) % 168.80/169.48 % Maximal term depth : 19 ( 2 avg) % 168.80/169.48 % Number of predicates : 146 ( 145 usr; 2 prp; 0-6 aty) % 168.80/169.48 % Number of functors : 390 ( 390 usr; 54 con; 0-7 aty) % 168.80/169.48 % Number of variables : 16647 (16508 !; 139 ?) % 168.80/169.48 % SPC : FOF_CAX_RFO_SEQ % 168.80/169.48 % 168.80/169.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 168.80/169.48 % 2011-03-01 12:44:50 % 168.80/169.48 %------------------------------------------------------------------------------ % 168.80/169.48 %----Relevant facts (4986) % 168.80/169.48 fof(fact_ext,axiom, % 168.80/169.48 ! [V_g_2,V_f_2] : % 168.80/169.48 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 168.80/169.48 => V_f_2 = V_g_2 ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_empty,axiom, % 168.80/169.48 ! [V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 168.80/169.48 % 168.80/169.48 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 168.80/169.48 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 168.80/169.48 % 168.80/169.48 fof(fact_cut,axiom, % 168.80/169.48 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 168.80/169.48 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_hoare__derivs_Oinsert,axiom, % 168.80/169.48 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 168.80/169.48 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_derivs__insertD,axiom, % 168.80/169.48 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) % 168.80/169.48 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 168.80/169.48 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_empty__not__insert,axiom, % 168.80/169.48 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 168.80/169.48 % 168.80/169.48 fof(fact_insert__not__empty,axiom, % 168.80/169.48 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 168.80/169.48 % 168.80/169.48 fof(fact_doubleton__eq__iff,axiom, % 168.80/169.48 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.80/169.48 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 168.80/169.48 <=> ( ( V_a_2 = V_ca_2 % 168.80/169.48 & V_b_2 = V_d_2 ) % 168.80/169.48 | ( V_a_2 = V_d_2 % 168.80/169.48 & V_b_2 = V_ca_2 ) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_singleton__inject,axiom, % 168.80/169.48 ! [V_b_2,V_a_2,T_a] : % 168.80/169.48 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 168.80/169.48 => V_a_2 = V_b_2 ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_bot__apply,axiom, % 168.80/169.48 ! [V_x_2,T_b,T_a] : % 168.80/169.48 ( class_Orderings_Obot(T_a) % 168.80/169.48 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_MGF__complete,axiom, % 168.80/169.48 ! [V_Q_2,V_P_2,V_ca_2] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 168.80/169.48 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_the__elem__eq,axiom, % 168.80/169.48 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ). % 168.80/169.48 % 168.80/169.48 fof(fact_insert__absorb2,axiom, % 168.80/169.48 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ). % 168.80/169.48 % 168.80/169.48 fof(fact_insert__commute,axiom, % 168.80/169.48 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ). % 168.80/169.48 % 168.80/169.48 fof(fact_insert__code,axiom, % 168.80/169.48 ! [V_x_2,V_A_2,V_y_2,T_a] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 168.80/169.48 <=> ( V_y_2 = V_x_2 % 168.80/169.48 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_hoare__sound,axiom, % 168.80/169.48 ! [V_ts_2,V_G_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_state__not__singleton__def,axiom, % 168.80/169.48 ( c_Hoare__Mirabelle_Ostate__not__singleton % 168.80/169.48 <=> ? [B_s,B_t] : B_s != B_t ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_triple_Oinject,axiom, % 168.80/169.48 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 168.80/169.48 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 168.80/169.48 <=> ( V_fun1_2 = V_fun1_H_2 % 168.80/169.48 & V_com_2 = V_com_H_2 % 168.80/169.48 & V_fun2_2 = V_fun2_H_2 ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_triple_Orecs,axiom, % 168.80/169.48 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 168.80/169.48 % 168.80/169.48 fof(fact_triple_Osimps_I2_J,axiom, % 168.80/169.48 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 168.80/169.48 % 168.80/169.48 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 168.80/169.48 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 168.80/169.48 % 168.80/169.48 fof(fact_hoare__derivs_OSkip,axiom, % 168.80/169.48 ! [V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ). % 168.80/169.48 % 168.80/169.48 fof(fact_conseq1,axiom, % 168.80/169.48 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_G_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 168.80/169.48 => ( ! [B_Z,B_s] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 168.80/169.48 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_conseq2,axiom, % 168.80/169.48 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_G_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 168.80/169.48 => ( ! [B_Z,B_s] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 168.80/169.48 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_Comp,axiom, % 168.80/169.48 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 168.80/169.48 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_conseq12,axiom, % 168.80/169.48 ! [V_Q_2,V_P_2,V_Q_H_2,V_ca_2,V_P_H_2,V_G_2,T_a] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 168.80/169.48 => ( ! [B_Z,B_s] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 168.80/169.48 => ! [B_s_H] : % 168.80/169.48 ( ! [B_Z_H] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s)) % 168.80/169.48 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) ) % 168.80/169.48 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_single__stateE,axiom, % 168.80/169.48 ( c_Hoare__Mirabelle_Ostate__not__singleton % 168.80/169.48 => ! [B_t] : % 168.80/169.48 ~ ! [B_s] : B_s = B_t ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_MGF__lemma1,axiom, % 168.80/169.48 ! [V_ca_2,V_G_2] : % 168.80/169.48 ( c_Hoare__Mirabelle_Ostate__not__singleton % 168.80/169.48 => ( ! [B_x] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) % 168.80/169.48 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 168.80/169.48 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_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)))) ) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_subset__singletonD,axiom, % 168.80/169.48 ! [V_x_2,V_A_2,T_a] : % 168.80/169.48 ( 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))))) % 168.80/169.48 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.48 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_singletonE,axiom, % 168.80/169.48 ! [V_a_2,V_b_2,T_a] : % 168.80/169.48 ( 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))))) % 168.80/169.48 => V_b_2 = V_a_2 ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_order__refl,axiom, % 168.80/169.48 ! [V_x,T_a] : % 168.80/169.48 ( class_Orderings_Opreorder(T_a) % 168.80/169.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_equalityCE,axiom, % 168.80/169.48 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 168.80/169.48 ( V_A_2 = V_B_2 % 168.80/169.48 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.48 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 168.80/169.48 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_equalityI,axiom, % 168.80/169.48 ! [V_B_2,V_A_2,T_a] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.80/169.48 => V_A_2 = V_B_2 ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_emptyE,axiom, % 168.80/169.48 ! [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)))) ). % 168.80/169.48 % 168.80/169.48 fof(fact_insertE,axiom, % 168.80/169.48 ! [V_A_2,V_b_2,V_a_2,T_a] : % 168.80/169.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 168.80/169.48 => ( V_a_2 != V_b_2 % 168.80/169.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 168.80/169.48 % 168.80/169.48 fof(fact_insertCI,axiom, % 168.80/169.49 ! [V_b_2,V_B_2,V_a_2,T_a] : % 168.80/169.49 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 168.80/169.49 => V_a_2 = V_b_2 ) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_subsetD,axiom, % 168.80/169.49 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_empty__subsetI,axiom, % 168.80/169.49 ! [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)) ). % 168.80/169.49 % 168.80/169.49 fof(fact_subset__refl,axiom, % 168.80/169.49 ! [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)) ). % 168.80/169.49 % 168.80/169.49 fof(fact_le__fun__def,axiom, % 168.80/169.49 ! [V_g_2,V_f_2,T_a,T_b] : % 168.80/169.49 ( class_Orderings_Oord(T_b) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.80/169.49 <=> ! [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))) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_mem__def,axiom, % 168.80/169.49 ! [V_A_2,V_x_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_linorder__linear,axiom, % 168.80/169.49 ! [V_y,V_x,T_a] : % 168.80/169.49 ( class_Orderings_Olinorder(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_set__eq__subset,axiom, % 168.80/169.49 ! [T_a,V_B_2,V_A_2] : % 168.80/169.49 ( V_A_2 = V_B_2 % 168.80/169.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_order__eq__iff,axiom, % 168.80/169.49 ! [V_y_2,V_x_2,T_a] : % 168.80/169.49 ( class_Orderings_Oorder(T_a) % 168.80/169.49 => ( V_x_2 = V_y_2 % 168.80/169.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_equalityD1,axiom, % 168.80/169.49 ! [T_a,V_B_2,V_A_2] : % 168.80/169.49 ( V_A_2 = V_B_2 % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_equalityD2,axiom, % 168.80/169.49 ! [T_a,V_B_2,V_A_2] : % 168.80/169.49 ( V_A_2 = V_B_2 % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_order__eq__refl,axiom, % 168.80/169.49 ! [V_y,V_x,T_a] : % 168.80/169.49 ( class_Orderings_Opreorder(T_a) % 168.80/169.49 => ( V_x = V_y % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_le__funD,axiom, % 168.80/169.49 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 168.80/169.49 ( class_Orderings_Oord(T_b) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.80/169.49 => 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))) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_eqset__imp__iff,axiom, % 168.80/169.49 ! [V_x_2,T_a,V_B_2,V_A_2] : % 168.80/169.49 ( V_A_2 = V_B_2 % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_eqelem__imp__iff,axiom, % 168.80/169.49 ! [V_A_2,T_a,V_y_2,V_x_2] : % 168.80/169.49 ( V_x_2 = V_y_2 % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_in__mono,axiom, % 168.80/169.49 ! [V_x_2,V_B_2,V_A_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_order__antisym__conv,axiom, % 168.80/169.49 ! [V_x_2,V_y_2,T_a] : % 168.80/169.49 ( class_Orderings_Oorder(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.49 <=> V_x_2 = V_y_2 ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_eq__mem__trans,axiom, % 168.80/169.49 ! [V_A_2,T_a,V_b_2,V_a_2] : % 168.80/169.49 ( V_a_2 = V_b_2 % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_ord__eq__le__trans,axiom, % 168.80/169.49 ! [V_c,V_b,V_a,T_a] : % 168.80/169.49 ( class_Orderings_Oord(T_a) % 168.80/169.49 => ( V_a = V_b % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_xt1_I3_J,axiom, % 168.80/169.49 ! [V_c,V_b,V_a,T_a] : % 168.80/169.49 ( class_Orderings_Oorder(T_a) % 168.80/169.49 => ( V_a = V_b % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_set__rev__mp,axiom, % 168.80/169.49 ! [V_B_2,V_A_2,V_x_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_set__mp,axiom, % 168.80/169.49 ! [V_x_2,V_B_2,V_A_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_subset__trans,axiom, % 168.80/169.49 ! [V_C_2,V_B_2,V_A_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_ord__le__eq__trans,axiom, % 168.80/169.49 ! [V_c,V_b,V_a,T_a] : % 168.80/169.49 ( class_Orderings_Oord(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.49 => ( V_b = V_c % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_xt1_I4_J,axiom, % 168.80/169.49 ! [V_c,V_a,V_b,T_a] : % 168.80/169.49 ( class_Orderings_Oorder(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 168.80/169.49 => ( V_b = V_c % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_order__antisym,axiom, % 168.80/169.49 ! [V_y,V_x,T_a] : % 168.80/169.49 ( class_Orderings_Oorder(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 168.80/169.49 => V_x = V_y ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_order__trans,axiom, % 168.80/169.49 ! [V_z,V_y,V_x,T_a] : % 168.80/169.49 ( class_Orderings_Opreorder(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_xt1_I5_J,axiom, % 168.80/169.49 ! [V_x,V_y,T_a] : % 168.80/169.49 ( class_Orderings_Oorder(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.49 => V_x = V_y ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_xt1_I6_J,axiom, % 168.80/169.49 ! [V_z,V_x,V_y,T_a] : % 168.80/169.49 ( class_Orderings_Oorder(T_a) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_equalityE,axiom, % 168.80/169.49 ! [T_a,V_B_2,V_A_2] : % 168.80/169.49 ( V_A_2 = V_B_2 % 168.80/169.49 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_le__funE,axiom, % 168.80/169.49 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 168.80/169.49 ( class_Orderings_Oord(T_b) % 168.80/169.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.80/169.49 => 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))) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_linorder__le__cases,axiom, % 168.80/169.49 ! [V_y,V_x,T_a] : % 168.80/169.49 ( class_Orderings_Olinorder(T_a) % 168.80/169.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_subset__insert,axiom, % 168.80/169.49 ! [V_B_2,V_A_2,V_x_2,T_a] : % 168.80/169.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 => ( 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))) % 168.80/169.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_insert__subset,axiom, % 168.80/169.49 ! [V_B_2,V_A_2,V_x_2,T_a] : % 168.80/169.49 ( 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)) % 168.80/169.49 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 168.80/169.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_bot__least,axiom, % 168.80/169.49 ! [V_x,T_a] : % 168.80/169.49 ( class_Orderings_Obot(T_a) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_all__not__in__conv,axiom, % 168.80/169.49 ! [V_A_2,T_a] : % 168.80/169.49 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.49 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_ex__in__conv,axiom, % 168.80/169.49 ! [V_A_2,T_a] : % 168.80/169.49 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.49 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_empty__iff,axiom, % 168.80/169.49 ! [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)))) ). % 168.80/169.49 % 168.80/169.49 fof(fact_equals0D,axiom, % 168.80/169.49 ! [V_a_2,T_a,V_A_2] : % 168.80/169.49 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.49 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_subset__empty,axiom, % 168.80/169.49 ! [V_A_2,T_a] : % 168.80/169.49 ( 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)))) % 168.80/169.49 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_insertI1,axiom, % 168.80/169.49 ! [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))) ). % 168.80/169.49 % 168.80/169.49 fof(fact_insert__iff,axiom, % 168.80/169.49 ! [V_A_2,V_b_2,V_a_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 168.80/169.49 <=> ( V_a_2 = V_b_2 % 168.80/169.49 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_insert__ident,axiom, % 168.80/169.49 ! [V_B_2,V_A_2,V_x_2,T_a] : % 168.80/169.49 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 168.80/169.49 => ( 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) % 168.80/169.49 <=> V_A_2 = V_B_2 ) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_insertI2,axiom, % 168.80/169.49 ! [V_b_2,V_B_2,V_a_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 168.80/169.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_insert__absorb,axiom, % 168.80/169.49 ! [V_A_2,V_a_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.49 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_subset__insertI,axiom, % 168.80/169.49 ! [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))) ). % 168.80/169.49 % 168.80/169.49 fof(fact_subset__insertI2,axiom, % 168.80/169.49 ! [V_b_2,V_B_2,V_A_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.49 => 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))) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_insert__mono,axiom, % 168.80/169.49 ! [V_a_2,V_D_2,V_C_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 168.80/169.49 => 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))) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_asm,axiom, % 168.80/169.49 ! [V_G_2,V_ts_2,T_a] : % 168.80/169.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_G_2)) % 168.80/169.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_weaken,axiom, % 168.80/169.49 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] : % 168.80/169.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2) % 168.80/169.49 => ( 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)) % 168.80/169.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_thin,axiom, % 168.80/169.49 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 168.80/169.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 168.80/169.49 => ( 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_G_2)) % 168.80/169.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_singleton__iff,axiom, % 168.80/169.49 ! [V_a_2,V_b_2,T_a] : % 168.80/169.49 ( 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))))) % 168.80/169.49 <=> V_b_2 = V_a_2 ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_WTs__elim__cases_I4_J,axiom, % 168.80/169.49 ! [V_c2,V_c1] : % 168.80/169.49 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 168.80/169.49 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 168.80/169.49 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_MGT__BodyN,axiom, % 168.80/169.49 ! [V_G_2,V_pn_2] : % 168.80/169.49 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 168.80/169.49 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_weak__Body,axiom, % 168.80/169.49 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] : % 168.80/169.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 168.80/169.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_BodyN,axiom, % 168.80/169.49 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 168.80/169.49 ( 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_G_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)))) % 168.80/169.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ). % 168.80/169.49 % 168.80/169.49 fof(fact_com_Osimps_I13_J,axiom, % 168.80/169.49 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 168.80/169.49 % 168.80/169.49 fof(fact_com_Osimps_I12_J,axiom, % 168.80/169.49 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 168.80/169.49 % 168.80/169.49 fof(fact_com_Osimps_I19_J,axiom, % 168.80/169.49 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 168.80/169.49 % 168.80/169.49 fof(fact_com_Osimps_I18_J,axiom, % 168.80/169.49 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 168.80/169.49 % 168.80/169.49 fof(fact_WT_OSkip,axiom, % 168.80/169.49 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 168.80/169.49 % 168.80/169.49 fof(fact_WT_Oequations_I1_J,axiom, % 168.80/169.49 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 168.80/169.49 % 168.80/169.49 fof(fact_com_Osimps_I48_J,axiom, % 168.80/169.49 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 168.80/169.49 % 168.80/169.49 fof(fact_com_Osimps_I6_J,axiom, % 168.80/169.50 ! [V_pname_H_2,V_pname_2] : % 168.80/169.50 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 168.80/169.50 <=> V_pname_2 = V_pname_H_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I3_J,axiom, % 168.80/169.50 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 168.80/169.50 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 168.80/169.50 <=> ( V_com1_2 = V_com1_H_2 % 168.80/169.50 & V_com2_2 = V_com2_H_2 ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WT_OSemi,axiom, % 168.80/169.50 ! [V_c1,V_c0] : % 168.80/169.50 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 168.80/169.50 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 168.80/169.50 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WT_Oequations_I4_J,axiom, % 168.80/169.50 ! [V_a2_2,V_a1_2] : % 168.80/169.50 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 168.80/169.50 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 168.80/169.50 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I49_J,axiom, % 168.80/169.50 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WT__bodiesD,axiom, % 168.80/169.50 ! [V_b,V_pn] : % 168.80/169.50 ( c_Com_OWT__bodies % 168.80/169.50 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 168.80/169.50 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_diff__single__insert,axiom, % 168.80/169.50 ! [V_B_2,V_x_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_subset__insert__iff,axiom, % 168.80/169.50 ! [V_B_2,V_x_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 168.80/169.50 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 168.80/169.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__dom__body,axiom, % 168.80/169.50 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WT_OBody,axiom, % 168.80/169.50 ! [V_pn] : % 168.80/169.50 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 168.80/169.50 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WTs__elim__cases_I8_J,axiom, % 168.80/169.50 ! [V_a_2,V_P_2,V_X_2] : % 168.80/169.50 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2))) % 168.80/169.50 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_rev__predicate1D,axiom, % 168.80/169.50 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 168.80/169.50 ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 168.80/169.50 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_predicate1D,axiom, % 168.80/169.50 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 168.80/169.50 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 168.80/169.50 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_subsetI,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,T_a] : % 168.80/169.50 ( ! [B_x] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) ) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WT_Oequations_I7_J,axiom, % 168.80/169.50 ! [V_a_2] : % 168.80/169.50 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 168.80/169.50 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_eq__mem,axiom, % 168.80/169.50 ! [V_y_2,V_x_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 168.80/169.50 <=> V_x_2 = V_y_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_DiffI,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 168.80/169.50 => 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))) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_DiffE,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 168.80/169.50 ( 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))) % 168.80/169.50 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I7_J,axiom, % 168.80/169.50 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 168.80/169.50 ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) % 168.80/169.50 <=> ( V_vname_2 = V_vname_H_2 % 168.80/169.50 & V_pname_2 = V_pname_H_2 % 168.80/169.50 & V_fun_2 = V_fun_H_2 ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__idemp,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__iff,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 168.80/169.50 ( 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))) % 168.80/169.50 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.50 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_DiffD1,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 168.80/169.50 ( 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))) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_DiffD2,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 168.80/169.50 ( 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))) % 168.80/169.50 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_empty__Diff,axiom, % 168.80/169.50 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__empty,axiom, % 168.80/169.50 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__cancel,axiom, % 168.80/169.50 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__subset,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__mono,axiom, % 168.80/169.50 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_double__diff,axiom, % 168.80/169.50 ! [V_C_2,V_B_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 168.80/169.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I63_J,axiom, % 168.80/169.50 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I62_J,axiom, % 168.80/169.50 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I51_J,axiom, % 168.80/169.50 ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I50_J,axiom, % 168.80/169.50 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I21_J,axiom, % 168.80/169.50 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 168.80/169.50 % 168.80/169.50 fof(fact_com_Osimps_I20_J,axiom, % 168.80/169.50 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 168.80/169.50 % 168.80/169.50 fof(fact_insert__Diff1,axiom, % 168.80/169.50 ! [V_A_2,V_B_2,V_x_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 168.80/169.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_insert__Diff__if,axiom, % 168.80/169.50 ! [V_A_2,V_B_2,V_x_2,T_a] : % 168.80/169.50 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 168.80/169.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) % 168.80/169.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 168.80/169.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__insert,axiom, % 168.80/169.50 ! [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)))) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__insert2,axiom, % 168.80/169.50 ! [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) ). % 168.80/169.50 % 168.80/169.50 fof(fact_insert__Diff__single,axiom, % 168.80/169.50 ! [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) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WT_OCall,axiom, % 168.80/169.50 ! [V_a_2,V_X_2,V_pn_2] : % 168.80/169.50 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) % 168.80/169.50 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WT_Oequations_I8_J,axiom, % 168.80/169.50 ! [V_a3_2,V_a1_2,V_a2_2] : % 168.80/169.50 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 168.80/169.50 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Diff__insert__absorb,axiom, % 168.80/169.50 ! [V_A_2,V_x_2,T_a] : % 168.80/169.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_insert__Diff,axiom, % 168.80/169.50 ! [V_A_2,V_a_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.50 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__Diff,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite_OinsertI,axiom, % 168.80/169.50 ! [V_a_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite_OemptyI,axiom, % 168.80/169.50 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 168.80/169.50 % 168.80/169.50 fof(fact_dom__minus,axiom, % 168.80/169.50 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 168.80/169.50 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 168.80/169.50 => 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) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_insert__dom,axiom, % 168.80/169.50 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 168.80/169.50 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 168.80/169.50 => 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) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_domI,axiom, % 168.80/169.50 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 168.80/169.50 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_domIff,axiom, % 168.80/169.50 ! [V_m_2,T_b,V_a_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 168.80/169.50 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__Diff__insert,axiom, % 168.80/169.50 ! [V_B_2,V_a_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)))) % 168.80/169.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_WTs__elim__cases_I7_J,axiom, % 168.80/169.50 ! [V_P] : % 168.80/169.50 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 168.80/169.50 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_the_Osimps,axiom, % 168.80/169.50 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 168.80/169.50 % 168.80/169.50 fof(fact_not__None__eq,axiom, % 168.80/169.50 ! [T_a,V_x_2] : % 168.80/169.50 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 168.80/169.50 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite,axiom, % 168.80/169.50 ! [V_A_2,T_a] : % 168.80/169.50 ( class_Finite__Set_Ofinite(T_a) % 168.80/169.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__code,axiom, % 168.80/169.50 ! [V_A_2,T_a] : % 168.80/169.50 ( class_Finite__Set_Ofinite(T_a) % 168.80/169.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_option_Oinject,axiom, % 168.80/169.50 ! [V_a_H_2,V_a_2,T_a] : % 168.80/169.50 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 168.80/169.50 <=> V_a_2 = V_a_H_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite_Oequations_I1_J,axiom, % 168.80/169.50 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__insert,axiom, % 168.80/169.50 ! [V_A_2,V_a_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 168.80/169.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_rev__finite__subset,axiom, % 168.80/169.50 ! [V_A_2,V_B_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__subset,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__Diff2,axiom, % 168.80/169.50 ! [V_A_2,V_B_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 168.80/169.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_option_Osimps_I2_J,axiom, % 168.80/169.50 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 168.80/169.50 % 168.80/169.50 fof(fact_option_Osimps_I3_J,axiom, % 168.80/169.50 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 168.80/169.50 % 168.80/169.50 fof(fact_not__Some__eq,axiom, % 168.80/169.50 ! [T_a,V_x_2] : % 168.80/169.50 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 168.80/169.50 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__image__simple_Oremove,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 168.80/169.50 => 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)))))) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one_Oremove,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 168.80/169.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => 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)))))) ) ) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 168.80/169.50 ! [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))) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,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)))))) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one_Oinsert__remove,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 168.80/169.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one_Oinsert,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_minus__apply,axiom, % 168.80/169.50 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 168.80/169.50 ( class_Groups_Ominus(T_a) % 168.80/169.50 => 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)) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_diff__eq__diff__less__eq,axiom, % 168.80/169.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.80/169.50 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.50 => ( 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) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 168.80/169.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__empty__induct,axiom, % 168.80/169.50 ! [V_P_2,V_A_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 168.80/169.50 => ( ! [B_a,B_A] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 168.80/169.50 => ( hBOOL(hAPP(V_P_2,B_A)) % 168.80/169.50 => 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)))))) ) ) ) % 168.80/169.50 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one__idem_Osubset__idem,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.80/169.50 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__subset__induct,axiom, % 168.80/169.50 ! [V_P_2,V_A_2,V_F_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 168.80/169.50 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 168.80/169.50 => ( ! [B_a,B_F] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 168.80/169.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 168.80/169.50 => ( hBOOL(hAPP(V_P_2,B_F)) % 168.80/169.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 168.80/169.50 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one__idem_Oidem,axiom, % 168.80/169.50 ! [V_x_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.80/169.50 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__image__simple_Oempty,axiom, % 168.80/169.50 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.50 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_diff__eq__diff__eq,axiom, % 168.80/169.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.80/169.50 ( class_Groups_Oab__group__add(T_a) % 168.80/169.50 => ( 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) % 168.80/169.50 => ( V_a_2 = V_b_2 % 168.80/169.50 <=> V_ca_2 = V_d_2 ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one_Osingleton,axiom, % 168.80/169.50 ! [V_x_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one__idem_Oin__idem,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_elem__set,axiom, % 168.80/169.50 ! [V_xo_2,V_x_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 168.80/169.50 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_set__empty__eq,axiom, % 168.80/169.50 ! [V_xo_2,T_a] : % 168.80/169.50 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 168.80/169.50 ! [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)) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__image__simple_Oinsert,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.80/169.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__one_Oclosed,axiom, % 168.80/169.50 ! [V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.50 => ( ! [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)))))) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_dom__fun__upd,axiom, % 168.80/169.50 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 168.80/169.50 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 168.80/169.50 => 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)))) ) % 168.80/169.50 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 168.80/169.50 => 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)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_psubset__insert__iff,axiom, % 168.80/169.50 ! [V_B_2,V_x_2,V_A_2,T_a] : % 168.80/169.50 ( 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))) % 168.80/169.50 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 168.80/169.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 168.80/169.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => 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)) ) % 168.80/169.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_option_Osimps_I5_J,axiom, % 168.80/169.50 ! [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) ). % 168.80/169.50 % 168.80/169.50 fof(fact_option_Orecs_I2_J,axiom, % 168.80/169.50 ! [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) ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 168.80/169.50 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.80/169.50 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_option_Osimps_I4_J,axiom, % 168.80/169.50 ! [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 ). % 168.80/169.50 % 168.80/169.50 fof(fact_option_Orecs_I1_J,axiom, % 168.80/169.50 ! [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 ). % 168.80/169.50 % 168.80/169.50 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 168.80/169.50 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.50 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.80/169.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_finite__induct,axiom, % 168.80/169.50 ! [V_P_2,V_F_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.80/169.50 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 168.80/169.50 => ( ! [B_x,B_F] : % 168.80/169.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 168.80/169.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 168.80/169.50 => ( hBOOL(hAPP(V_P_2,B_F)) % 168.80/169.50 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 168.80/169.50 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 168.80/169.50 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.50 => ( 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) % 168.80/169.50 => 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)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_linorder__cases,axiom, % 168.80/169.50 ! [V_y,V_x,T_a] : % 168.80/169.50 ( class_Orderings_Olinorder(T_a) % 168.80/169.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.50 => ( V_x != V_y % 168.80/169.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_order__less__asym,axiom, % 168.80/169.50 ! [V_y,V_x,T_a] : % 168.80/169.50 ( class_Orderings_Opreorder(T_a) % 168.80/169.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 168.80/169.50 % 168.80/169.50 fof(fact_xt1_I10_J,axiom, % 168.80/169.51 ! [V_z,V_x,V_y,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__trans,axiom, % 168.80/169.51 ! [V_z,V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_xt1_I2_J,axiom, % 168.80/169.51 ! [V_c,V_a,V_b,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 168.80/169.51 => ( V_b = V_c % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ord__less__eq__trans,axiom, % 168.80/169.51 ! [V_c,V_b,V_a,T_a] : % 168.80/169.51 ( class_Orderings_Oord(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.51 => ( V_b = V_c % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_psubset__trans,axiom, % 168.80/169.51 ! [V_C_2,V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_xt1_I1_J,axiom, % 168.80/169.51 ! [V_c,V_b,V_a,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( V_a = V_b % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ord__eq__less__trans,axiom, % 168.80/169.51 ! [V_c,V_b,V_a,T_a] : % 168.80/169.51 ( class_Orderings_Oord(T_a) % 168.80/169.51 => ( V_a = V_b % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_xt1_I9_J,axiom, % 168.80/169.51 ! [V_a,V_b,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__asym_H,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__imp__not__eq2,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => V_y != V_x ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__imp__not__eq,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => V_x != V_y ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__imp__not__less,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__not__sym,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_less__imp__neq,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => V_x != V_y ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__neqE,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( V_x != V_y % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__antisym__conv3,axiom, % 168.80/169.51 ! [V_x_2,V_y_2,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> V_x_2 = V_y_2 ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__less__linear,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 | V_x = V_y % 168.80/169.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_not__less__iff__gr__or__eq,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 168.80/169.51 | V_x_2 = V_y_2 ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__neq__iff,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( V_x_2 != V_y_2 % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__irrefl,axiom, % 168.80/169.51 ! [V_x,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_folding__image__simple__idem_Oidem,axiom, % 168.80/169.51 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.51 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 168.80/169.51 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 168.80/169.51 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ). % 168.80/169.51 % 168.80/169.51 fof(fact_less__fun__def,axiom, % 168.80/169.51 ! [V_g_2,V_f_2,T_a,T_b] : % 168.80/169.51 ( class_Orderings_Oord(T_b) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 168.80/169.51 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_xt1_I8_J,axiom, % 168.80/169.51 ! [V_z,V_x,V_y,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__le__less__trans,axiom, % 168.80/169.51 ! [V_z,V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_xt1_I7_J,axiom, % 168.80/169.51 ! [V_z,V_x,V_y,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__le__trans,axiom, % 168.80/169.51 ! [V_z,V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_xt1_I11_J,axiom, % 168.80/169.51 ! [V_a,V_b,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 168.80/169.51 => ( V_a != V_b % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__le__neq__trans,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.51 => ( V_a != V_b % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__le__imp__less__or__eq,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 | V_x = V_y ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__antisym__conv2,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> V_x_2 = V_y_2 ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__imp__le,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_leD,axiom, % 168.80/169.51 ! [V_x,V_y,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_xt1_I12_J,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( V_a != V_b % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__neq__le__trans,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( V_a != V_b % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__antisym__conv1,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> V_x_2 = V_y_2 ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_not__leE,axiom, % 168.80/169.51 ! [V_x,V_y,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_leI,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__le__less,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 | V_x_2 = V_y_2 ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_less__le__not__le,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Opreorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.51 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_order__less__le,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Oorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.51 & V_x_2 != V_y_2 ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__le__less__linear,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__not__le,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_linorder__not__less,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Orderings_Olinorder(T_a) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_psubsetD,axiom, % 168.80/169.51 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_not__psubset__empty,axiom, % 168.80/169.51 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 168.80/169.51 % 168.80/169.51 fof(fact_diff__eq__diff__less,axiom, % 168.80/169.51 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_subset__psubset__trans,axiom, % 168.80/169.51 ! [V_C_2,V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_psubset__subset__trans,axiom, % 168.80/169.51 ! [V_C_2,V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_psubset__imp__subset,axiom, % 168.80/169.51 ! [V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_subset__iff__psubset__eq,axiom, % 168.80/169.51 ! [V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 | V_A_2 = V_B_2 ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_psubset__eq,axiom, % 168.80/169.51 ! [V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 & V_A_2 != V_B_2 ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__upd__Some__unfold,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 168.80/169.51 ( 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) % 168.80/169.51 <=> ( ( V_x_2 = V_a_2 % 168.80/169.51 & V_b_2 = V_y_2 ) % 168.80/169.51 | ( V_x_2 != V_a_2 % 168.80/169.51 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__upd__triv,axiom, % 168.80/169.51 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 168.80/169.51 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 168.80/169.51 => 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 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__upd__eqD1,axiom, % 168.80/169.51 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 168.80/169.51 ( 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)) % 168.80/169.51 => V_x_2 = V_y_2 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 168.80/169.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 168.80/169.51 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__triv,axiom, % 168.80/169.51 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 168.80/169.51 % 168.80/169.51 fof(fact_ran__map__upd,axiom, % 168.80/169.51 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 168.80/169.51 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 168.80/169.51 => 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)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__None__restrict,axiom, % 168.80/169.51 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 168.80/169.51 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 168.80/169.51 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) % 168.80/169.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 168.80/169.51 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 168.80/169.51 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 168.80/169.51 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 168.80/169.51 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.51 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 168.80/169.51 | ? [B_x,B_y] : % 168.80/169.51 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 168.80/169.51 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 168.80/169.51 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__restrict__conv,axiom, % 168.80/169.51 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 168.80/169.51 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_restrict__fun__upd,axiom, % 168.80/169.51 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 168.80/169.51 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 168.80/169.51 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) % 168.80/169.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 168.80/169.51 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__restrict,axiom, % 168.80/169.51 ! [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) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__upd__left,axiom, % 168.80/169.51 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 168.80/169.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 168.80/169.51 => 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)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_Diff1__fold__graph,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__comp__None__iff,axiom, % 168.80/169.51 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 168.80/169.51 ( 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) % 168.80/169.51 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 168.80/169.51 | ? [B_k_H] : % 168.80/169.51 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 168.80/169.51 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ranI,axiom, % 168.80/169.51 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 168.80/169.51 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__assoc,axiom, % 168.80/169.51 ! [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) ). % 168.80/169.51 % 168.80/169.51 fof(fact_restrict__in,axiom, % 168.80/169.51 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph_Oequations_I1_J,axiom, % 168.80/169.51 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph_OemptyI,axiom, % 168.80/169.51 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_empty__fold__graphE,axiom, % 168.80/169.51 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) % 168.80/169.51 => V_x_2 = V_z_2 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph__imp__finite,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 168.80/169.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__None,axiom, % 168.80/169.51 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 168.80/169.51 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 168.80/169.51 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 168.80/169.51 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__find__right,axiom, % 168.80/169.51 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 168.80/169.51 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph_OinsertI,axiom, % 168.80/169.51 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 168.80/169.51 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 168.80/169.51 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 168.80/169.51 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 168.80/169.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 168.80/169.51 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 168.80/169.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__comp__simps_I1_J,axiom, % 168.80/169.51 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 168.80/169.51 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__comp__simps_I2_J,axiom, % 168.80/169.51 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 168.80/169.51 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__comp__Some__iff,axiom, % 168.80/169.51 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 168.80/169.51 ( 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) % 168.80/169.51 <=> ? [B_k_H] : % 168.80/169.51 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 168.80/169.51 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__SomeD,axiom, % 168.80/169.51 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 168.80/169.51 ( 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) % 168.80/169.51 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 168.80/169.51 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 168.80/169.51 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__Some__iff,axiom, % 168.80/169.51 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 168.80/169.51 ( 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) % 168.80/169.51 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 168.80/169.51 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 168.80/169.51 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_restrict__out,axiom, % 168.80/169.51 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_map__add__upd,axiom, % 168.80/169.51 ! [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)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_restrict__map__insert,axiom, % 168.80/169.51 ! [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)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__idem,axiom, % 168.80/169.51 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 168.80/169.51 ( hAPP(V_f_2,V_x_2) = V_y_2 % 168.80/169.51 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__other,axiom, % 168.80/169.51 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 168.80/169.51 ( V_z_2 != V_x_2 % 168.80/169.51 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__twist,axiom, % 168.80/169.51 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 168.80/169.51 ( V_a_2 != V_ca_2 % 168.80/169.51 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__apply,axiom, % 168.80/169.51 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 168.80/169.51 ( ( V_z_2 = V_x_2 % 168.80/169.51 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 168.80/169.51 & ( V_z_2 != V_x_2 % 168.80/169.51 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__same,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__upd,axiom, % 168.80/169.51 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__idem__iff,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 168.80/169.51 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 168.80/169.51 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold1Set_Ointros,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ran__restrictD,axiom, % 168.80/169.51 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 168.80/169.51 ( 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)))) % 168.80/169.51 => ? [B_x] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.80/169.51 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_restrict__upd__same,axiom, % 168.80/169.51 ! [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))))) ). % 168.80/169.51 % 168.80/169.51 fof(fact_restrict__complement__singleton__eq,axiom, % 168.80/169.51 ! [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)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph__permute__diff,axiom, % 168.80/169.51 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 168.80/169.51 ( class_Groups_Oab__semigroup__mult(T_a) % 168.80/169.51 => ( 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)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 168.80/169.51 => 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)) ) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fun__upd__image,axiom, % 168.80/169.51 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => 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)))))) ) % 168.80/169.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => 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) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__Diff1__less,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__Diff2__less,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_is__none__code_I2_J,axiom, % 168.80/169.51 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_is__none__def,axiom, % 168.80/169.51 ! [V_x_2,T_a] : % 168.80/169.51 ( c_Option_Ois__none(T_a,V_x_2) % 168.80/169.51 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_is__none__code_I1_J,axiom, % 168.80/169.51 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__eqI,axiom, % 168.80/169.51 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 168.80/169.51 ( V_b_2 = hAPP(V_f_2,V_x_2) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_finite__imageI,axiom, % 168.80/169.51 ! [V_h_2,T_b,V_F_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.80/169.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ComplI,axiom, % 168.80/169.51 ! [V_A_2,V_ca_2,T_a] : % 168.80/169.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 168.80/169.51 => 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))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 168.80/169.51 ! [V_c,V_b,V_a,T_a] : % 168.80/169.51 ( class_Groups_Oab__semigroup__mult(T_a) % 168.80/169.51 => 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)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_compl__eq__compl__iff,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Lattices_Oboolean__algebra(T_a) % 168.80/169.51 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 168.80/169.51 <=> V_x_2 = V_y_2 ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_neg__equal__iff__equal,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Ogroup__add(T_a) % 168.80/169.51 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 168.80/169.51 <=> V_a_2 = V_b_2 ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__equation__iff,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Ogroup__add(T_a) % 168.80/169.51 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 168.80/169.51 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_mult__left__idem,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_equation__minus__iff,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Ogroup__add(T_a) % 168.80/169.51 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 168.80/169.51 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_uminus__apply,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,T_b,T_a] : % 168.80/169.51 ( class_Groups_Ouminus(T_a) % 168.80/169.51 => 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)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_mult__idem,axiom, % 168.80/169.51 ! [V_x,T_a] : % 168.80/169.51 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.80/169.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_times_Oidem,axiom, % 168.80/169.51 ! [V_a,T_a] : % 168.80/169.51 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.80/169.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_double__compl,axiom, % 168.80/169.51 ! [V_x,T_a] : % 168.80/169.51 ( class_Lattices_Oboolean__algebra(T_a) % 168.80/169.51 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__minus,axiom, % 168.80/169.51 ! [V_a,T_a] : % 168.80/169.51 ( class_Groups_Ogroup__add(T_a) % 168.80/169.51 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_Compl__eq__Compl__iff,axiom, % 168.80/169.51 ! [V_B_2,V_A_2,T_a] : % 168.80/169.51 ( 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) % 168.80/169.51 <=> V_A_2 = V_B_2 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_double__complement,axiom, % 168.80/169.51 ! [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 ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__image__le,axiom, % 168.80/169.51 ! [V_f_2,T_b,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.51 => 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))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_rev__image__eqI,axiom, % 168.80/169.51 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_imageI,axiom, % 168.80/169.51 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => 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))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__iff,axiom, % 168.80/169.51 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 168.80/169.51 <=> ? [B_x] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 168.80/169.51 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__is__empty,axiom, % 168.80/169.51 ! [V_A_2,V_f_2,T_a,T_b] : % 168.80/169.51 ( 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)) % 168.80/169.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__empty,axiom, % 168.80/169.51 ! [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)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_empty__is__image,axiom, % 168.80/169.51 ! [V_A_2,V_f_2,T_b,T_a] : % 168.80/169.51 ( 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) % 168.80/169.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__insert,axiom, % 168.80/169.51 ! [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)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_le__minus__iff,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( 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))) % 168.80/169.51 <=> 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))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__le__iff,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( 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)) % 168.80/169.51 <=> 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)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_neg__le__iff__le,axiom, % 168.80/169.51 ! [V_a_2,V_b_2,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( 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))) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_compl__le__compl__iff,axiom, % 168.80/169.51 ! [V_y_2,V_x_2,T_a] : % 168.80/169.51 ( class_Lattices_Oboolean__algebra(T_a) % 168.80/169.51 => ( 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))) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_le__imp__neg__le,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.51 => 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))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_compl__mono,axiom, % 168.80/169.51 ! [V_y,V_x,T_a] : % 168.80/169.51 ( class_Lattices_Oboolean__algebra(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 168.80/169.51 => 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))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__mono,axiom, % 168.80/169.51 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => 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))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_subset__image__iff,axiom, % 168.80/169.51 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 168.80/169.51 ( 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))) % 168.80/169.51 <=> ? [B_AA] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 168.80/169.51 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_neg__less__iff__less,axiom, % 168.80/169.51 ! [V_a_2,V_b_2,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( 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))) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__less__iff,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_less__minus__iff,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ComplE,axiom, % 168.80/169.51 ! [V_A_2,V_ca_2,T_a] : % 168.80/169.51 ( 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))) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_ComplD,axiom, % 168.80/169.51 ! [V_A_2,V_ca_2,T_a] : % 168.80/169.51 ( 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))) % 168.80/169.51 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_Compl__iff,axiom, % 168.80/169.51 ! [V_A_2,V_ca_2,T_a] : % 168.80/169.51 ( 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))) % 168.80/169.51 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__diff__eq,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Groups_Oab__group__add(T_a) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_Compl__anti__mono,axiom, % 168.80/169.51 ! [V_B_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => 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))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_Compl__subset__Compl__iff,axiom, % 168.80/169.51 ! [V_B_2,V_A_2,T_a] : % 168.80/169.51 ( 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))) % 168.80/169.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_insert__image,axiom, % 168.80/169.51 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_finite__surj,axiom, % 168.80/169.51 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.51 => ( 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))) % 168.80/169.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__insert__le,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__mono,axiom, % 168.80/169.51 ! [V_A_2,V_B_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__seteq,axiom, % 168.80/169.51 ! [V_A_2,V_B_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 168.80/169.51 => V_A_2 = V_B_2 ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__diff__subset,axiom, % 168.80/169.51 ! [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)))) ). % 168.80/169.51 % 168.80/169.51 fof(fact_diff__card__le__card__Diff,axiom, % 168.80/169.51 ! [V_A_2,V_B_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_subset__Compl__self__eq,axiom, % 168.80/169.51 ! [V_A_2,T_a] : % 168.80/169.51 ( 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))) % 168.80/169.51 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold1Set__nonempty,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,V_f_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 168.80/169.51 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_empty__fold1SetE,axiom, % 168.80/169.51 ! [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)) ). % 168.80/169.51 % 168.80/169.51 fof(fact_psubset__card__mono,axiom, % 168.80/169.51 ! [V_A_2,V_B_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => 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))) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__Diff__subset,axiom, % 168.80/169.51 ! [V_A_2,V_B_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.80/169.51 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_image__map__upd,axiom, % 168.80/169.51 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 168.80/169.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__psubset,axiom, % 168.80/169.51 ! [V_A_2,V_B_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.51 => ( 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))) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold__graph__insert__swap,axiom, % 168.80/169.51 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 168.80/169.51 ( class_Groups_Oab__semigroup__mult(T_a) % 168.80/169.51 => ( 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)) % 168.80/169.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 168.80/169.51 => 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))) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__Diff1__le,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_fold1Set__sing,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,V_f_2,T_a] : % 168.80/169.51 ( 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)) % 168.80/169.51 <=> V_a_2 = V_b_2 ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__mult__right,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Rings_Oring(T_a) % 168.80/169.51 => 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)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__mult__left,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Rings_Oring(T_a) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__mult__commute,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Rings_Oring(T_a) % 168.80/169.51 => 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)) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_minus__mult__minus,axiom, % 168.80/169.51 ! [V_b,V_a,T_a] : % 168.80/169.51 ( class_Rings_Oring(T_a) % 168.80/169.51 => 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) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_square__eq__iff,axiom, % 168.80/169.51 ! [V_b_2,V_a_2,T_a] : % 168.80/169.51 ( class_Rings_Oidom(T_a) % 168.80/169.51 => ( 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) % 168.80/169.51 <=> ( V_a_2 = V_b_2 % 168.80/169.51 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 168.80/169.51 % 168.80/169.51 fof(fact_card__Diff__singleton__if,axiom, % 168.80/169.51 ! [V_x_2,V_A_2,T_a] : % 168.80/169.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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)) ) % 168.80/169.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__Diff__singleton,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__Suc__Diff1,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_insert__fold1SetE,axiom, % 168.80/169.52 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2)) % 168.80/169.52 => ~ ! [B_a,B_A] : % 168.80/169.52 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_fold1Set_Oequations,axiom, % 168.80/169.52 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2)) % 168.80/169.52 <=> ? [B_a,B_A] : % 168.80/169.52 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 168.80/169.52 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 168.80/169.52 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_one__reorient,axiom, % 168.80/169.52 ! [V_x_2,T_a] : % 168.80/169.52 ( class_Groups_Oone(T_a) % 168.80/169.52 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 168.80/169.52 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__1__left,axiom, % 168.80/169.52 ! [V_a,T_a] : % 168.80/169.52 ( class_Groups_Omonoid__mult(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__1,axiom, % 168.80/169.52 ! [V_a,T_a] : % 168.80/169.52 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__1__right,axiom, % 168.80/169.52 ! [V_a,T_a] : % 168.80/169.52 ( class_Groups_Omonoid__mult(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult_Ocomm__neutral,axiom, % 168.80/169.52 ! [V_a,T_a] : % 168.80/169.52 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__1__mult,axiom, % 168.80/169.52 ! [V_n,V_m,T_a] : % 168.80/169.52 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 168.80/169.52 => 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))) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_square__eq__1__iff,axiom, % 168.80/169.52 ! [V_x_2,T_a] : % 168.80/169.52 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 168.80/169.52 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 168.80/169.52 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_linorder__neqE__linordered__idom,axiom, % 168.80/169.52 ! [V_y,V_x,T_a] : % 168.80/169.52 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.52 => ( V_x != V_y % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__insert__disjoint,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__insert__if,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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) ) % 168.80/169.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__insert,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => 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)))))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__Diff__insert,axiom, % 168.80/169.52 ! [V_B_2,V_a_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 168.80/169.52 => 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)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__mono,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_lessI,axiom, % 168.80/169.52 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__Suc__1,axiom, % 168.80/169.52 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__Suc__eq__diff__pred,axiom, % 168.80/169.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__diff__iff,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__less__mono,axiom, % 168.80/169.52 ! [V_c,V_b,V_a] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__diff__le,axiom, % 168.80/169.52 ! [V_m,V_n] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__less__Suc,axiom, % 168.80/169.52 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__le__lessD,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__less__Suc__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 168.80/169.52 <=> V_n_2 = V_m_2 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_n__not__Suc__n,axiom, % 168.80/169.52 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__n__not__n,axiom, % 168.80/169.52 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat_Oinject,axiom, % 168.80/169.52 ! [V_nat_H_2,V_nat_2] : % 168.80/169.52 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 168.80/169.52 <=> V_nat_2 = V_nat_H_2 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__inject,axiom, % 168.80/169.52 ! [V_y,V_x] : % 168.80/169.52 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 168.80/169.52 => V_x = V_y ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__mult__cancel1,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( 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) % 168.80/169.52 <=> V_m_2 = V_n_2 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__not__refl,axiom, % 168.80/169.52 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__neq__iff,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( V_m_2 != V_n_2 % 168.80/169.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_linorder__neqE__nat,axiom, % 168.80/169.52 ! [V_y,V_x] : % 168.80/169.52 ( V_x != V_y % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__irrefl__nat,axiom, % 168.80/169.52 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__not__refl2,axiom, % 168.80/169.52 ! [V_m,V_n] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 168.80/169.52 => V_m != V_n ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__not__refl3,axiom, % 168.80/169.52 ! [V_t,V_s] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 168.80/169.52 => V_s != V_t ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__less__cases,axiom, % 168.80/169.52 ! [V_P_2,V_n_2,V_m_2] : % 168.80/169.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 168.80/169.52 => ( ( V_m_2 = V_n_2 % 168.80/169.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 168.80/169.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 168.80/169.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 168.80/169.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__refl,axiom, % 168.80/169.52 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__le__linear,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_eq__imp__le,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( V_m = V_n % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__trans,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__antisym,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.80/169.52 => V_m = V_n ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__le__mono,axiom, % 168.80/169.52 ! [V_l,V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 168.80/169.52 => 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))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__le__mono2,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => 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))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__le__mono1,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => 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))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__cube,axiom, % 168.80/169.52 ! [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)))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__square,axiom, % 168.80/169.52 ! [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))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__commute,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__mult__distrib,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__mult__distrib2,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__mult__eq__1__iff,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 168.80/169.52 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 168.80/169.52 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__mult__1__right,axiom, % 168.80/169.52 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__1__eq__mult__iff,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 168.80/169.52 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 168.80/169.52 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__mult__1,axiom, % 168.80/169.52 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 168.80/169.52 % 168.80/169.52 fof(fact_not__less__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__Suc__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 168.80/169.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 | V_m_2 = V_n_2 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__less__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__mult__less__cancel1,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( 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))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_not__less__less__Suc__eq,axiom, % 168.80/169.52 ! [V_m_2,V_n_2] : % 168.80/169.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 168.80/169.52 <=> V_n_2 = V_m_2 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__antisym,axiom, % 168.80/169.52 ! [V_m,V_n] : % 168.80/169.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 168.80/169.52 => V_m = V_n ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__SucI,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__lessI,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__trans__Suc,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__SucE,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => V_m = V_n ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__lessD,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__less__SucD,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__n__not__le__n,axiom, % 168.80/169.52 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_not__less__eq__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__Suc__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 168.80/169.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__le__mono,axiom, % 168.80/169.52 ! [V_m_2,V_n_2] : % 168.80/169.52 ( 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))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__SucI,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__SucE,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__leD,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__mult__le__cancel1,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( 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))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__less__le,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 & V_m_2 != V_n_2 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__eq__less__or__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 | V_m_2 = V_n_2 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__imp__le__nat,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__neq__implies__less,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => ( V_m != V_n % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__or__eq__imp__le,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 | V_m = V_n ) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__Suc__Suc,axiom, % 168.80/169.52 ! [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) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__diff__diff,axiom, % 168.80/169.52 ! [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) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__imp__diff__less,axiom, % 168.80/169.52 ! [V_n,V_k,V_j] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__less__mono2,axiom, % 168.80/169.52 ! [V_l,V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__le__self,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__le__mono2,axiom, % 168.80/169.52 ! [V_l,V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => 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))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__le__mono,axiom, % 168.80/169.52 ! [V_l,V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => 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))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__diff__cancel,axiom, % 168.80/169.52 ! [V_n,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 168.80/169.52 => 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 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_eq__diff__iff,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 168.80/169.52 => ( 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) % 168.80/169.52 <=> V_m_2 = V_n_2 ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Nat_Odiff__diff__eq,axiom, % 168.80/169.52 ! [V_n,V_m,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 168.80/169.52 => 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) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__diff__iff,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__eq__Suc__le,axiom, % 168.80/169.52 ! [V_m_2,V_n_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__Suc__eq__le,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__le__eq,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__imp__less__Suc,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__leI,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 168.80/169.52 ! [V_x,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__ring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Body__triple__valid__Suc,axiom, % 168.80/169.52 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 168.80/169.52 ( 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)) % 168.80/169.52 <=> 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card_Oremove,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_termination__basic__simps_I5_J,axiom, % 168.80/169.52 ! [V_y,V_x] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 168.80/169.52 ! [V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 168.80/169.52 ! [V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card_Oinsert__remove,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_folding__one__idem_Ohom__commute,axiom, % 168.80/169.52 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 168.80/169.52 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.80/169.52 => ( ! [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)) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.80/169.52 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.52 => 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)) ) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_fold1__insert,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( class_Groups_Oab__semigroup__mult(T_a) % 168.80/169.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => 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)) ) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card_Oinsert,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__add__commute,axiom, % 168.80/169.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__add__left__commute,axiom, % 168.80/169.52 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__add__assoc,axiom, % 168.80/169.52 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__add__left__cancel,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) % 168.80/169.52 <=> V_m_2 = V_n_2 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__add__right__cancel,axiom, % 168.80/169.52 ! [V_n_2,V_k_2,V_m_2] : % 168.80/169.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) % 168.80/169.52 <=> V_m_2 = V_n_2 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__mult__distrib,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__mult__assoc,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__mult__distrib2,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__mult__commute,axiom, % 168.80/169.52 ! [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) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 168.80/169.52 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 168.80/169.52 ! [V_d,V_c,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 168.80/169.52 ! [V_d,V_c,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 168.80/169.52 ! [V_c,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oab__semigroup__add(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__left__cancel,axiom, % 168.80/169.52 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 168.80/169.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2) % 168.80/169.52 <=> V_b_2 = V_ca_2 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__right__cancel,axiom, % 168.80/169.52 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 168.80/169.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2) % 168.80/169.52 <=> V_b_2 = V_ca_2 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__left__imp__eq,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 168.80/169.52 => V_b = V_c ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__imp__eq,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 168.80/169.52 => V_b = V_c ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__right__imp__eq,axiom, % 168.80/169.52 ! [V_c,V_a,V_b,T_a] : % 168.80/169.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) % 168.80/169.52 => V_b = V_c ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_crossproduct__eq,axiom, % 168.80/169.52 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 168.80/169.52 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 168.80/169.52 => ( 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)) % 168.80/169.52 <=> ( V_w_2 = V_x_2 % 168.80/169.52 | V_y_2 = V_z_2 ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 168.80/169.52 ! [V_b,V_m,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_crossproduct__noteq,axiom, % 168.80/169.52 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 168.80/169.52 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 168.80/169.52 => ( ( V_a_2 != V_b_2 % 168.80/169.52 & V_ca_2 != V_d_2 ) % 168.80/169.52 <=> 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 168.80/169.52 ! [V_z,V_y,V_x,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_termination__basic__simps_I2_J,axiom, % 168.80/169.52 ! [V_y,V_z,V_x] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_termination__basic__simps_I1_J,axiom, % 168.80/169.52 ! [V_z,V_y,V_x] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_termination__basic__simps_I4_J,axiom, % 168.80/169.52 ! [V_y,V_z,V_x] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_termination__basic__simps_I3_J,axiom, % 168.80/169.52 ! [V_z,V_y,V_x] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__le__imp__le__left,axiom, % 168.80/169.52 ! [V_b,V_a,V_c,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__le__imp__le__right,axiom, % 168.80/169.52 ! [V_b,V_c,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__mono,axiom, % 168.80/169.52 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__left__mono,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__right__mono,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__le__cancel__left,axiom, % 168.80/169.52 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__le__cancel__right,axiom, % 168.80/169.52 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__less__cancel__right,axiom, % 168.80/169.52 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__less__cancel__left,axiom, % 168.80/169.52 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__strict__right__mono,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__strict__left__mono,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__strict__mono,axiom, % 168.80/169.52 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__less__imp__less__right,axiom, % 168.80/169.52 ! [V_b,V_c,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__less__imp__less__left,axiom, % 168.80/169.52 ! [V_b,V_a,V_c,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_combine__common__factor,axiom, % 168.80/169.52 ! [V_c,V_b,V_e,V_a,T_a] : % 168.80/169.52 ( class_Rings_Osemiring(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__class_Odistrib,axiom, % 168.80/169.52 ! [V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__diff__cancel,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ogroup__add(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__add__cancel,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ogroup__add(T_a) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_minus__add__distrib,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oab__group__add(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_minus__add,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ogroup__add(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__minus__cancel,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ogroup__add(T_a) % 168.80/169.52 => 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 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_minus__add__cancel,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ogroup__add(T_a) % 168.80/169.52 => 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 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__Suc__right,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__Suc,axiom, % 168.80/169.52 ! [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)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__Suc__shift,axiom, % 168.80/169.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__Suc,axiom, % 168.80/169.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__Suc__right,axiom, % 168.80/169.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__lessD1,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__add__eq__less,axiom, % 168.80/169.52 ! [V_n,V_m,V_l,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__less__mono,axiom, % 168.80/169.52 ! [V_l,V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__less__mono1,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_trans__less__add2,axiom, % 168.80/169.52 ! [V_m,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_trans__less__add1,axiom, % 168.80/169.52 ! [V_m,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__add__left__cancel__less,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_not__add__less2,axiom, % 168.80/169.52 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_not__add__less1,axiom, % 168.80/169.52 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__leE,axiom, % 168.80/169.52 ! [V_n,V_k,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 168.80/169.52 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__leD1,axiom, % 168.80/169.52 ! [V_n,V_k,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__leD2,axiom, % 168.80/169.52 ! [V_n,V_k,V_m] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__le__mono,axiom, % 168.80/169.52 ! [V_l,V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__le__mono1,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_trans__le__add2,axiom, % 168.80/169.52 ! [V_m,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_trans__le__add1,axiom, % 168.80/169.52 ! [V_m,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__add__left__cancel__le,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__iff__add,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__add1,axiom, % 168.80/169.52 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__add2,axiom, % 168.80/169.52 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__cancel2,axiom, % 168.80/169.52 ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__cancel,axiom, % 168.80/169.52 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__diff__left,axiom, % 168.80/169.52 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__add__inverse,axiom, % 168.80/169.52 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__add__inverse2,axiom, % 168.80/169.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 168.80/169.52 ! [V_m,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 168.80/169.52 ! [V_a,V_m,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 168.80/169.52 ! [V_m,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 168.80/169.52 ! [V_y,V_x,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__ring__1(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__le__less__mono,axiom, % 168.80/169.52 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__less__le__mono,axiom, % 168.80/169.52 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__add__one,axiom, % 168.80/169.52 ! [V_a,T_a] : % 168.80/169.52 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_eq__add__iff1,axiom, % 168.80/169.52 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 168.80/169.52 ( class_Rings_Oring(T_a) % 168.80/169.52 => ( 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) % 168.80/169.52 <=> 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 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_eq__add__iff2,axiom, % 168.80/169.52 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 168.80/169.52 ( class_Rings_Oring(T_a) % 168.80/169.52 => ( 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) % 168.80/169.52 <=> 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) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__minus__eq__add,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ogroup__add(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_ab__diff__minus,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Oab__group__add(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__def,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Groups_Ogroup__add(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_triple__valid__Suc,axiom, % 168.80/169.52 ! [V_t,V_n,T_a] : % 168.80/169.52 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 168.80/169.52 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__add__Suc1,axiom, % 168.80/169.52 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__add__Suc2,axiom, % 168.80/169.52 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__iff__Suc__add,axiom, % 168.80/169.52 ! [V_n_2,V_m_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 168.80/169.52 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__diff__inverse,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__diff__conv,axiom, % 168.80/169.52 ! [V_k_2,V_j_2,V_i_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__add__assoc2,axiom, % 168.80/169.52 ! [V_i,V_j,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__diff__assoc2,axiom, % 168.80/169.52 ! [V_i,V_j,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__add__assoc,axiom, % 168.80/169.52 ! [V_i,V_j,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__imp__diff__is__add,axiom, % 168.80/169.52 ! [V_k_2,V_j_2,V_i_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 168.80/169.52 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__add__diff__inverse2,axiom, % 168.80/169.52 ! [V_m,V_n] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__diff__conv2,axiom, % 168.80/169.52 ! [V_i_2,V_j_2,V_k_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__diff__assoc,axiom, % 168.80/169.52 ! [V_i,V_j,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__add__diff__inverse,axiom, % 168.80/169.52 ! [V_m,V_n] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__add__diff,axiom, % 168.80/169.52 ! [V_m,V_n,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 168.80/169.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__diff__conv,axiom, % 168.80/169.52 ! [V_i_2,V_k_2,V_j_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) % 168.80/169.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__diff__right,axiom, % 168.80/169.52 ! [V_i,V_j,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__eq__plus1,axiom, % 168.80/169.52 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__eq__plus1__left,axiom, % 168.80/169.52 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 168.80/169.52 % 168.80/169.52 fof(fact_fold1__singleton,axiom, % 168.80/169.52 ! [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 ). % 168.80/169.52 % 168.80/169.52 fof(fact_fold1__singleton__def,axiom, % 168.80/169.52 ! [V_a_2,V_f_2,T_a,V_g_2] : % 168.80/169.52 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 168.80/169.52 => 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 ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_folding__one_Oeq__fold,axiom, % 168.80/169.52 ! [V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.52 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__add__iff1,axiom, % 168.80/169.52 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 168.80/169.52 ( class_Rings_Oordered__ring(T_a) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le__add__iff2,axiom, % 168.80/169.52 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 168.80/169.52 ( class_Rings_Oordered__ring(T_a) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__add__iff1,axiom, % 168.80/169.52 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 168.80/169.52 ( class_Rings_Oordered__ring(T_a) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__add__iff2,axiom, % 168.80/169.52 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 168.80/169.52 ( class_Rings_Oordered__ring(T_a) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__Suc__diff__eq2,axiom, % 168.80/169.52 ! [V_m,V_j,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_diff__Suc__diff__eq1,axiom, % 168.80/169.52 ! [V_m,V_j,V_k] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 168.80/169.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 168.80/169.52 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 168.80/169.52 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 168.80/169.52 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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))) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 168.80/169.52 ! [V_rx,V_ly,V_lx,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 168.80/169.52 ! [V_rx,V_ly,V_lx,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 168.80/169.52 ! [V_ry,V_rx,V_lx,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 168.80/169.52 ! [V_ry,V_rx,V_lx,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 168.80/169.52 ! [V_b,V_a,T_a] : % 168.80/169.52 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_fold1__insert__idem,axiom, % 168.80/169.52 ! [V_x_2,V_A_2,T_a] : % 168.80/169.52 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.80/169.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => 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)) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__less__add__iff1,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__less__add__iff2,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__eq__add__iff2,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 168.80/169.52 => ( 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) % 168.80/169.52 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__diff__add__eq2,axiom, % 168.80/169.52 ! [V_n,V_m,V_u,V_j,V_i] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 168.80/169.52 => 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)) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__le__add__iff2,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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))) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__eq__add__iff1,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 168.80/169.52 => ( 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) % 168.80/169.52 <=> 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 ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__diff__add__eq1,axiom, % 168.80/169.52 ! [V_n,V_m,V_u,V_i,V_j] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 168.80/169.52 => 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) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_nat__le__add__iff1,axiom, % 168.80/169.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 168.80/169.52 => ( 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))) % 168.80/169.52 <=> 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_fold1__in,axiom, % 168.80/169.52 ! [V_A_2,T_a] : % 168.80/169.52 ( class_Groups_Oab__semigroup__mult(T_a) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.52 => ( ! [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)))))) % 168.80/169.52 => 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)) ) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_left__add__mult__distrib,axiom, % 168.80/169.52 ! [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) ). % 168.80/169.52 % 168.80/169.52 fof(fact_hom__fold1__commute,axiom, % 168.80/169.52 ! [V_N_2,V_h_2,T_a] : % 168.80/169.52 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.80/169.52 => ( ! [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)) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 168.80/169.52 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.52 => 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)) ) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_convex__bound__lt,axiom, % 168.80/169.52 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 168.80/169.52 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 168.80/169.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 168.80/169.52 => 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)) ) ) ) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__Plus,axiom, % 168.80/169.52 ! [V_B_2,T_b,V_A_2,T_a] : % 168.80/169.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.80/169.52 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_fold1__eq__fold,axiom, % 168.80/169.52 ! [V_a_2,V_A_2,T_a] : % 168.80/169.52 ( class_Groups_Oab__semigroup__mult(T_a) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.52 => 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) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_mult__eq__if,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.80/169.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.52 => 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)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_card__inj__on__le,axiom, % 168.80/169.52 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.52 => ( 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)) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.80/169.52 => 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))) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_add__eq__if,axiom, % 168.80/169.52 ! [V_n,V_m] : % 168.80/169.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 168.80/169.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_semilattice__big_OF__eq,axiom, % 168.80/169.52 ! [V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.52 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 168.80/169.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.52 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_Suc__diff__1,axiom, % 168.80/169.52 ! [V_n] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.80/169.52 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_less__zeroE,axiom, % 168.80/169.52 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_le0,axiom, % 168.80/169.52 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 168.80/169.52 % 168.80/169.52 fof(fact_inj__on__empty,axiom, % 168.80/169.52 ! [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))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_inj__uminus,axiom, % 168.80/169.52 ! [V_A_2,T_a] : % 168.80/169.52 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.52 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_zero__less__Suc,axiom, % 168.80/169.52 ! [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))) ). % 168.80/169.52 % 168.80/169.52 fof(fact_bot__nat__def,axiom, % 168.80/169.52 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.52 % 168.80/169.52 fof(fact_zero__reorient,axiom, % 168.80/169.52 ! [V_x_2,T_a] : % 168.80/169.52 ( class_Groups_Ozero(T_a) % 168.80/169.52 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 168.80/169.52 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_inj__on__def,axiom, % 168.80/169.52 ! [V_A_2,V_f_2,T_b,T_a] : % 168.80/169.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.52 <=> ! [B_x] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.52 => ! [B_xa] : % 168.80/169.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 168.80/169.52 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 168.80/169.52 => B_x = B_xa ) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_inj__onD,axiom, % 168.80/169.52 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.52 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 168.80/169.52 => V_x_2 = V_y_2 ) ) ) ) ). % 168.80/169.52 % 168.80/169.52 fof(fact_inj__on__iff,axiom, % 168.80/169.52 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 168.80/169.53 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 168.80/169.53 <=> V_x_2 = V_y_2 ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__contraD,axiom, % 168.80/169.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.53 => ( V_x_2 != V_y_2 % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 168.80/169.53 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__Suc,axiom, % 168.80/169.53 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 168.80/169.53 % 168.80/169.53 fof(fact_subset__inj__on,axiom, % 168.80/169.53 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.53 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__diff,axiom, % 168.80/169.53 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.53 => 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)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__Some,axiom, % 168.80/169.53 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ). % 168.80/169.53 % 168.80/169.53 fof(fact_fold__empty,axiom, % 168.80/169.53 ! [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 ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__0__iff,axiom, % 168.80/169.53 ! [V_a_2,V_b_2,T_a] : % 168.80/169.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 168.80/169.53 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 168.80/169.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__0__left,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Omonoid__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__0,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Ocomm__monoid__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_double__zero__sym,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 168.80/169.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__0__right,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Omonoid__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add_Ocomm__neutral,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Ocomm__monoid__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Ocomm__semiring__1(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_divisors__zero,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Ono__zero__divisors(T_a) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_no__zero__divisors,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Ono__zero__divisors(T_a) % 168.80/169.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__eq__0__iff,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Rings_Oring__no__zero__divisors(T_a) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__zero__right,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Omult__zero(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__zero__left,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Omult__zero(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_right__minus__eq,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 <=> V_a_2 = V_b_2 ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_eq__iff__diff__eq__0,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Oab__group__add(T_a) % 168.80/169.53 => ( V_a_2 = V_b_2 % 168.80/169.53 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__self,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__0__right,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__neq__one,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Rings_Ozero__neq__one(T_a) % 168.80/169.53 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_one__neq__zero,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Rings_Ozero__neq__one(T_a) % 168.80/169.53 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_minus__zero,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__0__equal__iff__equal,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 168.80/169.53 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_equal__neg__zero,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 168.80/169.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__equal__0__iff__equal,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__equal__zero,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 168.80/169.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Suc__neq__Zero,axiom, % 168.80/169.53 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Zero__neq__Suc,axiom, % 168.80/169.53 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat_Osimps_I3_J,axiom, % 168.80/169.53 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Suc__not__Zero,axiom, % 168.80/169.53 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat_Osimps_I2_J,axiom, % 168.80/169.53 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Zero__not__Suc,axiom, % 168.80/169.53 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 168.80/169.53 % 168.80/169.53 fof(fact_gr0I,axiom, % 168.80/169.53 ! [V_n] : % 168.80/169.53 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_gr__implies__not0,axiom, % 168.80/169.53 ! [V_n,V_m] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 168.80/169.53 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_less__nat__zero__code,axiom, % 168.80/169.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neq0__conv,axiom, % 168.80/169.53 ! [V_n_2] : % 168.80/169.53 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_not__less0,axiom, % 168.80/169.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 168.80/169.53 % 168.80/169.53 fof(fact_plus__nat_Oadd__0,axiom, % 168.80/169.53 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 168.80/169.53 % 168.80/169.53 fof(fact_Nat_Oadd__0__right,axiom, % 168.80/169.53 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__is__0,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__eq__self__zero,axiom, % 168.80/169.53 ! [V_n,V_m] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 168.80/169.53 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_le__0__eq,axiom, % 168.80/169.53 ! [V_n_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 168.80/169.53 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 168.80/169.53 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diffs0__imp__equal,axiom, % 168.80/169.53 ! [V_n,V_m] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 => V_m = V_n ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__self__eq__0,axiom, % 168.80/169.53 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.53 % 168.80/169.53 fof(fact_minus__nat_Odiff__0,axiom, % 168.80/169.53 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__0__eq__0,axiom, % 168.80/169.53 ! [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) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__cancel2,axiom, % 168.80/169.53 ! [V_n_2,V_k_2,V_m_2] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) % 168.80/169.53 <=> ( V_m_2 = V_n_2 % 168.80/169.53 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__cancel1,axiom, % 168.80/169.53 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 168.80/169.53 <=> ( V_m_2 = V_n_2 % 168.80/169.53 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__is__0,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__0__right,axiom, % 168.80/169.53 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__0,axiom, % 168.80/169.53 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat__mult__eq__cancel__disj,axiom, % 168.80/169.53 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 168.80/169.53 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 | V_m_2 = V_n_2 ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_finite__imageD,axiom, % 168.80/169.53 ! [V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 168.80/169.53 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 168.80/169.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__image,axiom, % 168.80/169.53 ! [V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.53 => 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) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_finite__PlusD_I2_J,axiom, % 168.80/169.53 ! [V_B_2,V_A_2,T_b,T_a] : % 168.80/169.53 ( 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))) % 168.80/169.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_finite__PlusD_I1_J,axiom, % 168.80/169.53 ! [V_B_2,V_A_2,T_b,T_a] : % 168.80/169.53 ( 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))) % 168.80/169.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_finite__Plus,axiom, % 168.80/169.53 ! [V_B_2,T_b,V_A_2,T_a] : % 168.80/169.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.80/169.53 => 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))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_finite__Plus__iff,axiom, % 168.80/169.53 ! [V_B_2,V_A_2,T_b,T_a] : % 168.80/169.53 ( 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))) % 168.80/169.53 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__Plus__conv__if,axiom, % 168.80/169.53 ! [V_B_2,T_b,V_A_2,T_a] : % 168.80/169.53 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 168.80/169.53 => 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)) ) % 168.80/169.53 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 168.80/169.53 => 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) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__strict__subset,axiom, % 168.80/169.53 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.53 => 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))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__map__add__dom,axiom, % 168.80/169.53 ! [V_m_H_2,V_m_2,T_b,T_a] : % 168.80/169.53 ( 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)) % 168.80/169.53 <=> 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)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__nonneg__nonneg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__nonneg__eq__0__iff,axiom, % 168.80/169.53 ! [V_y_2,V_x_2,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__increasing,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__increasing2,axiom, % 168.80/169.53 ! [V_a,V_b,V_c,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__nonpos__nonpos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_split__mult__neg__le,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 168.80/169.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 168.80/169.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_split__mult__pos__le,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__ring(T_a) % 168.80/169.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 168.80/169.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__mono,axiom, % 168.80/169.53 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__mono_H,axiom, % 168.80/169.53 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__left__mono__neg,axiom, % 168.80/169.53 ! [V_c,V_a,V_b,T_a] : % 168.80/169.53 ( class_Rings_Oordered__ring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__right__mono__neg,axiom, % 168.80/169.53 ! [V_c,V_a,V_b,T_a] : % 168.80/169.53 ( class_Rings_Oordered__ring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_comm__mult__left__mono,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__comm__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__left__mono,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__right__mono,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__nonpos__nonpos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__ring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__nonpos__nonneg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__nonneg__nonpos2,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__nonneg__nonpos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__nonneg__nonneg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__le__0__iff,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 168.80/169.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__le__mult__iff,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) % 168.80/169.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 168.80/169.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__le__square,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring(T_a) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__neg__neg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__pos__pos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_pos__add__strict,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__strict__left__mono__neg,axiom, % 168.80/169.53 ! [V_c,V_a,V_b,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__strict__right__mono__neg,axiom, % 168.80/169.53 ! [V_c,V_a,V_b,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_comm__mult__strict__left__mono,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__strict__left__mono,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__strict__right__mono,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__neg__neg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__neg__pos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__cancel__left__neg,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__less__mult__pos2,axiom, % 168.80/169.53 ! [V_a,V_b,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__less__mult__pos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__pos__neg2,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__pos__neg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__pos__pos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__cancel__left__pos,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__cancel__left__disj,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 168.80/169.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__cancel__right__disj,axiom, % 168.80/169.53 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 168.80/169.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_not__square__less__zero,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring(T_a) % 168.80/169.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_le__iff__diff__le__0,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 168.80/169.53 <=> 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))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_less__iff__diff__less__0,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 168.80/169.53 <=> 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))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_sum__squares__eq__zero__iff,axiom, % 168.80/169.53 ! [V_y_2,V_x_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__scale__eq__noteq,axiom, % 168.80/169.53 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 168.80/169.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 168.80/169.53 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 => ( ( V_a = V_b % 168.80/169.53 & V_c != V_d ) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__le__one,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.53 => 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))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_not__one__le__zero,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.53 => ~ 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))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_not__one__less__zero,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__less__one,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_minus__le__self__iff,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__le__0__iff__le,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_le__minus__self__iff,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__0__le__iff__le,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_less__minus__self__iff,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__0__less__iff__less,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__less__0__iff__less,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Oordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_neg__less__nonneg,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_right__minus,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_eq__neg__iff__add__eq__0,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 168.80/169.53 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_left__minus,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_ab__left__minus,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Oab__group__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_minus__unique,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__0,axiom, % 168.80/169.53 ! [V_a,T_a] : % 168.80/169.53 ( class_Groups_Ogroup__add(T_a) % 168.80/169.53 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_gr0__conv__Suc,axiom, % 168.80/169.53 ! [V_n_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 168.80/169.53 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_less__Suc0,axiom, % 168.80/169.53 ! [V_n_2] : % 168.80/169.53 ( 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)))) % 168.80/169.53 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_less__Suc__eq__0__disj,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 168.80/169.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 | ? [B_j] : % 168.80/169.53 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_one__is__add,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( 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) % 168.80/169.53 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.80/169.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.80/169.53 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__is__1,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( 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)) % 168.80/169.53 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.80/169.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.80/169.53 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__gr__0,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( 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))) % 168.80/169.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 168.80/169.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card_Oempty,axiom, % 168.80/169.53 ! [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) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__infinite,axiom, % 168.80/169.53 ! [V_A_2,T_a] : % 168.80/169.53 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__eq__1__iff,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.80/169.53 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.80/169.53 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__less,axiom, % 168.80/169.53 ! [V_m,V_n] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 168.80/169.53 => 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)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__less__diff,axiom, % 168.80/169.53 ! [V_m_2,V_n_2] : % 168.80/169.53 ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__mono2,axiom, % 168.80/169.53 ! [V_k,V_j,V_i] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__mono1,axiom, % 168.80/169.53 ! [V_k,V_j,V_i] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__cancel2,axiom, % 168.80/169.53 ! [V_n_2,V_k_2,V_m_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 168.80/169.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__cancel1,axiom, % 168.80/169.53 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 168.80/169.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat__0__less__mult__iff,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 168.80/169.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat__mult__less__cancel1,axiom, % 168.80/169.53 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat__mult__eq__cancel1,axiom, % 168.80/169.53 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 168.80/169.53 <=> V_m_2 = V_n_2 ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__add__0,axiom, % 168.80/169.53 ! [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) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__is__0__eq_H,axiom, % 168.80/169.53 ! [V_n,V_m] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 168.80/169.53 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__is__0__eq,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_One__nat__def,axiom, % 168.80/169.53 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__eq__self__implies__10,axiom, % 168.80/169.53 ! [V_n,V_m] : % 168.80/169.53 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 168.80/169.53 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 168.80/169.53 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_endo__inj__surj,axiom, % 168.80/169.53 ! [V_f_2,V_A_2,T_a] : % 168.80/169.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( 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)) % 168.80/169.53 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 168.80/169.53 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_finite__surj__inj,axiom, % 168.80/169.53 ! [V_f_2,V_A_2,T_a] : % 168.80/169.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( 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))) % 168.80/169.53 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_eq__card__imp__inj__on,axiom, % 168.80/169.53 ! [V_f_2,T_b,V_A_2,T_a] : % 168.80/169.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( 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) % 168.80/169.53 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__iff__eq__card,axiom, % 168.80/169.53 ! [V_f_2,T_b,V_A_2,T_a] : % 168.80/169.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.53 <=> 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) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__image__set__diff,axiom, % 168.80/169.53 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 168.80/169.53 => 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)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_pigeonhole,axiom, % 168.80/169.53 ! [V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( 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))) % 168.80/169.53 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__fun__updI,axiom, % 168.80/169.53 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 168.80/169.53 => 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) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__pos__nonneg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__nonneg__pos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__strict__increasing,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__strict__increasing2,axiom, % 168.80/169.53 ! [V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__neg__nonpos,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_add__nonpos__neg,axiom, % 168.80/169.53 ! [V_b,V_a,T_a] : % 168.80/169.53 ( class_Groups_Oordered__comm__monoid__add(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__left__le__imp__le,axiom, % 168.80/169.53 ! [V_b,V_a,V_c,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__right__le__imp__le,axiom, % 168.80/169.53 ! [V_b,V_c,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__imp__less__left,axiom, % 168.80/169.53 ! [V_b,V_a,V_c,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__left__less__imp__less,axiom, % 168.80/169.53 ! [V_b,V_a,V_c,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__imp__less__right,axiom, % 168.80/169.53 ! [V_b,V_c,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__right__less__imp__less,axiom, % 168.80/169.53 ! [V_b,V_c,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__le__less__imp__less,axiom, % 168.80/169.53 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__less__le__imp__less,axiom, % 168.80/169.53 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__strict__mono_H,axiom, % 168.80/169.53 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__strict__mono,axiom, % 168.80/169.53 ! [V_d,V_c,V_b,V_a,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__le__cancel__left__neg,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__le__cancel__left__pos,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_sum__squares__le__zero__iff,axiom, % 168.80/169.53 ! [V_y_2,V_x_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_sum__squares__ge__zero,axiom, % 168.80/169.53 ! [V_y,V_x,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring(T_a) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_sum__squares__gt__zero__iff,axiom, % 168.80/169.53 ! [V_y_2,V_x_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring__strict(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) % 168.80/169.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.53 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_not__sum__squares__lt__zero,axiom, % 168.80/169.53 ! [V_y,V_x,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__ring(T_a) % 168.80/169.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__left__le__one__le,axiom, % 168.80/169.53 ! [V_y,V_x,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__right__le__one__le,axiom, % 168.80/169.53 ! [V_y,V_x,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_zero__less__two,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semidom(T_a) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__eq__0__iff,axiom, % 168.80/169.53 ! [V_A_2,T_a] : % 168.80/169.53 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.53 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__ge__0__finite,axiom, % 168.80/169.53 ! [V_A_2,T_a] : % 168.80/169.53 ( 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))) % 168.80/169.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Suc__pred,axiom, % 168.80/169.53 ! [V_n] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.80/169.53 => 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 ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_diff__Suc__less,axiom, % 168.80/169.53 ! [V_i,V_n] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.80/169.53 => 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)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_n__less__m__mult__n,axiom, % 168.80/169.53 ! [V_m,V_n] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_n__less__n__mult__m,axiom, % 168.80/169.53 ! [V_m,V_n] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_one__less__mult,axiom, % 168.80/169.53 ! [V_m,V_n] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat__diff__split__asm,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,V_P_2] : % 168.80/169.53 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 168.80/169.53 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 168.80/169.53 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 168.80/169.53 | ? [B_d] : % 168.80/169.53 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 168.80/169.53 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat__diff__split,axiom, % 168.80/169.53 ! [V_b_2,V_a_2,V_P_2] : % 168.80/169.53 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 168.80/169.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 168.80/169.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 168.80/169.53 & ! [B_d] : % 168.80/169.53 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 168.80/169.53 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_one__le__mult__iff,axiom, % 168.80/169.53 ! [V_n_2,V_m_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 168.80/169.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) % 168.80/169.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__le__cancel2,axiom, % 168.80/169.53 ! [V_n_2,V_k_2,V_m_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 168.80/169.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_mult__le__cancel1,axiom, % 168.80/169.53 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 168.80/169.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_nat__mult__le__cancel1,axiom, % 168.80/169.53 ! [V_n_2,V_m_2,V_k_2] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 168.80/169.53 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.53 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => 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) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__bij__eq,axiom, % 168.80/169.53 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.53 => ( 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)) % 168.80/169.53 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 168.80/169.53 => ( 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)) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.80/169.53 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Body__triple__valid__0,axiom, % 168.80/169.53 ! [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)) ). % 168.80/169.53 % 168.80/169.53 fof(fact_fold1__eq__fold__idem,axiom, % 168.80/169.53 ! [V_a_2,V_A_2,T_a] : % 168.80/169.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => 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) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_convex__bound__le,axiom, % 168.80/169.53 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__semiring__1(T_a) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 168.80/169.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 168.80/169.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_folding__one_Oeq__fold_H,axiom, % 168.80/169.53 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 168.80/169.53 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.53 => 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) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__gt__0__iff,axiom, % 168.80/169.53 ! [V_A_2,T_a] : % 168.80/169.53 ( 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))) % 168.80/169.53 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.53 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__insert,axiom, % 168.80/169.53 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 168.80/169.53 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.53 & ~ 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))))))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Suc__pred_H,axiom, % 168.80/169.53 ! [V_n] : % 168.80/169.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 168.80/169.53 => 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))) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__iff__card__le,axiom, % 168.80/169.53 ! [V_B_2,T_b,V_A_2,T_a] : % 168.80/169.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 168.80/169.53 => ( ? [B_f] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 168.80/169.53 & 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)) ) % 168.80/169.53 <=> 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))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_inj__on__iff__surj,axiom, % 168.80/169.53 ! [V_A_H_2,T_b,T_a,V_A_2] : % 168.80/169.53 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.53 => ( ? [B_f] : % 168.80/169.53 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 168.80/169.53 & 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)) ) % 168.80/169.53 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_triple_Osize_I1_J,axiom, % 168.80/169.53 ! [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) ). % 168.80/169.53 % 168.80/169.53 fof(fact_even__less__0__iff,axiom, % 168.80/169.53 ! [V_a_2,T_a] : % 168.80/169.53 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.53 => ( 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))) % 168.80/169.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_fun__left__comm_Ofold__rec,axiom, % 168.80/169.53 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.53 => 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)))))) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_triple_Osize_I2_J,axiom, % 168.80/169.53 ! [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) ). % 168.80/169.53 % 168.80/169.53 fof(fact_Plus__eq__empty__conv,axiom, % 168.80/169.53 ! [V_B_2,V_A_2,T_b,T_a] : % 168.80/169.53 ( 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)) % 168.80/169.53 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.53 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 168.80/169.53 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.53 => 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)))))) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_card__Suc__eq,axiom, % 168.80/169.53 ! [V_k_2,V_A_2,T_a] : % 168.80/169.53 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 168.80/169.53 <=> ? [B_b,B_B] : % 168.80/169.53 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 168.80/169.53 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 168.80/169.53 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 168.80/169.53 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 168.80/169.53 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 168.80/169.53 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.53 => 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)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_fun__left__comm,axiom, % 168.80/169.53 ! [T_a] : % 168.80/169.53 ( class_Groups_Oab__semigroup__mult(T_a) % 168.80/169.53 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 168.80/169.53 % 168.80/169.53 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 168.80/169.53 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 168.80/169.54 => V_y_2 = V_x_2 ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_finite__nat__set__iff__bounded,axiom, % 168.80/169.54 ! [V_N_2] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 168.80/169.54 <=> ? [B_m] : % 168.80/169.54 ! [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 168.80/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 168.80/169.54 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 168.80/169.54 ! [V_N_2] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 168.80/169.54 <=> ? [B_m] : % 168.80/169.54 ! [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 168.80/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm_Ofold__equality,axiom, % 168.80/169.54 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 168.80/169.54 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 168.80/169.54 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 168.80/169.54 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => 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) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm_Ofold__insert,axiom, % 168.80/169.54 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_double__eq__0__iff,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 168.80/169.54 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 168.80/169.54 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => ? [B_y_H] : % 168.80/169.54 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 168.80/169.54 & 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)) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OatMost__iff,axiom, % 168.80/169.54 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OatLeast__iff,axiom, % 168.80/169.54 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OlessThan__iff,axiom, % 168.80/169.54 ! [V_k_2,V_less_2,V_i_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OgreaterThan__iff,axiom, % 168.80/169.54 ! [V_k_2,V_less_2,V_i_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OatLeastAtMost__iff,axiom, % 168.80/169.54 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 168.80/169.54 ( 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))) % 168.80/169.54 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 168.80/169.54 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 168.80/169.54 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 168.80/169.54 ( 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))) % 168.80/169.54 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 168.80/169.54 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OatLeastLessThan__iff,axiom, % 168.80/169.54 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 168.80/169.54 ( 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))) % 168.80/169.54 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 168.80/169.54 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 168.80/169.54 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 168.80/169.54 ( 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))) % 168.80/169.54 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 168.80/169.54 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_option_Osize_I2_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__odd__less__0,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => ( 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))) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I4_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I12_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_the__inv__into__into,axiom, % 168.80/169.54 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_ex__least__nat__less,axiom, % 168.80/169.54 ! [V_n_2,V_P_2] : % 168.80/169.54 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 168.80/169.54 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 168.80/169.54 => ? [B_k] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 168.80/169.54 & ! [B_i] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 168.80/169.54 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 168.80/169.54 & 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)))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__neg,axiom, % 168.80/169.54 ! [V_a,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 168.80/169.54 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__sgn,axiom, % 168.80/169.54 ! [V_a,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => 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) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__0__0,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn0,axiom, % 168.80/169.54 ! [T_a] : % 168.80/169.54 ( class_Groups_Osgn__if(T_a) % 168.80/169.54 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__times,axiom, % 168.80/169.54 ! [V_b,V_a,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => 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)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__0,axiom, % 168.80/169.54 ! [T_a] : % 168.80/169.54 ( class_Rings_Oring__1(T_a) % 168.80/169.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__add,axiom, % 168.80/169.54 ! [V_b_2,V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Oring__1(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => 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))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__mult,axiom, % 168.80/169.54 ! [V_b_2,V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Oring__1(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => 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))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__diff,axiom, % 168.80/169.54 ! [V_b_2,V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Oring__1(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => 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))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__1,axiom, % 168.80/169.54 ! [T_a] : % 168.80/169.54 ( class_Rings_Oring__1(T_a) % 168.80/169.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__minus,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Oring__1(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => 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))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__less,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( 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))) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__greater,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( 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))) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_the__inv__into__f__f,axiom, % 168.80/169.54 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => 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 ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_the__inv__into__f__eq,axiom, % 168.80/169.54 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.54 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_option_Osize_I1_J,axiom, % 168.80/169.54 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I15_J,axiom, % 168.80/169.54 ! [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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_the__inv__into__onto,axiom, % 168.80/169.54 ! [V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.54 => 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 ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_inj__on__the__inv__into,axiom, % 168.80/169.54 ! [V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.54 => 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)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I16_J,axiom, % 168.80/169.54 ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I7_J,axiom, % 168.80/169.54 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I9_J,axiom, % 168.80/169.54 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I8_J,axiom, % 168.80/169.54 ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I1_J,axiom, % 168.80/169.54 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__double__eq__0__iff,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Int_Oring__char__0(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__pos,axiom, % 168.80/169.54 ! [V_a,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 168.80/169.54 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__1__pos,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_f__the__inv__into__f,axiom, % 168.80/169.54 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 168.80/169.54 => 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 ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_Ints__odd__nonzero,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Int_Oring__char__0(T_a) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__if,axiom, % 168.80/169.54 ! [V_x,T_a] : % 168.80/169.54 ( class_Groups_Osgn__if(T_a) % 168.80/169.54 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.54 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 168.80/169.54 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 168.80/169.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.80/169.54 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 168.80/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 168.80/169.54 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_sgn__1__neg,axiom, % 168.80/169.54 ! [V_a_2,T_a] : % 168.80/169.54 ( class_Rings_Olinordered__idom(T_a) % 168.80/169.54 => ( 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)) % 168.80/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_nat_Osize_I2_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_nat_Osize_I4_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_option_Osize_I4_J,axiom, % 168.80/169.54 ! [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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_option_Osize_I3_J,axiom, % 168.80/169.54 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 168.80/169.54 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 168.80/169.54 => ( 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)) % 168.80/169.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => ~ ! [B_y] : % 168.80/169.54 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 168.80/169.54 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 168.80/169.54 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 168.80/169.54 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__diff1__ring,axiom, % 168.80/169.54 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Rings_Oring(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_nat__size,axiom, % 168.80/169.54 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 168.80/169.54 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 168.80/169.54 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 168.80/169.54 => 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) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__empty,axiom, % 168.80/169.54 ! [V_f_2,T_b,T_a] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_a) % 168.80/169.54 => 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) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum_Oempty,axiom, % 168.80/169.54 ! [V_g_2,T_b,T_a] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_a) % 168.80/169.54 => 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) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum_Oinfinite,axiom, % 168.80/169.54 ! [V_g_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__infinite,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__eq__0__iff,axiom, % 168.80/169.54 ! [V_f_2,V_F_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.80/169.54 => ( 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) % 168.80/169.54 <=> ! [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 168.80/169.54 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm__idem__insert,axiom, % 168.80/169.54 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 168.80/169.54 % 168.80/169.54 fof(fact_fun__left__comm__idem,axiom, % 168.80/169.54 ! [T_a] : % 168.80/169.54 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 168.80/169.54 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__eq__Suc0__iff,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( 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)) % 168.80/169.54 <=> ? [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.54 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 168.80/169.54 & ! [B_xa] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 168.80/169.54 => ( B_x != B_xa % 168.80/169.54 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__eq__1__iff,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( 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) % 168.80/169.54 <=> ? [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.54 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 168.80/169.54 & ! [B_xa] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 168.80/169.54 => ( B_x != B_xa % 168.80/169.54 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_nat_Osize_I3_J,axiom, % 168.80/169.54 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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__insert,axiom, % 168.80/169.54 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.80/169.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum_Oinsert,axiom, % 168.80/169.54 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__diff,axiom, % 168.80/169.54 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Oab__group__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__diff__nat,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,V_B_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 168.80/169.54 => 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)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_nat_Osize_I1_J,axiom, % 168.80/169.54 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum_Oinsert__remove,axiom, % 168.80/169.54 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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)))))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__diff1__nat,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,V_a_2,T_a] : % 168.80/169.54 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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)) ) % 168.80/169.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__diff1_H,axiom, % 168.80/169.54 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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)))))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum_Oremove,axiom, % 168.80/169.54 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => 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)))))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__diff1,axiom, % 168.80/169.54 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Oab__group__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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)) ) % 168.80/169.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__mono2,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Oordered__comm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.54 => ( ! [B_b] : % 168.80/169.54 ( 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))) % 168.80/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 168.80/169.54 => 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))) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__mono3,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 168.80/169.54 ( ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 168.80/169.54 => ( ! [B_x] : % 168.80/169.54 ( 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))) % 168.80/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 168.80/169.54 => 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))) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__mono__zero__right,axiom, % 168.80/169.54 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.80/169.54 => ( ! [B_x] : % 168.80/169.54 ( 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))) % 168.80/169.54 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.80/169.54 => 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) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__mono__zero__left,axiom, % 168.80/169.54 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.80/169.54 => ( ! [B_x] : % 168.80/169.54 ( 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))) % 168.80/169.54 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.80/169.54 => 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) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__strict__mono,axiom, % 168.80/169.54 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( ( class_Groups_Ocomm__monoid__add(T_b) % 168.80/169.54 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 168.80/169.54 => ( ! [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 168.80/169.54 => 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))) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod_Oremove,axiom, % 168.80/169.54 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => 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)))))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I5_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I13_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_WTs__elim__cases_I5_J,axiom, % 168.80/169.54 ! [V_c2_2,V_c1_2,V_b_2] : % 168.80/169.54 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 168.80/169.54 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 168.80/169.54 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I4_J,axiom, % 168.80/169.54 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 168.80/169.54 ( 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) % 168.80/169.54 <=> ( V_fun_2 = V_fun_H_2 % 168.80/169.54 & V_com1_2 = V_com1_H_2 % 168.80/169.54 & V_com2_2 = V_com2_H_2 ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_WT_OIf,axiom, % 168.80/169.54 ! [V_b_2,V_c1_2,V_c0_2] : % 168.80/169.54 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 168.80/169.54 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 168.80/169.54 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_WT_Oequations_I5_J,axiom, % 168.80/169.54 ! [V_a2_2,V_a1_2,V_a3_2] : % 168.80/169.54 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 168.80/169.54 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 168.80/169.54 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I55_J,axiom, % 168.80/169.54 ! [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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I54_J,axiom, % 168.80/169.54 ! [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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I44_J,axiom, % 168.80/169.54 ! [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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I45_J,axiom, % 168.80/169.54 ! [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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I56_J,axiom, % 168.80/169.54 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I57_J,axiom, % 168.80/169.54 ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I14_J,axiom, % 168.80/169.54 ! [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) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I15_J,axiom, % 168.80/169.54 ! [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 ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__zero__iff,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( ( class_Rings_Ocomm__semiring__1(T_b) % 168.80/169.54 & class_Rings_Ono__zero__divisors(T_b) ) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( 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) % 168.80/169.54 <=> ? [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.54 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__zero,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Rings_Ocomm__semiring__1(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ? [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.54 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 168.80/169.54 => 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) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod_Oempty,axiom, % 168.80/169.54 ! [V_g_2,T_b,T_a] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.80/169.54 => 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) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__empty,axiom, % 168.80/169.54 ! [V_f_2,T_b,T_a] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_a) % 168.80/169.54 => 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) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__infinite,axiom, % 168.80/169.54 ! [V_f_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod_Oinfinite,axiom, % 168.80/169.54 ! [V_g_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__eq__1__iff,axiom, % 168.80/169.54 ! [V_f_2,V_F_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 168.80/169.54 => ( 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) % 168.80/169.54 <=> ! [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 168.80/169.54 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__pos__nat__iff,axiom, % 168.80/169.54 ! [V_f_2,V_S_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 168.80/169.54 => ( 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))) % 168.80/169.54 <=> ! [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 168.80/169.54 => 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))) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__insert,axiom, % 168.80/169.54 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod_Oinsert,axiom, % 168.80/169.54 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 168.80/169.54 => 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)) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod_Oinsert__remove,axiom, % 168.80/169.54 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => 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)))))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__diff1,axiom, % 168.80/169.54 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 168.80/169.54 ( class_Fields_Ofield(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 168.80/169.54 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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)) ) % 168.80/169.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 168.80/169.54 => 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) ) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__mono__one__left,axiom, % 168.80/169.54 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.80/169.54 => ( ! [B_x] : % 168.80/169.54 ( 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))) % 168.80/169.54 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.80/169.54 => 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) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setprod__mono__one__right,axiom, % 168.80/169.54 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 168.80/169.54 ( class_Groups_Ocomm__monoid__mult(T_b) % 168.80/169.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 168.80/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 168.80/169.54 => ( ! [B_x] : % 168.80/169.54 ( 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))) % 168.80/169.54 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 168.80/169.54 => 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) ) ) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_setsum__SucD,axiom, % 168.80/169.54 ! [V_n_2,V_A_2,V_f_2,T_a] : % 168.80/169.54 ( 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) % 168.80/169.54 => ? [B_x] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.54 & 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))) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_card_Oneutral,axiom, % 168.80/169.54 ! [V_A_2,T_a] : % 168.80/169.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 168.80/169.54 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 168.80/169.54 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 168.80/169.54 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_expand__Suc,axiom, % 168.80/169.54 ! [V_v] : % 168.80/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) % 168.80/169.54 => 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))) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I11_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osize_I3_J,axiom, % 168.80/169.54 ! [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))) ). % 168.80/169.54 % 168.80/169.54 fof(fact_WTs__elim__cases_I3_J,axiom, % 168.80/169.54 ! [V_ca_2,V_a_2,V_Y_2] : % 168.80/169.54 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) % 168.80/169.54 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_number__of__reorient,axiom, % 168.80/169.54 ! [V_x_2,V_w_2,T_a] : % 168.80/169.54 ( class_Int_Onumber(T_a) % 168.80/169.54 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 168.80/169.54 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_eq__number__of,axiom, % 168.80/169.54 ! [V_y_2,V_x_2,T_a] : % 168.80/169.54 ( ( class_Int_Onumber__ring(T_a) % 168.80/169.54 & class_Int_Oring__char__0(T_a) ) % 168.80/169.54 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 168.80/169.54 <=> V_x_2 = V_y_2 ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_com_Osimps_I2_J,axiom, % 168.80/169.54 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 168.80/169.54 ( 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) % 168.80/169.54 <=> ( V_loc_2 = V_loc_H_2 % 168.80/169.54 & V_fun_2 = V_fun_H_2 % 168.80/169.54 & V_com_2 = V_com_H_2 ) ) ). % 168.80/169.54 % 168.80/169.54 fof(fact_divide__eq__eq__number__of1,axiom, % 168.80/169.54 ! [V_a_2,V_w_2,V_b_2,T_a] : % 168.80/169.54 ( ( class_Fields_Ofield__inverse__zero(T_a) % 168.80/169.54 & class_Int_Onumber(T_a) ) % 168.80/169.54 => ( 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 % 168.80/169.54 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__eq__eq__number__of,axiom, % 169.04/169.54 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 169.04/169.54 ( ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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) % 169.04/169.54 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => 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) ) % 169.04/169.54 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_eq__divide__eq__number__of,axiom, % 169.04/169.54 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 169.04/169.54 ( ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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) % 169.04/169.54 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => 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 ) % 169.04/169.54 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_eq__divide__eq__number__of1,axiom, % 169.04/169.54 ! [V_w_2,V_b_2,V_a_2,T_a] : % 169.04/169.54 ( ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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)) % 169.04/169.54 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => 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 ) % 169.04/169.54 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__zero__left,axiom, % 169.04/169.54 ! [V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__zero,axiom, % 169.04/169.54 ! [V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_add__divide__distrib,axiom, % 169.04/169.54 ! [V_c,V_b,V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_times__divide__eq__right,axiom, % 169.04/169.54 ! [V_c,V_b,V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_le__number__of,axiom, % 169.04/169.54 ! [V_y_2,V_x_2,T_a] : % 169.04/169.54 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.54 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_less__number__of,axiom, % 169.04/169.54 ! [V_y_2,V_x_2,T_a] : % 169.04/169.54 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.54 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_diff__divide__distrib,axiom, % 169.04/169.54 ! [V_c,V_b,V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__1,axiom, % 169.04/169.54 ! [V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_number__of__add,axiom, % 169.04/169.54 ! [V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_add__number__of__eq,axiom, % 169.04/169.54 ! [V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_add__number__of__left,axiom, % 169.04/169.54 ! [V_z,V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_number__of__mult,axiom, % 169.04/169.54 ! [V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_arith__simps_I32_J,axiom, % 169.04/169.54 ! [V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_mult__number__of__left,axiom, % 169.04/169.54 ! [V_z,V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_minus__divide__left,axiom, % 169.04/169.54 ! [V_b,V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_diff__number__of__eq,axiom, % 169.04/169.54 ! [V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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))) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_number__of__diff,axiom, % 169.04/169.54 ! [V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_arith__simps_I30_J,axiom, % 169.04/169.54 ! [V_w,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_number__of__minus,axiom, % 169.04/169.54 ! [V_w,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__less__eq__number__of1,axiom, % 169.04/169.54 ! [V_a_2,V_w_2,V_b_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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)) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => 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)))) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => ( ( 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))) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ 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))) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__less__eq__number__of,axiom, % 169.04/169.54 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => 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))) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_less__divide__eq__number__of,axiom, % 169.04/169.54 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => 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))) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => 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))) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_less__divide__eq__number__of1,axiom, % 169.04/169.54 ! [V_w_2,V_b_2,V_a_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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)))) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => ( ( 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))) % 169.04/169.54 => 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)))) ) % 169.04/169.54 & ( ~ 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))) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I40_J,axiom, % 169.04/169.54 ! [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) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I41_J,axiom, % 169.04/169.54 ! [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) ). % 169.04/169.54 % 169.04/169.54 fof(fact_WT_Oequations_I3_J,axiom, % 169.04/169.54 ! [V_a1_2,V_a3_2,V_a2_2] : % 169.04/169.54 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 169.04/169.54 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_WT_OLocal,axiom, % 169.04/169.54 ! [V_a_2,V_Y_2,V_ca_2] : % 169.04/169.54 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 169.04/169.54 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I37_J,axiom, % 169.04/169.54 ! [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) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I36_J,axiom, % 169.04/169.54 ! [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) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I43_J,axiom, % 169.04/169.54 ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I42_J,axiom, % 169.04/169.54 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I34_J,axiom, % 169.04/169.54 ! [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) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I35_J,axiom, % 169.04/169.54 ! [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) ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I11_J,axiom, % 169.04/169.54 ! [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 ). % 169.04/169.54 % 169.04/169.54 fof(fact_com_Osimps_I10_J,axiom, % 169.04/169.54 ! [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) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__le__eq__number__of1,axiom, % 169.04/169.54 ! [V_a_2,V_w_2,V_b_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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)) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => 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)))) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => ( ( 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))) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ 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))) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__le__eq__number__of,axiom, % 169.04/169.54 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => 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))) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_le__divide__eq__number__of,axiom, % 169.04/169.54 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => 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))) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => 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))) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_le__divide__eq__number__of1,axiom, % 169.04/169.54 ! [V_w_2,V_b_2,V_a_2,T_a] : % 169.04/169.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 & class_Int_Onumber(T_a) ) % 169.04/169.54 => ( 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)))) % 169.04/169.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => 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)) ) % 169.04/169.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 169.04/169.54 => ( ( 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))) % 169.04/169.54 => 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)))) ) % 169.04/169.54 & ( ~ 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))) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_nonzero__eq__divide__eq,axiom, % 169.04/169.54 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 169.04/169.54 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_nonzero__divide__eq__eq,axiom, % 169.04/169.54 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 169.04/169.54 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__eq__imp,axiom, % 169.04/169.54 ! [V_a,V_b,V_c,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 169.04/169.54 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_eq__divide__imp,axiom, % 169.04/169.54 ! [V_b,V_a,V_c,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 169.04/169.54 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_right__inverse__eq,axiom, % 169.04/169.54 ! [V_a_2,V_b_2,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 169.04/169.54 <=> V_a_2 = V_b_2 ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__self,axiom, % 169.04/169.54 ! [V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__self__if,axiom, % 169.04/169.54 ! [V_a,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 169.04/169.54 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 169.04/169.54 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_le__number__of__eq__not__less,axiom, % 169.04/169.54 ! [V_w_2,V_v_2,T_a] : % 169.04/169.54 ( ( class_Int_Onumber(T_a) % 169.04/169.54 & class_Orderings_Olinorder(T_a) ) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> ~ 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))) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_nonzero__minus__divide__divide,axiom, % 169.04/169.54 ! [V_a,V_b,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => 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) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_nonzero__minus__divide__right,axiom, % 169.04/169.54 ! [V_a,V_b,T_a] : % 169.04/169.54 ( class_Rings_Odivision__ring(T_a) % 169.04/169.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.54 => 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)) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_right__distrib__number__of,axiom, % 169.04/169.54 ! [V_c,V_b,V_v,T_b] : % 169.04/169.54 ( ( class_Int_Onumber(T_b) % 169.04/169.54 & class_Rings_Osemiring(T_b) ) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_left__distrib__number__of,axiom, % 169.04/169.54 ! [V_v,V_b,V_a,T_b] : % 169.04/169.54 ( ( class_Int_Onumber(T_b) % 169.04/169.54 & class_Rings_Osemiring(T_b) ) % 169.04/169.54 => 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))) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_add__number__of__diff1,axiom, % 169.04/169.54 ! [V_c,V_w,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_add__number__of__diff2,axiom, % 169.04/169.54 ! [V_w,V_c,V_v,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_left__diff__distrib__number__of,axiom, % 169.04/169.54 ! [V_v,V_b,V_a,T_b] : % 169.04/169.54 ( ( class_Int_Onumber(T_b) % 169.04/169.54 & class_Rings_Oring(T_b) ) % 169.04/169.54 => 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))) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_right__diff__distrib__number__of,axiom, % 169.04/169.54 ! [V_c,V_b,V_v,T_b] : % 169.04/169.54 ( ( class_Int_Onumber(T_b) % 169.04/169.54 & class_Rings_Oring(T_b) ) % 169.04/169.54 => 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)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_minus__number__of__mult,axiom, % 169.04/169.54 ! [V_z,V_w,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_Ints__number__of,axiom, % 169.04/169.54 ! [V_w_2,T_a] : % 169.04/169.54 ( class_Int_Onumber__ring(T_a) % 169.04/169.54 => 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))) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__left__mono__neg,axiom, % 169.04/169.54 ! [V_c,V_b,V_a,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => ( 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))) % 169.04/169.54 => 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))) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_divide__left__mono,axiom, % 169.04/169.54 ! [V_c,V_a,V_b,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 169.04/169.54 => ( 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))) % 169.04/169.54 => 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))) ) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_neg__divide__le__eq,axiom, % 169.04/169.54 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => ( 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)) % 169.04/169.54 <=> 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)) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_neg__le__divide__eq,axiom, % 169.04/169.54 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> 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))) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_mult__imp__le__div__pos,axiom, % 169.04/169.54 ! [V_x,V_z,V_y,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.54 => ( 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)) % 169.04/169.54 => 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))) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_mult__imp__div__pos__le,axiom, % 169.04/169.54 ! [V_z,V_x,V_y,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.54 => ( 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))) % 169.04/169.54 => 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)) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_pos__divide__le__eq,axiom, % 169.04/169.54 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => ( 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)) % 169.04/169.54 <=> 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))) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_pos__le__divide__eq,axiom, % 169.04/169.54 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 169.04/169.54 ( class_Fields_Olinordered__field(T_a) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.54 => ( 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))) % 169.04/169.54 <=> 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)) ) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_times__numeral__code_I5_J,axiom, % 169.04/169.54 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_minus__numeral__code_I5_J,axiom, % 169.04/169.54 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_less__eq__number__of__int__code,axiom, % 169.04/169.54 ! [V_l_2,V_k_2] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 169.04/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_less__number__of__int__code,axiom, % 169.04/169.54 ! [V_l_2,V_k_2] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 169.04/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_minus__numeral__code_I6_J,axiom, % 169.04/169.54 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ). % 169.04/169.54 % 169.04/169.54 fof(fact_plus__numeral__code_I9_J,axiom, % 169.04/169.54 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zless__add1__eq,axiom, % 169.04/169.54 ! [V_z_2,V_w_2] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 169.04/169.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 169.04/169.54 | V_w_2 = V_z_2 ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zle__add1__eq__le,axiom, % 169.04/169.54 ! [V_z_2,V_w_2] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 169.04/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_add1__zle__eq,axiom, % 169.04/169.54 ! [V_z_2,V_w_2] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) % 169.04/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zless__imp__add1__zle,axiom, % 169.04/169.54 ! [V_z,V_w] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__strict__right__mono,axiom, % 169.04/169.54 ! [V_k,V_j,V_i] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__zmult__distrib2,axiom, % 169.04/169.54 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__zmult__distrib,axiom, % 169.04/169.54 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__assoc,axiom, % 169.04/169.54 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__left__commute,axiom, % 169.04/169.54 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__commute,axiom, % 169.04/169.54 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__left__mono,axiom, % 169.04/169.54 ! [V_k,V_j,V_i] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zminus__zadd__distrib,axiom, % 169.04/169.54 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_diff__int__def__symmetric,axiom, % 169.04/169.54 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ). % 169.04/169.54 % 169.04/169.54 fof(fact_diff__int__def,axiom, % 169.04/169.54 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zadd__zless__mono,axiom, % 169.04/169.54 ! [V_z,V_z_H,V_w,V_w_H] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zle__diff1__eq,axiom, % 169.04/169.54 ! [V_z_2,V_w_2] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 169.04/169.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zless__linear,axiom, % 169.04/169.54 ! [V_y,V_x] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 169.04/169.54 | V_x = V_y % 169.04/169.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zle__refl,axiom, % 169.04/169.54 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zle__linear,axiom, % 169.04/169.54 ! [V_w,V_z] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 169.04/169.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zle__trans,axiom, % 169.04/169.54 ! [V_k,V_j,V_i] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 169.04/169.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zle__antisym,axiom, % 169.04/169.54 ! [V_w,V_z] : % 169.04/169.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 169.04/169.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 169.04/169.54 => V_z = V_w ) ) ). % 169.04/169.54 % 169.04/169.54 fof(fact_zminus__zminus,axiom, % 169.04/169.54 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 169.04/169.54 % 169.04/169.54 fof(fact_zless__le,axiom, % 169.04/169.54 ! [V_w_2,V_z_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 169.04/169.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 169.04/169.55 & V_z_2 != V_w_2 ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zdiff__zmult__distrib2,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zdiff__zmult__distrib,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__zminus,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__assoc,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__commute,axiom, % 169.04/169.55 ! [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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__1__right,axiom, % 169.04/169.55 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__1,axiom, % 169.04/169.55 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 169.04/169.55 % 169.04/169.55 fof(fact_pos__zmult__eq__1__iff,axiom, % 169.04/169.55 ! [V_n_2,V_m_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 169.04/169.55 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 169.04/169.55 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 169.04/169.55 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__zless__mono2,axiom, % 169.04/169.55 ! [V_k,V_j,V_i] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__bin__lemma,axiom, % 169.04/169.55 ! [V_l_2,V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 169.04/169.55 <=> 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zminus__0,axiom, % 169.04/169.55 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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__one__le__iff__zero__less,axiom, % 169.04/169.55 ! [V_z_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__0__less__1,axiom, % 169.04/169.55 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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zadd__zminus__inverse2,axiom, % 169.04/169.55 ! [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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zadd__0,axiom, % 169.04/169.55 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 169.04/169.55 % 169.04/169.55 fof(fact_zadd__0__right,axiom, % 169.04/169.55 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 169.04/169.55 % 169.04/169.55 fof(fact_odd__nonzero,axiom, % 169.04/169.55 ! [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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__imp__0__less,axiom, % 169.04/169.55 ! [V_z] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.55 => 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_odd__less__0,axiom, % 169.04/169.55 ! [V_z_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zsgn__def,axiom, % 169.04/169.55 ! [V_i] : % 169.04/169.55 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.55 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.04/169.55 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 169.04/169.55 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 169.04/169.55 => 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)) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_times__divide__times__eq,axiom, % 169.04/169.55 ! [V_w,V_z,V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_minus__divide__divide,axiom, % 169.04/169.55 ! [V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => 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) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_minus__divide__right,axiom, % 169.04/169.55 ! [V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__right__mono__neg,axiom, % 169.04/169.55 ! [V_c,V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__right__mono,axiom, % 169.04/169.55 ! [V_c,V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__le__0__iff,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 169.04/169.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zero__le__divide__iff,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 169.04/169.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__strict__right__mono__neg,axiom, % 169.04/169.55 ! [V_c,V_a,V_b,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__strict__right__mono,axiom, % 169.04/169.55 ! [V_c,V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__neg__neg,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__neg__pos,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__pos__neg,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__pos__pos,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__less__0__iff,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 169.04/169.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zero__less__divide__iff,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 169.04/169.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__divide__eq,axiom, % 169.04/169.55 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 169.04/169.55 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 169.04/169.55 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__eq__eq,axiom, % 169.04/169.55 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 169.04/169.55 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 169.04/169.55 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__divide__mult__cancel__right,axiom, % 169.04/169.55 ! [V_b,V_a,V_c,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__divide__mult__cancel__left,axiom, % 169.04/169.55 ! [V_b,V_a,V_c,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_frac__eq__eq,axiom, % 169.04/169.55 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 169.04/169.55 ( class_Fields_Ofield(T_a) % 169.04/169.55 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => ( 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) % 169.04/169.55 <=> 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) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__nonneg__pos,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__nonneg__neg,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_frac__less2,axiom, % 169.04/169.55 ! [V_z,V_w,V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 169.04/169.55 => 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))) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_frac__less,axiom, % 169.04/169.55 ! [V_z,V_w,V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 169.04/169.55 => 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))) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_frac__le,axiom, % 169.04/169.55 ! [V_z,V_w,V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 169.04/169.55 => 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))) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__nonpos__pos,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__nonpos__neg,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__divide__eq,axiom, % 169.04/169.55 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => 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)) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__less__eq,axiom, % 169.04/169.55 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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)) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => 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))) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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)) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_pos__less__divide__eq,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> 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)) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_pos__divide__less__eq,axiom, % 169.04/169.55 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => ( 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)) % 169.04/169.55 <=> 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__imp__div__pos__less,axiom, % 169.04/169.55 ! [V_z,V_x,V_y,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.55 => ( 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))) % 169.04/169.55 => 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)) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__imp__less__div__pos,axiom, % 169.04/169.55 ! [V_x,V_z,V_y,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.55 => ( 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)) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_neg__less__divide__eq,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_neg__divide__less__eq,axiom, % 169.04/169.55 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => ( 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)) % 169.04/169.55 <=> 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)) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__strict__left__mono,axiom, % 169.04/169.55 ! [V_c,V_a,V_b,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 169.04/169.55 => ( 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))) % 169.04/169.55 => 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))) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__strict__left__mono__neg,axiom, % 169.04/169.55 ! [V_c,V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => ( 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))) % 169.04/169.55 => 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))) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__frac__eq,axiom, % 169.04/169.55 ! [V_w,V_x,V_z,V_y,T_a] : % 169.04/169.55 ( class_Fields_Ofield(T_a) % 169.04/169.55 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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)) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__add__eq__iff,axiom, % 169.04/169.55 ! [V_y,V_x,V_z,T_a] : % 169.04/169.55 ( class_Fields_Ofield(T_a) % 169.04/169.55 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__frac__num,axiom, % 169.04/169.55 ! [V_z,V_x,V_y,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__divide__eq__iff,axiom, % 169.04/169.55 ! [V_y,V_x,V_z,T_a] : % 169.04/169.55 ( class_Fields_Ofield(T_a) % 169.04/169.55 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__num__frac,axiom, % 169.04/169.55 ! [V_x,V_z,V_y,T_a] : % 169.04/169.55 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_diff__divide__eq__iff,axiom, % 169.04/169.55 ! [V_y,V_x,V_z,T_a] : % 169.04/169.55 ( class_Fields_Ofield(T_a) % 169.04/169.55 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__diff__eq__iff,axiom, % 169.04/169.55 ! [V_y,V_x,V_z,T_a] : % 169.04/169.55 ( class_Fields_Ofield(T_a) % 169.04/169.55 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_diff__frac__eq,axiom, % 169.04/169.55 ! [V_w,V_x,V_z,V_y,T_a] : % 169.04/169.55 ( class_Fields_Ofield(T_a) % 169.04/169.55 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 => 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)) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_gt__half__sum,axiom, % 169.04/169.55 ! [V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 169.04/169.55 => 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)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__half__sum,axiom, % 169.04/169.55 ! [V_b,V_a,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 169.04/169.55 => 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))))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__divide__eq,axiom, % 169.04/169.55 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => 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)) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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))) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__le__eq,axiom, % 169.04/169.55 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( 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)) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => 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))) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 169.04/169.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => 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)) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_self__quotient__aux2,axiom, % 169.04/169.55 ! [V_q,V_r,V_a] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.55 => ( 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)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_self__quotient__aux1,axiom, % 169.04/169.55 ! [V_q,V_r,V_a] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.55 => ( 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)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zdiv__mono2__neg__lemma,axiom, % 169.04/169.55 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 169.04/169.55 ( 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) % 169.04/169.55 => ( 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))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_unique__quotient__lemma__neg,axiom, % 169.04/169.55 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 169.04/169.55 ( 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))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zdiv__mono2__lemma,axiom, % 169.04/169.55 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 169.04/169.55 ( 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) % 169.04/169.55 => ( 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))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_unique__quotient__lemma,axiom, % 169.04/169.55 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 169.04/169.55 ( 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))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_q__neg__lemma,axiom, % 169.04/169.55 ! [V_r_H,V_q_H,V_b_H] : % 169.04/169.55 ( 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))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_number__of__is__id,axiom, % 169.04/169.55 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__0__neq__1,axiom, % 169.04/169.55 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 169.04/169.55 % 169.04/169.55 fof(fact_q__pos__lemma,axiom, % 169.04/169.55 ! [V_r_H,V_q_H,V_b_H] : % 169.04/169.55 ( 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))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 169.04/169.55 ! [V_y,V_x] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 169.04/169.55 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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 169.04/169.55 ! [V_y,V_x] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 169.04/169.55 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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__number__of__lemma,axiom, % 169.04/169.55 ! [V_v,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_field__le__mult__one__interval,axiom, % 169.04/169.55 ! [V_y,V_x,T_a] : % 169.04/169.55 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 => ( ! [B_z] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 169.04/169.55 => 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)) ) ) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_setprod__pos__nat,axiom, % 169.04/169.55 ! [V_f_2,V_S_2,T_a] : % 169.04/169.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.04/169.55 => ( ! [B_x] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 169.04/169.55 => 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))) ) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_negative__zle,axiom, % 169.04/169.55 ! [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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_negative__zless,axiom, % 169.04/169.55 ! [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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 169.04/169.55 ! [V_A_2] : % 169.04/169.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 169.04/169.55 <=> 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__eq__iff,axiom, % 169.04/169.55 ! [V_n_2,V_m_2,T_a] : % 169.04/169.55 ( class_Nat_Osemiring__char__0(T_a) % 169.04/169.55 => ( 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) % 169.04/169.55 <=> V_m_2 = V_n_2 ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 169.04/169.55 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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 169.04/169.55 ! [V_P_2] : % 169.04/169.55 ( ! [B_x] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 169.04/169.55 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.04/169.55 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 169.04/169.55 ! [V_P_2] : % 169.04/169.55 ( ? [B_x] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 169.04/169.55 & hBOOL(hAPP(V_P_2,B_x)) ) % 169.04/169.55 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 169.04/169.55 ! [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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 169.04/169.55 ! [V_y_2,V_x_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 169.04/169.55 ! [V_y_2,V_x_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 169.04/169.55 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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__eq__0__conv,axiom, % 169.04/169.55 ! [V_n_2] : % 169.04/169.55 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.55 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__0,axiom, % 169.04/169.55 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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zero__zle__int,axiom, % 169.04/169.55 ! [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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__less__0__conv,axiom, % 169.04/169.55 ! [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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zless__int,axiom, % 169.04/169.55 ! [V_n_2,V_m_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zle__int,axiom, % 169.04/169.55 ! [V_n_2,V_m_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zadd__int,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zadd__int__left,axiom, % 169.04/169.55 ! [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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zle__iff__zadd,axiom, % 169.04/169.55 ! [V_z_2,V_w_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 169.04/169.55 <=> ? [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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zero__le__imp__of__nat,axiom, % 169.04/169.55 ! [V_m,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__0__le__iff,axiom, % 169.04/169.55 ! [V_n,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_negative__eq__positive,axiom, % 169.04/169.55 ! [V_m_2,V_n_2] : % 169.04/169.55 ( 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) % 169.04/169.55 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.55 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__less__0__iff,axiom, % 169.04/169.55 ! [V_m,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => ~ 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__int__zless__negative,axiom, % 169.04/169.55 ! [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)))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__int,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__mult,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__0,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => 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) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__less__iff,axiom, % 169.04/169.55 ! [V_n_2,V_m_2,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__imp__of__nat__less,axiom, % 169.04/169.55 ! [V_n,V_m,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__less__imp__less,axiom, % 169.04/169.55 ! [V_n,V_m,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__1,axiom, % 169.04/169.55 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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__le__iff,axiom, % 169.04/169.55 ! [V_n_2,V_m_2,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__add,axiom, % 169.04/169.55 ! [V_n,V_m,T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__mult,axiom, % 169.04/169.55 ! [V_n,V_m,T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__1,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => 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) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Ints__of__nat,axiom, % 169.04/169.55 ! [V_n_2,T_a] : % 169.04/169.55 ( class_Rings_Oring__1(T_a) % 169.04/169.55 => 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__le__0__conv,axiom, % 169.04/169.55 ! [V_n_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__Suc0__eq__1,axiom, % 169.04/169.55 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) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zless__iff__Suc__zadd,axiom, % 169.04/169.55 ! [V_z_2,V_w_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 169.04/169.55 <=> ? [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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__zle__neg,axiom, % 169.04/169.55 ! [V_m_2,V_n_2] : % 169.04/169.55 ( 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)))) % 169.04/169.55 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.55 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__Suc,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_negative__zle__0,axiom, % 169.04/169.55 ! [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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zdiff__int,axiom, % 169.04/169.55 ! [V_m,V_n] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__Suc,axiom, % 169.04/169.55 ! [V_m,T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__diff,axiom, % 169.04/169.55 ! [V_m,V_n,T_a] : % 169.04/169.55 ( class_Rings_Oring__1(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 169.04/169.55 => 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)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zero__less__int__conv,axiom, % 169.04/169.55 ! [V_n_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zmult__zless__mono2__lemma,axiom, % 169.04/169.55 ! [V_k,V_j,V_i] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__zle__0__negative,axiom, % 169.04/169.55 ! [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))))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_negative__zless__0,axiom, % 169.04/169.55 ! [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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__0__less__iff,axiom, % 169.04/169.55 ! [V_n_2,T_a] : % 169.04/169.55 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zdiff__int__split,axiom, % 169.04/169.55 ! [V_y_2,V_x_2,V_P_2] : % 169.04/169.55 ( 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)))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 169.04/169.55 => 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)))) ) % 169.04/169.55 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 169.04/169.55 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_setsum__bounded,axiom, % 169.04/169.55 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 169.04/169.55 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 169.04/169.55 & class_Rings_Osemiring__1(T_b) ) % 169.04/169.55 => ( ! [B_i] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_tsub__def,axiom, % 169.04/169.55 ! [V_x,V_y] : % 169.04/169.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 169.04/169.55 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 169.04/169.55 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__number__of__eq,axiom, % 169.04/169.55 ! [V_v,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__number__of__eq,axiom, % 169.04/169.55 ! [V_y_2,V_x_2,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 169.04/169.55 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_nat__number__of__mult__left,axiom, % 169.04/169.55 ! [V_k,V_v_H,V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__nat__number__of,axiom, % 169.04/169.55 ! [V_v_H,V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 169.04/169.55 ! [V_A_2,V_x_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 169.04/169.55 <=> 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 169.04/169.55 ! [V_B_2,V_A_2] : % 169.04/169.55 ( V_A_2 = V_B_2 % 169.04/169.55 <=> 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) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 169.04/169.55 ! [V_y_2,V_x_2] : % 169.04/169.55 ( 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) % 169.04/169.55 <=> V_x_2 = V_y_2 ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__neg__int,axiom, % 169.04/169.55 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__int__eq,axiom, % 169.04/169.55 ! [V_n_2,V_m_2] : % 169.04/169.55 ( 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) % 169.04/169.55 <=> V_m_2 = V_n_2 ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 169.04/169.55 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))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 169.04/169.55 ! [V_B_2,V_A_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.55 <=> 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 169.04/169.55 ! [V_B_2,V_A_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.55 <=> 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__neg__number__of__Pls,axiom, % 169.04/169.55 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_iszero__Numeral0,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Pls__def,axiom, % 169.04/169.55 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I19_J,axiom, % 169.04/169.55 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I2_J,axiom, % 169.04/169.55 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__Pls,axiom, % 169.04/169.55 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__Pls__right,axiom, % 169.04/169.55 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__Pls,axiom, % 169.04/169.55 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 169.04/169.55 % 169.04/169.55 fof(fact_diff__bin__simps_I1_J,axiom, % 169.04/169.55 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 169.04/169.55 % 169.04/169.55 fof(fact_minus__Pls,axiom, % 169.04/169.55 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__neg__0,axiom, % 169.04/169.55 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__neg__1,axiom, % 169.04/169.55 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_iszero__def,axiom, % 169.04/169.55 ! [V_z_2,T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => ( c_Int_Oiszero(T_a,V_z_2) % 169.04/169.55 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_iszero__0,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__iszero__1,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_number__of__Pls,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_semiring__norm_I112_J,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__numeral__0__right,axiom, % 169.04/169.55 ! [V_a,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => 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 ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__numeral__0,axiom, % 169.04/169.55 ! [V_a,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => 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 ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_number__of2,axiom, % 169.04/169.55 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_bin__less__0__simps_I1_J,axiom, % 169.04/169.55 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_nat__number__of__Pls,axiom, % 169.04/169.55 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.04/169.55 % 169.04/169.55 fof(fact_semiring__norm_I113_J,axiom, % 169.04/169.55 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zero__is__num__zero,axiom, % 169.04/169.55 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__neg__eq__ge__0,axiom, % 169.04/169.55 ! [V_x_2] : % 169.04/169.55 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_neg__def,axiom, % 169.04/169.55 ! [V_Z_2] : % 169.04/169.55 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__special_I3_J,axiom, % 169.04/169.55 ! [V_x_2,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.55 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__special_I1_J,axiom, % 169.04/169.55 ! [V_y_2,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 169.04/169.55 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_neg__zminus__int,axiom, % 169.04/169.55 ! [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))))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__Numeral0,axiom, % 169.04/169.55 ! [V_x,T_a] : % 169.04/169.55 ( ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.55 & class_Int_Onumber__ring(T_a) ) % 169.04/169.55 => 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) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__0__number__of,axiom, % 169.04/169.55 ! [V_v_2] : % 169.04/169.55 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__number__of__0,axiom, % 169.04/169.55 ! [V_v_2] : % 169.04/169.55 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__nat__number__of,axiom, % 169.04/169.55 ! [V_v_H_2,V_v_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 169.04/169.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__nat__number__of,axiom, % 169.04/169.55 ! [V_v_H_2,V_v_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_neg__imp__number__of__eq__0,axiom, % 169.04/169.55 ! [V_v] : % 169.04/169.55 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_int__nat__number__of,axiom, % 169.04/169.55 ! [V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__special_I1_J,axiom, % 169.04/169.55 ! [V_y_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__special_I3_J,axiom, % 169.04/169.55 ! [V_x_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__special_I1_J,axiom, % 169.04/169.55 ! [V_y_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__special_I3_J,axiom, % 169.04/169.55 ! [V_x_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__0__number__of,axiom, % 169.04/169.55 ! [V_v_2] : % 169.04/169.55 ( 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))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__nat__number__of,axiom, % 169.04/169.55 ! [V_v_H,V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 169.04/169.55 => 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)) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__nat__number__of,axiom, % 169.04/169.55 ! [V_v_H_2,V_v_2] : % 169.04/169.55 ( 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) % 169.04/169.55 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 169.04/169.55 => 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))) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 169.04/169.55 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 169.04/169.55 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 169.04/169.55 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_nat__number__of__add__left,axiom, % 169.04/169.55 ! [V_k,V_v_H,V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 169.04/169.55 => 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) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 169.04/169.55 ! [V_y,V_x] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_tsub__eq,axiom, % 169.04/169.55 ! [V_x,V_y] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 169.04/169.55 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Suc__nat__number__of__add,axiom, % 169.04/169.55 ! [V_n,V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Suc__nat__number__of,axiom, % 169.04/169.55 ! [V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.55 => 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)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_nat__1__add__number__of,axiom, % 169.04/169.55 ! [V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_nat__number__of__add__1,axiom, % 169.04/169.55 ! [V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_nat__number__of__diff__1,axiom, % 169.04/169.55 ! [V_v] : % 169.04/169.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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) ) % 169.04/169.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 169.04/169.55 => 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)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nats__number__of,axiom, % 169.04/169.55 ! [V_w_2,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 169.04/169.55 => 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))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Suc__diff__number__of,axiom, % 169.04/169.55 ! [V_m,V_v] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 169.04/169.55 => 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_succ__pred,axiom, % 169.04/169.55 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__iff__pred__less,axiom, % 169.04/169.55 ! [V_l_2,V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_pred__def,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_succ__def,axiom, % 169.04/169.55 ! [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)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nats__0,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nats__add,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nats__mult,axiom, % 169.04/169.55 ! [V_b_2,V_a_2,T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 169.04/169.55 => 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))) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nats__1,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_of__nat__in__Nats,axiom, % 169.04/169.55 ! [V_n_2,T_a] : % 169.04/169.55 ( class_Rings_Osemiring__1(T_a) % 169.04/169.55 => 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))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_number__of__succ,axiom, % 169.04/169.55 ! [V_k,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_number__of__pred,axiom, % 169.04/169.55 ! [V_w,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_neg__number__of__pred__iff__0,axiom, % 169.04/169.55 ! [V_v_2] : % 169.04/169.55 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 169.04/169.55 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_decr__mult__lemma,axiom, % 169.04/169.55 ! [V_k_2,V_P_2,V_d_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 169.04/169.55 => ( ! [B_x] : % 169.04/169.55 ( hBOOL(hAPP(V_P_2,B_x)) % 169.04/169.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 169.04/169.55 => ! [B_x] : % 169.04/169.55 ( hBOOL(hAPP(V_P_2,B_x)) % 169.04/169.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_negD,axiom, % 169.04/169.55 ! [V_x] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.55 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_incr__mult__lemma,axiom, % 169.04/169.55 ! [V_k_2,V_P_2,V_d_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 169.04/169.55 => ( ! [B_x] : % 169.04/169.55 ( hBOOL(hAPP(V_P_2,B_x)) % 169.04/169.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 169.04/169.55 => ! [B_x] : % 169.04/169.55 ( hBOOL(hAPP(V_P_2,B_x)) % 169.04/169.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_zero__less__imp__eq__int,axiom, % 169.04/169.55 ! [V_k] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 169.04/169.55 => ? [B_n] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 169.04/169.55 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__special_I4_J,axiom, % 169.04/169.55 ! [V_x_2,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 169.04/169.55 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_eq__special_I2_J,axiom, % 169.04/169.55 ! [V_y_2,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 169.04/169.55 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_diff__special_I1_J,axiom, % 169.04/169.55 ! [V_w,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I51_J,axiom, % 169.04/169.55 ! [V_l_2,V_k_2] : % 169.04/169.55 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 169.04/169.55 <=> V_k_2 = V_l_2 ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__eq__int__code_I16_J,axiom, % 169.04/169.55 ! [V_k2_2,V_k1_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I34_J,axiom, % 169.04/169.55 ! [V_l_2,V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__int__code_I16_J,axiom, % 169.04/169.55 ! [V_k2_2,V_k1_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I17_J,axiom, % 169.04/169.55 ! [V_l_2,V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I39_J,axiom, % 169.04/169.55 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I46_J,axiom, % 169.04/169.55 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 169.04/169.55 % 169.04/169.55 fof(fact_bin__less__0__simps_I4_J,axiom, % 169.04/169.55 ! [V_w_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I22_J,axiom, % 169.04/169.55 ! [V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I12_J,axiom, % 169.04/169.55 ! [V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Bit1__def,axiom, % 169.04/169.55 ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k) ). % 169.04/169.55 % 169.04/169.55 fof(fact_neg__number__of__Bit1,axiom, % 169.04/169.55 ! [V_w_2] : % 169.04/169.55 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 169.04/169.55 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_minus__Bit1,axiom, % 169.04/169.55 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_iszero__number__of__Bit1,axiom, % 169.04/169.55 ! [V_w,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Int_Oring__char__0(T_a) ) % 169.04/169.55 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_succ__Pls,axiom, % 169.04/169.55 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 169.04/169.55 % 169.04/169.55 fof(fact_number__of__Bit1,axiom, % 169.04/169.55 ! [V_w,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__numeral__1__right,axiom, % 169.04/169.55 ! [V_a,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_mult__numeral__1,axiom, % 169.04/169.55 ! [V_a,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_numeral__1__eq__1,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_semiring__norm_I110_J,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I5_J,axiom, % 169.04/169.55 ! [V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_rel__simps_I29_J,axiom, % 169.04/169.55 ! [V_k_2] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__numeral__1,axiom, % 169.04/169.55 ! [V_a,T_a] : % 169.04/169.55 ( ( class_Fields_Ofield(T_a) % 169.04/169.55 & class_Int_Onumber__ring(T_a) ) % 169.04/169.55 => 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 ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_divide__Numeral1,axiom, % 169.04/169.55 ! [V_x,T_a] : % 169.04/169.55 ( ( class_Fields_Ofield(T_a) % 169.04/169.55 & class_Int_Onumber__ring(T_a) ) % 169.04/169.55 => 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 ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_one__is__num__one,axiom, % 169.04/169.55 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_nat__numeral__1__eq__1,axiom, % 169.04/169.55 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Numeral1__eq1__nat,axiom, % 169.04/169.55 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_not__iszero__Numeral1,axiom, % 169.04/169.55 ! [T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_numeral__1__eq__Suc__0,axiom, % 169.04/169.55 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_numeral__3__eq__3,axiom, % 169.04/169.55 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 169.04/169.55 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Suc3__eq__add__3,axiom, % 169.04/169.55 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ). % 169.04/169.55 % 169.04/169.55 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 169.04/169.55 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__special_I2_J,axiom, % 169.04/169.55 ! [V_y_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_le__special_I4_J,axiom, % 169.04/169.55 ! [V_x_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__special_I4_J,axiom, % 169.04/169.55 ! [V_x_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__special_I2_J,axiom, % 169.04/169.55 ! [V_y_2,T_a] : % 169.04/169.55 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.55 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__special_I2_J,axiom, % 169.04/169.55 ! [V_w,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_add__special_I3_J,axiom, % 169.04/169.55 ! [V_v,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_Suc__diff__eq__diff__pred,axiom, % 169.04/169.55 ! [V_m,V_n] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) % 169.04/169.55 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_diff__special_I2_J,axiom, % 169.04/169.55 ! [V_v,T_a] : % 169.04/169.55 ( class_Int_Onumber__ring(T_a) % 169.04/169.55 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_one__code__numeral__code,axiom, % 169.04/169.55 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ). % 169.04/169.55 % 169.04/169.55 fof(fact_less__2__cases,axiom, % 169.04/169.55 ! [V_n] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) % 169.04/169.55 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.55 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_decr__lemma,axiom, % 169.04/169.55 ! [V_z,V_x,V_d] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 169.04/169.55 => 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)) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_incr__lemma,axiom, % 169.04/169.55 ! [V_x,V_z,V_d] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 169.04/169.55 => 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)))) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_half__gt__zero__iff,axiom, % 169.04/169.55 ! [V_r_2,T_a] : % 169.04/169.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 & class_Int_Onumber__ring(T_a) ) % 169.04/169.55 => ( 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)))))) % 169.04/169.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_half__gt__zero,axiom, % 169.04/169.55 ! [V_r,T_a] : % 169.04/169.55 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.55 & class_Int_Onumber__ring(T_a) ) % 169.04/169.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 169.04/169.55 => 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)))))) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_setsum__reindex__cong,axiom, % 169.04/169.55 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 169.04/169.55 ( class_Groups_Ocomm__monoid__add(T_c) % 169.04/169.55 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.04/169.55 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 169.04/169.55 => ( ! [B_a] : % 169.04/169.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 169.04/169.55 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 169.04/169.55 => 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) ) ) ) ) ). % 169.04/169.55 % 169.04/169.55 fof(fact_code__numeral__zero__minus__one,axiom, % 169.04/169.55 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 169.04/169.55 % 169.04/169.55 fof(fact_abs__idempotent,axiom, % 169.04/169.55 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I48_J,axiom, % 169.04/169.56 ! [V_l_2,V_k_2] : % 169.04/169.56 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 169.04/169.56 <=> V_k_2 = V_l_2 ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__ge__self,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__le__D1,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__eq__0,axiom, % 169.04/169.56 ! [V_a_2,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__zero,axiom, % 169.04/169.56 ! [T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__add__abs,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__mult,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__mult__self,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => 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) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__minus__commute,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__one,axiom, % 169.04/169.56 ! [T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__minus__cancel,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__of__nat,axiom, % 169.04/169.56 ! [V_n,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => 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) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__divide,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I31_J,axiom, % 169.04/169.56 ! [V_l_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_less__eq__int__code_I13_J,axiom, % 169.04/169.56 ! [V_k2_2,V_k1_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I14_J,axiom, % 169.04/169.56 ! [V_l_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_less__int__code_I13_J,axiom, % 169.04/169.56 ! [V_k2_2,V_k1_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__int__eq,axiom, % 169.04/169.56 ! [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) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I44_J,axiom, % 169.04/169.56 ! [V_k_2] : % 169.04/169.56 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 169.04/169.56 <=> V_k_2 = c_Int_OPls ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I38_J,axiom, % 169.04/169.56 ! [V_l_2] : % 169.04/169.56 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 169.04/169.56 <=> c_Int_OPls = V_l_2 ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Bit0__Pls,axiom, % 169.04/169.56 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I50_J,axiom, % 169.04/169.56 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I49_J,axiom, % 169.04/169.56 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 169.04/169.56 % 169.04/169.56 fof(fact_add__Bit0__Bit0,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Bit0__def,axiom, % 169.04/169.56 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mult__Bit0,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_diff__bin__simps_I7_J,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_minus__Bit0,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__ge__zero,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__le__zero__iff,axiom, % 169.04/169.56 ! [V_a_2,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( 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))) % 169.04/169.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__of__nonneg,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__of__pos,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zero__less__abs__iff,axiom, % 169.04/169.56 ! [V_a_2,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( 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))) % 169.04/169.56 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__not__less__zero,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ~ 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))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__triangle__ineq,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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)))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__mult__less,axiom, % 169.04/169.56 ! [V_d,V_b,V_c,V_a,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 169.04/169.56 => 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))) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__triangle__ineq3,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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)))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__triangle__ineq2,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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)))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__triangle__ineq2__sym,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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)))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__le__D2,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__leI,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__le__iff,axiom, % 169.04/169.56 ! [V_b_2,V_a_2,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( 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)) % 169.04/169.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 169.04/169.56 & 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)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__ge__minus__self,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__less__iff,axiom, % 169.04/169.56 ! [V_b_2,V_a_2,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 169.04/169.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nonzero__abs__divide,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Fields_Olinordered__field(T_a) % 169.04/169.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_bin__less__0__simps_I3_J,axiom, % 169.04/169.56 ! [V_w_2] : % 169.04/169.56 ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I27_J,axiom, % 169.04/169.56 ! [V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I21_J,axiom, % 169.04/169.56 ! [V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I32_J,axiom, % 169.04/169.56 ! [V_l_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_less__eq__int__code_I14_J,axiom, % 169.04/169.56 ! [V_k2_2,V_k1_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I10_J,axiom, % 169.04/169.56 ! [V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I4_J,axiom, % 169.04/169.56 ! [V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I16_J,axiom, % 169.04/169.56 ! [V_l_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_less__int__code_I15_J,axiom, % 169.04/169.56 ! [V_k2_2,V_k1_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__zmult__eq__1,axiom, % 169.04/169.56 ! [V_n,V_m] : % 169.04/169.56 ( 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) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_add__Bit0__Bit1,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_add__Bit1__Bit0,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_diff__bin__simps_I3_J,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_diff__bin__simps_I10_J,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_diff__bin__simps_I9_J,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__sgn,axiom, % 169.04/169.56 ! [V_k,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mult__sgn__abs,axiom, % 169.04/169.56 ! [V_x,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => 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 ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__number__of__Bit0,axiom, % 169.04/169.56 ! [V_w_2] : % 169.04/169.56 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 169.04/169.56 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pred__Bit1,axiom, % 169.04/169.56 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pred__Bit0,axiom, % 169.04/169.56 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_iszero__number__of__Bit0,axiom, % 169.04/169.56 ! [V_w_2,T_a] : % 169.04/169.56 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.56 & class_Int_Oring__char__0(T_a) ) % 169.04/169.56 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 169.04/169.56 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_succ__Bit0,axiom, % 169.04/169.56 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 169.04/169.56 % 169.04/169.56 fof(fact_succ__Bit1,axiom, % 169.04/169.56 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__mult__pos,axiom, % 169.04/169.56 ! [V_y,V_x,T_a] : % 169.04/169.56 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__eq__mult,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Rings_Oordered__ring__abs(T_a) % 169.04/169.56 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 169.04/169.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 169.04/169.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__triangle__ineq4,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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)))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__diff__triangle__ineq,axiom, % 169.04/169.56 ! [V_d,V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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))))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__of__nonpos,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__minus__le__zero,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => 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))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__of__neg,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__if,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Groups_Oabs__if(T_a) % 169.04/169.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 169.04/169.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__div__pos,axiom, % 169.04/169.56 ! [V_x,V_y,T_a] : % 169.04/169.56 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_number__of__Bit0,axiom, % 169.04/169.56 ! [V_w,T_a] : % 169.04/169.56 ( class_Int_Onumber__ring(T_a) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zabs__less__one__iff,axiom, % 169.04/169.56 ! [V_z_2] : % 169.04/169.56 ( 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))) % 169.04/169.56 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zabs__def,axiom, % 169.04/169.56 ! [V_i] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 169.04/169.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_less__eq__int__code_I15_J,axiom, % 169.04/169.56 ! [V_k2_2,V_k1_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I33_J,axiom, % 169.04/169.56 ! [V_l_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_less__int__code_I14_J,axiom, % 169.04/169.56 ! [V_k2_2,V_k1_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_rel__simps_I15_J,axiom, % 169.04/169.56 ! [V_l_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mult__Bit1,axiom, % 169.04/169.56 ! [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) ). % 169.04/169.56 % 169.04/169.56 fof(fact_diff__bin__simps_I8_J,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_add__Bit1__Bit1,axiom, % 169.04/169.56 ! [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))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zero__code__numeral__code,axiom, % 169.04/169.56 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) ). % 169.04/169.56 % 169.04/169.56 fof(fact_abs__number__of,axiom, % 169.04/169.56 ! [V_x,T_a] : % 169.04/169.56 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.56 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.56 => ( ( 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))) % 169.04/169.56 => 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)) ) % 169.04/169.56 & ( ~ 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))) % 169.04/169.56 => 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) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_double__number__of__Bit0,axiom, % 169.04/169.56 ! [V_w,T_a] : % 169.04/169.56 ( class_Int_Onumber__ring(T_a) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_number__of1,axiom, % 169.04/169.56 ! [V_n] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mult__2__right,axiom, % 169.04/169.56 ! [V_z,T_a] : % 169.04/169.56 ( class_Int_Onumber__ring(T_a) % 169.04/169.56 => 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) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mult__2,axiom, % 169.04/169.56 ! [V_z,T_a] : % 169.04/169.56 ( class_Int_Onumber__ring(T_a) % 169.04/169.56 => 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) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_one__add__one__is__two,axiom, % 169.04/169.56 ! [T_a] : % 169.04/169.56 ( class_Int_Onumber__ring(T_a) % 169.04/169.56 => 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))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_numeral__2__eq__2,axiom, % 169.04/169.56 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))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_semiring__norm_I115_J,axiom, % 169.04/169.56 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))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 169.04/169.56 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_add__2__eq__Suc_H,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_add__2__eq__Suc,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__mult__2__right,axiom, % 169.04/169.56 ! [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) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__mult__2,axiom, % 169.04/169.56 ! [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) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 169.04/169.56 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)))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__1__add__1,axiom, % 169.04/169.56 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))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__number__of__Bit1,axiom, % 169.04/169.56 ! [V_v,V_w] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 169.04/169.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__zmod__mult__2,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__zmod__mult__2,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__zdiv__mult__2,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__zdiv__mult__2,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_of__nat__double,axiom, % 169.04/169.56 ! [V_x,T_a] : % 169.04/169.56 ( class_Rings_Osemiring__1(T_a) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.56 => 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))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zdiv__trivial,axiom, % 169.04/169.56 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__div__trivial,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_DIVISION__BY__ZERO,axiom, % 169.04/169.56 ! [V_a] : % 169.04/169.56 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mod__trivial,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zadd1__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__div__equality2,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__div__equality,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mod__equality2,axiom, % 169.04/169.56 ! [V_c,V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mod__equality,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zmod__equality2,axiom, % 169.04/169.56 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zmod__equality,axiom, % 169.04/169.56 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zmult1__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zdiv__equality,axiom, % 169.04/169.56 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmult__div__cancel,axiom, % 169.04/169.56 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zdiv__equality_H,axiom, % 169.04/169.56 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__0,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__by__0,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__self,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__add__self2,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__add__self1,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__add__right__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__add__left__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__add__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__simps_I2_J,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__simps_I1_J,axiom, % 169.04/169.56 ! [V_b,V_c,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__add__cong,axiom, % 169.04/169.56 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 169.04/169.56 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__cong,axiom, % 169.04/169.56 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 169.04/169.56 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__simps_I4_J,axiom, % 169.04/169.56 ! [V_b,V_c,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__mult2,axiom, % 169.04/169.56 ! [V_b,V_c,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__mult1,axiom, % 169.04/169.56 ! [V_b,V_a,V_c,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__left__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__right__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__diff__cong,axiom, % 169.04/169.56 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 169.04/169.56 ( class_Divides_Oring__div(T_a) % 169.04/169.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 169.04/169.56 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__diff__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Oring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__diff__left__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Oring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__diff__right__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Oring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__minus__cong,axiom, % 169.04/169.56 ! [V_a_H,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Oring__div(T_a) % 169.04/169.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__minus__eq,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Oring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zero,axiom, % 169.04/169.56 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zero,axiom, % 169.04/169.56 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__self,axiom, % 169.04/169.56 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__int,axiom, % 169.04/169.56 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zminus2,axiom, % 169.04/169.56 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zminus__zminus,axiom, % 169.04/169.56 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zmult1__eq,axiom, % 169.04/169.56 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__simps_I3_J,axiom, % 169.04/169.56 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiff__zmod__left,axiom, % 169.04/169.56 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiff__zmod__right,axiom, % 169.04/169.56 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zminus2,axiom, % 169.04/169.56 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zminus__zminus,axiom, % 169.04/169.56 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zminus__zmod,axiom, % 169.04/169.56 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__0,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__by__0,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__by__1,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__self1__is__0,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__self2__is__0,axiom, % 169.04/169.56 ! [V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zmult2__eq,axiom, % 169.04/169.56 ! [V_b,V_a,V_c] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__self2,axiom, % 169.04/169.56 ! [V_c,V_b,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__mult__self1,axiom, % 169.04/169.56 ! [V_b,V_c,V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__by__1,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zminus2__eq__if,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 169.04/169.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zminus1__eq__if,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) % 169.04/169.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__0,axiom, % 169.04/169.56 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 169.04/169.56 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 169.04/169.56 ! [V_y,V_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 169.04/169.56 ! [V_a_2,V_b_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 169.04/169.56 ! [V_a_2,V_b_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__neg__pos__less0,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_eq__nat__nat__iff,axiom, % 169.04/169.56 ! [V_z_H_2,V_z_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 169.04/169.56 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 169.04/169.56 <=> V_z_2 = V_z_H_2 ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_ex__nat,axiom, % 169.04/169.56 ! [V_P_2] : % 169.04/169.56 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.04/169.56 <=> ? [B_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 169.04/169.56 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_all__nat,axiom, % 169.04/169.56 ! [V_P_2] : % 169.04/169.56 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.04/169.56 <=> ! [B_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 169.04/169.56 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 169.04/169.56 ! [V_y_2,V_x_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 169.04/169.56 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 169.04/169.56 <=> V_x_2 = V_y_2 ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__self,axiom, % 169.04/169.56 ! [V_a] : % 169.04/169.56 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__le__nonneg__dividend,axiom, % 169.04/169.56 ! [V_k,V_m] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 169.04/169.56 ! [V_y,V_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__mod__bound,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__mod__bound,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__number__of__Bit0,axiom, % 169.04/169.56 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__number__of,axiom, % 169.04/169.56 ! [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) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__number__of__def,axiom, % 169.04/169.56 ! [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)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__eq__0__iff,axiom, % 169.04/169.56 ! [V_d_2,V_m_2] : % 169.04/169.56 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zminus1__not__zero,axiom, % 169.04/169.56 ! [V_l,V_k] : % 169.04/169.56 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zminus2__not__zero,axiom, % 169.04/169.56 ! [V_l,V_k] : % 169.04/169.56 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 169.04/169.56 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__nat,axiom, % 169.04/169.56 ! [V_z] : % 169.04/169.56 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 169.04/169.56 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_not__neg__nat,axiom, % 169.04/169.56 ! [V_z] : % 169.04/169.56 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 169.04/169.56 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mult__mult1,axiom, % 169.04/169.56 ! [V_b,V_a,V_c,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mult__mult2,axiom, % 169.04/169.56 ! [V_b,V_a,V_c,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mult__self1__is__id,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mult__self2__is__id,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mult__mult1__if,axiom, % 169.04/169.56 ! [V_b,V_a,V_c,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) % 169.04/169.56 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__self,axiom, % 169.04/169.56 ! [V_a,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__int__nat__set__return__embed,axiom, % 169.04/169.56 ! [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 ). % 169.04/169.56 % 169.04/169.56 fof(fact_split__pos__lemma,axiom, % 169.04/169.56 ! [V_n_2,V_P_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 169.04/169.56 <=> ! [B_i,B_j] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 169.04/169.56 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 169.04/169.56 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_split__neg__lemma,axiom, % 169.04/169.56 ! [V_n_2,V_P_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 169.04/169.56 <=> ! [B_i,B_j] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 169.04/169.56 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 169.04/169.56 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))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__le__0,axiom, % 169.04/169.56 ! [V_z] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__0__iff,axiom, % 169.04/169.56 ! [V_i_2] : % 169.04/169.56 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__eq__0__iff,axiom, % 169.04/169.56 ! [V_k_2,V_i_2] : % 169.04/169.56 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 169.04/169.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 169.04/169.56 ! [V_a_2,V_b_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 169.04/169.56 ! [V_i_2,V_k_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 169.04/169.56 ! [V_b_2,V_a_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 169.04/169.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__mono2,axiom, % 169.04/169.56 ! [V_b,V_b_H,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__nonneg__neg__le0,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__pos__pos__trivial,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 169.04/169.56 ! [V_a_2,V_b_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__nonpos__pos__le0,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__mono2__neg,axiom, % 169.04/169.56 ! [V_b,V_b_H,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__neg__neg__trivial,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__mono1,axiom, % 169.04/169.56 ! [V_b,V_a_H,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__mono1__neg,axiom, % 169.04/169.56 ! [V_b,V_a_H,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__mono__iff,axiom, % 169.04/169.56 ! [V_w_2,V_z_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 169.04/169.56 => ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zless__nat__conj,axiom, % 169.04/169.56 ! [V_z_2,V_w_2] : % 169.04/169.56 ( 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))) % 169.04/169.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 169.04/169.56 ! [V_y_2,V_x_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 169.04/169.56 => ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__1,axiom, % 169.04/169.56 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 169.04/169.56 % 169.04/169.56 fof(fact_int__div__less__self,axiom, % 169.04/169.56 ! [V_k,V_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zdiv__zmult2__eq,axiom, % 169.04/169.56 ! [V_b,V_a,V_c] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__0__le,axiom, % 169.04/169.56 ! [V_z] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.56 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_int__eq__iff,axiom, % 169.04/169.56 ! [V_z_2,V_m_2] : % 169.04/169.56 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 169.04/169.56 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_int__nat__eq,axiom, % 169.04/169.56 ! [V_z] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.56 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 169.04/169.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.56 => 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) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zless__nat__eq__int__zless,axiom, % 169.04/169.56 ! [V_z_2,V_m_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 169.04/169.56 <=> 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__mod__sign,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_pos__mod__conj,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__pos__pos__trivial,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__mod__sign,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_neg__mod__conj,axiom, % 169.04/169.56 ! [V_a,V_b] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__neg__neg__trivial,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__zminus__int,axiom, % 169.04/169.56 ! [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) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zminus2__eq__if,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.04/169.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmod__zminus1__eq__if,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.04/169.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__abs__mult__distrib,axiom, % 169.04/169.56 ! [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))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mult__self2,axiom, % 169.04/169.56 ! [V_c,V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__mult__self1,axiom, % 169.04/169.56 ! [V_c,V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__add__self1,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_div__add__self2,axiom, % 169.04/169.56 ! [V_a,V_b,T_a] : % 169.04/169.56 ( class_Divides_Osemiring__div(T_a) % 169.04/169.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zero__less__nat__eq,axiom, % 169.04/169.56 ! [V_z_2] : % 169.04/169.56 ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__less__eq__zless,axiom, % 169.04/169.56 ! [V_z_2,V_w_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 169.04/169.56 => ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 169.04/169.56 ! [V_y_2,V_x_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 169.04/169.56 => ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__eq__iff2,axiom, % 169.04/169.56 ! [V_w_2,V_m_2] : % 169.04/169.56 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 169.04/169.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 169.04/169.56 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 169.04/169.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 169.04/169.56 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__eq__iff,axiom, % 169.04/169.56 ! [V_m_2,V_w_2] : % 169.04/169.56 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 169.04/169.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 169.04/169.56 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 169.04/169.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 169.04/169.56 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__le__eq__zle,axiom, % 169.04/169.56 ! [V_z_2,V_w_2] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 169.04/169.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 169.04/169.56 => ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_split__nat,axiom, % 169.04/169.56 ! [V_i_2,V_P_2] : % 169.04/169.56 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 169.04/169.56 <=> ( ! [B_n] : % 169.04/169.56 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 169.04/169.56 => hBOOL(hAPP(V_P_2,B_n)) ) % 169.04/169.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__add__distrib,axiom, % 169.04/169.56 ! [V_z_H,V_z] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 169.04/169.56 ! [V_y,V_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_int__eq__iff__number__of,axiom, % 169.04/169.56 ! [V_v_2,V_m_2] : % 169.04/169.56 ( 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) % 169.04/169.56 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__mult__distrib,axiom, % 169.04/169.56 ! [V_z_H,V_z] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 169.04/169.56 ! [V_y,V_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_mod__pos__neg__trivial,axiom, % 169.04/169.56 ! [V_b,V_a] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__diff__distrib,axiom, % 169.04/169.56 ! [V_z,V_z_H] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 169.04/169.56 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)))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 169.04/169.56 ! [V_y,V_x] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.56 => 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)) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_one__less__nat__eq,axiom, % 169.04/169.56 ! [V_z_2] : % 169.04/169.56 ( 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))) % 169.04/169.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_split__zdiv,axiom, % 169.04/169.56 ! [V_k_2,V_n_2,V_P_2] : % 169.04/169.56 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 169.04/169.56 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.04/169.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 169.04/169.56 => ! [B_i] : % 169.04/169.56 ( ? [B_j] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 169.04/169.56 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 169.04/169.56 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 169.04/169.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ! [B_i] : % 169.04/169.56 ( ? [B_j] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 169.04/169.56 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_divmod__int__rel__div__eq,axiom, % 169.04/169.56 ! [V_r_1,V_y,V_b_1,V_a_1] : % 169.04/169.56 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) % 169.04/169.56 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 169.04/169.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 169.04/169.56 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_nat__less__iff,axiom, % 169.04/169.56 ! [V_m_2,V_w_2] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 169.04/169.56 <=> 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))) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 169.04/169.56 ! [V_z] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.56 => 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)) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 169.04/169.56 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)))) ). % 169.04/169.56 % 169.04/169.56 fof(fact_split__zmod,axiom, % 169.04/169.56 ! [V_k_2,V_n_2,V_P_2] : % 169.04/169.56 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 169.04/169.56 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.56 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 169.04/169.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 169.04/169.56 => ! [B_i,B_j] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 169.04/169.56 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 169.04/169.56 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 169.04/169.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => ! [B_i,B_j] : % 169.04/169.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 169.04/169.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 169.04/169.56 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmult2__lemma__aux3,axiom, % 169.04/169.56 ! [V_q,V_b,V_r,V_c] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmult2__lemma__aux4,axiom, % 169.04/169.56 ! [V_q,V_b,V_r,V_c] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmult2__lemma__aux1,axiom, % 169.04/169.56 ! [V_q,V_r,V_b,V_c] : % 169.04/169.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 169.04/169.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ). % 169.04/169.56 % 169.04/169.56 fof(fact_zmult2__lemma__aux2,axiom, % 169.04/169.57 ! [V_q,V_r,V_b,V_c] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_divmod__int__rel__mod__eq,axiom, % 169.04/169.57 ! [V_y,V_q_1,V_b_1,V_a_1] : % 169.04/169.57 ( 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) % 169.04/169.57 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 169.04/169.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 169.04/169.57 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.57 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__mult__distrib__neg,axiom, % 169.04/169.57 ! [V_z_H,V_z] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.57 => 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zmod__number__of__Bit0,axiom, % 169.04/169.57 ! [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))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__2,axiom, % 169.04/169.57 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))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zdiv__number__of__Bit1,axiom, % 169.04/169.57 ! [V_v,V_w] : % 169.04/169.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 169.04/169.57 => 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)) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__aux__def,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__of__aux__code,axiom, % 169.04/169.57 ! [V_n,V_i] : % 169.04/169.57 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.04/169.57 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 169.04/169.57 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_transfer__morphism__nat__int,axiom, % 169.04/169.57 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))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_z3div__def,axiom, % 169.04/169.57 ! [V_k,V_l] : % 169.04/169.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 169.04/169.57 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_z3mod__def,axiom, % 169.04/169.57 ! [V_k,V_l] : % 169.04/169.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 169.04/169.57 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_one__mod__nat__number__of,axiom, % 169.04/169.57 ! [V_v_H] : % 169.04/169.57 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 169.04/169.57 => 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)) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__add1__eq,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__mult2__eq,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__mult1__eq,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__mod__equality_H,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mult__div__cancel,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Divides_Omod__div__equality_H,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__le__dividend,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__le__mono,axiom, % 169.04/169.57 ! [V_k,V_n,V_m] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__mult2__eq,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__less,axiom, % 169.04/169.57 ! [V_n,V_m] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__less__eq__dividend,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__mult__distrib,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__mult__distrib2,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__1,axiom, % 169.04/169.57 ! [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 ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__less,axiom, % 169.04/169.57 ! [V_n,V_m] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__mult__div__cancel__disj,axiom, % 169.04/169.57 ! [V_n,V_m,V_k] : % 169.04/169.57 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => 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) ) % 169.04/169.57 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => 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) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__Suc,axiom, % 169.04/169.57 ! [V_n,V_m] : % 169.04/169.57 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 169.04/169.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 169.04/169.57 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__1,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__less__divisor,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__eq__0__iff,axiom, % 169.04/169.57 ! [V_d_2,V_m_2] : % 169.04/169.57 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__if,axiom, % 169.04/169.57 ! [V_n,V_m] : % 169.04/169.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => 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) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__geq,axiom, % 169.04/169.57 ! [V_n,V_m] : % 169.04/169.57 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__mult__self3,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_le__mod__geq,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zdiv__int,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zmod__int,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__le__mono2,axiom, % 169.04/169.57 ! [V_k,V_n,V_m] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__mult__div__cancel1,axiom, % 169.04/169.57 ! [V_n,V_m,V_k] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__mult__self1__is__m,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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 ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__mult__self__is__m,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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 ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__less__dividend,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__le__divisor,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__mult__self4,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__geq,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__if,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.04/169.57 => 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)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_split__div,axiom, % 169.04/169.57 ! [V_k_2,V_n_2,V_P_2] : % 169.04/169.57 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 169.04/169.57 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 169.04/169.57 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => ! [B_i,B_j] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 169.04/169.57 => ( 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) % 169.04/169.57 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__div__distrib,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__lemma,axiom, % 169.04/169.57 ! [V_q,V_b,V_r,V_c] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_split__mod,axiom, % 169.04/169.57 ! [V_k_2,V_n_2,V_P_2] : % 169.04/169.57 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 169.04/169.57 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 169.04/169.57 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => ! [B_i,B_j] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 169.04/169.57 => ( 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) % 169.04/169.57 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Suc__times__mod__eq,axiom, % 169.04/169.57 ! [V_m,V_k] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__mod__distrib,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_le__div__geq,axiom, % 169.04/169.57 ! [V_m,V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_split__div__lemma,axiom, % 169.04/169.57 ! [V_m_2,V_q_2,V_n_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 169.04/169.57 => ( ( 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)) % 169.04/169.57 & 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)))) ) % 169.04/169.57 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_split__div_H,axiom, % 169.04/169.57 ! [V_n_2,V_m_2,V_P_2] : % 169.04/169.57 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 169.04/169.57 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 169.04/169.57 | ? [B_q] : % 169.04/169.57 ( 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)) % 169.04/169.57 & 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)))) % 169.04/169.57 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Suc__div__eq__add3__div,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__Suc__eq__div__add3,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div2__Suc__Suc,axiom, % 169.04/169.57 ! [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))))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_add__self__div__2,axiom, % 169.04/169.57 ! [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 ). % 169.04/169.57 % 169.04/169.57 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Suc__mod__eq__add3__mod,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__Suc__eq__mod__add3,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod2__Suc__Suc,axiom, % 169.04/169.57 ! [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)))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__nat__number__of,axiom, % 169.04/169.57 ! [V_v_H,V_v] : % 169.04/169.57 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => 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) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__nat__number__of,axiom, % 169.04/169.57 ! [V_v_H,V_v] : % 169.04/169.57 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => 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) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 169.04/169.57 => 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) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 169.04/169.57 => 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))) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__2__gt__zero,axiom, % 169.04/169.57 ! [V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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)))))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_one__div__nat__number__of,axiom, % 169.04/169.57 ! [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))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod2__gr__0,axiom, % 169.04/169.57 ! [V_m_2] : % 169.04/169.57 ( 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)))))) % 169.04/169.57 <=> 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Suc__n__div__2__gt__zero,axiom, % 169.04/169.57 ! [V_n] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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)))))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_int__of__code,axiom, % 169.04/169.57 ! [V_k] : % 169.04/169.57 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.04/169.57 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.04/169.57 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.04/169.57 => ( ( 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) % 169.04/169.57 => 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)))))) ) % 169.04/169.57 & ( 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) % 169.04/169.57 => 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)) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 169.04/169.57 ! [V_B_2,V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__minus1__odd,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_odd__power__less__zero,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_odd__0__le__power__imp__0__le,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))))) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__diff,axiom, % 169.04/169.57 ! [V_y,V_x,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_int__power,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zpower__int,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 169.04/169.57 ! [V_q,V_y,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 169.04/169.57 ! [V_q,V_p,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zpower__zpower,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 169.04/169.57 ! [V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zpower__zmod,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__power__eq,axiom, % 169.04/169.57 ! [V_n,V_z] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 169.04/169.57 ! [V_n,V_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 169.04/169.57 ! [V_q,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 169.04/169.57 ! [V_q,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 169.04/169.57 ! [V_q,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 169.04/169.57 ! [V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 169.04/169.57 ! [V_q,V_p,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 169.04/169.57 ! [V_n,V_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 169.04/169.57 => 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zpower__zadd__distrib,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Ints__power,axiom, % 169.04/169.57 ! [V_n_2,V_a_2,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 169.04/169.57 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__nat__number__of,axiom, % 169.04/169.57 ! [V_n,V_v] : % 169.04/169.57 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => 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) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__nat__number__of__number__of,axiom, % 169.04/169.57 ! [V_w,V_v] : % 169.04/169.57 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => 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)) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__set__def,axiom, % 169.04/169.57 ! [V_S_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_S_2) % 169.04/169.57 <=> ! [B_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 169.04/169.57 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 169.04/169.57 ! [V_B_2,V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.04/169.57 => ( V_A_2 = V_B_2 % 169.04/169.57 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__le__zpower__abs,axiom, % 169.04/169.57 ! [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))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power3__eq__cube,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__eq__if,axiom, % 169.04/169.57 ! [V_p,V_m] : % 169.04/169.57 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 169.04/169.57 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => 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)))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__less__zpower__abs__iff,axiom, % 169.04/169.57 ! [V_n_2,V_x_2] : % 169.04/169.57 ( 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))) % 169.04/169.57 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.04/169.57 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 169.04/169.57 ! [V_x_2,V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__power2,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Rings_Osemiring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__eq__power2,axiom, % 169.04/169.57 ! [V_a_2,T_a] : % 169.04/169.57 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 169.04/169.57 => ( 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) % 169.04/169.57 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__eq__square,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 169.04/169.57 ! [V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_one__power2,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Rings_Osemiring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__minus,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__even__eq,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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)))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_abs__power2,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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)))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__abs,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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)))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_transfer__nat__int__set__return__embed,axiom, % 169.04/169.57 ! [V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__eq__imp__eq,axiom, % 169.04/169.57 ! [V_y,V_x,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( 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)))) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.57 => V_x = V_y ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__le__imp__le,axiom, % 169.04/169.57 ! [V_y,V_x,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( 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)))))) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__le__power2,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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)))))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__less__power2,axiom, % 169.04/169.57 ! [V_a_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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)))))) % 169.04/169.57 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__less__0,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ~ 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_sum__power2__eq__zero__iff,axiom, % 169.04/169.57 ! [V_y_2,V_x_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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) % 169.04/169.57 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__eq__square__number__of,axiom, % 169.04/169.57 ! [V_w,T_b] : % 169.04/169.57 ( ( class_Groups_Omonoid__mult(T_b) % 169.04/169.57 & class_Int_Onumber(T_b) ) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__eq__1__iff,axiom, % 169.04/169.57 ! [V_a_2,T_a] : % 169.04/169.57 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 169.04/169.57 => ( 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) % 169.04/169.57 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 169.04/169.57 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 169.04/169.57 ! [V_n,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__minus__even,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 169.04/169.57 ! [V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 169.04/169.57 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 169.04/169.57 ! [V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__less__imp__less,axiom, % 169.04/169.57 ! [V_y,V_x,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( 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)))))) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_sum__power2__ge__zero,axiom, % 169.04/169.57 ! [V_y,V_x,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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))))))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_sum__power2__le__zero__iff,axiom, % 169.04/169.57 ! [V_y_2,V_x_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_not__sum__power2__lt__zero,axiom, % 169.04/169.57 ! [V_y,V_x,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ~ 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_sum__power2__gt__zero__iff,axiom, % 169.04/169.57 ! [V_y_2,V_x_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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))))))) % 169.04/169.57 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power2__sum,axiom, % 169.04/169.57 ! [V_y,V_x,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__le__even__power_H,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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)))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 169.04/169.57 ! [V_n,V_x,T_a] : % 169.04/169.57 ( class_Rings_Ocomm__semiring__1(T_a) % 169.04/169.57 => 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__odd__eq,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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))))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__minus1__even,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_int__power__div__base,axiom, % 169.04/169.57 ! [V_k,V_m] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 169.04/169.57 => 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)))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 169.04/169.57 ! [V_B_2,V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__strict__mono,axiom, % 169.04/169.57 ! [V_n,V_b,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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))) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__diff,axiom, % 169.04/169.57 ! [V_m,V_n,V_a,T_a] : % 169.04/169.57 ( class_Fields_Ofield(T_a) % 169.04/169.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 169.04/169.57 => 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)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_one__less__power,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__le__imp__le__exp,axiom, % 169.04/169.57 ! [V_n,V_m,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => ( 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))) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__increasing__iff,axiom, % 169.04/169.57 ! [V_y_2,V_x_2,V_b_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_field__power__not__zero,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 169.04/169.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 169.04/169.57 ! [V_m_2,V_x_2] : % 169.04/169.57 ( 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)) % 169.04/169.57 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__Suc__0,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__power__less__imp__less,axiom, % 169.04/169.57 ! [V_n,V_m,V_i] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 169.04/169.57 => ( 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))) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__zero__less__power__iff,axiom, % 169.04/169.57 ! [V_n_2,V_x_2] : % 169.04/169.57 ( 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))) % 169.04/169.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 169.04/169.57 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__commutes,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__mult__distrib,axiom, % 169.04/169.57 ! [V_n,V_b,V_a,T_a] : % 169.04/169.57 ( class_Groups_Ocomm__monoid__mult(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__one,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__nat__power,axiom, % 169.04/169.57 ! [V_n,V_m,T_a] : % 169.04/169.57 ( class_Rings_Osemiring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__mult,axiom, % 169.04/169.57 ! [V_n,V_m,V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__divide,axiom, % 169.04/169.57 ! [V_n,V_b,V_a,T_a] : % 169.04/169.57 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__abs,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__one__right,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__mono,axiom, % 169.04/169.57 ! [V_n,V_b,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__le__power,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__less__power,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__eq__0__iff,axiom, % 169.04/169.57 ! [V_n_2,V_a_2,T_a] : % 169.04/169.57 ( ( class_Power_Opower(T_a) % 169.04/169.57 & class_Rings_Omult__zero(T_a) % 169.04/169.57 & class_Rings_Ono__zero__divisors(T_a) % 169.04/169.57 & class_Rings_Ozero__neq__one(T_a) ) % 169.04/169.57 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_one__le__power,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__0__Suc,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( ( class_Power_Opower(T_a) % 169.04/169.57 & class_Rings_Osemiring__0(T_a) ) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__inject__exp,axiom, % 169.04/169.57 ! [V_n_2,V_m_2,V_a_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 169.04/169.57 => ( 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) % 169.04/169.57 <=> V_m_2 = V_n_2 ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__Suc2,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__Suc,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Power_Opower(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__one__le__power,axiom, % 169.04/169.57 ! [V_n,V_i] : % 169.04/169.57 ( 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)) % 169.04/169.57 => 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__0,axiom, % 169.04/169.57 ! [V_a,T_a] : % 169.04/169.57 ( class_Power_Opower(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__add,axiom, % 169.04/169.57 ! [V_n,V_m,V_a,T_a] : % 169.04/169.57 ( class_Groups_Omonoid__mult(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nonzero__power__divide,axiom, % 169.04/169.57 ! [V_n,V_a,V_b,T_a] : % 169.04/169.57 ( class_Fields_Ofield(T_a) % 169.04/169.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__one__over,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_abs__power__minus,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__less__imp__less__base,axiom, % 169.04/169.57 ! [V_b,V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__le__imp__le__base,axiom, % 169.04/169.57 ! [V_b,V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( 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)))) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__inject__base,axiom, % 169.04/169.57 ! [V_b,V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( 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)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 169.04/169.57 => V_a = V_b ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__gt1__lemma,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => 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)))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__less__power__Suc,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => 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)))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__0__left,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( ( class_Power_Opower(T_a) % 169.04/169.57 & class_Rings_Osemiring__0(T_a) ) % 169.04/169.57 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => 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) ) % 169.04/169.57 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => 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) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__gt1,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => 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)))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__strict__increasing__iff,axiom, % 169.04/169.57 ! [V_y_2,V_x_2,V_b_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__less__imp__less__exp,axiom, % 169.04/169.57 ! [V_n,V_m,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => ( 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))) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__strict__increasing,axiom, % 169.04/169.57 ! [V_a,V_N,V_n,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zero__le__power__abs,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__increasing,axiom, % 169.04/169.57 ! [V_a,V_N,V_n,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__minus,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__Suc__less,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__eq__imp__eq__base,axiom, % 169.04/169.57 ! [V_b,V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( 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) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.04/169.57 => V_a = V_b ) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__Suc__less__one,axiom, % 169.04/169.57 ! [V_n,V_a,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__strict__decreasing,axiom, % 169.04/169.57 ! [V_a,V_N,V_n,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 169.04/169.57 => 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))) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__decreasing,axiom, % 169.04/169.57 ! [V_a,V_N,V_n,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__semidom(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 169.04/169.57 => 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))) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__power__power,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Power_Opower(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__m1__odd,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power__m1__even,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 169.04/169.57 ! [V_A_2,V_x_2] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x_2) % 169.04/169.57 => ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osize_I1_J,axiom, % 169.04/169.57 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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I24_J,axiom, % 169.04/169.57 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I7_J,axiom, % 169.04/169.57 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I40_J,axiom, % 169.04/169.57 c_Int_OMin != c_Int_OPls ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I37_J,axiom, % 169.04/169.57 c_Int_OPls != c_Int_OMin ). % 169.04/169.57 % 169.04/169.57 fof(fact_Bit1__Min,axiom, % 169.04/169.57 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I43_J,axiom, % 169.04/169.57 ! [V_l_2] : % 169.04/169.57 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 169.04/169.57 <=> c_Int_OMin = V_l_2 ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I47_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 169.04/169.57 <=> V_k_2 = c_Int_OMin ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I42_J,axiom, % 169.04/169.57 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I45_J,axiom, % 169.04/169.57 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 169.04/169.57 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x) % 169.04/169.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 169.04/169.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 169.04/169.57 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 169.04/169.57 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x) % 169.04/169.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 169.04/169.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x) % 169.04/169.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 169.04/169.57 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x) % 169.04/169.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 169.04/169.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 169.04/169.57 ! [V_n,V_x] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x) % 169.04/169.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_bin__less__0__simps_I2_J,axiom, % 169.04/169.57 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I23_J,axiom, % 169.04/169.57 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I20_J,axiom, % 169.04/169.57 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I30_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I26_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I6_J,axiom, % 169.04/169.57 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I3_J,axiom, % 169.04/169.57 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I13_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I9_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I28_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I8_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_eq__number__of__Pls__Min,axiom, % 169.04/169.57 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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Int_OMin__def,axiom, % 169.04/169.57 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mult__Min,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 169.04/169.57 ! [V_y,V_x] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x) % 169.04/169.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 169.04/169.57 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_neg__number__of__Min,axiom, % 169.04/169.57 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_pred__Pls,axiom, % 169.04/169.57 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 169.04/169.57 % 169.04/169.57 fof(fact_add__Min__right,axiom, % 169.04/169.57 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 169.04/169.57 % 169.04/169.57 fof(fact_add__Min,axiom, % 169.04/169.57 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 169.04/169.57 % 169.04/169.57 fof(fact_pred__Min,axiom, % 169.04/169.57 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nonzero__number__of__Min,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_succ__Min,axiom, % 169.04/169.57 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 169.04/169.57 % 169.04/169.57 fof(fact_diff__bin__simps_I2_J,axiom, % 169.04/169.57 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 169.04/169.57 % 169.04/169.57 fof(fact_is__nat__def,axiom, % 169.04/169.57 ! [V_x_2] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x_2) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mult__minus1,axiom, % 169.04/169.57 ! [V_z,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mult__minus1__right,axiom, % 169.04/169.57 ! [V_z,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_arith__simps_I31_J,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_number__of__Min,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_abs__minus__one,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.57 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_divide__minus1,axiom, % 169.04/169.57 ! [V_x,T_a] : % 169.04/169.57 ( ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.57 & class_Int_Onumber__ring(T_a) ) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I25_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_rel__simps_I11_J,axiom, % 169.04/169.57 ! [V_k_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zmod__minus1__right,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_diff__bin__simps_I4_J,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_minus__Min,axiom, % 169.04/169.57 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 169.04/169.57 % 169.04/169.57 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 169.04/169.57 ! [V_n,V_m] : % 169.04/169.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 169.04/169.57 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 169.04/169.57 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zmult__eq__1__iff,axiom, % 169.04/169.57 ! [V_n_2,V_m_2] : % 169.04/169.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 169.04/169.57 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 169.04/169.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 169.04/169.57 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 169.04/169.57 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_diff__bin__simps_I5_J,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_diff__bin__simps_I6_J,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_power_Opower_Opower__0,axiom, % 169.04/169.57 ! [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 ). % 169.04/169.57 % 169.04/169.57 fof(fact_power_Opower_Opower__Suc,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zdiv__minus1__right,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 169.04/169.57 ! [V_x_2,V_A_2] : % 169.04/169.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 169.04/169.57 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_minus1__divide,axiom, % 169.04/169.57 ! [V_x,T_a] : % 169.04/169.57 ( ( class_Fields_Ofield__inverse__zero(T_a) % 169.04/169.57 & class_Int_Onumber__ring(T_a) ) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_abs__power__minus__one,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( ( class_Int_Onumber__ring(T_a) % 169.04/169.57 & class_Rings_Olinordered__idom(T_a) ) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__eq__minus1,axiom, % 169.04/169.57 ! [V_b] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 169.04/169.57 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 169.04/169.57 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_div__pos__neg__trivial,axiom, % 169.04/169.57 ! [V_b,V_a] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.04/169.57 => ( 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))) % 169.04/169.57 => 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) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_zmod__minus1,axiom, % 169.04/169.57 ! [V_b] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osize_I2_J,axiom, % 169.04/169.57 ! [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))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_card__greaterThanLessThan__int,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__of__nat,axiom, % 169.04/169.57 ! [V_k,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.57 => 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)))) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.04/169.57 => 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)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nitpick_Oint__lcm__def,axiom, % 169.04/169.57 ! [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)))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osize_I3_J,axiom, % 169.04/169.57 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.04/169.57 % 169.04/169.57 fof(fact_finite__greaterThanLessThan__int,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__eq__iff,axiom, % 169.04/169.57 ! [V_z_2,V_w_2,T_a] : % 169.04/169.57 ( class_Int_Oring__char__0(T_a) % 169.04/169.57 => ( 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) % 169.04/169.57 <=> V_w_2 = V_z_2 ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Oinject,axiom, % 169.04/169.57 ! [V_code__numeral_H_2,V_code__numeral_2] : % 169.04/169.57 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 169.04/169.57 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_number__of__eq,axiom, % 169.04/169.57 ! [V_k,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_int__number__of__def,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__int__eq,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osimps_I3_J,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osimps_I2_J,axiom, % 169.04/169.57 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__0,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__0__eq__iff,axiom, % 169.04/169.57 ! [V_z_2,T_a] : % 169.04/169.57 ( class_Int_Oring__char__0(T_a) % 169.04/169.57 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 169.04/169.57 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__eq__0__iff,axiom, % 169.04/169.57 ! [V_z_2,T_a] : % 169.04/169.57 ( class_Int_Oring__char__0(T_a) % 169.04/169.57 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 169.04/169.57 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__le__iff,axiom, % 169.04/169.57 ! [V_z_2,V_w_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__less__iff,axiom, % 169.04/169.57 ! [V_z_2,V_w_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__add,axiom, % 169.04/169.57 ! [V_z,V_w,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__number__of__eq,axiom, % 169.04/169.57 ! [V_v,T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__mult,axiom, % 169.04/169.57 ! [V_z,V_w,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__1,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__diff,axiom, % 169.04/169.57 ! [V_z,V_w,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__of__nat__eq,axiom, % 169.04/169.57 ! [V_n,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__minus,axiom, % 169.04/169.57 ! [V_z,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Ints__of__int,axiom, % 169.04/169.57 ! [V_z_2,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__power,axiom, % 169.04/169.57 ! [V_n,V_z,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_greaterThanLessThan__empty,axiom, % 169.04/169.57 ! [V_k_2,V_l_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 169.04/169.57 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_image__uminus__greaterThanLessThan,axiom, % 169.04/169.57 ! [V_y_2,V_x_2,T_a] : % 169.04/169.57 ( class_Groups_Oordered__ab__group__add(T_a) % 169.04/169.57 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osize_I4_J,axiom, % 169.04/169.57 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__m1,axiom, % 169.04/169.57 ! [T_a] : % 169.04/169.57 ( class_Int_Onumber__ring(T_a) % 169.04/169.57 => 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) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Suc__code__numeral__minus__one,axiom, % 169.04/169.57 ! [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 ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__le__0__iff,axiom, % 169.04/169.57 ! [V_z_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__0__le__iff,axiom, % 169.04/169.57 ! [V_z_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__less__0__iff,axiom, % 169.04/169.57 ! [V_z_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__int__0__less__iff,axiom, % 169.04/169.57 ! [V_z_2,T_a] : % 169.04/169.57 ( class_Rings_Olinordered__idom(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_of__nat__nat,axiom, % 169.04/169.57 ! [V_z,T_a] : % 169.04/169.57 ( class_Rings_Oring__1(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 169.04/169.57 => 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) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nitpick_Onat__lcm__def,axiom, % 169.04/169.57 ! [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)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_card__Pow,axiom, % 169.04/169.57 ! [V_A_2,T_a] : % 169.04/169.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.04/169.57 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osimps_I5_J,axiom, % 169.04/169.57 ! [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) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat0__intermed__int__val,axiom, % 169.04/169.57 ! [V_k_2,V_f_2,V_n_2] : % 169.04/169.57 ( ! [B_i] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 169.04/169.57 => 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))) ) % 169.04/169.57 => ( 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)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 169.04/169.57 => ? [B_i] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 169.04/169.57 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_int__val__lemma,axiom, % 169.04/169.57 ! [V_k_2,V_f_2,V_n_2] : % 169.04/169.57 ( ! [B_i] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 169.04/169.57 => 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))) ) % 169.04/169.57 => ( 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)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 169.04/169.57 => ? [B_i] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 169.04/169.57 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_finite__greaterThanLessThan,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_PowI,axiom, % 169.04/169.57 ! [V_B_2,V_A_2,T_a] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Cantors__paradox,axiom, % 169.04/169.57 ! [V_A_2,T_a] : % 169.04/169.57 ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Pow__top,axiom, % 169.04/169.57 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Pow__not__empty,axiom, % 169.04/169.57 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Pow__bottom,axiom, % 169.04/169.57 ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Pow__empty,axiom, % 169.04/169.57 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_finite__Pow__iff,axiom, % 169.04/169.57 ! [V_A_2,T_a] : % 169.04/169.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 169.04/169.57 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Pow__iff,axiom, % 169.04/169.57 ! [V_B_2,V_A_2,T_a] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 169.04/169.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_Pow__mono,axiom, % 169.04/169.57 ! [V_B_2,V_A_2,T_a] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_PowD,axiom, % 169.04/169.57 ! [V_B_2,V_A_2,T_a] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_image__Pow__surj,axiom, % 169.04/169.57 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 169.04/169.57 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 169.04/169.57 => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_image__Pow__mono,axiom, % 169.04/169.57 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_card__greaterThanLessThan,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__gcd_Osimps,axiom, % 169.04/169.57 ! [V_x,V_y] : % 169.04/169.57 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 169.04/169.57 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => 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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_code__numeral_Osimps_I4_J,axiom, % 169.04/169.57 ! [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 ). % 169.04/169.57 % 169.04/169.57 fof(fact_Nitpick_Oint__gcd__def,axiom, % 169.04/169.57 ! [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)))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_card__atLeastAtMost__int,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__mod__eq__lemma,axiom, % 169.04/169.57 ! [V_y,V_n,V_x] : % 169.04/169.57 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 169.04/169.57 => ? [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)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_mod__induct__0,axiom, % 169.04/169.57 ! [V_i_2,V_P_2,V_p_2] : % 169.04/169.57 ( ! [B_i] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 169.04/169.57 => ( hBOOL(hAPP(V_P_2,B_i)) % 169.04/169.57 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 169.04/169.57 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 169.04/169.57 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_nat__intermed__int__val,axiom, % 169.04/169.57 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 169.04/169.57 ( ! [B_i] : % 169.04/169.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 169.04/169.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 169.04/169.57 => 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))) ) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 169.04/169.57 => ? [B_i] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 169.04/169.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 169.04/169.57 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_finite__atLeastAtMost__int,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 169.04/169.57 ! [V_y_2,V_x_2] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_x_2) % 169.04/169.57 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastatMost__empty__iff,axiom, % 169.04/169.57 ! [V_b_2,V_a_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.04/169.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastatMost__empty__iff2,axiom, % 169.04/169.57 ! [V_b_2,V_a_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) % 169.04/169.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastatMost__empty,axiom, % 169.04/169.57 ! [V_a_2,V_b_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 169.04/169.57 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastatMost__subset__iff,axiom, % 169.04/169.57 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 169.04/169.57 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 169.04/169.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 169.04/169.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastAtMost__singleton_H,axiom, % 169.04/169.57 ! [V_b_2,V_a_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( V_a_2 = V_b_2 % 169.04/169.57 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastAtMost__singleton__iff,axiom, % 169.04/169.57 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( 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))) % 169.04/169.57 <=> ( V_a_2 = V_b_2 % 169.04/169.57 & V_b_2 = V_ca_2 ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastAtMost__singleton,axiom, % 169.04/169.57 ! [V_a_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_image__uminus__atLeastAtMost,axiom, % 169.04/169.57 ! [V_y_2,V_x_2,T_a] : % 169.04/169.57 ( class_Groups_Oordered__ab__group__add(T_a) % 169.04/169.57 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 169.04/169.57 ! [V_y_2,V_x_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 169.04/169.57 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastatMost__psubset__iff,axiom, % 169.04/169.57 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.57 ( class_Orderings_Oorder(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 169.04/169.57 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 169.04/169.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 169.04/169.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 169.04/169.57 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 169.04/169.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 169.04/169.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_simp__from__to,axiom, % 169.04/169.57 ! [V_i_2,V_j_2] : % 169.04/169.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 169.04/169.57 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 169.04/169.57 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_bset_I8_J,axiom, % 169.04/169.57 ! [V_B_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_aset_I6_J,axiom, % 169.04/169.57 ! [V_A_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_bset_I3_J,axiom, % 169.04/169.57 ! [V_B_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 169.04/169.57 => ( ! [B_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 169.04/169.57 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 169.04/169.57 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_aset_I3_J,axiom, % 169.04/169.57 ! [V_A_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 169.04/169.57 => ( ! [B_x] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 169.04/169.57 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 169.04/169.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_aset_I5_J,axiom, % 169.04/169.57 ! [V_A_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_finite__atLeastAtMost,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_image__Suc__atLeastAtMost,axiom, % 169.04/169.57 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ). % 169.04/169.57 % 169.04/169.57 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 169.04/169.57 ! [V_k_2,V_f_2] : % 169.04/169.57 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.04/169.57 => 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)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_atLeastAtMostSuc__conv,axiom, % 169.04/169.57 ! [V_n_2,V_m_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 169.04/169.57 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_setsum__head__Suc,axiom, % 169.04/169.57 ! [V_f_2,V_n_2,V_m_2,T_a] : % 169.04/169.57 ( class_Groups_Ocomm__monoid__add(T_a) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.04/169.57 => 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))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_card__atLeastAtMost,axiom, % 169.04/169.57 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ). % 169.04/169.57 % 169.04/169.57 fof(fact_setsum__cl__ivl__Suc,axiom, % 169.04/169.57 ! [V_f_2,V_m_2,V_n_2,T_a] : % 169.04/169.57 ( class_Groups_Ocomm__monoid__add(T_a) % 169.04/169.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 169.04/169.57 => 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) ) % 169.04/169.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 169.04/169.57 => 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))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_setsum__ub__add__nat,axiom, % 169.04/169.57 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 169.04/169.57 ( class_Groups_Ocomm__monoid__add(T_a) % 169.04/169.57 => ( 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)))) % 169.04/169.57 => 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)))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 169.04/169.57 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 169.04/169.57 % 169.04/169.57 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 169.04/169.57 ! [V_n_2,V_m_2] : % 169.04/169.57 ( c_Nat__Transfer_Ois__nat(V_m_2) % 169.04/169.57 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 169.04/169.57 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_aset_I4_J,axiom, % 169.04/169.57 ! [V_A_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( B_x != V_t_2 % 169.04/169.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_bset_I4_J,axiom, % 169.04/169.57 ! [V_B_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( B_x != V_t_2 % 169.04/169.57 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_bset_I7_J,axiom, % 169.04/169.57 ! [V_B_2,V_t_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_bset_I6_J,axiom, % 169.04/169.57 ! [V_t_2,V_B_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 169.04/169.57 => 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)) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_aset_I8_J,axiom, % 169.04/169.57 ! [V_t_2,V_A_2,V_D_2] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.57 => ! [B_x] : % 169.04/169.57 ( ! [B_xa] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.57 => ! [B_xb] : % 169.04/169.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 169.04/169.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 169.04/169.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 169.04/169.57 % 169.04/169.57 fof(fact_all__nat__less,axiom, % 169.04/169.58 ! [V_P_2,V_n_2] : % 169.04/169.58 ( ! [B_m] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 169.04/169.58 => hBOOL(hAPP(V_P_2,B_m)) ) % 169.04/169.58 <=> ! [B_x] : % 169.04/169.58 ( 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))) % 169.04/169.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_ex__nat__less,axiom, % 169.04/169.58 ! [V_P_2,V_n_2] : % 169.04/169.58 ( ? [B_m] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 169.04/169.58 & hBOOL(hAPP(V_P_2,B_m)) ) % 169.04/169.58 <=> ? [B_x] : % 169.04/169.58 ( 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))) % 169.04/169.58 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_periodic__finite__ex,axiom, % 169.04/169.58 ! [V_P_2,V_d_2] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 169.04/169.58 => ( ! [B_x,B_k] : % 169.04/169.58 ( hBOOL(hAPP(V_P_2,B_x)) % 169.04/169.58 <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) ) % 169.04/169.58 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.04/169.58 <=> ? [B_x] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) % 169.04/169.58 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_aset_I7_J,axiom, % 169.04/169.58 ! [V_t_2,V_A_2,V_D_2] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.58 => ! [B_x] : % 169.04/169.58 ( ! [B_xa] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.58 => ! [B_xb] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 169.04/169.58 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 169.04/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_bset_I5_J,axiom, % 169.04/169.58 ! [V_t_2,V_B_2,V_D_2] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 169.04/169.58 => ! [B_x] : % 169.04/169.58 ( ! [B_xa] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 169.04/169.58 => ! [B_xb] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 169.04/169.58 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 169.04/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Powp__mono,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 169.04/169.58 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 169.04/169.58 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_log_Osimps,axiom, % 169.04/169.58 ! [V_i,V_b] : % 169.04/169.58 ( ( ( 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))) % 169.04/169.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 169.04/169.58 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 169.04/169.58 & ( ~ ( 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))) % 169.04/169.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 169.04/169.58 => 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))) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_mod__div__decomp,axiom, % 169.04/169.58 ! [V_b,V_a,T_a] : % 169.04/169.58 ( class_Divides_Osemiring__div(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__lessThan,axiom, % 169.04/169.58 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__atMost,axiom, % 169.04/169.58 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__eq__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 169.04/169.58 <=> V_x_2 = V_y_2 ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atMost__eq__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 169.04/169.58 <=> V_x_2 = V_y_2 ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__Suc__atMost,axiom, % 169.04/169.58 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ). % 169.04/169.58 % 169.04/169.58 fof(fact_card__lessThan,axiom, % 169.04/169.58 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__0,axiom, % 169.04/169.58 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeast0AtMost,axiom, % 169.04/169.58 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__Suc,axiom, % 169.04/169.58 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_card__atMost,axiom, % 169.04/169.58 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atMost__Suc,axiom, % 169.04/169.58 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atMost__iff,axiom, % 169.04/169.58 ! [V_k_2,V_i_2,T_a] : % 169.04/169.58 ( class_Orderings_Oord(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 169.04/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__iff,axiom, % 169.04/169.58 ! [V_k_2,V_i_2,T_a] : % 169.04/169.58 ( class_Orderings_Oord(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 169.04/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atMost__subset__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Orderings_Oorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2))) % 169.04/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__subset__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2))) % 169.04/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_lessThan__strict__subset__iff,axiom, % 169.04/169.58 ! [V_n_2,V_m_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2))) % 169.04/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atMost__0,axiom, % 169.04/169.58 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_single__Diff__lessThan,axiom, % 169.04/169.58 ! [V_k_2,T_a] : % 169.04/169.58 ( class_Orderings_Oorder(T_a) % 169.04/169.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_minus__shift__def,axiom, % 169.04/169.58 ! [V_r,V_l,V_k] : % 169.04/169.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 169.04/169.58 => 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) ) % 169.04/169.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 169.04/169.58 => 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) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_inc__shift__def,axiom, % 169.04/169.58 ! [V_k,V_v] : % 169.04/169.58 ( ( V_v = V_k % 169.04/169.58 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 169.04/169.58 & ( V_v != V_k % 169.04/169.58 => 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)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_image__atLeastZeroLessThan__int,axiom, % 169.04/169.58 ! [V_u_2] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 169.04/169.58 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_greaterThan__Suc,axiom, % 169.04/169.58 ! [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)))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_image__uminus__lessThan,axiom, % 169.04/169.58 ! [V_x_2,T_a] : % 169.04/169.58 ( class_Groups_Oordered__ab__group__add(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__atLeastLessThan__int,axiom, % 169.04/169.58 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_greaterThan__eq__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 169.04/169.58 <=> V_x_2 = V_y_2 ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 169.04/169.58 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( 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) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 169.04/169.58 => V_b_2 = V_d_2 ) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 169.04/169.58 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( 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) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 169.04/169.58 => V_a_2 = V_ca_2 ) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__eq__iff,axiom, % 169.04/169.58 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 169.04/169.58 => ( 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) % 169.04/169.58 <=> ( V_a_2 = V_ca_2 % 169.04/169.58 & V_b_2 = V_d_2 ) ) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__empty,axiom, % 169.04/169.58 ! [V_a_2,V_b_2,T_a] : % 169.04/169.58 ( class_Orderings_Oorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 169.04/169.58 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__empty__iff2,axiom, % 169.04/169.58 ! [V_b_2,V_a_2,T_a] : % 169.04/169.58 ( class_Orderings_Oorder(T_a) % 169.04/169.58 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) % 169.04/169.58 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__empty__iff,axiom, % 169.04/169.58 ! [V_b_2,V_a_2,T_a] : % 169.04/169.58 ( class_Orderings_Oorder(T_a) % 169.04/169.58 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.04/169.58 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__subset__iff,axiom, % 169.04/169.58 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2))) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 169.04/169.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 169.04/169.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_ivl__diff,axiom, % 169.04/169.58 ! [V_m_2,V_n_2,V_i_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 169.04/169.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 169.04/169.58 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_greaterThan__iff,axiom, % 169.04/169.58 ! [V_k_2,V_i_2,T_a] : % 169.04/169.58 ( class_Orderings_Oord(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 169.04/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_greaterThan__subset__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( 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))) % 169.04/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 169.04/169.58 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Compl__greaterThan,axiom, % 169.04/169.58 ! [V_k_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Compl__atMost,axiom, % 169.04/169.58 ! [V_k_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_card__atLeastZeroLessThan__int,axiom, % 169.04/169.58 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ). % 169.04/169.58 % 169.04/169.58 fof(fact_card__atLeastLessThan__int,axiom, % 169.04/169.58 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 169.04/169.58 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ). % 169.04/169.58 % 169.04/169.58 fof(fact_image__uminus__greaterThan,axiom, % 169.04/169.58 ! [V_x_2,T_a] : % 169.04/169.58 ( class_Groups_Oordered__ab__group__add(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeast__Suc,axiom, % 169.04/169.58 ! [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)))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_greaterThan__0,axiom, % 169.04/169.58 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))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_ivl__disj__un_I18_J,axiom, % 169.04/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_ivl__disj__un_I3_J,axiom, % 169.04/169.58 ! [V_u_2,V_l_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_setsum__ivl__cong,axiom, % 169.04/169.58 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 169.04/169.58 ( ( class_Groups_Ocomm__monoid__add(T_b) % 169.04/169.58 & class_Orderings_Oord(T_a) ) % 169.04/169.58 => ( V_a_2 = V_ca_2 % 169.04/169.58 => ( V_b_2 = V_d_2 % 169.04/169.58 => ( ! [B_x] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 169.04/169.58 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 169.04/169.58 => 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)) ) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_top1I,axiom, % 169.04/169.58 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup1CI,axiom, % 169.04/169.58 ! [T_a,V_A_2,V_x_2,V_B_2] : % 169.04/169.58 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 169.04/169.58 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup1E,axiom, % 169.04/169.58 ! [V_x_2,V_B_2,V_A_2,T_a] : % 169.04/169.58 ( 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)) % 169.04/169.58 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 169.04/169.58 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__atLeastLessThan,axiom, % 169.04/169.58 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_UNIV__I,axiom, % 169.04/169.58 ! [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)))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_UnCI,axiom, % 169.04/169.58 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 169.04/169.58 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 169.04/169.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_UnE,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.04/169.58 ( 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))) % 169.04/169.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.04/169.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeastLessThan__add__Un,axiom, % 169.04/169.58 ! [V_k_2,V_j_2,V_i_2] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 169.04/169.58 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_ivl__disj__un_I14_J,axiom, % 169.04/169.58 ! [V_u_2,V_l_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__Diff,axiom, % 169.04/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__Diff__cancel2,axiom, % 169.04/169.58 ! [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) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__Diff__cancel,axiom, % 169.04/169.58 ! [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) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Pow__UNIV,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeast__0,axiom, % 169.04/169.58 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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Sup__fin_Oidem,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__apply,axiom, % 169.04/169.58 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__assoc,axiom, % 169.04/169.58 ! [V_z,V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_inf__sup__aci_I6_J,axiom, % 169.04/169.58 ! [V_z,V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup_Oassoc,axiom, % 169.04/169.58 ! [V_c,V_b,V_a,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__left__commute,axiom, % 169.04/169.58 ! [V_z,V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_inf__sup__aci_I7_J,axiom, % 169.04/169.58 ! [V_z,V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup_Oleft__commute,axiom, % 169.04/169.58 ! [V_c,V_a,V_b,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__left__idem,axiom, % 169.04/169.58 ! [V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_inf__sup__aci_I8_J,axiom, % 169.04/169.58 ! [V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup_Oleft__idem,axiom, % 169.04/169.58 ! [V_b,V_a,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__commute,axiom, % 169.04/169.58 ! [V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_inf__sup__aci_I5_J,axiom, % 169.04/169.58 ! [V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup_Ocommute,axiom, % 169.04/169.58 ! [V_b,V_a,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__idem,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup_Oidem,axiom, % 169.04/169.58 ! [V_a,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__top__right,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Obounded__lattice__top(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__top__left,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Obounded__lattice__top(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup1I2,axiom, % 169.04/169.58 ! [V_A_2,T_a,V_x_2,V_B_2] : % 169.04/169.58 ( hBOOL(hAPP(V_B_2,V_x_2)) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup1I1,axiom, % 169.04/169.58 ! [V_B_2,T_a,V_x_2,V_A_2] : % 169.04/169.58 ( hBOOL(hAPP(V_A_2,V_x_2)) % 169.04/169.58 => 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)) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_ball__Un,axiom, % 169.04/169.58 ! [V_P_2,V_B_2,V_A_2,T_a] : % 169.04/169.58 ( ! [B_x] : % 169.04/169.58 ( 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))) % 169.04/169.58 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.04/169.58 <=> ( ! [B_x] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.04/169.58 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.04/169.58 & ! [B_x] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 169.04/169.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_bex__Un,axiom, % 169.04/169.58 ! [V_P_2,V_B_2,V_A_2,T_a] : % 169.04/169.58 ( ? [B_x] : % 169.04/169.58 ( 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))) % 169.04/169.58 & hBOOL(hAPP(V_P_2,B_x)) ) % 169.04/169.58 <=> ( ? [B_x] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.04/169.58 & hBOOL(hAPP(V_P_2,B_x)) ) % 169.04/169.58 | ? [B_x] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 169.04/169.58 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__assoc,axiom, % 169.04/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__left__commute,axiom, % 169.04/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__left__absorb,axiom, % 169.04/169.58 ! [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) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__commute,axiom, % 169.04/169.58 ! [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) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__absorb,axiom, % 169.04/169.58 ! [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 ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__UNIV__right,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__UNIV__left,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_top__apply,axiom, % 169.04/169.58 ! [V_x_2,T_b,T_a] : % 169.04/169.58 ( class_Orderings_Otop(T_a) % 169.04/169.58 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_atLeast__eq__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Orderings_Olinorder(T_a) % 169.04/169.58 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 169.04/169.58 <=> V_x_2 = V_y_2 ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_UNIV__Plus__UNIV,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Compl__partition2,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Compl__partition,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_compl__sup__top,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__compl__top,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.04/169.58 => 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) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__Un,axiom, % 169.04/169.58 ! [V_G_2,V_F_2,T_a] : % 169.04/169.58 ( 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_G_2))) % 169.04/169.58 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 169.04/169.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__UnI,axiom, % 169.04/169.58 ! [V_G_2,V_F_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 169.04/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) % 169.04/169.58 => 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_G_2))) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_UnI2,axiom, % 169.04/169.58 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_UnI1,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__iff,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.04/169.58 ( 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))) % 169.04/169.58 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.04/169.58 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__fun__UNIVD2,axiom, % 169.04/169.58 ! [T_b,T_a] : % 169.04/169.58 ( 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)))) % 169.04/169.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__Prod__UNIV,axiom, % 169.04/169.58 ! [T_b,T_a] : % 169.04/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 169.04/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 169.04/169.58 => 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)))) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__option__UNIV,axiom, % 169.04/169.58 ! [T_a] : % 169.04/169.58 ( 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)))) % 169.04/169.58 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__eq__bot__iff,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Lattices_Obounded__lattice__bot(T_a) % 169.04/169.58 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 169.04/169.58 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 169.04/169.58 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__bot__right,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Obounded__lattice__bot(T_a) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__bot__left,axiom, % 169.04/169.58 ! [V_x,T_a] : % 169.04/169.58 ( class_Lattices_Obounded__lattice__bot(T_a) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__empty,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,T_a] : % 169.04/169.58 ( 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)) % 169.04/169.58 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.04/169.58 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__empty__right,axiom, % 169.04/169.58 ! [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 ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__empty__left,axiom, % 169.04/169.58 ! [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 ). % 169.04/169.58 % 169.04/169.58 fof(fact_finite__UNIV,axiom, % 169.04/169.58 ! [T_a] : % 169.04/169.58 ( class_Finite__Set_Ofinite(T_a) % 169.04/169.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_UNIV__not__empty,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_image__Un,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__insert__left,axiom, % 169.04/169.58 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__insert__right,axiom, % 169.04/169.58 ! [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)) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__Pow__subset,axiom, % 169.04/169.58 ! [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)))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_le__supE,axiom, % 169.04/169.58 ! [V_x,V_b,V_a,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( 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)) % 169.04/169.58 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 169.04/169.58 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__mono,axiom, % 169.04/169.58 ! [V_d,V_b,V_c,V_a,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 169.04/169.58 => 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))) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__least,axiom, % 169.04/169.58 ! [V_z,V_x,V_y,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 169.04/169.58 => 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)) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_le__supI,axiom, % 169.04/169.58 ! [V_b,V_x,V_a,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 169.04/169.58 => 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)) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__absorb1,axiom, % 169.04/169.58 ! [V_x,V_y,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__absorb2,axiom, % 169.04/169.58 ! [V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_le__supI2,axiom, % 169.04/169.58 ! [V_a,V_b,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 169.04/169.58 => 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))) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_le__supI1,axiom, % 169.04/169.58 ! [V_b,V_a,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 169.04/169.58 => 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))) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_le__sup__iff,axiom, % 169.04/169.58 ! [V_z_2,V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( 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)) % 169.04/169.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 169.04/169.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_le__iff__sup,axiom, % 169.04/169.58 ! [V_y_2,V_x_2,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 169.04/169.58 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__ge2,axiom, % 169.04/169.58 ! [V_x,V_y,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_inf__sup__ord_I4_J,axiom, % 169.04/169.58 ! [V_x,V_y,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_sup__ge1,axiom, % 169.04/169.58 ! [V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_inf__sup__ord_I3_J,axiom, % 169.04/169.58 ! [V_y,V_x,T_a] : % 169.04/169.58 ( class_Lattices_Olattice(T_a) % 169.04/169.58 => 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))) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__upper1,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__upper2,axiom, % 169.04/169.58 ! [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))) ). % 169.04/169.58 % 169.04/169.58 fof(fact_subset__Un__eq,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.58 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__absorb1,axiom, % 169.04/169.58 ! [V_B_2,V_A_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__absorb2,axiom, % 169.04/169.58 ! [V_A_2,V_B_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.04/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__least,axiom, % 169.04/169.58 ! [V_B_2,V_C_2,V_A_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 169.04/169.58 => 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)) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_Un__mono,axiom, % 169.04/169.58 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 169.04/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 169.04/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 169.04/169.58 => 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))) ) ) ). % 169.04/169.58 % 169.04/169.58 fof(fact_less__supI2,axiom, % 169.04/169.58 ! [V_a,V_b,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 169.19/169.58 => 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))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_less__supI1,axiom, % 169.19/169.58 ! [V_b,V_a,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 169.19/169.58 => 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))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_subset__UNIV,axiom, % 169.19/169.58 ! [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)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_injD,axiom, % 169.19/169.58 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 169.19/169.58 => V_x_2 = V_y_2 ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__eq,axiom, % 169.19/169.58 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 169.19/169.58 <=> V_x_2 = V_y_2 ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__int,axiom, % 169.19/169.58 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))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__Plus__UNIV__iff,axiom, % 169.19/169.58 ! [T_b,T_a] : % 169.19/169.58 ( 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)))) % 169.19/169.58 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 169.19/169.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 169.19/169.58 ! [V_B_2,V_A_2] : % 169.19/169.58 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.19/169.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.19/169.58 => 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)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_fun__left__comm__idem__sup,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.19/169.58 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_infinite__UNIV__nat,axiom, % 169.19/169.58 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_top__greatest,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Orderings_Otop(T_a) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_UNIV__option__conv,axiom, % 169.19/169.58 ! [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)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I1_J,axiom, % 169.19/169.58 ! [V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I13_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I12_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_all__nat__less__eq,axiom, % 169.19/169.58 ! [V_P_2,V_n_2] : % 169.19/169.58 ( ! [B_m] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 169.19/169.58 => hBOOL(hAPP(V_P_2,B_m)) ) % 169.19/169.58 <=> ! [B_x] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 169.19/169.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ex__nat__less__eq,axiom, % 169.19/169.58 ! [V_P_2,V_n_2] : % 169.19/169.58 ( ? [B_m] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 169.19/169.58 & hBOOL(hAPP(V_P_2,B_m)) ) % 169.19/169.58 <=> ? [B_x] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) % 169.19/169.58 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_insert__is__Un,axiom, % 169.19/169.58 ! [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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_union__fold__insert,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => 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) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I17_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__partition,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.58 => 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 ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__subset__conv,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : % 169.19/169.58 ( 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)) % 169.19/169.58 <=> 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))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 169.19/169.58 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__on__Un__image__eq__iff,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.58 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 169.19/169.58 <=> V_A_2 = V_B_2 ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_rangeI,axiom, % 169.19/169.58 ! [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))))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_range__eqI,axiom, % 169.19/169.58 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 169.19/169.58 ( V_b_2 = hAPP(V_f_2,V_x_2) % 169.19/169.58 => 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))))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeastLessThan0,axiom, % 169.19/169.58 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 169.19/169.58 ! [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))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeast0LessThan,axiom, % 169.19/169.58 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__UNIV,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 169.19/169.58 => ( 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))) % 169.19/169.58 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__Diff__eq,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__image__eq__iff,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 169.19/169.58 <=> V_A_2 = V_B_2 ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_card__atLeastLessThan,axiom, % 169.19/169.58 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__empty__eq,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__UNIV__eq,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__compl,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 169.19/169.58 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__eq__Diff__UNIV,axiom, % 169.19/169.58 ! [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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_dom__map__add,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__Suc__atLeastLessThan,axiom, % 169.19/169.58 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_the__inv__f__f,axiom, % 169.19/169.58 ! [V_x_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => 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 ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 169.19/169.58 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__fun__UNIVD1,axiom, % 169.19/169.58 ! [T_b,T_a] : % 169.19/169.58 ( 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)))) % 169.19/169.58 => ( 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)) % 169.19/169.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 169.19/169.58 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__of__nat,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( class_Nat_Osemiring__char__0(T_a) % 169.19/169.58 => 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))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 169.19/169.58 ! [V_B_2,V_A_2] : % 169.19/169.58 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.19/169.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.19/169.58 => 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))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeast__iff,axiom, % 169.19/169.58 ! [V_k_2,V_i_2,T_a] : % 169.19/169.58 ( class_Orderings_Oord(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 169.19/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_fold__sup__insert,axiom, % 169.19/169.58 ! [V_a_2,V_b_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => 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)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeast__subset__iff,axiom, % 169.19/169.58 ! [V_y_2,V_x_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => ( 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))) % 169.19/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_setsum__add__nat__ivl,axiom, % 169.19/169.58 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 169.19/169.58 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 169.19/169.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_setsum__diff__nat__ivl,axiom, % 169.19/169.58 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 169.19/169.58 ( class_Groups_Oab__group__add(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 169.19/169.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_compl__top__eq,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.58 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_compl__bot__eq,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.58 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I21_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_range__ex1__eq,axiom, % 169.19/169.58 ! [V_b_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => ( 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))))) % 169.19/169.58 <=> ? [B_x] : % 169.19/169.58 ( V_b_2 = hAPP(V_f_2,B_x) % 169.19/169.58 & ! [B_y] : % 169.19/169.58 ( V_b_2 = hAPP(V_f_2,B_y) % 169.19/169.58 => B_y = B_x ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__image__mem__iff,axiom, % 169.19/169.58 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 169.19/169.58 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__UNIV__inj__surj,axiom, % 169.19/169.58 ! [V_f_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 169.19/169.58 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => 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)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__UNIV__surj__inj,axiom, % 169.19/169.58 ! [V_f_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 169.19/169.58 => ( 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)) % 169.19/169.58 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I8_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__image__subset__iff,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) % 169.19/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__set__diff,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_surj__Compl__image__subset,axiom, % 169.19/169.58 ! [V_A_2,V_f_2,T_a,T_b] : % 169.19/169.58 ( 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)) % 169.19/169.58 => 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)))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeastLessThan__singleton,axiom, % 169.19/169.58 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__lessThan,axiom, % 169.19/169.58 ! [V_k_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => 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) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__atLeast,axiom, % 169.19/169.58 ! [V_k_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => 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) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_folding__one__idem_Ounion__idem,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 169.19/169.58 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeast__Suc__greaterThan,axiom, % 169.19/169.58 ! [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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Pow__insert,axiom, % 169.19/169.58 ! [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))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_subset__card__intvl__is__intvl,axiom, % 169.19/169.58 ! [V_k_2,V_A_2] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) % 169.19/169.58 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_sup__le__fold__sup,axiom, % 169.19/169.58 ! [V_b_2,V_a_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__sup(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.58 => 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))) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__range__updI,axiom, % 169.19/169.58 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( 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))))) % 169.19/169.58 => 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))))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 169.19/169.58 ! [V_k_2,V_f_2,T_a] : % 169.19/169.58 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.58 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 169.19/169.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_setsum__head__upt__Suc,axiom, % 169.19/169.58 ! [V_f_2,V_n_2,V_m_2,T_a] : % 169.19/169.58 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_fold1__Un2,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I15_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__UNIV__card__ge__0,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 169.19/169.58 => 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))))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeastLessThanSuc,axiom, % 169.19/169.58 ! [V_n_2,V_m_2] : % 169.19/169.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.58 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) % 169.19/169.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.58 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I2_J,axiom, % 169.19/169.58 ! [V_u_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__image__Compl__subset,axiom, % 169.19/169.58 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),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)))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I10_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I7_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__uminus__atMost,axiom, % 169.19/169.58 ! [V_x_2,T_a] : % 169.19/169.58 ( class_Groups_Oordered__ab__group__add(T_a) % 169.19/169.58 => 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)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__uminus__atLeast,axiom, % 169.19/169.58 ! [V_x_2,T_a] : % 169.19/169.58 ( class_Groups_Oordered__ab__group__add(T_a) % 169.19/169.58 => 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)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_setsum__op__ivl__Suc,axiom, % 169.19/169.58 ! [V_f_2,V_m_2,V_n_2,T_a] : % 169.19/169.58 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 169.19/169.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 169.19/169.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 169.19/169.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I6_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I19_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),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) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I4_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_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) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oremove,axiom, % 169.19/169.58 ! [V_x_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 169.19/169.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => 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)))))) ) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_iso__tuple__UNIV__I,axiom, % 169.19/169.58 ! [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)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I5_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__greaterThanAtMost,axiom, % 169.19/169.58 ! [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))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__greaterThanAtMost__int,axiom, % 169.19/169.58 ! [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))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_card__UNIV__unit,axiom, % 169.19/169.58 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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_infinite__UNIV__int,axiom, % 169.19/169.58 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Osingleton,axiom, % 169.19/169.58 ! [V_x_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => 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 ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_greaterThanAtMost__empty,axiom, % 169.19/169.58 ! [V_k_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 169.19/169.58 => 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)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 169.19/169.58 ! [V_l_2,V_k_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => ( 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) % 169.19/169.58 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_greaterThanAtMost__empty__iff,axiom, % 169.19/169.58 ! [V_l_2,V_k_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => ( 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)) % 169.19/169.58 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I20_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 169.19/169.58 => 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) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 169.19/169.58 ! [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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_card__greaterThanAtMost,axiom, % 169.19/169.58 ! [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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oin__idem,axiom, % 169.19/169.58 ! [V_x_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.58 => 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) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_OF__eq,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => 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) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I22_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 169.19/169.58 ! [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) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__uminus__greaterThanAtMost,axiom, % 169.19/169.58 ! [V_y_2,V_x_2,T_a] : % 169.19/169.58 ( class_Groups_Oordered__ab__group__add(T_a) % 169.19/169.58 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__uminus__atLeastLessThan,axiom, % 169.19/169.58 ! [V_y_2,V_x_2,T_a] : % 169.19/169.58 ( class_Groups_Oordered__ab__group__add(T_a) % 169.19/169.58 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_card__UNIV__bool,axiom, % 169.19/169.58 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))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I9_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I11_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 169.19/169.58 => 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) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oinsert__idem,axiom, % 169.19/169.58 ! [V_x_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => 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)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Osubset__idem,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.58 => 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) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_card__greaterThanAtMost__int,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Ounion__idem,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 169.19/169.58 ! [V_a_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => 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) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__un_I16_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Olinorder(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 169.19/169.58 => 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) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oinsert,axiom, % 169.19/169.58 ! [V_x_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => 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)) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oinsert__remove,axiom, % 169.19/169.58 ! [V_x_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => 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 ) % 169.19/169.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => 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)))))) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 169.19/169.58 ! [V_x_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.58 => 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) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Oclosed,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => ( ! [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)))))) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin_Ohom__commute,axiom, % 169.19/169.58 ! [V_N_2,V_h_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( ! [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)) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => 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)) ) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fold__sup,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => 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) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__range__map__of__map__add,axiom, % 169.19/169.58 ! [V_l_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( 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))))) % 169.19/169.58 => 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))))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__dom__map__of,axiom, % 169.19/169.58 ! [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)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__UnionD,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 169.19/169.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__range__map__of,axiom, % 169.19/169.58 ! [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))))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_sup__Sup__fold__sup,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => 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) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__fin__Sup,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_UnionI,axiom, % 169.19/169.58 ! [V_A_2,V_C_2,V_X_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 169.19/169.58 => 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))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__binary,axiom, % 169.19/169.58 ! [V_b_2,V_a_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => 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) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Un__eq__Union,axiom, % 169.19/169.58 ! [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))))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__UNIV,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => 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) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__Pow__eq,axiom, % 169.19/169.58 ! [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 ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__upper,axiom, % 169.19/169.58 ! [V_A_2,V_B_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.58 => 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))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__le__iff,axiom, % 169.19/169.58 ! [V_b_2,V_A_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => ( 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)) % 169.19/169.58 <=> ! [B_x] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_less__Sup__iff,axiom, % 169.19/169.58 ! [V_S_2,V_a_2,T_a] : % 169.19/169.58 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 & class_Orderings_Olinorder(T_a) ) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 169.19/169.58 <=> ? [B_x] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 169.19/169.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__empty,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__mono,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( 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)) % 169.19/169.58 => 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))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__insert,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_subset__Pow__Union,axiom, % 169.19/169.58 ! [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)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__UNIV,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__Un__distrib,axiom, % 169.19/169.58 ! [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)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__upper,axiom, % 169.19/169.58 ! [V_A_2,V_x_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.58 => 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))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__empty,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => 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) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__singleton,axiom, % 169.19/169.58 ! [V_a_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => 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 ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Sup__insert,axiom, % 169.19/169.58 ! [V_A_2,V_a_2,T_a] : % 169.19/169.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.58 => 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)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__Union,axiom, % 169.19/169.58 ! [V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 169.19/169.58 => ( ! [B_M] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 169.19/169.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 169.19/169.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_body__def,axiom, % 169.19/169.58 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__map__freshness,axiom, % 169.19/169.58 ! [V_f_2,T_b,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 169.19/169.58 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 169.19/169.58 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_setsum__Un__nat,axiom, % 169.19/169.58 ! [V_f_2,V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.58 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf1E,axiom, % 169.19/169.58 ! [V_x_2,V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 169.19/169.58 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 169.19/169.58 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf1I,axiom, % 169.19/169.58 ! [T_a,V_B_2,V_x_2,V_A_2] : % 169.19/169.58 ( hBOOL(hAPP(V_A_2,V_x_2)) % 169.19/169.58 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 169.19/169.58 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_IntI,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 169.19/169.58 => 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))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_IntE,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.19/169.58 ( 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))) % 169.19/169.58 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.19/169.58 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_finite__Int,axiom, % 169.19/169.58 ! [V_G_2,V_F_2,T_a] : % 169.19/169.58 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 169.19/169.58 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) % 169.19/169.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_G_2))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__Int__subset,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),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)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_fun__left__comm__idem__inf,axiom, % 169.19/169.58 ! [T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_sup__inf__distrib2,axiom, % 169.19/169.58 ! [V_x,V_z,V_y,T_a] : % 169.19/169.58 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__distrib2,axiom, % 169.19/169.58 ! [V_x,V_z,V_y,T_a] : % 169.19/169.58 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_sup__inf__distrib1,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__distrib1,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_sup__inf__absorb,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__absorb,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Un__Int__crazy,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Un__Int__distrib2,axiom, % 169.19/169.58 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__Un__distrib2,axiom, % 169.19/169.58 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Un__Int__distrib,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__Un__distrib,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_insert__inter__insert,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__on__Int,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.19/169.58 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 169.19/169.58 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 169.19/169.58 ! [V_B_2,V_A_2] : % 169.19/169.58 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.19/169.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.19/169.58 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_restrict__restrict,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__Int2,axiom, % 169.19/169.58 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__Int__distrib2,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__Diff,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__Int__distrib,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Pow__Int__eq,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Inf__fin_Oidem,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__apply,axiom, % 169.19/169.58 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__assoc,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__aci_I2_J,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf_Oassoc,axiom, % 169.19/169.58 ! [V_c,V_b,V_a,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__left__commute,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__aci_I3_J,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf_Oleft__commute,axiom, % 169.19/169.58 ! [V_c,V_a,V_b,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__left__idem,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__aci_I4_J,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf_Oleft__idem,axiom, % 169.19/169.58 ! [V_b,V_a,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__commute,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__aci_I1_J,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf_Ocommute,axiom, % 169.19/169.58 ! [V_b,V_a,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__idem,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf_Oidem,axiom, % 169.19/169.58 ! [V_a,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf1D2,axiom, % 169.19/169.58 ! [V_x_2,V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 169.19/169.58 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf1D1,axiom, % 169.19/169.58 ! [V_x_2,V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 169.19/169.58 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__assoc,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__left__commute,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__left__absorb,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__commute,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__absorb,axiom, % 169.19/169.58 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 169.19/169.58 % 169.19/169.58 fof(fact_disjoint__iff__not__equal,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 <=> ! [B_x] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.58 => ! [B_xa] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 169.19/169.58 => B_x != B_xa ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__empty__right,axiom, % 169.19/169.58 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__empty__left,axiom, % 169.19/169.58 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__bot__right,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Obounded__lattice__bot(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__bot__left,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Obounded__lattice__bot(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_IntD2,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.19/169.58 ( 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))) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_IntD1,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.19/169.58 ( 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))) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__iff,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 169.19/169.58 ( 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))) % 169.19/169.58 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.19/169.58 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_le__infE,axiom, % 169.19/169.58 ! [V_b,V_a,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) % 169.19/169.58 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 169.19/169.58 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__mono,axiom, % 169.19/169.58 ! [V_d,V_b,V_c,V_a,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__greatest,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_le__infI,axiom, % 169.19/169.58 ! [V_b,V_a,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__absorb2,axiom, % 169.19/169.58 ! [V_x,V_y,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__absorb1,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_le__infI2,axiom, % 169.19/169.58 ! [V_a,V_x,V_b,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_le__infI1,axiom, % 169.19/169.58 ! [V_b,V_x,V_a,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_le__inf__iff,axiom, % 169.19/169.58 ! [V_z_2,V_y_2,V_x_2,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))) % 169.19/169.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 169.19/169.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_le__iff__inf,axiom, % 169.19/169.58 ! [V_y_2,V_x_2,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 169.19/169.58 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__le2,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__ord_I2_J,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__le1,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__sup__ord_I1_J,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__lower1,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__lower2,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__absorb2,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__absorb1,axiom, % 169.19/169.58 ! [V_A_2,V_B_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__greatest,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_C_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__mono,axiom, % 169.19/169.58 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_less__infI2,axiom, % 169.19/169.58 ! [V_a,V_x,V_b,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_less__infI1,axiom, % 169.19/169.58 ! [V_b,V_x,V_a,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__UNIV__left,axiom, % 169.19/169.58 ! [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 ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__UNIV__right,axiom, % 169.19/169.58 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__top__left,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Obounded__lattice__top(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__top__right,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Obounded__lattice__top(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__eq__top__iff,axiom, % 169.19/169.58 ! [V_y_2,V_x_2,T_a] : % 169.19/169.58 ( class_Lattices_Obounded__lattice__top(T_a) % 169.19/169.58 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 169.19/169.58 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 169.19/169.58 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_distrib__sup__le,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_distrib__inf__le,axiom, % 169.19/169.58 ! [V_z,V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__compl__bot,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_compl__inf__bot,axiom, % 169.19/169.58 ! [V_x,T_a] : % 169.19/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_diff__eq,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_compl__inf,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.58 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_compl__sup,axiom, % 169.19/169.58 ! [V_y,V_x,T_a] : % 169.19/169.58 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.58 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__insert__right,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_a_2,T_a] : % 169.19/169.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 169.19/169.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__insert__left,axiom, % 169.19/169.58 ! [V_B_2,V_C_2,V_a_2,T_a] : % 169.19/169.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 169.19/169.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__insert__right__if0,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_a_2,T_a] : % 169.19/169.58 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__insert__left__if0,axiom, % 169.19/169.58 ! [V_B_2,V_C_2,V_a_2,T_a] : % 169.19/169.58 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__insert__right__if1,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_a_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Int__insert__left__if1,axiom, % 169.19/169.58 ! [V_B_2,V_C_2,V_a_2,T_a] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__Int__subset,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__disjoint,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__triv,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Un__Int__assoc__eq,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 169.19/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Un__Diff__Int,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__Un,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__Int,axiom, % 169.19/169.58 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__int_I11_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 169.19/169.58 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__disjoint,axiom, % 169.19/169.58 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__disjoint2,axiom, % 169.19/169.58 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Union__disjoint,axiom, % 169.19/169.58 ! [V_A_2,V_C_2,T_a] : % 169.19/169.58 ( 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)) % 169.19/169.58 <=> ! [B_x] : % 169.19/169.58 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 169.19/169.58 => 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)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__Un,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Compl__Int,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__Compl,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Diff__eq,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__int_I14_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_dom__restrict,axiom, % 169.19/169.58 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ). % 169.19/169.58 % 169.19/169.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 169.19/169.58 ! [V_B_2,V_A_2] : % 169.19/169.58 ( c_Nat__Transfer_Onat__set(V_A_2) % 169.19/169.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_fold__inf__insert,axiom, % 169.19/169.58 ! [V_a_2,V_b_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => 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)) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inf__Sup__absorb,axiom, % 169.19/169.58 ! [V_a_2,V_A_2,T_a] : % 169.19/169.58 ( class_Lattices_Olattice(T_a) % 169.19/169.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_inj__on__image__Int,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 169.19/169.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 169.19/169.58 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_image__Int,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.58 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_disjoint__eq__subset__Compl,axiom, % 169.19/169.58 ! [V_B_2,V_A_2,T_a] : % 169.19/169.58 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__int_I15_J,axiom, % 169.19/169.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__int_I4_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__int_I2_J,axiom, % 169.19/169.58 ! [V_u_2,V_l_2,T_a] : % 169.19/169.58 ( class_Orderings_Oorder(T_a) % 169.19/169.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.58 % 169.19/169.58 fof(fact_ivl__disj__int_I16_J,axiom, % 169.19/169.59 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I13_J,axiom, % 169.19/169.59 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I12_J,axiom, % 169.19/169.59 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I9_J,axiom, % 169.19/169.59 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I8_J,axiom, % 169.19/169.59 ! [V_u_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I7_J,axiom, % 169.19/169.59 ! [V_u_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_map__add__comm,axiom, % 169.19/169.59 ! [V_m2_2,V_m1_2,T_b,T_a] : % 169.19/169.59 ( 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)) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I3_J,axiom, % 169.19/169.59 ! [V_u_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I1_J,axiom, % 169.19/169.59 ! [V_u_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I10_J,axiom, % 169.19/169.59 ! [V_u_2,V_m_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I6_J,axiom, % 169.19/169.59 ! [V_u_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ivl__disj__int_I5_J,axiom, % 169.19/169.59 ! [V_u_2,V_l_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_folding__image__simple_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_compl__unique,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Lattices_Oboolean__algebra(T_a) % 169.19/169.59 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 169.19/169.59 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 169.19/169.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__inf__le__inf,axiom, % 169.19/169.59 ! [V_b_2,V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold1__belowI,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_below__fold1__iff,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__Un__Int,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod_Ounion__inter,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__Un__Int,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_card__Un__Int,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_card_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_card__Diff__subset__Int,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( 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))) % 169.19/169.59 => 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))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_atMost__Int__atLeast,axiom, % 169.19/169.59 ! [V_n_2,T_a] : % 169.19/169.59 ( class_Orderings_Oorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_folding__one_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_folding__one_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__Un__disjoint,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__Un,axiom, % 169.19/169.59 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Oab__group__add(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__Un__disjoint,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_card__Un__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inj__on__Un,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( 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)) % 169.19/169.59 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.19/169.59 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 169.19/169.59 & 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold1__Un,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Groups_Oab__semigroup__mult(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Sup__fin_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_card_Ounion__inter__neutral,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( ( ? [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))) % 169.19/169.59 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__Un,axiom, % 169.19/169.59 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Fields_Ofield(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( 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))) % 169.19/169.59 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 169.19/169.59 => 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))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod_Ounion__inter__neutral,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( 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))) % 169.19/169.59 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__Un__one,axiom, % 169.19/169.59 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( 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))) % 169.19/169.59 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__Un__zero,axiom, % 169.19/169.59 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( 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))) % 169.19/169.59 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum_Ounion__inter__neutral,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( 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))) % 169.19/169.59 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oremove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_insert__partition,axiom, % 169.19/169.59 ! [V_F_2,V_x_2,T_a] : % 169.19/169.59 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( 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))) % 169.19/169.59 => ! [B_xa] : % 169.19/169.59 ( 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))) % 169.19/169.59 => ( B_x != B_xa % 169.19/169.59 => 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)) ) ) ) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Osingleton,axiom, % 169.19/169.59 ! [V_x_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_sup__Inf__absorb,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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 ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oin__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_OF__eq,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oinsert__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Osubset__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Ounion__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__le__Sup,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oinsert,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oinsert__remove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Oclosed,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( ! [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)))))) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__Un__disjoint,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin_Ohom__commute,axiom, % 169.19/169.59 ! [V_N_2,V_h_2,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_card__partition,axiom, % 169.19/169.59 ! [V_k_2,V_C_2,T_a] : % 169.19/169.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 169.19/169.59 => ( ! [B_c] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 169.19/169.59 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 169.19/169.59 => ( ! [B_c1] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 169.19/169.59 => ! [B_c2] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 169.19/169.59 => ( B_c1 != B_c2 % 169.19/169.59 => 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)) ) ) ) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__image__empty,axiom, % 169.19/169.59 ! [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 ). % 169.19/169.59 % 169.19/169.59 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 169.19/169.59 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__image__insert,axiom, % 169.19/169.59 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Oab__semigroup__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum_Oeq__fold,axiom, % 169.19/169.59 ! [V_g_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum_OF__eq,axiom, % 169.19/169.59 ! [V_g_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.59 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) % 169.19/169.59 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod_OF__eq,axiom, % 169.19/169.59 ! [V_g_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) % 169.19/169.59 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod_Oeq__fold,axiom, % 169.19/169.59 ! [V_g_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__image__Un__Int,axiom, % 169.19/169.59 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_comm__monoid__big_OF__eq,axiom, % 169.19/169.59 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 169.19/169.59 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.59 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) % 169.19/169.59 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.59 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__image__Un__one,axiom, % 169.19/169.59 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( 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))) % 169.19/169.59 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fold__inf,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 169.19/169.59 => hAPP(V_g_2,B_x) = V_z_2 ) % 169.19/169.59 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_finite__Inter,axiom, % 169.19/169.59 ! [V_M_2,T_a] : % 169.19/169.59 ( ? [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 169.19/169.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 169.19/169.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_InterD,axiom, % 169.19/169.59 ! [V_X_2,V_C_2,V_A_2,T_a] : % 169.19/169.59 ( 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))) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_InterE,axiom, % 169.19/169.59 ! [V_X_2,V_C_2,V_A_2,T_a] : % 169.19/169.59 ( 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))) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_le__Inf__iff,axiom, % 169.19/169.59 ! [V_A_2,V_b_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__less__iff,axiom, % 169.19/169.59 ! [V_a_2,V_S_2,T_a] : % 169.19/169.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 & class_Orderings_Olinorder(T_a) ) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 169.19/169.59 <=> ? [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 169.19/169.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__lower,axiom, % 169.19/169.59 ! [V_A_2,V_B_2,T_a] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__anti__mono,axiom, % 169.19/169.59 ! [V_A_2,V_B_2,T_a] : % 169.19/169.59 ( 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)) % 169.19/169.59 => 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))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__empty,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__insert,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__UNIV,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__lower,axiom, % 169.19/169.59 ! [V_A_2,V_x_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__Un__distrib,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__singleton,axiom, % 169.19/169.59 ! [V_a_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__empty,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__UNIV,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__insert,axiom, % 169.19/169.59 ! [V_A_2,V_a_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__eq__Inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = 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))))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__Un__subset,axiom, % 169.19/169.59 ! [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)))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__binary,axiom, % 169.19/169.59 ! [V_b_2,V_a_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inf__Inf__fold__inf,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inf__fin__Inf,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_comm__monoid__big_Oinfinite,axiom, % 169.19/169.59 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 169.19/169.59 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.59 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__image__1,axiom, % 169.19/169.59 ! [V_f_2,V_S_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 169.19/169.59 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__image__cong,axiom, % 169.19/169.59 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Oab__semigroup__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inf__le__fold__inf,axiom, % 169.19/169.59 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold__sup__le__sup,axiom, % 169.19/169.59 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 169.19/169.59 ( class_Lattices_Osemilattice__sup(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inj__on__Inter,axiom, % 169.19/169.59 ! [V_f_2,T_b,T_a,V_S_2] : % 169.19/169.59 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 169.19/169.59 => ( ! [B_A] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 169.19/169.59 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Inter__subset,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( ! [B_X] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_InterI,axiom, % 169.19/169.59 ! [V_A_2,V_C_2,T_a] : % 169.19/169.59 ( ! [B_X] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 169.19/169.59 => 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))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_UnionE,axiom, % 169.19/169.59 ! [V_C_2,V_A_2,T_a] : % 169.19/169.59 ( 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))) % 169.19/169.59 => ~ ! [B_X] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 169.19/169.59 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__pos,axiom, % 169.19/169.59 ! [V_f_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Rings_Olinordered__semidom(T_b) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__nonneg,axiom, % 169.19/169.59 ! [V_f_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Rings_Olinordered__semidom(T_b) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_bool_Osize_I1_J,axiom, % 169.19/169.59 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.19/169.59 % 169.19/169.59 fof(fact_bool_Osize_I2_J,axiom, % 169.19/169.59 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold1__antimono,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => 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))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_field__le__epsilon,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Fields_Olinordered__field(T_a) % 169.19/169.59 => ( ! [B_e] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 169.19/169.59 => 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))) ) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osize_I6_J,axiom, % 169.19/169.59 ! [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))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osize_I14_J,axiom, % 169.19/169.59 ! [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))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_WTs__elim__cases_I6_J,axiom, % 169.19/169.59 ! [V_ca_2,V_b_2] : % 169.19/169.59 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) % 169.19/169.59 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I39_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I38_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I60_J,axiom, % 169.19/169.59 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I61_J,axiom, % 169.19/169.59 ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I47_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I46_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inf__min,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( ( class_Lattices_Osemilattice__inf(T_a) % 169.19/169.59 & class_Orderings_Olinorder(T_a) ) % 169.19/169.59 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I58_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I59_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_WT_Oequations_I6_J,axiom, % 169.19/169.59 ! [V_a1_2,V_a2_2] : % 169.19/169.59 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 169.19/169.59 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_While,axiom, % 169.19/169.59 ! [V_b_2,V_ca_2] : % 169.19/169.59 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 169.19/169.59 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I53_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I52_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__diff,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__diff__distrib__left,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Groups_Oordered__ab__group__add(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__Suc__Suc,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oidem,axiom, % 169.19/169.59 ! [V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__assoc,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf_Oassoc,axiom, % 169.19/169.59 ! [V_c,V_b,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__left__commute,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 169.19/169.59 ! [V_c,V_a,V_b,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__left__idem,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 169.19/169.59 ! [V_b,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__commute,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf_Ocommute,axiom, % 169.19/169.59 ! [V_b,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf_Oidem,axiom, % 169.19/169.59 ! [V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I5_J,axiom, % 169.19/169.59 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 169.19/169.59 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 169.19/169.59 <=> ( V_fun_2 = V_fun_H_2 % 169.19/169.59 & V_com_2 = V_com_H_2 ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__0L,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__0R,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__infE,axiom, % 169.19/169.59 ! [V_b,V_a,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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))) % 169.19/169.59 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 169.19/169.59 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__mono,axiom, % 169.19/169.59 ! [V_d,V_b,V_c,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__greatest,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__infI,axiom, % 169.19/169.59 ! [V_b,V_a,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__absorb2,axiom, % 169.19/169.59 ! [V_x,V_y,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__absorb1,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__infI2,axiom, % 169.19/169.59 ! [V_a,V_x,V_b,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__infI1,axiom, % 169.19/169.59 ! [V_b,V_x,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__inf__iff,axiom, % 169.19/169.59 ! [V_z_2,V_y_2,V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 169.19/169.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__iff__inf,axiom, % 169.19/169.59 ! [V_y_2,V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 169.19/169.59 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__le2,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__le1,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__le__iff__disj,axiom, % 169.19/169.59 ! [V_z_2,V_y_2,V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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)) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 169.19/169.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__add__distrib__left,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oless__infI2,axiom, % 169.19/169.59 ! [V_a,V_x,V_b,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oless__infI1,axiom, % 169.19/169.59 ! [V_b,V_x,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__less__iff__disj,axiom, % 169.19/169.59 ! [V_z_2,V_y_2,V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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)) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 169.19/169.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__less__iff__conj,axiom, % 169.19/169.59 ! [V_y_2,V_x_2,V_z_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 169.19/169.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I17_J,axiom, % 169.19/169.59 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 169.19/169.59 % 169.19/169.59 fof(fact_com_Osimps_I16_J,axiom, % 169.19/169.59 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__number__of,axiom, % 169.19/169.59 ! [V_v,V_u,T_b] : % 169.19/169.59 ( ( class_Int_Onumber(T_b) % 169.19/169.59 & class_Orderings_Oord(T_b) ) % 169.19/169.59 => ( ( 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))) % 169.19/169.59 => 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) ) % 169.19/169.59 & ( ~ 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))) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ofold__inf__insert,axiom, % 169.19/169.59 ! [V_a_2,V_b_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__atLeastAtMostR1,axiom, % 169.19/169.59 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__atLeastAtMostL1,axiom, % 169.19/169.59 ! [V_d_2,V_b_2,V_a_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 169.19/169.59 ! [V_b_2,V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ofold1__belowI,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold1__below__iff,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 <=> ? [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Obelow__fold1__iff,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_strict__below__fold1__iff,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fold1__strict__below__iff,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 <=> ? [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__ord__min,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( class_Orderings_Oord(T_a) % 169.19/169.59 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oremove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oremove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oeq__fold_H,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inf__nat__def,axiom, % 169.19/169.59 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Osingleton,axiom, % 169.19/169.59 ! [V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min__le,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 169.19/169.59 ! [V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min__in,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oin__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_OF__eq,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min__antimono,axiom, % 169.19/169.59 ! [V_N_2,V_M_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 169.19/169.59 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.59 => 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))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min__insert,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Osubset__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min__Un,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oeq__fold__idem_H,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oinsert,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oinsert__remove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( ! [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)))))) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Oclosed,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( ! [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)))))) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 169.19/169.59 ! [V_N_2,V_h_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( ! [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)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min_Ohom__commute,axiom, % 169.19/169.59 ! [V_N_2,V_h_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( ! [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)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_minus__Min__eq__Max,axiom, % 169.19/169.59 ! [V_S_2,T_a] : % 169.19/169.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.59 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_minus__Max__eq__Min,axiom, % 169.19/169.59 ! [V_S_2,T_a] : % 169.19/169.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.59 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 169.19/169.59 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Min__eqI,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ! [B_y] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Osingleton,axiom, % 169.19/169.59 ! [V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max__ge,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max__in,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max__mono,axiom, % 169.19/169.59 ! [V_N_2,V_M_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 169.19/169.59 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.59 => 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))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oremove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max__eqI,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ! [B_y] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oeq__fold_H,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 169.19/169.59 ! [V_x,V_z,V_y,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__inf__distrib2,axiom, % 169.19/169.59 ! [V_x,V_z,V_y,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__inf__distrib1,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__sup__absorb,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__inf__absorb,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_sup__max,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( ( class_Lattices_Osemilattice__sup(T_a) % 169.19/169.59 & class_Orderings_Olinorder(T_a) ) % 169.19/169.59 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__diff__distrib__left,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Groups_Oordered__ab__group__add(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oidem,axiom, % 169.19/169.59 ! [V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__assoc,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup_Oassoc,axiom, % 169.19/169.59 ! [V_c,V_b,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__left__commute,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup_Oleft__commute,axiom, % 169.19/169.59 ! [V_c,V_a,V_b,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__left__idem,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup_Oleft__idem,axiom, % 169.19/169.59 ! [V_b,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__commute,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup_Ocommute,axiom, % 169.19/169.59 ! [V_b,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup_Oidem,axiom, % 169.19/169.59 ! [V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__Suc__Suc,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__0L,axiom, % 169.19/169.59 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__0R,axiom, % 169.19/169.59 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__supE,axiom, % 169.19/169.59 ! [V_x,V_b,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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)) % 169.19/169.59 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 169.19/169.59 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__mono,axiom, % 169.19/169.59 ! [V_d,V_b,V_c,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__least,axiom, % 169.19/169.59 ! [V_z,V_x,V_y,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__supI,axiom, % 169.19/169.59 ! [V_b,V_x,V_a,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__absorb1,axiom, % 169.19/169.59 ! [V_x,V_y,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__absorb2,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.19/169.59 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__supI2,axiom, % 169.19/169.59 ! [V_a,V_b,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__supI1,axiom, % 169.19/169.59 ! [V_b,V_a,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__sup__iff,axiom, % 169.19/169.59 ! [V_z_2,V_y_2,V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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)) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 169.19/169.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ole__iff__sup,axiom, % 169.19/169.59 ! [V_y_2,V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 169.19/169.59 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_le__maxI2,axiom, % 169.19/169.59 ! [V_x,V_y,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_le__maxI1,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_le__max__iff__disj,axiom, % 169.19/169.59 ! [V_y_2,V_x_2,V_z_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 169.19/169.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__add__distrib__left,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oless__supI2,axiom, % 169.19/169.59 ! [V_a,V_b,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oless__supI1,axiom, % 169.19/169.59 ! [V_b,V_a,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__less__iff__conj,axiom, % 169.19/169.59 ! [V_z_2,V_y_2,V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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)) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 169.19/169.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_less__max__iff__disj,axiom, % 169.19/169.59 ! [V_y_2,V_x_2,V_z_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( 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))) % 169.19/169.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 169.19/169.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__number__of,axiom, % 169.19/169.59 ! [V_v,V_u,T_b] : % 169.19/169.59 ( ( class_Int_Onumber(T_b) % 169.19/169.59 & class_Orderings_Oord(T_b) ) % 169.19/169.59 => ( ( 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))) % 169.19/169.59 => 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) ) % 169.19/169.59 & ( ~ 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))) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Odistrib__sup__le,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Odistrib__inf__le,axiom, % 169.19/169.59 ! [V_z,V_y,V_x,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_minus__max__eq__min,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_minus__min__eq__max,axiom, % 169.19/169.59 ! [V_y,V_x,T_a] : % 169.19/169.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_nat__minus__add__max,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ofold__sup__insert,axiom, % 169.19/169.59 ! [V_a_2,V_b_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oin__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__atLeastAtMost,axiom, % 169.19/169.59 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__atLeastLessThan,axiom, % 169.19/169.59 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__greaterThanAtMost,axiom, % 169.19/169.59 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__greaterThanLessThan,axiom, % 169.19/169.59 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__atLeastAtMostR2,axiom, % 169.19/169.59 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Int__atLeastAtMostL2,axiom, % 169.19/169.59 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_OF__eq,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__le__fold__sup,axiom, % 169.19/169.59 ! [V_b_2,V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max__insert,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Osubset__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Osup__Inf__absorb,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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 ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max__Un,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oeq__fold__idem_H,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oinsert,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oinsert__remove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_max__ord__max,axiom, % 169.19/169.59 ! [T_a] : % 169.19/169.59 ( class_Orderings_Oord(T_a) % 169.19/169.59 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Oclosed,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( ! [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)))))) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OInf__le__Sup,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oremove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_sup__nat__def,axiom, % 169.19/169.59 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 169.19/169.59 ! [V_x_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => 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 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.59 => 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 ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 169.19/169.59 ! [V_a_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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 ) % 169.19/169.59 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 169.19/169.59 => 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)))))) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 169.19/169.59 ! [V_B_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( 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)) % 169.19/169.59 => 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)) ) ) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.59 => 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) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 169.19/169.59 ! [V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => ( ! [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)))))) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 169.19/169.59 ! [V_N_2,V_h_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( ! [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)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_Max_Ohom__commute,axiom, % 169.19/169.59 ! [V_N_2,V_h_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( ! [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)) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 169.19/169.59 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 169.19/169.59 ( class_Orderings_Olinorder(T_a) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => ( ! [B_x] : % 169.19/169.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 169.19/169.59 => 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))) ) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_subtract__code__numeral__def,axiom, % 169.19/169.59 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.59 % 169.19/169.59 fof(fact_minus__code__numeral__code,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_pair__box_Osize_I1_J,axiom, % 169.19/169.59 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_b,T_a] : c_Nitpick_Opair__box_Opair__box__size(T_a,T_b,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_2,V_b_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(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_arith__series__int,axiom, % 169.19/169.59 ! [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)))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__abs,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__abs__ge__zero,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.19/169.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_sup__fun__def,axiom, % 169.19/169.59 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_sup__Un__eq,axiom, % 169.19/169.59 ! [V_x_2,V_S_2,V_R_2,T_a] : % 169.19/169.59 ( 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)) % 169.19/169.59 <=> 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))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inf__fun__def,axiom, % 169.19/169.59 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Lattices_Olattice(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inf__Int__eq,axiom, % 169.19/169.59 ! [V_x_2,V_S_2,V_R_2,T_a] : % 169.19/169.59 ( 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)) % 169.19/169.59 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_ran__empty,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__dividef,axiom, % 169.19/169.59 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Fields_Ofield__inverse__zero(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inj__fun,axiom, % 169.19/169.59 ! [T_c,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.59 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_range__composition,axiom, % 169.19/169.59 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inj__singleton,axiom, % 169.19/169.59 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_finite__range__imageI,axiom, % 169.19/169.59 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 169.19/169.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 169.19/169.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_pred__subset__eq,axiom, % 169.19/169.59 ! [V_S_2,V_R_2,T_a] : % 169.19/169.59 ( 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))) % 169.19/169.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__addf,axiom, % 169.19/169.59 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_of__int__setsum,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Rings_Oring__1(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__0,axiom, % 169.19/169.59 ! [V_A_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__negf,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Oab__group__add(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__divide__distrib,axiom, % 169.19/169.59 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Fields_Ofield(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_abs__setsum__abs,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.19/169.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__commute,axiom, % 169.19/169.59 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.59 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__right__distrib,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 169.19/169.59 ( class_Rings_Osemiring__0(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__left__distrib,axiom, % 169.19/169.59 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Rings_Osemiring__0(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__product,axiom, % 169.19/169.59 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Rings_Osemiring__0(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_int__setsum,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_image__image,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_image__ident,axiom, % 169.19/169.59 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 169.19/169.59 % 169.19/169.59 fof(fact_bot__fun__def,axiom, % 169.19/169.59 ! [V_x_2,T_b,T_a] : % 169.19/169.59 ( class_Orderings_Obot(T_a) % 169.19/169.59 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_bot__empty__eq,axiom, % 169.19/169.59 ! [V_x_2,T_a] : % 169.19/169.59 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 169.19/169.59 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_pred__equals__eq,axiom, % 169.19/169.59 ! [V_S_2,V_R_2,T_a] : % 169.19/169.59 ( 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) % 169.19/169.59 <=> V_R_2 = V_S_2 ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_map__comp__empty_I1_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_map__comp__empty_I2_J,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_map__comp__def,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_empty__upd__none,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_map__add__empty,axiom, % 169.19/169.59 ! [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 ). % 169.19/169.59 % 169.19/169.59 fof(fact_empty__map__add,axiom, % 169.19/169.59 ! [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 ). % 169.19/169.59 % 169.19/169.59 fof(fact_map__add__def,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_restrict__map__empty,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 169.19/169.59 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 169.19/169.59 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 169.19/169.59 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_pair__box_Oinject,axiom, % 169.19/169.59 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.59 ( c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a_H_2,V_b_H_2) % 169.19/169.59 <=> ( V_a_2 = V_a_H_2 % 169.19/169.59 & V_b_2 = V_b_H_2 ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fun__upd__def,axiom, % 169.19/169.59 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 169.19/169.59 ( ( V_x_2 = V_a_2 % 169.19/169.59 => 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 ) % 169.19/169.59 & ( V_x_2 != V_a_2 % 169.19/169.59 => 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) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fun__Compl__def,axiom, % 169.19/169.59 ! [V_x_2,V_A_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Ouminus(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_abs__setprod,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Fields_Olinordered__field(T_a) % 169.19/169.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__1,axiom, % 169.19/169.59 ! [V_A_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_a) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod__timesf,axiom, % 169.19/169.59 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_int__setprod,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_of__int__setprod,axiom, % 169.19/169.59 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 169.19/169.59 & class_Rings_Oring__1(T_a) ) % 169.19/169.59 => 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) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_fun__diff__def,axiom, % 169.19/169.59 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Ominus(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__subtractf,axiom, % 169.19/169.59 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.59 ( class_Groups_Oab__group__add(T_a) % 169.19/169.59 => 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)) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_less__eq__Suc__le__raw,axiom, % 169.19/169.59 ! [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)) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setprod_Odistrib,axiom, % 169.19/169.59 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => 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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum_Odistrib,axiom, % 169.19/169.59 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 169.19/169.59 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.59 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_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)) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_image__constant__conv,axiom, % 169.19/169.59 ! [V_ca_2,T_b,T_a,V_A_2] : % 169.19/169.59 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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)) ) % 169.19/169.59 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.59 => 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))) ) ) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inj__on__add__nat,axiom, % 169.19/169.59 ! [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) ). % 169.19/169.59 % 169.19/169.59 fof(fact_inj__on__id2,axiom, % 169.19/169.59 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 169.19/169.59 % 169.19/169.59 fof(fact_nat__number__of__Bit0,axiom, % 169.19/169.59 ! [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))) ). % 169.19/169.59 % 169.19/169.59 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 169.19/169.59 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 169.19/169.60 ! [V_A_2,V_f_2,T_a] : % 169.19/169.60 ( ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 & class_Groups_Ocomm__monoid__mult(T_a) ) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 169.19/169.60 ! [V_n_2,V_m_2,V_f_2,T_a] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_card__eq__setsum,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_map__upd__nonempty,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 169.19/169.60 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 169.19/169.60 ! [V_n_2,V_m_2,V_f_2,T_a] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_restrict__map__to__empty,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_of__nat__setsum,axiom, % 169.19/169.60 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.60 ( class_Rings_Osemiring__1(T_a) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_restrict__map__def,axiom, % 169.19/169.60 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 169.19/169.60 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.60 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_dom__const,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_dom__eq__empty__conv,axiom, % 169.19/169.60 ! [V_f_2,T_b,T_a] : % 169.19/169.60 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_dom__empty,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_fold__image__def,axiom, % 169.19/169.60 ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_of__nat__setprod,axiom, % 169.19/169.60 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.60 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 169.19/169.60 & class_Rings_Osemiring__1(T_a) ) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__add__atLeastAtMost,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__add__atLeastLessThan,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__delta_H,axiom, % 169.19/169.60 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__delta,axiom, % 169.19/169.60 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__constant,axiom, % 169.19/169.60 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setprod__delta_H,axiom, % 169.19/169.60 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setprod__delta,axiom, % 169.19/169.60 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__constant,axiom, % 169.19/169.60 ! [V_A_2,V_y_2,T_b,T_a] : % 169.19/169.60 ( class_Rings_Osemiring__1(T_a) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_power__number__of__even,axiom, % 169.19/169.60 ! [V_w_2,V_z_2,T_a] : % 169.19/169.60 ( class_Int_Onumber__ring(T_a) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_fold__image__distrib,axiom, % 169.19/169.60 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_dual__max,axiom, % 169.19/169.60 ! [T_a] : % 169.19/169.60 ( class_Orderings_Olinorder(T_a) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_dual__min,axiom, % 169.19/169.60 ! [T_a] : % 169.19/169.60 ( class_Orderings_Olinorder(T_a) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setprod__constant,axiom, % 169.19/169.60 ! [V_y_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_zpower__number__of__even,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__lessThan__Suc,axiom, % 169.19/169.60 ! [V_n_2,V_f_2,T_a] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__atMost__Suc,axiom, % 169.19/169.60 ! [V_n_2,V_f_2,T_a] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 169.19/169.60 ! [V_A_2,V_f_2,T_a] : % 169.19/169.60 ( ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 & class_Groups_Ocomm__monoid__mult(T_a) ) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__add__int__atLeastLessThan,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 169.19/169.60 ! [V_f_2,V_A_2,T_a] : % 169.19/169.60 ( ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 & class_Groups_Ocomm__monoid__mult(T_a) ) % 169.19/169.60 => ( c_Nat__Transfer_Onat__set(V_A_2) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Powp__Pow__eq,axiom, % 169.19/169.60 ! [V_x_2,V_A_2,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__restrict__set,axiom, % 169.19/169.60 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => 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) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__eq__fold__image,axiom, % 169.19/169.60 ! [V_f_2,T_b,V_A_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_power__number__of__even__number__of,axiom, % 169.19/169.60 ! [V_w_2,V_v_2,T_a] : % 169.19/169.60 ( class_Int_Onumber__ring(T_a) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_card__def,axiom, % 169.19/169.60 ! [V_A_2,T_a] : % 169.19/169.60 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_card_Oeq__fold__g,axiom, % 169.19/169.60 ! [V_A_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_fun__left__comm__idem__remove,axiom, % 169.19/169.60 ! [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))))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_diff__nat__eq__if,axiom, % 169.19/169.60 ! [V_z_2,V_z_H_2] : % 169.19/169.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 169.19/169.60 ! [V_f_2,V_A_2,T_a] : % 169.19/169.60 ( ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 & class_Groups_Ocomm__monoid__mult(T_a) ) % 169.19/169.60 => ( c_Nat__Transfer_Onat__set(V_A_2) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_LoopF,axiom, % 169.19/169.60 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_hoare__derivs_OBody,axiom, % 169.19/169.60 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 169.19/169.60 ( 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_G_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)) % 169.19/169.60 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__head,axiom, % 169.19/169.60 ! [V_P_2,V_n_2,V_m_2,T_a] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_minus__fold__remove,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),V_A_2) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Body__sound__lemma,axiom, % 169.19/169.60 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 169.19/169.60 ( 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_G_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)) % 169.19/169.60 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_dom__eq__singleton__conv,axiom, % 169.19/169.60 ! [V_x_2,V_f_2,T_b,T_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> ? [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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Suc__eq__number__of,axiom, % 169.19/169.60 ! [V_v_2,V_n_2] : % 169.19/169.60 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 169.19/169.60 <=> 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))))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_eq__number__of__Suc,axiom, % 169.19/169.60 ! [V_n_2,V_v_2] : % 169.19/169.60 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 169.19/169.60 <=> 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))))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__number__of__Bit1,axiom, % 169.19/169.60 ! [V_w_2] : % 169.19/169.60 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 169.19/169.60 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 169.19/169.60 => 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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_geometric__sum,axiom, % 169.19/169.60 ! [V_n_2,V_x_2,T_a] : % 169.19/169.60 ( class_Fields_Ofield(T_a) % 169.19/169.60 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_gauss__sum,axiom, % 169.19/169.60 ! [V_n_2,T_a] : % 169.19/169.60 ( class_Rings_Ocomm__semiring__1(T_a) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__natinterval__difff,axiom, % 169.19/169.60 ! [V_f_2,V_n_2,V_m_2,T_a] : % 169.19/169.60 ( class_Groups_Oab__group__add(T_a) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.60 => 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)))) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.60 => 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) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_less__number__of__Suc,axiom, % 169.19/169.60 ! [V_n_2,V_v_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> 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)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_less__Suc__number__of,axiom, % 169.19/169.60 ! [V_v_2,V_n_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> 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))))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_le__Suc__number__of,axiom, % 169.19/169.60 ! [V_v_2,V_n_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> 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))))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_le__number__of__Suc,axiom, % 169.19/169.60 ! [V_n_2,V_v_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> 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)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__Suc__number__of,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__number__of__Suc,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_power__number__of__odd,axiom, % 169.19/169.60 ! [V_z_2,V_w_2,T_a] : % 169.19/169.60 ( class_Int_Onumber__ring(T_a) % 169.19/169.60 => ( ( 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))) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( ~ 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))) % 169.19/169.60 => 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) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Body1,axiom, % 169.19/169.60 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 169.19/169.60 ( 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_G_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)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 169.19/169.60 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setprod__gen__delta,axiom, % 169.19/169.60 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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)))) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 169.19/169.60 => 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)) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 169.19/169.60 ! [V_x_2,V_y_2,V_ca_2] : % 169.19/169.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 169.19/169.60 => 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)) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_zpower__number__of__odd,axiom, % 169.19/169.60 ! [V_z_2,V_w_2] : % 169.19/169.60 ( ( 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))) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( ~ 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))) % 169.19/169.60 => 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) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_arith__series__general,axiom, % 169.19/169.60 ! [V_n_2,V_d_2,V_a_2,T_a] : % 169.19/169.60 ( class_Rings_Ocomm__semiring__1(T_a) % 169.19/169.60 => 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)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_min__Suc__number__of,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_min__number__of__Suc,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_arith__series__nat,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_power__number__of__odd__number__of,axiom, % 169.19/169.60 ! [V_v_2,V_w_2,T_a] : % 169.19/169.60 ( class_Int_Onumber__ring(T_a) % 169.19/169.60 => ( ( 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))) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( ~ 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))) % 169.19/169.60 => 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) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_diff__nat__number__of,axiom, % 169.19/169.60 ! [V_v_2,V_v_H_2] : % 169.19/169.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__case__add__eq__if,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__case__number__of,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__rec__add__eq__if,axiom, % 169.19/169.60 ! [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))))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 169.19/169.60 ! [V_n_2,T_a] : % 169.19/169.60 ( class_Rings_Osemiring__1(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__rec__0,axiom, % 169.19/169.60 ! [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 ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__rec__Suc,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__case__0,axiom, % 169.19/169.60 ! [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 ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__case__Suc,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 169.19/169.60 ! [V_i_2,V_inc_2,T_a] : % 169.19/169.60 ( class_Rings_Osemiring__1(T_a) % 169.19/169.60 => 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 ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 169.19/169.60 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 169.19/169.60 ( class_Rings_Osemiring__1(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__Suc2,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__Suc1,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 169.19/169.60 ! [V_n_2,V_m_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 169.19/169.60 <=> 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_diff__Suc,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_min__Suc1,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_min__Suc2,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__rec__number__of,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__box_Osize_I2_J,axiom, % 169.19/169.60 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__box_Osimps_I2_J,axiom, % 169.19/169.60 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__case(T_b,T_c,T_a,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__box_Orecs,axiom, % 169.19/169.60 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__rec(T_b,T_c,T_a,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 169.19/169.60 ! [V_f_2,V_A_2,T_a] : % 169.19/169.60 ( ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.60 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 169.19/169.60 ! [V_f_2,V_A_2,T_a] : % 169.19/169.60 ( ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.60 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_finite__pointwise,axiom, % 169.19/169.60 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_G_2,T_b,V_U_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 169.19/169.60 => ( ! [B_p] : % 169.19/169.60 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_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)))) % 169.19/169.60 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_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)))) ) % 169.19/169.60 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_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)) % 169.19/169.60 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_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)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_of__int__num,axiom, % 169.19/169.60 ! [V_k_2,T_a] : % 169.19/169.60 ( class_Rings_Oring__1(T_a) % 169.19/169.60 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 169.19/169.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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))))) ) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_adjust__eq,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__nonneg__0,axiom, % 169.19/169.60 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Oordered__ab__group__add(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 169.19/169.60 => ( ! [B_i] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 169.19/169.60 => ( 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) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 169.19/169.60 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_sup__Un__eq2,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inf__Int__eq2,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pred__subset__eq2,axiom, % 169.19/169.60 ! [V_S_2,V_R_2,T_b,T_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_bot__empty__eq2,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pred__equals__eq2,axiom, % 169.19/169.60 ! [V_S_2,V_R_2,T_b,T_a] : % 169.19/169.60 ( 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) % 169.19/169.60 <=> V_R_2 = V_S_2 ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__mod__div,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_adjust__def,axiom, % 169.19/169.60 ! [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))))))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Nitpick_OFrac__def,axiom, % 169.19/169.60 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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__imageI,axiom, % 169.19/169.60 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2)) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_norm__frac_Osimps,axiom, % 169.19/169.60 ! [V_a_2,V_b_2] : % 169.19/169.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.19/169.60 => 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))) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_sup2CI,axiom, % 169.19/169.60 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 169.19/169.60 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_sup2E,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inf2I,axiom, % 169.19/169.60 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inf2E,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 169.19/169.60 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mem__splitI,axiom, % 169.19/169.60 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_prod__caseI,axiom, % 169.19/169.60 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_splitI,axiom, % 169.19/169.60 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_bot2E,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_swap__inj__on,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_splitD_H,axiom, % 169.19/169.60 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_splitD,axiom, % 169.19/169.60 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_predicate2D,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_rev__predicate2D,axiom, % 169.19/169.60 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_less__by__empty,axiom, % 169.19/169.60 ! [V_B_2,T_a,V_A_2] : % 169.19/169.60 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inf2D1,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inf2D2,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_sup2I2,axiom, % 169.19/169.60 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_sup2I1,axiom, % 169.19/169.60 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__paired__All,axiom, % 169.19/169.60 ! [T_b,T_a,V_P_2] : % 169.19/169.60 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.19/169.60 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Pair__eq,axiom, % 169.19/169.60 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.60 ( 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) % 169.19/169.60 <=> ( V_a_2 = V_a_H_2 % 169.19/169.60 & V_b_2 = V_b_H_2 ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Pair__inject,axiom, % 169.19/169.60 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 169.19/169.60 ( 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) % 169.19/169.60 => ~ ( V_a = V_a_H % 169.19/169.60 => V_b != V_b_H ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__weak__cong,axiom, % 169.19/169.60 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 169.19/169.60 ( V_p_2 = V_q_2 % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__twice,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__conv,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_prod_Osimps_I2_J,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__eta,axiom, % 169.19/169.60 ! [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 ). % 169.19/169.60 % 169.19/169.60 fof(fact_in__rel__def,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__mod__code__numeral__def,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 169.19/169.60 ! [V_w] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( 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)))) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( ~ 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)))) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg__div__mod,axiom, % 169.19/169.60 ! [V_l,V_k] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg__minus1,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg_Osimps,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( ( ( 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))) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ ( 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))) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg__eqn__number__of,axiom, % 169.19/169.60 ! [V_w,V_v] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( 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)))) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( ~ 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)))) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg__eqn,axiom, % 169.19/169.60 ! [V_a,V_b] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => ( ( 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))) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ 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))) % 169.19/169.60 => 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))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Nitpick_Orefl_H__def,axiom, % 169.19/169.60 ! [V_r_2,T_a] : % 169.19/169.60 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 169.19/169.60 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 169.19/169.60 ! [V_w] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( 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))) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ 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))) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg_Osimps,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg__0,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg__div__mod,axiom, % 169.19/169.60 ! [V_l,V_k] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg__eqn,axiom, % 169.19/169.60 ! [V_a,V_b] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 169.19/169.60 => 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))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg__eqn__number__of,axiom, % 169.19/169.60 ! [V_w,V_v] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( 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))) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ 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))) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__def,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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))) ) ) ) ) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => 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))) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__step,axiom, % 169.19/169.60 ! [V_m,V_n] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__pdivmod,axiom, % 169.19/169.60 ! [V_l_2,V_k_2] : % 169.19/169.60 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)))) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negateSnd__def,axiom, % 169.19/169.60 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_apsnd__conv,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__zero,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__base,axiom, % 169.19/169.60 ! [V_n,V_m] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negateSnd__eq,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__div__mod,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__if,axiom, % 169.19/169.60 ! [V_m_2,V_n_2] : % 169.19/169.60 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pdivmod__def,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pdivmod__posDivAlg,axiom, % 169.19/169.60 ! [V_k,V_l] : % 169.19/169.60 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__code,axiom, % 169.19/169.60 ! [V_l_2,V_k_2] : % 169.19/169.60 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)))) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 169.19/169.60 ! [V_a,V_r,V_q,V_c,V_b] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 169.19/169.60 => 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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 169.19/169.60 ! [V_c,V_r,V_q,V_b,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg_Opsimps,axiom, % 169.19/169.60 ! [V_b_2,V_a_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( ( 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))) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ ( 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))) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__rel__unique,axiom, % 169.19/169.60 ! [V_qr_H,V_qr,V_n,V_m] : % 169.19/169.60 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 169.19/169.60 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 169.19/169.60 => V_qr = V_qr_H ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_accp__downward,axiom, % 169.19/169.60 ! [V_a_2,V_b_2,V_r_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 169.19/169.60 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_accp_Oequations,axiom, % 169.19/169.60 ! [V_a_2,V_r_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 169.19/169.60 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_accp_Osimps,axiom, % 169.19/169.60 ! [V_a_2,V_r_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 169.19/169.60 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__eq,axiom, % 169.19/169.60 ! [V_qr,V_n,V_m] : % 169.19/169.60 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 169.19/169.60 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 169.19/169.60 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_accp__subset,axiom, % 169.19/169.60 ! [V_R2_2,V_R1_2,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__eq,axiom, % 169.19/169.60 ! [V_r,V_q,V_n,V_m] : % 169.19/169.60 ( 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))) % 169.19/169.60 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__eq,axiom, % 169.19/169.60 ! [V_r,V_q,V_n,V_m] : % 169.19/169.60 ( 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))) % 169.19/169.60 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__rel,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__rel__add1__eq,axiom, % 169.19/169.60 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( 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))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg_Opsimps,axiom, % 169.19/169.60 ! [V_b_2,V_a_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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) ) % 169.19/169.60 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_norm__frac_Opsimps,axiom, % 169.19/169.60 ! [V_b_2,V_a_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 169.19/169.60 => 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))) ) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg_Opinduct,axiom, % 169.19/169.60 ! [V_P_2,V_a1_2,V_a0_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ! [B_a,B_b] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( ~ ( 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))) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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))) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg_Opinduct,axiom, % 169.19/169.60 ! [V_P_2,V_a1_2,V_a0_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ! [B_a,B_b] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 169.19/169.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 169.19/169.60 => 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))) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__gcd_Opsimps,axiom, % 169.19/169.60 ! [V_y_2,V_x_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.60 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 169.19/169.60 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.60 => 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)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_zmult2__lemma,axiom, % 169.19/169.60 ! [V_c,V_r,V_q,V_b,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_unique__remainder,axiom, % 169.19/169.60 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( 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))) % 169.19/169.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => V_r = V_r_H ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_unique__quotient,axiom, % 169.19/169.60 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( 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))) % 169.19/169.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => V_q = V_q_H ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_self__remainder,axiom, % 169.19/169.60 ! [V_r,V_q,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__rel__0,axiom, % 169.19/169.60 ! [V_b] : % 169.19/169.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__rel__neg,axiom, % 169.19/169.60 ! [V_qr,V_b,V_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__correct,axiom, % 169.19/169.60 ! [V_a,V_b] : % 169.19/169.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_self__quotient,axiom, % 169.19/169.60 ! [V_r,V_q,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__rel__mod,axiom, % 169.19/169.60 ! [V_r,V_q,V_b,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__rel__div,axiom, % 169.19/169.60 ! [V_r,V_q,V_b,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_negDivAlg__correct,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__rel__div__mod,axiom, % 169.19/169.60 ! [V_a,V_b] : % 169.19/169.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_posDivAlg__correct,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_zadd1__lemma,axiom, % 169.19/169.60 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( 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))) % 169.19/169.60 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_zminus1__lemma,axiom, % 169.19/169.60 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => 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))))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__relI,axiom, % 169.19/169.60 ! [V_r,V_q,V_b,V_a] : % 169.19/169.60 ( 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) % 169.19/169.60 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 169.19/169.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 169.19/169.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_zmult1__lemma,axiom, % 169.19/169.60 ! [V_a,V_r,V_q,V_c,V_b] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 169.19/169.60 => 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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__int__rel__def,axiom, % 169.19/169.60 ! [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))))))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__pos__neg__1__number__of,axiom, % 169.19/169.60 ! [V_w] : % 169.19/169.60 ( 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))) % 169.19/169.60 => 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))))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_in__measure,axiom, % 169.19/169.60 ! [V_f_2,V_y_2,V_x_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))) % 169.19/169.60 <=> 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_norm__frac_Opinduct,axiom, % 169.19/169.60 ! [V_P_2,V_a1_2,V_a0_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ! [B_a,B_b] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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))) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_snd__apsnd,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_apsnd__eq__conv,axiom, % 169.19/169.60 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 169.19/169.60 ( 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) % 169.19/169.60 <=> 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_snd__def,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_snd__eqD,axiom, % 169.19/169.60 ! [V_a,V_y,V_x,T_a,T_b] : % 169.19/169.60 ( 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 % 169.19/169.60 => V_y = V_a ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_snd__conv,axiom, % 169.19/169.60 ! [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 ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__int__def,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__neg__pos,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__pos__pos,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__pos__pos__1__number__of,axiom, % 169.19/169.60 ! [V_w] : % 169.19/169.60 ( 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))) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__pos__neg,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__neg__neg,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__pos__neg__1__number__of,axiom, % 169.19/169.60 ! [V_w] : % 169.19/169.60 ( 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))) % 169.19/169.60 => 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))))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__gcd_Opinduct,axiom, % 169.19/169.60 ! [V_P_2,V_a1_2,V_a0_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ! [B_x,B_y] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mlex__leq,axiom, % 169.19/169.60 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Pair__fst__snd__eq,axiom, % 169.19/169.60 ! [T_b,T_a,V_t_2,V_s_2] : % 169.19/169.60 ( V_s_2 = V_t_2 % 169.19/169.60 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 169.19/169.60 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_prod__eqI,axiom, % 169.19/169.60 ! [V_q,V_p,T_b,T_a] : % 169.19/169.60 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 169.19/169.60 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 169.19/169.60 => V_p = V_q ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_fst__conv,axiom, % 169.19/169.60 ! [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 ). % 169.19/169.60 % 169.19/169.60 fof(fact_fst__eqD,axiom, % 169.19/169.60 ! [V_a,V_y,V_x,T_b,T_a] : % 169.19/169.60 ( 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 % 169.19/169.60 => V_x = V_a ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_fst__def,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_fst__apsnd,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_surjective__pairing,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__collapse,axiom, % 169.19/169.60 ! [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 ). % 169.19/169.60 % 169.19/169.60 fof(fact_prod__case__beta,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__int__def,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mod__nat__def,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__beta,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__comp__eq,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_split__def,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__neg__pos,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__pos__pos,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__pos__pos__1__number__of,axiom, % 169.19/169.60 ! [V_w] : % 169.19/169.60 ( 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))) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__pos__neg,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__neg__neg,axiom, % 169.19/169.60 ! [V_b,V_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 169.19/169.60 => 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)))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mlex__less,axiom, % 169.19/169.60 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 169.19/169.60 ( 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))) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_prod__size__simp,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_exI__realizer,axiom, % 169.19/169.60 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 169.19/169.60 => 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)))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_conjI__realizer,axiom, % 169.19/169.60 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 169.19/169.60 ( hBOOL(hAPP(V_P_2,V_p_2)) % 169.19/169.60 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 169.19/169.60 => ( 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)))) % 169.19/169.60 & 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)))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_div__nat__def,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_divmod__nat__rel__def,axiom, % 169.19/169.60 ! [V_qr_2,V_n_2,V_m_2] : % 169.19/169.60 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 169.19/169.60 <=> ( 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)) % 169.19/169.60 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.60 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 169.19/169.60 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 169.19/169.60 => ( 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))) % 169.19/169.60 & 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)) ) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 169.19/169.60 => ( 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))) % 169.19/169.60 & 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))) ) ) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_range,axiom, % 169.19/169.60 ! [V_s,V_k] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_prod_Orecs,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_map__add__map__of__foldr,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_in__lex__prod,axiom, % 169.19/169.60 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2)) % 169.19/169.60 | ( V_a_2 = V_a_H_2 % 169.19/169.60 & 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)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_in__finite__psubset,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) % 169.19/169.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.60 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_setsum__nonneg__leq__bound,axiom, % 169.19/169.60 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 169.19/169.60 ( class_Groups_Oordered__ab__group__add(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 169.19/169.60 => ( ! [B_i] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 169.19/169.60 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_same__fstI,axiom, % 169.19/169.60 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 169.19/169.60 ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.60 => ( 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))) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_sum__diff__distrib,axiom, % 169.19/169.60 ! [V_n_2,V_P_2,V_Q_2] : % 169.19/169.60 ( ! [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))) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_full__small__int__def,axiom, % 169.19/169.60 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_small_H_Osimps,axiom, % 169.19/169.60 ! [V_f_2,V_i_2,V_d_2] : % 169.19/169.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 169.19/169.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 169.19/169.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_apsnd__apfst,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_apfst__eq__conv,axiom, % 169.19/169.60 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 169.19/169.60 ( 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) % 169.19/169.60 <=> 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_fst__apfst,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_apfst__conv,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_snd__apfst,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_apsnd__apfst__commute,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_apfst__apsnd,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_small_H_Opsimps,axiom, % 169.19/169.60 ! [V_i_2,V_d_2,V_f_2] : % 169.19/169.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))) % 169.19/169.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 169.19/169.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 169.19/169.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 169.19/169.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_small__int__def,axiom, % 169.19/169.60 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__lessI2,axiom, % 169.19/169.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_small__prod__def,axiom, % 169.19/169.60 ! [V_d_2,V_f_2,T_a,T_b] : % 169.19/169.60 ( ( class_Smallcheck_Osmall(T_b) % 169.19/169.60 & class_Smallcheck_Osmall(T_a) ) % 169.19/169.60 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__lessI1,axiom, % 169.19/169.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_small_H_Opinduct,axiom, % 169.19/169.60 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 169.19/169.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2)))) % 169.19/169.60 => ( ! [B_f,B_d,B_i] : % 169.19/169.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))) % 169.19/169.60 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 169.19/169.60 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 169.19/169.60 => 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)))) ) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 169.19/169.60 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__leqI2,axiom, % 169.19/169.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_smin__insertI,axiom, % 169.19/169.60 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => 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)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_smin__emptyI,axiom, % 169.19/169.60 ! [V_X_2] : % 169.19/169.60 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__leqI1,axiom, % 169.19/169.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_wmax__insertI,axiom, % 169.19/169.60 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => 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)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_wmin__insertI,axiom, % 169.19/169.60 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => 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)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_smax__insertI,axiom, % 169.19/169.60 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => ( 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)) % 169.19/169.60 => 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)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_wmin__emptyI,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_wmax__emptyI,axiom, % 169.19/169.60 ! [V_X_2] : % 169.19/169.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_smax__emptyI,axiom, % 169.19/169.60 ! [V_Y_2] : % 169.19/169.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 169.19/169.60 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_min__weak__def,axiom, % 169.19/169.60 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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__weak__def,axiom, % 169.19/169.60 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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__rpair__set,axiom, % 169.19/169.60 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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__strict__def,axiom, % 169.19/169.60 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__ext__additive,axiom, % 169.19/169.60 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_min__strict__def,axiom, % 169.19/169.60 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 169.19/169.60 % 169.19/169.60 fof(fact_min__rpair__set,axiom, % 169.19/169.60 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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_max__extp__max__ext__eq,axiom, % 169.19/169.60 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 169.19/169.60 ( 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) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_less__than__iff,axiom, % 169.19/169.60 ! [V_y_2,V_x_2] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_intrel__iff,axiom, % 169.19/169.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_pair__less__def,axiom, % 169.19/169.60 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 169.19/169.60 % 169.19/169.60 fof(fact_mlex__prod__def,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_rp__inv__image__rp,axiom, % 169.19/169.60 ! [V_f_2,T_b,V_P_2,T_a] : % 169.19/169.60 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 169.19/169.60 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INFI__fold__inf,axiom, % 169.19/169.60 ! [V_f_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__D,axiom, % 169.19/169.60 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__E,axiom, % 169.19/169.60 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 169.19/169.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 169.19/169.60 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF1__D,axiom, % 169.19/169.60 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF1__E,axiom, % 169.19/169.60 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 169.19/169.60 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 169.19/169.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF2__E,axiom, % 169.19/169.60 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 169.19/169.60 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 169.19/169.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF2__D,axiom, % 169.19/169.60 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_finite__INT,axiom, % 169.19/169.60 ! [V_A_2,T_b,V_I_2,T_a] : % 169.19/169.60 ( ? [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 169.19/169.60 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 169.19/169.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Pow__INT__eq,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF__commute,axiom, % 169.19/169.60 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INFI__apply,axiom, % 169.19/169.60 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I8_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I8_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Inter__def,axiom, % 169.19/169.60 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I10_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I10_J,axiom, % 169.19/169.60 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__subset__iff,axiom, % 169.19/169.60 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__Int__distrib,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__iff,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF__INT__eq2,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I5_J,axiom, % 169.19/169.60 ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I5_J,axiom, % 169.19/169.60 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I7_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I6_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I7_J,axiom, % 169.19/169.60 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Un__INT__distrib,axiom, % 169.19/169.60 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I6_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Un__INT__distrib2,axiom, % 169.19/169.60 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_le__INF__iff,axiom, % 169.19/169.60 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2))) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF__less__iff,axiom, % 169.19/169.60 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 & class_Orderings_Olinorder(T_a) ) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2)) % 169.19/169.60 <=> ? [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__insert__distrib,axiom, % 169.19/169.60 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__lower,axiom, % 169.19/169.60 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF__INT__eq,axiom, % 169.19/169.60 ! [V_x_2,V_r_2,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__absorb,axiom, % 169.19/169.60 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 169.19/169.60 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF__const,axiom, % 169.19/169.60 ! [V_M_2,T_a,V_A_2,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__constant,axiom, % 169.19/169.60 ! [V_ca_2,T_b,T_a,V_A_2] : % 169.19/169.60 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 169.19/169.60 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__empty,axiom, % 169.19/169.60 ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I1_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I2_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__insert,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__Un,axiom, % 169.19/169.60 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Un__Inter,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_rp__inv__image__def,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Inter__image__eq,axiom, % 169.19/169.60 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INTER__eq__Inter__image,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF__subset,axiom, % 169.19/169.60 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I2_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I1_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I3_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I3_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF__leI,axiom, % 169.19/169.60 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Int__Inter__image,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__greaterThan__UNIV,axiom, % 169.19/169.60 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inf__INFI__fold__inf,axiom, % 169.19/169.60 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_in__inv__image,axiom, % 169.19/169.60 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2))) % 169.19/169.60 <=> 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUPR__fold__sup,axiom, % 169.19/169.60 ! [V_f_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_map__of__mapk__SomeI,axiom, % 169.19/169.60 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 169.19/169.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.60 => ( 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) % 169.19/169.60 => 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) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP1__I,axiom, % 169.19/169.60 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__I,axiom, % 169.19/169.60 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP2__I,axiom, % 169.19/169.60 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inj__mapI,axiom, % 169.19/169.60 ! [V_f_2,T_b,T_a] : % 169.19/169.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF1__iff,axiom, % 169.19/169.60 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INF2__iff,axiom, % 169.19/169.60 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I7_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I7_J,axiom, % 169.19/169.60 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I9_J,axiom, % 169.19/169.60 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I9_J,axiom, % 169.19/169.60 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Compl__UN,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Compl__INT,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP__UN__eq2,axiom, % 169.19/169.60 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UNION__empty__conv_I1_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( 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) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__empty2,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__constant,axiom, % 169.19/169.60 ! [V_ca_2,T_b,T_a,V_A_2] : % 169.19/169.60 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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 ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UNION__empty__conv_I2_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_finite__UN,axiom, % 169.19/169.60 ! [V_B_2,T_b,V_A_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__Un,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__Un__distrib,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__iff,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> ? [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Int__UN__distrib2,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I4_J,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Int__UN__distrib,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I5_J,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I4_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I5_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__Pow__subset,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__subset__iff,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I10_J,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__UN,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I10_J,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Union__def,axiom, % 169.19/169.60 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I8_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I8_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUPR__apply,axiom, % 169.19/169.60 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP__commute,axiom, % 169.19/169.60 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I6_J,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I6_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_map__ident,axiom, % 169.19/169.60 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 169.19/169.60 % 169.19/169.60 fof(fact_map__injective,axiom, % 169.19/169.60 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.60 ( 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) % 169.19/169.60 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 169.19/169.60 => V_xs_2 = V_ys_2 ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inj__mapD,axiom, % 169.19/169.60 ! [V_f_2,T_b,T_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inj__map__eq__map,axiom, % 169.19/169.60 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.60 => ( 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) % 169.19/169.60 <=> V_xs_2 = V_ys_2 ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_inj__map,axiom, % 169.19/169.60 ! [V_f_2,T_b,T_a] : % 169.19/169.60 ( 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))) % 169.19/169.60 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP__le__iff,axiom, % 169.19/169.60 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 => ( 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)) % 169.19/169.60 <=> ! [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_less__SUP__iff,axiom, % 169.19/169.60 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 169.19/169.60 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.60 & class_Orderings_Olinorder(T_a) ) % 169.19/169.60 => ( 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))) % 169.19/169.60 <=> ? [B_x] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP__const,axiom, % 169.19/169.60 ! [V_M_2,T_a,V_A_2,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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 ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__insert__distrib,axiom, % 169.19/169.60 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 169.19/169.60 => 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)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__upper,axiom, % 169.19/169.60 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.60 => 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP__UN__eq,axiom, % 169.19/169.60 ! [V_x_2,V_r_2,T_b,T_a] : % 169.19/169.60 ( 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)) % 169.19/169.60 <=> 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))) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__absorb,axiom, % 169.19/169.60 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 169.19/169.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 169.19/169.60 => 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) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I1_J,axiom, % 169.19/169.60 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__singleton,axiom, % 169.19/169.60 ! [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 ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I1_J,axiom, % 169.19/169.60 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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))) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I3_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I2_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I3_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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 ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I2_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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 ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => 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)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__insert,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__extend__simps_I4_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__Union,axiom, % 169.19/169.60 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Int__Union2,axiom, % 169.19/169.60 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Int__Union,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Union__image__eq,axiom, % 169.19/169.60 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UNION__eq__Union__image,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__lessThan__UNIV,axiom, % 169.19/169.60 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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__atMost__UNIV,axiom, % 169.19/169.60 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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__atLeast__UNIV,axiom, % 169.19/169.60 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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_SUP__subset,axiom, % 169.19/169.60 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_image__eq__UN,axiom, % 169.19/169.60 ! [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)))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_INT__simps_I4_J,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 169.19/169.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 169.19/169.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__UN__finite__eq,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_le__SUPI,axiom, % 169.19/169.60 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 169.19/169.60 => 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))) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Un__Union__image,axiom, % 169.19/169.60 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__le__add__shift,axiom, % 169.19/169.60 ! [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) ). % 169.19/169.60 % 169.19/169.60 fof(fact_sup__SUPR__fold__sup,axiom, % 169.19/169.60 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 169.19/169.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 169.19/169.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.60 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__le__eq__Un0,axiom, % 169.19/169.60 ! [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))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_measure__def,axiom, % 169.19/169.60 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 169.19/169.60 % 169.19/169.60 fof(fact_irrefl__def,axiom, % 169.19/169.60 ! [V_r_2,T_a] : % 169.19/169.60 ( c_Relation_Oirrefl(T_a,V_r_2) % 169.19/169.60 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 169.19/169.60 % 169.19/169.60 fof(fact_nat__def,axiom, % 169.19/169.60 ! [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)))))) ). % 169.19/169.60 % 169.19/169.60 fof(fact_Field__insert,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__UN__flatten,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__simps_I9_J,axiom, % 169.19/169.60 ! [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)) ). % 169.19/169.60 % 169.19/169.60 fof(fact_UN__extend__simps_I9_J,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_SUP2__iff,axiom, % 169.19/169.61 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 169.19/169.61 ( 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)) % 169.19/169.61 <=> ? [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.61 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_SUP1__iff,axiom, % 169.19/169.61 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.61 ( 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)) % 169.19/169.61 <=> ? [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.61 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_ball__UN,axiom, % 169.19/169.61 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 169.19/169.61 ( ! [B_x] : % 169.19/169.61 ( 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))) % 169.19/169.61 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.61 <=> ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.61 => ! [B_xa] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 169.19/169.61 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Rep__Integ__inject,axiom, % 169.19/169.61 ! [V_y_2,V_x_2] : % 169.19/169.61 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 169.19/169.61 <=> V_x_2 = V_y_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_infinite__UNIV__listI,axiom, % 169.19/169.61 ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Field__Union,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Field__empty,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_mono__Field,axiom, % 169.19/169.61 ! [V_s_2,V_r_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 169.19/169.61 => 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))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Field__Un,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Field,axiom, % 169.19/169.61 ! [V_r_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 169.19/169.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__finite2__subset,axiom, % 169.19/169.61 ! [V_B_2,V_k_2,V_A_2,T_a] : % 169.19/169.61 ( ! [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))) % 169.19/169.61 => 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))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__finite2__eq,axiom, % 169.19/169.61 ! [V_B_2,V_k_2,V_A_2,T_a] : % 169.19/169.61 ( ! [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) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__finite__subset,axiom, % 169.19/169.61 ! [V_C_2,V_A_2,T_a] : % 169.19/169.61 ( ! [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)) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Id__on__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_image__INT,axiom, % 169.19/169.61 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 169.19/169.61 => 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)) ) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equiv__intrel__iff,axiom, % 169.19/169.61 ! [V_y_2,V_x_2] : % 169.19/169.61 ( 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)))) % 169.19/169.61 <=> 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__empty,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__Un,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__Id__on,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__UN,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__Int__subset,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__mono,axiom, % 169.19/169.61 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 169.19/169.61 ( 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)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 169.19/169.61 => 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))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Un__Image,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Id__on__def_H,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__INT__subset,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__iff,axiom, % 169.19/169.61 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 169.19/169.61 <=> ? [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 169.19/169.61 & 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_rev__ImageI,axiom, % 169.19/169.61 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => ( 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)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Id__on__empty,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__eq__UN,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Id__on__eqI,axiom, % 169.19/169.61 ! [V_A_2,T_a,V_b_2,V_a_2] : % 169.19/169.61 ( V_a_2 = V_b_2 % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Id__on__iff,axiom, % 169.19/169.61 ! [V_A_2,V_y_2,V_x_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2))) % 169.19/169.61 <=> ( V_x_2 = V_y_2 % 169.19/169.61 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__singleton__iff,axiom, % 169.19/169.61 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 169.19/169.61 ( 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)))))) % 169.19/169.61 <=> 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_of__int,axiom, % 169.19/169.61 ! [V_j_2,V_i_2,T_a] : % 169.19/169.61 ( class_Rings_Oring__1(T_a) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_One__int__def,axiom, % 169.19/169.61 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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_mult,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Rep__Integ__inverse,axiom, % 169.19/169.61 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 169.19/169.61 % 169.19/169.61 fof(fact_minus,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Zero__int__def,axiom, % 169.19/169.61 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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_int__def,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_add,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nat,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_minus__int__def,axiom, % 169.19/169.61 ! [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))))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_less,axiom, % 169.19/169.61 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 169.19/169.61 ( 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))))))) % 169.19/169.61 <=> 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))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_le,axiom, % 169.19/169.61 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 169.19/169.61 ( 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))))))) % 169.19/169.61 <=> 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))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_eq__Abs__Integ,axiom, % 169.19/169.61 ! [V_z_2] : % 169.19/169.61 ~ ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Id__onE,axiom, % 169.19/169.61 ! [V_A_2,V_ca_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 169.19/169.61 => ~ ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.61 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__is__empty,axiom, % 169.19/169.61 ! [V_r_2,V_A_2,T_a] : % 169.19/169.61 ( 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)) % 169.19/169.61 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__is__empty2,axiom, % 169.19/169.61 ! [V_r_2,V_A_2,T_a] : % 169.19/169.61 ( 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) % 169.19/169.61 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__empty,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__diff1,axiom, % 169.19/169.61 ! [V_a_2,V_A_2,V_r_2,T_a] : % 169.19/169.61 ( 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) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotientI,axiom, % 169.19/169.61 ! [V_r_2,V_A_2,V_x_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 => 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))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_singleton__quotient,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_card__quotient__disjoint,axiom, % 169.19/169.61 ! [V_r_2,V_A_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( 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) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equiv__class__nondisjoint,axiom, % 169.19/169.61 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( 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))))))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_subset__equiv__class,axiom, % 169.19/169.61 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( 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)))))) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotientE,axiom, % 169.19/169.61 ! [V_r_2,V_A_2,V_X_2,T_a] : % 169.19/169.61 ( 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))) % 169.19/169.61 => ~ ! [B_x] : % 169.19/169.61 ( 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)))) % 169.19/169.61 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equiv__intrel,axiom, % 169.19/169.61 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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Union__quotient,axiom, % 169.19/169.61 ! [V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => 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 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equiv__class__self,axiom, % 169.19/169.61 ! [V_a_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => 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)))))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__disj,axiom, % 169.19/169.61 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( V_X_2 = V_Y_2 % 169.19/169.61 | 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)) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equiv__class__eq,axiom, % 169.19/169.61 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 169.19/169.61 => 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)))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__eq__iff,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 169.19/169.61 => ( V_X_2 = V_Y_2 % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_quotient__eqI,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.61 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_eq__equiv__class,axiom, % 169.19/169.61 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 169.19/169.61 ( 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)))) % 169.19/169.61 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_eq__equiv__class__iff,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 169.19/169.61 => ( 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)))) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equiv__class__eq__iff,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.61 <=> ( 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)))) % 169.19/169.61 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equiv__class__subset,axiom, % 169.19/169.61 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 169.19/169.61 => 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)))))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_eq__equiv__class__iff2,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 169.19/169.61 => ( 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) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__equiv__class2,axiom, % 169.19/169.61 ! [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] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 169.19/169.61 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 169.19/169.61 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 169.19/169.61 => 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) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__equiv__class,axiom, % 169.19/169.61 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equivp__equiv,axiom, % 169.19/169.61 ! [V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 169.19/169.61 <=> 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_identity__equivp,axiom, % 169.19/169.61 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equivp__def,axiom, % 169.19/169.61 ! [V_R_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 169.19/169.61 <=> ! [B_x,B_y] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 169.19/169.61 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equivp__reflp,axiom, % 169.19/169.61 ! [V_x_2,V_R_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 169.19/169.61 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equivp__symp,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_R_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_equivp__transp,axiom, % 169.19/169.61 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_congruent2__implies__congruent,axiom, % 169.19/169.61 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 169.19/169.61 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_congruent2D,axiom, % 169.19/169.61 ! [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] : % 169.19/169.61 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 169.19/169.61 => ( 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)) % 169.19/169.61 => ( 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)) % 169.19/169.61 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_congruentD,axiom, % 169.19/169.61 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2)) % 169.19/169.61 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_congruent2__implies__congruent__UN,axiom, % 169.19/169.61 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 169.19/169.61 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 169.19/169.61 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 169.19/169.61 => 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)) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__equiv__class__inject,axiom, % 169.19/169.61 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 169.19/169.61 => ( 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) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.61 => ! [B_y] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 169.19/169.61 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) ) % 169.19/169.61 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__equiv__class__type2,axiom, % 169.19/169.61 ! [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] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 169.19/169.61 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 169.19/169.61 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( ! [B_x1] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 169.19/169.61 => ! [B_x2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 169.19/169.61 => 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)) ) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__equiv__class__type,axiom, % 169.19/169.61 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 169.19/169.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.61 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 169.19/169.61 => ( 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))) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 169.19/169.61 => 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)) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Integ__def,axiom, % 169.19/169.61 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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_ImageE,axiom, % 169.19/169.61 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 169.19/169.61 => ~ ! [B_x] : % 169.19/169.61 ( 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)) % 169.19/169.61 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_escape,axiom, % 169.19/169.61 ! [V_Q_2,V_ca_2,V_G_2,T_a,V_P_2] : % 169.19/169.61 ( ! [B_Z,B_s] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 169.19/169.61 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) % 169.19/169.61 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Rep__Integ,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition__Integ,axiom, % 169.19/169.61 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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__map__keys,axiom, % 169.19/169.61 ! [V_m_2,T_b,V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 169.19/169.61 => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 169.19/169.61 ( ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.61 & class_Groups_Ocomm__monoid__mult(T_a) ) % 169.19/169.61 => ( V_A_2 = V_B_2 % 169.19/169.61 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 169.19/169.61 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 169.19/169.61 => 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) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__set,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__eq__conv,axiom, % 169.19/169.61 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2) % 169.19/169.61 <=> ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 169.19/169.61 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__map,axiom, % 169.19/169.61 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inj__on__map__eq__map,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 169.19/169.61 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 169.19/169.61 <=> V_xs_2 = V_ys_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__inj__on,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 169.19/169.61 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) % 169.19/169.61 => V_xs_2 = V_ys_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__fun__upd,axiom, % 169.19/169.61 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 169.19/169.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__eq__dom,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,T_b,T_a] : % 169.19/169.61 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 169.19/169.61 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__SomeD,axiom, % 169.19/169.61 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__is__SomeD,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_dom__map__of__conv__image__fst,axiom, % 169.19/169.61 ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inj__on__mapI,axiom, % 169.19/169.61 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2))) % 169.19/169.61 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__eq__None__iff,axiom, % 169.19/169.61 ! [V_x_2,V_xys_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 169.19/169.61 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition_OAbs__image,axiom, % 169.19/169.61 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 169.19/169.61 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition_ORep__range,axiom, % 169.19/169.61 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 169.19/169.61 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 169.19/169.61 => 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 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition_OAbs__inject,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 169.19/169.61 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 169.19/169.61 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 169.19/169.61 <=> V_x_2 = V_y_2 ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition_ORep__inject,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 169.19/169.61 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 169.19/169.61 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 169.19/169.61 <=> V_x_2 = V_y_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition_ORep__inverse,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 169.19/169.61 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 169.19/169.61 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition_ORep,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 169.19/169.61 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition_OAbs__inverse,axiom, % 169.19/169.61 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 169.19/169.61 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 169.19/169.61 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_ran__distinct,axiom, % 169.19/169.61 ! [V_al_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2))) % 169.19/169.61 => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Some__eq__map__of__iff,axiom, % 169.19/169.61 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 169.19/169.61 => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__eq__Some__iff,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 169.19/169.61 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__map,axiom, % 169.19/169.61 ! [V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 169.19/169.61 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 169.19/169.61 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__inject__set,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 169.19/169.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))) % 169.19/169.61 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 169.19/169.61 <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__is__SomeI,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) % 169.19/169.61 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__map__of__compr,axiom, % 169.19/169.61 ! [V_xs_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 169.19/169.61 => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_greaterThanLessThan__upto,axiom, % 169.19/169.61 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_weak__map__of__SomeI,axiom, % 169.19/169.61 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2))) % 169.19/169.61 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_CollectI,axiom, % 169.19/169.61 ! [T_a,V_a_2,V_P_2] : % 169.19/169.61 ( hBOOL(hAPP(V_P_2,V_a_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Collect__conjI,axiom, % 169.19/169.61 ! [V_Q_2,V_P_2,T_a] : % 169.19/169.61 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 169.19/169.61 => 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)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__upto,axiom, % 169.19/169.61 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_CollectE,axiom, % 169.19/169.61 ! [V_P_2,V_a_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_CollectD,axiom, % 169.19/169.61 ! [V_P_2,V_a_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_mem__Collect__eq,axiom, % 169.19/169.61 ! [V_P_2,V_a_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__mem__eq,axiom, % 169.19/169.61 ! [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 ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Collect__disjI,axiom, % 169.19/169.61 ! [V_Q_2,V_P_2,T_a] : % 169.19/169.61 ( 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)))) % 169.19/169.61 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__def,axiom, % 169.19/169.61 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__neg__eq,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__conj__eq,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__disj__eq,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__empty__eq,axiom, % 169.19/169.61 ! [V_P_2,T_a] : % 169.19/169.61 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_empty__Collect__eq,axiom, % 169.19/169.61 ! [V_P_2,T_a] : % 169.19/169.61 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 169.19/169.61 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_empty__def,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insert__Collect,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UNIV__def,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_atLeastAtMost__upto,axiom, % 169.19/169.61 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__upto,axiom, % 169.19/169.61 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insert__compr,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insert__compr__raw,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Un__def,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Int__def,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Int__Collect,axiom, % 169.19/169.61 ! [V_P_2,V_A_2,V_x_2,T_a] : % 169.19/169.61 ( 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)))) % 169.19/169.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_singleton__conv2,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_singleton__conv,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__conv__if2,axiom, % 169.19/169.61 ! [T_a,V_a_2,V_P_2] : % 169.19/169.61 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 169.19/169.61 => 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))) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__conv__if,axiom, % 169.19/169.61 ! [T_a,V_a_2,V_P_2] : % 169.19/169.61 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 169.19/169.61 => 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))) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__diff__eq,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Collect__not,axiom, % 169.19/169.61 ! [V_P_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 => ( 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)))) % 169.19/169.61 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insert__def,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Compl__eq,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Collect__imp__eq,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_dom__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__setsum__restrict,axiom, % 169.19/169.61 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_c) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inj__graph,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_if__image__distrib,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_dom__if,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__psubset__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__restrict__set_H,axiom, % 169.19/169.61 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__image__gen,axiom, % 169.19/169.61 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inv__image__def,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_atLeastLessThan__upto,axiom, % 169.19/169.61 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Image__singleton,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__cases,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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))))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_greaterThanAtMost__upto,axiom, % 169.19/169.61 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Nitpick_Oprod__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_int__ge__less__than2__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_int__ge__less__than__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Collect__less__nat,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Collect__le__nat,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Collect__subsets,axiom, % 169.19/169.61 ! [V_A_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Pow__def,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__M__bounded__by__nat,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nat__seg__image__imp__finite,axiom, % 169.19/169.61 ! [V_n_2,V_f_2,T_a,V_A_2] : % 169.19/169.61 ( 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))) % 169.19/169.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_card__less__Suc,axiom, % 169.19/169.61 ! [V_i_2,V_M_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 169.19/169.61 => 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))))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_card__less,axiom, % 169.19/169.61 ! [V_i_2,V_M_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_card__less__Suc2,axiom, % 169.19/169.61 ! [V_i_2,V_M_2] : % 169.19/169.61 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 169.19/169.61 => 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))))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_dom__override__on,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nat__list__def,axiom, % 169.19/169.61 ! [V_l_2] : % 169.19/169.61 ( c_List_Onat__list(V_l_2) % 169.19/169.61 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__multicount,axiom, % 169.19/169.61 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 169.19/169.61 => 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 ) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_override__on__apply__in,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_override__on__apply__notin,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_override__on__emptyset,axiom, % 169.19/169.61 ! [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 ). % 169.19/169.61 % 169.19/169.61 fof(fact_override__on__def,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => 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) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))))) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__Collect__bounded__ex,axiom, % 169.19/169.61 ! [V_Q_2,T_b,V_P_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 => ( 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))))) % 169.19/169.61 <=> ! [B_y] : % 169.19/169.61 ( hBOOL(hAPP(V_P_2,B_y)) % 169.19/169.61 => 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)))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__image__set,axiom, % 169.19/169.61 ! [V_f_2,T_b,V_P_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 169.19/169.61 => 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))))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_ran__def,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Pow__Compl,axiom, % 169.19/169.61 ! [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))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_add__Max__commute,axiom, % 169.19/169.61 ! [V_k_2,V_N_2,T_a] : % 169.19/169.61 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.61 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_add__Min__commute,axiom, % 169.19/169.61 ! [V_k_2,V_N_2,T_a] : % 169.19/169.61 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 169.19/169.61 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_sup__Inf1__distrib,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,T_a] : % 169.19/169.61 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_sup__Inf2__distrib,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,T_a] : % 169.19/169.61 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))))) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inf__Sup1__distrib,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,T_a] : % 169.19/169.61 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inf__Sup2__distrib,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,T_a] : % 169.19/169.61 ( class_Lattices_Odistrib__lattice(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))))) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.61 => 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))))))) ) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__multicount__gen,axiom, % 169.19/169.61 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 169.19/169.61 => 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) ) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__map__restrict,axiom, % 169.19/169.61 ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__remove1__eq,axiom, % 169.19/169.61 ! [V_x_2,V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inj__comp,axiom, % 169.19/169.61 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.61 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 169.19/169.61 => 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))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inj__on__imageI2,axiom, % 169.19/169.61 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 169.19/169.61 ( 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) % 169.19/169.61 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__remove1,axiom, % 169.19/169.61 ! [V_x,V_xs,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__map,axiom, % 169.19/169.61 ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_List_Omap_Ocompositionality,axiom, % 169.19/169.61 ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__comp__map,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_List_Omap_Ocomp,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_apsnd__compose,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_fun__upd__comp,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_o__assoc,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_o__apply,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_o__eq__dest,axiom, % 169.19/169.61 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 169.19/169.61 ( 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) % 169.19/169.61 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_o__eq__elim,axiom, % 169.19/169.61 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 169.19/169.61 ( 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) % 169.19/169.61 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_comp__cong,axiom, % 169.19/169.61 ! [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] : % 169.19/169.61 ( 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)) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_remove1__commute,axiom, % 169.19/169.61 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 169.19/169.61 ! [V_x_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 169.19/169.61 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_o__eq__dest__lhs,axiom, % 169.19/169.61 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 169.19/169.61 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 169.19/169.61 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_o__def,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_K__record__comp,axiom, % 169.19/169.61 ! [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 ). % 169.19/169.61 % 169.19/169.61 fof(fact_apfst__compose,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_image__compose,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_comp__surj,axiom, % 169.19/169.61 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 169.19/169.61 ( 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)) % 169.19/169.61 => ( 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)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_comp__inj__on__iff,axiom, % 169.19/169.61 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.19/169.61 => ( 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)) % 169.19/169.61 <=> 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_comp__inj__on,axiom, % 169.19/169.61 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.19/169.61 => ( 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)) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_inj__on__imageI,axiom, % 169.19/169.61 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 169.19/169.61 ( 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) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_in__set__remove1,axiom, % 169.19/169.61 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 169.19/169.61 ( V_a_2 != V_b_2 % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2)))) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_notin__set__remove1,axiom, % 169.19/169.61 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_remove1__idem,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__remove1__subset,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__reindex,axiom, % 169.19/169.61 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_c) % 169.19/169.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setprod__reindex__cong,axiom, % 169.19/169.61 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 169.19/169.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.19/169.61 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 169.19/169.61 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 169.19/169.61 => 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) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setprod__reindex,axiom, % 169.19/169.61 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 169.19/169.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum_Oreindex,axiom, % 169.19/169.61 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setprod_Oreindex,axiom, % 169.19/169.61 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_the__inv__into__comp,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 169.19/169.61 ( 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)) % 169.19/169.61 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 169.19/169.61 => ( 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)))) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_fold__image__reindex,axiom, % 169.19/169.61 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 169.19/169.61 ( class_Groups_Oab__semigroup__mult(T_c) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_sorted__list__of__set__remove,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Oremove,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__image_Oreindex,axiom, % 169.19/169.61 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.61 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 169.19/169.61 ! [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] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ocommute__comp,axiom, % 169.19/169.61 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ocommute__left__comp,axiom, % 169.19/169.61 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_UN__o,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_foldr__map,axiom, % 169.19/169.61 ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__image_Odistrib,axiom, % 169.19/169.61 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_split__comp,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 169.19/169.61 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ocommute__comp_H_H,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ocommute__left__comp_H,axiom, % 169.19/169.61 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ocommute__comp_H,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Oeq__fold,axiom, % 169.19/169.61 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__image_Oeq__fold,axiom, % 169.19/169.61 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 169.19/169.61 => 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) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Oinsert,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ounion__inter,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Oinsert__remove,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding_Ounion,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => ( 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)) % 169.19/169.61 => 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)) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Loop__sound__lemma,axiom, % 169.19/169.61 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 169.19/169.61 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_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)))) % 169.19/169.61 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_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)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_hoare__derivs_OIf,axiom, % 169.19/169.61 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 169.19/169.61 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 169.19/169.61 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 169.19/169.61 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Loop,axiom, % 169.19/169.61 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 169.19/169.61 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) % 169.19/169.61 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_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)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_peek__and__def,axiom, % 169.19/169.61 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 169.19/169.61 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 169.19/169.61 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__reindex__nonzero,axiom, % 169.19/169.61 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_c) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 169.19/169.61 => ! [B_y] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 169.19/169.61 => ( B_x != B_y % 169.19/169.61 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 169.19/169.61 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_sorted__list__of__set__insert,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__map,axiom, % 169.19/169.61 ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_option__map__comp,axiom, % 169.19/169.61 ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Option_Omap_Ocompositionality,axiom, % 169.19/169.61 ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Option_Omap_Ocomp,axiom, % 169.19/169.61 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_option__map__o__empty,axiom, % 169.19/169.61 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 169.19/169.61 % 169.19/169.61 fof(fact_remove1__insort,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_option__map__None,axiom, % 169.19/169.61 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ). % 169.19/169.61 % 169.19/169.61 fof(fact_option__map__is__None,axiom, % 169.19/169.61 ! [V_opt_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 169.19/169.61 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_option__map__Some,axiom, % 169.19/169.61 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_option__map__eq__Some,axiom, % 169.19/169.61 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 169.19/169.61 <=> ? [B_z] : % 169.19/169.61 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 169.19/169.61 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_fun__left__comm__insort,axiom, % 169.19/169.61 ! [T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insort__left__comm,axiom, % 169.19/169.61 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insort__key__left__comm,axiom, % 169.19/169.61 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 169.19/169.61 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_dom__option__map,axiom, % 169.19/169.61 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__insort,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( class_Orderings_Olinorder(T_b) % 169.19/169.61 => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_option__map__o__map__upd,axiom, % 169.19/169.61 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__insort,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( class_Orderings_Olinorder(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))) % 169.19/169.61 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Option_Omap__def,axiom, % 169.19/169.61 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insort__insert__insort__key,axiom, % 169.19/169.61 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 169.19/169.61 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insort__insert__insort,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__idem_Ounion__idem,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 169.19/169.61 => 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)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__insort__insert,axiom, % 169.19/169.61 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 169.19/169.61 ( class_Orderings_Olinorder(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__idem_Oidem__comp,axiom, % 169.19/169.61 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__idem_Oidem__left__comp,axiom, % 169.19/169.61 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => 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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insort__insert__triv,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__insort__insert,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insort__insert__key__triv,axiom, % 169.19/169.61 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 169.19/169.61 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__idem_Oin__comp__idem,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__idem_Oinsert__idem,axiom, % 169.19/169.61 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 169.19/169.61 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 169.19/169.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 169.19/169.61 => 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) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__zip__map,axiom, % 169.19/169.61 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_strong__setprod__reindex__cong,axiom, % 169.19/169.61 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__mult(T_c) % 169.19/169.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.19/169.61 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 169.19/169.61 => ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.61 => 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) ) % 169.19/169.61 => 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) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__removeAll__inj__on,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( 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))) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__zipI2,axiom, % 169.19/169.61 ! [V_xs,T_b,V_ys,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__removeAll,axiom, % 169.19/169.61 ! [V_x,V_xs,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__zipI1,axiom, % 169.19/169.61 ! [V_ys,T_b,V_xs,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__same__conv__map,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_removeAll__id,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__map__fst__snd,axiom, % 169.19/169.61 ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2 ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__remove1__removeAll,axiom, % 169.19/169.61 ! [V_x,V_xs,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.61 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__zip__map2,axiom, % 169.19/169.61 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__zip__map,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__removeAll__inj,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.61 => 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)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_in__set__zipE,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 169.19/169.61 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__zip__rightD,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__zip__leftD,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__same,axiom, % 169.19/169.61 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2)))) % 169.19/169.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 & V_a_2 = V_b_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__map2,axiom, % 169.19/169.61 ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__map1,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__map__map,axiom, % 169.19/169.61 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__removeAll,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__zip__upd,axiom, % 169.19/169.61 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 169.19/169.61 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 169.19/169.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 169.19/169.61 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2)) % 169.19/169.61 => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__map__remove1,axiom, % 169.19/169.61 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__lists__length__le,axiom, % 169.19/169.61 ! [V_n_2,V_A_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_length__zip,axiom, % 169.19/169.61 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__eq__imp__length__eq,axiom, % 169.19/169.61 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2) % 169.19/169.61 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_length__map,axiom, % 169.19/169.61 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__triv,axiom, % 169.19/169.61 ! [V_xs_2,V_r_2,T_b,T_a] : % 169.19/169.61 ( class_Rings_Osemiring__1(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_neq__if__length__neq,axiom, % 169.19/169.61 ! [V_ys,V_xs,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) % 169.19/169.61 => V_xs != V_ys ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 169.19/169.61 ! [V_ns_2] : % 169.19/169.61 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.61 <=> ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 169.19/169.61 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_length__insort,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 169.19/169.61 ( class_Orderings_Olinorder(T_b) % 169.19/169.61 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__0,axiom, % 169.19/169.61 ! [V_xs_2,T_b,T_a] : % 169.19/169.61 ( class_Groups_Omonoid__add(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__addf,axiom, % 169.19/169.61 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__mult__const,axiom, % 169.19/169.61 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( class_Rings_Osemiring__0(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_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) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__const__mult,axiom, % 169.19/169.61 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 169.19/169.61 ( class_Rings_Osemiring__0(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__subtractf,axiom, % 169.19/169.61 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( class_Groups_Oab__group__add(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_card__length,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__card,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_card__distinct,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__zip__inject,axiom, % 169.19/169.61 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 169.19/169.61 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 169.19/169.61 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 169.19/169.61 => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) % 169.19/169.61 => V_ys_2 = V_zs_2 ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__fst__zip,axiom, % 169.19/169.61 ! [V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.61 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__snd__zip,axiom, % 169.19/169.61 ! [V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.61 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__abs,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : % 169.19/169.61 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_uminus__listsum__map,axiom, % 169.19/169.61 ! [V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.61 ( class_Groups_Oab__group__add(T_a) % 169.19/169.61 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_length__pos__if__in__set,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__listsum__conv__Setsum,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__eq__conv,axiom, % 169.19/169.61 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.61 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 169.19/169.61 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2 % 169.19/169.61 & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2 ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 169.19/169.61 ! [V_f_2,V_xs_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 169.19/169.61 ! [V_l_2,V_k_2,V_f_2,T_a] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 169.19/169.61 ! [V_j_2,V_i_2,V_f_2,T_a] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.61 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_finite__lists__length__eq,axiom, % 169.19/169.61 ! [V_n_2,V_A_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__zip__is__None,axiom, % 169.19/169.61 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.61 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b) % 169.19/169.61 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__zip__is__Some,axiom, % 169.19/169.61 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_length__remove1,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_dom__map__of__zip,axiom, % 169.19/169.61 ! [V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_select__weight__member,axiom, % 169.19/169.61 ! [V_s_2,V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_pick__member,axiom, % 169.19/169.61 ! [V_xs_2,T_a,V_i_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_length__sublist,axiom, % 169.19/169.61 ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__sublistI,axiom, % 169.19/169.61 ! [V_I_2,V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_in__set__sublistD,axiom, % 169.19/169.61 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_notin__set__sublistI,axiom, % 169.19/169.61 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__sublist__subset,axiom, % 169.19/169.61 ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_select__weight__def,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Nitpick_Osetsum_H__def,axiom, % 169.19/169.61 ! [V_f_2,V_A_2,T_a,T_b] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.61 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_scomp__apply,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_scomp__Pair,axiom, % 169.19/169.61 ! [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 ). % 169.19/169.61 % 169.19/169.61 fof(fact_tfl__some,axiom, % 169.19/169.61 ! [T_a,B_P] : % 169.19/169.61 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 169.19/169.61 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_someI,axiom, % 169.19/169.61 ! [T_a,V_x_2,V_P_2] : % 169.19/169.61 ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.61 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_some__sym__eq__trivial,axiom, % 169.19/169.61 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 169.19/169.61 % 169.19/169.61 fof(fact_some__eq__trivial,axiom, % 169.19/169.61 ! [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 ). % 169.19/169.61 % 169.19/169.61 fof(fact_some__eq__ex,axiom, % 169.19/169.61 ! [T_a,V_P_2] : % 169.19/169.61 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 169.19/169.61 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_someI__ex,axiom, % 169.19/169.61 ! [T_a,V_P_2] : % 169.19/169.61 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.19/169.61 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_scomp__scomp,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Pair__scomp,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_exE__some,axiom, % 169.19/169.61 ! [T_a,V_ca_2,V_P_2] : % 169.19/169.61 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.19/169.61 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 169.19/169.61 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_scomp__def,axiom, % 169.19/169.61 ! [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)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_scomp__unfold,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Nitpick_Ocard_H__def,axiom, % 169.19/169.61 ! [V_A_2,T_a] : % 169.19/169.61 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.61 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_iterate_Osimps,axiom, % 169.19/169.61 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 169.19/169.61 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.61 => 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) ) % 169.19/169.61 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Eps__split__eq,axiom, % 169.19/169.61 ! [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) ). % 169.19/169.61 % 169.19/169.61 fof(fact_split__paired__Eps,axiom, % 169.19/169.61 ! [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)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Eps__split,axiom, % 169.19/169.61 ! [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))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__zip,axiom, % 169.19/169.61 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_a,T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_pick_Osimps,axiom, % 169.19/169.61 ! [V_xs,V_x,T_a,V_i] : % 169.19/169.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 169.19/169.61 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) % 169.19/169.61 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_impossible__Cons,axiom, % 169.19/169.61 ! [V_x,V_ys,V_xs,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) % 169.19/169.61 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__simps_I2_J,axiom, % 169.19/169.61 ! [V_xs,V_x,T_a] : % 169.19/169.61 ( class_Groups_Omonoid__add(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__eq__iff__nth__eq,axiom, % 169.19/169.61 ! [T_a,V_ys_2,V_xs_2] : % 169.19/169.61 ( V_xs_2 = V_ys_2 % 169.19/169.61 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 169.19/169.61 & ! [B_i] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__ConsD,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) % 169.19/169.61 => ( V_y_2 = V_x_2 % 169.19/169.61 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__subset__Cons,axiom, % 169.19/169.61 ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_List_Oset_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_removeAll_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_xs,T_a,V_y,V_x] : % 169.19/169.61 ( ( V_x = V_y % 169.19/169.61 => 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) ) % 169.19/169.61 & ( V_x != V_y % 169.19/169.61 => 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)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_insort__key_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 169.19/169.61 ( class_Orderings_Olinorder(T_a) % 169.19/169.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 169.19/169.61 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) % 169.19/169.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 169.19/169.61 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__Cons_H,axiom, % 169.19/169.61 ! [V_xs,V_x,T_a,V_n] : % 169.19/169.61 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 169.19/169.61 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__Cons__number__of,axiom, % 169.19/169.61 ! [V_xs,V_x,T_a,V_v] : % 169.19/169.61 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x ) % 169.19/169.61 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__Cons__0,axiom, % 169.19/169.61 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__Cons__Suc,axiom, % 169.19/169.61 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ). % 169.19/169.61 % 169.19/169.61 fof(fact_not__Cons__self,axiom, % 169.19/169.61 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 169.19/169.61 % 169.19/169.61 fof(fact_not__Cons__self2,axiom, % 169.19/169.61 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 169.19/169.61 % 169.19/169.61 fof(fact_list_Oinject,axiom, % 169.19/169.61 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 169.19/169.61 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2) % 169.19/169.61 <=> ( V_a_2 = V_a_H_2 % 169.19/169.61 & V_list_2 = V_list_H_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth_Osimps,axiom, % 169.19/169.61 ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_remove1_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_xs,T_a,V_y,V_x] : % 169.19/169.61 ( ( V_x = V_y % 169.19/169.61 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 169.19/169.61 & ( V_x != V_y % 169.19/169.61 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_foldr_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__Cons__Cons,axiom, % 169.19/169.61 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__zip,axiom, % 169.19/169.61 ! [V_ys,T_b,V_xs,T_a,V_i] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys))) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_all__set__conv__all__nth,axiom, % 169.19/169.61 ! [V_P_2,V_xs_2,T_a] : % 169.19/169.61 ( ! [B_x] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.61 <=> ! [B_i] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__map,axiom, % 169.19/169.61 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__eq__iff__index__eq,axiom, % 169.19/169.61 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) % 169.19/169.61 <=> V_i_2 = V_j_2 ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__conv__nth,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 <=> ! [B_i] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => ! [B_j] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => ( B_i != B_j % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 169.19/169.61 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of__Cons__code_I2_J,axiom, % 169.19/169.61 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 169.19/169.61 ( ( V_l = V_k % 169.19/169.61 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) ) % 169.19/169.61 & ( V_l != V_k % 169.19/169.61 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_elem__le__listsum__nat,axiom, % 169.19/169.61 ! [V_ns,V_k] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__mem,axiom, % 169.19/169.61 ! [V_xs_2,T_a,V_n_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_in__set__conv__nth,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.61 <=> ? [B_i] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list_Osize_I4_J,axiom, % 169.19/169.61 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__conv__nth,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_select__weight__cons__zero,axiom, % 169.19/169.61 ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__setsum__nth,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : % 169.19/169.61 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__of_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__sublist,axiom, % 169.19/169.61 ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__Cons__def,axiom, % 169.19/169.61 ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_pick__same,axiom, % 169.19/169.61 ! [V_xs_2,T_a,V_l_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_l_2) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 169.19/169.61 ! [V_m_2,V_n_2] : % 169.19/169.61 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 169.19/169.61 <=> V_n_2 = V_m_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 169.19/169.61 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.61 % 169.19/169.61 fof(fact_times__code__numeral__code,axiom, % 169.19/169.61 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zero__code__numeral__def,axiom, % 169.19/169.61 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_one__code__numeral__def,axiom, % 169.19/169.61 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_less__code__numeral__code,axiom, % 169.19/169.61 ! [V_m_2,V_n_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_code__numeral_Oof__nat__inject,axiom, % 169.19/169.61 ! [V_y_2,V_x_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 169.19/169.61 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 169.19/169.61 <=> V_x_2 = V_y_2 ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_number__of__code__numeral__def,axiom, % 169.19/169.61 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ). % 169.19/169.61 % 169.19/169.61 fof(fact_plus__code__numeral__code,axiom, % 169.19/169.61 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_less__eq__code__numeral__code,axiom, % 169.19/169.61 ! [V_m_2,V_n_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_subtract__code__numeral__code,axiom, % 169.19/169.61 ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_code__numeral__not__eq__zero,axiom, % 169.19/169.61 ! [V_i_2] : % 169.19/169.61 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 169.19/169.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_listsum__update__nat,axiom, % 169.19/169.61 ! [V_n,V_ns,V_k] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) % 169.19/169.61 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_distinct__list__update,axiom, % 169.19/169.61 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 169.19/169.61 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update__id,axiom, % 169.19/169.61 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__list__update__neq,axiom, % 169.19/169.61 ! [V_x,V_xs,T_a,V_j,V_i] : % 169.19/169.61 ( V_i != V_j % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update_Osimps_I2_J,axiom, % 169.19/169.61 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2) ). % 169.19/169.61 % 169.19/169.61 fof(fact_zip__update,axiom, % 169.19/169.61 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_map__update,axiom, % 169.19/169.61 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_length__list__update,axiom, % 169.19/169.61 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update__code_I2_J,axiom, % 169.19/169.61 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update__code_I3_J,axiom, % 169.19/169.61 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ). % 169.19/169.61 % 169.19/169.61 fof(fact_update__zip,axiom, % 169.19/169.61 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update__overwrite,axiom, % 169.19/169.61 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update__swap,axiom, % 169.19/169.61 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 169.19/169.61 ( V_i != V_i_H % 169.19/169.61 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update__beyond,axiom, % 169.19/169.61 ! [V_x,V_i,V_xs,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)) % 169.19/169.61 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__update__subsetI,axiom, % 169.19/169.61 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2)) % 169.19/169.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__update__subset__insert,axiom, % 169.19/169.61 ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__list__update,axiom, % 169.19/169.61 ! [V_x,V_j,V_xs,T_a,V_i] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.61 => ( ( V_i = V_j % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) % 169.19/169.61 & ( V_i != V_j % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_list__update__same__conv,axiom, % 169.19/169.61 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 169.19/169.61 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nth__list__update__eq,axiom, % 169.19/169.61 ! [V_x,V_xs,T_a,V_i] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_set__update__memI,axiom, % 169.19/169.61 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Cons__in__lex,axiom, % 169.19/169.61 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 169.19/169.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2))) % 169.19/169.61 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.61 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) % 169.19/169.61 | ( V_x_2 = V_y_2 % 169.19/169.61 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) ) ) ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_select__def,axiom, % 169.19/169.61 ! [V_xs_2,T_a] : c_Random_Oselect(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_code__numeral_Onat__of__inject,axiom, % 169.19/169.61 ! [V_y_2,V_x_2] : % 169.19/169.61 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 169.19/169.61 <=> V_x_2 = V_y_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 169.19/169.61 ! [V_l_2,V_k_2] : % 169.19/169.61 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 169.19/169.61 <=> V_k_2 = V_l_2 ) ). % 169.19/169.61 % 169.19/169.61 fof(fact_nat__of__of__nat,axiom, % 169.19/169.61 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 169.19/169.61 % 169.19/169.61 fof(fact_of__nat__nat__of,axiom, % 169.19/169.61 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 169.19/169.61 % 169.19/169.61 fof(fact_nat__of__inverse,axiom, % 169.19/169.61 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 169.19/169.61 % 169.19/169.61 fof(fact_type__definition__code__numeral,axiom, % 169.19/169.61 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 169.19/169.61 % 169.19/169.61 fof(fact_less__code__numeral__def,axiom, % 169.19/169.62 ! [V_m_2,V_n_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 169.19/169.62 <=> 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nat__of,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nat__of__number,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_int__of__def,axiom, % 169.19/169.62 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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_less__eq__code__numeral__def,axiom, % 169.19/169.62 ! [V_m_2,V_n_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 169.19/169.62 <=> 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nat__of__code,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nat__of__aux__def,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Suc__code__numeral__def,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_minus__code__numeral__def,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_of__nat__inverse,axiom, % 169.19/169.62 ! [V_y_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 169.19/169.62 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_plus__code__numeral__def,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_div__code__numeral__def,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_times__code__numeral__def,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_mod__code__numeral__def,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_code__numeral__decr,axiom, % 169.19/169.62 ! [V_k] : % 169.19/169.62 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lenlex__conv,axiom, % 169.19/169.62 ! [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)))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lenlex__def,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__iff__nth,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 169.19/169.62 & ! [B_n] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.62 => 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)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_select__weigth__select,axiom, % 169.19/169.62 ! [T_a,V_xs_2] : % 169.19/169.62 ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__Nil1,axiom, % 169.19/169.62 ! [V_r_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__Nil2,axiom, % 169.19/169.62 ! [V_r_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel_ONil,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listsum__simps_I1_J,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Groups_Omonoid__add(T_a) % 169.19/169.62 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct_Osimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldr_Osimps_I1_J,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_remove1_Osimps_I1_J,axiom, % 169.19/169.62 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__mono,axiom, % 169.19/169.62 ! [V_s_2,V_r_2,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__Nil,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_insort__not__Nil,axiom, % 169.19/169.62 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 169.19/169.62 ( class_Orderings_Olinorder(T_b) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__Nil,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip_Osimps_I1_J,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_removeAll_Osimps_I1_J,axiom, % 169.19/169.62 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__nil,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_List_Oset_Osimps_I1_J,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__empty2,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__empty,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list_Osize_I3_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__0__conv,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__is__Nil__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.62 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map_Osimps_I1_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Nil__is__map__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list_Osimps_I3_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list_Osimps_I2_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__update__code_I1_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__update_Osimps_I1_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__update__nonempty,axiom, % 169.19/169.62 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_insort__key_Osimps_I1_J,axiom, % 169.19/169.62 ! [V_x_2,V_f_2,T_a,T_b] : % 169.19/169.62 ( class_Orderings_Olinorder(T_b) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__of__Cons__code_I1_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upto__empty,axiom, % 169.19/169.62 ! [V_i,V_j] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 169.19/169.62 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__list__of__set__empty,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__empty,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__of_Osimps_I1_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__greater__0__conv,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__Cons__sing__Nil,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Nil__notin__lex,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Nil2__notin__lex,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__eq__len,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upto_Osimps,axiom, % 169.19/169.62 ! [V_j,V_i] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 169.19/169.62 => 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)) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 169.19/169.62 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__singleton,axiom, % 169.19/169.62 ! [V_x_2,T_a,V_A_2] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 169.19/169.62 => 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)) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upto__rec__number__of,axiom, % 169.19/169.62 ! [V_n,V_m] : % 169.19/169.62 ( ( 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))) % 169.19/169.62 => 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))) ) % 169.19/169.62 & ( ~ 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))) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_select,axiom, % 169.19/169.62 ! [V_s_2,T_a,V_xs_2] : % 169.19/169.62 ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel_OCons,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__Cons,axiom, % 169.19/169.62 ! [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))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upto_Opsimps,axiom, % 169.19/169.62 ! [V_j_2,V_i_2] : % 169.19/169.62 ( 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))) % 169.19/169.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 169.19/169.62 => 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)) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 169.19/169.62 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_anamorph_Osimps,axiom, % 169.19/169.62 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 169.19/169.62 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listset_Osimps_I1_J,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__Cons,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list_Osimps_I5_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list_Osimps_I4_J,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_listset_Osimps_I2_J,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__Cons1,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrelp__listrel__eq,axiom, % 169.19/169.62 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__Cons1,axiom, % 169.19/169.62 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => ~ ! [B_y,B_ys] : % 169.19/169.62 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 169.19/169.62 => ( 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)) % 169.19/169.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrelp_ONil,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrelp_Oequations_I1_J,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrelp_OCons,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 169.19/169.62 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrelp_Oequations_I2_J,axiom, % 169.19/169.62 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 169.19/169.62 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__Cons2,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => ~ ! [B_x,B_xs] : % 169.19/169.62 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 169.19/169.62 => ( 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)) % 169.19/169.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__iff__zip,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 169.19/169.62 & ! [B_x] : % 169.19/169.62 ( 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)))) % 169.19/169.62 => 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)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_ball__empty,axiom, % 169.19/169.62 ! [V_P_2,T_a,B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 169.19/169.62 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_INFI__bool__eq,axiom, % 169.19/169.62 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Powp__def,axiom, % 169.19/169.62 ! [V_B_2,V_A_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 169.19/169.62 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Collect__ball__eq,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_congruent__def,axiom, % 169.19/169.62 ! [V_f_2,V_r_2,T_b,T_a] : % 169.19/169.62 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_INTER__def,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Sup__Inf,axiom, % 169.19/169.62 ! [V_A_2,T_a] : % 169.19/169.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.62 => 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)))))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Inf__Sup,axiom, % 169.19/169.62 ! [V_A_2,T_a] : % 169.19/169.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.62 => 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))))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__eq__iff__zip__eq,axiom, % 169.19/169.62 ! [T_a,V_ys_2,V_xs_2] : % 169.19/169.62 ( V_xs_2 = V_ys_2 % 169.19/169.62 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 169.19/169.62 & ! [B_x] : % 169.19/169.62 ( 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)))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_WT__bodies__def,axiom, % 169.19/169.62 ( c_Com_OWT__bodies % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upto_Opinduct,axiom, % 169.19/169.62 ! [V_P_2,V_a1_2,V_a0_2] : % 169.19/169.62 ( 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))) % 169.19/169.62 => ( ! [B_i,B_j] : % 169.19/169.62 ( 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))) % 169.19/169.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 169.19/169.62 => 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)) ) % 169.19/169.62 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 169.19/169.62 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__Cons,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_triples__valid__Suc,axiom, % 169.19/169.62 ! [V_n_2,V_ts_2,T_a] : % 169.19/169.62 ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 169.19/169.62 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 169.19/169.62 => ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 169.19/169.62 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_eq__Nil__appendI,axiom, % 169.19/169.62 ! [T_a,V_ys,V_xs] : % 169.19/169.62 ( V_xs = V_ys % 169.19/169.62 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__self__conv2,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__self__conv,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 169.19/169.62 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__is__Nil__conv,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 169.19/169.62 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_self__append__conv2,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_ys_2] : % 169.19/169.62 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_self__append__conv,axiom, % 169.19/169.62 ! [V_ys_2,T_a,V_xs_2] : % 169.19/169.62 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 169.19/169.62 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__Nil2,axiom, % 169.19/169.62 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 169.19/169.62 % 169.19/169.62 fof(fact_Nil__is__append__conv,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 169.19/169.62 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 169.19/169.62 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__Nil,axiom, % 169.19/169.62 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__append,axiom, % 169.19/169.62 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 169.19/169.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us) % 169.19/169.62 => ( 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) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__of__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listsum__append,axiom, % 169.19/169.62 ! [V_ys,V_xs,T_a] : % 169.19/169.62 ( class_Groups_Omonoid__add(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_removeAll__append,axiom, % 169.19/169.62 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__assoc,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__eq__append__conv2,axiom, % 169.19/169.62 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> ? [B_us] : % 169.19/169.62 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 169.19/169.62 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 169.19/169.62 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 169.19/169.62 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_same__append__eq,axiom, % 169.19/169.62 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> V_ys_2 = V_zs_2 ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__same__eq,axiom, % 169.19/169.62 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> V_ys_2 = V_zs_2 ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__eq__appendI,axiom, % 169.19/169.62 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 169.19/169.62 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 169.19/169.62 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldr__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__Cons,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Cons__eq__appendI,axiom, % 169.19/169.62 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 169.19/169.62 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 169.19/169.62 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__eq__Cons__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 169.19/169.62 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 169.19/169.62 | ? [B_ys_H] : % 169.19/169.62 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 169.19/169.62 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Cons__eq__append__conv,axiom, % 169.19/169.62 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 169.19/169.62 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 169.19/169.62 | ? [B_ys_H] : % 169.19/169.62 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 169.19/169.62 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append1__eq__conv,axiom, % 169.19/169.62 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 <=> ( V_xs_2 = V_ys_2 % 169.19/169.62 & V_x_2 = V_y_2 ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hoare__valids__def,axiom, % 169.19/169.62 ! [V_ts_2,V_G_2,T_a] : % 169.19/169.62 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) % 169.19/169.62 <=> ! [B_n] : % 169.19/169.62 ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2)) % 169.19/169.62 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 169.19/169.62 => ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 169.19/169.62 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__append__length,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__append__length__plus,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__update__append1,axiom, % 169.19/169.62 ! [V_x,V_ys,V_xs,T_a,V_i] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__update__length,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remove1__append,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Inter__eq,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__append,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 169.19/169.62 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 169.19/169.62 & 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__append,axiom, % 169.19/169.62 ! [V_ys,V_xs,T_a,V_n] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__update__append,axiom, % 169.19/169.62 ! [V_x,V_ys,V_xs,T_a,V_n] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__append,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__append1,axiom, % 169.19/169.62 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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)))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__append__left__rightI,axiom, % 169.19/169.62 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__add__upds,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__Nil1,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__Nil2,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__apply__nontin,axiom, % 169.19/169.62 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_fun__upds__append__drop,axiom, % 169.19/169.62 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_fun__upds__append2__drop,axiom, % 169.19/169.62 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__Cons,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__Nil__right,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__append__leftI,axiom, % 169.19/169.62 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__list__update2__drop,axiom, % 169.19/169.62 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__twist,axiom, % 169.19/169.62 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 169.19/169.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_restrict__map__upds,axiom, % 169.19/169.62 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 169.19/169.62 => ( 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)) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__lex,axiom, % 169.19/169.62 ! [V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 & 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__cons__cons,axiom, % 169.19/169.62 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ( 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)) % 169.19/169.62 | ( V_a_2 = V_b_2 % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__take__index__conv,axiom, % 169.19/169.62 ! [V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ( ( 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))) % 169.19/169.62 & 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 ) % 169.19/169.62 | ? [B_i] : % 169.19/169.62 ( 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)))) % 169.19/169.62 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 169.19/169.62 & 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)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_snoc__listrel1__snoc__iff,axiom, % 169.19/169.62 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 & V_x_2 = V_y_2 ) % 169.19/169.62 | ( V_xs_2 = V_ys_2 % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__Nil,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__0,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__eq__Nil,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__take,axiom, % 169.19/169.62 ! [V_xs,T_a,V_n,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__take,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__map,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__zip,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__take,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__take,axiom, % 169.19/169.62 ! [V_i,V_xs,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__all,axiom, % 169.19/169.62 ! [V_n,V_xs,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__Suc__Cons,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__take__subset,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_in__set__takeD,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 169.19/169.62 ( 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)))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__upt__eq__take,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__take__subset__set__take,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.62 => 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)))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__1__Cons,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1__mono,axiom, % 169.19/169.62 ! [V_s_2,V_r_2,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1I2,axiom, % 169.19/169.62 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1__eq__len,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_not__listrel1__Nil,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_not__Nil__listrel1,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__listrel1I,axiom, % 169.19/169.62 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 & V_us_2 = V_vs_2 ) % 169.19/169.62 | ( V_xs_2 = V_ys_2 % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__Cons,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__Cons_H,axiom, % 169.19/169.62 ! [V_xs,V_x,T_a,V_n] : % 169.19/169.62 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dom__map__upds,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Cons__listrel1__Cons,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.62 & V_xs_2 = V_ys_2 ) % 169.19/169.62 | ( V_x_2 = V_y_2 % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1I1,axiom, % 169.19/169.62 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__Cons__number__of,axiom, % 169.19/169.62 ! [V_xs,V_x,T_a,V_v] : % 169.19/169.62 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upd__upds__conv__if,axiom, % 169.19/169.62 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 169.19/169.62 ( ( 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)))) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( ~ 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)))) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__Suc__conv__app__nth,axiom, % 169.19/169.62 ! [V_xs,T_a,V_i] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1I,axiom, % 169.19/169.62 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.62 => ( 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)) % 169.19/169.62 => ( 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)) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1__iff__update,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ? [B_y,B_n] : % 169.19/169.62 ( 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)) % 169.19/169.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.62 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1E,axiom, % 169.19/169.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => ~ ! [B_x,B_y] : % 169.19/169.62 ( 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)) % 169.19/169.62 => ! [B_us,B_vs] : % 169.19/169.62 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 169.19/169.62 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__append__leftD,axiom, % 169.19/169.62 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => ( ! [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)) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate1__def,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate1__is__Nil__conv,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__rotate1,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct1__rotate,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 169.19/169.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__rotate1,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__simps,axiom, % 169.19/169.62 ! [V_xs,V_x,T_b,T_a] : % 169.19/169.62 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 169.19/169.62 & 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate1__length01,axiom, % 169.19/169.62 ! [V_xs,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel1__subset__listrel,axiom, % 169.19/169.62 ! [V_r_H_2,V_r_2,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 169.19/169.62 => 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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexn__length,axiom, % 169.19/169.62 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 169.19/169.62 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__on__Id__on,axiom, % 169.19/169.62 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexn_Osimps_I1_J,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__on__empty,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__on__Un,axiom, % 169.19/169.62 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.62 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__on__Int,axiom, % 169.19/169.62 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.62 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__onD2,axiom, % 169.19/169.62 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__onD1,axiom, % 169.19/169.62 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__onD,axiom, % 169.19/169.62 ! [V_a_2,V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lex__def,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_refl__on__def_H,axiom, % 169.19/169.62 ! [V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.62 <=> ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 169.19/169.62 => 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)) ) % 169.19/169.62 & ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.62 => 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)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexn_Osimps_I2_J,axiom, % 169.19/169.62 ! [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)))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_reflp__def,axiom, % 169.19/169.62 ! [V_r_2,T_a] : % 169.19/169.62 ( c_Predicate_Oreflp(T_a,V_r_2) % 169.19/169.62 <=> 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair__imageI,axiom, % 169.19/169.62 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_snd__prod__fun,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_fst__map__pair,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_reflpE,axiom, % 169.19/169.62 ! [V_x_2,V_r_2,T_a] : % 169.19/169.62 ( c_Predicate_Oreflp(T_a,V_r_2) % 169.19/169.62 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair__ident,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_fst__comp__map__pair,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_snd__comp__map__pair,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair_Ocompositionality,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair__compose,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair_Ocomp,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair__simp,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair__def,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__pair__surj,axiom, % 169.19/169.62 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 169.19/169.62 ( 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)) % 169.19/169.62 => ( 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)) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_prod__fun__imageE,axiom, % 169.19/169.62 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 => ~ ! [B_x,B_y] : % 169.19/169.62 ( 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)) % 169.19/169.62 => ~ 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upd__conv__take__nth__drop,axiom, % 169.19/169.62 ! [V_a,V_xs,T_a,V_i] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_in__set__dropD,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 169.19/169.62 ( 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)))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__drop__subset,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__1__Cons,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__via__drop,axiom, % 169.19/169.62 ! [V_ys,V_y,V_xs,V_n,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__Suc__Cons,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__drop,axiom, % 169.19/169.62 ! [V_i,V_xs,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__0,axiom, % 169.19/169.62 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__drop,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__zip,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__drop,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__map,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__Nil,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__drop,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__take,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__take__drop__id,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__drop__subset__set__drop,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 169.19/169.62 => 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)))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__all,axiom, % 169.19/169.62 ! [V_n,V_xs,T_a] : % 169.19/169.62 ( 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)) % 169.19/169.62 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__eq__Nil,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__eq__conv__conj,axiom, % 169.19/169.62 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 169.19/169.62 <=> ( 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) % 169.19/169.62 & 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__Cons,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__Cons_H,axiom, % 169.19/169.62 ! [V_xs,V_x,T_a,V_n] : % 169.19/169.62 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__drop,axiom, % 169.19/169.62 ! [V_xs,T_a,V_i,V_n] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__eq__append__conv__if,axiom, % 169.19/169.62 ! [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] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> ( ( 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))) % 169.19/169.62 => ( 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) % 169.19/169.62 & 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) ) ) % 169.19/169.62 & ( ~ 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))) % 169.19/169.62 => ( 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 % 169.19/169.62 & 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 ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__drop_H,axiom, % 169.19/169.62 ! [V_xs,T_a,V_i] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__Cons__number__of,axiom, % 169.19/169.62 ! [V_xs,V_x,T_a,V_v] : % 169.19/169.62 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__add,axiom, % 169.19/169.62 ! [V_xs,T_a,V_j,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__append2,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__append1,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_id__take__nth__drop,axiom, % 169.19/169.62 ! [V_xs,T_a,V_i] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__hd__drop,axiom, % 169.19/169.62 ! [V_xs,T_a,V_n] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__drop__conv__nth,axiom, % 169.19/169.62 ! [V_n,T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd_Osimps,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__map,axiom, % 169.19/169.62 ! [V_f_2,T_b,T_a,V_xs_2] : % 169.19/169.62 ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__append2,axiom, % 169.19/169.62 ! [V_ys,T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__append,axiom, % 169.19/169.62 ! [V_ys,T_a,V_xs] : % 169.19/169.62 ( ( V_xs = c_List_Olist_ONil(T_a) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__in__set,axiom, % 169.19/169.62 ! [T_a,V_xs_2] : % 169.19/169.62 ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__conv__nth,axiom, % 169.19/169.62 ! [T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate1__hd__tl,axiom, % 169.19/169.62 ! [T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__rotate__conv__nth,axiom, % 169.19/169.62 ! [V_n,T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__tl,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_tl__drop,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate1__rotate__swap,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__rotate,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_tl_Osimps_I2_J,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__rotate,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 169.19/169.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__tl,axiom, % 169.19/169.62 ! [V_xs,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__rotate,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__rotate,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__map,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__tl,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_tl_Osimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__is__Nil__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_tl__append2,axiom, % 169.19/169.62 ! [V_ys,T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__tl,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__conv__mod,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__Suc,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__Suc,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_tl__append,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__add,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__id,axiom, % 169.19/169.62 ! [V_xs,T_a,V_n] : % 169.19/169.62 ( 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) % 169.19/169.62 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__length01,axiom, % 169.19/169.62 ! [V_n,V_xs,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__tl,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_tl__take,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__Suc,axiom, % 169.19/169.62 ! [V_n,T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__drop__take,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_fold1__set,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 169.19/169.62 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list_Osize_I2_J,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__size__map,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldr__conv__foldl,axiom, % 169.19/169.62 ! [V_a_2,V_xs_2,T_a] : % 169.19/169.62 ( class_Groups_Oab__semigroup__add(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__append,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__Nil,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__map,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__absorb0,axiom, % 169.19/169.62 ! [V_zs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Groups_Omonoid__add(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__assoc,axiom, % 169.19/169.62 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 169.19/169.62 ( class_Groups_Osemigroup__add(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_start__le__sum,axiom, % 169.19/169.62 ! [V_ns_2,V_n_2,V_m_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__Cons,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listsum__foldl,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Groups_Omonoid__add(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__foldr1__lemma,axiom, % 169.19/169.62 ! [V_xs_2,V_a_2,T_a] : % 169.19/169.62 ( class_Groups_Omonoid__add(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__foldr1,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( class_Groups_Omonoid__add(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sum__eq__0__conv,axiom, % 169.19/169.62 ! [V_ns_2,V_m_2] : % 169.19/169.62 ( 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) % 169.19/169.62 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 & ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 169.19/169.62 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list_Osize_I1_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 169.19/169.62 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 169.19/169.62 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Sup__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Inf__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Sup__fin__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Lattices_Olattice(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Inf__fin__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Lattices_Olattice(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Min__fin__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Max__fin__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_min__max_OInf__fin__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_min__max_OSup__fin__set__fold,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_SUPR__set__fold,axiom, % 169.19/169.62 ! [V_f_2,V_xs_2,T_b,T_a] : % 169.19/169.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_INFI__set__fold,axiom, % 169.19/169.62 ! [V_f_2,V_xs_2,T_b,T_a] : % 169.19/169.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__size__estimation,axiom, % 169.19/169.62 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 169.19/169.62 => 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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__size__estimation_H,axiom, % 169.19/169.62 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 169.19/169.62 => 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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__fold__map__upd,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_elem__le__sum,axiom, % 169.19/169.62 ! [V_ns_2,V_n_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__size__conv__listsum,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__append__rightI,axiom, % 169.19/169.62 ! [V_r_2,V_x_2,T_a,V_y_2] : % 169.19/169.62 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__Nil__left,axiom, % 169.19/169.62 ! [V_r_2,V_y_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__list__update,axiom, % 169.19/169.62 ! [V_x,V_k,T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => ( ( 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)) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 169.19/169.62 & ( 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)) % 169.19/169.62 => 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) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listsum__mono,axiom, % 169.19/169.62 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 169.19/169.62 ( ( class_Groups_Omonoid__add(T_b) % 169.19/169.62 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 169.19/169.62 => ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 169.19/169.62 => 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)))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last_Osimps,axiom, % 169.19/169.62 ! [V_x,T_a,V_xs] : % 169.19/169.62 ( ( V_xs = c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 169.19/169.62 & ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__ConsR,axiom, % 169.19/169.62 ! [V_x,T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__ConsL,axiom, % 169.19/169.62 ! [V_x,T_a,V_xs] : % 169.19/169.62 ( V_xs = c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__map,axiom, % 169.19/169.62 ! [V_f_2,T_b,T_a,V_xs_2] : % 169.19/169.62 ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__appendL,axiom, % 169.19/169.62 ! [V_xs,T_a,V_ys] : % 169.19/169.62 ( V_ys = c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__appendR,axiom, % 169.19/169.62 ! [V_xs,T_a,V_ys] : % 169.19/169.62 ( V_ys != c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__append,axiom, % 169.19/169.62 ! [V_xs,T_a,V_ys] : % 169.19/169.62 ( ( V_ys = c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 169.19/169.62 & ( V_ys != c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__in__set,axiom, % 169.19/169.62 ! [T_a,V_as_2] : % 169.19/169.62 ( V_as_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__snoc,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__drop,axiom, % 169.19/169.62 ! [V_xs,T_a,V_n] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__conv__nth,axiom, % 169.19/169.62 ! [T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__irreflexive,axiom, % 169.19/169.62 ! [V_y_2,V_r_2,T_a] : % 169.19/169.62 ( ! [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)) % 169.19/169.62 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lexord__linear,axiom, % 169.19/169.62 ! [V_y_2,V_x_2,V_r_2,T_a] : % 169.19/169.62 ( ! [B_a,B_b] : % 169.19/169.62 ( 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)) % 169.19/169.62 | B_a = B_b % 169.19/169.62 | 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)) ) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.62 | V_x_2 = V_y_2 % 169.19/169.62 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_list__size__pointwise,axiom, % 169.19/169.62 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 169.19/169.62 ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast__take,axiom, % 169.19/169.62 ! [V_xs,T_a,V_n] : % 169.19/169.62 ( 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))) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lists__empty,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lists_ONil,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__butlast,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast__drop,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lists__mono,axiom, % 169.19/169.62 ! [V_B_2,V_A_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast_Osimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__butlast,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_in__set__butlastD,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_x,T_a,V_xs] : % 169.19/169.62 ( ( V_xs = c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 169.19/169.62 & ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast__append,axiom, % 169.19/169.62 ! [V_xs,T_a,V_ys] : % 169.19/169.62 ( ( V_ys = c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 169.19/169.62 & ( V_ys != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__butlast,axiom, % 169.19/169.62 ! [T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__in__lists__conv,axiom, % 169.19/169.62 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lists__UNIV,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_equiv__listrel,axiom, % 169.19/169.62 ! [V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listrel__refl__on,axiom, % 169.19/169.62 ! [V_r_2,V_A_2,T_a] : % 169.19/169.62 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_in__set__butlast__appendI,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 169.19/169.62 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 169.19/169.62 => 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))))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast__snoc,axiom, % 169.19/169.62 ! [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 ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__butlast,axiom, % 169.19/169.62 ! [V_xs,T_a,V_n] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__butlast,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Cons__in__lists__iff,axiom, % 169.19/169.62 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( 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))) % 169.19/169.62 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_in__lists__conv__set,axiom, % 169.19/169.62 ! [V_A_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lists__eq__set,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast__conv__take,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_butlast__list__update,axiom, % 169.19/169.62 ! [V_x,V_xs,T_a,V_k] : % 169.19/169.62 ( ( 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)) % 169.19/169.62 => 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) ) % 169.19/169.62 & ( 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)) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_append__butlast__last__id,axiom, % 169.19/169.62 ! [T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => 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 ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_snoc__eq__iff__butlast,axiom, % 169.19/169.62 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 169.19/169.62 ( 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 % 169.19/169.62 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 169.19/169.62 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_lists_Osimps,axiom, % 169.19/169.62 ! [V_A_2,V_a_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 169.19/169.62 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 169.19/169.62 | ? [B_a,B_l] : % 169.19/169.62 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 169.19/169.62 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__take__lemma,axiom, % 169.19/169.62 ! [V_ys,V_xs,T_a,V_k] : % 169.19/169.62 ( 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))) % 169.19/169.62 => ( 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))) % 169.19/169.62 => ( ! [B_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 169.19/169.62 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__aux__max,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_partition__set,axiom, % 169.19/169.62 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 169.19/169.62 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__filter__le,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__is__subset,axiom, % 169.19/169.62 ! [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))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__empty__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__id__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 169.19/169.62 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => 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)) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__filter,axiom, % 169.19/169.62 ! [V_P_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__remove1,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remove1__filter__not,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 169.19/169.62 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__filter,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__insort__triv,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 169.19/169.62 ( class_Orderings_Olinorder(T_b) % 169.19/169.62 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_removeAll__filter__not,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 169.19/169.62 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_removeAll__filter__not__eq,axiom, % 169.19/169.62 ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_partition__filter1,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter_Osimps_I1_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__append,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sum__length__filter__compl,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_partition__filter__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_partition__filter2,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__map,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__filter,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__filter__map,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__filter__less,axiom, % 169.19/169.62 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => 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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__minus__filter__out,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_partition__P,axiom, % 169.19/169.62 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 169.19/169.62 => ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 169.19/169.62 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.62 & ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 169.19/169.62 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_partition_Osimps_I1_J,axiom, % 169.19/169.62 ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__in__sublist,axiom, % 169.19/169.62 ! [V_s_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => 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) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_partition_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__filter__conv__card,axiom, % 169.19/169.62 ! [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))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__filter__def,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__max__length,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__map__map,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__filter__simps_I2_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose_Osimps_I1_J,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose_Osimps_I2_J,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__empty,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.62 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__of__filter__in,axiom, % 169.19/169.62 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 169.19/169.62 ( 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) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 169.19/169.62 => 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) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__filter__simps_I1_J,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__shift__lemma__Suc,axiom, % 169.19/169.62 ! [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)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_select__weigth__drop__zero,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_pick__drop__zero,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__transpose,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_i_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__transpose,axiom, % 169.19/169.62 ! [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)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__filter__map__filter,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_insort__key__remove1,axiom, % 169.19/169.62 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 169.19/169.62 ( class_Orderings_Olinorder(T_b) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 169.19/169.62 => ( 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 % 169.19/169.62 => 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 ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__def,axiom, % 169.19/169.62 ! [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))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted_ONil,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__single,axiom, % 169.19/169.62 ! [V_x,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__same,axiom, % 169.19/169.62 ! [V_xs_2,V_g_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => 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)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__filter,axiom, % 169.19/169.62 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 169.19/169.62 => 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))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_take__upt,axiom, % 169.19/169.62 ! [V_n,V_m,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) % 169.19/169.62 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__add__eq__append,axiom, % 169.19/169.62 ! [V_k,V_j,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__Suc,axiom, % 169.19/169.62 ! [V_j,V_i] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__Suc__append,axiom, % 169.19/169.62 ! [V_j,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__eq__Nil__conv,axiom, % 169.19/169.62 ! [V_j_2,V_i_2] : % 169.19/169.62 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 169.19/169.62 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__conv__Nil,axiom, % 169.19/169.62 ! [V_i,V_j] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 169.19/169.62 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__many__eq,axiom, % 169.19/169.62 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))) % 169.19/169.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 169.19/169.62 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__many,axiom, % 169.19/169.62 ! [V_zs,V_y,V_x,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__drop,axiom, % 169.19/169.62 ! [V_n,V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_drop__upt,axiom, % 169.19/169.62 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__upt,axiom, % 169.19/169.62 ! [V_j,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__distinct__set__unique,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 169.19/169.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 169.19/169.62 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 169.19/169.62 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__rec,axiom, % 169.19/169.62 ! [V_j,V_i] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__conv__Cons,axiom, % 169.19/169.62 ! [V_j,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__upt,axiom, % 169.19/169.62 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__insort__insert,axiom, % 169.19/169.62 ! [V_x_2,V_xs_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__remove1,axiom, % 169.19/169.62 ! [V_a,V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__upto,axiom, % 169.19/169.62 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__upt,axiom, % 169.19/169.62 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__list__of__set__range,axiom, % 169.19/169.62 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__insort,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) % 169.19/169.62 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__0,axiom, % 169.19/169.62 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted_Oequations_I1_J,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__take,axiom, % 169.19/169.62 ! [V_n,V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__tl,axiom, % 169.19/169.62 ! [V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__Suc__upt,axiom, % 169.19/169.62 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__insort__key,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))) % 169.19/169.62 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__map__remove1,axiom, % 169.19/169.62 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__butlast,axiom, % 169.19/169.62 ! [V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__insort__insert__key,axiom, % 169.19/169.62 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_atLeastLessThan__upt,axiom, % 169.19/169.62 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__upt,axiom, % 169.19/169.62 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__map__same,axiom, % 169.19/169.62 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => 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))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__upt,axiom, % 169.19/169.62 ! [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) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__Cons,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 169.19/169.62 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 & ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__append,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 169.19/169.62 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 169.19/169.62 & ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ! [B_xa] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__rec__number__of,axiom, % 169.19/169.62 ! [V_n,V_m] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 169.19/169.62 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) % 169.19/169.62 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_upt__eq__Cons__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 169.19/169.62 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 169.19/169.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 169.19/169.62 & V_i_2 = V_x_2 % 169.19/169.62 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__upt,axiom, % 169.19/169.62 ! [V_j,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__insort,axiom, % 169.19/169.62 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 169.19/169.62 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__nth,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2 ). % 169.19/169.62 % 169.19/169.62 fof(fact_atLeastAtMost__upt,axiom, % 169.19/169.62 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_atLeast__upt,axiom, % 169.19/169.62 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 169.19/169.62 ! [V_n_2,V_m_2,V_f_2,T_a] : % 169.19/169.62 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.62 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 169.19/169.62 ! [V_n_2,V_m_2,V_f_2,T_a] : % 169.19/169.62 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.62 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__upt,axiom, % 169.19/169.62 ! [V_j,V_k,V_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_greaterThanAtMost__upt,axiom, % 169.19/169.62 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted_Oequations_I2_J,axiom, % 169.19/169.62 ! [V_a1_2,V_a2_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 169.19/169.62 <=> ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 169.19/169.62 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_greaterThanLessThan__upt,axiom, % 169.19/169.62 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__map__upt,axiom, % 169.19/169.62 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__list__of__set,axiom, % 169.19/169.62 ! [V_A_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.62 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 169.19/169.62 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 169.19/169.62 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_atMost__upto,axiom, % 169.19/169.62 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_insort__remove1,axiom, % 169.19/169.62 ! [V_xs_2,V_a_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__equals__nth__mono,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 <=> ! [B_j] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.62 => ! [B_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__nth__mono,axiom, % 169.19/169.62 ! [V_j,V_i,V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__sorted__distinct__set__unique,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.62 ( class_Orderings_Olinorder(T_b) % 169.19/169.62 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 169.19/169.62 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 169.19/169.62 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 169.19/169.62 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 169.19/169.62 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublist__shift__lemma,axiom, % 169.19/169.62 ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__rectangle,axiom, % 169.19/169.62 ! [V_n_2,T_a,V_xs_2] : % 169.19/169.62 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 169.19/169.62 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 169.19/169.62 => ( ! [B_i] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 ) % 169.19/169.62 => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose_Opsimps_I2_J,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2))) % 169.19/169.62 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose_Opsimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) % 169.19/169.62 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__column,axiom, % 169.19/169.62 ! [V_i_2,V_xs_2,T_a] : % 169.19/169.62 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__aux__filter__head,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_inj__on__rev,axiom, % 169.19/169.62 ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_singleton__rev__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2) % 169.19/169.62 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__singleton__conv,axiom, % 169.19/169.62 ! [V_x_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) % 169.19/169.62 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev_Osimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Nil__is__rev__conv,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__is__Nil__conv,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__concat,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__map,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__foldl__cons,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat__conv__foldl,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__conv__concat,axiom, % 169.19/169.62 ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__append,axiom, % 169.19/169.62 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat__append,axiom, % 169.19/169.62 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__rev,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 169.19/169.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__rev,axiom, % 169.19/169.62 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__is__rev__conv,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 169.19/169.62 <=> V_xs_2 = V_ys_2 ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__swap,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 169.19/169.62 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__rev__ident,axiom, % 169.19/169.62 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 169.19/169.62 % 169.19/169.62 fof(fact_listsum__rev,axiom, % 169.19/169.62 ! [V_xs,T_a] : % 169.19/169.62 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.62 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__rev,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__rev,axiom, % 169.19/169.62 ! [V_ys,T_b,V_xs,T_a] : % 169.19/169.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) % 169.19/169.62 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__filter,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldl__foldr,axiom, % 169.19/169.62 ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldr__foldl,axiom, % 169.19/169.62 ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat_Osimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat__eq__Nil__conv,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : % 169.19/169.62 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 169.19/169.62 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_Nil__eq__concat__conv,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : % 169.19/169.62 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 169.19/169.62 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__concat,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__concat,axiom, % 169.19/169.62 ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__eq__Cons__iff,axiom, % 169.19/169.62 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 169.19/169.62 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__concat,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__concat,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_last__rev,axiom, % 169.19/169.62 ! [T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__rev,axiom, % 169.19/169.62 ! [T_a,V_xs] : % 169.19/169.62 ( V_xs != c_List_Olist_ONil(T_a) % 169.19/169.62 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__transpose,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__drop,axiom, % 169.19/169.62 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__take,axiom, % 169.19/169.62 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rotate__rev,axiom, % 169.19/169.62 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose_Osimps_I3_J,axiom, % 169.19/169.62 ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__nth,axiom, % 169.19/169.62 ! [V_xs,T_a,V_n] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat__injective,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 169.19/169.62 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 169.19/169.62 => ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 169.19/169.62 => V_xs_2 = V_ys_2 ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat__eq__concat__iff,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a] : % 169.19/169.62 ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 169.19/169.62 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 169.19/169.62 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 169.19/169.62 <=> V_xs_2 = V_ys_2 ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_rev__update,axiom, % 169.19/169.62 ! [V_y,V_xs,T_a,V_k] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_concat__map__singleton,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__rev__nth__mono,axiom, % 169.19/169.62 ! [V_j,V_i,V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_foldr__max__sorted,axiom, % 169.19/169.62 ! [V_y_2,V_xs_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 169.19/169.62 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 169.19/169.62 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose_Opsimps_I3_J,axiom, % 169.19/169.62 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2))) % 169.19/169.62 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__transpose__sorted,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 169.19/169.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 169.19/169.62 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 169.19/169.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__column__length,axiom, % 169.19/169.62 ! [V_i_2,V_xs_2,T_a] : % 169.19/169.62 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__aux__filter__tail,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__nth__transpose__sorted,axiom, % 169.19/169.62 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 169.19/169.62 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)))) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transpose__transpose,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 169.19/169.62 => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),V_xs_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 169.19/169.62 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__takeWhile__snd,axiom, % 169.19/169.62 ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_zip__takeWhile__fst,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__eq__all__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__takeWhileD,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__takeWhile__le,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__eq__take,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__takeWhile,axiom, % 169.19/169.62 ! [V_P_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 169.19/169.62 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile_Osimps_I1_J,axiom, % 169.19/169.62 ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__takeWhile,axiom, % 169.19/169.62 ! [V_P_2,V_xs_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__tail,axiom, % 169.19/169.62 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 169.19/169.62 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__map,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_return__list__def,axiom, % 169.19/169.62 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__append1,axiom, % 169.19/169.62 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_nth__length__takeWhile,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.62 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__nth,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__upds__def,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__not__last,axiom, % 169.19/169.62 ! [T_a,V_xs_2] : % 169.19/169.62 ( V_xs_2 != c_List_Olist_ONil(T_a) % 169.19/169.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 169.19/169.62 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 169.19/169.62 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transfer__nat__int__list__return__embed,axiom, % 169.19/169.62 ! [V_l] : % 169.19/169.62 ( c_List_Onat__list(V_l) % 169.19/169.62 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__remdups__concat,axiom, % 169.19/169.62 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__remdups,axiom, % 169.19/169.62 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__remdups__leq,axiom, % 169.19/169.62 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups__map__remdups,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__remdups,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__remdups,axiom, % 169.19/169.62 ! [V_l,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups_Osimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups__eq__nil__right__iff,axiom, % 169.19/169.62 ! [V_x_2,T_a] : % 169.19/169.62 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 169.19/169.62 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups__eq__nil__iff,axiom, % 169.19/169.62 ! [V_x_2,T_a] : % 169.19/169.62 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__remdups__id,axiom, % 169.19/169.62 ! [V_xs,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.62 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups__id__iff__distinct,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 169.19/169.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__remdups__eq,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 169.19/169.62 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups__remdups,axiom, % 169.19/169.62 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups__filter,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remove1__remdups,axiom, % 169.19/169.62 ! [V_x,V_xs,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.62 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_embed__list__def,axiom, % 169.19/169.62 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_remdups_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__remdups__card__conv,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 169.19/169.62 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 169.19/169.62 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 169.19/169.62 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 169.19/169.62 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__neq__rev,axiom, % 169.19/169.62 ! [V_x_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile__neq__rev,axiom, % 169.19/169.62 ! [V_x_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__dropWhile,axiom, % 169.19/169.62 ! [V_P_2,V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile_Osimps_I1_J,axiom, % 169.19/169.62 ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__dropWhile,axiom, % 169.19/169.62 ! [V_P_2,V_xs_2,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 169.19/169.62 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) ) % 169.19/169.62 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile__eq__Nil__conv,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 169.19/169.62 <=> ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__dropWhile__le,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_takeWhile__dropWhile__id,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2 ). % 169.19/169.62 % 169.19/169.62 fof(fact_hd__dropWhile,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 169.19/169.62 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile__map,axiom, % 169.19/169.62 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile__append1,axiom, % 169.19/169.62 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.62 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile__eq__Cons__conv,axiom, % 169.19/169.62 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 169.19/169.62 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 169.19/169.62 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) % 169.19/169.62 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile__eq__drop,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 169.19/169.62 % 169.19/169.62 fof(fact_dropWhile__nth,axiom, % 169.19/169.62 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 169.19/169.62 => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_listsum__map__filter,axiom, % 169.19/169.62 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 169.19/169.62 ( class_Groups_Omonoid__add(T_b) % 169.19/169.62 => ( ! [B_x] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.62 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 169.19/169.62 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 169.19/169.62 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sorted__nth__monoI,axiom, % 169.19/169.62 ! [V_xs,T_a] : % 169.19/169.62 ( class_Orderings_Olinorder(T_a) % 169.19/169.62 => ( ! [B_i,B_j] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 169.19/169.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) ) % 169.19/169.62 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_n__lists_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublists__powset,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__n__lists,axiom, % 169.19/169.62 ! [V_n,V_xs,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_distinct__set__sublists,axiom, % 169.19/169.62 ! [V_xs_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__n__lists,axiom, % 169.19/169.62 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__n__lists__elem,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 169.19/169.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)))) % 169.19/169.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublists_Osimps_I1_J,axiom, % 169.19/169.62 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_n__lists_Osimps_I1_J,axiom, % 169.19/169.62 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_n__lists__Nil,axiom, % 169.19/169.62 ! [T_a,V_n] : % 169.19/169.62 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) % 169.19/169.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.62 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_sublists_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_set__n__lists,axiom, % 169.19/169.62 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 169.19/169.62 % 169.19/169.62 fof(fact_length__sublists,axiom, % 169.19/169.62 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_product_Osimps_I2_J,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) ). % 169.19/169.62 % 169.19/169.62 fof(fact_map__of__zip__enum__inject,axiom, % 169.19/169.62 ! [V_ys_2,V_xs_2,T_a,T_b] : % 169.19/169.62 ( ( class_Enum_Oenum(T_b) % 169.19/169.62 & class_Enum_Oenum(T_a) ) % 169.19/169.62 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 169.19/169.62 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 169.19/169.62 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2))) % 169.19/169.62 => V_xs_2 = V_ys_2 ) ) ) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_enum__prod__def,axiom, % 169.19/169.62 ! [T_b,T_a] : % 169.19/169.62 ( ( class_Enum_Oenum(T_a) % 169.19/169.62 & class_Enum_Oenum(T_b) ) % 169.19/169.62 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_enum__distinct,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Enum_Oenum(T_a) % 169.19/169.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_enum__UNIV,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Enum_Oenum(T_a) % 169.19/169.62 => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_UNIV__enum,axiom, % 169.19/169.62 ! [T_a] : % 169.19/169.62 ( class_Enum_Oenum(T_a) % 169.19/169.62 => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ) ). % 169.19/169.62 % 169.19/169.62 fof(fact_in__enum,axiom, % 169.19/169.62 ! [V_x_2,T_a] : % 169.19/169.62 ( class_Enum_Oenum(T_a) % 169.19/169.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__option__def,axiom, % 169.19/169.63 ! [T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__fun__def,axiom, % 169.19/169.63 ! [T_b,T_a] : % 169.19/169.63 ( ( class_Enum_Oenum(T_a) % 169.19/169.63 & class_Enum_Oenum(T_b) ) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__fun__code,axiom, % 169.19/169.63 ! [T_b,T_a] : % 169.19/169.63 ( ( class_Enum_Oenum(T_a) % 169.19/169.63 & class_HOL_Oequal(T_a) % 169.19/169.63 & class_Enum_Oenum(T_b) ) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_product_Osimps_I1_J,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_distinct__product,axiom, % 169.19/169.63 ! [V_ys,T_b,V_xs,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 169.19/169.63 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_ex__n__lists__def,axiom, % 169.19/169.63 ! [V_n_2,V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 169.19/169.63 <=> ? [B_x] : % 169.19/169.63 ( 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))))) % 169.19/169.63 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_all__n__lists__def,axiom, % 169.19/169.63 ! [V_n_2,V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 169.19/169.63 <=> ! [B_x] : % 169.19/169.63 ( 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))))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__all__fun__def,axiom, % 169.19/169.63 ! [V_P_2,T_a,T_b] : % 169.19/169.63 ( ( class_Enum_Oenum(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 169.19/169.63 <=> 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__ex__fun__def,axiom, % 169.19/169.63 ! [V_P_2,T_a,T_b] : % 169.19/169.63 ( ( class_Enum_Oenum(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 169.19/169.63 <=> 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_all__code,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.19/169.63 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_exists__code,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 169.19/169.63 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__all,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 169.19/169.63 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__ex,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 169.19/169.63 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__all__option__def,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 169.19/169.63 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 169.19/169.63 & 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)))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__ex__option__def,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 169.19/169.63 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 169.19/169.63 | 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)))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__ex__prod__def,axiom, % 169.19/169.63 ! [V_P_2,T_a,T_b] : % 169.19/169.63 ( ( class_Enum_Oenum(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 169.19/169.63 <=> 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))))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__all__prod__def,axiom, % 169.19/169.63 ! [V_P_2,T_a,T_b] : % 169.19/169.63 ( ( class_Enum_Oenum(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 169.19/169.63 <=> 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))))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_order__fun_I1_J,axiom, % 169.19/169.63 ! [V_g_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( ( class_Orderings_Oorder(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 169.19/169.63 <=> 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_order__fun_I2_J,axiom, % 169.19/169.63 ! [V_g_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( ( class_Orderings_Oorder(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 169.19/169.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 169.19/169.63 & 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)))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__ex__fun__code,axiom, % 169.19/169.63 ! [V_P_2,T_a,T_b] : % 169.19/169.63 ( ( class_Enum_Oenum(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) % 169.19/169.63 & class_HOL_Oequal(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 169.19/169.63 <=> 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__all__fun__code,axiom, % 169.19/169.63 ! [V_P_2,T_a,T_b] : % 169.19/169.63 ( ( class_Enum_Oenum(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) % 169.19/169.63 & class_HOL_Oequal(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 169.19/169.63 <=> 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sort__foldl__insort,axiom, % 169.19/169.63 ! [V_xs_2,T_a] : % 169.19/169.63 ( class_Orderings_Olinorder(T_a) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_map__of__zip__enum__is__Some,axiom, % 169.19/169.63 ! [V_x,V_ys,T_b,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( 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)) % 169.19/169.63 => ? [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) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_distinct__sort,axiom, % 169.19/169.63 ! [V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( class_Orderings_Olinorder(T_b) % 169.19/169.63 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 169.19/169.63 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_filter__sort,axiom, % 169.19/169.63 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 169.19/169.63 ( class_Orderings_Olinorder(T_b) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_length__sort,axiom, % 169.19/169.63 ! [V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( class_Orderings_Olinorder(T_b) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sort__key__simps_I1_J,axiom, % 169.19/169.63 ! [V_f_2,T_a,T_b] : % 169.19/169.63 ( class_Orderings_Olinorder(T_b) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sorted__sort,axiom, % 169.19/169.63 ! [V_xs_2,T_a] : % 169.19/169.63 ( class_Orderings_Olinorder(T_a) % 169.19/169.63 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_set__sort,axiom, % 169.19/169.63 ! [V_xs_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( class_Orderings_Olinorder(T_b) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sorted__sort__key,axiom, % 169.19/169.63 ! [V_xs_2,V_f_2,T_b,T_a] : % 169.19/169.63 ( class_Orderings_Olinorder(T_a) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sort__key__simps_I2_J,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( class_Orderings_Olinorder(T_b) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 169.19/169.63 ! [V_xs_2,T_a] : % 169.19/169.63 ( class_Orderings_Olinorder(T_a) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_takeWhile__eq__filter,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.63 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_takeWhile__eq__take__P__nth,axiom, % 169.19/169.63 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 169.19/169.63 ( ! [B_i] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 169.19/169.63 => ( 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))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 169.19/169.63 => ( ( 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))) % 169.19/169.63 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 169.19/169.63 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_length__takeWhile__less__P__nth,axiom, % 169.19/169.63 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 169.19/169.63 ( ! [B_i] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 169.19/169.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_lists__Int__eq,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp_ONil,axiom, % 169.19/169.63 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp__conj__eq,axiom, % 169.19/169.63 ! [V_x_2,V_B_2,V_A_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 169.19/169.63 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp__infI,axiom, % 169.19/169.63 ! [V_B_2,V_l_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 169.19/169.63 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp__inf__eq,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp_Oequations_I1_J,axiom, % 169.19/169.63 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__listsp__conv__set,axiom, % 169.19/169.63 ! [V_xs_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 169.19/169.63 <=> ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_append__in__listsp__conv,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 169.19/169.63 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 169.19/169.63 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp_Oequations_I2_J,axiom, % 169.19/169.63 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 169.19/169.63 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 169.19/169.63 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp__mono,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listsp__lists__eq,axiom, % 169.19/169.63 ! [V_x_2,V_A_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_lists__IntI,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_l_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__def,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 <=> ( 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) % 169.19/169.63 & ! [B_x] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sorted_Osimps,axiom, % 169.19/169.63 ! [V_a_2,T_a] : % 169.19/169.63 ( class_Orderings_Olinorder(T_a) % 169.19/169.63 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 169.19/169.63 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 169.19/169.63 | ? [B_xs,B_x] : % 169.19/169.63 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 169.19/169.63 & ! [B_xa] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 169.19/169.63 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__map2,axiom, % 169.19/169.63 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__map1,axiom, % 169.19/169.63 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 169.19/169.63 ( 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) % 169.19/169.63 <=> 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__Cons,axiom, % 169.19/169.63 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 169.19/169.63 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__appendI,axiom, % 169.19/169.63 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 169.19/169.63 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__append,axiom, % 169.19/169.63 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.63 ( 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) % 169.19/169.63 => ( 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)) % 169.19/169.63 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__rev,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__rev1,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 169.19/169.63 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__Nil,axiom, % 169.19/169.63 ! [V_ys_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 169.19/169.63 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__Nil2,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 169.19/169.63 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__takeI,axiom, % 169.19/169.63 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__dropI,axiom, % 169.19/169.63 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__lengthD,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__eq,axiom, % 169.19/169.63 ! [T_a,V_ys_2,V_xs_2] : % 169.19/169.63 ( V_xs_2 = V_ys_2 % 169.19/169.63 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__conv__all__nth,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 <=> ( 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) % 169.19/169.63 & ! [B_i] : % 169.19/169.63 ( 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))) % 169.19/169.63 => 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))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__nthD,axiom, % 169.19/169.63 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__nthD2,axiom, % 169.19/169.63 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__update__cong2,axiom, % 169.19/169.63 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 169.19/169.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__update__cong,axiom, % 169.19/169.63 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2I,axiom, % 169.19/169.63 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 169.19/169.63 => ( 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) % 169.19/169.63 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_all__nth__imp__all__set,axiom, % 169.19/169.63 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 169.19/169.63 ( ! [B_i] : % 169.19/169.63 ( 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))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_List_Oinsert__def,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.63 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 169.19/169.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => 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) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_not__in__set__insert,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_insert__remdups,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_distinct__insert,axiom, % 169.19/169.63 ! [V_x,V_xs,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 169.19/169.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__set__insert,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_List_Oset__insert,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_insert__Nil,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_concat__map__maps,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_maps__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_maps__simps_I2_J,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_maps__simps_I1_J,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__conv__nat__seg__image,axiom, % 169.19/169.63 ! [V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 <=> ? [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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_distinct__concat,axiom, % 169.19/169.63 ! [V_xs_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 169.19/169.63 => ( ! [B_ys] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 169.19/169.63 => ( ! [B_ys] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.63 => ! [B_zs] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 169.19/169.63 => ( B_ys != B_zs % 169.19/169.63 => 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)) ) ) ) % 169.19/169.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 169.19/169.63 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 169.19/169.63 ( ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.63 & class_Groups_Ocomm__monoid__mult(T_a) ) % 169.19/169.63 => ( V_A_2 = V_B_2 % 169.19/169.63 => ( c_Nat__Transfer_Onat__set(V_B_2) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 169.19/169.63 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 169.19/169.63 => 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) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_accp__acc__eq,axiom, % 169.19/169.63 ! [V_x_2,V_r_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Cons__acc__listrel1I,axiom, % 169.19/169.63 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 169.19/169.63 => ( 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)))) % 169.19/169.63 => 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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_lists__accI,axiom, % 169.19/169.63 ! [V_r_2,V_xs_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_lists__accD,axiom, % 169.19/169.63 ! [V_r_2,V_xs_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acc__subset,axiom, % 169.19/169.63 ! [V_R2_2,V_R1_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acc_Osimps,axiom, % 169.19/169.63 ! [V_r_2,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 169.19/169.63 <=> ! [B_x] : % 169.19/169.63 ( 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)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acc__downward,axiom, % 169.19/169.63 ! [V_a_2,V_r_2,V_b_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 169.19/169.63 => ( 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)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_measures__lesseq,axiom, % 169.19/169.63 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__def,axiom, % 169.19/169.63 ! [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))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__compI,axiom, % 169.19/169.63 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__UNION__distrib2,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__UNION__distrib,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__mono,axiom, % 169.19/169.63 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_union__comp__emptyL,axiom, % 169.19/169.63 ! [V_B_2,V_C_2,V_A_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_union__comp__emptyR,axiom, % 169.19/169.63 ! [V_C_2,V_B_2,V_A_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__empty1,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__empty2,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_O__assoc,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__distrib2,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__distrib,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__measures_I1_J,axiom, % 169.19/169.63 ! [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))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_measures__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_max__ext__compat,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_min__ext__compat,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_measures__less,axiom, % 169.19/169.63 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 169.19/169.63 ( 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))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__measures_I2_J,axiom, % 169.19/169.63 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 <=> ( 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))) % 169.19/169.63 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 169.19/169.63 & 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))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pred__comp__rel__comp__eq,axiom, % 169.19/169.63 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_reduction__pairI,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_R_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__less__than,axiom, % 169.19/169.63 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pred__comp_Ointros,axiom, % 169.19/169.63 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__empty,axiom, % 169.19/169.63 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__inv__image,axiom, % 169.19/169.63 ! [V_f_2,T_b,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__lex,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__lex__prod,axiom, % 169.19/169.63 ! [V_rb_2,T_b,V_ra_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_ra_2) % 169.19/169.63 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 169.19/169.63 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__lenlex,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__measure,axiom, % 169.19/169.63 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acc__wfD,axiom, % 169.19/169.63 ! [V_x_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__acc__iff,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__no__loop,axiom, % 169.19/169.63 ! [V_R_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__union__merge,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__measures,axiom, % 169.19/169.63 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__comp__self,axiom, % 169.19/169.63 ! [V_R_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_R_2) % 169.19/169.63 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__less,axiom, % 169.19/169.63 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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__lexn,axiom, % 169.19/169.63 ! [V_n_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_max__ext__wf,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__pair__less,axiom, % 169.19/169.63 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__mlex,axiom, % 169.19/169.63 ! [V_f_2,V_R_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_R_2) % 169.19/169.63 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pred__comp_Oequations,axiom, % 169.19/169.63 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> ? [B_b] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 169.19/169.63 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__finite__psubset,axiom, % 169.19/169.63 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_min__ext__wf,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__int__ge__less__than2,axiom, % 169.19/169.63 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__int__ge__less__than,axiom, % 169.19/169.63 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__irrefl,axiom, % 169.19/169.63 ! [V_a_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ~ 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__asym,axiom, % 169.19/169.63 ! [V_x_2,V_a_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => ~ 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__not__sym,axiom, % 169.19/169.63 ! [V_x_2,V_a_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => ~ 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__not__refl,axiom, % 169.19/169.63 ! [V_a_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ~ 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__subset,axiom, % 169.19/169.63 ! [V_p_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__Int1,axiom, % 169.19/169.63 ! [V_r_H_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__Int2,axiom, % 169.19/169.63 ! [V_r_H_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 <=> ~ ? [B_f] : % 169.19/169.63 ! [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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfE__pf,axiom, % 169.19/169.63 ! [V_A_2,V_R_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_R_2) % 169.19/169.63 => ( 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))) % 169.19/169.63 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__union__compatible,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_R_2) % 169.19/169.63 => ( c_Wellfounded_Owf(T_a,V_S_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf,axiom, % 169.19/169.63 ! [T_a] : % 169.19/169.63 ( class_Orderings_Owellorder(T_a) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_reduction__pair__def,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 169.19/169.63 <=> ( 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)) % 169.19/169.63 & 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_reduction__pair__lemma,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,V_P_2,T_a] : % 169.19/169.63 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 169.19/169.63 => ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => ( c_Wellfounded_Owf(T_a,V_S_2) % 169.19/169.63 => 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)) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__map__pair__image,axiom, % 169.19/169.63 ! [V_f_2,T_b,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__if__measure,axiom, % 169.19/169.63 ! [T_a,V_g_2,V_f_2,V_P_2] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(V_P_2,B_x)) % 169.19/169.63 => 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))) ) % 169.19/169.63 => 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))))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_max__extp_Oequations,axiom, % 169.19/169.63 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 169.19/169.63 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 169.19/169.63 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 169.19/169.63 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 & ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 169.19/169.63 => ? [B_xa] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 169.19/169.63 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pred__nat__def,axiom, % 169.19/169.63 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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__same__fst,axiom, % 169.19/169.63 ! [T_a,V_R_2,T_b,V_P_2] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(V_P_2,B_x)) % 169.19/169.63 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 169.19/169.63 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__pred__nat,axiom, % 169.19/169.63 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 169.19/169.63 % 169.19/169.63 fof(fact_max__ext_Ointros,axiom, % 169.19/169.63 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 169.19/169.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 169.19/169.63 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 169.19/169.63 => ? [B_xa] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 169.19/169.63 & 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)) ) ) % 169.19/169.63 => 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))) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Ozero__frac__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Oone__frac__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Ofrac__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__Collect__split,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_RangeI,axiom, % 169.19/169.63 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__Diff__subset,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__empty__iff,axiom, % 169.19/169.63 ! [V_r_2,T_a,T_b] : % 169.19/169.63 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__empty,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__Un__eq,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__Union,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__Id__on,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__Range,axiom, % 169.19/169.63 ! [V_r_2,T_b,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_snd__eq__Range,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__iff,axiom, % 169.19/169.63 ! [V_r_2,T_b,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 169.19/169.63 <=> ? [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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__insert,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__Int__subset,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_RangeP__Range__eq,axiom, % 169.19/169.63 ! [V_x_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_RangeE,axiom, % 169.19/169.63 ! [V_r_2,T_b,V_b_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 169.19/169.63 => ~ ! [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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_RangeP_Ointros,axiom, % 169.19/169.63 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 169.19/169.63 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_RangeP_Oequations,axiom, % 169.19/169.63 ! [V_a2_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 169.19/169.63 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__Un,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ( c_Wellfounded_Owf(T_a,V_s_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_the__elem__def,axiom, % 169.19/169.63 ! [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))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_DomainI,axiom, % 169.19/169.63 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__empty__iff,axiom, % 169.19/169.63 ! [V_r_2,T_b,T_a] : % 169.19/169.63 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__empty,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__Un__eq,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__mono,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__Domain,axiom, % 169.19/169.63 ! [V_r_2,T_b,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__Id__on,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_fst__eq__Domain,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_split__paired__The,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_The__split__eq,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__iff,axiom, % 169.19/169.63 ! [V_r_2,T_b,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 169.19/169.63 <=> ? [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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_the__inv__into__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_fold__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__insert,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_divmod__nat__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__Int__subset,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_fold1__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__Diff__subset,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Field__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_The__split,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__Union,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__Collect__split,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_DomainP__Domain__eq,axiom, % 169.19/169.63 ! [V_x_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_enum__the__def,axiom, % 169.19/169.63 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 169.19/169.63 % 169.19/169.63 fof(fact_DomainP_Ointros,axiom, % 169.19/169.63 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 169.19/169.63 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_DomainP_Oequations,axiom, % 169.19/169.63 ! [V_a1_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 169.19/169.63 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_flat__lub__def,axiom, % 169.19/169.63 ! [V_b_2,V_A_2,T_a] : % 169.19/169.63 ( ( 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))))) % 169.19/169.63 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 169.19/169.63 & ( ~ 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))))) % 169.19/169.63 => 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)))))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_inj__vimage__singleton,axiom, % 169.19/169.63 ! [V_a_2,V_f_2,T_b,T_a] : % 169.19/169.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.63 => 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))))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimageI,axiom, % 169.19/169.63 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 169.19/169.63 ( hAPP(V_f_2,V_a_2) = V_b_2 % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_image__vimage__eq,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__vimageI,axiom, % 169.19/169.63 ! [V_h_2,T_b,V_F_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 169.19/169.63 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__Diff,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__UN,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__Union,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__subsetD,axiom, % 169.19/169.63 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__singleton__eq,axiom, % 169.19/169.63 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 169.19/169.63 ( 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)))))) % 169.19/169.63 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__Un,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__empty,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__mono,axiom, % 169.19/169.63 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_image__vimage__subset,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__Int,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__INT,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__UNIV,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__ident,axiom, % 169.19/169.63 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__code,axiom, % 169.19/169.63 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 169.19/169.63 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__Compl,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimageI2,axiom, % 169.19/169.63 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimageD,axiom, % 169.19/169.63 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__eq,axiom, % 169.19/169.63 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_surj__image__vimage__eq,axiom, % 169.19/169.63 ! [V_A_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__compose,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__vimageD,axiom, % 169.19/169.63 ! [V_F_2,V_h_2,T_b,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 169.19/169.63 => ( 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)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__insert,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__Collect__eq,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_inj__vimage__image__eq,axiom, % 169.19/169.63 ! [V_A_2,V_f_2,T_b,T_a] : % 169.19/169.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.63 => 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 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__const,axiom, % 169.19/169.63 ! [T_b,V_A_2,V_ca_2,T_a] : % 169.19/169.63 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.19/169.63 => 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)) ) % 169.19/169.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__eq__UN,axiom, % 169.19/169.63 ! [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))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__subsetI,axiom, % 169.19/169.63 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 169.19/169.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__if,axiom, % 169.19/169.63 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 169.19/169.63 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.19/169.63 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 169.19/169.63 => 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)) ) % 169.19/169.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 169.19/169.63 => 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 ) ) ) % 169.19/169.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 169.19/169.63 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 169.19/169.63 => 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) ) % 169.19/169.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 169.19/169.63 => 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)) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_image__split__eq__Sigma,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_DomainE,axiom, % 169.19/169.63 ! [V_r_2,T_b,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 169.19/169.63 => ~ ! [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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_SigmaI,axiom, % 169.19/169.63 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_setprod__cartesian__product,axiom, % 169.19/169.63 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 169.19/169.63 ( class_Groups_Ocomm__monoid__mult(T_a) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_setsum__cartesian__product,axiom, % 169.19/169.63 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 169.19/169.63 ( class_Groups_Ocomm__monoid__add(T_a) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_card__cartesian__product__singleton,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_UNIV__Times__UNIV,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Times__eq__cancel2,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 169.19/169.63 => ( 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)) % 169.19/169.63 <=> V_A_2 = V_B_2 ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Compl__Times__UNIV2,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Compl__Times__UNIV1,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_card__cartesian__product,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__cartesian__product,axiom, % 169.19/169.63 ! [V_B_2,T_b,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 169.19/169.63 => 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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_SigmaE2,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.63 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_SigmaD2,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_SigmaD1,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_mem__Sigma__iff,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 169.19/169.63 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__Int__distrib2,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Times__Int__distrib1,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__Int__distrib1,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel__subset,axiom, % 169.19/169.63 ! [V_A_2,V_r_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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))))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Id__on__subset__Times,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_equiv__type,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__empty1,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__empty2,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Times__empty,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__Un__distrib2,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Times__Un__distrib1,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__Un__distrib1,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__comp__subset__Sigma,axiom, % 169.19/169.63 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => ( 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)))) % 169.19/169.63 => 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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Times__subset__cancel2,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 169.19/169.63 => ( 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)))) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__Union,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__Diff__distrib2,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Times__Diff__distrib1,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__Diff__distrib1,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Image__subset,axiom, % 169.19/169.63 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__cartesian__productD2,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,T_b,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__cartesian__productD1,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,T_b,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_SetCompr__Sigma__eq,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Collect__split,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_fst__image__times,axiom, % 169.19/169.63 ! [V_A_2,T_b,T_a,V_B_2] : % 169.19/169.63 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 => 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)) ) % 169.19/169.63 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 => 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 ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_snd__image__times,axiom, % 169.19/169.63 ! [V_B_2,T_b,T_a,V_A_2] : % 169.19/169.63 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 => 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)) ) % 169.19/169.63 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 => 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 ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_map__pair__surj__on,axiom, % 169.19/169.63 ! [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] : % 169.19/169.63 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 169.19/169.63 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_product__list__set,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_swap__product,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_refl__on__def,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.63 <=> ( 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)))) % 169.19/169.63 & ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_insert__times__insert,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__equiv__class,axiom, % 169.19/169.63 ! [V_X_2,V_r_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( 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)))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_map__pair__inj__on,axiom, % 169.19/169.63 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 169.19/169.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 169.19/169.63 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_UN__Times__distrib,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__def,axiom, % 169.19/169.63 ! [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))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__quotient,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( 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)))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__Times,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_setsum__mult__setsum__if__inj,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 169.19/169.63 ( class_Rings_Osemiring__0(T_c) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))))))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 169.19/169.63 ! [V_A_2,V_I_2,T_b,T_a] : % 169.19/169.63 ? [B_f] : % 169.19/169.63 ( 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)) % 169.19/169.63 & 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_surj__id,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_image__id,axiom, % 169.19/169.63 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 169.19/169.63 % 169.19/169.63 fof(fact_folding_Oempty,axiom, % 169.19/169.63 ! [V_F_2,V_f_2,T_b,T_a] : % 169.19/169.63 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 169.19/169.63 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_List_Omap_Oidentity,axiom, % 169.19/169.63 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_List_Omap_Oid,axiom, % 169.19/169.63 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_apsnd__def,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_apfst__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_apfst__id,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_id__def,axiom, % 169.19/169.63 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 169.19/169.63 % 169.19/169.63 fof(fact_id__apply,axiom, % 169.19/169.63 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 169.19/169.63 % 169.19/169.63 fof(fact_apsnd__id,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_of__int__eq__id,axiom, % 169.19/169.63 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 169.19/169.63 % 169.19/169.63 fof(fact_inj__on__id,axiom, % 169.19/169.63 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Option_Omap_Oid,axiom, % 169.19/169.63 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Option_Omap_Oidentity,axiom, % 169.19/169.63 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_map__pair_Oidentity,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_map__pair_Oid,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rotate0,axiom, % 169.19/169.63 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_id__o,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_o__id,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_o__eq__id__dest,axiom, % 169.19/169.63 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 169.19/169.63 ( 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) % 169.19/169.63 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_split__Pair,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_vimage__id,axiom, % 169.19/169.63 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 169.19/169.63 % 169.19/169.63 fof(fact_setsum__reindex__id,axiom, % 169.19/169.63 ! [V_B_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( class_Groups_Ocomm__monoid__add(T_b) % 169.19/169.63 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_setprod__reindex__id,axiom, % 169.19/169.63 ! [V_B_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( class_Groups_Ocomm__monoid__mult(T_b) % 169.19/169.63 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_setprod__Sigma,axiom, % 169.19/169.63 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 169.19/169.63 ( class_Groups_Ocomm__monoid__mult(T_c) % 169.19/169.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_refl__onI,axiom, % 169.19/169.63 ! [V_A_2,V_r_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => 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)) ) % 169.19/169.63 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_setsum__Sigma,axiom, % 169.19/169.63 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 169.19/169.63 ( class_Groups_Ocomm__monoid__add(T_c) % 169.19/169.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_fold__image__Sigma,axiom, % 169.19/169.63 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 169.19/169.63 ( class_Groups_Ocomm__monoid__mult(T_c) % 169.19/169.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 169.19/169.63 => 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_card__SigmaI,axiom, % 169.19/169.63 ! [V_B_2,T_b,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 169.19/169.63 => 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) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__SigmaI,axiom, % 169.19/169.63 ! [V_B_2,T_b,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( ! [B_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_SigmaE,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => ! [B_y] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 169.19/169.63 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_foldl__apply,axiom, % 169.19/169.63 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => 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)) ) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfP__def,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_OwfP(T_a,V_r_2) % 169.19/169.63 <=> 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Rep__Integ__induct,axiom, % 169.19/169.63 ! [V_P_2,V_y_2] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 169.19/169.63 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfP__empty,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfP__accp__iff,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_OwfP(T_a,V_r_2) % 169.19/169.63 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_accp__wfPD,axiom, % 169.19/169.63 ! [V_x_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_OwfP(T_a,V_r_2) % 169.19/169.63 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfP__subset,axiom, % 169.19/169.63 ! [V_p_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_OwfP(T_a,V_r_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__in__rel,axiom, % 169.19/169.63 ! [V_R_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_R_2) % 169.19/169.63 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfP__wf__eq,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfP__acyclicP,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_OwfP(T_a,V_r_2) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Rep__Integ__cases,axiom, % 169.19/169.63 ! [V_y_2] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 169.19/169.63 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acyclic__subset,axiom, % 169.19/169.63 ! [V_r_2,V_s_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__acyclic,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__iff__acyclic__if__finite,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 169.19/169.63 => ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__acyclic__wf,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 169.19/169.63 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Owf_H__def,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Nitpick_Owf_H(T_a,V_r_2) % 169.19/169.63 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 169.19/169.63 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 169.19/169.63 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_inj__on__INTER,axiom, % 169.19/169.63 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 169.19/169.63 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 => ( ! [B_i] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 169.19/169.63 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_zip__obtain__same__length,axiom, % 169.19/169.63 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 169.19/169.63 ( ( 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)) % 169.19/169.63 => 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)))) ) % 169.19/169.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_map__of__eqI,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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) ) % 169.19/169.63 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_the__sym__eq__trivial,axiom, % 169.19/169.63 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 169.19/169.63 % 169.19/169.63 fof(fact_the__eq__trivial,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_pigeonhole__infinite,axiom, % 169.19/169.63 ! [V_f_2,T_b,V_A_2,T_a] : % 169.19/169.63 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 169.19/169.63 => ? [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 & ~ 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)))))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Abs__Integ__induct,axiom, % 169.19/169.63 ! [V_x_2,V_P_2] : % 169.19/169.63 ( ! [B_y] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 169.19/169.63 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 169.19/169.63 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Abs__Integ__cases,axiom, % 169.19/169.63 ! [V_x_2] : % 169.19/169.63 ~ ! [B_y] : % 169.19/169.63 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 169.19/169.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__UN__I,axiom, % 169.19/169.63 ! [V_B_2,T_b,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ( ! [B_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 169.19/169.63 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_inj__on__diff__nat,axiom, % 169.19/169.63 ! [V_k_2,V_N_2] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfP__SUP,axiom, % 169.19/169.63 ! [T_a,V_r_2,T_b] : % 169.19/169.63 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 169.19/169.63 => ( ! [B_i,B_j] : % 169.19/169.63 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 169.19/169.63 => 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)) ) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pos__not__random__dseq__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_dropWhile__append2,axiom, % 169.19/169.63 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all2__all__nthI,axiom, % 169.19/169.63 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 169.19/169.63 ( 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) % 169.19/169.63 => ( ! [B_n] : % 169.19/169.63 ( 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))) % 169.19/169.63 => 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))) ) % 169.19/169.63 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_mem__splitI2,axiom, % 169.19/169.63 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 169.19/169.63 ( ! [B_a,B_b] : % 169.19/169.63 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_mem__splitE,axiom, % 169.19/169.63 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ ! [B_x,B_y] : % 169.19/169.63 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 169.19/169.63 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__sorted__distinct__unique,axiom, % 169.19/169.63 ! [V_A_2,T_a] : % 169.19/169.63 ( class_Orderings_Olinorder(T_a) % 169.19/169.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 169.19/169.63 => ? [B_x] : % 169.19/169.63 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 169.19/169.63 & c_List_Olinorder__class_Osorted(T_a,B_x) % 169.19/169.63 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 169.19/169.63 & ! [B_y] : % 169.19/169.63 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 169.19/169.63 & c_List_Olinorder__class_Osorted(T_a,B_y) % 169.19/169.63 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 169.19/169.63 => B_y = B_x ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_takeWhile__append2,axiom, % 169.19/169.63 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_insort__is__Cons,axiom, % 169.19/169.63 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 169.19/169.63 ( class_Orderings_Olinorder(T_b) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 169.19/169.63 => 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) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wfI__pf,axiom, % 169.19/169.63 ! [V_R_2,T_a] : % 169.19/169.63 ( ! [B_A] : % 169.19/169.63 ( 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))) % 169.19/169.63 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 169.19/169.63 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Cons__eq__filter__iff,axiom, % 169.19/169.63 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 169.19/169.63 ( 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) % 169.19/169.63 <=> ? [B_us,B_vs] : % 169.19/169.63 ( 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)) % 169.19/169.63 & ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 169.19/169.63 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.63 & hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.63 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_filter__eq__Cons__iff,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 169.19/169.63 ( 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) % 169.19/169.63 <=> ? [B_us,B_vs] : % 169.19/169.63 ( 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)) % 169.19/169.63 & ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 169.19/169.63 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.63 & hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.63 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Sigma__mono,axiom, % 169.19/169.63 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => 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))) ) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_not__acc__down,axiom, % 169.19/169.63 ! [V_R_2,V_x_2,T_a] : % 169.19/169.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 169.19/169.63 => ~ ! [B_z] : % 169.19/169.63 ( 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)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acc_OaccI,axiom, % 169.19/169.63 ! [V_r_2,V_x_2,T_a] : % 169.19/169.63 ( ! [B_y] : % 169.19/169.63 ( 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)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ball__nth,axiom, % 169.19/169.63 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_max__ext_Osimps,axiom, % 169.19/169.63 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 169.19/169.63 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 169.19/169.63 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 169.19/169.63 & ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 169.19/169.63 => ? [B_xa] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 169.19/169.63 & 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)) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sorted_OCons,axiom, % 169.19/169.63 ! [V_x_2,V_xs_2,T_a] : % 169.19/169.63 ( class_Orderings_Olinorder(T_a) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 169.19/169.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 169.19/169.63 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__no__infinite__down__chainE,axiom, % 169.19/169.63 ! [V_f_2,V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => ~ ! [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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex__length,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 169.19/169.63 <=> ? [B_n] : % 169.19/169.63 ( 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))) % 169.19/169.63 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_less__eq,axiom, % 169.19/169.63 ! [V_n_2,V_m_2] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_less__than__def,axiom, % 169.19/169.63 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex__simps_I2_J,axiom, % 169.19/169.63 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex__append,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 169.19/169.63 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 169.19/169.63 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex__rev,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 169.19/169.63 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex__iff,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 169.19/169.63 <=> ? [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex__simps_I1_J,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 169.19/169.63 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.63 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__trancl,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acyclic__def,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 169.19/169.63 <=> ! [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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl_Or__into__trancl,axiom, % 169.19/169.63 ! [V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__subset__Field2,axiom, % 169.19/169.63 ! [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))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_r__into__trancl_H,axiom, % 169.19/169.63 ! [V_r_2,V_p_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__empty,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__domain,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__range,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__trancl,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 169.19/169.63 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__trans,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__into__trancl2,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_r__r__into__trancl,axiom, % 169.19/169.63 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__mono,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,V_p_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 169.19/169.63 => ( 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)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__unfold,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__subset__Sigma,axiom, % 169.19/169.63 ! [V_A_2,V_r_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__Int__subset,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__insert,axiom, % 169.19/169.63 ! [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)))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_reflcl__set__eq,axiom, % 169.19/169.63 ! [V_y_2,V_x_2,V_r_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_r__into__rtrancl,axiom, % 169.19/169.63 ! [V_r_2,V_p_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl_Ortrancl__refl,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_IdI,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__into__rtrancl,axiom, % 169.19/169.63 ! [V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel__rtrancl__refl,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__unfold__left,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__unfold__right,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_reflcl__trancl,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__reflcl,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__eq__or__trancl,axiom, % 169.19/169.63 ! [V_R_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> ( V_x_2 = V_y_2 % 169.19/169.63 | ( V_x_2 != V_y_2 % 169.19/169.63 & 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))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__into__trancl2,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtranclD,axiom, % 169.19/169.63 ! [V_R_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( V_a_2 = V_b_2 % 169.19/169.63 | ( V_a_2 != V_b_2 % 169.19/169.63 & 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))) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__into__trancl1,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__rtrancl__trancl,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__trancl__trancl,axiom, % 169.19/169.63 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__trancl__absorb,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__rtrancl__absorb,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__rtrancl,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__rtrancl,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__idemp,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__trans,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 169.19/169.63 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_refl__rtrancl,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__Un__subset,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__mono,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__subset,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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))) % 169.19/169.63 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__subset__rtrancl,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Image__closed__trancl,axiom, % 169.19/169.63 ! [V_X_2,V_r_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__empty,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__reflcl,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__Un__rtrancl,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__reflcl__absorb,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__rtrancl__UnI,axiom, % 169.19/169.63 ! [V_S_2,V_R_2,V_x_2,T_a] : % 169.19/169.63 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 169.19/169.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__idemp__self__comp,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_r__comp__rtrancl__eq,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__unfold,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__Int__subset,axiom, % 169.19/169.63 ! [V_r_2,V_s_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__r__diff__Id,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel__rtrancl__trans,axiom, % 169.19/169.63 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_R__O__Id,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_Id__O__R,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_refl__Id,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pair__in__Id__conv,axiom, % 169.19/169.63 ! [V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> V_a_2 = V_b_2 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Image__Id,axiom, % 169.19/169.63 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__Id,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__Id,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 169.19/169.63 ! [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)))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pair__leq__def,axiom, % 169.19/169.63 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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Not__Domain__rtrancl,axiom, % 169.19/169.63 ! [V_y_2,V_R_2,V_x_2,T_a] : % 169.19/169.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 169.19/169.63 => ( 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))) % 169.19/169.63 <=> V_x_2 = V_y_2 ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acc__downwards__aux,axiom, % 169.19/169.63 ! [V_r_2,V_a_2,V_b_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acc__downwards,axiom, % 169.19/169.63 ! [V_b_2,V_r_2,V_a_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__insert,axiom, % 169.19/169.63 ! [V_r_2,V_x_2,V_y_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 & ~ 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 169.19/169.63 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__listrel1__eq__len,axiom, % 169.19/169.63 ! [V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 169.19/169.63 => 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) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acyclic__insert,axiom, % 169.19/169.63 ! [V_r_2,V_x_2,V_y_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 169.19/169.63 & ~ 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel__reflcl__if__listrel1,axiom, % 169.19/169.63 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 169.19/169.63 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_refl__reflcl,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Id__def,axiom, % 169.19/169.63 ! [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))))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_irrefl__diff__Id,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_pred__nat__trancl__eq__le,axiom, % 169.19/169.63 ! [V_n_2,V_m_2] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__subset__Sigma__aux,axiom, % 169.19/169.63 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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)))) % 169.19/169.63 => ( V_a_2 = V_b_2 % 169.19/169.63 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_irrefl__tranclI,axiom, % 169.19/169.63 ! [V_x_2,V_r_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ~ 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_sequence__trans,axiom, % 169.19/169.63 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 169.19/169.63 ( ! [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))) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__converse,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__converseD,axiom, % 169.19/169.63 ! [V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__converseI,axiom, % 169.19/169.63 ! [V_r_2,V_x_2,V_y_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__Id,axiom, % 169.19/169.63 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acyclic__converse,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 169.19/169.63 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__UNION,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__converse,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Domain__converse,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Range__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__converse,axiom, % 169.19/169.63 ! [V_r_2,T_b,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 169.19/169.63 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__converse,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_Field__converse,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__Id__on,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__iff,axiom, % 169.19/169.63 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converseI,axiom, % 169.19/169.63 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converseD,axiom, % 169.19/169.63 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__INTER,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__listrel1__converse,axiom, % 169.19/169.63 ! [V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_listrel1__converse,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_refl__on__converse,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 169.19/169.63 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__Int,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__inv__image,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__Un,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__rel__comp,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_equiv__comp__eq,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 169.19/169.63 => 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 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__converse__trancl,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 169.19/169.63 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__converse,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__converseD,axiom, % 169.19/169.63 ! [V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__converseI,axiom, % 169.19/169.63 ! [V_r_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Image__subset__eq,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 <=> 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))))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_refl__on__comp__subset,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_comp__equivI,axiom, % 169.19/169.63 ! [V_A_2,V_r_2,T_a] : % 169.19/169.63 ( 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 % 169.19/169.63 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 169.19/169.63 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__acyclic__wf__converse,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 169.19/169.63 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 169.19/169.63 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converse__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Image__INT__eq,axiom, % 169.19/169.63 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 169.19/169.63 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_total__on__diff__Id,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valued__Id,axiom, % 169.19/169.63 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_total__on__converse,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 169.19/169.63 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valued__rel__comp,axiom, % 169.19/169.63 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 169.19/169.63 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 169.19/169.63 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_total__on__empty,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valued__subset,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 169.19/169.63 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valued__Id__on,axiom, % 169.19/169.63 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valuedD,axiom, % 169.19/169.63 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 169.19/169.63 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 169.19/169.63 => ( 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)) % 169.19/169.63 => ( 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)) % 169.19/169.63 => V_y_2 = V_z_2 ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valued__def,axiom, % 169.19/169.63 ! [V_r_2,T_b,T_a] : % 169.19/169.63 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 169.19/169.63 <=> ! [B_x,B_y] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ! [B_z] : % 169.19/169.63 ( 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)) % 169.19/169.63 => B_y = B_z ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_total__on__def,axiom, % 169.19/169.63 ! [V_r_2,V_A_2,T_a] : % 169.19/169.63 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 169.19/169.63 <=> ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => ! [B_xa] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 169.19/169.63 => ( B_x != B_xa % 169.19/169.63 => ( 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)) % 169.19/169.63 | 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)) ) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valued__confluent,axiom, % 169.19/169.63 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 169.19/169.63 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 169.19/169.63 => ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 => ( 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))) % 169.19/169.63 | 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))) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Image__Int__eq,axiom, % 169.19/169.63 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 169.19/169.63 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 169.19/169.63 ! [V_R_2,V_p_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_acyclicI,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( ! [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))) % 169.19/169.63 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_single__valued__rel__pow,axiom, % 169.19/169.63 ! [V_n_2,V_R_2,T_a] : % 169.19/169.63 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_funpow_Osimps_I2_J,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_funpow__add,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_comp__funpow,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__exp,axiom, % 169.19/169.63 ! [V_R_2,V_n_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_funpow__swap1,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_funpow__mult,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_relpow_Osimps_I2_J,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__commute,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__add,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__1,axiom, % 169.19/169.63 ! [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 ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__Suc__I2,axiom, % 169.19/169.63 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ( 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))) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__Suc__I,axiom, % 169.19/169.63 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( 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)) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__0__I,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__0__E,axiom, % 169.19/169.63 ! [V_R_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => V_x_2 = V_y_2 ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_relpow_Osimps_I1_J,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__imp__rtrancl,axiom, % 169.19/169.63 ! [V_R_2,V_n_2,V_p_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__power,axiom, % 169.19/169.63 ! [V_R_2,V_p_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 169.19/169.63 <=> ? [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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_funpow_Osimps_I1_J,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_trancl__power,axiom, % 169.19/169.63 ! [V_R_2,V_p_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 169.19/169.63 <=> ? [B_n] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 169.19/169.63 & 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_funpow__code__def,axiom, % 169.19/169.63 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__E2,axiom, % 169.19/169.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.63 => V_x_2 != V_z_2 ) % 169.19/169.63 => ~ ! [B_y,B_m] : % 169.19/169.63 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 169.19/169.63 => ( 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)) % 169.19/169.63 => ~ 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))) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rotate__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__E,axiom, % 169.19/169.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.63 => V_x_2 != V_z_2 ) % 169.19/169.63 => ~ ! [B_y,B_m] : % 169.19/169.63 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 169.19/169.63 => ( 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))) % 169.19/169.63 => ~ 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)) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__Un__separator__converseE,axiom, % 169.19/169.63 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ! [B_y] : % 169.19/169.63 ( 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)) % 169.19/169.63 => B_y = B_x ) ) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rtrancl__Un__separatorE,axiom, % 169.19/169.63 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 169.19/169.63 ( 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)))) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ! [B_y] : % 169.19/169.63 ( 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)) % 169.19/169.63 => B_x = B_y ) ) % 169.19/169.63 => 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__Suc__E,axiom, % 169.19/169.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ ! [B_y] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__Suc__D2,axiom, % 169.19/169.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ? [B_y] : % 169.19/169.63 ( 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)) % 169.19/169.63 & 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__pow__Suc__E2,axiom, % 169.19/169.63 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ ! [B_y] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ~ 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_tranclD2,axiom, % 169.19/169.63 ! [V_R_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ? [B_z] : % 169.19/169.63 ( 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))) % 169.19/169.63 & 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_tranclD,axiom, % 169.19/169.63 ! [V_R_2,V_y_2,V_x_2,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ? [B_z] : % 169.19/169.63 ( 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)) % 169.19/169.63 & 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))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_IdE,axiom, % 169.19/169.63 ! [V_p_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 169.19/169.63 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__set__conv__decomp,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 <=> ? [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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__set__conv__decomp__first,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 <=> ? [B_ys] : % 169.19/169.63 ( ? [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)) % 169.19/169.63 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_in__set__conv__decomp__last,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 <=> ? [B_ys,B_zs] : % 169.19/169.63 ( 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)) % 169.19/169.63 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_wf__eq__minimal,axiom, % 169.19/169.63 ! [V_r_2,T_a] : % 169.19/169.63 ( c_Wellfounded_Owf(T_a,V_r_2) % 169.19/169.63 <=> ! [B_Q] : % 169.19/169.63 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 169.19/169.63 => ? [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 169.19/169.63 & ! [B_y] : % 169.19/169.63 ( 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)) % 169.19/169.63 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_transfer__nat__int__set__cong,axiom, % 169.19/169.63 ! [V_P_H_2,V_P_2] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 169.19/169.63 => ( hBOOL(hAPP(V_P_2,B_x)) % 169.19/169.63 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 169.19/169.63 => 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)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Int__Collect__mono,axiom, % 169.19/169.63 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 169.19/169.63 => ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 169.19/169.63 => ( hBOOL(hAPP(V_P_2,B_x)) % 169.19/169.63 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 169.19/169.63 => 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)))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_converseE,axiom, % 169.19/169.63 ! [V_r_2,V_yx_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ ! [B_x,B_y] : % 169.19/169.63 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 169.19/169.63 => ~ 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_rel__compE,axiom, % 169.19/169.63 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 169.19/169.63 ( 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))) % 169.19/169.63 => ~ ! [B_x,B_y,B_z] : % 169.19/169.63 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 169.19/169.63 => ( 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)) % 169.19/169.63 => ~ 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)) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Oplus__frac__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Otimes__frac__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Oof__frac__def,axiom, % 169.19/169.63 ! [V_q,T_a,T_b] : % 169.19/169.63 ( ( class_Rings_Oinverse(T_b) % 169.19/169.63 & class_Rings_Oring__1(T_b) ) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 169.19/169.63 ! [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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Oless__frac__def,axiom, % 169.19/169.63 ! [V_r_2,V_q_2,T_a] : % 169.19/169.63 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 169.19/169.63 <=> 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 169.19/169.63 ! [V_r_2,V_q_2,T_a] : % 169.19/169.63 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 169.19/169.63 <=> 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Onum__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Nitpick_Odenom__def,axiom, % 169.19/169.63 ! [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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all__length,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 169.19/169.63 <=> ! [B_n] : % 169.19/169.63 ( 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))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_internal__split__def,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all__simps_I2_J,axiom, % 169.19/169.63 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all__append,axiom, % 169.19/169.63 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 169.19/169.63 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 169.19/169.63 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all__rev,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 169.19/169.63 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all__iff,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 169.19/169.63 <=> ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all__simps_I1_J,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 169.19/169.63 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.63 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_Ball__set__list__all,axiom, % 169.19/169.63 ! [V_P_2,V_xs_2,T_a] : % 169.19/169.63 ( ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.63 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__all__iff__raw,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 169.19/169.63 <=> ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_internal__split__conv,axiom, % 169.19/169.63 ! [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) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex1__simps_I2_J,axiom, % 169.19/169.63 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 169.19/169.63 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.63 => 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) ) % 169.19/169.63 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.63 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_finite__less__ub,axiom, % 169.19/169.63 ! [V_u_2,V_f_2] : % 169.19/169.63 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 169.19/169.63 => 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)))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_exists1__code,axiom, % 169.19/169.63 ! [V_P_2,T_a] : % 169.19/169.63 ( class_Enum_Oenum(T_a) % 169.19/169.63 => ( ? [B_x] : % 169.19/169.63 ( hBOOL(hAPP(V_P_2,B_x)) % 169.19/169.63 & ! [B_y] : % 169.19/169.63 ( hBOOL(hAPP(V_P_2,B_y)) % 169.19/169.63 => B_y = B_x ) ) % 169.19/169.63 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex1__simps_I1_J,axiom, % 169.19/169.63 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_list__ex1__iff,axiom, % 169.19/169.63 ! [V_xs_2,V_P_2,T_a] : % 169.19/169.63 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 169.19/169.63 <=> ? [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 & hBOOL(hAPP(V_P_2,B_x)) % 169.19/169.63 & ! [B_y] : % 169.19/169.63 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 169.19/169.63 & hBOOL(hAPP(V_P_2,B_y)) ) % 169.19/169.63 => B_y = B_x ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_measure__function__int,axiom, % 169.19/169.63 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))) ). % 169.19/169.63 % 169.19/169.63 fof(fact_equal__fun__def,axiom, % 169.19/169.63 ! [V_g_2,V_f_2,T_a,T_b] : % 169.19/169.63 ( ( class_HOL_Oequal(T_b) % 169.19/169.63 & class_Enum_Oenum(T_a) ) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 169.19/169.63 <=> ! [B_x] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 169.19/169.63 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_eq__equal,axiom, % 169.19/169.63 ! [T_a] : % 169.19/169.63 ( class_HOL_Oequal(T_a) % 169.19/169.63 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_equal__eq,axiom, % 169.19/169.63 ! [V_y_2,V_x_2,T_a] : % 169.19/169.63 ( class_HOL_Oequal(T_a) % 169.19/169.63 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 169.19/169.63 <=> V_x_2 = V_y_2 ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_equal__refl,axiom, % 169.19/169.63 ! [V_x,T_a] : % 169.19/169.63 ( class_HOL_Oequal(T_a) % 169.19/169.63 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_equal,axiom, % 169.19/169.63 ! [T_a] : % 169.19/169.63 ( class_HOL_Oequal(T_a) % 169.19/169.63 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_measure__size,axiom, % 169.19/169.63 ! [T_a] : % 169.19/169.63 ( class_Nat_Osize(T_a) % 169.19/169.63 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_is__measure_Osimps,axiom, % 169.19/169.63 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 169.19/169.63 % 169.19/169.63 fof(fact_is__measure_Oequations,axiom, % 169.19/169.63 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 169.19/169.63 % 169.19/169.63 fof(fact_is__measure_Ointros,axiom, % 169.19/169.63 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 169.19/169.63 % 169.19/169.63 fof(fact_measure__snd,axiom, % 169.19/169.63 ! [T_b,V_f_2,T_a] : % 169.19/169.63 ( c_FunDef_Ois__measure(T_a,V_f_2) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_measure__fst,axiom, % 169.19/169.63 ! [T_b,V_f_2,T_a] : % 169.19/169.63 ( c_FunDef_Ois__measure(T_a,V_f_2) % 169.19/169.63 => 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))) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_transfer__morphism__int__nat,axiom, % 169.19/169.63 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)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 169.19/169.63 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 169.19/169.63 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.63 => 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) ) % 169.19/169.63 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.63 => 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)) ) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_equal__int__def,axiom, % 169.19/169.63 ! [V_l_2,V_k_2] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 169.19/169.63 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 169.19/169.63 % 169.19/169.63 fof(fact_eq__int__code_I2_J,axiom, % 169.19/169.63 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_eq__int__code_I5_J,axiom, % 169.19/169.63 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 169.19/169.63 % 169.19/169.63 fof(fact_eq__int__code_I12_J,axiom, % 169.19/169.63 ! [V_k1_2] : % 169.19/169.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 169.19/169.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I8_J,axiom, % 169.19/169.64 ! [V_k2_2] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I11_J,axiom, % 169.19/169.64 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I7_J,axiom, % 169.19/169.64 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I9_J,axiom, % 169.19/169.64 ! [V_k1_2] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I3_J,axiom, % 169.19/169.64 ! [V_k2_2] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I15_J,axiom, % 169.19/169.64 ! [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))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I14_J,axiom, % 169.19/169.64 ! [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))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I6_J,axiom, % 169.19/169.64 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I13_J,axiom, % 169.19/169.64 ! [V_k2_2,V_k1_2] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I1_J,axiom, % 169.19/169.64 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I16_J,axiom, % 169.19/169.64 ! [V_k2_2,V_k1_2] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__number__of__int__code,axiom, % 169.19/169.64 ! [V_l_2,V_k_2] : % 169.19/169.64 ( 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))) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I10_J,axiom, % 169.19/169.64 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__code_I4_J,axiom, % 169.19/169.64 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_bool_Osize_I4_J,axiom, % 169.19/169.64 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(fact_bool_Osize_I3_J,axiom, % 169.19/169.64 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__int__refl,axiom, % 169.19/169.64 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_neg__bind__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_size__code,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_lazy__sequence__size__code,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_seq__case,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_yieldn__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 169.19/169.64 ! [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))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_lazy__sequence_Oinject,axiom, % 169.19/169.64 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 169.19/169.64 ( 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) % 169.19/169.64 <=> ( V_a_2 = V_a_H_2 % 169.19/169.64 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact__01,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 169.19/169.64 ! [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))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_neg__map__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 169.19/169.64 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 169.19/169.64 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.64 => 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) ) % 169.19/169.64 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 169.19/169.64 => 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)) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_neg__single__def,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__DSequence_Oneg__single__def,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__DSequence_Opos__empty__def,axiom, % 169.19/169.64 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 169.19/169.64 % 169.19/169.64 fof(fact_pos__empty__def,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__DSequence_Opos__bind__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_pos__bind__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_length__splice,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_splice__Nil2,axiom, % 169.19/169.64 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 169.19/169.64 % 169.19/169.64 fof(fact_splice_Osimps_I1_J,axiom, % 169.19/169.64 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 169.19/169.64 % 169.19/169.64 fof(fact_splice_Osimps_I3_J,axiom, % 169.19/169.64 ! [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))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_splice_Osimps_I2_J,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_pos__map__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_acyclicP__converse,axiom, % 169.19/169.64 ! [V_r_2,T_a] : % 169.19/169.64 ( 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)))) % 169.19/169.64 <=> 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))) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversep__eq,axiom, % 169.19/169.64 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversep__conversep,axiom, % 169.19/169.64 ! [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 ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversep__iff,axiom, % 169.19/169.64 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversep_Oequations,axiom, % 169.19/169.64 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 169.19/169.64 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversep_Ointros,axiom, % 169.19/169.64 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 169.19/169.64 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversepD,axiom, % 169.19/169.64 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 169.19/169.64 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversep__noteq,axiom, % 169.19/169.64 ! [V_y_2,V_x_2,T_a] : % 169.19/169.64 ( 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)) % 169.19/169.64 <=> V_x_2 != V_y_2 ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_converse__meet,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_converse__pred__comp,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_converse__join,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_conversep__converse__eq,axiom, % 169.19/169.64 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 169.19/169.64 ( 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)) % 169.19/169.64 <=> 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))) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_pos__single__def,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_tl__replicate,axiom, % 169.19/169.64 ! [V_x,T_a,V_n] : % 169.19/169.64 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.64 => 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) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__length__filter,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_length__replicate,axiom, % 169.19/169.64 ! [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 ). % 169.19/169.64 % 169.19/169.64 fof(fact_map__replicate__const,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__append__same,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_drop__replicate,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__empty,axiom, % 169.19/169.64 ! [V_x_2,V_n_2,T_a] : % 169.19/169.64 ( c_List_Oreplicate(T_a,V_n_2,V_x_2) = c_List_Olist_ONil(T_a) % 169.19/169.64 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_empty__replicate,axiom, % 169.19/169.64 ! [V_x_2,V_n_2,T_a] : % 169.19/169.64 ( c_List_Olist_ONil(T_a) = c_List_Oreplicate(T_a,V_n_2,V_x_2) % 169.19/169.64 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__0,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_filter__replicate,axiom, % 169.19/169.64 ! [V_n_2,T_a,V_x_2,V_P_2] : % 169.19/169.64 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.64 => 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) ) % 169.19/169.64 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 169.19/169.64 => 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) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_concat__replicate__trivial,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_map__replicate,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_append__replicate__commute,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__add,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_rev__replicate,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_Bex__set__replicate,axiom, % 169.19/169.64 ! [V_P_2,V_a_2,V_n_2,T_a] : % 169.19/169.64 ( ? [B_x] : % 169.19/169.64 ( 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)))) % 169.19/169.64 & hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.64 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 169.19/169.64 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_Ball__set__replicate,axiom, % 169.19/169.64 ! [V_P_2,V_a_2,V_n_2,T_a] : % 169.19/169.64 ( ! [B_x] : % 169.19/169.64 ( 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)))) % 169.19/169.64 => hBOOL(hAPP(V_P_2,B_x)) ) % 169.19/169.64 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 169.19/169.64 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_hd__replicate,axiom, % 169.19/169.64 ! [V_x,T_a,V_n] : % 169.19/169.64 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.64 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_last__replicate,axiom, % 169.19/169.64 ! [V_x,T_a,V_n] : % 169.19/169.64 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.64 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_take__replicate,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__eq__replicate,axiom, % 169.19/169.64 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] : % 169.19/169.64 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2) % 169.19/169.64 <=> ( V_m_2 = V_n_2 % 169.19/169.64 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.64 => V_x_2 = V_y_2 ) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_nth__replicate,axiom, % 169.19/169.64 ! [V_x,T_a,V_n,V_i] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 169.19/169.64 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__app__Cons__same,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_replicate__Suc,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_in__set__replicate,axiom, % 169.19/169.64 ! [V_y_2,V_n_2,V_x_2,T_a] : % 169.19/169.64 ( 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)))) % 169.19/169.64 <=> ( V_x_2 = V_y_2 % 169.19/169.64 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_zip__replicate,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_map__replicate__trivial,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_set__replicate__conv__if,axiom, % 169.19/169.64 ! [V_x_2,T_a,V_n_2] : % 169.19/169.64 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.64 => 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)) ) % 169.19/169.64 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.64 => 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))) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_set__replicate,axiom, % 169.19/169.64 ! [V_x_2,T_a,V_n_2] : % 169.19/169.64 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 169.19/169.64 => 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))) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_set__replicate__Suc,axiom, % 169.19/169.64 ! [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))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__DSequence_Opos__single__def,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(fact_eq__comp__r,axiom, % 169.19/169.64 ! [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 ). % 169.19/169.64 % 169.19/169.64 fof(fact__02,axiom, % 169.19/169.64 ! [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)))) ). % 169.19/169.64 % 169.19/169.64 fof(fact_small__lazy_H_Opinduct,axiom, % 169.19/169.64 ! [V_P_2,V_a1_2,V_a0_2] : % 169.19/169.64 ( 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_a0_2),V_a1_2))) % 169.19/169.64 => ( ! [B_d,B_i] : % 169.19/169.64 ( 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),B_d),B_i))) % 169.19/169.64 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 169.19/169.64 => hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) % 169.19/169.64 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) ) % 169.19/169.64 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_small__lazy_H_Opsimps,axiom, % 169.19/169.64 ! [V_i_2,V_d_2] : % 169.19/169.64 ( 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))) % 169.19/169.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 169.19/169.64 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 169.19/169.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 169.19/169.64 => 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)))) ) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_small__lazy__list_Osimps,axiom, % 169.19/169.64 ! [V_d_2,T_a] : % 169.19/169.64 ( class_Lazy__Sequence_Osmall__lazy(T_a) % 169.19/169.64 => 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)))) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_small__lazy_H_Osimps,axiom, % 169.19/169.64 ! [V_i,V_d] : % 169.19/169.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 169.19/169.64 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 169.19/169.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 169.19/169.64 => 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)))) ) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_small__lazy__prod__def,axiom, % 169.19/169.64 ! [V_d,T_b,T_a] : % 169.19/169.64 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 169.19/169.64 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 169.19/169.64 => 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)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact__03,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_small__lazy__int__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_New__DSequence_Opos__union__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(fact_refl__on__INTER,axiom, % 169.19/169.64 ! [V_r_2,V_A_2,T_b,V_S_2,T_a] : % 169.19/169.64 ( ! [B_x] : % 169.19/169.64 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 169.19/169.64 => c_Relation_Orefl__on(T_b,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 169.19/169.64 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(fact_pos__union__def,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 %----Arity declarations (239) % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 169.19/169.64 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Obounded__lattice(T_1) % 169.19/169.64 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 169.19/169.64 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Obounded__lattice(T_1) % 169.19/169.64 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Obounded__lattice(T_1) % 169.19/169.64 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Olattice(T_1) % 169.19/169.64 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Olattice(T_1) % 169.19/169.64 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Odistrib__lattice(T_1) % 169.19/169.64 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Oboolean__algebra(T_1) % 169.19/169.64 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Orderings_Opreorder,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Orderings_Opreorder(T_1) % 169.19/169.64 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Finite__Set_Ofinite,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Finite__Set_Ofinite(T_2) % 169.19/169.64 & class_Finite__Set_Ofinite(T_1) ) % 169.19/169.64 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Lattices_Olattice,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Lattices_Olattice(T_1) % 169.19/169.64 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Orderings_Oorder,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Orderings_Oorder(T_1) % 169.19/169.64 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Orderings_Otop,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Orderings_Otop(T_1) % 169.19/169.64 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Orderings_Oord,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Orderings_Oord(T_1) % 169.19/169.64 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Orderings_Obot,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Orderings_Obot(T_1) % 169.19/169.64 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Groups_Ouminus,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Groups_Ouminus(T_1) % 169.19/169.64 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Groups_Ominus,axiom, % 169.19/169.64 ! [T_2,T_1] : % 169.19/169.64 ( class_Groups_Ominus(T_1) % 169.19/169.64 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Enum_Oenum(T_2) % 169.19/169.64 & class_HOL_Oequal(T_1) ) % 169.19/169.64 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_fun__Enum_Oenum,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Enum_Oenum(T_2) % 169.19/169.64 & class_Enum_Oenum(T_1) ) % 169.19/169.64 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Com_Ocom) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Com__Ocom__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_Com_Ocom) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 169.19/169.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 169.19/169.64 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 169.19/169.64 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 169.19/169.64 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 169.19/169.64 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 169.19/169.64 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 169.19/169.64 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 169.19/169.64 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 169.19/169.64 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 169.19/169.64 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 169.19/169.64 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 169.19/169.64 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 169.19/169.64 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 169.19/169.64 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 169.19/169.64 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 169.19/169.64 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 169.19/169.64 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 169.19/169.64 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 169.19/169.64 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 169.19/169.64 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 169.19/169.64 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 169.19/169.64 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 169.19/169.64 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 169.19/169.64 class_Divides_Osemiring__div(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 169.19/169.64 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 169.19/169.64 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 169.19/169.64 class_Groups_Oab__group__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 169.19/169.64 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 169.19/169.64 class_Rings_Oordered__ring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 169.19/169.64 class_Orderings_Opreorder(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 169.19/169.64 class_Orderings_Olinorder(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 169.19/169.64 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 169.19/169.64 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 169.19/169.64 class_Groups_Omonoid__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 169.19/169.64 class_Smallcheck_Osmall(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 169.19/169.64 class_Rings_Osemiring__1(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 169.19/169.64 class_Rings_Osemiring__0(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 169.19/169.64 class_Lattices_Olattice(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 169.19/169.64 class_Groups_Ogroup__add(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 169.19/169.64 class_Divides_Oring__div(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 169.19/169.64 class_Rings_Omult__zero(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 169.19/169.64 class_Orderings_Oorder(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 169.19/169.64 class_Int_Oring__char__0(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 169.19/169.64 class_Int_Onumber__ring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 169.19/169.64 class_Rings_Osemiring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Orderings_Oord,axiom, % 169.19/169.64 class_Orderings_Oord(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 169.19/169.64 class_Groups_Ouminus(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 169.19/169.64 class_Groups_Osgn__if(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 169.19/169.64 class_Groups_Oabs__if(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 169.19/169.64 class_Rings_Oring__1(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ominus,axiom, % 169.19/169.64 class_Groups_Ominus(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Power_Opower,axiom, % 169.19/169.64 class_Power_Opower(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Ozero,axiom, % 169.19/169.64 class_Groups_Ozero(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oring,axiom, % 169.19/169.64 class_Rings_Oring(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Rings_Oidom,axiom, % 169.19/169.64 class_Rings_Oidom(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Int_Onumber,axiom, % 169.19/169.64 class_Int_Onumber(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__Groups_Oone,axiom, % 169.19/169.64 class_Groups_Oone(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Int__Oint__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Int_Oint) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 169.19/169.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 169.19/169.64 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 169.19/169.64 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 169.19/169.64 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 169.19/169.64 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 169.19/169.64 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 169.19/169.64 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 169.19/169.64 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 169.19/169.64 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 169.19/169.64 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 169.19/169.64 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 169.19/169.64 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 169.19/169.64 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 169.19/169.64 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 169.19/169.64 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 169.19/169.64 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 169.19/169.64 class_Orderings_Owellorder(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 169.19/169.64 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 169.19/169.64 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 169.19/169.64 class_Orderings_Opreorder(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 169.19/169.64 class_Orderings_Olinorder(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 169.19/169.64 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 169.19/169.64 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 169.19/169.64 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 169.19/169.64 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 169.19/169.64 class_Lattices_Olattice(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 169.19/169.64 class_Rings_Omult__zero(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 169.19/169.64 class_Orderings_Oorder(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 169.19/169.64 class_Rings_Osemiring(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 169.19/169.64 class_Orderings_Oord(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 169.19/169.64 class_Orderings_Obot(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 169.19/169.64 class_Groups_Ominus(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Power_Opower,axiom, % 169.19/169.64 class_Power_Opower(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 169.19/169.64 class_Groups_Ozero(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Int_Onumber,axiom, % 169.19/169.64 class_Int_Onumber(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Groups_Oone,axiom, % 169.19/169.64 class_Groups_Oone(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nat__Onat__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_Nat_Onat) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 169.19/169.64 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 169.19/169.64 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 169.19/169.64 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 169.19/169.64 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 169.19/169.64 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 169.19/169.64 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 169.19/169.64 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 169.19/169.64 class_Orderings_Opreorder(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 169.19/169.64 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 169.19/169.64 class_Lattices_Olattice(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 169.19/169.64 class_Orderings_Oorder(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 169.19/169.64 class_Orderings_Otop(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 169.19/169.64 class_Orderings_Oord(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 169.19/169.64 class_Orderings_Obot(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 169.19/169.64 class_Groups_Ouminus(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 169.19/169.64 class_Groups_Ominus(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 169.19/169.64 class_Enum_Oenum(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_HOL__Obool__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_HOL_Obool) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Com_Ostate) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Com__Ostate__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_Com_Ostate) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Com__Ovname__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Com_Ovname) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Com__Ovname__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_Com_Ovname) ). % 169.19/169.64 % 169.19/169.64 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 169.19/169.64 ! [T_1] : % 169.19/169.64 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 169.19/169.64 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_List__Olist__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_List__Olist__Nat_Osize,axiom, % 169.19/169.64 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_sum__Finite__Set_Ofinite,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Finite__Set_Ofinite(T_2) % 169.19/169.64 & class_Finite__Set_Ofinite(T_1) ) % 169.19/169.64 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_sum__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_sum__Enum_Oenum,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Enum_Oenum(T_2) % 169.19/169.64 & class_Enum_Oenum(T_1) ) % 169.19/169.64 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_sum__Nat_Osize,axiom, % 169.19/169.64 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 169.19/169.64 ! [T_1] : % 169.19/169.64 ( class_Finite__Set_Ofinite(T_1) % 169.19/169.64 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 169.19/169.64 ! [T_1] : % 169.19/169.64 ( class_Enum_Oenum(T_1) % 169.19/169.64 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Option__Ooption__Nat_Osize,axiom, % 169.19/169.64 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 169.19/169.64 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 169.19/169.64 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 169.19/169.64 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_prod__Finite__Set_Ofinite,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Finite__Set_Ofinite(T_2) % 169.19/169.64 & class_Finite__Set_Ofinite(T_1) ) % 169.19/169.64 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_prod__Smallcheck_Osmall,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Smallcheck_Osmall(T_2) % 169.19/169.64 & class_Smallcheck_Osmall(T_1) ) % 169.19/169.64 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_prod__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_prod__Enum_Oenum,axiom, % 169.19/169.64 ! [T_1,T_2] : % 169.19/169.64 ( ( class_Enum_Oenum(T_2) % 169.19/169.64 & class_Enum_Oenum(T_1) ) % 169.19/169.64 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 169.19/169.64 % 169.19/169.64 fof(arity_prod__Nat_Osize,axiom, % 169.19/169.64 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 169.19/169.64 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 169.19/169.64 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 169.19/169.64 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 169.19/169.64 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_Product__Type_Ounit) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 169.19/169.64 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 169.19/169.64 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 169.19/169.64 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 169.19/169.64 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 169.19/169.64 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 169.19/169.64 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 169.19/169.64 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 169.19/169.64 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 169.19/169.64 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 169.19/169.64 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 169.19/169.64 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 169.19/169.64 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 169.19/169.64 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 169.19/169.64 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 169.19/169.64 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 169.19/169.64 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 169.19/169.64 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 169.19/169.64 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 169.19/169.64 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 169.19/169.64 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 169.19/169.64 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 169.19/169.64 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 169.19/169.64 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 169.19/169.64 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 169.19/169.64 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 169.19/169.64 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 169.19/169.64 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 169.19/169.64 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 169.19/169.64 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 169.19/169.64 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 169.19/169.64 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 169.19/169.64 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 169.19/169.64 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 169.19/169.64 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 169.19/169.64 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 169.19/169.64 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 169.19/169.64 % 169.19/169.64 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 169.19/169.64 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 169.19/169.64 % 169.19/169.64 %----Helper facts (20) % 169.19/169.64 fof(help_c__COMBI__1,axiom, % 169.19/169.64 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 169.19/169.64 % 169.19/169.64 fof(help_c__COMBK__1,axiom, % 169.19/169.64 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 169.19/169.64 % 169.19/169.64 fof(help_c__COMBB__1,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__COMBC__1,axiom, % 169.19/169.64 ! [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) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__COMBS__1,axiom, % 169.19/169.64 ! [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)) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fequal__1,axiom, % 169.19/169.64 ! [V_y_2,V_x_2] : % 169.19/169.64 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 169.19/169.64 | V_x_2 = V_y_2 ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fequal__2,axiom, % 169.19/169.64 ! [V_y_2,V_x_2] : % 169.19/169.64 ( V_x_2 != V_y_2 % 169.19/169.64 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fFalse__1,axiom, % 169.19/169.64 ~ hBOOL(c_fFalse) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fTrue__1,axiom, % 169.19/169.64 hBOOL(c_fTrue) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fNot__1,axiom, % 169.19/169.64 ! [V_P_2] : % 169.19/169.64 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 169.19/169.64 | ~ hBOOL(V_P_2) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fNot__2,axiom, % 169.19/169.64 ! [V_P_2] : % 169.19/169.64 ( ~ ~ hBOOL(V_P_2) % 169.19/169.64 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fconj__1,axiom, % 169.19/169.64 ! [V_Q_2,V_P_2] : % 169.19/169.64 ( ~ hBOOL(V_P_2) % 169.19/169.64 | ~ hBOOL(V_Q_2) % 169.19/169.64 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fconj__2,axiom, % 169.19/169.64 ! [V_Q_2,V_P_2] : % 169.19/169.64 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 169.19/169.64 | hBOOL(V_P_2) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fconj__3,axiom, % 169.19/169.64 ! [V_Q_2,V_P_2] : % 169.19/169.64 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 169.19/169.64 | hBOOL(V_Q_2) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fdisj__1,axiom, % 169.19/169.64 ! [V_Q_2,V_P_2] : % 169.19/169.64 ( ~ hBOOL(V_P_2) % 169.19/169.64 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fdisj__2,axiom, % 169.19/169.64 ! [V_P_2,V_Q_2] : % 169.19/169.64 ( ~ hBOOL(V_Q_2) % 169.19/169.64 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fdisj__3,axiom, % 169.19/169.64 ! [V_Q_2,V_P_2] : % 169.19/169.64 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 169.19/169.64 | hBOOL(V_P_2) % 169.19/169.64 | hBOOL(V_Q_2) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fimplies__1,axiom, % 169.19/169.64 ! [V_Q_2,V_P_2] : % 169.19/169.64 ( hBOOL(V_P_2) % 169.19/169.64 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fimplies__2,axiom, % 169.19/169.64 ! [V_P_2,V_Q_2] : % 169.19/169.64 ( ~ hBOOL(V_Q_2) % 169.19/169.64 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 169.19/169.64 % 169.19/169.64 fof(help_c__fimplies__3,axiom, % 169.19/169.64 ! [V_Q_2,V_P_2] : % 169.19/169.64 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 169.19/169.64 | ~ hBOOL(V_P_2) % 169.19/169.64 | hBOOL(V_Q_2) ) ). % 169.19/169.64 % 169.19/169.64 %----Conjectures (4) % 169.19/169.64 fof(conj_0,hypothesis, % 169.19/169.64 c_Hoare__Mirabelle_Ostate__not__singleton ). % 169.19/169.64 % 169.19/169.64 fof(conj_1,hypothesis, % 169.19/169.64 c_Com_OWT__bodies ). % 169.19/169.64 % 169.19/169.64 fof(conj_2,hypothesis, % 169.19/169.64 hBOOL(hAPP(c_Com_OWT,v_c)) ). % 169.19/169.64 % 169.19/169.64 fof(conj_3,conjecture, % 169.19/169.64 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(v_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 169.19/169.64 % 169.19/169.64 %------------------------------------------------------------------------------ % 169.19/169.64 %------------------------------------------- % 169.19/169.64 % Proof found % 169.19/169.64 % SZS status Theorem for theBenchmark % 169.19/169.64 % SZS output start Proof % 169.19/169.64 %ClaNum:10189(EqnAxiom:2881) % 169.19/169.64 %VarNum:69831(SingletonVarNum:20400) % 169.19/169.64 %MaxLitNum:8 % 169.19/169.64 %MaxfuncDepth:13 % 169.19/169.64 %SharedTerms:1052 % 169.19/169.64 %goalClause: 4590 % 169.19/169.64 %singleGoalClaCount:1 % 169.19/169.64 [2882]P1(a5000) % 169.19/169.64 [2883]P2(a5000) % 169.19/169.64 [2887]P24(a871) % 169.19/169.64 [2888]P24(a877) % 169.19/169.64 [2889]P104(a194) % 169.19/169.64 [2890]P105(a871) % 169.19/169.64 [2891]P105(a877) % 169.19/169.64 [2892]P105(a1) % 169.19/169.64 [2893]P105(a102) % 169.19/169.64 [2894]P106(a871) % 169.19/169.64 [2895]P106(a877) % 169.19/169.64 [2896]P106(a1) % 169.19/169.64 [2897]P106(a102) % 169.19/169.64 [2898]P107(a877) % 169.19/169.64 [2899]P107(a1) % 169.19/169.64 [2900]P107(a102) % 169.19/169.64 [2901]P108(a871) % 169.19/169.64 [2902]P108(a877) % 169.19/169.64 [2903]P108(a1) % 169.19/169.64 [2904]P108(a102) % 169.19/169.64 [2905]P25(a871) % 169.19/169.64 [2906]P25(a880) % 169.19/169.64 [2907]P63(a871) % 169.19/169.64 [2908]P63(a877) % 169.19/169.64 [2909]P63(a1) % 169.19/169.64 [2910]P63(a102) % 169.19/169.64 [2911]P75(a1) % 169.19/169.64 [2912]P64(a1) % 169.19/169.64 [2913]P65(a877) % 169.19/169.64 [2914]P65(a1) % 169.19/169.64 [2915]P65(a102) % 169.19/169.64 [2916]P79(a871) % 169.19/169.64 [2917]P67(a1) % 169.19/169.64 [2918]P80(a871) % 169.19/169.64 [2919]P80(a1) % 169.19/169.64 [2920]P109(a1) % 169.19/169.64 [2921]P110(a1) % 169.19/169.64 [2922]P76(a877) % 169.19/169.64 [2923]P76(a1) % 169.19/169.64 [2924]P76(a102) % 169.19/169.64 [2925]P77(a877) % 169.19/169.64 [2926]P77(a1) % 169.19/169.64 [2927]P77(a102) % 169.19/169.64 [2928]P68(a877) % 169.19/169.64 [2929]P68(a1) % 169.19/169.64 [2930]P68(a102) % 169.19/169.64 [2931]P119(a877) % 169.19/169.64 [2932]P119(a1) % 169.19/169.64 [2933]P119(a102) % 169.19/169.64 [2934]P136(a1) % 169.19/169.64 [2935]P120(a1) % 169.19/169.64 [2936]P111(a1) % 169.19/169.64 [2937]P115(a877) % 169.19/169.64 [2938]P115(a1) % 169.19/169.64 [2939]P115(a102) % 169.19/169.64 [2940]P66(a877) % 169.19/169.64 [2941]P66(a1) % 169.19/169.64 [2942]P66(a102) % 169.19/169.64 [2943]P69(a877) % 169.19/169.64 [2944]P69(a1) % 169.19/169.64 [2945]P69(a102) % 169.19/169.64 [2946]P70(a877) % 169.19/169.64 [2947]P70(a1) % 169.19/169.64 [2948]P70(a102) % 169.19/169.64 [2949]P138(a877) % 169.19/169.64 [2950]P138(a1) % 169.19/169.64 [2951]P81(a877) % 169.19/169.64 [2952]P81(a1) % 169.19/169.64 [2953]P81(a102) % 169.19/169.64 [2954]P82(a877) % 169.19/169.64 [2955]P82(a1) % 169.19/169.64 [2956]P82(a102) % 169.19/169.64 [2957]P84(a877) % 169.19/169.64 [2958]P84(a1) % 169.19/169.64 [2959]P84(a102) % 169.19/169.64 [2960]P139(a877) % 169.19/169.64 [2961]P139(a1) % 169.19/169.64 [2962]P139(a102) % 169.19/169.64 [2963]P116(a877) % 169.19/169.64 [2964]P116(a1) % 169.19/169.64 [2965]P116(a102) % 169.19/169.64 [2966]P125(a1) % 169.19/169.64 [2967]P126(a1) % 169.19/169.64 [2968]P88(a877) % 169.19/169.64 [2969]P88(a1) % 169.19/169.64 [2970]P88(a102) % 169.19/169.64 [2971]P78(a877) % 169.19/169.64 [2972]P78(a1) % 169.19/169.64 [2973]P78(a102) % 169.19/169.64 [2974]P72(a877) % 169.19/169.64 [2975]P72(a1) % 169.19/169.64 [2976]P72(a102) % 169.19/169.64 [2977]P73(a1) % 169.19/169.64 [2978]P129(a877) % 169.19/169.64 [2979]P129(a1) % 169.19/169.64 [2980]P129(a102) % 169.19/169.64 [2981]P140(a1) % 169.19/169.64 [2982]P130(a877) % 169.19/169.64 [2983]P130(a1) % 169.19/169.64 [2984]P130(a102) % 169.19/169.64 [2985]P141(a877) % 169.19/169.64 [2986]P141(a1) % 169.19/169.64 [2987]P141(a102) % 169.19/169.64 [2988]P85(a877) % 169.19/169.64 [2989]P85(a1) % 169.19/169.64 [2990]P85(a102) % 169.19/169.64 [2991]P132(a877) % 169.19/169.64 [2992]P132(a1) % 169.19/169.64 [2993]P132(a102) % 169.19/169.64 [2994]P134(a877) % 169.19/169.64 [2995]P134(a1) % 169.19/169.64 [2996]P134(a102) % 169.19/169.64 [2997]P133(a877) % 169.19/169.64 [2998]P133(a1) % 169.19/169.64 [2999]P133(a102) % 169.19/169.64 [3000]P123(a1) % 169.19/169.64 [3001]P124(a1) % 169.19/169.64 [3002]P121(a877) % 169.19/169.64 [3003]P121(a1) % 169.19/169.64 [3004]P121(a102) % 169.19/169.64 [3005]P131(a877) % 169.19/169.64 [3006]P131(a1) % 169.19/169.64 [3007]P131(a102) % 169.19/169.64 [3008]P127(a877) % 169.19/169.64 [3009]P127(a1) % 169.19/169.64 [3010]P127(a102) % 169.19/169.64 [3011]P128(a1) % 169.19/169.64 [3012]P86(a1) % 169.19/169.64 [3013]P137(a1) % 169.19/169.64 [3014]P89(a1) % 169.19/169.64 [3015]P90(a877) % 169.19/169.64 [3016]P90(a1) % 169.19/169.64 [3017]P90(a102) % 169.19/169.64 [3018]P92(a1) % 169.19/169.64 [3019]P94(a877) % 169.19/169.64 [3020]P94(a1) % 169.19/169.64 [3021]P94(a102) % 169.19/169.64 [3022]P142(a877) % 169.19/169.64 [3023]P142(a1) % 169.19/169.64 [3024]P142(a102) % 169.19/169.64 [3025]P83(a1) % 169.19/169.64 [3026]P135(a1) % 169.19/169.64 [3027]P71(a1) % 169.19/169.64 [3028]P26(a877) % 169.19/169.64 [3029]P26(a1) % 169.19/169.64 [3030]P26(a102) % 169.19/169.64 [3031]P27(a1) % 169.19/169.64 [3032]P112(a877) % 169.19/169.64 [3033]P112(a1) % 169.19/169.64 [3034]P112(a102) % 169.19/169.64 [3035]P143(a877) % 169.19/169.64 [3036]P143(a1) % 169.19/169.64 [3037]P143(a102) % 169.19/169.64 [3038]P95(a871) % 169.19/169.64 [3039]P95(a877) % 169.19/169.64 [3040]P95(a1) % 169.19/169.64 [3041]P100(a871) % 169.19/169.64 [3042]P100(a877) % 169.19/169.64 [3043]P100(a1) % 169.19/169.64 [3044]P96(a871) % 169.19/169.64 [3045]P113(a871) % 169.19/169.64 [3046]P97(a871) % 169.19/169.64 [3047]P28(a871) % 169.19/169.64 [3048]P101(a871) % 169.19/169.64 [3049]P101(a877) % 169.19/169.64 [3050]P101(a1) % 169.19/169.64 [3051]P99(a871) % 169.19/169.64 [3052]P99(a877) % 169.19/169.64 [3053]P99(a1) % 169.19/169.64 [3054]P144(a1) % 169.19/169.64 [3055]P144(a880) % 169.19/169.64 [3056]P74(a877) % 169.19/169.64 [3057]P74(a1) % 169.19/169.64 [3058]P74(a102) % 169.19/169.64 [3059]P87(a877) % 169.19/169.64 [3060]P87(a1) % 169.19/169.64 [3061]P87(a102) % 169.19/169.64 [3062]P58(a871) % 169.19/169.64 [3063]P58(a880) % 169.19/169.64 [3064]P91(a871) % 169.19/169.64 [3065]P91(a872) % 169.19/169.64 [3066]P91(a873) % 169.19/169.64 [3067]P91(a877) % 169.19/169.64 [3068]P91(a1) % 169.19/169.64 [3069]P91(a102) % 169.19/169.64 [3070]P91(a880) % 169.19/169.64 [3071]P91(a330) % 169.19/169.64 [3072]P91(a875) % 169.19/169.64 [3073]P114(a877) % 169.19/169.64 [3074]P103(a871) % 169.19/169.64 [3075]P103(a872) % 169.19/169.64 [3076]P103(a873) % 169.19/169.64 [3077]P103(a877) % 169.19/169.64 [3078]P103(a102) % 169.19/169.64 [3079]P103(a880) % 169.19/169.64 [3080]P103(a330) % 169.19/169.64 [3081]P103(a875) % 169.19/169.64 [3082]P102(a1) % 169.19/169.64 [3083]P102(a880) % 169.19/169.64 [3084]P98(a871) % 169.19/169.64 [3104]P39(a877,a253) % 169.19/169.64 [3105]P39(a877,a324) % 169.19/169.64 [4488]~E(a100,a84) % 169.19/169.64 [4489]~P104(a246) % 169.19/169.64 [2884]E(f2(a1),a84) % 169.19/169.64 [2885]E(f3(a102),a4) % 169.19/169.64 [2886]E(f103(a102),a5) % 169.19/169.64 [3085]E(f195(a877),f2(a877)) % 169.19/169.64 [3086]E(f32(a24),f2(a877)) % 169.19/169.64 [3087]E(f85(a194),f2(a877)) % 169.19/169.64 [3088]E(f85(a246),f2(a877)) % 169.19/169.64 [3089]E(f104(a877),f247(a877)) % 169.19/169.64 [3090]E(f113(a877),f248(a877)) % 169.19/169.64 [3091]E(f105(a1),f35(a1)) % 169.19/169.64 [3092]P29(f79(a1)) % 169.19/169.64 [3093]P29(f2(a1)) % 169.19/169.64 [3143]P104(f334(a25,a24)) % 169.19/169.64 [3144]P104(f334(a25,a883)) % 169.19/169.64 [3159]P39(f885(a877,a877),a36) % 169.19/169.64 [3515]E(f327(a877,a877,a253,a253),a36) % 169.19/169.64 [4490]~E(f79(a1),f2(a1)) % 169.19/169.64 [3094]E(f114(f2(a877)),f2(a877)) % 169.19/169.64 [3095]E(f6(f2(a102)),f2(a877)) % 169.19/169.64 [3107]E(f334(f80(a1),a84),a84) % 169.19/169.64 [3110]E(f334(a115,f2(a877)),f79(a877)) % 169.19/169.64 [3111]E(f334(a107,f79(a1)),f79(a877)) % 169.19/169.64 [3112]E(f334(a5,f79(a877)),f79(a102)) % 169.19/169.64 [3114]E(f334(a5,f2(a877)),f2(a102)) % 169.19/169.64 [3116]E(f334(f106(a1),a84),f2(a1)) % 169.19/169.64 [3117]E(f334(f106(a102),a84),f2(a102)) % 169.19/169.64 [3118]E(f334(a107,f2(a1)),f2(a877)) % 169.19/169.64 [3119]E(f334(f196(a871),a194),f2(a877)) % 169.19/169.64 [3120]E(f334(f196(a871),a246),f2(a877)) % 169.19/169.64 [3121]E(f334(f196(a873),a24),f2(a877)) % 169.19/169.64 [3122]E(f334(f106(a877),a84),f2(a877)) % 169.19/169.64 [3127]E(f334(f80(a1),f79(a1)),a100) % 169.19/169.64 [3134]E(f334(f80(a1),f2(a1)),f2(a1)) % 169.19/169.64 [3136]E(f334(f196(a102),f2(a102)),f2(a877)) % 169.19/169.64 [3137]E(f334(f103(a1),f79(a877)),f79(a1)) % 169.19/169.64 [3138]E(f334(f103(a1),f2(a877)),f2(a1)) % 169.19/169.64 [3155]E(f334(a107,f79(a1)),f334(a115,f2(a877))) % 169.19/169.64 [3156]E(f334(f179(a874,a873),a27),a28) % 169.19/169.64 [3157]E(f325(f885(a877,a877),a36),a37) % 169.19/169.64 [3158]E(f326(f885(a877,a877),a36),a38) % 169.19/169.64 [3180]E(f334(f255(a877),f2(a877)),f195(f886(a877,a871))) % 169.19/169.64 [3181]E(f334(f256(a877),f2(a877)),f257(f886(a877,a871))) % 169.19/169.64 [3189]P41(f195(f886(a1,a871))) % 169.19/169.64 [3225]E(f334(f334(f3(a102),f2(a102)),f79(a102)),f2(a102)) % 169.19/169.64 [3304]P104(f334(f334(f250(a1),a100),f2(a1))) % 169.19/169.64 [3329]P104(f334(f334(f249(a1),f2(a1)),f79(a1))) % 169.19/169.64 [3331]P104(f334(f334(f250(a1),f2(a1)),f79(a1))) % 169.19/169.64 [3507]P104(f334(f63(a874),f185(a874,a873,a28))) % 169.19/169.64 [3545]E(f334(f334(f291(a877,a877,a877),a324),f310(a877,a324)),a253) % 169.19/169.64 [3585]P42(a1,a877,a107,f334(f249(a1),f2(a1))) % 169.19/169.64 [3589]E(f334(f334(f43(a877,f886(a877,a871)),f257(f886(a877,a871))),f306(a877)),f195(f886(a877,a871))) % 169.19/169.64 [3590]E(f334(f334(f44(a877,f886(a877,a871)),f257(f886(a877,a871))),f303(a877)),f257(f886(a877,a871))) % 169.19/169.64 [3591]E(f334(f334(f44(a877,f886(a877,a871)),f257(f886(a877,a871))),f255(a877)),f257(f886(a877,a871))) % 169.19/169.64 [3592]E(f334(f334(f44(a877,f886(a877,a871)),f257(f886(a877,a871))),f256(a877)),f257(f886(a877,a871))) % 169.19/169.64 [3608]P21(a877,a1,f103(a1),f257(f886(a877,a871))) % 169.19/169.64 [3621]P42(a877,a1,f103(a1),f334(f18(a871,a877),a194)) % 169.19/169.64 [3757]E(f334(f74(a877,a102,a1,a5),a107),f106(a102)) % 169.19/169.64 [3986]P54(a102,a877,a21,a5,f257(f886(a877,a871))) % 169.19/169.64 [3995]P54(a1,f886(f885(a877,a877),a871),a110,a90,a101) % 169.19/169.64 [4263]E(f274(a1,a1,a1,a1,f35(a1),f80(a1)),a52) % 169.19/169.64 [4513]~E(f334(f106(a1),a100),f334(f106(a1),a84)) % 169.19/169.64 [4514]~P104(f334(a201,f79(a1))) % 169.19/169.64 [4515]~P104(f334(a201,f2(a1))) % 169.19/169.64 [4565]~P104(f334(f334(f250(a1),a84),f2(a1))) % 169.19/169.64 [3172]E(f334(f334(f3(a1),a100),a100),a84) % 169.19/169.64 [3187]E(f334(f103(a1),f334(a115,f2(a877))),f79(a1)) % 169.19/169.64 [3255]E(f334(f39(a880),f257(f886(a880,a871))),f79(a877)) % 169.19/169.64 [3276]P104(f334(a201,f334(f106(a1),a100))) % 169.19/169.64 [3278]P104(f334(f334(f249(a1),a100),a84)) % 169.19/169.64 [3280]P104(f334(f334(f250(a1),a100),a84)) % 169.19/169.64 [3341]E(f334(f334(f312(a877),f2(a877)),f195(f886(a877,a871))),f334(f303(a877),f2(a877))) % 169.19/169.64 [3398]P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),a84))) % 169.19/169.64 [3410]E(f334(f313(a877,a877,a115),f257(f886(a877,a871))),f334(f306(a877),f2(a877))) % 169.19/169.64 [3450]P6(f885(a877,a877),f257(f886(f885(a877,a877),a871)),a111) % 169.19/169.64 [3765]E(f334(f74(a877,a1,a102,f103(a1)),a21),a22) % 169.19/169.64 [3828]P39(a877,f334(f254(f885(a877,a877)),f334(f273(a877,a877,a871),f250(a877)))) % 169.19/169.64 [4554]~P104(f334(a201,f334(f106(a1),a84))) % 169.19/169.64 [4555]~P104(f334(f334(f249(a1),a84),a100)) % 169.19/169.64 [4556]~P104(f334(f334(f250(a1),a84),a84)) % 169.19/169.64 [4557]~P104(f334(f334(f250(a1),a84),a100)) % 169.19/169.64 [4558]~P104(f334(f334(f250(a1),a100),a100)) % 169.19/169.64 [4559]~P104(f334(f334(f92(a1),a84),a100)) % 169.19/169.64 [4560]~P104(f334(f334(f92(a1),a100),a84)) % 169.19/169.64 [4575]~P104(f334(f63(a877),f257(f886(a877,a871)))) % 169.19/169.64 [4576]~P104(f334(f63(a1),f257(f886(a1,a871)))) % 169.19/169.64 [4434]E(f334(f273(a1,a1,a871),f334(f334(f10(f886(a1,a871),f886(a1,a871),a1),f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f250(a1),f2(a1))))),f334(f334(f9(a1,a1,f886(a1,a871)),f334(f334(f10(f886(a1,f886(a1,a871)),f886(a1,f886(a1,a871)),a1),f9(a1,a1,a871)),f334(f334(f10(f886(a1,a1),f886(a1,f886(a1,a871)),a1),f334(f10(a1,f886(a1,a871),a1),a331)),a226))),f79(a1)))),a222) % 169.19/169.64 [4590]~P20(a872,f195(f886(f876(a872),a871)),f334(f334(f312(f876(a872)),f94(a883)),f195(f886(f876(a872),a871)))) % 169.19/169.64 [3488]E(f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100),f334(f80(a1),a100)) % 169.19/169.64 [3528]E(f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100),f334(f334(f3(a1),a84),a100)) % 169.19/169.64 [3690]E(f334(f334(f62(f885(a877,a877)),f257(f886(f885(a877,a877),a871))),a111),a101) % 169.19/169.64 [3719]E(f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f79(a1)) % 169.19/169.64 [3720]E(f334(f106(a102),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f79(a102)) % 169.19/169.64 [3721]E(f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f79(a877)) % 169.19/169.64 [3725]E(f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(a115,f2(a877))) % 169.19/169.64 [4122]E(f334(f334(f113(f886(f885(f885(a877,a877),f885(a877,a877)),a871)),a36),f310(f885(a877,a877),f195(f886(f885(f885(a877,a877),f885(a877,a877)),a871)))),a71) % 169.19/169.64 [4193]E(f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),f79(a877)),f2(a877))),f195(f886(f885(a877,a877),a871))))),f79(a1)) % 169.19/169.64 [4194]E(f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),f2(a877)),f2(a877))),f195(f886(f885(a877,a877),a871))))),f2(a1)) % 169.19/169.64 [4209]E(f334(f254(f885(a877,a877)),f334(f273(a877,a877,a871),f334(f334(f10(a877,f886(a877,a871),a877),f334(f9(a877,a877,a871),a331)),a115))),a324) % 169.19/169.64 [4179]E(f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),f334(a115,f334(a115,f2(a877)))) % 169.19/169.64 [4182]E(f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),f334(f334(f81(a877),f79(a877)),f79(a877))) % 169.19/169.64 [4183]E(f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),f334(f39(a871),f257(f886(a871,a871)))) % 169.19/169.64 [4249]P29(f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))) % 169.19/169.64 [4321]P22(f886(f885(a877,a877),a871),f334(f334(f269(f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871),f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871)),a37),a72)) % 169.19/169.64 [4322]P22(f886(f885(a877,a877),a871),f334(f334(f269(f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871),f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871)),a38),a70)) % 169.19/169.64 [4362]E(f334(f334(f113(f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871)),f326(f885(a877,a877),a71)),f334(f334(f312(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),f195(f886(f885(a877,a877),a871))),f195(f886(f885(a877,a877),a871)))),f195(f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871)))),a70) % 169.19/169.64 [4363]E(f334(f334(f113(f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871)),f325(f885(a877,a877),a71)),f334(f334(f312(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),f195(f886(f885(a877,a877),a871))),f195(f886(f885(a877,a877),a871)))),f195(f886(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a871)))),a72) % 169.19/169.64 [4251]E(f334(a107,f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(a115,f334(a115,f2(a877)))) % 169.19/169.64 [4298]E(f334(f103(a1),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))) % 169.19/169.64 [4333]P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.64 [4334]E(f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100)),f334(a115,f334(a115,f334(a115,f2(a877))))) % 169.19/169.64 [4376]P29(f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))) % 169.19/169.64 [4404]E(f334(f103(a1),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))) % 169.19/169.64 [4419]P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100)))) % 169.19/169.64 [3106]P5(x31061,a331) % 169.19/169.64 [3516]P21(a877,a877,a115,x35161) % 169.19/169.64 [3096]P91(f876(x30961)) % 169.19/169.64 [3097]P91(f881(x30971)) % 169.19/169.64 [3098]P91(f878(x30981)) % 169.19/169.64 [3099]P91(f879(x30991)) % 169.19/169.64 [3100]P103(f876(x31001)) % 169.19/169.64 [3101]P103(f881(x31011)) % 169.19/169.64 [3102]P103(f878(x31021)) % 169.19/169.64 [3103]P103(f879(x31031)) % 169.19/169.64 [3123]P39(a1,f108(x31231)) % 169.19/169.64 [3124]P39(a1,f109(x31241)) % 169.19/169.64 [3126]P40(x31261,f198(x31261)) % 169.19/169.64 [3177]P39(f886(x31771,a871),f309(x31771)) % 169.19/169.64 [3201]E(f258(x32011,x32011,a331),a331) % 169.19/169.64 [3216]E(f46(a1,x32161,x32161),f2(a1)) % 169.19/169.64 [3273]P11(x32731,f886(x32731,a871),f312(x32731)) % 169.19/169.64 [4492]~E(f334(a26,x44921),a24) % 169.19/169.64 [4494]~E(f334(a115,x44941),x44941) % 169.19/169.64 [4504]~E(f334(a115,x45041),f2(a877)) % 169.19/169.64 [3108]E(f334(f196(a877),x31081),x31081) % 169.19/169.64 [3109]E(f334(f106(a1),x31091),x31091) % 169.19/169.64 [3125]E(f334(a90,f335(x31251)),x31251) % 169.19/169.64 [3139]E(f117(x31391,f116(x31391)),f116(x31391)) % 169.19/169.64 [3140]E(f152(x31401,f116(x31401)),f116(x31401)) % 169.19/169.64 [3145]E(f32(f334(a26,x31451)),f2(a877)) % 169.19/169.64 [3152]E(f334(f168(x31521),f116(x31521)),f116(x31521)) % 169.19/169.64 [3153]E(f334(f172(x31531),f116(x31531)),f116(x31531)) % 169.19/169.64 [3154]E(f334(f169(x31541),f116(x31541)),f116(x31541)) % 169.19/169.64 [3160]E(f334(f106(a1),x31601),f334(f105(a1),x31601)) % 169.19/169.64 [3161]E(f334(a90,f334(a110,x31611)),x31611) % 169.19/169.64 [3163]E(f334(a5,f334(a21,x31631)),x31631) % 169.19/169.64 [3164]E(f334(a21,f334(a5,x31641)),x31641) % 169.19/169.64 [3165]P29(f334(f103(a1),x31651)) % 169.19/169.64 [3170]E(f334(f196(f881(x31701)),f198(x31701)),f2(a877)) % 169.19/169.64 [3171]E(f334(f196(f878(x31711)),f116(x31711)),f2(a877)) % 169.19/169.64 [3176]E(f334(f196(a873),f334(a26,x31761)),f2(a877)) % 169.19/169.64 [3185]E(f240(x31851,f198(x31851)),f195(f886(x31851,a871))) % 169.19/169.64 [3192]E(f334(f334(f3(a877),x31921),f2(a877)),x31921) % 169.19/169.64 [3193]E(f334(f334(f82(a877),x31931),f79(a877)),x31931) % 169.19/169.64 [3194]E(f334(f334(f82(a1),x31941),f79(a1)),x31941) % 169.19/169.64 [3195]E(f334(f334(f81(a877),x31951),f2(a877)),x31951) % 169.19/169.64 [3196]E(f334(f334(f81(a1),x31961),f2(a1)),x31961) % 169.19/169.64 [3197]E(f334(f334(f248(a877),x31971),f2(a877)),x31971) % 169.19/169.64 [3198]E(f334(f334(f82(a877),x31981),f2(a877)),f2(a877)) % 169.19/169.64 [3199]E(f334(f334(f40(a1),x31991),f2(a1)),f2(a1)) % 169.19/169.64 [3200]E(f334(f334(f247(a877),x32001),f2(a877)),f2(a877)) % 169.19/169.64 [3207]E(f334(f173(x32071),f116(x32071)),f195(f886(x32071,a871))) % 169.19/169.64 [3211]P104(f334(f137(x32111),f116(x32111))) % 169.19/169.64 [3217]E(f334(f154(x32171,x32171),f7(x32171)),f35(f878(x32171))) % 169.19/169.64 [3218]E(f334(f154(x32181,x32181),f35(x32181)),f35(f878(x32181))) % 169.19/169.64 [3219]E(f334(f207(x32191,x32191),f7(x32191)),f35(f881(x32191))) % 169.19/169.64 [3220]E(f334(f207(x32201,x32201),f35(x32201)),f35(f881(x32201))) % 169.19/169.64 [3221]E(f46(a1,x32211,f2(a1)),x32211) % 169.19/169.64 [3222]E(f334(f249(a877),f334(a115,x32221)),f334(f250(a877),x32221)) % 169.19/169.64 [3223]E(f334(f255(a877),f334(a115,x32231)),f334(f303(a877),x32231)) % 169.19/169.64 [3224]E(f334(f256(a877),f334(a115,x32241)),f334(f306(a877),x32241)) % 169.19/169.64 [3226]E(f46(a1,f2(a1),x32261),f2(a1)) % 169.19/169.64 [3239]E(f334(f334(f81(a877),x32391),f79(a877)),f334(a115,x32391)) % 169.19/169.64 [3249]E(f334(f304(a877,x32491),f2(a877)),f195(f886(a877,a871))) % 169.19/169.64 [3261]E(f305(a877,f2(a877),x32611),f334(f303(a877),x32611)) % 169.19/169.64 [3307]E(f334(f334(f3(a877),f334(a115,x33071)),f79(a877)),x33071) % 169.19/169.64 [3320]E(f48(f2(a1),x33201),f334(f334(f269(a1,a1),f2(a1)),f2(a1))) % 169.19/169.64 [3372]P104(f334(f334(f250(a877),x33721),f334(a115,x33721))) % 169.19/169.64 [3384]P104(f334(f334(f250(a877),f2(a877)),f334(a115,x33841))) % 169.19/169.64 [3676]E(f334(f334(f3(a102),f334(a5,f334(a115,f334(a21,x36761)))),f79(a102)),x36761) % 169.19/169.64 [3749]P104(f334(f334(f249(a1),f334(f80(a1),f334(f103(a1),x37491))),f2(a1))) % 169.19/169.64 [3902]P104(f334(f334(f250(a1),f334(f80(a1),f334(f103(a1),f334(a115,x39021)))),f2(a1))) % 169.19/169.64 [4521]~E(f257(f886(x45211,a871)),f195(f886(x45211,a871))) % 169.19/169.64 [4568]~P104(f334(f334(f250(a877),x45681),f2(a877))) % 169.19/169.64 [4584]~P104(f334(f334(f250(a1),f334(f103(a1),x45841)),f2(a1))) % 169.19/169.64 [3175]E(f181(x31751,f116(f878(x31751))),f116(f878(x31751))) % 169.19/169.64 [3178]E(f334(f334(f82(a1),a84),x31781),a84) % 169.19/169.64 [3179]E(f334(f334(f81(a1),a84),x31791),x31791) % 169.19/169.64 [3182]E(f334(a107,f334(f103(a1),x31821)),x31821) % 169.19/169.64 [3183]E(f334(f334(f3(a1),x31831),a84),x31831) % 169.19/169.64 [3184]E(f334(f334(f81(a1),x31841),a84),x31841) % 169.19/169.64 [3186]E(f334(f334(f3(a877),x31861),x31861),f2(a877)) % 169.19/169.64 [3190]E(f334(f80(a1),f334(f80(a1),x31901)),x31901) % 169.19/169.64 [3191]E(f334(f39(a877),f334(f255(a877),x31911)),x31911) % 169.19/169.64 [3202]E(f334(f334(f82(a877),f79(a877)),x32021),x32021) % 169.19/169.64 [3203]E(f334(f334(f82(a1),f79(a1)),x32031),x32031) % 169.19/169.64 [3204]E(f334(f334(f81(a877),f2(a877)),x32041),x32041) % 169.19/169.64 [3205]E(f334(f334(f81(a1),f2(a1)),x32051),x32051) % 169.19/169.64 [3206]E(f334(f334(f248(a877),f2(a877)),x32061),x32061) % 169.19/169.64 [3212]E(f334(f334(f3(a877),f2(a877)),x32121),f2(a877)) % 169.19/169.64 [3213]E(f334(f334(f82(a877),f2(a877)),x32131),f2(a877)) % 169.19/169.64 [3214]E(f334(f334(f40(a1),f2(a1)),x32141),f2(a1)) % 169.19/169.64 [3215]E(f334(f334(f247(a877),f2(a877)),x32151),f2(a877)) % 169.19/169.64 [3227]E(f125(x32271,f334(f80(a1),x32271)),f132(a1,x32271)) % 169.19/169.64 [3233]E(f334(f304(a877,f2(a877)),x32331),f334(f255(a877),x32331)) % 169.19/169.64 [3234]E(f334(f334(f82(a1),a100),x32341),f334(f80(a1),x32341)) % 169.19/169.64 [3241]E(f334(a107,f334(f106(a1),x32411)),f334(f106(a877),x32411)) % 169.19/169.64 [3242]E(f334(a21,f334(f106(a102),x32421)),f334(f106(a877),x32421)) % 169.19/169.64 [3243]E(f334(f39(a877),f334(f303(a877),x32431)),f334(a115,x32431)) % 169.19/169.64 [3253]E(f334(f334(f81(a877),f79(a877)),x32531),f334(a115,x32531)) % 169.19/169.64 [3257]E(f334(f76(a1),f334(f103(a1),x32571)),f334(f103(a1),x32571)) % 169.19/169.64 [3258]E(f334(f105(a1),f334(f103(a1),x32581)),f334(f103(a1),x32581)) % 169.19/169.64 [3263]E(f334(f39(x32631),f195(f886(x32631,a871))),f2(a877)) % 169.19/169.64 [3265]E(f334(f334(f40(a877),x32651),f334(a115,f2(a877))),x32651) % 169.19/169.64 [3274]E(f46(a877,x32741,f334(a115,f2(a877))),f2(a877)) % 169.19/169.64 [3275]E(f46(a1,x32751,f334(f106(a1),a100)),f2(a1)) % 169.19/169.64 [3291]E(f334(f334(f40(a1),x32911),f334(f106(a1),a100)),f334(f80(a1),x32911)) % 169.19/169.64 [3295]E(f139(a877,f334(f304(a877,x32951),f2(a877))),f116(a877)) % 169.19/169.64 [3296]E(f334(f334(f81(a1),x32961),f79(a1)),f334(f334(f3(a1),x32961),a100)) % 169.19/169.64 [3297]E(f334(f334(f3(a1),x32971),f79(a1)),f334(f334(f81(a1),x32971),a100)) % 169.19/169.64 [3301]P104(f334(f334(f249(a877),x33011),x33011)) % 169.19/169.64 [3302]P104(f334(f334(f249(a1),x33021),x33021)) % 169.19/169.64 [3303]P104(f334(f334(f92(a1),x33031),x33031)) % 169.19/169.64 [3308]E(f334(f80(a1),f334(f106(a1),x33081)),f334(f106(a1),f334(f80(a1),x33081))) % 169.19/169.64 [3309]P104(f334(f63(a877),f334(f303(a877),x33091))) % 169.19/169.64 [3310]P104(f334(f63(a877),f334(f255(a877),x33101))) % 169.19/169.64 [3318]E(f161(x33181,f257(f886(x33181,a871))),f257(f886(f878(x33181),a871))) % 169.19/169.64 [3323]P104(f334(f334(f249(a877),f2(a877)),x33231)) % 169.19/169.64 [3334]E(f334(f334(f81(a877),f114(x33341)),f334(a115,f2(a877))),f114(f334(a115,x33341))) % 169.19/169.64 [3335]E(f334(f254(x33351),f334(f18(a871,x33351),a246)),f195(f886(x33351,a871))) % 169.19/169.64 [3336]E(f334(f254(x33361),f334(f18(a871,x33361),a194)),f257(f886(x33361,a871))) % 169.19/169.64 [3340]E(f334(f334(f312(a877),x33401),f334(f255(a877),x33401)),f334(f255(a877),f334(a115,x33401))) % 169.19/169.64 [3352]E(f334(f334(f81(a1),f79(a1)),f334(f103(a1),x33521)),f334(f103(a1),f334(a115,x33521))) % 169.19/169.64 [3355]E(f334(f334(f151(f878(x33551)),f116(x33551)),f116(f878(x33551))),f55(x33551,f116(x33551))) % 169.19/169.64 [3375]E(f195(f886(f885(x33751,x33751),a871)),f266(x33751,f195(f886(x33751,a871)))) % 169.19/169.64 [3376]E(f334(f311(x33761),f257(f886(x33761,a871))),f257(f886(f886(x33761,a871),a871))) % 169.19/169.64 [3377]E(f334(f80(f886(x33771,a871)),f195(f886(x33771,a871))),f257(f886(x33771,a871))) % 169.19/169.64 [3378]E(f334(f80(f886(x33781,a871)),f257(f886(x33781,a871))),f195(f886(x33781,a871))) % 169.19/169.64 [3380]P104(f334(f63(x33801),f195(f886(x33801,a871)))) % 169.19/169.64 [3382]E(f334(f304(a877,x33821),f334(a115,x33821)),f334(f334(f312(a877),x33821),f195(f886(a877,a871)))) % 169.19/169.64 [3383]E(f86(f885(a877,a877),f49(x33831,f2(a877))),f334(f334(f269(a877,a877),f2(a877)),x33831)) % 169.19/169.64 [3397]E(f334(f334(f312(a877),f334(a115,x33971)),f334(f303(a877),x33971)),f334(f303(a877),f334(a115,x33971))) % 169.19/169.64 [3401]P39(x34011,f195(f886(f885(x34011,x34011),a871))) % 169.19/169.64 [3404]P104(f334(f334(f249(a1),f2(a1)),f334(f103(a1),x34041))) % 169.19/169.64 [3412]E(f334(f334(f81(a877),f334(f196(a877),x34121)),f334(a115,f2(a877))),f334(f196(a877),f334(a115,x34121))) % 169.19/169.64 [3523]P41(f334(f313(a877,a1,f103(a1)),x35231)) % 169.19/169.64 [3561]P49(x35611,f195(f886(x35611,a871)),f195(f886(f885(x35611,x35611),a871))) % 169.19/169.64 [3581]E(f334(f334(f269(a1,a1),f334(f106(a1),a100)),f334(f334(f3(a1),x35811),f79(a1))),f51(f334(f106(a1),a100),x35811)) % 169.19/169.64 [3633]P57(x36331,f334(f18(f886(x36331,a871),x36331),f334(f18(a871,x36331),a246))) % 169.19/169.64 [3840]P104(f334(f334(f336(f886(f885(a877,a877),a871)),f335(x38401)),a101)) % 169.19/169.64 [3866]P104(f334(f334(f336(f886(f885(a877,a877),a871)),f334(a110,x38661)),a101)) % 169.19/169.64 [4004]P21(x40041,f886(x40041,a871),f334(f334(f9(x40041,f886(x40041,a871),f886(x40041,a871)),f312(x40041)),f195(f886(x40041,a871))),f257(f886(x40041,a871))) % 169.19/169.64 [4517]~E(f334(f334(f81(a1),x45171),x45171),a100) % 169.19/169.64 [4553]~E(f334(a5,f334(a115,f334(a21,x45531))),f2(a102)) % 169.19/169.64 [4561]~P104(f334(a201,f334(f103(a1),x45611))) % 169.19/169.64 [4564]~P104(f334(f334(f250(a877),x45641),x45641)) % 169.19/169.64 [4577]~P104(f334(f334(f249(a877),f334(a115,x45771)),x45771)) % 169.19/169.64 [3325]E(f334(a107,f334(f80(a1),f334(f103(a1),x33251))),f2(a877)) % 169.19/169.64 [3328]E(f334(f334(f81(a1),f334(f80(a1),x33281)),x33281),f2(a1)) % 169.19/169.64 [3333]E(f334(f39(a1),f334(f304(a1,f2(a1)),x33331)),f334(a107,x33331)) % 169.19/169.64 [3345]E(f334(f334(f259(a877),f334(a115,f2(a877))),x33451),f334(a115,f2(a877))) % 169.19/169.64 [3447]E(f334(f287(x34471),f195(f886(f885(x34471,x34471),a871))),f195(f886(x34471,a871))) % 169.19/169.64 [3455]E(f41(f886(x34551,a871),f195(f886(f886(x34551,a871),a871))),f195(f886(x34551,a871))) % 169.19/169.64 [3456]E(f41(f886(x34561,a871),f257(f886(f886(x34561,a871),a871))),f257(f886(x34561,a871))) % 169.19/169.64 [3457]E(f42(f886(x34571,a871),f195(f886(f886(x34571,a871),a871))),f257(f886(x34571,a871))) % 169.19/169.64 [3458]E(f42(f886(x34581,a871),f257(f886(f886(x34581,a871),a871))),f195(f886(x34581,a871))) % 169.19/169.64 [3505]E(f334(f334(f312(f878(x35051)),f116(x35051)),f195(f886(f878(x35051),a871))),f162(x35051,f116(f886(x35051,a871)))) % 169.19/169.64 [3506]E(f334(f334(f312(f878(x35061)),f116(x35061)),f195(f886(f878(x35061),a871))),f161(x35061,f195(f886(x35061,a871)))) % 169.19/169.64 [3544]E(f334(f334(f81(a877),f6(x35441)),f334(a115,f2(a877))),f6(f334(a5,f334(a115,f334(a21,x35441))))) % 169.19/169.64 [3572]E(f334(f39(a1),f334(f313(a877,a1,f103(a1)),x35721)),f334(f39(a877),x35721)) % 169.19/169.64 [3573]P104(f334(f334(f249(a877),x35731),f334(f334(f82(a877),x35731),x35731))) % 169.19/169.64 [3612]E(f334(f313(a1,a877,a107),f305(a1,f2(a1),f334(f103(a1),x36121))),f334(f303(a877),x36121)) % 169.19/169.64 [3628]E(f334(f334(f40(a877),f334(a115,f2(a877))),f334(f106(a877),x36281)),f334(a107,f334(f334(f40(a1),f79(a1)),f334(f106(a1),x36281)))) % 169.19/169.64 [3630]E(f334(f173(a877),f139(a877,f334(f304(a877,f2(a877)),f334(a115,x36301)))),f334(f303(a877),x36301)) % 169.19/169.64 [3631]E(f334(f334(f81(a877),f334(f196(a102),x36311)),f334(a115,f2(a877))),f334(f196(a102),f334(a5,f334(a115,f334(a21,x36311))))) % 169.19/169.64 [3649]E(f334(f313(a1,a877,a107),f334(f313(a877,a1,f103(a1)),x36491)),x36491) % 169.19/169.64 [3682]E(f334(f334(f312(a877),f2(a877)),f334(f313(a877,a877,a115),f334(f255(a877),x36821))),f334(f255(a877),f334(a115,x36821))) % 169.19/169.64 [3689]P52(x36891,x36891,f310(x36891,f195(f886(f885(x36891,x36891),a871)))) % 169.19/169.64 [3695]P104(f334(a201,f334(f80(a1),f334(f103(a1),f334(a115,x36951))))) % 169.19/169.64 [3706]E(f334(f334(f3(f886(a877,a871)),f334(f256(a877),x37061)),f334(f334(f312(a877),x37061),f195(f886(a877,a871)))),f334(f256(a877),f334(a115,x37061))) % 169.19/169.64 [3722]E(f334(f334(f81(a1),f334(f334(f3(a1),a84),x37221)),f334(f334(f3(a1),a84),x37221)),f334(f334(f3(a1),a84),f334(f334(f81(a1),x37221),x37221))) % 169.19/169.64 [3738]E(f334(f334(f312(f886(x37381,a871)),f195(f886(x37381,a871))),f195(f886(f886(x37381,a871),a871))),f334(f311(x37381),f195(f886(x37381,a871)))) % 169.19/169.64 [3766]E(f334(f334(f3(f886(a877,a871)),f334(f306(a877),x37661)),f334(f334(f312(a877),f334(a115,x37661)),f195(f886(a877,a871)))),f334(f306(a877),f334(a115,x37661))) % 169.19/169.64 [3775]E(f334(f334(f312(f881(x37751)),f198(x37751)),f334(f313(x37751,f881(x37751),f241(x37751)),f257(f886(x37751,a871)))),f257(f886(f881(x37751),a871))) % 169.19/169.64 [3878]E(f334(f106(a877),f334(f334(f81(a1),x38781),x38781)),f334(f334(f87(a877,a877),f334(f106(a877),x38781)),f334(f334(f20(a877,a877,a877),f81(a877)),f7(a877)))) % 169.19/169.64 [4272]P11(x42721,f886(x42721,a871),f334(f334(f10(f886(x42721,a871),f886(f886(x42721,a871),f886(x42721,a871)),x42721),f334(f9(f886(x42721,a871),f886(x42721,a871),f886(x42721,a871)),f3(f886(x42721,a871)))),f334(f334(f9(x42721,f886(x42721,a871),f886(x42721,a871)),f312(x42721)),f195(f886(x42721,a871))))) % 169.19/169.64 [4361]E(f334(f254(f885(a1,a1)),f334(f273(a1,a1,a871),f334(f334(f10(f886(a1,a871),f886(a1,a871),a1),f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),x43611)))),f250(a1)))),f108(x43611)) % 169.19/169.64 [4394]E(f334(f254(f885(a1,a1)),f334(f273(a1,a1,a871),f334(f334(f20(a1,f886(a1,a871),f886(a1,a871)),f334(f334(f10(f886(a871,a871),f886(f886(a1,a871),f886(a1,a871)),a1),f10(a871,a871,a1)),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),x43941)))),f250(a1)))),f109(x43941)) % 169.19/169.64 [4449]E(f334(f254(f885(f886(x44491,a871),f886(x44491,a871))),f334(f273(f886(x44491,a871),f886(x44491,a871),a871),f334(f334(f9(f886(x44491,a871),f886(f886(x44491,a871),a871),f886(f886(x44491,a871),a871)),f334(f334(f10(f886(f886(x44491,a871),f886(a871,a871)),f886(f886(f886(x44491,a871),a871),f886(f886(x44491,a871),a871)),f886(x44491,a871)),f20(f886(x44491,a871),a871,a871)),f334(f334(f10(f886(f886(x44491,a871),a871),f886(f886(x44491,a871),f886(a871,a871)),f886(x44491,a871)),f334(f10(a871,f886(a871,a871),f886(x44491,a871)),a332)),f250(f886(x44491,a871))))),f63(x44491)))),f309(x44491)) % 169.19/169.64 [4581]~P104(f334(f63(f878(x45811)),f257(f886(f878(x45811),a871)))) % 169.19/169.64 [4586]~P104(f334(f334(f92(a1),a100),f334(f334(f81(a1),x45861),x45861))) % 169.19/169.64 [4597]~P104(f334(f334(f249(a1),f2(a1)),f334(f80(a1),f334(f103(a1),f334(a115,x45971))))) % 169.19/169.64 [3482]E(f334(f334(f3(a1),f334(f334(f81(a1),x34821),a100)),a100),x34821) % 169.19/169.64 [3498]E(f334(f173(a877),f139(a877,f334(f304(a877,f2(a877)),x34981))),f334(f255(a877),x34981)) % 169.19/169.64 [3745]E(f334(f334(f81(a1),f334(f334(f81(a1),f79(a1)),x37451)),x37451),f334(f334(f3(a1),f334(f334(f81(a1),x37451),x37451)),a100)) % 169.19/169.64 [3794]E(f334(f289(x37941,x37941),f310(x37941,f195(f886(f885(x37941,x37941),a871)))),f310(x37941,f195(f886(f885(x37941,x37941),a871)))) % 169.19/169.64 [3843]P104(f334(f334(f249(a877),x38431),f334(f334(f82(a877),x38431),f334(f334(f82(a877),x38431),x38431)))) % 169.19/169.64 [4126]P104(f334(f63(a877),f334(f254(a877),f334(f334(f9(a877,a877,a871),f249(a877)),x41261)))) % 169.19/169.64 [4127]P104(f334(f63(a877),f334(f254(a877),f334(f334(f9(a877,a877,a871),f250(a877)),x41271)))) % 169.19/169.64 [4414]E(f334(f254(f885(x44141,x44141)),f334(f334(f10(f886(x44141,a871),a871,f885(x44141,x44141)),f88(x44141)),f334(f334(f9(f885(x44141,x44141),f886(x44141,f885(x44141,x44141)),f886(x44141,a871)),f334(f334(f10(f886(f885(x44141,x44141),a871),f886(f886(x44141,f885(x44141,x44141)),f886(x44141,a871)),f885(x44141,x44141)),f10(f885(x44141,x44141),a871,x44141)),a331)),f334(f334(f20(x44141,x44141,f885(x44141,x44141)),f269(x44141,x44141)),f7(x44141))))),f310(x44141,f195(f886(f885(x44141,x44141),a871)))) % 169.19/169.64 [4583]~E(f334(f334(f3(a1),f334(f334(f81(a1),x45831),x45831)),a100),a84) % 169.19/169.64 [4585]~E(f334(f334(f81(a1),f334(f334(f81(a1),f79(a1)),x45851)),x45851),f2(a1)) % 169.19/169.64 [4594]~P104(f334(f334(f92(a1),f334(f334(f81(a1),x45941),x45941)),a100)) % 169.19/169.64 [3891]E(f334(f334(f81(a1),f334(f334(f3(a1),a100),x38911)),f334(f334(f3(a1),a100),x38911)),f334(f334(f3(a1),a100),f334(f334(f3(a1),f334(f334(f81(a1),x38911),x38911)),a100))) % 169.19/169.64 [4013]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),a100),x40131)),f334(f334(f3(a1),a100),x40131))),a100),f334(f334(f3(a1),a100),f334(f334(f81(a1),x40131),x40131))) % 169.19/169.64 [4048]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f81(a1),x40481),a100)),f334(f334(f81(a1),x40481),a100))),a100),f334(f334(f81(a1),f334(f334(f81(a1),x40481),x40481)),a100)) % 169.19/169.64 [4086]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),a100),x40861)),f334(f334(f3(a1),a100),x40861))),a100),f334(f334(f3(a1),a84),f334(f334(f3(a1),f334(f334(f81(a1),x40861),x40861)),a100))) % 169.19/169.64 [4189]E(f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x41891),f2(a877))),f195(f886(f885(a877,a877),a871))))),f334(f103(a1),x41891)) % 169.19/169.64 [4199]E(f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),f339(x41991)),f542(x41991))),f195(f886(f885(a877,a877),a871))))),x41991) % 169.19/169.64 [4234]E(f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x42341)),f334(f313(a877,a1,f103(a1)),f334(f254(a877),f334(f334(f10(a1,a871,a877),x42341),f103(a1))))) % 169.19/169.64 [4280]P41(f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x42801))) % 169.19/169.64 [4301]P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x43011),f195(f886(f885(a877,a877),a871)))),a72)) % 169.19/169.64 [4307]E(f334(f313(a1,a877,a107),f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),f334(f334(f10(a877,a871,a1),x43071),a107)))),f334(f254(a877),x43071)) % 169.19/169.64 [4463]E(f315(a877,f334(f334(f44(f885(a877,a877),f886(a877,a871)),f334(a110,x44631)),f334(f273(a877,a877,f886(a877,a871)),f334(f334(f9(a877,f886(a877,a871),f886(a877,f886(a877,a871))),f334(f334(f10(f886(a877,f886(f886(a877,a871),f886(a877,a871))),f886(f886(a877,a871),f886(a877,f886(a877,a871))),a877),f9(a877,f886(a877,a871),f886(a877,a871))),f334(f334(f10(f886(a877,a877),f886(a877,f886(f886(a877,a871),f886(a877,a871))),a877),f334(f10(a877,f886(f886(a877,a871),f886(a877,a871)),a877),f312(a877))),f3(a877)))),f195(f886(a877,a871)))))),f334(a107,x44631)) % 169.19/169.64 [4599]~P104(f334(f334(f92(a1),a84),f334(f334(f3(a1),f334(f334(f81(a1),x45991),x45991)),a100))) % 169.19/169.64 [3936]E(f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),x39361),x39361)),a100)),a100),f334(f334(f81(a1),x39361),x39361)) % 169.19/169.64 [3987]E(f334(f334(f3(a1),f334(f334(f3(a1),f334(f334(f81(a1),x39871),x39871)),a100)),a100),f334(f334(f81(a1),f334(f334(f3(a1),x39871),a100)),f334(f334(f3(a1),x39871),a100))) % 169.19/169.64 [4207]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f81(a1),f334(f80(a1),x42071)),a100)),f334(f334(f81(a1),f334(f80(a1),x42071)),a100))),a100),f334(f80(a1),f334(f334(f3(a1),f334(f334(f81(a1),x42071),x42071)),a100))) % 169.19/169.64 [4607]~P104(f334(f334(f92(a1),f334(f334(f3(a1),f334(f334(f81(a1),x46071),x46071)),a100)),a84)) % 169.19/169.64 [4252]E(f334(f334(f81(a877),x42521),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(a115,f334(a115,x42521))) % 169.19/169.64 [4253]E(f334(f334(f82(a877),x42531),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f81(a877),x42531),x42531)) % 169.19/169.64 [4254]E(f334(f334(f40(a877),f334(f334(f81(a877),x42541),x42541)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x42541) % 169.19/169.64 [4336]E(f46(a877,f334(a115,f334(a115,x43361)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f46(a877,x43361,f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.64 [4478]E(f334(a90,f334(f334(f44(f885(a877,a877),f886(f885(a877,a877),a871)),f334(a110,x44781)),f334(f273(a877,a877,f886(f885(a877,a877),a871)),f334(f334(f10(f886(a877,f886(f885(a877,a877),a871)),f886(a877,f886(f885(a877,a877),a871)),a877),f334(f10(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871),a877),f288(f885(a877,a877),f885(a877,a877),a111))),f334(f334(f9(a877,f886(f885(a877,a877),a871),f886(a877,f886(f885(a877,a877),a871))),f334(f334(f10(f886(a877,f886(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f886(f886(f885(a877,a877),a871),f886(a877,f886(f885(a877,a877),a871))),a877),f9(a877,f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f10(f886(a877,f885(a877,a877)),f886(a877,f886(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),a877),f334(f10(f885(a877,a877),f886(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),a877),f312(f885(a877,a877)))),f334(f9(a877,a877,f885(a877,a877)),f269(a877,a877))))),f195(f886(f885(a877,a877),a871))))))),f334(f80(a1),x44781)) % 169.19/169.64 [4331]E(f334(f334(f81(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x43311),f334(a115,f334(a115,x43311))) % 169.19/169.64 [4332]E(f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x43321),f334(f334(f81(a877),x43321),x43321)) % 169.19/169.64 [4366]E(f334(f334(f40(a877),f334(a115,f334(a115,x43661))),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(a115,f334(f334(f40(a877),x43661),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.64 [4420]E(f334(f334(f81(a877),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),x44201),f334(a115,f334(a115,f334(a115,x44201)))) % 169.19/169.64 [4486]E(f334(f273(a1,a1,f885(a1,a1)),f334(f334(f20(a1,f886(a1,f885(a1,a1)),f886(a1,f885(a1,a1))),f334(f334(f10(f886(a1,f886(f885(a1,a1),f885(a1,a1))),f886(f886(a1,f885(a1,a1)),f886(a1,f885(a1,a1))),a1),f20(a1,f885(a1,a1),f885(a1,a1))),f334(f334(f10(f886(a1,f885(a1,a1)),f886(a1,f886(f885(a1,a1),f885(a1,a1))),a1),f334(f20(a1,f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),f334(f334(f10(a871,f886(f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),a1),f99(f885(a1,a1))),f334(f334(f10(a1,a871,a1),f334(f249(a1),f2(a1))),f334(f334(f9(a1,a1,a1),f3(a1)),x44861))))),f334(f334(f9(a1,f886(a1,a1),f886(a1,f885(a1,a1))),f334(f334(f10(f886(a1,f885(a1,a1)),f886(f886(a1,a1),f886(a1,f885(a1,a1))),a1),f10(a1,f885(a1,a1),a1)),f334(f334(f10(a1,f886(a1,f885(a1,a1)),a1),f269(a1,a1)),f334(f334(f9(a1,a1,a1),f334(f334(f10(a1,f886(a1,a1),a1),f81(a1)),f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f79(a1))))),f334(f334(f9(a1,a1,a1),f3(a1)),x44861))))),f334(f334(f10(a1,f886(a1,f885(a1,a1)),a1),f269(a1,a1)),f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))))),f45(x44861)) % 169.19/169.64 [3146]P91(f884(x31461,x31462)) % 169.19/169.64 [3147]P91(f885(x31471,x31472)) % 169.19/169.64 [3148]P91(f882(x31481,x31482)) % 169.19/169.64 [3149]P103(f884(x31491,x31492)) % 169.19/169.64 [3150]P103(f885(x31501,x31502)) % 169.19/169.64 [3151]P103(f882(x31511,x31512)) % 169.19/169.64 [3168]P30(a1,f180(x31681,x31682)) % 169.19/169.64 [3169]P39(x31691,f153(x31691,x31692)) % 169.19/169.64 [3235]P33(x32351,x32352,f116(x32351)) % 169.19/169.64 [3269]P49(x32691,x32692,f266(x32691,x32692)) % 169.19/169.64 [3270]P52(x32701,x32701,f266(x32701,x32702)) % 169.19/169.64 [3547]P21(x35471,x35471,f7(x35471),x35472) % 169.19/169.64 [3548]P21(x35481,x35481,f35(x35481),x35482) % 169.19/169.64 [3556]P34(x35561,x35562,f116(x35561),f116(x35561)) % 169.19/169.64 [3557]P21(x35571,f881(x35571),f241(x35571),x35572) % 169.19/169.64 [3566]P21(f878(x35661),f878(x35661),f169(x35661),x35662) % 169.19/169.64 [4497]~E(f34(x44971,x44972),a24) % 169.19/169.64 [4498]~E(f33(x44981,x44982),a24) % 169.19/169.64 [4530]~P35(x45301,x45302,f116(x45301)) % 169.19/169.64 [4531]~P37(x45311,x45312,f116(x45311)) % 169.19/169.64 [3128]E(f334(f7(x31281),x31282),x31282) % 169.19/169.64 [3129]E(f334(f254(x31291),x31292),x31292) % 169.19/169.64 [3131]E(f334(f35(x31311),x31312),x31312) % 169.19/169.64 [3141]E(f334(f199(x31411),x31412),f118(x31411)) % 169.19/169.64 [3166]E(f91(x31661,f334(a331,x31662)),x31662) % 169.19/169.64 [3167]E(f86(x31671,f334(a331,x31672)),x31672) % 169.19/169.64 [3188]E(f334(f136(x31881,x31882),f116(x31881)),f116(x31881)) % 169.19/169.64 [3208]E(f152(x32081,f152(x32081,x32082)),f152(x32081,x32082)) % 169.19/169.64 [3209]E(f310(x32091,f310(x32091,x32092)),f310(x32091,x32092)) % 169.19/169.64 [3230]E(f334(f334(f134(x32301),x32302),f116(x32301)),x32302) % 169.19/169.64 [3236]E(f174(x32361,x32362,f116(x32361)),x32362) % 169.19/169.64 [3237]E(f174(x32371,f116(x32371),x32372),x32372) % 169.19/169.64 [3238]E(f170(x32381,f2(a877),x32382),f116(x32381)) % 169.19/169.64 [3244]E(f334(f334(f176(x32441),x32442),f116(x32441)),f116(x32441)) % 169.19/169.64 [3245]E(f334(f334(f138(x32451),x32452),f116(x32451)),f116(x32451)) % 169.19/169.64 [3247]E(f242(x32471,x32472,f198(x32471)),f2(a877)) % 169.19/169.64 [3248]E(f155(x32481,x32482,f116(x32481)),f2(a877)) % 169.19/169.64 [3250]E(f171(x32501,x32502,f116(x32501)),f116(x32501)) % 169.19/169.64 [3251]E(f178(x32511,x32512,f116(x32511)),f116(x32511)) % 169.19/169.64 [3252]E(f177(x32521,f116(x32521),x32522),f116(x32521)) % 169.19/169.64 [3256]E(f334(f173(x32561),f152(x32561,x32562)),f334(f173(x32561),x32562)) % 169.19/169.64 [3259]E(f334(f265(x32591,x32591),f266(x32591,x32592)),x32592) % 169.19/169.64 [3260]E(f334(f267(x32601,x32601),f266(x32601,x32602)),x32602) % 169.19/169.64 [3268]E(f334(f289(x32681,x32681),f266(x32681,x32682)),f266(x32681,x32682)) % 169.19/169.64 [3283]E(f310(f878(x32831),f157(x32831,x32832)),f158(x32831,f310(x32831,x32832))) % 169.19/169.64 [3285]P104(f334(f137(a1),f180(x32851,x32852))) % 169.19/169.64 [3293]E(f334(f265(x32931,x32931),f310(x32931,x32932)),f257(f886(x32931,a871))) % 169.19/169.64 [3294]E(f334(f267(x32941,x32941),f310(x32941,x32942)),f257(f886(x32941,a871))) % 169.19/169.64 [3298]P104(f334(f137(x32981),f152(x32981,x32982))) % 169.19/169.64 [3300]P104(f334(f160(x33001,x33002),f116(x33001))) % 169.19/169.64 [3306]E(f334(f173(a1),f180(x33061,x33062)),f305(a1,x33061,x33062)) % 169.19/169.64 [3321]P53(x33211,f195(f886(x33211,a871)),x33212) % 169.19/169.64 [3326]E(f334(f272(a1,a1),f47(x33261,x33262)),f46(a1,x33261,x33262)) % 169.19/169.64 [3327]E(f334(f304(a877,x33271),f334(a115,x33272)),f305(a877,x33271,x33272)) % 169.19/169.64 [3344]E(f334(f334(f151(x33441),x33442),f116(x33441)),f140(x33441,x33442,f116(x33441))) % 169.19/169.64 [3357]E(f305(a877,f334(a115,x33571),x33572),f307(a877,x33571,x33572)) % 169.19/169.64 [3360]P49(x33601,f257(f886(x33601,a871)),f310(x33601,x33602)) % 169.19/169.64 [3424]E(f334(f334(f3(a877),x34241),f334(a115,x34242)),f334(f39(a877),f308(a877,x34242,x34241))) % 169.19/169.64 [3483]E(f167(x34831,x34832,f116(x34831)),f334(f334(f269(f878(x34831),f878(x34831)),f116(x34831)),f116(x34831))) % 169.19/169.64 [3503]E(f334(f273(x35031,x35032,f885(x35031,x35032)),f269(x35031,x35032)),f35(f885(x35031,x35032))) % 169.19/169.64 [3508]P104(f334(f334(f336(f878(x35081)),f116(x35081)),f161(x35081,x35082))) % 169.19/169.64 [3509]E(f334(f196(f878(x35091)),f117(x35091,x35092)),f334(f334(f3(a877),f334(f196(f878(x35091)),x35092)),f79(a877))) % 169.19/169.64 [3517]P104(f334(f63(a877),f308(a877,x35171,x35172))) % 169.19/169.64 [3518]P104(f334(f63(a877),f305(a877,x35181,x35182))) % 169.19/169.64 [3519]P104(f334(f63(a877),f307(a877,x35191,x35192))) % 169.19/169.64 [3520]P104(f334(f63(a1),f308(a1,x35201,x35202))) % 169.19/169.64 [3521]P104(f334(f63(a1),f305(a1,x35211,x35212))) % 169.19/169.64 [3522]P104(f334(f63(a1),f307(a1,x35221,x35222))) % 169.19/169.64 [3627]E(f334(f313(a877,a877,a115),f305(a877,x36271,x36272)),f305(a877,f334(a115,x36271),f334(a115,x36272))) % 169.19/169.64 [3646]E(f334(f334(f291(x36461,x36461,x36461),f310(x36461,x36462)),f310(x36461,x36462)),f310(x36461,x36462)) % 169.19/169.64 [3680]E(f334(f334(f269(a1,a1),f334(f334(f40(a1),x36801),x36802)),f46(a1,x36801,x36802)),f47(x36801,x36802)) % 169.19/169.64 [3681]E(f334(f334(f269(a102,a102),f334(f334(f40(a102),x36811),x36812)),f46(a102,x36811,x36812)),f23(x36811,x36812)) % 169.19/169.64 [3710]E(f334(f334(f269(a877,a877),f334(f334(f40(a877),x37101),x37102)),f46(a877,x37101,x37102)),f86(f885(a877,a877),f49(x37101,x37102))) % 169.19/169.64 [3762]P104(f334(f334(f250(a877),f334(f334(f3(a877),x37621),x37622)),f334(a115,x37621))) % 169.19/169.64 [3865]E(f334(f334(f81(a1),f334(f334(f82(a1),x38651),f334(f334(f40(a1),x38652),x38651))),f46(a1,x38652,x38651)),x38652) % 169.19/169.64 [3869]E(f334(f334(f44(a877,f886(f885(f878(x38691),f878(x38691)),a871)),f257(f886(a877,a871))),f143(x38691,x38692)),f145(x38691,x38692)) % 169.19/169.64 [4101]P104(f334(f334(f336(f885(f878(x41011),f878(x41011))),f334(f334(f269(f878(x41011),f878(x41011)),f116(x41011)),f116(x41011))),f158(x41011,x41012))) % 169.19/169.64 [4219]E(f270(x42191,x42191,x42191,a331,f270(x42191,x42191,x42191,x42192,a331)),x42192) % 169.19/169.64 [4265]E(f274(x42651,x42651,x42652,x42652,f7(x42651),f7(x42652)),f35(f885(x42651,x42652))) % 169.19/169.64 [4267]E(f274(x42671,x42671,x42672,x42672,f35(x42671),f35(x42672)),f35(f885(x42671,x42672))) % 169.19/169.64 [4506]~E(f334(f241(x45061),x45062),f198(x45061)) % 169.19/169.64 [4518]~P40(x45181,f334(f241(x45181),x45182)) % 169.19/169.64 [3228]E(f334(f245(x32281),f334(f241(x32281),x32282)),x32282) % 169.19/169.64 [3229]E(f334(f169(x32291),f334(f169(x32291),x32292)),x32292) % 169.19/169.64 [3231]E(f334(f334(f138(x32311),f2(a877)),x32312),x32312) % 169.19/169.64 [3246]E(f334(f334(f176(x32461),f2(a877)),x32462),f116(x32461)) % 169.19/169.64 [3254]E(f334(f334(f134(x32541),f116(x32541)),x32542),x32542) % 169.19/169.64 [3262]E(f334(f196(f881(x32621)),f334(f241(x32621),x32622)),f2(a877)) % 169.19/169.64 [3264]E(f41(f886(x32641,a871),f334(f311(x32641),x32642)),x32642) % 169.19/169.64 [3266]E(f334(f173(x32661),f334(f168(x32661),x32662)),f334(f173(x32661),x32662)) % 169.19/169.64 [3267]E(f334(f173(x32671),f334(f169(x32671),x32672)),f334(f173(x32671),x32672)) % 169.19/169.64 [3272]E(f334(f334(f3(a102),x32721),x32722),f334(f334(a4,x32721),x32722)) % 169.19/169.64 [3287]E(f334(f334(f82(a877),x32871),x32872),f334(f334(f82(a877),x32872),x32871)) % 169.19/169.64 [3288]E(f334(f334(f82(a1),x32881),x32882),f334(f334(f82(a1),x32882),x32881)) % 169.19/169.64 [3289]E(f334(f334(f81(a877),x32891),x32892),f334(f334(f81(a877),x32892),x32891)) % 169.19/169.64 [3290]E(f334(f334(f81(a1),x32901),x32902),f334(f334(f81(a1),x32902),x32901)) % 169.19/169.64 [3313]E(f334(f334(f190(x33131,x33131),f2(a877)),x33132),f35(x33131)) % 169.19/169.64 [3314]E(f334(f196(f878(x33141)),f334(f168(x33141),x33142)),f334(f196(f878(x33141)),x33142)) % 169.19/169.64 [3315]E(f334(f196(f878(x33151)),f334(f169(x33151),x33152)),f334(f196(f878(x33151)),x33152)) % 169.19/169.64 [3316]E(f177(x33161,x33162,f195(f886(a877,a871))),f116(x33161)) % 169.19/169.64 [3317]E(f334(f334(f154(x33171,x33171),f7(x33171)),x33172),x33172) % 169.19/169.64 [3319]E(f334(f268(a1,a1),f47(x33191,x33192)),f334(f334(f40(a1),x33191),x33192)) % 169.19/169.64 [3337]E(f334(f196(f878(x33371)),f152(x33371,x33372)),f334(f39(x33371),f334(f173(x33371),x33372))) % 169.19/169.64 [3338]E(f32(f33(x33381,x33382)),f334(f334(f81(a877),f32(x33382)),f334(a115,f2(a877)))) % 169.19/169.64 [3339]E(f334(f287(x33391),f334(f289(x33391,x33391),x33392)),f334(f287(x33391),x33392)) % 169.19/169.64 [3343]P104(f334(f63(x33431),f334(f173(x33431),x33432))) % 169.19/169.64 [3351]E(f334(f334(f81(a1),x33511),f334(f80(a1),x33512)),f334(f334(f3(a1),x33511),x33512)) % 169.19/169.64 [3359]P20(x33591,x33592,f195(f886(f876(x33591),a871))) % 169.19/169.64 [3361]E(f334(f313(x33611,x33611,f7(x33611)),x33612),x33612) % 169.19/169.64 [3362]E(f334(f313(x33621,x33621,f35(x33621)),x33622),x33622) % 169.19/169.64 [3363]E(f334(f314(x33631,x33631,f7(x33631)),x33632),x33632) % 169.19/169.64 [3364]E(f334(f314(x33641,x33641,f35(x33641)),x33642),x33642) % 169.19/169.64 [3365]P104(f334(f257(f886(x33651,a871)),x33652)) % 169.19/169.64 [3367]E(f334(f39(a877),f334(f304(a877,x33671),x33672)),f334(f334(f3(a877),x33672),x33671)) % 169.19/169.64 [3368]E(f334(f304(a877,f334(a115,x33681)),x33682),f308(a877,x33681,x33682)) % 169.19/169.64 [3381]E(f334(f334(f312(x33811),x33812),f195(f886(x33811,a871))),f334(f254(x33811),f334(a331,x33812))) % 169.19/169.64 [3385]E(f334(f334(f312(x33851),x33852),f195(f886(x33851,a871))),f240(x33851,f334(f241(x33851),x33852))) % 169.19/169.64 [3388]E(f310(x33881,f334(f289(x33881,x33881),x33882)),f334(f289(x33881,x33881),f310(x33881,x33882))) % 169.19/169.64 [3392]E(f334(f334(f81(a877),f334(a115,x33921)),x33922),f334(f334(f81(a877),x33921),f334(a115,x33922))) % 169.19/169.64 [3393]E(f334(f334(f3(a877),f334(a115,x33931)),f334(a115,x33932)),f334(f334(f3(a877),x33931),x33932)) % 169.19/169.64 [3399]E(f56(x33991,f2(a877),x33992),f334(f334(f151(f878(x33991)),f116(x33991)),f116(f878(x33991)))) % 169.19/169.64 [3400]E(f334(f39(a877),f307(a877,x34001,x34002)),f334(f334(f3(a877),x34002),x34001)) % 169.19/169.64 [3409]P39(x34091,f334(f334(f290(a877,x34091),a253),x34092)) % 169.19/169.64 [3411]P30(a877,f139(a877,f334(f304(a877,x34111),x34112))) % 169.19/169.64 [3413]P104(f334(f63(a877),f334(f304(a877,x34131),x34132))) % 169.19/169.64 [3414]P104(f334(f63(a1),f334(f304(a1,x34141),x34142))) % 169.19/169.64 [3417]E(f334(f289(f878(x34171),f878(x34171)),f157(x34171,x34172)),f157(x34171,f334(f289(x34171,x34171),x34172))) % 169.19/169.64 [3418]E(f334(f196(a873),f33(x34181,x34182)),f334(f334(f81(a877),f334(f196(a873),x34182)),f334(a115,f2(a877)))) % 169.19/169.64 [3420]E(f334(f304(a1,x34201),f334(f334(f81(a1),x34202),f79(a1))),f305(a1,x34201,x34202)) % 169.19/169.64 [3423]E(f334(f334(f40(a1),f334(f80(a1),x34231)),f334(f80(a1),x34232)),f334(f334(f40(a1),x34231),x34232)) % 169.19/169.64 [3431]E(f185(x34311,x34312,f334(f18(f881(x34312),x34311),f198(x34312))),f195(f886(x34311,a871))) % 169.19/169.64 [3432]E(f187(x34321,x34322,f334(f18(f881(x34322),x34321),f198(x34322))),f195(f886(x34322,a871))) % 169.19/169.64 [3433]E(f334(f334(f190(f885(x34331,x34331),a871),f79(a877)),x34332),x34332) % 169.19/169.64 [3435]E(f334(f334(f3(f886(x34351,a871)),x34352),f195(f886(x34351,a871))),x34352) % 169.19/169.64 [3436]E(f334(f334(f113(f886(x34361,a871)),x34362),f195(f886(x34361,a871))),x34362) % 169.19/169.64 [3437]E(f334(f334(f104(f886(x34371,a871)),x34372),f257(f886(x34371,a871))),x34372) % 169.19/169.64 [3438]E(f334(f268(a877,a877),f86(f885(a877,a877),f49(x34381,x34382))),f334(f334(f40(a877),x34381),x34382)) % 169.19/169.64 [3445]E(f316(x34451,f334(a22,x34452),f334(f80(a1),f334(a22,x34452))),f334(f334(f319(a1),x34451),x34452)) % 169.19/169.64 [3446]E(f305(a1,f334(f334(f81(a1),x34461),f79(a1)),x34462),f307(a1,x34461,x34462)) % 169.19/169.64 [3451]E(f334(f272(a877,a877),f86(f885(a877,a877),f49(x34511,x34512))),f46(a877,x34511,x34512)) % 169.19/169.64 [3459]E(f317(x34591,f334(a22,x34592),f334(f80(a1),f334(a22,x34592))),f318(a1,x34591,x34592)) % 169.19/169.64 [3462]P104(f334(f334(f336(x34621),x34622),f257(f886(x34621,a871)))) % 169.19/169.64 [3467]E(f334(f334(f3(a877),f334(a115,x34671)),x34672),f334(f39(a877),f305(a877,x34672,x34671))) % 169.19/169.64 [3494]E(f334(f334(f3(f886(x34941,a871)),x34942),f257(f886(x34941,a871))),f195(f886(x34941,a871))) % 169.19/169.64 [3495]E(f334(f334(f113(f886(x34951,a871)),x34952),f257(f886(x34951,a871))),f257(f886(x34951,a871))) % 169.19/169.64 [3496]E(f334(f334(f104(f886(x34961,a871)),x34962),f195(f886(x34961,a871))),f195(f886(x34961,a871))) % 169.19/169.64 [3512]E(f46(a1,f334(f80(a1),x35121),f334(f80(a1),x35122)),f334(f80(a1),f46(a1,x35121,x35122))) % 169.19/169.64 [3513]E(f46(a1,f334(f103(a1),x35131),f334(f103(a1),x35132)),f334(f103(a1),f46(a877,x35131,x35132))) % 169.19/169.64 [3524]E(f334(f196(f878(x35241)),f334(f172(x35241),x35242)),f334(f334(f3(a877),f334(f196(f878(x35241)),x35242)),f79(a877))) % 169.19/169.64 [3549]E(f334(f334(f40(a1),f46(a1,x35491,x35492)),x35492),f2(a1)) % 169.19/169.64 [3559]E(f334(a5,f46(a877,f334(a21,x35591),f334(a21,x35592))),f46(a102,x35591,x35592)) % 169.19/169.64 [3594]E(f334(a5,f334(f334(f3(a877),f334(a21,x35941)),f334(a21,x35942))),f334(f334(f3(a102),x35941),x35942)) % 169.19/169.64 [3595]E(f334(a5,f334(f334(f82(a877),f334(a21,x35951)),f334(a21,x35952))),f334(f334(f82(a102),x35951),x35952)) % 169.19/169.64 [3596]E(f334(a5,f334(f334(f81(a877),f334(a21,x35961)),f334(a21,x35962))),f334(f334(f81(a102),x35961),x35962)) % 169.19/169.64 [3597]E(f334(a5,f334(f334(f40(a877),f334(a21,x35971)),f334(a21,x35972))),f334(f334(f40(a102),x35971),x35972)) % 169.19/169.64 [3606]E(f334(f313(a877,a877,a115),f334(f304(a877,x36061),x36062)),f334(f304(a877,f334(a115,x36061)),f334(a115,x36062))) % 169.19/169.64 [3632]P104(f334(f49(x36321,x36322),f86(f885(a877,a877),f49(x36321,x36322)))) % 169.19/169.64 [3652]E(f334(f334(f81(a877),f334(f334(f81(a877),f32(x36521)),f32(x36522))),f334(a115,f2(a877))),f32(f34(x36521,x36522))) % 169.19/169.64 [3653]E(f46(a877,f334(a115,f46(a877,x36531,x36532)),x36532),f46(a877,f334(a115,x36531),x36532)) % 169.19/169.64 [3667]E(f334(f334(f44(f886(x36671,a871),f886(x36671,a871)),x36672),f7(f886(x36671,a871))),f41(f886(x36671,a871),x36672)) % 169.19/169.64 [3668]E(f334(f334(f43(f886(x36681,a871),f886(x36681,a871)),x36682),f7(f886(x36681,a871))),f42(f886(x36681,a871),x36682)) % 169.19/169.64 [3669]E(f334(f313(f878(x36691),f886(x36691,a871),f173(x36691)),f334(f173(f878(x36691)),f55(x36691,x36692))),f334(f311(x36691),f334(f173(x36691),x36692))) % 169.19/169.64 [3673]P104(f334(f334(f336(f886(x36731,a871)),x36732),f334(f311(x36731),x36732))) % 169.19/169.64 [3679]E(f46(a1,f334(f80(a1),f46(a1,x36791,x36792)),x36792),f46(a1,f334(f80(a1),x36791),x36792)) % 169.19/169.64 [3691]P104(f334(f334(f249(f886(x36911,a871)),x36912),f257(f886(x36911,a871)))) % 169.19/169.64 [3693]E(f334(f334(f291(x36931,x36931,x36931),f310(x36931,x36932)),f310(x36931,f310(x36931,x36932))),f310(x36931,x36932)) % 169.19/169.64 [3694]E(f334(f334(f113(f886(x36941,a871)),f334(f267(x36941,x36941),x36942)),f334(f265(x36941,x36941),x36942)),f334(f287(x36941),x36942)) % 169.19/169.64 [3715]E(f321(x37151,x37152,f257(f886(x37151,a871)),f257(f886(x37152,a871))),f257(f886(f884(x37151,x37152),a871))) % 169.19/169.64 [3767]P104(f334(f334(f249(a877),f46(a877,x37671,x37672)),x37671)) % 169.19/169.64 [3792]P104(f334(f334(f249(a1),f334(f80(a1),f334(f103(a1),x37921))),f334(f103(a1),x37922))) % 169.19/169.64 [3819]P104(f334(f334(f336(f886(x38191,a871)),f195(f886(x38191,a871))),f334(f311(x38191),x38192))) % 169.19/169.64 [3824]E(f310(x38241,f334(f334(f291(x38241,x38241,x38241),x38242),f310(x38241,x38242))),f310(x38241,x38242)) % 169.19/169.64 [3827]E(f334(f334(f291(x38271,x38271,x38271),f310(x38271,x38272)),x38272),f334(f334(f291(x38271,x38271,x38271),x38272),f310(x38271,x38272))) % 169.19/169.64 [3829]E(f334(a107,f334(f334(f81(a1),f334(f334(f3(a1),x38291),x38292)),f79(a1))),f334(f39(a1),f305(a1,x38292,x38291))) % 169.19/169.64 [3844]E(f334(f265(x38441,x38441),f334(f334(f291(x38441,x38441,x38441),x38442),f310(x38441,x38442))),f334(f265(x38441,x38441),x38442)) % 169.19/169.64 [3845]E(f334(f267(x38451,x38451),f334(f334(f291(x38451,x38451,x38451),x38452),f310(x38451,x38452))),f334(f267(x38451,x38451),x38452)) % 169.19/169.64 [3861]E(f334(f334(f81(a877),f334(f334(f81(a877),f334(f196(a873),x38611)),f334(f196(a873),x38612))),f334(a115,f2(a877))),f334(f196(a873),f34(x38611,x38612))) % 169.19/169.64 [3864]E(f334(f142(f878(x38641),f878(x38641),f134(x38641),f116(x38641)),f170(f878(x38641),x38642,f116(x38641))),f116(x38641)) % 169.19/169.64 [3873]P21(a877,a877,f334(f334(f9(a877,a877,a877),f81(a877)),x38731),x38732) % 169.19/169.64 [3875]P30(a877,f334(f169(a877),f334(f334(f154(f878(x38751),a877),f196(f878(x38751))),f181(x38751,x38752)))) % 169.19/169.64 [3922]P104(f334(f334(f250(a1),f334(f80(a1),f334(f103(a1),f334(a115,x39221)))),f334(f103(a1),x39222))) % 169.19/169.64 [3968]E(f334(f142(f878(x39681),x39681,f334(f9(x39681,f878(x39681),f878(x39681)),f151(x39681)),f116(x39681)),x39682),f334(f169(x39681),x39682)) % 169.19/169.64 [4020]P104(f334(f334(f249(f886(f885(f878(x40201),f878(x40201)),a871)),f158(x40201,x40202)),f310(f878(x40201),f157(x40201,x40202)))) % 169.19/169.64 [4052]P104(f334(f49(x40521,x40522),f334(f334(f269(a877,a877),f334(f334(f40(a877),x40521),x40522)),f46(a877,x40521,x40522)))) % 169.19/169.64 [4063]P104(f334(f334(f249(f886(f885(f878(x40631),f878(x40631)),a871)),f157(x40631,f310(x40631,x40632))),f310(f878(x40631),f157(x40631,x40632)))) % 169.19/169.64 [4291]E(f334(f334(f275(f885(a102,a102),a102,f885(a102,a102),f885(x42911,f885(a102,a102))),f279(f334(f166(a102),f334(f334(f154(f885(a102,x42911),a102),f268(a102,x42911)),x42912)))),f334(f334(f10(x42911,f886(f885(a102,a102),f885(x42911,f885(a102,a102))),a102),f269(x42911,f885(a102,a102))),f280(x42911,x42912))),f278(x42911,x42912)) % 169.19/169.64 [4402]E(f334(f243(a877,f885(x44021,f879(x44021)),f2(a877),f334(f273(x44021,f879(x44021),a877),f334(f18(f886(f879(x44021),a877),x44021),f334(f334(f9(f879(x44021),a877,a877),f334(f334(f10(a877,f886(a877,a877),f879(x44021)),f81(a877)),f196(f879(x44021)))),f79(a877))))),f334(f135(x44021),x44022)),f334(f196(f879(x44021)),x44022)) % 169.19/169.64 [4477]E(f334(f273(f886(f885(x44771,x44771),a871),f886(f885(x44771,x44771),a871),f886(f886(x44772,x44771),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871)))),f334(f334(f9(f886(f885(x44771,x44771),a871),f886(f886(f885(x44771,x44771),a871),f886(f886(x44772,x44771),f886(f885(x44772,x44772),a871))),f886(f886(f885(x44771,x44771),a871),f886(f886(x44772,x44771),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871))))),f334(f334(f10(f886(f886(f886(x44772,x44771),f886(f885(x44772,x44772),a871)),f886(f886(x44772,x44771),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871)))),f886(f886(f886(f885(x44771,x44771),a871),f886(f886(x44772,x44771),f886(f885(x44772,x44772),a871))),f886(f886(f885(x44771,x44771),a871),f886(f886(x44772,x44771),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871))))),f886(f885(x44771,x44771),a871)),f10(f886(f886(x44772,x44771),f886(f885(x44772,x44772),a871)),f886(f886(x44772,x44771),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871))),f886(f885(x44771,x44771),a871))),f334(f334(f10(f886(f886(x44772,x44771),f886(f886(f885(x44772,x44772),a871),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871)))),f886(f886(f886(x44772,x44771),f886(f885(x44772,x44772),a871)),f886(f886(x44772,x44771),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871)))),f886(f885(x44771,x44771),a871)),f20(f886(x44772,x44771),f886(f885(x44772,x44772),a871),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871)))),f334(f334(f10(f886(f886(x44772,x44771),f886(f885(x44772,x44772),a871)),f886(f886(x44772,x44771),f886(f886(f885(x44772,x44772),a871),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871)))),f886(f885(x44771,x44771),a871)),f334(f10(f886(f885(x44772,x44772),a871),f886(f886(f885(x44772,x44772),a871),f885(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871))),f886(x44772,x44771)),f269(f886(f885(x44772,x44772),a871),f886(f885(x44772,x44772),a871)))),f290(x44771,x44772))))),f290(x44771,x44772))),f75(x44771,x44772)) % 169.19/169.64 [4562]~E(f334(f311(x45621),x45622),f195(f886(f886(x45621,a871),a871))) % 169.19/169.64 [4580]~P104(f334(f334(f336(x45801),x45802),f195(f886(x45801,a871)))) % 169.19/169.64 [4591]~P104(f334(f334(f250(f886(x45911,a871)),x45912),f195(f886(x45911,a871)))) % 169.19/169.64 [3370]E(f334(f334(f3(a877),x33701),f334(f334(f81(a877),x33701),x33702)),f2(a877)) % 169.19/169.64 [3373]E(f334(f334(f113(f886(x33731,a871)),x33732),x33732),x33732) % 169.19/169.64 [3374]E(f334(f334(f104(f886(x33741,a871)),x33742),x33742),x33742) % 169.19/169.64 [3402]E(f334(f334(f3(f886(x34021,a871)),x34022),x34022),f195(f886(x34021,a871))) % 169.19/169.64 [3405]E(f334(f143(x34051,x34052),f2(a877)),f195(f886(f885(f878(x34051),f878(x34051)),a871))) % 169.19/169.64 [3406]E(f334(f334(f81(a877),x34061),f334(a115,x34062)),f334(a115,f334(f334(f81(a877),x34061),x34062))) % 169.19/169.64 [3419]E(f202(f334(f103(a1),x34191),f334(f103(a1),x34192)),f334(f103(a1),f334(f334(f3(a877),x34191),x34192))) % 169.19/169.64 [3422]E(f334(f334(f40(a1),f334(f80(a1),x34221)),x34222),f334(f334(f40(a1),x34221),f334(f80(a1),x34222))) % 169.19/169.64 [3426]E(f334(f39(a1),f334(f304(a1,x34261),x34262)),f334(a107,f334(f334(f3(a1),x34262),x34261))) % 169.19/169.64 [3429]E(f334(f334(f81(a877),f334(a115,x34291)),x34292),f334(a115,f334(f334(f81(a877),x34291),x34292))) % 169.19/169.64 [3434]E(f334(f80(f886(x34341,a871)),f334(f80(f886(x34341,a871)),x34342)),x34342) % 169.19/169.64 [3448]E(f181(x34481,f334(f334(f151(f878(x34481)),f116(x34481)),x34482)),f181(x34481,x34482)) % 169.19/169.64 [3452]E(f334(f334(f81(a877),x34521),f334(f334(f82(a877),x34521),x34522)),f334(f334(f82(a877),x34521),f334(a115,x34522))) % 169.19/169.64 [3460]E(f334(f334(a4,f334(a5,x34601)),f334(a5,x34602)),f334(a5,f334(f334(f3(a877),x34601),x34602))) % 169.19/169.64 [3474]E(f334(f334(f82(a1),f334(f80(a1),x34741)),x34742),f334(f80(a1),f334(f334(f82(a1),x34741),x34742))) % 169.19/169.64 [3476]E(f334(f334(f259(a1),f334(f103(a1),x34761)),x34762),f334(f103(a1),f334(f334(f259(a877),x34761),x34762))) % 169.19/169.64 [3477]E(f334(f334(f82(a102),f334(a5,x34771)),f334(a5,x34772)),f334(a5,f334(f334(f82(a877),x34771),x34772))) % 169.19/169.64 [3478]E(f334(f334(f81(a102),f334(a5,x34781)),f334(a5,x34782)),f334(a5,f334(f334(f81(a877),x34781),x34782))) % 169.19/169.64 [3479]E(f334(f334(f247(a877),f334(a115,x34791)),f334(a115,x34792)),f334(a115,f334(f334(f247(a877),x34791),x34792))) % 169.19/169.64 [3480]E(f334(f334(f248(a877),f334(a115,x34801)),f334(a115,x34802)),f334(a115,f334(f334(f248(a877),x34801),x34802))) % 169.19/169.64 [3486]E(f334(f173(a877),f139(a877,f334(f304(a877,x34861),x34862))),f334(f304(a877,x34861),x34862)) % 169.19/169.64 [3487]E(f315(x34871,f334(f334(f312(x34871),x34872),f195(f886(x34871,a871)))),x34872) % 169.19/169.64 [3492]E(f334(f265(x34921,x34922),f195(f886(f885(x34921,x34922),a871))),f195(f886(x34922,a871))) % 169.19/169.64 [3493]E(f334(f267(x34931,x34932),f195(f886(f885(x34931,x34932),a871))),f195(f886(x34931,a871))) % 169.19/169.64 [3497]E(f334(a107,f334(f334(f3(a1),x34971),x34972)),f334(f39(a1),f307(a1,x34972,x34971))) % 169.19/169.64 [3502]E(f334(f334(f81(a877),x35021),f334(f334(f82(a877),x35022),x35021)),f334(f334(f82(a877),f334(a115,x35022)),x35021)) % 169.19/169.64 [3504]E(f334(f334(f62(x35041),f195(f886(x35041,a871))),x35042),f195(f886(f886(x35041,a871),a871))) % 169.19/169.64 [3514]E(f334(f196(f878(a877)),f139(a877,f334(f304(a877,x35141),x35142))),f334(f334(f3(a877),x35142),x35141)) % 169.19/169.64 [3529]E(f334(f334(f113(f886(x35291,a871)),f195(f886(x35291,a871))),x35292),x35292) % 169.19/169.64 [3530]E(f334(f334(f104(f886(x35301,a871)),f257(f886(x35301,a871))),x35302),x35302) % 169.19/169.64 [3531]E(f334(f334(f81(a1),f334(f80(a1),x35311)),f334(f80(a1),x35312)),f334(f80(a1),f334(f334(f81(a1),x35311),x35312))) % 169.19/169.64 [3535]E(f334(f334(f82(a1),f334(f106(a1),x35351)),f334(f106(a1),x35352)),f334(f106(a1),f334(f334(f82(a1),x35351),x35352))) % 169.19/169.64 [3537]E(f334(f334(f82(a1),f334(f103(a1),x35371)),f334(f103(a1),x35372)),f334(f103(a1),f334(f334(f82(a877),x35371),x35372))) % 169.19/169.64 [3538]E(f334(f334(f81(a1),f334(f106(a1),x35381)),f334(f106(a1),x35382)),f334(f106(a1),f334(f334(f81(a1),x35381),x35382))) % 169.19/169.64 [3540]E(f334(f334(f81(a1),f334(f103(a1),x35401)),f334(f103(a1),x35402)),f334(f103(a1),f334(f334(f81(a877),x35401),x35402))) % 169.19/169.64 [3541]E(f334(f334(f40(a1),f334(f103(a1),x35411)),f334(f103(a1),x35412)),f334(f103(a1),f334(f334(f40(a877),x35411),x35412))) % 169.19/169.64 [3560]E(f334(f334(f8(x35601,a877),f334(f18(a877,x35601),f79(a877))),x35602),f334(f39(x35601),x35602)) % 169.19/169.64 [3567]E(f334(f80(a1),f46(a1,f334(f80(a1),x35671),x35672)),f46(a1,x35671,f334(f80(a1),x35672))) % 169.19/169.64 [3569]E(f334(f173(a1),f180(x35691,f334(f334(f3(a1),x35692),f79(a1)))),f334(f304(a1,x35691),x35692)) % 169.19/169.64 [3574]P104(f334(f334(f249(a877),x35741),f334(f334(f81(a877),x35742),x35741))) % 169.19/169.64 [3575]P104(f334(f334(f249(a877),x35751),f334(f334(f81(a877),x35751),x35752))) % 169.19/169.64 [3577]E(f334(f334(f3(f886(x35771,a871)),f195(f886(x35771,a871))),x35772),f195(f886(x35771,a871))) % 169.19/169.64 [3578]E(f334(f334(f113(f886(x35781,a871)),f257(f886(x35781,a871))),x35782),f257(f886(x35781,a871))) % 169.19/169.64 [3579]E(f334(f334(f104(f886(x35791,a871)),f195(f886(x35791,a871))),x35792),f195(f886(x35791,a871))) % 169.19/169.64 [3586]E(f334(f334(f269(a1,a1),x35861),f334(f80(a1),x35862)),f334(a52,f334(f334(f269(a1,a1),x35861),x35862))) % 169.19/169.64 [3587]E(f334(f304(a1,f334(f334(f81(a1),x35871),f79(a1))),x35872),f308(a1,x35871,x35872)) % 169.19/169.64 [3598]E(f334(f334(f82(a877),x35981),f334(f334(f40(a877),x35982),x35981)),f334(f334(f3(a877),x35982),f46(a877,x35982,x35981))) % 169.19/169.64 [3599]E(f334(f334(f82(a1),x35991),f334(f334(f40(a1),x35992),x35991)),f334(f334(f3(a1),x35992),f46(a1,x35992,x35991))) % 169.19/169.64 [3603]E(f334(f173(a1),f180(f334(f334(f81(a1),x36031),f79(a1)),x36032)),f307(a1,x36031,x36032)) % 169.19/169.64 [3607]P104(f334(f334(f249(f886(x36071,a871)),x36072),x36072)) % 169.19/169.64 [3610]E(f334(f334(f113(f886(x36101,a871)),x36102),f334(f80(f886(x36101,a871)),x36102)),f257(f886(x36101,a871))) % 169.19/169.64 [3611]E(f334(f334(f104(f886(x36111,a871)),x36112),f334(f80(f886(x36111,a871)),x36112)),f195(f886(x36111,a871))) % 169.19/169.64 [3619]E(f334(f334(f3(a877),f334(f334(f3(a877),x36191),f79(a877))),x36192),f334(f334(f3(a877),x36191),f334(a115,x36192))) % 169.19/169.64 [3624]E(f334(f334(f3(f886(x36241,a871)),f257(f886(x36241,a871))),x36242),f334(f80(f886(x36241,a871)),x36242)) % 169.19/169.64 [3625]E(f334(f334(f3(a1),f334(f106(a1),x36251)),f334(f106(a1),x36252)),f334(f106(a1),f334(f334(f81(a1),x36251),f334(f80(a1),x36252)))) % 169.19/169.64 [3638]E(f334(f173(a877),f139(a877,f334(f304(a877,x36381),f334(a115,x36382)))),f305(a877,x36381,x36382)) % 169.19/169.64 [3650]E(f334(f196(f878(f878(x36501))),f55(x36501,x36502)),f334(f334(f259(a877),f334(a115,f334(a115,f2(a877)))),f334(f196(f878(x36501)),x36502))) % 169.19/169.64 [3671]E(f334(f334(f190(f885(x36711,x36711),a871),f2(a877)),x36712),f310(x36711,f195(f886(f885(x36711,x36711),a871)))) % 169.19/169.64 [3675]P104(f334(f137(a877),f139(a877,f334(f304(a877,x36751),x36752)))) % 169.19/169.64 [3692]E(f334(f313(a1,a877,a107),f305(a1,f334(f103(a1),x36921),f334(f103(a1),x36922))),f305(a877,x36921,x36922)) % 169.19/169.64 [3702]E(f192(a877,f2(a877),f7(a877),f334(f334(f3(a877),x37021),x37022)),f334(f334(f3(a877),x37021),f334(a115,x37022))) % 169.19/169.64 [3703]E(f334(a107,f334(f334(f3(a1),x37031),f334(f334(f81(a1),x37032),f79(a1)))),f334(f39(a1),f308(a1,x37032,x37031))) % 169.19/169.64 [3739]E(f334(f334(f154(a877,a877),a115),f139(a877,f334(f304(a877,x37391),x37392))),f139(a877,f334(f304(a877,f334(a115,x37391)),f334(a115,x37392)))) % 169.19/169.64 [3747]E(f334(f173(a1),f180(f334(f334(f81(a1),x37471),f79(a1)),f334(f334(f3(a1),x37472),f79(a1)))),f308(a1,x37471,x37472)) % 169.19/169.64 [3758]P104(f334(f334(f249(f886(x37581,a871)),f195(f886(x37581,a871))),x37582)) % 169.19/169.64 [3763]E(f91(x37631,f334(f334(f9(x37631,x37631,a871),a331),x37632)),x37632) % 169.19/169.64 [3764]E(f86(x37641,f334(f334(f9(x37641,x37641,a871),a331),x37642)),x37642) % 169.19/169.64 [3768]E(f334(f173(a877),f139(a877,f334(f304(a877,f334(a115,x37681)),f334(a115,x37682)))),f307(a877,x37681,x37682)) % 169.19/169.64 [3795]E(f334(f334(f271(x37951,x37952),f257(f886(x37951,a871))),f334(f18(f886(x37952,a871),x37951),f257(f886(x37952,a871)))),f257(f886(f885(x37951,x37952),a871))) % 169.19/169.64 [3831]E(f334(f254(x38311),f334(f334(f10(a871,a871,x38311),a329),x38312)),f334(f80(f886(x38311,a871)),f334(f254(x38311),x38312))) % 169.19/169.64 [3834]E(f334(f254(x38341),f334(f334(f9(x38341,x38341,a871),a331),x38342)),f334(f334(f312(x38341),x38342),f195(f886(x38341,a871)))) % 169.19/169.64 [3841]E(f334(f334(f81(a1),f334(f334(f3(a1),x38411),x38412)),f334(f334(f3(a1),x38411),x38412)),f334(f334(f3(a1),f334(f334(f81(a1),x38411),x38411)),f334(f334(f81(a1),x38412),x38412))) % 169.19/169.64 [3842]E(f334(f334(f81(a1),f334(f334(f81(a1),x38421),x38421)),f334(f334(f81(a1),x38422),x38422)),f334(f334(f81(a1),f334(f334(f81(a1),x38421),x38422)),f334(f334(f81(a1),x38421),x38422))) % 169.19/169.64 [3858]P104(f334(f334(f249(a877),f334(f39(x38581),f334(f173(x38581),x38582))),f334(f196(f878(x38581)),x38582))) % 169.19/169.64 [3859]P104(f334(f334(f249(a877),f334(f196(f878(x38591)),f152(x38591,x38592))),f334(f196(f878(x38591)),x38592))) % 169.19/169.64 [3870]E(f334(f254(x38701),f334(f334(f9(x38701,f886(x38701,a871),a871),f336(x38701)),x38702)),x38702) % 169.19/169.64 [3886]E(f334(f334(f176(x38861),f334(f334(f3(a877),f334(f196(f878(x38861)),x38862)),f79(a877))),x38862),f117(x38861,x38862)) % 169.19/169.64 [3909]E(f192(a877,f2(a877),f334(f334(f10(a877,a877,a877),a115),f334(f247(a877),x39091)),x39092),f334(f334(f247(a877),f334(a115,x39091)),x39092)) % 169.19/169.64 [3913]E(f41(f886(x39131,a871),f334(f313(f886(f885(x39131,x39131),a871),f886(x39131,a871),f287(x39131)),x39132)),f334(f287(x39131),f41(f886(f885(x39131,x39131),a871),x39132))) % 169.19/169.64 [3914]E(f192(a877,f334(a115,x39141),f334(f334(f10(a877,a877,a877),a115),f334(f248(a877),x39141)),x39142),f334(f334(f248(a877),f334(a115,x39141)),x39142)) % 169.19/169.64 [3916]E(f334(f334(f269(a1,a1),f334(f334(f40(a1),f334(f76(a1),x39161)),f334(f76(a1),x39162))),f46(a1,f334(f76(a1),x39161),f334(f76(a1),x39162))),f54(x39161,x39162)) % 169.19/169.64 [3939]P104(f334(f334(f249(f886(f886(x39391,a871),a871)),x39392),f334(f311(x39391),f41(f886(x39391,a871),x39392)))) % 169.19/169.64 [3973]E(f334(f334(f44(x39731,f886(x39731,a871)),x39732),f334(f334(f9(x39731,f886(x39731,a871),f886(x39731,a871)),f312(x39731)),f195(f886(x39731,a871)))),x39732) % 169.19/169.64 [3974]E(f334(f334(f291(x39741,x39741,x39741),f334(f289(x39741,x39741),x39742)),f310(x39741,f334(f289(x39741,x39741),x39742))),f334(f289(x39741,x39741),f334(f334(f291(x39741,x39741,x39741),x39742),f310(x39741,x39742)))) % 169.19/169.64 [4043]E(f334(f173(x40431),f334(f142(f878(x40431),f878(x40431),f134(x40431),f116(x40431)),x40432)),f334(f334(f44(f878(x40431),f886(x40431,a871)),f334(f173(f878(x40431)),x40432)),f173(x40431))) % 169.19/169.64 [4075]E(f334(f334(f113(f886(f885(x40751,x40751),a871)),f310(x40751,f195(f886(f885(x40751,x40751),a871)))),f334(f334(f291(x40751,x40751,x40751),f310(x40751,x40752)),x40752)),f310(x40751,x40752)) % 169.19/169.64 [4111]E(f334(f334(f183(x41111,x41111),x41112),x41112),f334(f334(f154(x41111,f885(x41111,x41111)),f334(f334(f20(x41111,x41111,f885(x41111,x41111)),f269(x41111,x41111)),f7(x41111))),x41112)) % 169.19/169.64 [4228]E(f334(f142(a877,f878(x42281),f334(f9(f878(x42281),a877,a877),f334(f334(f10(a877,f886(a877,a877),f878(x42281)),f248(a877)),f196(f878(x42281)))),f2(a877)),f334(f169(f878(x42281)),x42282)),f334(f196(f878(f878(x42281))),f181(x42281,x42282))) % 169.19/169.64 [4306]E(f334(f334(f290(f885(a877,f878(x43061)),f878(x43061)),f327(a877,f878(x43061),a253,f145(x43061,x43062))),f334(f334(f20(f878(x43061),f878(x43061),f885(a877,f878(x43061))),f334(f334(f10(a877,f886(f878(x43061),f885(a877,f878(x43061))),f878(x43061)),f269(a877,f878(x43061))),f196(f878(x43061)))),f7(f878(x43061)))),f146(x43061,x43062)) % 169.19/169.64 [4436]E(f334(f254(x44361),f334(f334(f10(f886(f886(x44361,a871),a871),a871,x44361),f89(f886(x44361,a871))),f334(f334(f10(f886(f886(x44361,a871),a871),f886(f886(x44361,a871),a871),x44361),f334(f20(f886(x44361,a871),a871,a871),f334(f334(f10(a871,f886(a871,a871),f886(x44361,a871)),a337),f334(f334(f9(f886(x44361,a871),f886(f886(x44361,a871),a871),a871),f336(f886(x44361,a871))),x44362)))),f336(x44361)))),f42(f886(x44361,a871),x44362)) % 169.19/169.64 [4592]~P104(f334(f334(f250(a1),f334(f103(a1),x45921)),f334(f80(a1),f334(f103(a1),x45922)))) % 169.19/169.64 [4608]~P104(f334(f334(f92(a1),f334(f334(f3(a1),f334(f334(f81(a1),x46081),x46081)),a100)),f334(f334(f81(a1),x46082),x46082))) % 169.19/169.64 [3500]E(f334(f334(f3(a877),f334(f334(f81(a877),x35001),x35002)),x35002),x35001) % 169.19/169.64 [3501]E(f334(f334(f3(a877),f334(f334(f81(a877),x35011),x35012)),x35011),x35012) % 169.19/169.64 [3568]E(f334(f334(f81(a877),f334(f334(f3(a877),x35681),x35682)),x35682),f334(f334(f248(a877),x35681),x35682)) % 169.19/169.64 [3678]E(f334(f334(f82(a877),f334(f334(f40(a877),x36781),x36782)),x36782),f334(f334(f3(a877),x36781),f46(a877,x36781,x36782))) % 169.19/169.64 [3707]E(f334(f173(a877),f139(a877,f334(f304(a877,f334(a115,x37071)),x37072))),f308(a877,x37071,x37072)) % 169.19/169.64 [3714]E(f334(f103(a1),f225(f334(a107,f334(f76(a1),x37141)),f334(a107,f334(f76(a1),x37142)))),f334(f334(a226,x37141),x37142)) % 169.19/169.64 [3716]E(f334(f334(f113(f886(x37161,a871)),f334(f80(f886(x37161,a871)),x37162)),x37162),f257(f886(x37161,a871))) % 169.19/169.64 [3717]E(f334(f334(f104(f886(x37171,a871)),f334(f80(f886(x37171,a871)),x37172)),x37172),f195(f886(x37171,a871))) % 169.19/169.64 [3735]P104(f334(f334(f249(a877),f334(f334(f3(a877),x37351),x37352)),x37351)) % 169.19/169.64 [3736]P104(f334(f334(f249(a877),f334(f334(f40(a877),x37361),x37362)),x37361)) % 169.19/169.64 [3760]P104(f334(f334(f250(a877),x37601),f334(a115,f334(f334(f81(a877),x37602),x37601)))) % 169.19/169.64 [3761]P104(f334(f334(f250(a877),x37611),f334(a115,f334(f334(f81(a877),x37611),x37612)))) % 169.19/169.64 [3779]E(f334(f334(f82(a877),f334(a107,f334(f76(a1),x37791))),f334(a107,f334(f76(a1),x37792))),f334(a107,f334(f76(a1),f334(f334(f82(a1),x37791),x37792)))) % 169.19/169.64 [3791]P104(f334(f334(f249(a1),f2(a1)),f334(f334(f259(a1),f334(f76(a1),x37911)),x37912))) % 169.19/169.64 [3863]E(f334(f288(f878(x38631),f878(x38631),f158(x38631,x38632)),f334(f334(f312(f878(x38631)),f116(x38631)),f195(f886(f878(x38631),a871)))),f334(f334(f312(f878(x38631)),f116(x38631)),f195(f886(f878(x38631),a871)))) % 169.19/169.64 [3884]E(f334(f334(f113(f886(f885(x38841,x38841),a871)),f310(x38841,x38842)),f310(x38841,f195(f886(f885(x38841,x38841),a871)))),f310(x38841,x38842)) % 169.19/169.64 [3899]E(f334(f334(f40(a1),f334(f106(a1),f334(f334(f81(a1),x38991),x38991))),f334(f106(a1),f334(f334(f81(a1),x38992),x38992))),f334(f334(f40(a1),f334(f106(a1),x38991)),f334(f106(a1),x38992))) % 169.19/169.64 [3963]E(f334(f334(f259(a1),x39631),f334(f106(a877),f334(f334(f81(a1),x39632),x39632))),f334(f334(f87(a1,a1),f334(f334(f259(a1),x39631),f334(f106(a877),x39632))),f334(f334(f20(a1,a1,a1),f82(a1)),f7(a1)))) % 169.19/169.64 [3969]E(f334(f254(f886(x39691,a871)),f334(f334(f9(f886(x39691,a871),f886(x39691,a871),a871),f249(f886(x39691,a871))),x39692)),f334(f311(x39691),x39692)) % 169.19/169.64 [3984]E(f334(f334(f154(a1,a877),a107),f334(f334(f134(a1),f334(f334(f154(a877,a1),f103(a1)),x39841)),f334(f334(f154(a877,a1),f103(a1)),x39842))),f334(f334(f134(a877),x39841),x39842)) % 169.19/169.64 [4019]E(f334(f313(a1,a1,f334(f334(f9(a1,a1,a1),f81(a1)),x40191)),f334(f304(a1,f2(a1)),f334(f334(f3(a1),x40192),x40191))),f334(f304(a1,x40191),x40192)) % 169.19/169.64 [4021]P50(x40211,f334(f334(f3(f886(f885(x40211,x40211),a871)),x40212),f310(x40211,f195(f886(f885(x40211,x40211),a871))))) % 169.19/169.64 [4041]E(f334(f196(f878(x40411)),f334(f142(f878(x40411),f878(x40411),f134(x40411),f116(x40411)),x40412)),f334(f166(a877),f334(f334(f154(f878(x40411),a877),f196(f878(x40411))),x40412))) % 169.19/169.64 [4046]P49(x40461,f257(f886(x40461,a871)),f334(f334(f113(f886(f885(x40461,x40461),a871)),x40462),f310(x40461,f195(f886(f885(x40461,x40461),a871))))) % 169.19/169.64 [4091]E(f192(a877,f2(a877),f334(f334(f10(a877,a877,a877),a115),f334(f334(f9(a877,a877,a877),f247(a877)),x40911)),x40912),f334(f334(f247(a877),x40912),f334(a115,x40911))) % 169.19/169.64 [4094]E(f192(a877,f334(a115,x40941),f334(f334(f10(a877,a877,a877),a115),f334(f334(f9(a877,a877,a877),f248(a877)),x40941)),x40942),f334(f334(f248(a877),x40942),f334(a115,x40941))) % 169.19/169.64 [4097]E(f334(f313(x40971,f878(x40971),f334(f334(f9(x40971,f878(x40971),f878(x40971)),f151(x40971)),f116(x40971))),x40972),f175(x40971,x40972,f334(f334(f312(f878(x40971)),f116(x40971)),f195(f886(f878(x40971),a871))))) % 169.19/169.64 [4098]E(f334(f334(f113(f886(f885(x40981,x40981),a871)),f334(f334(f291(x40981,x40981,x40981),x40982),f310(x40981,x40982))),f310(x40981,f195(f886(f885(x40981,x40981),a871)))),f310(x40981,x40982)) % 169.19/169.64 [4106]P104(f334(f334(f249(f886(f885(x41061,x41061),a871)),f266(x41061,x41062)),f334(f334(f271(x41061,x41061),x41062),f334(f18(f886(x41061,a871),x41061),x41062)))) % 169.19/169.64 [4109]E(f334(f313(a1,a877,a107),f334(f334(f113(f886(a1,a871)),f334(f313(a877,a1,f103(a1)),x41091)),f334(f313(a877,a1,f103(a1)),x41092))),f334(f334(f113(f886(a877,a871)),x41091),x41092)) % 169.19/169.64 [4110]E(f334(f313(a1,a877,a107),f334(f334(f104(f886(a1,a871)),f334(f313(a877,a1,f103(a1)),x41101)),f334(f313(a877,a1,f103(a1)),x41102))),f334(f334(f104(f886(a877,a871)),x41101),x41102)) % 169.19/169.64 [4114]E(f334(f254(x41141),f334(f334(f10(a871,a871,x41141),a329),f334(f334(f9(x41141,f886(x41141,a871),a871),f336(x41141)),x41142))),f334(f80(f886(x41141,a871)),x41142)) % 169.19/169.64 [4141]E(f334(f142(f878(x41411),f878(x41411),f134(x41411),f116(x41411)),f334(f334(f154(f878(x41411),f878(x41411)),f169(x41411)),f334(f169(f878(x41411)),x41412))),f334(f169(x41411),f334(f142(f878(x41411),f878(x41411),f134(x41411),f116(x41411)),x41412))) % 169.19/169.64 [4170]E(f334(f334(f44(a877,f886(f885(x41701,x41701),a871)),f257(f886(a877,a871))),f334(f334(f9(a877,f886(f885(x41701,x41701),a871),f886(f885(x41701,x41701),a871)),f190(f885(x41701,x41701),a871)),x41702)),f310(x41701,x41702)) % 169.19/169.64 [4190]E(f86(x41901,f334(f334(f10(f886(x41901,a871),a871,x41901),f334(a331,x41902)),f334(f334(f9(x41901,f886(x41901,a871),f886(x41901,a871)),f312(x41901)),f195(f886(x41901,a871))))),f315(x41901,x41902)) % 169.19/169.64 [4198]E(f334(f196(f878(x41981)),f152(x41981,f334(f142(f878(x41981),f878(x41981),f134(x41981),f116(x41981)),x41982))),f334(f39(x41981),f334(f334(f44(f878(x41981),f886(x41981,a871)),f334(f173(f878(x41981)),x41982)),f173(x41981)))) % 169.19/169.64 [4214]E(f334(f334(f113(f886(f885(x42141,x42141),a871)),x42142),f334(f334(f291(x42141,x42141,x42141),f334(f334(f291(x42141,x42141,x42141),x42142),f310(x42141,x42142))),x42142)),f334(f334(f291(x42141,x42141,x42141),x42142),f310(x42141,x42142))) % 169.19/169.64 [4238]P104(f334(f334(f249(f886(f885(x42381,x42381),a871)),f334(f334(f291(x42381,x42381,x42381),x42382),f310(x42381,x42382))),f334(f334(f271(x42381,x42381),f334(f287(x42381),x42382)),f334(f18(f886(x42381,a871),x42381),f334(f287(x42381),x42382))))) % 169.19/169.64 [4281]E(f334(f254(f878(x42811)),f334(f334(f9(f878(x42811),f886(x42811,a871),a871),f334(f334(f10(f886(x42811,a871),f886(f886(x42811,a871),a871),f878(x42811)),f249(f886(x42811,a871))),f173(x42811))),x42812)),f161(x42811,x42812)) % 169.19/169.64 [4293]E(f334(f156(f878(x42931),x42931,f116(x42931),f334(f334(f10(f878(x42931),f886(f878(x42931),f878(x42931)),x42931),f334(f9(f878(x42931),f878(x42931),f878(x42931)),f134(x42931))),f334(f334(f9(x42931,f878(x42931),f878(x42931)),f151(x42931)),f116(x42931)))),x42932),f334(f168(x42931),x42932)) % 169.19/169.64 [4335]P21(f886(x43351,x43352),f886(f885(x43351,x43352),a871),f334(f334(f10(f886(f885(x43351,x43352),a871),f886(f885(x43351,x43352),a871),f886(x43351,x43352)),f254(f885(x43351,x43352))),f334(f334(f10(f886(x43351,f886(x43352,a871)),f886(f885(x43351,x43352),a871),f886(x43351,x43352)),f273(x43351,x43352,a871)),f334(f10(x43352,f886(x43352,a871),x43351),f334(f9(x43352,x43352,a871),a331)))),f257(f886(f886(x43351,x43352),a871))) % 169.19/169.64 [4340]E(f46(a1,f334(f106(a1),f334(f334(f81(a1),x43401),x43401)),f334(f106(a1),f334(f334(f81(a1),x43402),x43402))),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f46(a1,f334(f106(a1),x43401),f334(f106(a1),x43402)))) % 169.19/169.64 [4383]E(f334(f334(f44(x43831,f886(f885(x43831,x43831),a871)),x43832),f334(f334(f9(x43831,f886(f885(x43831,x43831),a871),f886(f885(x43831,x43831),a871)),f334(f334(f10(f885(x43831,x43831),f886(f886(f885(x43831,x43831),a871),f886(f885(x43831,x43831),a871)),x43831),f312(f885(x43831,x43831))),f334(f334(f20(x43831,x43831,f885(x43831,x43831)),f269(x43831,x43831)),f7(x43831)))),f195(f886(f885(x43831,x43831),a871)))),f266(x43831,x43832)) % 169.19/169.64 [4391]E(f211(x43911,f334(f334(f269(a1,a1),f334(f80(a1),f334(f334(f74(f885(a1,a1),a1,x43911,f268(a1,a1)),f221(x43911)),x43912))),f334(f334(f74(f885(a1,a1),a1,x43911,f272(a1,a1)),f221(x43911)),x43912))),f235(x43911,x43912)) % 169.19/169.64 [4472]E(f334(f254(f886(x44721,a871)),f334(f334(f10(f886(f886(x44721,a871),a871),a871,f886(x44721,a871)),f88(f886(x44721,a871))),f334(f334(f9(f886(x44721,a871),f886(f886(x44721,a871),a871),f886(f886(x44721,a871),a871)),f334(f334(f10(f886(f886(x44721,a871),f886(a871,a871)),f886(f886(f886(x44721,a871),a871),f886(f886(x44721,a871),a871)),f886(x44721,a871)),f20(f886(x44721,a871),a871,a871)),f334(f334(f10(f886(f886(x44721,a871),a871),f886(f886(x44721,a871),f886(a871,a871)),f886(x44721,a871)),f334(f10(a871,f886(a871,a871),f886(x44721,a871)),a332)),f334(f334(f9(f886(x44721,a871),f886(f886(x44721,a871),f886(x44721,a871)),f886(f886(x44721,a871),a871)),f334(f334(f10(f886(f886(x44721,a871),a871),f886(f886(f886(x44721,a871),f886(x44721,a871)),f886(f886(x44721,a871),a871)),f886(x44721,a871)),f10(f886(x44721,a871),a871,f886(x44721,a871))),a331)),f80(f886(x44721,a871)))))),f334(f334(f10(f886(f886(x44721,a871),a871),a871,f886(x44721,a871)),f334(f336(f886(x44721,a871)),x44722)),f311(x44721))))),f334(f311(x44721),f334(f80(f886(x44721,a871)),x44722))) % 169.19/169.64 [4588]~E(f334(f334(f81(a1),x45881),x45881),f334(f334(f3(a1),f334(f334(f81(a1),x45882),x45882)),a100)) % 169.19/169.64 [4595]~P104(f334(f334(f250(a877),f334(f334(f81(a877),x45951),x45952)),x45952)) % 169.19/169.64 [4596]~P104(f334(f334(f250(a877),f334(f334(f81(a877),x45961),x45962)),x45961)) % 169.19/169.64 [3796]E(f334(f334(f3(a877),x37961),f334(f334(f82(a877),f334(f334(f40(a877),x37961),x37962)),x37962)),f46(a877,x37961,x37962)) % 169.19/169.64 [3797]E(f334(f334(f3(a1),x37971),f334(f334(f82(a1),f334(f334(f40(a1),x37971),x37972)),x37972)),f46(a1,x37971,x37972)) % 169.19/169.64 [3832]E(f334(f334(f154(a877,x38321),f334(f165(x38321),x38322)),f139(a877,f334(f304(a877,f2(a877)),f334(f196(f878(x38321)),x38322)))),x38322) % 169.19/169.64 [3895]E(f334(f288(x38951,x38951,f310(x38951,f195(f886(f885(x38951,x38951),a871)))),x38952),x38952) % 169.19/169.64 [4024]E(f310(x40241,f334(f334(f3(f886(f885(x40241,x40241),a871)),x40242),f310(x40241,f195(f886(f885(x40241,x40241),a871))))),f310(x40241,x40242)) % 169.19/169.64 [4025]E(f310(x40251,f334(f334(f113(f886(f885(x40251,x40251),a871)),x40252),f310(x40251,f195(f886(f885(x40251,x40251),a871))))),f310(x40251,x40252)) % 169.19/169.64 [4078]E(f334(f334(f3(a1),f334(f334(f3(a1),f334(f334(f81(a1),x40781),x40781)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x40782),x40782)),a100)),f334(f334(f81(a1),f334(f334(f3(a1),x40781),x40782)),f334(f334(f3(a1),x40781),x40782))) % 169.19/169.64 [4119]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f81(a1),x41191),x41192)),f334(f334(f81(a1),x41191),x41192))),a100),f334(f334(f81(a1),f334(f334(f81(a1),x41191),x41191)),f334(f334(f3(a1),f334(f334(f81(a1),x41192),x41192)),a100))) % 169.19/169.64 [4145]E(f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),x41451),x41451)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x41452),x41452)),a100)),f334(f334(f81(a1),f334(f334(f81(a1),x41451),f334(f334(f3(a1),x41452),a100))),f334(f334(f81(a1),x41451),f334(f334(f3(a1),x41452),a100)))) % 169.19/169.64 [4156]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),x41561),x41562)),f334(f334(f3(a1),x41561),x41562))),a100),f334(f334(f3(a1),f334(f334(f3(a1),f334(f334(f81(a1),x41561),x41561)),a100)),f334(f334(f81(a1),x41562),x41562))) % 169.19/169.64 [4157]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f81(a1),x41571),x41572)),f334(f334(f81(a1),x41571),x41572))),a100),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),x41571),x41571)),a100)),f334(f334(f81(a1),x41572),x41572))) % 169.19/169.64 [4211]E(f334(f103(a1),f334(f334(f40(a877),f334(f334(f82(a877),f334(a107,f334(f76(a1),x42111))),f334(a107,f334(f76(a1),x42112)))),f225(f334(a107,f334(f76(a1),x42111)),f334(a107,f334(f76(a1),x42112))))),f227(x42111,x42112)) % 169.19/169.64 [4258]E(f334(f334(f275(f885(a102,a102),a102,f885(a102,a102),f885(x42581,f885(a102,a102))),f279(f334(a5,f334(f196(f878(x42581)),x42582)))),f334(f334(f10(x42581,f886(f885(a102,a102),f885(x42581,f885(a102,a102))),a102),f269(x42581,f885(a102,a102))),f334(f334(f10(a877,x42581,a102),f334(f165(x42581),x42582)),a21))),f285(x42581,x42582)) % 169.19/169.64 [4341]E(f334(f142(a877,f878(x43411),f334(f9(f878(x43411),a877,a877),f334(f334(f10(a877,f886(a877,a877),f878(x43411)),f248(a877)),f196(f878(x43411)))),f2(a877)),f334(f169(f878(x43411)),f181(x43411,x43412))),f334(f196(f878(f878(x43411))),f334(f136(f878(x43411),f334(f334(f10(a871,a871,f878(x43411)),a329),f334(f334(f9(f878(x43411),f878(x43411),a871),a331),f116(x43411)))),x43412))) % 169.19/169.64 [4347]E(f334(f334(f44(a877,f886(x43471,a871)),f257(f886(a877,a871))),f334(f334(f9(a877,f886(a877,f886(x43471,a871)),f886(x43471,a871)),f334(f334(f10(f886(a877,a871),f886(f886(a877,f886(x43471,a871)),f886(x43471,a871)),a877),f44(a877,f886(x43471,a871))),f304(a877,f2(a877)))),x43472)),f334(f334(f44(a877,f886(x43471,a871)),f257(f886(a877,a871))),x43472)) % 169.19/169.64 [4367]P104(f334(f63(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),x43671)),f334(f334(f9(a877,a877,a871),f250(a877)),x43672))))) % 169.19/169.64 [4483]E(f334(f254(f885(f878(x44831),f878(x44831))),f334(f273(f878(x44831),f878(x44831),a871),f334(f334(f20(f878(x44831),f886(f878(x44831),a871),f886(f878(x44831),a871)),f334(f334(f10(f886(f878(x44831),f886(a871,a871)),f886(f886(f878(x44831),a871),f886(f878(x44831),a871)),f878(x44831)),f20(f878(x44831),a871,a871)),f334(f334(f10(f886(f878(x44831),a871),f886(f878(x44831),f886(a871,a871)),f878(x44831)),f334(f10(a871,f886(a871,a871),f878(x44831)),a333)),f334(f334(f9(f878(x44831),f886(f878(x44831),a877),f886(f878(x44831),a871)),f334(f334(f10(f886(a877,a871),f886(f886(f878(x44831),a877),f886(f878(x44831),a871)),f878(x44831)),f10(a877,a871,f878(x44831))),f334(f334(f10(a877,f886(a877,a871),f878(x44831)),f250(a877)),f196(f878(x44831))))),f196(f878(x44831)))))),f334(f334(f20(f878(x44831),f886(f878(x44831),a871),f886(f878(x44831),a871)),f334(f334(f10(f886(f878(x44831),f886(a871,a871)),f886(f886(f878(x44831),a871),f886(f878(x44831),a871)),f878(x44831)),f20(f878(x44831),a871,a871)),f334(f334(f10(f886(f878(x44831),a871),f886(f878(x44831),f886(a871,a871)),f878(x44831)),f334(f10(a871,f886(a871,a871),f878(x44831)),a332)),f334(f334(f9(f878(x44831),f886(f878(x44831),a877),f886(f878(x44831),a871)),f334(f334(f10(f886(a877,a871),f886(f886(f878(x44831),a877),f886(f878(x44831),a871)),f878(x44831)),f10(a877,a871,f878(x44831))),f334(f334(f10(a877,f886(a877,a871),f878(x44831)),a331),f196(f878(x44831))))),f196(f878(x44831)))))),f334(f334(f9(f878(x44831),f886(f885(f878(x44831),f878(x44831)),a871),f886(f878(x44831),a871)),f334(f334(f10(f886(f878(x44831),f886(f886(f885(f878(x44831),f878(x44831)),a871),a871)),f886(f886(f885(f878(x44831),f878(x44831)),a871),f886(f878(x44831),a871)),f878(x44831)),f9(f878(x44831),f886(f885(f878(x44831),f878(x44831)),a871),a871)),f334(f334(f10(f886(f878(x44831),f885(f878(x44831),f878(x44831))),f886(f878(x44831),f886(f886(f885(f878(x44831),f878(x44831)),a871),a871)),f878(x44831)),f334(f10(f885(f878(x44831),f878(x44831)),f886(f886(f885(f878(x44831),f878(x44831)),a871),a871),f878(x44831)),f336(f885(f878(x44831),f878(x44831))))),f269(f878(x44831),f878(x44831))))),f145(x44831,x44832)))))),f146(x44831,x44832)) % 169.19/169.64 [4601]~P104(f334(f334(f92(a1),f334(f334(f81(a1),x46011),x46011)),f334(f334(f3(a1),f334(f334(f81(a1),x46012),x46012)),a100))) % 169.19/169.64 [4148]E(f334(f334(f81(a1),f334(f334(f81(a1),f334(f334(f82(a1),x41481),x41482)),f334(f334(f82(a1),x41481),x41482))),x41482),f334(f334(f82(a1),f334(f334(f3(a1),f334(f334(f81(a1),x41481),x41481)),a100)),x41482)) % 169.19/169.64 [4256]E(f334(a107,f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x42561),x42562)),f195(f886(f885(a877,a877),a871)))))),f334(f334(f3(a877),x42561),x42562)) % 169.19/169.64 [4261]E(f334(f334(f291(x42611,x42611,x42611),f334(f334(f113(f886(f885(x42611,x42611),a871)),x42612),f310(x42611,f195(f886(f885(x42611,x42611),a871))))),f310(x42611,f334(f334(f113(f886(f885(x42611,x42611),a871)),x42612),f310(x42611,f195(f886(f885(x42611,x42611),a871)))))),f310(x42611,x42612)) % 169.19/169.64 [4299]E(f278(x42991,f334(f136(f885(a102,x42991),f334(f273(a102,x42991,a871),f334(f334(f10(a871,f886(x42991,a871),a102),f18(a871,x42991)),f334(f250(a102),f2(a102))))),x42992)),f278(x42991,x42992)) % 169.19/169.64 [4300]E(f280(x43001,f334(f136(f885(a102,x43001),f334(f273(a102,x43001,a871),f334(f334(f10(a871,f886(x43001,a871),a102),f18(a871,x43001)),f334(f250(a102),f2(a102))))),x43002)),f280(x43001,x43002)) % 169.19/169.64 [4302]E(f334(f80(a1),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x43021),x43022)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x43022),x43021)),f195(f886(f885(a877,a877),a871)))))) % 169.19/169.64 [4359]E(f334(f334(f290(f878(a877),x43591),f145(a877,a253)),f334(f334(f9(x43591,f878(f886(x43591,a877)),f878(a877)),f334(f334(f10(f886(f886(x43591,a877),a877),f886(f878(f886(x43591,a877)),f878(a877)),x43591),f154(f886(x43591,a877),a877)),f334(f9(f886(x43591,a877),x43591,a877),f7(f886(x43591,a877))))),x43592)),f153(x43591,x43592)) % 169.19/169.64 [4380]E(f334(f334(f87(a1,a877),f334(f106(a1),f334(f334(f81(a1),x43801),a100))),f334(f334(f20(a1,a877,a877),f334(f334(f9(a1,a877,f886(a877,a877)),f334(f334(f10(a871,f886(a877,f886(a877,a877)),a1),f99(a877)),a201)),f2(a877))),f334(f334(f10(a877,a877,a1),a115),f334(f334(f10(a877,a877,a1),f334(f247(a877),x43802)),a107)))),f334(f334(f247(a877),f334(a115,x43802)),f334(f106(a877),x43801))) % 169.19/169.64 [4381]E(f334(f334(f87(a1,a877),f334(f106(a1),f334(f334(f81(a1),x43811),a100))),f334(f334(f20(a1,a877,a877),f334(f334(f9(a1,a877,f886(a877,a877)),f334(f334(f10(a871,f886(a877,f886(a877,a877)),a1),f99(a877)),a201)),f334(a115,x43812))),f334(f334(f10(a877,a877,a1),a115),f334(f334(f10(a877,a877,a1),f334(f248(a877),x43812)),a107)))),f334(f334(f248(a877),f334(a115,x43812)),f334(f106(a877),x43811))) % 169.19/169.64 [4401]E(f334(f142(f878(x44011),f878(x44011),f134(x44011),f116(x44011)),f334(f334(f154(f878(x44011),f878(x44011)),f156(f878(x44011),x44011,f116(x44011),f334(f334(f10(f878(x44011),f886(f878(x44011),f878(x44011)),x44011),f18(f878(x44011),f878(x44011))),f334(f334(f9(x44011,f878(x44011),f878(x44011)),f151(x44011)),f116(x44011))))),x44012)),f334(f334(f154(f878(x44011),x44011),f141(x44011)),f334(f136(f878(x44011),f334(f334(f10(a871,a871,f878(x44011)),a329),f334(f334(f9(f878(x44011),f878(x44011),a871),a331),f116(x44011)))),x44012))) % 169.19/169.64 [4464]E(f334(f273(a1,a1,a871),f334(f334(f9(a1,f886(a1,a871),f886(a1,a871)),f334(f334(f10(f886(a1,f886(a871,a871)),f886(f886(a1,a871),f886(a1,a871)),a1),f20(a1,a871,a871)),f334(f334(f10(f886(a1,a871),f886(a1,f886(a871,a871)),a1),f334(f10(a871,f886(a871,a871),a1),a332)),f334(f334(f10(f886(a1,a1),f886(a1,a871),a1),f334(f10(a1,a871,a1),f334(a331,x44641))),f334(f334(f10(a1,f886(a1,a1),a1),f81(a1)),f334(f82(a1),x44642)))))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),f334(a337,f334(f334(f250(a1),f2(a1)),x44642))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),f334(f334(f9(a1,a1,a871),f250(a1)),x44642))))),f334(f334(f10(a871,a871,a1),f334(a337,f334(a329,f334(f334(f250(a1),f2(a1)),x44642)))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f250(a1),x44642))),f334(f334(f9(a1,a1,a871),f249(a1)),f2(a1))))))),f50(x44641,x44642)) % 169.19/169.64 [4466]E(f334(f254(x44661),f334(f334(f10(f886(a877,a871),a871,x44661),f88(a877)),f334(f334(f9(x44661,f886(a877,a871),f886(a877,a871)),f334(f334(f10(f886(a877,f886(a871,a871)),f886(f886(a877,a871),f886(a877,a871)),x44661),f20(a877,a871,a871)),f334(f334(f10(f886(a877,a871),f886(a877,f886(a871,a871)),x44661),f334(f10(a871,f886(a871,a871),a877),a332)),f334(f334(f9(x44661,f886(a877,x44661),f886(a877,a871)),f334(f334(f10(f886(x44661,a871),f886(f886(a877,x44661),f886(a877,a871)),x44661),f10(x44661,a871,a877)),a331)),f334(f165(x44661),x44662))))),f334(f334(f9(a877,a877,a871),f250(a877)),f334(f196(f878(x44661)),x44662))))),f334(f173(x44661),x44662)) % 169.19/169.64 [4271]E(f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),x42711),a100)),x42712)),f334(f334(f3(a1),f334(f334(f81(a1),x42711),a100)),x42712))),a100),f334(f334(f3(a1),f334(f334(f81(a1),x42711),x42711)),f334(f334(f3(a1),f334(f334(f81(a1),x42712),x42712)),a100))) % 169.19/169.64 [4396]E(f334(f142(f878(f878(x43961)),f878(f878(x43961)),f134(f878(x43961)),f116(f878(x43961))),f334(f334(f154(f878(x43961),f878(f878(x43961))),f156(f878(f878(x43961)),x43961,f116(f878(x43961)),f334(f18(f886(f878(x43961),f878(f878(x43961))),x43961),f334(f334(f9(f878(x43961),f878(f878(x43961)),f878(f878(x43961))),f151(f878(x43961))),f116(f878(x43961)))))),x43962)),f334(f334(f154(f878(x43961),f878(x43961)),f172(x43961)),f334(f136(f878(x43961),f334(f334(f10(a871,a871,f878(x43961)),a329),f334(f334(f9(f878(x43961),f878(x43961),a871),a331),f116(x43961)))),x43962))) % 169.19/169.64 [4407]E(f334(f334(f87(a1,a877),f334(f106(a1),f334(f334(f81(a1),x44071),a100))),f334(f334(f20(a1,a877,a877),f334(f334(f9(a1,a877,f886(a877,a877)),f334(f334(f10(a871,f886(a877,f886(a877,a877)),a1),f99(a877)),a201)),f2(a877))),f334(f334(f10(a877,a877,a1),a115),f334(f334(f9(a1,a877,a877),f334(f334(f10(a877,f886(a877,a877),a1),f247(a877)),a107)),x44072)))),f334(f334(f247(a877),f334(f106(a877),x44071)),f334(a115,x44072))) % 169.19/169.64 [4408]E(f334(f334(f87(a1,a877),f334(f106(a1),f334(f334(f81(a1),x44081),a100))),f334(f334(f20(a1,a877,a877),f334(f334(f9(a1,a877,f886(a877,a877)),f334(f334(f10(a871,f886(a877,f886(a877,a877)),a1),f99(a877)),a201)),f334(a115,x44082))),f334(f334(f10(a877,a877,a1),a115),f334(f334(f9(a1,a877,a877),f334(f334(f10(a877,f886(a877,a877),a1),f248(a877)),a107)),x44082)))),f334(f334(f248(a877),f334(f106(a877),x44081)),f334(a115,x44082))) % 169.19/169.64 [4395]E(f334(f273(x43951,x43951,a871),f334(f334(f20(x43951,a871,f886(x43951,a871)),f334(f334(f10(f886(x43951,f886(a871,a871)),f886(a871,f886(x43951,a871)),x43951),f9(x43951,a871,a871)),f334(f334(f10(f886(x43951,a871),f886(x43951,f886(a871,a871)),x43951),f334(f10(a871,f886(a871,a871),x43951),a332)),a331))),x43952)),f266(x43951,x43952)) % 169.19/169.64 [4442]E(f334(f334(f40(a877),x44421),f334(f334(f81(a877),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),x44422)),f334(f334(f40(a877),x44421),f334(a115,f334(a115,f334(a115,x44422))))) % 169.19/169.64 [4443]E(f46(a877,x44431,f334(f334(f81(a877),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),x44432)),f46(a877,x44431,f334(a115,f334(a115,f334(a115,x44432))))) % 169.19/169.64 [4444]E(f46(a877,f334(f334(f81(a877),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),x44441),x44442),f46(a877,f334(a115,f334(a115,f334(a115,x44441))),x44442)) % 169.19/169.64 [4457]E(f124(f334(x44571,f334(f334(f82(a102),f334(f106(a102),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),x44572))),f334(f209(x44571),x44572)) % 169.19/169.64 [4458]E(f334(f334(f40(a877),f334(f334(f81(a877),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),x44581)),x44582),f334(f334(f40(a877),f334(a115,f334(a115,f334(a115,x44581)))),x44582)) % 169.19/169.64 [4507]~E(f34(x45071,x45072),f334(a26,x45073)) % 169.19/169.64 [4508]~E(f33(x45081,x45082),f334(a26,x45083)) % 169.19/169.64 [4509]~E(f334(a26,x45091),f34(x45092,x45093)) % 169.19/169.64 [4510]~E(f334(a26,x45101),f33(x45102,x45103)) % 169.19/169.64 [4525]~E(f29(x45251,x45252,x45253),a24) % 169.19/169.64 [4526]~E(f31(x45261,x45262,x45263),a24) % 169.19/169.64 [4527]~E(f30(x45271,x45272,x45273),a24) % 169.19/169.64 [3210]E(f334(f200(x32101,x32102),x32103),f122(x32101,x32102)) % 169.19/169.64 [3232]E(f334(f208(x32321,x32322),x32323),f334(f126(x32321),x32322)) % 169.19/169.64 [3311]E(f334(f334(f154(x33111,x33112),x33113),f116(x33111)),f116(x33112)) % 169.19/169.64 [3312]E(f334(f334(f207(x33121,x33122),x33123),f198(x33121)),f198(x33122)) % 169.19/169.64 [3332]E(f32(f29(x33321,x33322,x33323)),f2(a877)) % 169.19/169.64 [3353]E(f334(f191(x33531,x33532,x33533),f2(a877)),x33532) % 169.19/169.64 [3354]E(f334(f196(a873),f29(x33541,x33542,x33543)),f2(a877)) % 169.19/169.64 [3356]E(f334(f334(f183(x33561,x33562),x33563),f116(x33562)),f116(f885(x33561,x33562))) % 169.19/169.64 [3371]E(f334(f196(f878(x33711)),f170(x33711,x33712,x33713)),x33712) % 169.19/169.64 [3391]E(f86(x33911,f64(x33911,x33912,x33913)),f334(f65(x33911,x33912),x33913)) % 169.19/169.64 [3395]E(f258(x33951,x33952,f258(x33952,x33951,x33953)),x33953) % 169.19/169.64 [3415]E(f334(f169(x34151),f170(x34151,x34152,x34153)),f170(x34151,x34152,x34153)) % 169.19/169.64 [3444]E(f140(x34441,x34442,f152(x34441,x34443)),f152(x34441,f140(x34441,x34442,x34443))) % 169.19/169.64 [3463]E(f334(f268(f878(x34631),f878(x34631)),f167(x34631,x34632,x34633)),f334(f136(x34631,x34632),x34633)) % 169.19/169.64 [3510]E(f334(f334(f151(x35101),x35102),f170(x35101,x35103,x35102)),f170(x35101,f334(a115,x35103),x35102)) % 169.19/169.64 [3542]E(f19(x35421,x35422,x35423,f2(a102)),x35422) % 169.19/169.64 [3543]E(f192(x35431,x35432,x35433,f2(a877)),x35432) % 169.19/169.64 [3550]E(f163(x35501,x35502,x35503,f116(x35501)),f116(x35502)) % 169.19/169.64 [3551]E(f164(x35511,x35512,x35513,f116(x35511)),f116(x35512)) % 169.19/169.64 [3558]E(f334(f334(f165(x35581),f334(f334(f151(x35581),x35582),x35583)),f2(a877)),x35582) % 169.19/169.64 [3588]E(f61(x35881,x35882,f116(x35881),x35883),f116(f885(x35881,x35882))) % 169.19/169.64 [3609]P21(x36091,x36092,x36093,f195(f886(x36091,a871))) % 169.19/169.64 [3770]E(f334(f74(x37701,x37702,x37701,x37703),f35(x37701)),x37703) % 169.19/169.64 [3954]P104(f334(f334(f336(f885(x39541,x39541)),f334(f334(f269(x39541,x39541),x39542),x39542)),f310(x39541,x39543))) % 169.19/169.64 [4602]~P104(f334(f334(f336(f885(f878(x46021),f878(x46021))),f334(f334(f269(f878(x46021),f878(x46021)),x46022),f116(x46021))),f145(x46021,x46023))) % 169.19/169.64 [4603]~P104(f334(f334(f336(f885(f878(x46031),f878(x46031))),f334(f334(f269(f878(x46031),f878(x46031)),x46032),f116(x46031))),f147(x46031,x46033))) % 169.19/169.64 [4604]~P104(f334(f334(f336(f885(f878(x46041),f878(x46041))),f334(f334(f269(f878(x46041),f878(x46041)),x46042),f116(x46041))),f157(x46041,x46043))) % 169.19/169.64 [4605]~P104(f334(f334(f336(f885(f878(x46051),f878(x46051))),f334(f334(f269(f878(x46051),f878(x46051)),f116(x46051)),x46052)),f145(x46051,x46053))) % 169.19/169.64 [4606]~P104(f334(f334(f336(f885(f878(x46061),f878(x46061))),f334(f334(f269(f878(x46061),f878(x46061)),f116(x46061)),x46062)),f157(x46061,x46063))) % 169.19/169.64 [3286]E(f334(f334(f210(x32861),x32862),x32863),f211(x32861,f224(x32862,x32863))) % 169.19/169.64 [3342]E(f334(f289(x33421,x33422),f334(f289(x33422,x33421),x33423)),x33423) % 169.19/169.64 [3366]E(f334(f334(f183(x33661,x33662),f116(x33661)),x33663),f116(f885(x33661,x33662))) % 169.19/169.64 [3369]E(f177(x33691,x33692,f334(f255(a877),x33693)),f334(f334(f176(x33691),x33693),x33692)) % 169.19/169.64 [3387]E(f152(x33871,f334(f136(x33871,x33872),x33873)),f334(f136(x33871,x33872),f152(x33871,x33873))) % 169.19/169.64 [3389]E(f334(f265(x33891,x33892),f334(f289(x33892,x33891),x33893)),f334(f267(x33892,x33891),x33893)) % 169.19/169.64 [3390]E(f334(f267(x33901,x33902),f334(f289(x33902,x33901),x33903)),f334(f265(x33902,x33901),x33903)) % 169.19/169.64 [3407]E(f334(f136(x34071,x34072),f334(f169(x34071),x34073)),f334(f169(x34071),f334(f136(x34071,x34072),x34073))) % 169.19/169.64 [3421]E(f334(f334(f138(x34211),x34212),f334(f172(x34211),x34213)),f334(f334(f138(x34211),f334(a115,x34212)),x34213)) % 169.19/169.64 [3439]E(f32(f30(x34391,x34392,x34393)),f334(f334(f81(a877),f32(x34393)),f334(a115,f2(a877)))) % 169.19/169.64 [3440]E(f334(f313(x34401,x34402,x34403),f195(f886(x34401,a871))),f195(f886(x34402,a871))) % 169.19/169.64 [3441]E(f334(f288(x34411,x34412,x34413),f195(f886(x34411,a871))),f195(f886(x34412,a871))) % 169.19/169.64 [3442]E(f334(f314(x34421,x34422,x34423),f195(f886(x34422,a871))),f195(f886(x34421,a871))) % 169.19/169.64 [3443]E(f334(f314(x34431,x34432,x34433),f257(f886(x34432,a871))),f257(f886(x34431,a871))) % 169.19/169.64 [3472]E(f334(f334(f312(x34721),x34722),f334(f173(x34721),x34723)),f334(f173(x34721),f140(x34721,x34722,x34723))) % 169.19/169.64 [3484]E(f242(x34841,x34842,f334(f241(x34841),x34843)),f334(f334(f81(a877),f334(x34842,x34843)),f334(a115,f2(a877)))) % 169.19/169.64 [3562]E(f334(f196(a873),f30(x35621,x35622,x35623)),f334(f334(f81(a877),f334(f196(a873),x35623)),f334(a115,f2(a877)))) % 169.19/169.64 [3563]E(f334(f313(f885(x35631,x35632),x35632,f272(x35631,x35632)),x35633),f334(f265(x35631,x35632),x35633)) % 169.19/169.64 [3564]E(f334(f313(f885(x35641,x35642),x35641,f268(x35641,x35642)),x35643),f334(f267(x35641,x35642),x35643)) % 169.19/169.64 [3580]E(f334(f173(x35801),f170(x35801,f334(a115,x35802),x35803)),f334(f334(f312(x35801),x35803),f195(f886(x35801,a871)))) % 169.19/169.64 [3637]E(f334(f334(f269(x36371,x36372),f334(f268(x36371,x36372),x36373)),f334(f272(x36371,x36372),x36373)),x36373) % 169.19/169.64 [3644]E(f334(f196(f879(x36441)),f127(x36441,x36442,x36443)),f334(f334(f81(a877),f334(f196(f879(x36441)),x36443)),f334(a115,f2(a877)))) % 169.19/169.64 [3645]E(f334(f334(f273(x36451,x36452,x36451),f18(x36451,x36452)),x36453),f334(f268(x36451,x36452),x36453)) % 169.19/169.64 [3665]E(f186(x36651,x36652,x36653,f334(f18(f881(x36652),x36651),f198(x36652))),x36653) % 169.19/169.64 [3666]E(f186(x36661,x36662,f334(f18(f881(x36662),x36661),f198(x36662)),x36663),x36663) % 169.19/169.64 [3723]E(f32(f31(x37231,x37232,x37233)),f334(f334(f81(a877),f334(f334(f81(a877),f32(x37232)),f32(x37233))),f334(a115,f2(a877)))) % 169.19/169.64 [3774]E(f334(f74(x37741,x37741,x37742,f35(x37741)),x37743),x37743) % 169.19/169.64 [3782]E(f334(f334(f134(x37821),f170(x37821,x37822,x37823)),f334(f334(f151(x37821),x37823),f116(x37821))),f334(f334(f151(x37821),x37823),f170(x37821,x37822,x37823))) % 169.19/169.64 [3887]E(f334(f196(a873),f31(x38871,x38872,x38873)),f334(f334(f81(a877),f334(f334(f81(a877),f334(f196(a873),x38872)),f334(f196(a873),x38873))),f334(a115,f2(a877)))) % 169.19/169.64 [3964]P104(f334(f334(f249(f886(x39641,a871)),f334(f173(x39641),f334(f136(x39641,x39642),x39643))),f334(f173(x39641),x39643))) % 169.19/169.64 [4009]P104(f334(f334(f249(f886(x40091,a871)),f334(f173(x40091),f334(f334(f176(x40091),x40092),x40093))),f334(f173(x40091),x40093))) % 169.19/169.64 [4010]P104(f334(f334(f249(f886(x40101,a871)),f334(f173(x40101),f334(f334(f138(x40101),x40102),x40103))),f334(f173(x40101),x40103))) % 169.19/169.64 [4015]P104(f334(f334(f249(f886(x40151,a871)),f334(f173(x40151),f171(x40151,x40152,x40153))),f334(f173(x40151),x40153))) % 169.19/169.64 [4016]P104(f334(f334(f249(f886(x40161,a871)),f334(f173(x40161),f177(x40161,x40162,x40163))),f334(f173(x40161),x40162))) % 169.19/169.64 [4039]P21(f885(x40391,x40392),f885(x40392,x40391),f334(f273(x40391,x40392,f885(x40392,x40391)),f334(f9(x40392,x40391,f885(x40392,x40391)),f269(x40392,x40391))),x40393) % 169.19/169.64 [4051]E(f334(f334(f334(f190(f878(x40511),f878(x40511)),f46(a877,x40512,f334(f196(f878(x40511)),x40513))),f168(x40511)),x40513),f334(f334(f334(f190(f878(x40511),f878(x40511)),x40512),f168(x40511)),x40513)) % 169.19/169.64 [4095]P104(f334(f334(f336(f885(f878(x40951),f878(x40951))),f334(f334(f269(f878(x40951),f878(x40951)),x40952),x40952)),f158(x40951,f310(x40951,x40953)))) % 169.19/169.64 [4241]E(f91(f885(x42411,x42412),f334(f334(f20(f885(x42411,x42412),x42412,a871),f334(f334(f10(x42411,f886(x42412,a871),f885(x42411,x42412)),x42413),f268(x42411,x42412))),f272(x42411,x42412))),f91(f885(x42411,x42412),f334(f273(x42411,x42412,a871),x42413))) % 169.19/169.64 [4242]E(f86(f885(x42421,x42422),f334(f334(f20(f885(x42421,x42422),x42422,a871),f334(f334(f10(x42421,f886(x42422,a871),f885(x42421,x42422)),x42423),f268(x42421,x42422))),f272(x42421,x42422))),f86(f885(x42421,x42422),f334(f273(x42421,x42422,a871),x42423))) % 169.19/169.64 [4278]E(f334(f334(f290(f885(a877,x42781),x42781),f327(a877,x42781,a253,x42782)),f334(f334(f20(x42781,x42781,f885(a877,x42781)),f334(f334(f10(a877,f886(x42781,f885(a877,x42781)),x42781),f269(a877,x42781)),x42783)),f7(x42781))),f328(x42781,x42783,x42782)) % 169.19/169.64 [4343]E(f334(f274(x43431,x43431,x43432,x43432,f7(x43431),f7(x43432)),x43433),x43433) % 169.19/169.64 [4418]E(f334(f142(f878(f878(x44181)),f878(f878(x44181)),f134(f878(x44181)),f116(f878(x44181))),f334(f334(f154(f878(x44181),f878(f878(x44181))),f334(f334(f9(f878(x44181),f878(x44181),f878(f878(x44181))),f334(f334(f10(f886(x44181,f878(x44181)),f886(f878(x44181),f878(f878(x44181))),f878(x44181)),f154(x44181,f878(x44181))),f334(f9(x44181,f878(x44181),f878(x44181)),f151(x44181)))),x44182)),f56(x44181,x44183,x44182))),f56(x44181,f334(a115,x44183),x44182)) % 169.19/169.64 [4479]E(f334(f243(a877,f885(x44791,f879(x44791)),f2(a877),f334(f273(x44791,f879(x44791),a877),f334(f334(f9(x44791,a877,f886(f879(x44791),a877)),f334(f334(f10(f886(f879(x44791),f886(a877,a877)),f886(a877,f886(f879(x44791),a877)),x44791),f9(f879(x44791),a877,a877)),f334(f334(f10(f886(f879(x44791),a877),f886(f879(x44791),f886(a877,a877)),x44791),f334(f10(a877,f886(a877,a877),f879(x44791)),f81(a877))),f334(f334(f9(x44791,f886(f879(x44791),a877),f886(f879(x44791),a877)),f334(f334(f10(f886(a877,a877),f886(f886(f879(x44791),a877),f886(f879(x44791),a877)),x44791),f10(a877,a877,f879(x44791))),f334(f334(f10(a877,f886(a877,a877),x44791),f81(a877)),x44792))),f129(x44791,x44792))))),f79(a877)))),f334(f135(x44791),x44793)),f334(f129(x44791,x44792),x44793)) % 169.19/169.64 [4482]E(f334(f334(f87(a1,x44821),f227(f334(f334(f74(f885(a1,a1),a1,x44821,f272(a1,a1)),f221(x44821)),x44822),f334(f334(f74(f885(a1,a1),a1,x44821,f272(a1,a1)),f221(x44821)),x44823))),f334(f334(f20(a1,a1,x44821),f334(f334(f10(a1,f886(a1,x44821),a1),f210(x44821)),f334(f334(f20(a1,a1,a1),f334(f334(f10(a1,f886(a1,a1),a1),f81(a1)),f334(f334(f10(a1,a1,a1),f334(f82(a1),f334(f334(f74(f885(a1,a1),a1,x44821,f268(a1,a1)),f221(x44821)),x44822))),f334(f334(f9(a1,a1,a1),f40(a1)),f334(f334(f74(f885(a1,a1),a1,x44821,f272(a1,a1)),f221(x44821)),x44822))))),f334(f334(f10(a1,a1,a1),f334(f82(a1),f334(f334(f74(f885(a1,a1),a1,x44821,f268(a1,a1)),f221(x44821)),x44823))),f334(f334(f9(a1,a1,a1),f40(a1)),f334(f334(f74(f885(a1,a1),a1,x44821,f272(a1,a1)),f221(x44821)),x44823)))))),f7(a1))),f238(x44821,x44822,x44823)) % 169.19/169.64 [4520]~E(f334(f334(f151(x45201),x45202),x45203),x45203) % 169.19/169.64 [4529]~E(f334(f334(f151(x45291),x45292),x45293),f116(x45291)) % 169.19/169.64 [4551]~E(f334(f334(f312(x45511),x45512),x45513),f195(f886(x45511,a871))) % 169.19/169.64 [4578]~E(f334(f313(x45781,f886(x45781,a871),x45782),x45783),f334(f311(x45781),x45783)) % 169.19/169.64 [3347]E(f334(f334(f159(x33471,f116(x33471)),x33472),x33473),f116(x33471)) % 169.19/169.64 [3348]E(f334(f141(x33481),f334(f334(f151(x33481),x33482),x33483)),x33482) % 169.19/169.64 [3349]E(f334(f172(x33491),f334(f334(f151(x33491),x33492),x33493)),x33493) % 169.19/169.64 [3394]E(f334(f334(f138(x33941),f79(a877)),f334(f334(f151(x33941),x33942),x33943)),x33943) % 169.19/169.64 [3428]E(f117(x34281,f334(f334(f138(x34281),x34282),x34283)),f334(f334(f138(x34281),x34282),f117(x34281,x34283))) % 169.19/169.64 [3430]E(f334(f334(f159(x34301,x34302),x34303),f334(f334(f165(x34301),x34302),x34303)),x34302) % 169.19/169.64 [3454]E(f334(f334(f312(x34541),x34542),f334(f334(f312(x34541),x34542),x34543)),f334(f334(f312(x34541),x34542),x34543)) % 169.19/169.64 [3465]E(f334(f334(f179(x34651,x34652),f116(f885(x34651,x34652))),x34653),f198(x34652)) % 169.19/169.64 [3468]E(f334(f334(f312(x34681),x34682),f334(f173(x34681),x34683)),f334(f173(x34681),f334(f334(f151(x34681),x34682),x34683))) % 169.19/169.64 [3470]E(f334(f334(f138(x34701),x34702),f334(f172(x34701),x34703)),f334(f172(x34701),f334(f334(f138(x34701),x34702),x34703))) % 169.19/169.64 [3481]E(f334(f334(f176(x34811),f79(a877)),f334(f334(f151(x34811),x34812),x34813)),f334(f334(f151(x34811),x34812),f116(x34811))) % 169.19/169.64 [3527]E(f334(f65(x35271,x35272),f334(f334(f312(x35271),x35273),f195(f886(x35271,a871)))),x35273) % 169.19/169.64 [3570]E(f334(f334(f81(a877),x35701),f334(f334(f81(a877),x35702),x35703)),f334(f334(f81(a877),x35702),f334(f334(f81(a877),x35701),x35703))) % 169.19/169.64 [3571]E(f334(f334(f81(a1),x35711),f334(f334(f81(a1),x35712),x35713)),f334(f334(f81(a1),x35712),f334(f334(f81(a1),x35711),x35713))) % 169.19/169.64 [3576]E(f334(f334(f271(x35761,x35762),f195(f886(x35761,a871))),x35763),f195(f886(f885(x35761,x35762),a871))) % 169.19/169.64 [3601]E(f334(f334(f113(f886(x36011,a871)),x36012),x36013),f334(f334(f113(f886(x36011,a871)),x36013),x36012)) % 169.19/169.64 [3602]E(f334(f334(f104(f886(x36021,a871)),x36022),x36023),f334(f334(f104(f886(x36021,a871)),x36023),x36022)) % 169.19/169.64 [3604]E(f334(f334(f134(x36041),x36042),f334(f334(f151(x36041),x36043),f116(x36041))),f334(f168(x36041),f334(f334(f151(x36041),x36043),x36042))) % 169.19/169.64 [3605]E(f334(f334(f134(x36051),f334(f169(x36051),x36052)),f334(f169(x36051),x36053)),f334(f169(x36051),f334(f334(f134(x36051),x36053),x36052))) % 169.19/169.64 [3615]E(f334(f172(x36151),f334(f334(f176(x36151),f334(a115,x36152)),x36153)),f334(f334(f176(x36151),x36152),f334(f172(x36151),x36153))) % 169.19/169.64 [3622]P104(f334(f334(f336(x36221),x36222),f334(f334(f312(x36221),x36222),x36223))) % 169.19/169.64 [3626]E(f334(f334(f43(x36261,f886(x36262,a871)),f195(f886(x36261,a871))),x36263),f257(f886(x36262,a871))) % 169.19/169.64 [3629]E(f334(f288(x36291,x36291,f266(x36291,x36292)),x36293),f334(f334(f104(f886(x36291,a871)),x36292),x36293)) % 169.19/169.64 [3643]E(f334(f196(f878(x36431)),f334(f334(f151(x36431),x36432),x36433)),f334(f334(f81(a877),f334(f196(f878(x36431)),x36433)),f334(a115,f2(a877)))) % 169.19/169.64 [3647]E(f144(x36471,f334(f334(f134(x36471),x36472),f334(f334(f151(x36471),x36473),f116(x36471)))),x36473) % 169.19/169.64 [3648]E(f117(x36481,f334(f334(f134(x36481),x36482),f334(f334(f151(x36481),x36483),f116(x36481)))),x36482) % 169.19/169.64 [3654]E(f334(f334(f134(x36541),f334(f334(f176(x36541),x36542),x36543)),f334(f334(f138(x36541),x36542),x36543)),x36543) % 169.19/169.64 [3663]E(f334(f334(f3(a877),f334(f334(f81(a877),x36631),x36632)),f334(f334(f81(a877),x36633),x36632)),f334(f334(f3(a877),x36631),x36633)) % 169.19/169.64 [3664]E(f334(f334(f3(a877),f334(f334(f81(a877),x36641),x36642)),f334(f334(f81(a877),x36641),x36643)),f334(f334(f3(a877),x36642),x36643)) % 169.19/169.64 [3672]E(f334(f334(f134(x36721),f334(f169(x36721),x36722)),f334(f334(f151(x36721),x36723),f116(x36721))),f334(f169(x36721),f334(f334(f151(x36721),x36723),x36722))) % 169.19/169.64 [3674]E(f334(f334(f81(a877),f334(f196(f878(x36741)),x36742)),f334(f196(f878(x36741)),x36743)),f334(f196(f878(x36741)),f334(f334(f134(x36741),x36742),x36743))) % 169.19/169.64 [3677]E(f334(f334(f81(a877),f334(f196(f878(x36771)),x36772)),f334(f196(f878(x36771)),x36773)),f334(f196(f878(x36771)),f174(x36771,x36772,x36773))) % 169.19/169.64 [3685]E(f334(f334(f113(f886(x36851,a871)),f334(f173(x36851),x36852)),f334(f173(x36851),x36853)),f334(f173(x36851),f334(f334(f134(x36851),x36852),x36853))) % 169.19/169.64 [3686]E(f46(a877,f334(f334(f82(a877),x36861),x36862),f334(f334(f82(a877),x36861),x36863)),f334(f334(f82(a877),x36861),f46(a877,x36862,x36863))) % 169.19/169.64 [3699]E(f334(f334(f176(x36991),f334(f334(f3(a877),x36992),f79(a877))),f334(f172(x36991),x36993)),f334(f172(x36991),f334(f334(f176(x36991),x36992),x36993))) % 169.19/169.64 [3704]E(f334(f334(f104(f886(x37041,a871)),x37042),f334(f80(f886(x37041,a871)),x37043)),f334(f334(f3(f886(x37041,a871)),x37042),x37043)) % 169.19/169.64 [3705]E(f334(f334(f3(f886(x37051,a871)),x37052),f334(f80(f886(x37051,a871)),x37053)),f334(f334(f104(f886(x37051,a871)),x37052),x37053)) % 169.19/169.64 [3727]E(f334(f334(f271(x37271,x37272),x37273),f334(f18(f886(x37272,a871),x37271),f195(f886(x37272,a871)))),f195(f886(f885(x37271,x37272),a871))) % 169.19/169.64 [3729]E(f334(f334(f3(a877),f334(f334(f82(a877),x37291),x37292)),f334(f334(f82(a877),x37291),x37293)),f334(f334(f82(a877),x37291),f334(f334(f3(a877),x37292),x37293))) % 169.19/169.64 [3730]E(f334(f334(f81(a877),f334(f334(f82(a877),x37301),x37302)),f334(f334(f82(a877),x37301),x37303)),f334(f334(f82(a877),x37301),f334(f334(f81(a877),x37302),x37303))) % 169.19/169.64 [3731]E(f334(f334(f3(a1),f334(f334(f82(a1),x37311),x37312)),f334(f334(f82(a1),x37311),x37313)),f334(f334(f82(a1),x37311),f334(f334(f3(a1),x37312),x37313))) % 169.19/169.64 [3732]E(f334(f334(f81(a1),f334(f334(f82(a1),x37321),x37322)),f334(f334(f82(a1),x37321),x37323)),f334(f334(f82(a1),x37321),f334(f334(f81(a1),x37322),x37323))) % 169.19/169.64 [3733]E(f334(f334(f82(a1),f334(f334(f259(a1),x37331),x37332)),f334(f334(f259(a1),x37331),x37333)),f334(f334(f259(a1),x37331),f334(f334(f81(a877),x37332),x37333))) % 169.19/169.64 [3748]E(f334(f334(f44(x37481,f886(x37482,a871)),x37483),f334(f18(f886(x37482,a871),x37481),f195(f886(x37482,a871)))),f195(f886(x37482,a871))) % 169.19/169.64 [3750]E(f46(a877,f334(f334(f82(a877),x37501),x37502),f334(f334(f82(a877),x37503),x37502)),f334(f334(f82(a877),f46(a877,x37501,x37503)),x37502)) % 169.19/169.64 [3754]E(f46(a1,f334(f334(f3(a1),x37541),f46(a1,x37542,x37543)),x37543),f46(a1,f334(f334(f3(a1),x37541),x37542),x37543)) % 169.19/169.64 [3755]E(f46(a1,f334(f334(f82(a1),x37551),f46(a1,x37552,x37553)),x37553),f46(a1,f334(f334(f82(a1),x37551),x37552),x37553)) % 169.19/169.64 [3756]P104(f334(f334(f249(f886(x37561,a871)),x37562),f334(f334(f312(x37561),x37563),x37562))) % 169.19/169.64 [3759]E(f334(f313(f885(x37591,x37592),x37591,f268(x37591,x37592)),f334(f173(f885(x37591,x37592)),x37593)),f185(x37591,x37592,f334(f179(x37591,x37592),x37593))) % 169.19/169.64 [3811]P104(f334(f63(x38111),f185(x38111,x38112,f334(f179(x38111,x38112),x38113)))) % 169.19/169.64 [3836]E(f334(f334(f43(f886(x38361,a871),f886(x38361,a871)),x38362),f334(f113(f886(x38361,a871)),x38363)),f334(f334(f113(f886(x38361,a871)),x38363),f42(f886(x38361,a871),x38362))) % 169.19/169.64 [3837]E(f334(f334(f44(f886(x38371,a871),f886(x38371,a871)),x38372),f334(f104(f886(x38371,a871)),x38373)),f334(f334(f104(f886(x38371,a871)),x38373),f41(f886(x38371,a871),x38372))) % 169.19/169.64 [3848]E(f334(f173(x38481),f334(f334(f334(f190(f878(x38481),f878(x38481)),x38482),f168(x38481)),x38483)),f334(f173(x38481),x38483)) % 169.19/169.64 [3852]E(f334(f334(f176(x38521),f334(f196(f878(x38521)),f178(x38521,x38522,x38523))),x38523),f178(x38521,x38522,x38523)) % 169.19/169.64 [3853]E(f185(x38531,x38532,f334(f334(f10(x38532,f881(x38532),x38531),f241(x38532)),x38533)),f257(f886(x38531,a871))) % 169.19/169.64 [3857]E(f334(f196(f878(x38571)),f334(f334(f334(f190(f878(x38571),f878(x38571)),x38572),f168(x38571)),x38573)),f334(f196(f878(x38571)),x38573)) % 169.19/169.64 [3860]E(f334(f334(f273(x38601,x38602,x38602),f334(f18(f886(x38602,x38602),x38601),f7(x38602))),x38603),f334(f272(x38601,x38602),x38603)) % 169.19/169.64 [3867]E(f46(a1,f334(f334(f3(a1),f46(a1,x38671,x38672)),x38673),x38672),f46(a1,f334(f334(f3(a1),x38671),x38673),x38672)) % 169.19/169.64 [3868]E(f46(a1,f334(f334(f259(a1),f46(a1,x38681,x38682)),x38683),x38682),f46(a1,f334(f334(f259(a1),x38681),x38683),x38682)) % 169.19/169.64 [3871]E(f334(f334(f44(f886(f885(x38711,x38712),a871),f886(x38712,a871)),x38713),f265(x38711,x38712)),f334(f265(x38711,x38712),f41(f886(f885(x38711,x38712),a871),x38713))) % 169.19/169.64 [3872]E(f334(f334(f44(f886(f885(x38721,x38722),a871),f886(x38721,a871)),x38723),f267(x38721,x38722)),f334(f267(x38721,x38722),f41(f886(f885(x38721,x38722),a871),x38723))) % 169.19/169.64 [3900]E(f334(f74(x39001,x39001,x39001,x39002),f334(f334(f190(x39001,x39001),x39003),x39002)),f334(f334(f190(x39001,x39001),f334(a115,x39003)),x39002)) % 169.19/169.64 [3910]E(f243(f881(x39101),x39102,f198(x39101),f334(f334(f10(x39101,f881(x39101),x39102),f241(x39101)),x39103)),f334(f207(x39102,x39101),x39103)) % 169.19/169.64 [3917]E(f334(f334(f138(x39171),f334(f334(f3(a877),f334(f196(f878(x39171)),x39172)),x39173)),f334(f169(x39171),x39172)),f334(f169(x39171),f334(f334(f176(x39171),x39173),x39172))) % 169.19/169.64 [3918]E(f334(f334(f176(x39181),f334(f334(f3(a877),f334(f196(f878(x39181)),x39182)),x39183)),f334(f169(x39181),x39182)),f334(f169(x39181),f334(f334(f138(x39181),x39183),x39182))) % 169.19/169.64 [3921]E(f334(f334(f81(a877),f334(f166(a877),f334(f334(f154(x39211,a877),x39212),x39213))),f334(f196(f878(x39211)),x39213)),f155(x39211,x39212,x39213)) % 169.19/169.64 [3940]E(f334(f168(x39401),f334(f334(f334(f190(f878(x39401),f878(x39401)),x39402),f168(x39401)),x39403)),f334(f334(f334(f190(f878(x39401),f878(x39401)),f334(a115,x39402)),f168(x39401)),x39403)) % 169.19/169.64 [3955]P104(f334(f334(f249(a877),f334(f196(f878(x39551)),f334(f136(x39551,x39552),x39553))),f334(f196(f878(x39551)),x39553))) % 169.19/169.64 [3972]E(f334(f334(f113(f886(f886(x39721,a871),a871)),f334(f311(x39721),x39722)),f334(f313(f886(x39721,a871),f886(x39721,a871),f334(f312(x39721),x39723)),f334(f311(x39721),x39722))),f334(f311(x39721),f334(f334(f312(x39721),x39723),x39722))) % 169.19/169.64 [3991]P20(x39911,x39912,f334(f334(f312(f876(x39911)),f334(f334(f334(f93(x39911),x39913),a24),x39913)),f195(f886(f876(x39911),a871)))) % 169.19/169.64 [4006]P104(f334(f334(f249(a877),f334(f196(f878(x40061)),f178(x40061,x40062,x40063))),f334(f196(f878(x40061)),x40063))) % 169.19/169.64 [4014]E(f334(f267(x40141,x40142),f334(f254(f885(x40141,x40142)),f334(f273(x40141,x40142,a871),x40143))),f334(f254(x40141),f334(f334(f10(f886(x40142,a871),a871,x40141),f88(x40142)),x40143))) % 169.19/169.64 [4026]E(f334(f313(a877,a877,f334(f334(f9(a877,a877,a877),f81(a877)),x40261)),f305(a877,x40262,x40263)),f305(a877,f334(f334(f81(a877),x40262),x40261),f334(f334(f81(a877),x40263),x40261))) % 169.19/169.64 [4029]P104(f334(f63(f881(x40291)),f334(f313(x40292,f881(x40291),f334(f179(x40292,x40291),x40293)),f257(f886(x40292,a871))))) % 169.19/169.64 [4042]E(f334(f313(a877,a877,f334(f334(f9(a877,a877,a877),f81(a877)),x40421)),f334(f304(a877,x40422),x40423)),f334(f304(a877,f334(f334(f81(a877),x40422),x40421)),f334(f334(f81(a877),x40423),x40421))) % 169.19/169.64 [4060]E(f334(f334(f183(x40601,x40602),f334(f334(f154(f885(x40601,x40602),x40601),f268(x40601,x40602)),x40603)),f334(f334(f154(f885(x40601,x40602),x40602),f272(x40601,x40602)),x40603)),x40603) % 169.19/169.64 [4065]E(f334(f334(f81(a877),f334(f334(f82(a877),x40651),f46(a877,f334(f334(f40(a877),x40652),x40651),x40653))),f46(a877,x40652,x40651)),f46(a877,x40652,f334(f334(f82(a877),x40651),x40653))) % 169.19/169.64 [4079]E(f334(f334(f134(x40791),x40792),f334(f142(f878(x40791),f878(x40791),f134(x40791),f116(x40791)),x40793)),f334(f142(f878(x40791),f878(x40791),f134(x40791),x40792),x40793)) % 169.19/169.64 [4099]P104(f334(f334(f336(f885(x40991,x40991)),f334(f334(f269(x40991,x40991),x40992),x40992)),f334(f334(f190(f885(x40991,x40991),a871),f2(a877)),x40993))) % 169.19/169.64 [4105]E(f334(f254(x41051),f334(f334(f10(f886(x41052,a871),a871,x41051),f88(x41052)),f334(f9(x41052,x41051,a871),x41053))),f334(f265(x41052,x41051),f334(f254(f885(x41052,x41051)),f334(f273(x41052,x41051,a871),x41053)))) % 169.19/169.64 [4123]E(f334(f334(f113(f886(x41231,a871)),f334(f334(f44(a877,f886(x41231,a871)),f305(a877,f79(a877),x41232)),x41233)),f334(x41233,f2(a877))),f334(f334(f44(a877,f886(x41231,a871)),f334(f303(a877),x41232)),x41233)) % 169.19/169.64 [4138]E(f334(f142(f878(x41381),f878(x41381),f134(x41381),f116(x41381)),f334(f334(f154(f878(x41381),f878(x41381)),f136(x41381,x41382)),x41383)),f334(f136(x41381,x41382),f334(f142(f878(x41381),f878(x41381),f134(x41381),f116(x41381)),x41383))) % 169.19/169.64 [4143]E(f334(f272(f878(x41431),f878(x41431)),f167(x41431,x41432,x41433)),f334(f136(x41431,f334(f74(a871,a871,x41431,a329),x41432)),x41433)) % 169.19/169.64 [4192]E(f334(f334(f81(a1),f334(f334(f81(a1),f334(f334(f82(a1),x41921),f334(f334(f40(a1),x41922),x41921))),f46(a1,x41922,x41921))),x41923),f334(f334(f81(a1),x41922),x41923)) % 169.19/169.64 [4230]E(f334(f334(f81(a1),f334(f334(f81(a1),f334(f334(f82(a1),f334(f334(f40(a1),x42301),x42302)),x42302)),f46(a1,x42301,x42302))),x42303),f334(f334(f81(a1),x42301),x42303)) % 169.19/169.64 [4259]E(f91(f885(x42591,x42592),f334(f273(x42591,x42592,a871),f334(f334(f10(f886(x42592,f885(x42591,x42592)),f886(x42592,a871),x42591),f334(f10(f885(x42591,x42592),a871,x42592),x42593)),f269(x42591,x42592)))),f91(f885(x42591,x42592),x42593)) % 169.19/169.64 [4260]E(f86(f885(x42601,x42602),f334(f273(x42601,x42602,a871),f334(f334(f10(f886(x42602,f885(x42601,x42602)),f886(x42602,a871),x42601),f334(f10(f885(x42601,x42602),a871,x42602),x42603)),f269(x42601,x42602)))),f86(f885(x42601,x42602),x42603)) % 169.19/169.64 [4288]P104(f334(f334(f249(f886(x42881,a871)),f41(f886(x42881,a871),f334(f334(f104(f886(f886(x42881,a871),a871)),x42882),x42883))),f334(f334(f104(f886(x42881,a871)),f41(f886(x42881,a871),x42882)),f41(f886(x42881,a871),x42883)))) % 169.19/169.64 [4289]E(f334(f169(x42891),f334(f334(f334(f190(f878(x42891),f878(x42891)),f334(f334(f3(a877),f334(f196(f878(x42891)),x42892)),f46(a877,x42893,f334(f196(f878(x42891)),x42892)))),f168(x42891)),x42892)),f334(f334(f334(f190(f878(x42891),f878(x42891)),x42893),f168(x42891)),f334(f169(x42891),x42892))) % 169.19/169.64 [4303]E(f334(f254(x43031),f334(f334(f10(a871,a871,x43031),a329),f334(f334(f9(x43031,f881(x43032),a871),f334(f334(f10(f881(x43032),f886(f881(x43032),a871),x43031),a331),x43033)),f198(x43032)))),f185(x43031,x43032,x43033)) % 169.19/169.64 [4328]P104(f334(f334(f249(a877),f334(f196(f878(x43281)),f334(f334(f138(x43281),f334(f196(f878(x43281)),f178(x43281,x43282,x43283))),x43283))),f334(f196(f878(x43281)),x43283))) % 169.19/169.64 [4369]E(f334(f254(x43691),f334(f334(f10(f886(x43692,a871),a871,x43691),f88(x43692)),f334(f334(f10(f881(x43691),f886(x43692,a871),x43691),f334(f9(x43692,f881(x43691),a871),f334(f334(f10(f881(x43691),f886(f881(x43691),a871),x43692),a331),x43693))),f241(x43691)))),f187(x43692,x43691,x43693)) % 169.19/169.64 [4593]~P104(f334(f64(x45931,x45932,f195(f886(x45931,a871))),x45933)) % 169.19/169.64 [4600]~P104(f334(f334(f336(f885(x46001,x46001)),f334(f334(f269(x46001,x46001),x46002),x46003)),f153(x46001,f116(f886(x46001,a877))))) % 169.19/169.64 [3616]E(f334(f196(f878(x36161)),f334(f334(f176(x36161),x36162),x36163)),f334(f334(f247(a877),f334(f196(f878(x36161)),x36163)),x36162)) % 169.19/169.64 [3617]E(f334(f196(f878(x36171)),f334(f334(f138(x36171),x36172),x36173)),f334(f334(f3(a877),f334(f196(f878(x36171)),x36173)),x36172)) % 169.19/169.64 [3642]E(f334(f196(f878(f878(x36421))),f56(x36421,x36422,x36423)),f334(f334(f259(a877),f334(f196(f878(x36421)),x36423)),x36422)) % 169.19/169.64 [3656]E(f334(f334(f40(a877),f334(f334(f40(a877),x36561),x36562)),x36563),f334(f334(f40(a877),x36561),f334(f334(f82(a877),x36562),x36563))) % 169.19/169.64 [3657]E(f334(f334(f3(a877),f334(f334(f3(a877),x36571),x36572)),x36573),f334(f334(f3(a877),x36571),f334(f334(f81(a877),x36572),x36573))) % 169.19/169.64 [3658]E(f334(f334(f82(a877),f334(f334(f82(a877),x36581),x36582)),x36583),f334(f334(f82(a877),x36581),f334(f334(f82(a877),x36582),x36583))) % 169.19/169.64 [3659]E(f334(f334(f82(a1),f334(f334(f82(a1),x36591),x36592)),x36593),f334(f334(f82(a1),x36591),f334(f334(f82(a1),x36592),x36593))) % 169.19/169.64 [3660]E(f334(f334(f81(a877),f334(f334(f81(a877),x36601),x36602)),x36603),f334(f334(f81(a877),x36601),f334(f334(f81(a877),x36602),x36603))) % 169.19/169.64 [3661]E(f334(f334(f81(a1),f334(f334(f81(a1),x36611),x36612)),x36613),f334(f334(f81(a1),x36611),f334(f334(f81(a1),x36612),x36613))) % 169.19/169.64 [3662]E(f334(f334(f259(a1),f334(f334(f259(a1),x36621),x36622)),x36623),f334(f334(f259(a1),x36621),f334(f334(f82(a877),x36622),x36623))) % 169.19/169.64 [3683]E(f162(x36831,f334(f334(f151(f886(x36831,a871)),x36832),x36833)),f175(x36831,x36832,f162(x36831,x36833))) % 169.19/169.64 [3728]E(f334(f334(f3(a877),f334(f334(f3(a877),x37281),x37282)),x37283),f334(f334(f3(a877),f334(f334(f3(a877),x37281),x37283)),x37282)) % 169.19/169.64 [3734]E(f334(f241(f885(x37341,f879(x37341))),f334(f334(f269(x37341,f879(x37341)),x37342),x37343)),f334(f135(x37341),f127(x37341,x37342,x37343))) % 169.19/169.64 [3737]E(f334(f334(f104(f886(x37371,a871)),x37372),f334(f334(f3(f886(x37371,a871)),x37373),x37372)),f195(f886(x37371,a871))) % 169.19/169.64 [3741]E(f334(f334(f154(a877,x37411),f334(f18(x37411,a877),x37412)),f139(a877,f334(f304(a877,f2(a877)),x37413))),f170(x37411,x37413,x37412)) % 169.19/169.64 [3780]E(f41(f886(x37801,a871),f334(f334(f312(f886(x37801,a871)),x37802),x37803)),f334(f334(f113(f886(x37801,a871)),x37802),f41(f886(x37801,a871),x37803))) % 169.19/169.64 [3781]E(f42(f886(x37811,a871),f334(f334(f312(f886(x37811,a871)),x37812),x37813)),f334(f334(f104(f886(x37811,a871)),x37812),f42(f886(x37811,a871),x37813))) % 169.19/169.64 [3783]E(f170(x37831,f334(f196(f878(x37831)),f334(f136(x37831,f334(a331,x37832)),x37833)),x37832),f334(f136(x37831,f334(a331,x37832)),x37833)) % 169.19/169.64 [3785]E(f334(f334(f3(a877),f334(f334(f82(a877),x37851),x37852)),f334(f334(f82(a877),x37853),x37852)),f334(f334(f82(a877),f334(f334(f3(a877),x37851),x37853)),x37852)) % 169.19/169.64 [3786]E(f334(f334(f81(a877),f334(f334(f82(a877),x37861),x37862)),f334(f334(f82(a877),x37863),x37862)),f334(f334(f82(a877),f334(f334(f81(a877),x37861),x37863)),x37862)) % 169.19/169.64 [3787]E(f334(f334(f3(a1),f334(f334(f82(a1),x37871),x37872)),f334(f334(f82(a1),x37873),x37872)),f334(f334(f82(a1),f334(f334(f3(a1),x37871),x37873)),x37872)) % 169.19/169.64 [3788]E(f334(f334(f81(a1),f334(f334(f82(a1),x37881),x37882)),f334(f334(f82(a1),x37883),x37882)),f334(f334(f82(a1),f334(f334(f81(a1),x37881),x37883)),x37882)) % 169.19/169.64 [3790]E(f334(f334(f247(a877),f334(f334(f3(a877),x37901),x37902)),f334(f334(f3(a877),x37903),x37902)),f334(f334(f3(a877),f334(f334(f247(a877),x37901),x37903)),x37902)) % 169.19/169.64 [3814]E(f334(f334(f104(f886(f878(x38141),a871)),f160(x38141,x38142)),f160(x38141,x38143)),f160(x38141,f334(f334(f104(f886(x38141,a871)),x38142),x38143))) % 169.19/169.64 [3816]E(f334(f334(f113(f886(x38161,a871)),x38162),f334(f334(f3(f886(x38161,a871)),x38163),x38162)),f334(f334(f113(f886(x38161,a871)),x38162),x38163)) % 169.19/169.64 [3817]E(f334(f334(f113(f886(x38171,a871)),x38172),f334(f334(f113(f886(x38171,a871)),x38172),x38173)),f334(f334(f113(f886(x38171,a871)),x38172),x38173)) % 169.19/169.64 [3818]E(f334(f334(f104(f886(x38181,a871)),x38182),f334(f334(f104(f886(x38181,a871)),x38182),x38183)),f334(f334(f104(f886(x38181,a871)),x38182),x38183)) % 169.19/169.64 [3830]E(f334(f334(f291(x38301,x38302,x38302),x38303),f310(x38302,f195(f886(f885(x38302,x38302),a871)))),x38303) % 169.19/169.64 [3833]E(f334(f334(f113(f886(x38331,a871)),f334(f334(f312(x38331),x38332),f195(f886(x38331,a871)))),x38333),f334(f334(f312(x38331),x38332),x38333)) % 169.19/169.64 [3851]E(f334(f334(f3(a877),f334(f334(f3(a877),f334(a115,x38511)),x38512)),f334(a115,x38513)),f334(f334(f3(a877),f334(f334(f3(a877),x38511),x38512)),x38513)) % 169.19/169.64 [3881]E(f334(f334(f104(f886(f886(x38811,a871),a871)),f334(f311(x38811),x38812)),f334(f311(x38811),x38813)),f334(f311(x38811),f334(f334(f104(f886(x38811,a871)),x38812),x38813))) % 169.19/169.64 [3885]E(f334(f334(f113(f886(x38851,a871)),f334(f80(f886(x38851,a871)),x38852)),x38853),f334(f80(f886(x38851,a871)),f334(f334(f3(f886(x38851,a871)),x38852),x38853))) % 169.19/169.64 [3897]E(f334(f334(f312(x38971),x38972),f334(f334(f3(f886(x38971,a871)),x38973),f334(f334(f312(x38971),x38972),f195(f886(x38971,a871))))),f334(f334(f312(x38971),x38972),x38973)) % 169.19/169.64 [3907]P104(f334(f334(f249(f886(x39071,a871)),x39072),f334(f334(f113(f886(x39071,a871)),x39073),x39072))) % 169.19/169.64 [3908]P104(f334(f334(f249(f886(x39081,a871)),x39082),f334(f334(f113(f886(x39081,a871)),x39082),x39083))) % 169.19/169.64 [3911]E(f334(f334(f104(f886(x39111,a871)),f334(f80(f886(x39111,a871)),x39112)),f334(f80(f886(x39111,a871)),x39113)),f334(f80(f886(x39111,a871)),f334(f334(f113(f886(x39111,a871)),x39112),x39113))) % 169.19/169.64 [3912]E(f334(f334(f113(f886(x39121,a871)),f334(f80(f886(x39121,a871)),x39122)),f334(f80(f886(x39121,a871)),x39123)),f334(f80(f886(x39121,a871)),f334(f334(f104(f886(x39121,a871)),x39122),x39123))) % 169.19/169.64 [3926]P104(f334(f334(f249(f886(x39261,a871)),f334(f173(x39261),x39262)),f334(f173(x39261),f334(f334(f151(x39261),x39263),x39262)))) % 169.19/169.64 [3937]E(f334(f334(f113(f886(x39371,a871)),f334(f334(f3(f886(x39371,a871)),x39372),x39373)),f334(f334(f104(f886(x39371,a871)),x39372),x39373)),x39372) % 169.19/169.64 [3993]E(f334(f334(f8(x39931,a1),f334(f334(f10(a877,a1,x39931),f103(a1)),x39932)),x39933),f334(f103(a1),f334(f334(f8(x39931,a877),x39932),x39933))) % 169.19/169.64 [3994]E(f334(f334(f11(x39941,a1),f334(f334(f10(a877,a1,x39941),f103(a1)),x39942)),x39943),f334(f103(a1),f334(f334(f11(x39941,a877),x39942),x39943))) % 169.19/169.64 [4044]E(f334(f334(f134(x40441),f178(x40441,x40442,x40443)),f334(f334(f138(x40441),f334(f196(f878(x40441)),f178(x40441,x40442,x40443))),x40443)),x40443) % 169.19/169.64 [4049]E(f334(f80(f886(f885(x40491,x40492),a871)),f334(f334(f271(x40491,x40492),x40493),f334(f18(f886(x40492,a871),x40491),f257(f886(x40492,a871))))),f334(f334(f271(x40491,x40492),f334(f80(f886(x40491,a871)),x40493)),f334(f18(f886(x40492,a871),x40491),f257(f886(x40492,a871))))) % 169.19/169.64 [4050]E(f334(f80(f886(f885(x40501,x40502),a871)),f334(f334(f271(x40501,x40502),f257(f886(x40501,a871))),f334(f18(f886(x40502,a871),x40501),x40503))),f334(f334(f271(x40501,x40502),f257(f886(x40501,a871))),f334(f18(f886(x40502,a871),x40501),f334(f80(f886(x40502,a871)),x40503)))) % 169.19/169.64 [4100]E(f334(f334(f44(f886(x41001,a871),f886(x41001,a871)),x41002),f334(f334(f9(f886(x41001,a871),f886(x41001,a871),f886(x41001,a871)),f104(f886(x41001,a871))),x41003)),f334(f334(f104(f886(x41001,a871)),f41(f886(x41001,a871),x41002)),x41003)) % 169.19/169.64 [4107]E(f334(f142(f878(x41071),f878(x41071),f134(x41071),f116(x41071)),f334(f334(f151(f878(x41071)),x41072),x41073)),f334(f334(f134(x41071),x41072),f334(f142(f878(x41071),f878(x41071),f134(x41071),f116(x41071)),x41073))) % 169.19/169.64 [4129]E(f334(f334(f312(f886(x41291,a871)),f334(f288(x41291,x41291,x41292),f334(f334(f312(x41291),x41293),f195(f886(x41291,a871))))),f195(f886(f886(x41291,a871),a871))),f334(f334(f62(x41291),f334(f334(f312(x41291),x41293),f195(f886(x41291,a871)))),x41292)) % 169.19/169.64 [4139]E(f334(f334(f81(a877),f334(f334(f82(a877),x41391),f334(f334(f40(a877),x41392),x41393))),f334(f334(f40(a877),f334(f334(f82(a877),x41391),f46(a877,x41392,x41393))),x41393)),f334(f334(f40(a877),f334(f334(f82(a877),x41391),x41392)),x41393)) % 169.19/169.64 [4140]E(f334(f334(f81(a1),f334(f334(f82(a1),x41401),f334(f334(f40(a1),x41402),x41403))),f334(f334(f40(a1),f334(f334(f82(a1),x41401),f46(a1,x41402,x41403))),x41403)),f334(f334(f40(a1),f334(f334(f82(a1),x41401),x41402)),x41403)) % 169.19/169.64 [4177]E(f334(f334(f3(f886(x41771,a871)),f334(f173(x41771),x41772)),f334(f334(f312(x41771),x41773),f195(f886(x41771,a871)))),f334(f173(x41771),f334(f136(x41771,f334(f334(f10(a871,a871,x41771),a329),f334(a331,x41773))),x41772))) % 169.19/169.64 [4227]E(f334(f334(f134(x42271),f334(f142(f878(x42271),f878(x42271),f134(x42271),f116(x42271)),x42272)),f334(f142(f878(x42271),f878(x42271),f134(x42271),f116(x42271)),x42273)),f334(f142(f878(x42271),f878(x42271),f134(x42271),f116(x42271)),f334(f334(f134(f878(x42271)),x42272),x42273))) % 169.19/169.64 [4232]E(f334(f334(f269(f878(x42321),f878(x42321)),f334(f136(x42321,x42322),x42323)),f334(f136(x42321,f334(f74(a871,a871,x42321,a329),x42322)),x42323)),f167(x42321,x42322,x42323)) % 169.19/169.64 [4235]E(f334(f334(f81(a877),f334(f334(f81(a877),f334(f334(f40(a877),x42351),x42352)),f334(f334(f40(a877),x42353),x42352))),f334(f334(f40(a877),f334(f334(f81(a877),f46(a877,x42351,x42352)),f46(a877,x42353,x42352))),x42352)),f334(f334(f40(a877),f334(f334(f81(a877),x42351),x42353)),x42352)) % 169.19/169.64 [4236]E(f334(f334(f81(a1),f334(f334(f81(a1),f334(f334(f40(a1),x42361),x42362)),f334(f334(f40(a1),x42363),x42362))),f334(f334(f40(a1),f334(f334(f81(a1),f46(a1,x42361,x42362)),f46(a1,x42363,x42362))),x42362)),f334(f334(f40(a1),f334(f334(f81(a1),x42361),x42363)),x42362)) % 169.19/169.64 [4292]E(f334(f334(f104(f886(f878(x42921),a871)),f334(f334(f9(f878(x42921),f886(f878(x42921),a871),a871),f336(f878(x42921))),f161(x42921,x42922))),f334(f334(f9(f878(x42921),f886(f878(x42921),a871),a871),f336(f878(x42921))),f161(x42921,x42923))),f160(x42921,f334(f334(f104(f886(x42921,a871)),f334(f334(f9(x42921,f886(x42921,a871),a871),f336(x42921)),x42922)),f334(f334(f9(x42921,f886(x42921,a871),a871),f336(x42921)),x42923)))) % 169.19/169.64 [4305]E(f334(f254(x43051),f334(f334(f20(x43051,a871,a871),f334(f334(f10(a871,f886(a871,a871),x43051),a333),f334(f334(f9(x43051,x43051,a871),a331),x43052))),f334(f334(f9(x43051,f886(x43051,a871),a871),f336(x43051)),x43053))),f334(f334(f312(x43051),x43052),x43053)) % 169.19/169.64 [4325]E(f334(f334(f87(f878(f878(x43251)),f878(f878(x43251))),f55(x43251,x43252)),f334(f334(f20(f878(f878(x43251)),f878(f878(x43251)),f878(f878(x43251))),f334(f334(f10(f878(f878(x43251)),f886(f878(f878(x43251)),f878(f878(x43251))),f878(f878(x43251))),f134(f878(x43251))),f334(f154(f878(x43251),f878(x43251)),f334(f151(x43251),x43253)))),f7(f878(f878(x43251))))),f55(x43251,f334(f334(f151(x43251),x43253),x43252))) % 169.19/169.64 [4329]E(f334(f254(x43291),f334(f334(f20(x43291,a871,a871),f334(f334(f10(a871,f886(a871,a871),x43291),a333),f334(f334(f9(x43291,f886(x43291,a871),a871),f336(x43291)),x43292))),f334(f334(f9(x43291,f886(x43291,a871),a871),f336(x43291)),x43293))),f334(f334(f113(f886(x43291,a871)),x43292),x43293)) % 169.19/169.64 [4330]E(f334(f254(x43301),f334(f334(f20(x43301,a871,a871),f334(f334(f10(a871,f886(a871,a871),x43301),a332),f334(f334(f9(x43301,f886(x43301,a871),a871),f336(x43301)),x43302))),f334(f334(f9(x43301,f886(x43301,a871),a871),f336(x43301)),x43303))),f334(f334(f104(f886(x43301,a871)),x43302),x43303)) % 169.19/169.64 [4421]E(f334(f334(f44(x44211,f886(f886(x44211,a871),a871)),x44212),f334(f334(f9(x44211,f886(f886(x44211,a871),a871),f886(f886(x44211,a871),a871)),f334(f334(f10(f886(x44211,a871),f886(f886(f886(x44211,a871),a871),f886(f886(x44211,a871),a871)),x44211),f312(f886(x44211,a871))),f334(f334(f10(f886(x44211,a871),f886(x44211,a871),x44211),f288(x44211,x44211,x44213)),f334(f334(f9(x44211,f886(x44211,a871),f886(x44211,a871)),f312(x44211)),f195(f886(x44211,a871)))))),f195(f886(f886(x44211,a871),a871)))),f334(f334(f62(x44211),x44212),x44213)) % 169.19/169.64 [4423]E(f334(f334(f210(x44231),f334(f334(f82(a1),f334(f334(f74(f885(a1,a1),a1,x44231,f268(a1,a1)),f221(x44231)),x44232)),f334(f334(f74(f885(a1,a1),a1,x44231,f268(a1,a1)),f221(x44231)),x44233))),f334(f334(f82(a1),f334(f334(f74(f885(a1,a1),a1,x44231,f272(a1,a1)),f221(x44231)),x44232)),f334(f334(f74(f885(a1,a1),a1,x44231,f272(a1,a1)),f221(x44231)),x44233))),f236(x44231,x44232,x44233)) % 169.19/169.64 [4426]E(f334(f254(f878(x44261)),f334(f334(f20(f878(x44261),a871,a871),f334(f334(f10(a871,f886(a871,a871),f878(x44261)),a332),f334(f334(f9(f878(x44261),a877,a871),f334(f334(f10(a877,f886(a877,a871),f878(x44261)),a331),f196(f878(x44261)))),x44262))),f334(f334(f9(f878(x44261),f886(x44261,a871),a871),f334(f334(f10(f886(x44261,a871),f886(f886(x44261,a871),a871),f878(x44261)),f249(f886(x44261,a871))),f173(x44261))),f334(f173(x44261),x44263)))),f334(f173(f878(x44261)),f56(x44261,x44262,x44263))) % 169.19/169.64 [3803]E(f46(a877,f334(f334(f81(a877),f334(f334(f82(a877),x38031),x38032)),x38033),x38032),f46(a877,x38033,x38032)) % 169.19/169.64 [3850]E(f139(a877,f334(f304(a877,f334(f334(f81(a877),x38501),x38502)),x38503)),f334(f334(f138(a877),x38502),f139(a877,f334(f304(a877,x38501),x38503)))) % 169.19/169.64 [3896]E(f334(f334(f81(a1),f334(f103(a1),x38961)),f334(f334(f81(a1),f334(f103(a1),x38962)),x38963)),f334(f334(f81(a1),f334(f103(a1),f334(f334(f81(a877),x38961),x38962))),x38963)) % 169.19/169.64 [3903]E(f334(f334(f3(f886(x39031,a871)),f334(f334(f3(f886(x39031,a871)),x39032),x39033)),x39033),f334(f334(f3(f886(x39031,a871)),x39032),x39033)) % 169.19/169.64 [3904]E(f334(f334(f113(f886(x39041,a871)),f334(f334(f3(f886(x39041,a871)),x39042),x39043)),x39043),f334(f334(f113(f886(x39041,a871)),x39042),x39043)) % 169.19/169.64 [3927]E(f334(f334(f291(x39271,x39271,x39272),f310(x39271,f195(f886(f885(x39271,x39271),a871)))),x39273),x39273) % 169.19/169.64 [3934]E(f334(f334(f113(f886(x39341,a871)),f334(f287(x39341),x39342)),f334(f287(x39341),x39343)),f334(f287(x39341),f334(f334(f113(f886(f885(x39341,x39341),a871)),x39342),x39343))) % 169.19/169.64 [3945]E(f278(x39451,f334(f334(f151(f885(a102,x39451)),f334(f334(f269(a102,x39451),f2(a102)),x39452)),x39453)),f278(x39451,x39453)) % 169.19/169.64 [3948]E(f334(f334(f113(f886(x39481,a871)),f41(f886(x39481,a871),x39482)),f41(f886(x39481,a871),x39483)),f41(f886(x39481,a871),f334(f334(f113(f886(f886(x39481,a871),a871)),x39482),x39483))) % 169.19/169.64 [3949]E(f334(f334(f104(f886(x39491,a871)),f42(f886(x39491,a871),x39492)),f42(f886(x39491,a871),x39493)),f42(f886(x39491,a871),f334(f334(f113(f886(f886(x39491,a871),a871)),x39492),x39493))) % 169.19/169.64 [3985]E(f334(f334(f291(x39851,x39851,x39851),f334(f334(f190(f885(x39851,x39851),a871),x39852),x39853)),x39853),f334(f334(f190(f885(x39851,x39851),a871),f334(a115,x39852)),x39853)) % 169.19/169.64 [4035]P104(f334(f334(f249(f886(x40351,a871)),f334(f334(f3(f886(x40351,a871)),x40352),x40353)),x40352)) % 169.19/169.64 [4036]P104(f334(f334(f249(f886(x40361,a871)),f334(f334(f104(f886(x40361,a871)),x40362),x40363)),x40363)) % 169.19/169.64 [4037]P104(f334(f334(f249(f886(x40371,a871)),f334(f334(f104(f886(x40371,a871)),x40372),x40373)),x40372)) % 169.19/169.64 [4062]E(f310(x40621,f334(f334(f113(f886(f885(x40621,x40621),a871)),f310(x40621,x40622)),f310(x40621,x40623))),f310(x40621,f334(f334(f113(f886(f885(x40621,x40621),a871)),x40622),x40623))) % 169.19/169.64 [4066]E(f41(f886(x40661,a871),f334(f334(f312(f886(x40661,a871)),x40662),f334(f334(f312(f886(x40661,a871)),x40663),f195(f886(f886(x40661,a871),a871))))),f334(f334(f113(f886(x40661,a871)),x40662),x40663)) % 169.19/169.64 [4067]E(f42(f886(x40671,a871),f334(f334(f312(f886(x40671,a871)),x40672),f334(f334(f312(f886(x40671,a871)),x40673),f195(f886(f886(x40671,a871),a871))))),f334(f334(f104(f886(x40671,a871)),x40672),x40673)) % 169.19/169.64 [4073]E(f334(f334(f291(x40731,x40731,x40731),f334(f334(f190(f885(x40731,x40731),a871),x40732),x40733)),x40733),f334(f334(f291(x40731,x40731,x40731),x40733),f334(f334(f190(f885(x40731,x40731),a871),x40732),x40733))) % 169.19/169.64 [4144]E(f334(f334(f113(f886(x41441,a871)),f334(f254(x41441),f334(f334(f9(x41441,x41441,a871),a331),x41442))),x41443),f334(f334(f312(x41441),x41442),x41443)) % 169.19/169.64 [4146]E(f334(a107,f334(f334(f8(x41461,a1),f334(f334(f10(a877,a1,x41461),f103(a1)),x41462)),x41463)),f334(f334(f8(x41461,a877),x41462),x41463)) % 169.19/169.64 [4147]E(f334(a107,f334(f334(f11(x41471,a1),f334(f334(f10(a877,a1,x41471),f103(a1)),x41472)),x41473)),f334(f334(f11(x41471,a877),x41472),x41473)) % 169.19/169.64 [4224]E(f334(f156(f878(x42241),x42241,f334(f172(x42241),x42242),f334(f18(f886(f878(x42241),f878(x42241)),x42241),f334(f334(f9(f878(x42241),f878(x42241),f878(x42241)),f134(x42241)),x42242))),x42243),f334(f172(x42241),f334(f334(f134(x42241),x42243),x42242))) % 169.19/169.64 [4255]P104(f334(f334(f249(f886(f886(x42551,a871),a871)),f334(f334(f113(f886(f886(x42551,a871),a871)),f334(f311(x42551),x42552)),f334(f311(x42551),x42553))),f334(f311(x42551),f334(f334(f113(f886(x42551,a871)),x42552),x42553)))) % 169.19/169.64 [4348]E(f334(f254(x43481),f334(f334(f20(x43481,a871,a871),f334(f334(f10(a871,f886(a871,a871),x43481),a332),f334(f334(f9(x43481,f886(x43481,a871),a871),f336(x43481)),x43482))),f334(f334(f10(a871,a871,x43481),a329),f334(f334(f9(x43481,f886(x43481,a871),a871),f336(x43481)),x43483)))),f334(f334(f3(f886(x43481,a871)),x43482),x43483)) % 169.19/169.64 [4370]E(f334(f39(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,a877,a871),f250(a877)),f334(f196(f878(x43701)),x43702)))),f334(f334(f10(x43701,a871,a877),x43703),f334(f165(x43701),x43702))))),f334(f196(f878(x43701)),f334(f136(x43701,x43703),x43702))) % 169.19/169.64 [4372]E(f334(f196(f878(x43721)),f177(x43721,x43722,x43723)),f334(f39(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,a877,a871),f250(a877)),f334(f196(f878(x43721)),x43722)))),f334(f334(f9(a877,f886(a877,a871),a871),f336(a877)),x43723))))) % 169.19/169.64 [4469]E(f334(f334(f104(f886(f885(f878(x44691),f878(x44691)),a871)),f334(f313(f885(f885(x44691,f878(x44691)),f885(x44691,f878(x44691))),f885(f878(x44691),f878(x44691)),f274(f885(x44691,f878(x44691)),f878(x44691),f885(x44691,f878(x44691)),f878(x44691),f334(f273(x44691,f878(x44691),f878(x44691)),f151(x44691)),f334(f273(x44691,f878(x44691),f878(x44691)),f151(x44691)))),f327(x44691,f878(x44691),x44692,f334(f143(x44691,x44692),x44693)))),f334(f254(f885(f878(x44691),f878(x44691))),f334(f273(f878(x44691),f878(x44691),a871),f334(f334(f9(f878(x44691),f886(f878(x44691),a871),f886(f878(x44691),a871)),f334(f334(f10(f886(a871,a871),f886(f886(f878(x44691),a871),f886(f878(x44691),a871)),f878(x44691)),f10(a871,a871,f878(x44691))),f334(f334(f10(a871,f886(a871,a871),f878(x44691)),a332),f334(f334(f9(f878(x44691),a877,a871),f334(f334(f10(a877,f886(a877,a871),f878(x44691)),a331),f196(f878(x44691)))),f334(a115,x44693))))),f334(f334(f9(f878(x44691),a877,a871),f334(f334(f10(a877,f886(a877,a871),f878(x44691)),a331),f196(f878(x44691)))),f334(a115,x44693)))))),f334(f143(x44691,x44692),f334(a115,x44693))) % 169.19/169.64 [3950]E(f46(a877,f334(a115,f334(f334(f81(a877),f334(f334(f82(a877),x39501),x39502)),x39503)),x39502),f46(a877,f334(a115,x39503),x39502)) % 169.19/169.64 [4212]E(f334(f254(x42121),f334(f334(f20(x42121,a871,a871),f334(f334(f10(a871,f886(a871,a871),x42121),a332),x42122)),x42123)),f334(f334(f104(f886(x42121,a871)),f334(f254(x42121),x42122)),f334(f254(x42121),x42123))) % 169.19/169.64 [4213]E(f334(f254(x42131),f334(f334(f20(x42131,a871,a871),f334(f334(f10(a871,f886(a871,a871),x42131),a333),x42132)),x42133)),f334(f334(f113(f886(x42131,a871)),f334(f254(x42131),x42132)),f334(f254(x42131),x42133))) % 169.19/169.64 [4215]E(f334(f334(f134(x42151),f334(f334(f138(x42151),f46(a877,x42152,f334(f196(f878(x42151)),x42153))),x42153)),f334(f334(f176(x42151),f46(a877,x42152,f334(f196(f878(x42151)),x42153))),x42153)),f334(f334(f334(f190(f878(x42151),f878(x42151)),x42152),f168(x42151)),x42153)) % 169.19/169.64 [4221]E(f334(f254(x42211),f334(f334(f20(x42211,a871,a871),f334(f334(f10(a871,f886(a871,a871),x42211),a337),x42212)),x42213)),f334(f334(f113(f886(x42211,a871)),f334(f80(f886(x42211,a871)),f334(f254(x42211),x42212))),f334(f254(x42211),x42213))) % 169.19/169.64 [4237]E(f334(f334(f81(a877),f334(f196(f878(x42371)),f334(f136(x42371,x42372),x42373))),f334(f196(f878(x42371)),f334(f136(x42371,f334(f334(f10(a871,a871,x42371),a329),x42372)),x42373))),f334(f196(f878(x42371)),x42373)) % 169.19/169.64 [4262]P104(f334(f334(f249(f886(x42621,a871)),f334(f334(f113(f886(x42621,a871)),f42(f886(x42621,a871),x42622)),f42(f886(x42621,a871),x42623))),f42(f886(x42621,a871),f334(f334(f104(f886(f886(x42621,a871),a871)),x42622),x42623)))) % 169.19/169.64 [4276]E(f334(f173(x42761),f334(f136(x42761,f334(f334(f10(a871,a871,x42761),a329),f334(f334(f9(x42761,x42761,a871),a331),x42762))),x42763)),f334(f334(f3(f886(x42761,a871)),f334(f173(x42761),x42763)),f334(f334(f312(x42761),x42762),f195(f886(x42761,a871))))) % 169.19/169.64 [4285]P104(f334(f334(f249(f886(f885(x42851,x42851),a871)),f334(f334(f113(f886(f885(x42851,x42851),a871)),f310(x42851,x42852)),f310(x42851,x42853))),f310(x42851,f334(f334(f113(f886(f885(x42851,x42851),a871)),x42852),x42853)))) % 169.19/169.64 [4310]E(f334(f334(f82(a877),f334(a115,f334(a115,f2(a877)))),f334(f334(f8(a877,a877),f334(f334(f10(a877,a877,a877),f334(f81(a877),x43101)),f334(f334(f9(a877,a877,a877),f82(a877)),x43102))),f334(f255(a877),x43103))),f334(f334(f82(a877),x43103),f334(f334(f81(a877),x43101),f334(f334(f81(a877),x43101),f334(f334(f82(a877),f334(f334(f3(a877),x43103),f79(a877))),x43102))))) % 169.19/169.64 [4320]E(f334(f254(x43201),f334(f334(f20(x43201,a871,a871),f334(f334(f10(a871,f886(a871,a871),x43201),a332),f334(f334(f9(x43201,f886(x43201,a871),a871),f336(x43201)),f334(f173(x43201),x43202)))),x43203)),f334(f173(x43201),f334(f136(x43201,x43203),x43202))) % 169.19/169.64 [4468]E(f334(f254(x44681),f334(f334(f10(f886(a877,a871),a871,x44681),f88(a877)),f334(f334(f9(x44681,f886(a877,a871),f886(a877,a871)),f334(f334(f10(f886(a877,f886(a871,a871)),f886(f886(a877,a871),f886(a877,a871)),x44681),f20(a877,a871,a871)),f334(f334(f10(f886(a877,a871),f886(a877,f886(a871,a871)),x44681),f334(f10(a871,f886(a871,a871),a877),a332)),f334(f334(f9(x44681,f886(a877,x44681),f886(a877,a871)),f334(f334(f10(f886(x44681,a871),f886(f886(a877,x44681),f886(a877,a871)),x44681),f10(x44681,a871,a877)),a331)),f334(f165(x44681),x44682))))),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,a877,a871),f250(a877)),f334(f196(f878(x44681)),x44682)))),f334(f334(f9(a877,f886(a877,a871),a871),f336(a877)),x44683))))),f334(f173(x44681),f177(x44681,x44682,x44683))) % 169.19/169.64 [4360]E(f334(f254(x43601),f334(f334(f20(x43601,a871,a871),f334(f334(f10(a871,f886(a871,a871),x43601),a337),f334(f334(f10(a871,a871,x43601),a329),f334(f334(f9(x43601,x43601,a871),a331),x43602)))),x43603)),f334(f334(f312(x43601),x43602),f334(f254(x43601),x43603))) % 169.19/169.64 [4392]E(f334(f334(f154(f885(x43921,a877),x43921),f268(x43921,a877)),f334(f136(f885(x43921,a877),f334(f334(f9(f885(x43921,a877),f886(a877,a871),a871),f334(f334(f10(a877,f886(f886(a877,a871),a871),f885(x43921,a877)),f336(a877)),f272(x43921,a877))),x43922)),f334(f334(f183(x43921,a877),x43923),f139(a877,f334(f304(a877,f2(a877)),f334(f196(f878(x43921)),x43923)))))),f177(x43921,x43923,x43922)) % 169.19/169.64 [4422]E(f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f8(a877,a1),f334(f334(f10(a1,a1,a877),f334(f81(a1),x44221)),f334(f334(f9(a877,a1,a1),f334(f334(f10(a1,f886(a1,a1),a877),f82(a1)),f103(a1))),x44222))),f334(f255(a877),x44223))),f334(f334(f82(a1),f334(f103(a1),x44223)),f334(f334(f81(a1),x44221),f334(f334(f81(a1),x44221),f334(f334(f82(a1),f334(f103(a1),f334(f334(f3(a877),x44223),f79(a877)))),x44222))))) % 169.19/169.64 [4462]E(f334(f254(f885(x44621,x44622)),f334(f273(x44621,x44622,a871),f334(f334(f9(x44621,f886(f885(x44622,x44621),a871),f886(x44622,a871)),f334(f334(f10(f886(x44622,f886(f886(f885(x44622,x44621),a871),a871)),f886(f886(f885(x44622,x44621),a871),f886(x44622,a871)),x44621),f9(x44622,f886(f885(x44622,x44621),a871),a871)),f334(f334(f10(f886(x44622,f885(x44622,x44621)),f886(x44622,f886(f886(f885(x44622,x44621),a871),a871)),x44621),f334(f10(f885(x44622,x44621),f886(f886(f885(x44622,x44621),a871),a871),x44622),f336(f885(x44622,x44621)))),f334(f9(x44622,x44621,f885(x44622,x44621)),f269(x44622,x44621))))),x44623))),f334(f289(x44622,x44621),x44623)) % 169.19/169.64 [4484]E(f334(f254(f878(x44841)),f334(f334(f10(f886(x44841,a871),a871,f878(x44841)),f88(x44841)),f334(f334(f10(f886(x44841,f886(f878(x44841),a871)),f886(x44841,a871),f878(x44841)),f334(f10(f886(f878(x44841),a871),a871,x44841),f88(f878(x44841)))),f334(f334(f9(f878(x44841),f886(x44841,f886(f878(x44841),a871)),f886(x44841,f886(f878(x44841),a871))),f334(f334(f10(f886(x44841,f886(f886(f878(x44841),a871),f886(f878(x44841),a871))),f886(f886(x44841,f886(f878(x44841),a871)),f886(x44841,f886(f878(x44841),a871))),f878(x44841)),f20(x44841,f886(f878(x44841),a871),f886(f878(x44841),a871))),f334(f334(f10(f886(x44841,f886(f878(x44841),f886(a871,a871))),f886(x44841,f886(f886(f878(x44841),a871),f886(f878(x44841),a871))),f878(x44841)),f334(f10(f886(f878(x44841),f886(a871,a871)),f886(f886(f878(x44841),a871),f886(f878(x44841),a871)),x44841),f20(f878(x44841),a871,a871))),f334(f334(f10(f886(x44841,f886(f878(x44841),a871)),f886(x44841,f886(f878(x44841),f886(a871,a871))),f878(x44841)),f334(f10(f886(f878(x44841),a871),f886(f878(x44841),f886(a871,a871)),x44841),f334(f10(a871,f886(a871,a871),f878(x44841)),a332))),f334(f334(f9(f878(x44841),f886(x44841,f886(f878(x44841),f878(x44841))),f886(x44841,f886(f878(x44841),a871))),f334(f334(f10(f886(f886(f878(x44841),f878(x44841)),f886(f878(x44841),a871)),f886(f886(x44841,f886(f878(x44841),f878(x44841))),f886(x44841,f886(f878(x44841),a871))),f878(x44841)),f10(f886(f878(x44841),f878(x44841)),f886(f878(x44841),a871),x44841)),f334(f334(f10(f886(f878(x44841),a871),f886(f886(f878(x44841),f878(x44841)),f886(f878(x44841),a871)),f878(x44841)),f10(f878(x44841),a871,f878(x44841))),a331))),f151(x44841)))))),f334(f334(f9(x44841,f886(f878(x44841),a871),f886(f878(x44841),a871)),f334(f334(f10(f886(a871,a871),f886(f886(f878(x44841),a871),f886(f878(x44841),a871)),x44841),f10(a871,a871,f878(x44841))),f334(f334(f10(a871,f886(a871,a871),x44841),a332),f334(f334(f9(x44841,f886(x44841,a871),a871),f336(x44841)),x44842)))),f334(f334(f9(f878(x44841),f886(f878(x44841),a871),a871),f336(f878(x44841))),x44843)))))),f175(x44841,x44842,x44843)) % 169.19/169.64 [4481]E(f334(f334(f87(a1,f885(a1,a1)),f334(f334(f3(a1),x44811),x44812)),f334(f334(f9(a1,f885(a1,a1),f885(a1,a1)),f334(f334(f20(a1,f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),f334(f334(f10(a871,f886(f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),a1),f99(f885(a1,a1))),f334(f249(a1),f2(a1)))),f334(f269(a1,a1),f334(f334(f81(a1),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x44813)),f79(a1))))),f334(f334(f269(a1,a1),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x44813)),x44811))),f334(f45(x44812),f334(f334(f269(a1,a1),x44813),x44811))) % 169.19/169.64 [4512]~E(f33(x45121,x45122),f34(x45123,x45124)) % 169.19/169.64 [4532]~E(f334(a26,x45321),f29(x45322,x45323,x45324)) % 169.19/169.64 [4533]~E(f334(a26,x45331),f31(x45332,x45333,x45334)) % 169.19/169.64 [4534]~E(f334(a26,x45341),f30(x45342,x45343,x45344)) % 169.19/169.64 [4535]~E(f29(x45351,x45352,x45353),f334(a26,x45354)) % 169.19/169.64 [4536]~E(f31(x45361,x45362,x45363),f334(a26,x45364)) % 169.19/169.64 [4537]~E(f30(x45371,x45372,x45373),f334(a26,x45374)) % 169.19/169.64 [3491]E(f334(f334(f334(f73(x34911,x34912),x34913),x34914),f334(x34913,x34914)),x34913) % 169.19/169.64 [3499]E(f119(x34991,f334(x34992,x34993),f334(x34994,x34993)),f334(f212(x34991,x34992,x34994),x34993)) % 169.19/169.64 [3552]E(f334(f334(f260(x35521,x35522,x35523),x35524),f2(a877)),x35522) % 169.19/169.64 [3593]E(f192(x35931,x35932,x35933,f334(a115,x35934)),f334(x35933,x35934)) % 169.19/169.64 [3634]E(f171(x36341,x36342,f171(x36341,x36343,x36344)),f171(x36341,x36343,f171(x36341,x36342,x36344))) % 169.19/169.64 [3635]E(f119(x36351,f127(x36351,x36352,x36353),x36354),f127(x36351,x36352,f119(x36351,x36353,x36354))) % 169.19/169.64 [3769]E(f334(f243(x37691,x37692,x37693,x37694),f198(x37692)),x37693) % 169.19/169.64 [3771]E(f334(f156(x37711,x37712,x37713,x37714),f116(x37712)),x37713) % 169.19/169.64 [3772]E(f334(f142(x37721,x37722,x37723,x37724),f116(x37722)),x37724) % 169.19/169.64 [3810]E(f334(f196(f882(x38101,x38102)),f229(x38101,x38102,x38103,x38104)),f2(a877)) % 169.19/169.64 [3880]E(f334(f334(f134(x38801),f170(x38801,x38802,x38803)),f170(x38801,x38804,x38803)),f334(f334(f134(x38801),f170(x38801,x38804,x38803)),f170(x38801,x38802,x38803))) % 169.19/169.64 [3893]E(f334(f243(f881(x38931),x38932,f198(x38931),f334(f18(f881(x38931),x38932),f198(x38931))),f334(x38933,x38934)),f198(x38931)) % 169.19/169.64 [3938]E(f334(f334(f113(f886(x39381,a871)),f185(x39381,x39382,x39383)),f185(x39381,x39382,x39384)),f185(x39381,x39382,f186(x39381,x39382,x39384,x39383))) % 169.19/169.64 [3970]E(f334(f334(f275(x39701,x39702,x39703,f885(x39702,x39703)),x39704),f269(x39702,x39703)),x39704) % 169.19/169.64 [3979]E(f244(x39791,x39792,x39793,x39794,f198(x39792)),x39793) % 169.19/169.64 [3980]E(f188(x39801,x39802,x39803,x39804,f116(x39802)),x39803) % 169.19/169.64 [3981]E(f188(x39811,x39812,x39813,f116(x39811),x39814),x39813) % 169.19/169.64 [4269]P43(x42691,x42692,x42693,x42694,f195(f886(x42691,a871)),x42694) % 169.19/169.64 [3292]E(f334(f334(f18(x32921,x32922),x32923),x32924),x32923) % 169.19/169.64 [3408]E(f334(f334(f207(x34081,x34082),x34083),f334(f241(x34081),x34084)),f334(f241(x34082),f334(x34083,x34084))) % 169.19/169.64 [3583]E(f171(x35831,x35832,f334(f136(x35831,x35833),x35834)),f334(f136(x35831,x35833),f171(x35831,x35832,x35834))) % 169.19/169.64 [3618]E(f334(f334(f66(x36181,x36182,x36183),x36184),f195(f886(x36181,a871))),x36184) % 169.19/169.64 [3641]E(f334(f334(f165(x36411),f334(f334(f151(x36411),x36412),x36413)),f334(a115,x36414)),f334(f334(f165(x36411),x36413),x36414)) % 169.19/169.64 [3684]P31(x36841,f2(a877),f334(f334(f334(f93(x36841),x36842),f334(a26,x36843)),x36844)) % 169.19/169.64 [3709]E(f334(f334(x37091,x37092),f334(f191(x37093,x37094,x37091),x37092)),f334(f191(x37093,x37094,x37091),f334(a115,x37092))) % 169.19/169.64 [3808]E(f334(f334(f159(x38081,f334(f334(f151(x38081),x38082),x38083)),f2(a877)),x38084),f334(f334(f151(x38081),x38084),x38083)) % 169.19/169.64 [3820]E(f334(f334(f44(f886(x38201,a871),f886(x38202,a871)),x38203),f313(x38201,x38202,x38204)),f334(f313(x38201,x38202,x38204),f41(f886(x38201,a871),x38203))) % 169.19/169.64 [3821]E(f334(f334(f44(f886(x38211,a871),f886(x38212,a871)),x38213),f314(x38212,x38211,x38214)),f334(f314(x38212,x38211,x38214),f41(f886(x38211,a871),x38213))) % 169.19/169.64 [3920]E(f185(x39201,x39202,f189(x39201,x39202,x39203,x39204)),f334(f334(f104(f886(x39201,a871)),f185(x39201,x39202,x39203)),x39204)) % 169.19/169.64 [3924]E(f334(f129(x39241,x39242),f127(x39241,x39243,x39244)),f334(f334(f81(a877),f334(f334(f81(a877),f334(x39242,x39243)),f334(f129(x39241,x39242),x39244))),f334(a115,f2(a877)))) % 169.19/169.64 [3944]E(f334(f142(x39441,x39442,f334(f9(x39442,x39441,x39441),x39443),x39444),f334(f169(x39442),f116(x39442))),x39444) % 169.19/169.64 [3992]E(f77(x39921,x39922,x39923,x39924,f195(f886(x39921,a871))),x39923) % 169.19/169.64 [4038]E(f334(f334(f334(f334(f73(x40381,f881(x40382)),f334(f18(f881(x40382),x40381),f198(x40382))),x40383),f198(x40382)),x40384),f198(x40382)) % 169.19/169.64 [4195]E(f334(f273(x41951,x41952,x41953),f334(f334(f10(f886(x41952,f885(x41951,x41952)),f886(x41952,x41953),x41951),f334(f10(f885(x41951,x41952),x41953,x41952),x41954)),f269(x41951,x41952))),x41954) % 169.19/169.64 [3489]E(f334(f272(x34891,x34892),f334(f334(f269(x34891,x34892),x34893),x34894)),x34894) % 169.19/169.64 [3490]E(f334(f268(x34901,x34902),f334(f334(f269(x34901,x34902),x34903),x34904)),x34903) % 169.19/169.64 [3525]E(f334(f196(f878(x35251)),f334(f334(f154(x35252,x35251),x35253),x35254)),f334(f196(f878(x35252)),x35254)) % 169.19/169.64 [3526]E(f334(f196(f878(x35261)),f334(f334(f159(x35261,x35262),x35263),x35264)),f334(f196(f878(x35261)),x35262)) % 169.19/169.64 [3546]E(f334(f334(f138(x35461),f334(a115,x35462)),f334(f334(f151(x35461),x35463),x35464)),f334(f334(f138(x35461),x35462),x35464)) % 169.19/169.64 [3613]E(f334(f334(f176(x36131),x36132),f170(x36131,x36133,x36134)),f170(x36131,f334(f334(f247(a877),x36132),x36133),x36134)) % 169.19/169.64 [3614]E(f334(f334(f138(x36141),x36142),f170(x36141,x36143,x36144)),f170(x36141,f334(f334(f3(a877),x36143),x36142),x36144)) % 169.19/169.64 [3620]E(f334(f334(f312(x36201),x36202),f334(f334(f312(x36201),x36203),x36204)),f334(f334(f312(x36201),x36203),f334(f334(f312(x36201),x36202),x36204))) % 169.19/169.64 [3623]E(f334(f334(f154(x36231,x36232),x36233),f117(x36231,x36234)),f117(x36232,f334(f334(f154(x36231,x36232),x36233),x36234))) % 169.19/169.64 [3639]E(f334(f169(x36391),f334(f334(f154(x36392,x36391),x36393),x36394)),f334(f334(f154(x36392,x36391),x36393),f334(f169(x36392),x36394))) % 169.19/169.64 [3640]E(f334(f334(f154(x36401,x36402),x36403),f334(f172(x36401),x36404)),f334(f172(x36402),f334(f334(f154(x36401,x36402),x36403),x36404))) % 169.19/169.64 [3651]E(f334(f334(f176(x36511),f334(a115,x36512)),f334(f334(f151(x36511),x36513),x36514)),f334(f334(f151(x36511),x36513),f334(f334(f176(x36511),x36512),x36514))) % 169.19/169.64 [3655]E(f334(f173(x36551),f334(f334(f154(x36552,x36551),x36553),x36554)),f334(f313(x36552,x36551,x36553),f334(f173(x36552),x36554))) % 169.19/169.64 [3670]E(f334(f334(f154(x36701,x36702),f334(f18(x36702,x36701),x36703)),x36704),f170(x36702,f334(f196(f878(x36701)),x36704),x36703)) % 169.19/169.64 [3708]E(f19(x37081,x37082,x37083,f334(a5,f334(a115,f334(a21,x37084)))),f334(x37083,x37084)) % 169.19/169.64 [3711]E(f334(f334(f134(x37111),f334(f136(x37111,x37112),x37113)),f334(f136(x37111,x37112),x37114)),f334(f136(x37111,x37112),f334(f334(f134(x37111),x37113),x37114))) % 169.19/169.64 [3724]E(f152(x37241,f334(f334(f154(x37242,x37241),x37243),f152(x37242,x37244))),f152(x37241,f334(f334(f154(x37242,x37241),x37243),x37244))) % 169.19/169.64 [3740]E(f334(f289(x37401,x37401),f334(f334(f290(x37402,x37401),x37403),x37404)),f334(f334(f290(x37402,x37401),f334(f289(x37402,x37402),x37403)),x37404)) % 169.19/169.64 [3751]E(f334(f334(f291(x37511,x37512,x37513),x37514),f195(f886(f885(x37512,x37513),a871))),f195(f886(f885(x37511,x37513),a871))) % 169.19/169.64 [3752]E(f334(f334(f176(x37521),f334(f334(f3(a877),x37522),x37523)),f334(f334(f138(x37521),x37523),x37524)),f334(f334(f138(x37521),x37523),f334(f334(f176(x37521),x37522),x37524))) % 169.19/169.64 [3773]E(f334(f334(f134(x37731),f170(x37731,x37732,x37733)),f170(x37731,x37734,x37733)),f170(x37731,f334(f334(f81(a877),x37732),x37734),x37733)) % 169.19/169.64 [3800]E(f41(f886(x38001,a871),f334(f313(x38002,f886(x38001,a871),x38003),x38004)),f334(f334(f44(x38002,f886(x38001,a871)),x38004),x38003)) % 169.19/169.64 [3801]E(f42(f886(x38011,a871),f334(f313(x38012,f886(x38011,a871),x38013),x38014)),f334(f334(f43(x38012,f886(x38011,a871)),x38014),x38013)) % 169.19/169.64 [3802]E(f334(f196(f878(f885(x38021,x38022))),f334(f334(f183(x38021,x38022),x38023),x38024)),f334(f334(f247(a877),f334(f196(f878(x38021)),x38023)),f334(f196(f878(x38022)),x38024))) % 169.19/169.64 [3804]E(f334(f314(x38041,x38042,x38043),f334(f80(f886(x38042,a871)),x38044)),f334(f80(f886(x38041,a871)),f334(f314(x38041,x38042,x38043),x38044))) % 169.19/169.64 [3835]E(f334(f189(x38351,x38352,x38353,f195(f886(x38351,a871))),x38354),f198(x38352)) % 169.19/169.64 [3856]E(f334(f314(x38561,x38562,x38563),f334(f254(x38562),x38564)),f334(f254(x38561),f334(f334(f10(x38562,a871,x38561),x38564),x38563))) % 169.19/169.64 [3874]E(f334(f334(f165(x38741),f334(f334(f134(x38741),x38742),f334(f334(f151(x38741),x38743),x38744))),f334(f196(f878(x38741)),x38742)),x38743) % 169.19/169.64 [3879]E(f334(f189(x38791,x38792,f334(f18(f881(x38792),x38791),f198(x38792)),x38793),x38794),f198(x38792)) % 169.19/169.64 [3901]E(f334(f313(x39011,x39012,x39013),f334(f314(x39011,x39012,x39013),x39014)),f334(f334(f104(f886(x39012,a871)),x39014),f334(f313(x39011,x39012,x39013),f257(f886(x39011,a871))))) % 169.19/169.64 [3919]P104(f334(f334(f336(x39191),f334(x39192,x39193)),f334(f313(x39194,x39191,x39192),f257(f886(x39194,a871))))) % 169.19/169.64 [3931]E(f334(f334(f134(x39311),f170(x39311,x39312,x39313)),f334(f334(f151(x39311),x39313),x39314)),f334(f334(f151(x39311),x39313),f334(f334(f134(x39311),f170(x39311,x39312,x39313)),x39314))) % 169.19/169.64 [3933]E(f334(f334(f271(x39331,x39332),f334(f173(x39331),x39333)),f334(f18(f886(x39332,a871),x39331),f334(f173(x39332),x39334))),f334(f173(f885(x39331,x39332)),f61(x39331,x39332,x39333,x39334))) % 169.19/169.64 [3947]E(f155(x39471,x39472,f334(f334(f151(x39471),x39473),x39474)),f334(f334(f81(a877),f334(f334(f81(a877),f334(x39472,x39473)),f155(x39471,x39472,x39474))),f334(a115,f2(a877)))) % 169.19/169.64 [3961]E(f192(f878(x39611),f334(f334(f151(x39611),x39612),x39613),f334(f334(f9(a877,f878(x39611),f878(x39611)),f138(x39611)),x39613),x39614),f334(f334(f138(x39611),x39614),f334(f334(f151(x39611),x39612),x39613))) % 169.19/169.64 [3962]P21(x39621,f885(x39622,x39621),f338(x39623,x39624,x39622,x39621),f334(f334(f44(x39622,f886(x39621,a871)),x39624),x39623)) % 169.19/169.64 [3971]E(f334(f334(f3(f886(x39711,a871)),f334(f334(f3(f886(x39711,a871)),x39712),x39713)),f334(f334(f312(x39711),x39714),f195(f886(x39711,a871)))),f334(f334(f3(f886(x39711,a871)),x39712),f334(f334(f312(x39711),x39714),x39713))) % 169.19/169.64 [3983]E(f334(f334(f190(f886(x39831,x39832),f886(x39831,x39832)),x39833),f74(x39832,x39832,x39831,x39834)),f74(x39832,x39832,x39831,f334(f334(f190(x39832,x39832),x39833),x39834))) % 169.19/169.64 [4061]E(f334(f334(f334(f190(f878(x40611),f878(x40611)),x40612),f168(x40611)),f334(f334(f334(f190(f878(x40611),f878(x40611)),x40613),f168(x40611)),x40614)),f334(f334(f334(f190(f878(x40611),f878(x40611)),f334(f334(f81(a877),x40612),x40613)),f168(x40611)),x40614)) % 169.19/169.64 [4149]P104(f334(f334(f249(f886(x41491,a871)),f334(f173(x41491),f334(f334(f159(x41491,x41492),x41493),x41494))),f334(f334(f312(x41491),x41494),f334(f173(x41491),x41492)))) % 169.19/169.64 [4185]E(f334(f334(f44(f886(x41851,a871),f886(f885(x41851,x41852),a871)),x41853),f334(f334(f9(f886(x41851,a871),f886(x41851,f886(x41852,a871)),f886(f885(x41851,x41852),a871)),f271(x41851,x41852)),x41854)),f334(f334(f271(x41851,x41852),f41(f886(x41851,a871),x41853)),x41854)) % 169.19/169.64 [4223]E(f218(x42231,x42232,x42233,f334(f74(x42232,f886(a102,f886(a102,f886(f885(a102,a102),f886(a102,f879(x42232))))),x42231,f217(x42232)),x42234)),f219(x42231,x42232,x42234,x42233)) % 169.19/169.64 [4240]E(f214(x42401,x42402,x42403,f334(f74(x42402,f886(a102,f886(a102,f886(f885(a102,a102),f886(a102,f879(f881(x42402)))))),x42401,f213(x42402)),x42404)),f215(x42401,x42402,x42404,x42403)) % 169.19/169.64 [4245]P104(f334(f68(x42451,x42452,x42453,x42454,f195(f886(x42451,a871))),x42454)) % 169.19/169.64 [4287]E(f334(f334(f44(x42871,f886(x42872,a871)),x42873),f334(f334(f9(x42871,f886(x42872,a871),f886(x42872,a871)),f334(f334(f10(x42872,f886(f886(x42872,a871),f886(x42872,a871)),x42871),f312(x42872)),x42874)),f195(f886(x42872,a871)))),f334(f313(x42871,x42872,x42874),x42873)) % 169.19/169.64 [4294]P104(f334(f334(f249(f886(x42941,a871)),f334(f265(x42942,x42941),f334(f334(f104(f886(f885(x42942,x42941),a871)),x42943),x42944))),f334(f334(f104(f886(x42941,a871)),f334(f265(x42942,x42941),x42943)),f334(f265(x42942,x42941),x42944)))) % 169.19/169.64 [4295]P104(f334(f334(f249(f886(x42951,a871)),f334(f267(x42951,x42952),f334(f334(f104(f886(f885(x42951,x42952),a871)),x42953),x42954))),f334(f334(f104(f886(x42951,a871)),f334(f267(x42951,x42952),x42953)),f334(f267(x42951,x42952),x42954)))) % 169.19/169.64 [4357]P104(f334(f334(f249(f886(f885(x43571,x43572),a871)),f334(f313(x43572,f885(x43571,x43572),f338(x43573,x43574,x43571,x43572)),f334(f334(f44(x43571,f886(x43572,a871)),x43574),x43573))),f334(f334(f271(x43571,x43572),x43574),x43573))) % 169.19/169.64 [4358]E(f334(f121(x43581,f885(x43581,x43582),x43583),f334(f334(f10(f886(x43582,f879(f885(x43581,x43582))),f879(f885(x43581,x43582)),x43581),f121(x43582,f885(x43581,x43582),x43584)),f334(f334(f10(f886(x43582,f885(x43581,x43582)),f886(x43582,f879(f885(x43581,x43582))),x43581),f334(f10(f885(x43581,x43582),f879(f885(x43581,x43582)),x43582),f126(f885(x43581,x43582)))),f269(x43581,x43582)))),f131(x43581,x43582,x43583,x43584)) % 169.19/169.64 [4398]E(f91(f885(x43981,x43982),f334(f273(x43981,x43982,a871),f334(f334(f9(x43981,f886(x43982,a871),f886(x43982,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x43982,a871),f886(x43982,a871)),x43981),f10(a871,a871,x43982)),f334(f334(f10(a871,f886(a871,a871),x43981),a332),f334(a331,x43983)))),f334(a331,x43984)))),f334(f334(f269(x43981,x43982),x43983),x43984)) % 169.19/169.64 [4399]E(f86(f885(x43991,x43992),f334(f273(x43991,x43992,a871),f334(f334(f9(x43991,f886(x43992,a871),f886(x43992,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x43992,a871),f886(x43992,a871)),x43991),f10(a871,a871,x43992)),f334(f334(f10(a871,f886(a871,a871),x43991),a332),f334(a331,x43993)))),f334(a331,x43994)))),f334(f334(f269(x43991,x43992),x43993),x43994)) % 169.19/169.64 [4470]E(f334(f334(f273(f878(x44701),f878(x44701),f885(f878(x44701),f878(x44701))),f334(f334(f20(f878(x44701),f886(f878(x44701),f885(f878(x44701),f878(x44701))),f886(f878(x44701),f885(f878(x44701),f878(x44701)))),f334(f334(f10(f886(f878(x44701),f886(f885(f878(x44701),f878(x44701)),f885(f878(x44701),f878(x44701)))),f886(f886(f878(x44701),f885(f878(x44701),f878(x44701))),f886(f878(x44701),f885(f878(x44701),f878(x44701)))),f878(x44701)),f20(f878(x44701),f885(f878(x44701),f878(x44701)),f885(f878(x44701),f878(x44701)))),f334(f334(f10(f886(f878(x44701),f885(f878(x44701),f878(x44701))),f886(f878(x44701),f886(f885(f878(x44701),f878(x44701)),f885(f878(x44701),f878(x44701)))),f878(x44701)),f334(f10(f885(f878(x44701),f878(x44701)),f886(f885(f878(x44701),f878(x44701)),f885(f878(x44701),f878(x44701))),f878(x44701)),f334(f99(f885(f878(x44701),f878(x44701))),f334(x44702,x44703)))),f334(f334(f10(f878(x44701),f886(f878(x44701),f885(f878(x44701),f878(x44701))),f878(x44701)),f269(f878(x44701),f878(x44701))),f334(f151(x44701),x44703))))),f334(f334(f9(f878(x44701),f886(f878(x44701),f878(x44701)),f886(f878(x44701),f885(f878(x44701),f878(x44701)))),f334(f334(f10(f886(f878(x44701),f885(f878(x44701),f878(x44701))),f886(f886(f878(x44701),f878(x44701)),f886(f878(x44701),f885(f878(x44701),f878(x44701)))),f878(x44701)),f10(f878(x44701),f885(f878(x44701),f878(x44701)),f878(x44701))),f269(f878(x44701),f878(x44701)))),f334(f151(x44701),x44703)))),f167(x44701,x44702,x44704)),f167(x44701,x44702,f334(f334(f151(x44701),x44703),x44704))) % 169.19/169.64 [4476]E(f334(f142(f886(x44761,f881(x44762)),f885(x44761,x44762),f334(f9(f885(x44761,x44762),f886(x44761,f881(x44762)),f886(x44761,f881(x44762))),f334(f273(x44761,x44762,f886(f886(x44761,f881(x44762)),f886(x44761,f881(x44762)))),f334(f334(f9(x44761,f886(x44762,f881(x44762)),f886(x44762,f886(f886(x44761,f881(x44762)),f886(x44761,f881(x44762))))),f334(f334(f10(f886(f881(x44762),f886(f886(x44761,f881(x44762)),f886(x44761,f881(x44762)))),f886(f886(x44762,f881(x44762)),f886(x44762,f886(f886(x44761,f881(x44762)),f886(x44761,f881(x44762))))),x44761),f10(f881(x44762),f886(f886(x44761,f881(x44762)),f886(x44761,f881(x44762))),x44762)),f334(f334(f10(f886(f886(x44761,f881(x44762)),f886(f881(x44762),f886(x44761,f881(x44762)))),f886(f881(x44762),f886(f886(x44761,f881(x44762)),f886(x44761,f881(x44762)))),x44761),f9(f886(x44761,f881(x44762)),f881(x44762),f886(x44761,f881(x44762)))),f334(f9(f886(x44761,f881(x44762)),x44761,f886(f881(x44762),f886(x44761,f881(x44762)))),f73(x44761,f881(x44762)))))),f241(x44762)))),x44763),f334(f169(f885(x44761,x44762)),x44764)),f186(x44761,x44762,x44763,f334(f179(x44761,x44762),x44764))) % 169.19/169.64 [3565]E(f334(f196(f876(x35651)),f334(f334(f334(f93(x35651),x35652),x35653),x35654)),f2(a877)) % 169.19/169.64 [3687]E(f334(f334(f176(x36871),x36872),f334(f334(f176(x36871),x36873),x36874)),f334(f334(f176(x36871),f334(f334(f247(a877),x36872),x36873)),x36874)) % 169.19/169.64 [3688]E(f334(f334(f138(x36881),x36882),f334(f334(f138(x36881),x36883),x36884)),f334(f334(f138(x36881),f334(f334(f81(a877),x36882),x36883)),x36884)) % 169.19/169.64 [3700]E(f334(f334(f134(x37001),f334(f334(f151(x37001),x37002),x37003)),x37004),f334(f334(f151(x37001),x37002),f334(f334(f134(x37001),x37003),x37004))) % 169.19/169.64 [3701]E(f334(f334(f134(x37011),f334(f334(f134(x37011),x37012),x37013)),x37014),f334(f334(f134(x37011),x37012),f334(f334(f134(x37011),x37013),x37014))) % 169.19/169.64 [3784]E(f334(f334(f165(x37841),f334(f334(f151(x37841),x37842),x37843)),x37844),f192(x37841,x37842,f334(f165(x37841),x37843),x37844)) % 169.19/169.64 [3793]E(f334(f334(f190(x37931,x37931),x37932),f334(f334(f190(x37931,x37931),x37933),x37934)),f334(f334(f190(x37931,x37931),f334(f334(f82(a877),x37933),x37932)),x37934)) % 169.19/169.64 [3823]E(f334(f334(f113(f886(x38231,a871)),x38232),f334(f334(f312(x38231),x38233),x38234)),f334(f334(f312(x38231),x38233),f334(f334(f113(f886(x38231,a871)),x38232),x38234))) % 169.19/169.64 [3838]E(f334(f334(f334(f190(x38381,x38381),x38382),x38383),f334(x38383,x38384)),f334(x38383,f334(f334(f334(f190(x38381,x38381),x38382),x38383),x38384))) % 169.19/169.64 [3846]E(f334(f334(f291(x38461,x38462,x38463),f195(f886(f885(x38461,x38462),a871))),x38464),f195(f886(f885(x38461,x38463),a871))) % 169.19/169.64 [3862]E(f334(f334(f113(f886(x38621,a871)),f334(f334(f312(x38621),x38622),x38623)),x38624),f334(f334(f312(x38621),x38622),f334(f334(f113(f886(x38621,a871)),x38623),x38624))) % 169.19/169.64 [3882]E(f186(x38821,x38822,f334(f179(x38821,x38822),x38823),f334(f179(x38821,x38822),x38824)),f334(f179(x38821,x38822),f334(f334(f134(f885(x38821,x38822)),x38824),x38823))) % 169.19/169.64 [3883]E(f334(f39(f885(x38831,x38832)),f334(f334(f271(x38831,x38832),x38833),f334(f18(f886(x38832,a871),x38831),x38834))),f334(f334(f82(a877),f334(f39(x38831),x38833)),f334(f39(x38832),x38834))) % 169.19/169.64 [3890]E(f334(f334(f104(f886(x38901,a871)),f334(f334(f312(x38901),x38902),x38903)),f334(f334(f312(x38901),x38902),x38904)),f334(f334(f312(x38901),x38902),f334(f334(f104(f886(x38901,a871)),x38903),x38904))) % 169.19/169.64 [3905]E(f334(f334(f113(f886(x39051,a871)),x39052),f334(f334(f113(f886(x39051,a871)),x39053),x39054)),f334(f334(f113(f886(x39051,a871)),x39053),f334(f334(f113(f886(x39051,a871)),x39052),x39054))) % 169.19/169.64 [3906]E(f334(f334(f104(f886(x39061,a871)),x39062),f334(f334(f104(f886(x39061,a871)),x39063),x39064)),f334(f334(f104(f886(x39061,a871)),x39063),f334(f334(f104(f886(x39061,a871)),x39062),x39064))) % 169.19/169.64 [3915]E(f66(x39151,x39152,f334(f334(f10(x39152,f886(x39152,x39152),x39151),x39153),x39154)),f334(f67(x39152,x39151,x39153),x39154)) % 169.19/169.64 [3925]E(f181(x39251,f334(f334(f154(f878(x39252),f878(x39251)),f334(f154(x39252,x39251),x39253)),x39254)),f334(f334(f154(f878(x39252),f878(x39251)),f334(f154(x39252,x39251),x39253)),f181(x39252,x39254))) % 169.19/169.64 [3943]E(f334(f142(f878(x39431),f878(x39431),f134(x39431),f116(x39431)),f334(f334(f154(x39432,f878(x39431)),x39433),x39434)),f164(x39432,x39431,x39433,x39434)) % 169.19/169.64 [3946]E(f189(x39461,x39462,x39463,f334(f80(f886(x39461,a871)),f334(f334(f312(x39461),x39464),f195(f886(x39461,a871))))),f334(f334(f334(f73(x39461,f881(x39462)),x39463),x39464),f198(x39462))) % 169.19/169.64 [3988]E(f334(f334(f334(f73(x39881,f881(x39882)),f334(f179(x39881,x39882),x39883)),f334(f268(x39881,x39882),x39884)),f334(f241(x39882),f334(f272(x39881,x39882),x39884))),f334(f179(x39881,x39882),f334(f334(f151(f885(x39881,x39882)),x39884),x39883))) % 169.19/169.64 [4005]E(f334(f74(x40051,x40051,x40051,f334(f334(f190(x40051,x40051),x40052),x40053)),f334(f334(f190(x40051,x40051),x40054),x40053)),f334(f334(f190(x40051,x40051),f334(f334(f81(a877),x40052),x40054)),x40053)) % 169.19/169.64 [4030]E(f334(f334(f104(f886(x40301,a871)),f334(f334(f3(f886(x40301,a871)),x40302),x40303)),f334(f334(f3(f886(x40301,a871)),x40302),x40304)),f334(f334(f3(f886(x40301,a871)),x40302),f334(f334(f113(f886(x40301,a871)),x40303),x40304))) % 169.19/169.64 [4031]E(f334(f334(f113(f886(x40311,a871)),f334(f334(f3(f886(x40311,a871)),x40312),x40313)),f334(f334(f3(f886(x40311,a871)),x40312),x40314)),f334(f334(f3(f886(x40311,a871)),x40312),f334(f334(f104(f886(x40311,a871)),x40313),x40314))) % 169.19/169.64 [4032]E(f334(f334(f104(f886(x40321,a871)),f334(f334(f113(f886(x40321,a871)),x40322),x40323)),f334(f334(f113(f886(x40321,a871)),x40322),x40324)),f334(f334(f113(f886(x40321,a871)),x40322),f334(f334(f104(f886(x40321,a871)),x40323),x40324))) % 169.19/169.64 [4033]E(f334(f334(f3(f886(x40331,a871)),f334(f334(f104(f886(x40331,a871)),x40332),x40333)),f334(f334(f104(f886(x40331,a871)),x40332),x40334)),f334(f334(f104(f886(x40331,a871)),x40332),f334(f334(f3(f886(x40331,a871)),x40333),x40334))) % 169.19/169.64 [4034]E(f334(f334(f113(f886(x40341,a871)),f334(f334(f104(f886(x40341,a871)),x40342),x40343)),f334(f334(f104(f886(x40341,a871)),x40342),x40344)),f334(f334(f104(f886(x40341,a871)),x40342),f334(f334(f113(f886(x40341,a871)),x40343),x40344))) % 169.19/169.64 [4040]E(f334(f39(f885(x40401,x40402)),f334(f334(f271(x40401,x40402),f334(f334(f312(x40401),x40403),f195(f886(x40401,a871)))),f334(f18(f886(x40402,a871),x40401),x40404))),f334(f39(x40402),x40404)) % 169.19/169.64 [4076]E(f334(f334(f44(x40761,f886(x40762,a871)),x40763),f334(f334(f10(f886(x40762,a871),f886(x40762,a871),x40761),f80(f886(x40762,a871))),x40764)),f334(f80(f886(x40762,a871)),f334(f334(f43(x40761,f886(x40762,a871)),x40763),x40764))) % 169.19/169.64 [4077]E(f334(f334(f43(x40771,f886(x40772,a871)),x40773),f334(f334(f10(f886(x40772,a871),f886(x40772,a871),x40771),f80(f886(x40772,a871))),x40774)),f334(f80(f886(x40772,a871)),f334(f334(f44(x40771,f886(x40772,a871)),x40773),x40774))) % 169.19/169.64 [4093]E(f334(f334(f291(x40931,x40931,x40931),f334(f334(f190(f885(x40931,x40931),a871),x40932),x40933)),f334(f334(f190(f885(x40931,x40931),a871),x40934),x40933)),f334(f334(f190(f885(x40931,x40931),a871),f334(f334(f81(a877),x40932),x40934)),x40933)) % 169.19/169.64 [4124]E(f334(f334(f43(x41241,f886(f886(x41242,a871),a871)),x41243),f334(f334(f10(f886(x41242,a871),f886(f886(x41242,a871),a871),x41241),f311(x41242)),x41244)),f334(f311(x41242),f334(f334(f43(x41241,f886(x41242,a871)),x41243),x41244))) % 169.19/169.64 [4154]E(f334(f334(f43(f886(x41541,a871),f886(x41542,a871)),x41543),f334(f334(f9(f886(x41541,a871),f886(x41541,f886(x41542,a871)),f886(x41542,a871)),f43(x41541,f886(x41542,a871))),x41544)),f334(f334(f43(x41541,f886(x41542,a871)),f41(f886(x41541,a871),x41543)),x41544)) % 169.19/169.64 [4155]E(f334(f334(f44(f886(x41551,a871),f886(x41552,a871)),x41553),f334(f334(f9(f886(x41551,a871),f886(x41551,f886(x41552,a871)),f886(x41552,a871)),f44(x41551,f886(x41552,a871))),x41554)),f334(f334(f44(x41551,f886(x41552,a871)),f41(f886(x41551,a871),x41553)),x41554)) % 169.19/169.64 [4160]E(f334(f334(f154(x41601,x41602),x41603),f334(f142(f878(x41601),f878(x41601),f134(x41601),f116(x41601)),x41604)),f334(f142(f878(x41602),f878(x41602),f134(x41602),f116(x41602)),f334(f334(f154(f878(x41601),f878(x41602)),f334(f154(x41601,x41602),x41603)),x41604))) % 169.19/169.64 [4163]E(f192(f878(x41631),f116(x41631),f334(f334(f10(f878(x41631),f878(x41631),a877),f334(f151(x41631),x41632)),f334(f334(f9(a877,f878(x41631),f878(x41631)),f176(x41631)),x41633)),x41634),f334(f334(f176(x41631),x41634),f334(f334(f151(x41631),x41632),x41633))) % 169.19/169.64 [4205]P104(f334(f334(f249(f886(x42051,a871)),f334(f313(x42052,x42051,x42053),f334(f314(x42052,x42051,x42053),x42054))),x42054)) % 169.19/169.64 [4208]E(f334(f313(f885(x42081,x42082),f885(x42082,x42081),f334(f273(x42081,x42082,f885(x42082,x42081)),f334(f9(x42082,x42081,f885(x42082,x42081)),f269(x42082,x42081)))),f334(f334(f271(x42081,x42082),x42083),f334(f18(f886(x42082,a871),x42081),x42084))),f334(f334(f271(x42082,x42081),x42084),f334(f18(f886(x42081,a871),x42082),x42083))) % 169.19/169.64 [4217]E(f334(f334(f44(x42171,f886(x42172,a871)),x42173),f334(f334(f10(f886(x42171,a871),f886(x42172,a871),x42171),f288(x42171,x42172,x42174)),f334(f334(f9(x42171,f886(x42171,a871),f886(x42171,a871)),f312(x42171)),f195(f886(x42171,a871))))),f334(f288(x42171,x42172,x42174),x42173)) % 169.19/169.64 [4218]E(f334(f334(f44(x42181,f886(x42182,a871)),x42183),f334(f334(f10(f886(x42181,a871),f886(x42182,a871),x42181),f314(x42182,x42181,x42184)),f334(f334(f9(x42181,f886(x42181,a871),f886(x42181,a871)),f312(x42181)),f195(f886(x42181,a871))))),f334(f314(x42182,x42181,x42184),x42183)) % 169.19/169.64 [4309]E(f334(f334(f113(f886(x43091,a871)),f334(f334(f113(f886(x43091,a871)),f334(f334(f104(f886(x43091,a871)),x43092),x43093)),f334(f334(f104(f886(x43091,a871)),x43093),x43094))),f334(f334(f104(f886(x43091,a871)),x43094),x43092)),f334(f334(f104(f886(x43091,a871)),f334(f334(f104(f886(x43091,a871)),f334(f334(f113(f886(x43091,a871)),x43092),x43093)),f334(f334(f113(f886(x43091,a871)),x43093),x43094))),f334(f334(f113(f886(x43091,a871)),x43094),x43092))) % 169.19/169.64 [4371]E(f334(f142(f878(x43711),f878(x43711),f134(x43711),f116(x43711)),f334(f334(f154(x43712,f878(x43711)),f334(f334(f9(x43712,f878(x43711),f878(x43711)),f334(f334(f10(x43711,f886(f878(x43711),f878(x43711)),x43712),f151(x43711)),x43713)),f116(x43711))),x43714)),f334(f334(f154(x43712,x43711),x43713),x43714)) % 169.19/169.64 [4382]E(f334(f334(f87(a1,x43821),f334(f106(a1),f334(f334(f81(a1),x43822),a100))),f334(f334(f20(a1,x43821,x43821),f334(f334(f9(a1,x43821,f886(x43821,x43821)),f334(f334(f10(a871,f886(x43821,f886(x43821,x43821)),a1),f99(x43821)),a201)),x43823)),f334(f334(f10(a877,x43821,a1),x43824),a107))),f192(x43821,x43823,x43824,f334(f106(a877),x43822))) % 169.19/169.64 [4598]~P104(f334(f334(f195(f886(x45981,f886(x45982,a871))),x45983),x45984)) % 169.19/169.64 [3849]E(f334(f334(f165(x38491),f334(f334(f134(x38491),x38492),x38493)),f334(f334(f81(a877),f334(f196(f878(x38491)),x38492)),x38494)),f334(f334(f165(x38491),x38493),x38494)) % 169.19/169.64 [3855]E(f334(f334(f138(x38551),x38552),f334(f334(f176(x38551),f334(f334(f81(a877),x38553),x38552)),x38554)),f334(f334(f176(x38551),x38553),f334(f334(f138(x38551),x38552),x38554))) % 169.19/169.64 [3959]E(f334(f334(f113(f886(x39591,a871)),f334(f265(x39592,x39591),x39593)),f334(f265(x39592,x39591),x39594)),f334(f265(x39592,x39591),f334(f334(f113(f886(f885(x39592,x39591),a871)),x39593),x39594))) % 169.19/169.64 [3960]E(f334(f334(f113(f886(x39601,a871)),f334(f267(x39601,x39602),x39603)),f334(f267(x39601,x39602),x39604)),f334(f267(x39601,x39602),f334(f334(f113(f886(f885(x39601,x39602),a871)),x39603),x39604))) % 169.19/169.64 [3965]E(f334(f334(f3(f886(x39651,a871)),f334(f334(f104(f886(x39651,a871)),x39652),x39653)),x39654),f334(f334(f104(f886(x39651,a871)),x39652),f334(f334(f3(f886(x39651,a871)),x39653),x39654))) % 169.19/169.64 [3966]E(f334(f334(f113(f886(x39661,a871)),f334(f334(f113(f886(x39661,a871)),x39662),x39663)),x39664),f334(f334(f113(f886(x39661,a871)),x39662),f334(f334(f113(f886(x39661,a871)),x39663),x39664))) % 169.19/169.64 [3967]E(f334(f334(f104(f886(x39671,a871)),f334(f334(f104(f886(x39671,a871)),x39672),x39673)),x39674),f334(f334(f104(f886(x39671,a871)),x39672),f334(f334(f104(f886(x39671,a871)),x39673),x39674))) % 169.19/169.64 [4007]E(f334(f334(f113(f886(f885(x40071,x40072),a871)),f334(f289(x40072,x40071),x40073)),f334(f289(x40072,x40071),x40074)),f334(f289(x40072,x40071),f334(f334(f113(f886(f885(x40072,x40071),a871)),x40073),x40074))) % 169.19/169.64 [4008]E(f334(f334(f104(f886(f885(x40081,x40082),a871)),f334(f289(x40082,x40081),x40083)),f334(f289(x40082,x40081),x40084)),f334(f289(x40082,x40081),f334(f334(f104(f886(f885(x40082,x40081),a871)),x40083),x40084))) % 169.19/169.64 [4022]E(f334(f334(f113(f886(x40221,f886(x40222,a871))),f258(x40222,x40221,x40223)),f258(x40222,x40221,x40224)),f258(x40222,x40221,f334(f334(f113(f886(x40222,f886(x40221,a871))),x40223),x40224))) % 169.19/169.64 [4023]E(f334(f334(f104(f886(x40231,f886(x40232,a871))),f258(x40232,x40231,x40233)),f258(x40232,x40231,x40234)),f258(x40232,x40231,f334(f334(f104(f886(x40232,f886(x40231,a871))),x40233),x40234))) % 169.19/169.64 [4080]E(f334(f334(f113(f886(x40801,a871)),f334(f334(f3(f886(x40801,a871)),x40802),x40803)),f334(f334(f3(f886(x40801,a871)),x40804),x40803)),f334(f334(f3(f886(x40801,a871)),f334(f334(f113(f886(x40801,a871)),x40802),x40804)),x40803)) % 169.19/169.64 [4081]E(f334(f334(f104(f886(x40811,a871)),f334(f334(f113(f886(x40811,a871)),x40812),x40813)),f334(f334(f113(f886(x40811,a871)),x40814),x40813)),f334(f334(f113(f886(x40811,a871)),f334(f334(f104(f886(x40811,a871)),x40812),x40814)),x40813)) % 169.19/169.64 [4082]E(f334(f334(f3(f886(x40821,a871)),f334(f334(f104(f886(x40821,a871)),x40822),x40823)),f334(f334(f104(f886(x40821,a871)),x40824),x40823)),f334(f334(f104(f886(x40821,a871)),f334(f334(f3(f886(x40821,a871)),x40822),x40824)),x40823)) % 169.19/169.64 [4083]E(f334(f334(f113(f886(x40831,a871)),f334(f334(f104(f886(x40831,a871)),x40832),x40833)),f334(f334(f104(f886(x40831,a871)),x40834),x40833)),f334(f334(f104(f886(x40831,a871)),f334(f334(f113(f886(x40831,a871)),x40832),x40834)),x40833)) % 169.19/169.64 [4084]E(f334(f334(f3(f886(x40841,a871)),f334(f334(f104(f886(x40841,a871)),x40842),x40843)),f334(f334(f104(f886(x40841,a871)),x40844),x40843)),f334(f334(f3(f886(x40841,a871)),f334(f334(f104(f886(x40841,a871)),x40842),x40843)),x40844)) % 169.19/169.64 [4096]E(f334(f334(f3(f886(x40961,a871)),f334(f334(f3(f886(x40961,a871)),x40962),f334(f334(f312(x40961),x40963),f195(f886(x40961,a871))))),x40964),f334(f334(f3(f886(x40961,a871)),x40962),f334(f334(f312(x40961),x40963),x40964))) % 169.19/169.64 [4151]E(f334(f334(f113(f886(x41511,a871)),f334(f334(f312(x41511),x41512),f334(f334(f312(x41511),x41513),f195(f886(x41511,a871))))),f334(f287(x41511),x41514)),f334(f287(x41511),f334(f334(f312(f885(x41511,x41511)),f334(f334(f269(x41511,x41511),x41512),x41513)),x41514))) % 169.19/169.64 [4180]E(f334(f334(f44(a877,f886(x41801,a871)),f334(f303(a877),x41802)),f334(f334(f10(a877,f886(x41801,a871),a877),x41803),f334(f334(f9(a877,a877,a877),f81(a877)),x41804))),f334(f334(f44(a877,f886(x41801,a871)),f305(a877,x41804,f334(f334(f81(a877),x41802),x41804))),x41803)) % 169.19/169.64 [4181]E(f175(x41811,f334(f288(x41811,x41811,x41812),f334(f334(f312(x41811),x41813),f195(f886(x41811,a871)))),f334(f288(f878(x41811),f878(x41811),f158(x41811,x41812)),f334(f334(f312(f878(x41811)),x41814),f195(f886(f878(x41811),a871))))),f334(f288(f878(x41811),f878(x41811),f158(x41811,x41812)),f334(f334(f312(f878(x41811)),f334(f334(f151(x41811),x41813),x41814)),f195(f886(f878(x41811),a871))))) % 169.19/169.64 [4243]E(f334(f179(x42431,x42432),f334(f334(f154(x42431,f885(x42431,x42432)),f334(f334(f20(x42431,x42432,f885(x42431,x42432)),f269(x42431,x42432)),x42433)),x42434)),f189(x42431,x42432,f334(f74(x42432,f881(x42432),x42431,f241(x42432)),x42433),f334(f173(x42431),x42434))) % 169.19/169.64 [4248]E(f334(f254(x42481),f334(f334(f9(x42481,f886(x42482,a871),a871),f334(f334(f10(x42482,f886(f886(x42482,a871),a871),x42481),f336(x42482)),x42483)),x42484)),f334(f314(x42481,x42482,x42483),x42484)) % 169.19/169.64 [4342]E(f334(f254(x43421),f334(f334(f9(x43421,f886(f885(x43422,x43421),a871),a871),f334(f334(f10(f885(x43422,x43421),f886(f886(f885(x43422,x43421),a871),a871),x43421),f336(f885(x43422,x43421))),f334(f269(x43422,x43421),x43423))),x43424)),f334(f288(x43422,x43421,x43424),f334(f334(f312(x43422),x43423),f195(f886(x43422,a871))))) % 169.19/169.64 [4356]E(f334(f334(f154(f885(x43561,a877),x43561),f268(x43561,a877)),f334(f136(f885(x43561,a877),f334(f334(f10(a877,a871,f885(x43561,a877)),x43562),f334(f334(f10(a877,a877,f885(x43561,a877)),a115),f272(x43561,a877)))),f334(f334(f183(x43561,a877),x43563),x43564))),f334(f334(f154(f885(x43561,a877),x43561),f268(x43561,a877)),f334(f136(f885(x43561,a877),f334(f334(f10(a877,a871,f885(x43561,a877)),x43562),f272(x43561,a877))),f334(f334(f183(x43561,a877),x43563),f334(f334(f154(a877,a877),a115),x43564))))) % 169.19/169.64 [4364]P104(f334(f334(f249(f886(f886(x43641,a871),a871)),f334(f334(f44(x43642,f886(f886(x43641,a871),a871)),x43643),f334(f334(f10(f886(x43641,a871),f886(f886(x43641,a871),a871),x43642),f311(x43641)),x43644))),f334(f311(x43641),f334(f334(f44(x43642,f886(x43641,a871)),x43643),x43644)))) % 169.19/169.64 [4406]E(f334(f334(f87(a1,x44061),f334(f106(a1),f334(f334(f81(a1),x44062),a100))),f334(f334(f20(a1,x44061,x44061),f334(f334(f9(a1,x44061,f886(x44061,x44061)),f334(f334(f10(a871,f886(x44061,f886(x44061,x44061)),a1),f99(x44061)),a201)),x44063)),f334(f334(f20(a1,x44061,x44061),f334(f334(f10(a877,f886(x44061,x44061),a1),x44064),a107)),f334(f334(f10(a877,x44061,a1),f191(x44061,x44063,x44064)),a107)))),f334(f191(x44061,x44063,x44064),f334(f106(a877),x44062))) % 169.19/169.64 [4409]E(f334(f334(f154(x44091,x44092),f334(f74(f881(x44092),x44092,x44091,f245(x44092)),x44093)),f334(f136(x44091,f334(f334(f10(a871,a871,x44091),a329),f334(f334(f9(x44091,f881(x44092),a871),f334(f334(f10(f881(x44092),f886(f881(x44092),a871),x44091),a331),x44093)),f198(x44092)))),x44094)),f163(x44091,x44092,x44093,x44094)) % 169.19/169.64 [4432]E(f334(f254(f885(x44321,x44322)),f334(f273(x44321,x44322,a871),f334(f334(f9(x44321,f886(x44322,a871),f886(x44322,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x44322,a871),f886(x44322,a871)),x44321),f10(a871,a871,x44322)),f334(f334(f10(a871,f886(a871,a871),x44321),a332),f334(f334(f9(x44321,f886(x44321,a871),a871),f336(x44321)),x44323)))),f334(f334(f9(x44322,f886(x44322,a871),a871),f336(x44322)),x44324)))),f237(x44321,x44322,x44323,x44324)) % 169.19/169.64 [4465]E(f334(f334(f44(x44651,f886(f885(x44651,x44652),a871)),x44653),f334(f334(f20(x44651,f886(x44652,f886(f885(x44651,x44652),a871)),f886(f885(x44651,x44652),a871)),f334(f334(f10(f886(x44652,a871),f886(f886(x44652,f886(f885(x44651,x44652),a871)),f886(f885(x44651,x44652),a871)),x44651),f44(x44652,f886(f885(x44651,x44652),a871))),x44654)),f334(f334(f9(x44651,f886(f885(x44651,x44652),a871),f886(x44652,f886(f885(x44651,x44652),a871))),f334(f334(f10(f886(x44652,f886(f886(f885(x44651,x44652),a871),f886(f885(x44651,x44652),a871))),f886(f886(f885(x44651,x44652),a871),f886(x44652,f886(f885(x44651,x44652),a871))),x44651),f9(x44652,f886(f885(x44651,x44652),a871),f886(f885(x44651,x44652),a871))),f334(f334(f10(f886(x44652,f885(x44651,x44652)),f886(x44652,f886(f886(f885(x44651,x44652),a871),f886(f885(x44651,x44652),a871))),x44651),f334(f10(f885(x44651,x44652),f886(f886(f885(x44651,x44652),a871),f886(f885(x44651,x44652),a871)),x44652),f312(f885(x44651,x44652)))),f269(x44651,x44652)))),f195(f886(f885(x44651,x44652),a871))))),f334(f334(f271(x44651,x44652),x44653),x44654)) % 169.19/169.64 [4017]E(f334(f334(f134(x40171),f334(f334(f176(x40171),x40172),x40173)),f334(f334(f176(x40171),f334(f334(f3(a877),x40172),f334(f196(f878(x40171)),x40173))),x40174)),f334(f334(f176(x40171),x40172),f334(f334(f134(x40171),x40173),x40174))) % 169.19/169.64 [4018]E(f334(f334(f134(x40181),f334(f334(f138(x40181),x40182),x40183)),f334(f334(f138(x40181),f334(f334(f3(a877),x40182),f334(f196(f878(x40181)),x40183))),x40184)),f334(f334(f138(x40181),x40182),f334(f334(f134(x40181),x40183),x40184))) % 169.19/169.64 [4070]E(f334(f334(f81(a877),f334(f334(f82(a877),x40701),x40702)),f334(f334(f81(a877),f334(f334(f82(a877),x40703),x40702)),x40704)),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f81(a877),x40701),x40703)),x40702)),x40704)) % 169.19/169.64 [4273]P104(f334(f334(f249(f886(x42731,a871)),f334(f334(f3(f886(x42731,a871)),f334(f265(x42732,x42731),x42733)),f334(f265(x42732,x42731),x42734))),f334(f265(x42732,x42731),f334(f334(f3(f886(f885(x42732,x42731),a871)),x42733),x42734)))) % 169.19/169.64 [4274]P104(f334(f334(f249(f886(x42741,a871)),f334(f334(f3(f886(x42741,a871)),f334(f267(x42741,x42742),x42743)),f334(f267(x42741,x42742),x42744))),f334(f267(x42741,x42742),f334(f334(f3(f886(f885(x42741,x42742),a871)),x42743),x42744)))) % 169.19/169.64 [4384]E(f334(f334(f81(a1),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x43841),x43842)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x43843),x43844)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),f334(f334(f81(a877),x43841),x43843)),f334(f334(f81(a877),x43842),x43844))),f195(f886(f885(a877,a877),a871)))))) % 169.19/169.64 [4427]E(f334(f334(f82(a1),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x44271),x44272)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x44273),x44274)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),f334(f334(f81(a877),f334(f334(f82(a877),x44271),x44273)),f334(f334(f82(a877),x44272),x44274))),f334(f334(f81(a877),f334(f334(f82(a877),x44271),x44274)),f334(f334(f82(a877),x44272),x44273)))),f195(f886(f885(a877,a877),a871)))))) % 169.19/169.64 [4447]E(f334(f254(x44471),f334(f334(f10(f886(x44472,a871),a871,x44471),f89(x44472)),f334(f334(f10(f886(x44472,a871),f886(x44472,a871),x44471),f334(f20(x44472,a871,a871),f334(f334(f10(a871,f886(a871,a871),x44472),a337),f334(f334(f9(x44472,f886(x44472,a871),a871),f336(x44472)),x44473)))),f334(f334(f9(x44471,f886(x44472,f886(x44471,a871)),f886(x44472,a871)),f334(f334(f10(f886(f886(x44471,a871),a871),f886(f886(x44472,f886(x44471,a871)),f886(x44472,a871)),x44471),f10(f886(x44471,a871),a871,x44472)),f336(x44471))),x44474)))),f334(f334(f43(x44472,f886(x44471,a871)),x44473),x44474)) % 169.19/169.64 [4480]E(f334(f334(f291(x44801,x44801,x44801),f334(f334(f312(f885(x44801,x44801)),f334(f334(f269(x44801,x44801),x44802),x44803)),x44804)),f310(x44801,f334(f334(f312(f885(x44801,x44801)),f334(f334(f269(x44801,x44801),x44802),x44803)),x44804))),f334(f334(f113(f886(f885(x44801,x44801),a871)),f334(f334(f291(x44801,x44801,x44801),x44804),f310(x44801,x44804))),f334(f254(f885(x44801,x44801)),f334(f273(x44801,x44801,a871),f334(f334(f9(x44801,f886(x44801,a871),f886(x44801,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x44801,a871),f886(x44801,a871)),x44801),f10(a871,a871,x44801)),f334(f334(f10(a871,f886(a871,a871),x44801),a332),f334(f334(f9(x44801,f886(f885(x44801,x44801),a871),a871),f334(f334(f10(f885(x44801,x44801),f886(f886(f885(x44801,x44801),a871),a871),x44801),f336(f885(x44801,x44801))),f334(f334(f9(x44801,x44801,f885(x44801,x44801)),f269(x44801,x44801)),x44802))),f310(x44801,x44804))))),f334(f334(f9(x44801,f886(f885(x44801,x44801),a871),a871),f334(f334(f10(f885(x44801,x44801),f886(f886(f885(x44801,x44801),a871),a871),x44801),f336(f885(x44801,x44801))),f334(f269(x44801,x44801),x44803))),f310(x44801,x44804))))))) % 169.19/169.64 [4275]E(f334(f136(x42751,f334(f334(f20(x42751,a871,a871),f334(f334(f10(a871,f886(a871,a871),x42751),a332),x42752)),x42753)),x42754),f334(f136(x42751,x42753),f334(f136(x42751,x42752),x42754))) % 169.19/169.64 [4378]E(f334(f334(f134(x43781),f334(f334(f334(f99(f878(x43781)),f334(f334(f336(a877),f2(a877)),x43782)),f334(f334(f151(x43781),x43783),f116(x43781))),f116(x43781))),f177(x43781,x43784,f334(f254(a877),f334(f334(f9(a877,f886(a877,a871),a871),f334(f334(f10(a877,f886(f886(a877,a871),a871),a877),f336(a877)),a115)),x43782)))),f177(x43781,f334(f334(f151(x43781),x43783),x43784),x43782)) % 169.19/169.64 [4474]E(f334(f254(f885(x44741,x44742)),f334(f334(f10(f886(a877,a871),a871,f885(x44741,x44742)),f88(a877)),f334(f334(f9(f885(x44741,x44742),f886(a877,a871),f886(a877,a871)),f334(f334(f10(f886(a877,f886(a871,a871)),f886(f886(a877,a871),f886(a877,a871)),f885(x44741,x44742)),f20(a877,a871,a871)),f334(f334(f10(f886(a877,a871),f886(a877,f886(a871,a871)),f885(x44741,x44742)),f334(f10(a871,f886(a871,a871),a877),a332)),f334(f334(f9(f885(x44741,x44742),f886(a877,f885(x44741,x44742)),f886(a877,a871)),f334(f334(f10(f886(f885(x44741,x44742),a871),f886(f886(a877,f885(x44741,x44742)),f886(a877,a871)),f885(x44741,x44742)),f10(f885(x44741,x44742),a871,a877)),a331)),f334(f334(f20(a877,x44742,f885(x44741,x44742)),f334(f334(f10(x44741,f886(x44742,f885(x44741,x44742)),a877),f269(x44741,x44742)),f334(f165(x44741),x44743))),f334(f165(x44742),x44744)))))),f334(f334(f9(a877,a877,a871),f250(a877)),f334(f334(f247(a877),f334(f196(f878(x44741)),x44743)),f334(f196(f878(x44742)),x44744)))))),f334(f173(f885(x44741,x44742)),f334(f334(f183(x44741,x44742),x44743),x44744))) % 169.19/169.64 [4397]E(f334(f254(f885(x43971,x43972)),f334(f273(x43971,x43972,a871),f334(f334(f9(x43971,f886(x43972,a871),f886(x43972,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x43972,a871),f886(x43972,a871)),x43971),f10(a871,a871,x43972)),f334(f334(f10(a871,f886(a871,a871),x43971),a332),x43973))),x43974))),f334(f334(f271(x43971,x43972),f334(f254(x43971),x43973)),f334(f18(f886(x43972,a871),x43971),f334(f254(x43972),x43974)))) % 169.19/169.64 [4400]E(f334(f254(f885(x44001,x44002)),f334(f273(x44001,x44002,a871),f334(f334(f20(x44001,f886(x44002,a871),f886(x44002,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x44002,a871),f886(x44002,a871)),x44001),f10(a871,a871,x44002)),f334(f334(f10(a871,f886(a871,a871),x44001),a332),x44003))),x44004))),f334(f334(f271(x44001,x44002),f334(f254(x44001),x44003)),f334(f334(f10(f886(x44002,a871),f886(x44002,a871),x44001),f254(x44002)),x44004))) % 169.19/169.64 [4416]E(f334(f254(x44161),f334(f334(f10(f886(x44162,a871),a871,x44161),f89(x44162)),f334(f334(f10(f886(x44162,a871),f886(x44162,a871),x44161),f334(f20(x44162,a871,a871),f334(f334(f10(a871,f886(a871,a871),x44162),a337),f334(f334(f9(x44162,f886(x44162,a871),a871),f336(x44162)),x44163)))),x44164))),f334(f334(f43(x44162,f886(x44161,a871)),x44163),f334(f334(f10(f886(x44161,a871),f886(x44161,a871),x44162),f254(x44161)),f334(f9(x44161,x44162,a871),x44164)))) % 169.19/169.64 [4460]E(f334(f334(f154(f885(x44601,a877),x44601),f268(x44601,a877)),f334(f136(f885(x44601,a877),f334(f334(f9(f885(x44601,a877),f886(a877,a871),a871),f334(f334(f10(a877,f886(f886(a877,a871),a871),f885(x44601,a877)),f336(a877)),f272(x44601,a877))),x44602)),f334(f334(f183(x44601,a877),x44603),f139(a877,f334(f304(a877,x44604),f334(f334(f81(a877),x44604),f334(f196(f878(x44601)),x44603))))))),f334(f334(f154(f885(x44601,a877),x44601),f268(x44601,a877)),f334(f136(f885(x44601,a877),f334(f334(f9(f885(x44601,a877),f886(a877,a871),a871),f334(f334(f10(a877,f886(f886(a877,a871),a871),f885(x44601,a877)),f336(a877)),f334(f334(f9(f885(x44601,a877),a877,a877),f334(f334(f10(a877,f886(a877,a877),f885(x44601,a877)),f81(a877)),f272(x44601,a877))),x44604))),x44602)),f334(f334(f183(x44601,a877),x44603),f139(a877,f334(f304(a877,f2(a877)),f334(f196(f878(x44601)),x44603))))))) % 169.19/169.64 [4461]E(f334(a115,f334(f334(f248(a877),f334(f196(f878(x44611)),x44612)),f334(f142(a877,f878(x44613),f334(f9(f878(x44613),a877,a877),f334(f334(f10(a877,f886(a877,a877),f878(x44613)),f248(a877)),f334(f334(f9(f878(x44613),a877,a877),f334(f334(f10(a877,f886(a877,a877),f878(x44613)),f3(a877)),f196(f878(x44613)))),f334(a115,f2(a877))))),f2(a877)),f334(f169(f878(x44613)),f334(f136(f878(x44613),f334(f334(f10(a871,a871,f878(x44613)),a329),f334(f334(f9(f878(x44613),f878(x44613),a871),a331),f116(x44613)))),x44614))))),f334(f334(f248(a877),f334(a115,f334(f196(f878(x44611)),x44612))),f334(f142(a877,f878(x44613),f334(f9(f878(x44613),a877,a877),f334(f334(f10(a877,f886(a877,a877),f878(x44613)),f248(a877)),f196(f878(x44613)))),f2(a877)),f334(f169(f878(x44613)),x44614)))) % 169.19/169.64 [4415]E(f334(f334(f134(x44151),f177(x44151,x44152,x44153)),f177(x44151,x44154,f334(f254(a877),f334(f334(f9(a877,f886(a877,a871),a871),f334(f334(f10(a877,f886(f886(a877,a871),a871),a877),f336(a877)),f334(f334(f9(a877,a877,a877),f81(a877)),f334(f196(f878(x44151)),x44152)))),x44153)))),f177(x44151,f334(f334(f134(x44151),x44152),x44154),x44153)) % 169.19/169.64 [4467]E(f334(f334(f151(f878(x44671)),f334(f334(f151(x44671),x44672),f334(f142(f878(x44671),f878(x44671),f134(x44671),f116(x44671)),f334(f334(f154(f878(x44671),f878(x44671)),f156(f878(x44671),x44671,f116(x44671),f334(f334(f10(f878(x44671),f886(f878(x44671),f878(x44671)),x44671),f18(f878(x44671),f878(x44671))),f334(f334(f9(x44671,f878(x44671),f878(x44671)),f151(x44671)),f116(x44671))))),x44673)))),f181(x44671,f334(f334(f151(f878(x44671)),x44674),f334(f142(f878(f878(x44671)),f878(f878(x44671)),f134(f878(x44671)),f116(f878(x44671))),f334(f334(f154(f878(x44671),f878(f878(x44671))),f156(f878(f878(x44671)),x44671,f116(f878(x44671)),f334(f18(f886(f878(x44671),f878(f878(x44671))),x44671),f334(f334(f9(f878(x44671),f878(f878(x44671)),f878(f878(x44671))),f151(f878(x44671))),f116(f878(x44671)))))),x44673))))),f181(x44671,f334(f334(f151(f878(x44671)),f334(f334(f151(x44671),x44672),x44674)),x44673))) % 169.19/169.64 [4475]E(f334(f254(f885(x44751,x44751)),f334(f273(x44751,x44751,a871),f334(f334(f9(x44751,f886(f885(x44752,x44752),a871),f886(x44751,a871)),f334(f334(f10(f886(x44751,f886(f886(f885(x44752,x44752),a871),a871)),f886(f886(f885(x44752,x44752),a871),f886(x44751,a871)),x44751),f9(x44751,f886(f885(x44752,x44752),a871),a871)),f334(f334(f10(f886(x44751,f885(x44752,x44752)),f886(x44751,f886(f886(f885(x44752,x44752),a871),a871)),x44751),f334(f10(f885(x44752,x44752),f886(f886(f885(x44752,x44752),a871),a871),x44751),f336(f885(x44752,x44752)))),f334(f334(f9(x44751,f886(x44751,x44752),f886(x44751,f885(x44752,x44752))),f334(f334(f10(f886(x44752,f885(x44752,x44752)),f886(f886(x44751,x44752),f886(x44751,f885(x44752,x44752))),x44751),f10(x44752,f885(x44752,x44752),x44751)),f334(f334(f10(x44752,f886(x44752,f885(x44752,x44752)),x44751),f269(x44752,x44752)),x44753))),x44753)))),x44754))),f334(f334(f290(x44752,x44751),x44754),x44753)) % 169.19/169.64 [4538]~E(f34(x45381,x45382),f29(x45383,x45384,x45385)) % 169.19/169.64 [4539]~E(f34(x45391,x45392),f31(x45393,x45394,x45395)) % 169.19/169.64 [4540]~E(f34(x45401,x45402),f30(x45403,x45404,x45405)) % 169.19/169.64 [4541]~E(f33(x45411,x45412),f29(x45413,x45414,x45415)) % 169.19/169.64 [4542]~E(f33(x45421,x45422),f31(x45423,x45424,x45425)) % 169.19/169.64 [4543]~E(f33(x45431,x45432),f30(x45433,x45434,x45435)) % 169.19/169.64 [4544]~E(f29(x45441,x45442,x45443),f34(x45444,x45445)) % 169.19/169.64 [4545]~E(f29(x45451,x45452,x45453),f33(x45454,x45455)) % 169.19/169.64 [4546]~E(f31(x45461,x45462,x45463),f34(x45464,x45465)) % 169.19/169.64 [4547]~E(f31(x45471,x45472,x45473),f33(x45474,x45475)) % 169.19/169.64 [4548]~E(f30(x45481,x45482,x45483),f34(x45484,x45485)) % 169.19/169.64 [4549]~E(f30(x45491,x45492,x45493),f33(x45494,x45495)) % 169.19/169.64 [3584]E(f334(f334(f154(x35841,x35842),x35843),f170(x35841,x35844,x35845)),f170(x35842,x35844,f334(x35843,x35845))) % 169.19/169.64 [3957]E(f334(f186(x39571,x39572,x39573,x39574),x39575),f334(f243(f881(x39572),x39572,f334(x39573,x39575),f241(x39572)),f334(x39574,x39575))) % 169.19/169.64 [4045]E(f186(x40451,x40452,f186(x40451,x40452,x40453,x40454),x40455),f186(x40451,x40452,x40453,f186(x40451,x40452,x40454,x40455))) % 169.19/169.64 [4222]E(f270(x42221,x42222,x42223,f258(x42222,x42221,x42224),f258(x42223,x42222,x42225)),f258(x42223,x42221,f270(x42223,x42222,x42221,x42225,x42224))) % 169.19/169.64 [4229]E(f334(f334(f113(f886(x42291,a871)),f334(f173(x42291),f334(f334(f176(x42291),f334(f196(f878(x42292)),x42293)),x42294))),f185(x42291,x42292,x42295)),f185(x42291,x42292,f188(x42291,x42292,x42295,x42294,x42293))) % 169.19/169.64 [3778]E(f334(f334(f273(x37781,x37782,x37783),x37784),x37785),f334(f334(x37784,f334(f268(x37781,x37782),x37785)),f334(f272(x37781,x37782),x37785))) % 169.19/169.64 [3805]E(f334(f243(x38051,x38052,x38053,x38054),f334(f241(x38052),x38055)),f334(x38054,x38055)) % 169.19/169.64 [3815]E(f334(f334(f334(f67(x38151,x38152,x38153),x38154),x38155),f195(f886(x38152,a871))),x38155) % 169.19/169.64 [3989]E(f244(x39891,x39892,x39893,x39894,f334(f241(x39892),x39895)),f334(x39894,x39895)) % 169.19/169.64 [4102]E(f334(f74(f881(x41021),f881(x41022),f881(x41023),f334(f207(x41021,x41022),x41024)),f334(f207(x41023,x41021),x41025)),f334(f207(x41023,x41022),f334(f74(x41021,x41022,x41023,x41024),x41025))) % 169.19/169.64 [4104]E(f334(f74(f878(x41041),f878(x41042),f878(x41043),f334(f154(x41041,x41042),x41044)),f334(f154(x41043,x41041),x41045)),f334(f154(x41043,x41042),f334(f74(x41041,x41042,x41043,x41044),x41045))) % 169.19/169.64 [4161]E(f334(f243(x41611,f885(x41612,f879(x41612)),x41613,f334(f273(x41612,f879(x41612),x41611),x41614)),f334(f135(x41612),x41615)),f130(x41611,x41612,x41613,x41614,x41615)) % 169.19/169.64 [4184]E(f86(x41841,f68(x41842,x41841,x41843,x41844,x41845)),f334(f334(f66(x41842,x41841,x41843),x41844),x41845)) % 169.19/169.64 [4220]E(f334(f334(f81(a877),f334(f334(f81(a877),f334(x42201,f334(f268(x42202,x42203),x42204))),f334(x42205,f334(f272(x42202,x42203),x42204)))),f334(a115,f2(a877))),f277(x42202,x42203,x42201,x42205,x42204)) % 169.19/169.64 [4411]E(f163(x44111,x44112,f334(f334(f9(x44111,f881(x44112),f881(x44112)),f334(f334(f20(x44111,f881(x44112),f886(f881(x44112),f881(x44112))),f334(f334(f10(a871,f886(f881(x44112),f886(f881(x44112),f881(x44112))),x44111),f99(f881(x44112))),x44113)),f334(f334(f10(x44112,f881(x44112),x44111),f241(x44112)),x44114))),f198(x44112)),x44115),f334(f334(f154(x44111,x44112),x44114),f334(f136(x44111,x44113),x44115))) % 169.19/169.64 [4589]~E(f334(f334(f334(f73(x45891,f881(x45892)),x45893),x45894),f334(f241(x45892),x45895)),f334(f18(f881(x45892),x45891),f198(x45892))) % 169.19/169.64 [3712]E(f334(f334(f176(x37121),x37122),f334(f334(f154(x37123,x37121),x37124),x37125)),f334(f334(f154(x37123,x37121),x37124),f334(f334(f176(x37123),x37122),x37125))) % 169.19/169.64 [3713]E(f334(f334(f138(x37131),x37132),f334(f334(f154(x37133,x37131),x37134),x37135)),f334(f334(f154(x37133,x37131),x37134),f334(f334(f138(x37133),x37132),x37135))) % 169.19/169.64 [3746]E(f334(f334(f154(x37461,x37462),x37463),f334(f334(f151(x37461),x37464),x37465)),f334(f334(f151(x37462),f334(x37463,x37464)),f334(f334(f154(x37461,x37462),x37463),x37465))) % 169.19/169.64 [3809]E(f334(f313(x38091,x38092,x38093),f334(f334(f312(x38091),x38094),x38095)),f334(f334(f312(x38092),f334(x38093,x38094)),f334(f313(x38091,x38092,x38093),x38095))) % 169.19/169.64 [3839]E(f174(x38391,f334(f334(f151(x38391),x38392),x38393),f334(f334(f151(x38391),x38394),x38395)),f334(f334(f151(x38391),x38392),f334(f334(f151(x38391),x38394),f174(x38391,x38393,x38395)))) % 169.19/169.64 [3876]E(f334(f334(f183(x38761,x38762),f334(f334(f176(x38761),x38763),x38764)),f334(f334(f176(x38762),x38763),x38765)),f334(f334(f176(f885(x38761,x38762)),x38763),f334(f334(f183(x38761,x38762),x38764),x38765))) % 169.19/169.64 [3877]E(f334(f334(f183(x38771,x38772),f334(f334(f138(x38771),x38773),x38774)),f334(f334(f138(x38772),x38773),x38775)),f334(f334(f138(f885(x38771,x38772)),x38773),f334(f334(f183(x38771,x38772),x38774),x38775))) % 169.19/169.64 [3889]E(f334(f334(f159(x38891,f334(f334(f151(x38891),x38892),x38893)),f334(a115,x38894)),x38895),f334(f334(f151(x38891),x38892),f334(f334(f159(x38891,x38893),x38894),x38895))) % 169.19/169.64 [3892]E(f334(f243(f881(x38921),x38922,f198(x38921),x38923),f334(f334(f18(f881(x38922),x38924),f198(x38922)),x38925)),f198(x38921)) % 169.19/169.64 [3894]E(f334(f334(f134(x38941),f334(f334(f154(x38942,x38941),x38943),x38944)),f334(f334(f154(x38942,x38941),x38943),x38945)),f334(f334(f154(x38942,x38941),x38943),f334(f334(f134(x38942),x38944),x38945))) % 169.19/169.64 [3898]E(f334(f334(x38981,x38982),f334(f334(f260(x38983,x38984,x38981),x38982),x38985)),f334(f334(f260(x38983,x38984,x38981),x38982),f334(a115,x38985))) % 169.19/169.64 [3928]E(f164(x39281,x39282,x39283,f334(f334(f151(x39281),x39284),x39285)),f334(f334(f134(x39282),f334(x39283,x39284)),f164(x39281,x39282,x39283,x39285))) % 169.19/169.64 [3941]E(f334(f334(f291(x39411,x39412,x39413),f334(f289(x39412,x39411),x39414)),f334(f289(x39413,x39412),x39415)),f334(f289(x39413,x39411),f334(f334(f291(x39413,x39412,x39411),x39415),x39414))) % 169.19/169.64 [3975]E(f334(f334(f334(f190(f878(x39751),f878(x39751)),x39752),f168(x39751)),f334(f334(f154(x39753,x39751),x39754),x39755)),f334(f334(f154(x39753,x39751),x39754),f334(f334(f334(f190(f878(x39753),f878(x39753)),x39752),f168(x39753)),x39755))) % 169.19/169.64 [3976]E(f334(f334(f275(x39761,x39762,x39761,x39763),f334(f269(x39762,x39761),x39764)),x39765),f334(x39765,x39764)) % 169.19/169.64 [4003]E(f155(x40031,x40032,f334(f334(f154(x40033,x40031),x40034),x40035)),f155(x40033,f334(f74(x40031,a877,x40033,x40032),x40034),x40035)) % 169.19/169.64 [4068]E(f334(f334(f74(f881(x40681),f881(x40682),x40683,f334(f207(x40681,x40682),x40684)),f334(f18(f881(x40681),x40683),f198(x40681))),x40685),f198(x40682)) % 169.19/169.64 [4069]E(f178(f885(x40691,x40692),f334(f74(x40692,a871,f885(x40691,x40692),x40693),f272(x40691,x40692)),f334(f334(f183(x40691,x40692),x40694),x40695)),f334(f334(f183(x40691,x40692),x40694),f178(x40692,x40693,x40695))) % 169.19/169.64 [4074]E(f334(f313(x40741,x40742,f334(f334(f10(x40743,x40742,x40741),x40744),x40745)),f257(f886(x40741,a871))),f334(f313(x40743,x40742,x40744),f334(f313(x40741,x40743,x40745),f257(f886(x40741,a871))))) % 169.19/169.64 [4087]E(f178(f885(x40871,x40872),f334(f74(x40871,a871,f885(x40871,x40872),x40873),f268(x40871,x40872)),f334(f334(f183(x40871,x40872),x40874),x40875)),f334(f334(f183(x40871,x40872),f178(x40871,x40873,x40874)),x40875)) % 169.19/169.64 [4108]E(f334(f334(f113(f886(x41081,a871)),f334(f314(x41081,x41082,x41083),f334(f334(f312(x41082),x41084),f195(f886(x41082,a871))))),f334(f314(x41081,x41082,x41083),x41085)),f334(f314(x41081,x41082,x41083),f334(f334(f312(x41082),x41084),x41085))) % 169.19/169.64 [4168]E(f334(f334(f134(f885(x41681,x41682)),f334(f334(f154(x41682,f885(x41681,x41682)),f334(f269(x41681,x41682),x41683)),x41684)),f61(x41681,x41682,x41685,x41684)),f61(x41681,x41682,f334(f334(f151(x41681),x41683),x41685),x41684)) % 169.19/169.64 [4169]E(f334(f334(f154(x41691,x41692),x41693),f178(x41691,f334(f74(x41692,a871,x41691,x41694),x41693),x41695)),f178(x41692,x41694,f334(f334(f154(x41691,x41692),x41693),x41695))) % 169.19/169.64 [4175]E(f334(f142(x41751,x41752,f334(f9(x41752,x41751,x41751),f334(f9(x41751,x41752,x41751),x41753)),x41754),f334(f169(x41752),f334(f169(x41752),x41755))),f334(f142(x41751,x41752,x41753,x41754),x41755)) % 169.19/169.64 [4176]E(f334(f334(f334(f73(x41761,f881(x41762)),f189(x41761,x41762,x41763,x41764)),x41765),f334(x41763,x41765)),f189(x41761,x41762,x41763,f334(f334(f312(x41761),x41765),x41764))) % 169.19/169.64 [4246]E(f334(f243(f878(x42461),x42461,f163(x42462,x42461,x42463,x42464),f334(f334(f9(x42461,f878(x42461),f878(x42461)),f151(x42461)),f163(x42462,x42461,x42463,x42464))),f334(x42463,x42465)),f163(x42462,x42461,x42463,f334(f334(f151(x42462),x42465),x42464))) % 169.19/169.64 [4283]P104(f334(f334(f249(f886(x42831,a871)),f334(f313(x42832,x42831,x42833),f334(f334(f104(f886(x42832,a871)),x42834),x42835))),f334(f334(f104(f886(x42831,a871)),f334(f313(x42832,x42831,x42833),x42834)),f334(f313(x42832,x42831,x42833),x42835)))) % 169.19/169.64 [4284]P104(f334(f334(f249(f886(x42841,a871)),f334(f288(x42842,x42841,x42843),f334(f334(f104(f886(x42842,a871)),x42844),x42845))),f334(f334(f104(f886(x42841,a871)),f334(f288(x42842,x42841,x42843),x42844)),f334(f288(x42842,x42841,x42843),x42845)))) % 169.19/169.64 [4385]E(f334(f272(x43851,x43852),f334(f274(x43853,x43851,x43852,x43852,x43854,f35(x43852)),x43855)),f334(f272(x43853,x43852),x43855)) % 169.19/169.64 [4386]E(f334(f268(x43861,x43862),f334(f274(x43861,x43861,x43863,x43862,f35(x43861),x43864),x43865)),f334(f268(x43861,x43863),x43865)) % 169.19/169.64 [4471]E(f334(f142(f886(x44711,f881(x44712)),f885(x44711,x44712),f334(f334(f10(f886(x44711,f886(x44712,f886(x44711,f881(x44712)))),f886(f885(x44711,x44712),f886(x44711,f881(x44712))),f886(x44711,f881(x44712))),f273(x44711,x44712,f886(x44711,f881(x44712)))),f334(f334(f9(f886(x44711,f881(x44712)),f886(x44712,f881(x44712)),f886(x44711,f886(x44712,f886(x44711,f881(x44712))))),f334(f334(f10(f886(x44711,f886(f886(x44712,f881(x44712)),f886(x44712,f886(x44711,f881(x44712))))),f886(f886(x44712,f881(x44712)),f886(x44711,f886(x44712,f886(x44711,f881(x44712))))),f886(x44711,f881(x44712))),f9(x44711,f886(x44712,f881(x44712)),f886(x44712,f886(x44711,f881(x44712))))),f334(f334(f10(f886(x44711,f886(f881(x44712),f886(x44711,f881(x44712)))),f886(x44711,f886(f886(x44712,f881(x44712)),f886(x44712,f886(x44711,f881(x44712))))),f886(x44711,f881(x44712))),f334(f10(f886(f881(x44712),f886(x44711,f881(x44712))),f886(f886(x44712,f881(x44712)),f886(x44712,f886(x44711,f881(x44712)))),x44711),f10(f881(x44712),f886(x44711,f881(x44712)),x44712))),f73(x44711,f881(x44712))))),f241(x44712))),x44713),f334(f334(f183(x44711,x44712),x44714),x44715)),f188(x44711,x44712,x44713,x44714,x44715)) % 169.19/169.64 [4473]P20(x44731,x44732,f334(f334(f312(f876(x44731)),f334(f334(f334(f93(x44731),f334(f334(f9(x44731,f886(a872,a871),f886(a872,a871)),f334(f334(f10(f886(a872,f886(a871,a871)),f886(f886(a872,a871),f886(a872,a871)),x44731),f20(a872,a871,a871)),f334(f334(f10(f886(a872,a871),f886(a872,f886(a871,a871)),x44731),f334(f10(a871,f886(a871,a871),a872),a332)),x44733))),f334(f334(f10(a871,a871,a872),a329),x44734))),f33(x44734,x44735)),x44733)),f195(f886(f876(x44731),a871)))) % 169.19/169.64 [3553]E(f334(f334(f334(f334(f213(x35531),x35532),x35533),x35534),x35535),f200(x35531,x35532)) % 169.19/169.64 [3554]E(f334(f334(f334(f334(f217(x35541),x35542),x35543),x35544),x35545),f208(x35541,x35542)) % 169.19/169.64 [3600]E(f96(x36001,x36002,f334(f334(f334(f93(x36001),x36003),x36004),x36005)),f2(a877)) % 169.19/169.64 [3696]E(f334(f334(f334(f334(f73(x36961,x36962),x36963),x36964),x36965),x36964),x36965) % 169.19/169.64 [3929]E(f334(f334(f43(x39291,f886(x39292,a871)),f334(f334(f312(x39291),x39293),x39294)),x39295),f334(f334(f104(f886(x39292,a871)),f334(x39295,x39293)),f334(f334(f43(x39291,f886(x39292,a871)),x39294),x39295))) % 169.19/169.64 [3930]E(f334(f334(f44(x39301,f886(x39302,a871)),f334(f334(f312(x39301),x39303),x39304)),x39305),f334(f334(f113(f886(x39302,a871)),f334(x39305,x39303)),f334(f334(f44(x39301,f886(x39302,a871)),x39304),x39305))) % 169.19/169.64 [3982]E(f334(f121(x39821,x39822,f334(x39823,x39824)),f334(f334(f9(x39821,a102,f879(x39822)),x39825),x39824)),f334(f205(x39821,x39822,x39823,x39825),x39824)) % 169.19/169.64 [3996]E(f334(f334(f113(f886(x39961,a871)),f334(f313(x39962,x39961,x39963),x39964)),f334(f313(x39962,x39961,x39963),x39965)),f334(f313(x39962,x39961,x39963),f334(f334(f113(f886(x39962,a871)),x39964),x39965))) % 169.19/169.64 [3997]E(f334(f334(f113(f886(x39971,a871)),f334(f288(x39972,x39971,x39973),x39974)),f334(f288(x39972,x39971,x39973),x39975)),f334(f288(x39972,x39971,x39973),f334(f334(f113(f886(x39972,a871)),x39974),x39975))) % 169.19/169.64 [3998]E(f334(f334(f3(f886(x39981,a871)),f334(f314(x39981,x39982,x39983),x39984)),f334(f314(x39981,x39982,x39983),x39985)),f334(f314(x39981,x39982,x39983),f334(f334(f3(f886(x39982,a871)),x39984),x39985))) % 169.19/169.64 [3999]E(f334(f334(f113(f886(x39991,a871)),f334(f314(x39991,x39992,x39993),x39994)),f334(f314(x39991,x39992,x39993),x39995)),f334(f314(x39991,x39992,x39993),f334(f334(f113(f886(x39992,a871)),x39994),x39995))) % 169.19/169.64 [4000]E(f334(f334(f104(f886(x40001,a871)),f334(f314(x40001,x40002,x40003),x40004)),f334(f314(x40001,x40002,x40003),x40005)),f334(f314(x40001,x40002,x40003),f334(f334(f104(f886(x40002,a871)),x40004),x40005))) % 169.19/169.64 [4002]E(f189(x40021,x40022,f189(x40021,x40022,x40023,x40024),x40025),f189(x40021,x40022,x40023,f334(f334(f104(f886(x40021,a871)),x40024),x40025))) % 169.19/169.64 [4064]E(f334(f334(f159(x40641,f334(f334(f134(x40641),x40642),f334(f334(f151(x40641),x40643),x40644))),f334(f196(f878(x40641)),x40642)),x40645),f334(f334(f134(x40641),x40642),f334(f334(f151(x40641),x40645),x40644))) % 169.19/169.64 [4072]E(f334(f334(f43(x40721,f886(x40722,a871)),x40723),f334(f334(f10(f886(x40722,a871),f886(x40722,a871),x40721),f334(f312(x40722),x40724)),x40725)),f334(f334(f312(x40722),x40724),f334(f334(f43(x40721,f886(x40722,a871)),x40723),x40725))) % 169.19/169.64 [4142]E(f189(x41421,x41422,f334(f334(f334(f73(x41421,f881(x41422)),x41423),x41424),f334(f241(x41422),x41425)),f334(f80(f886(x41421,a871)),f334(f334(f312(x41421),x41424),f195(f886(x41421,a871))))),f189(x41421,x41422,x41423,f334(f80(f886(x41421,a871)),f334(f334(f312(x41421),x41424),f195(f886(x41421,a871)))))) % 169.19/169.64 [4233]E(f334(f334(f154(x42331,x42332),x42333),f334(f136(x42331,f334(f74(x42332,a871,x42331,x42334),x42333)),x42335)),f334(f136(x42332,x42334),f334(f334(f154(x42331,x42332),x42333),x42335))) % 169.19/169.64 [4239]E(f334(f196(f878(x42391)),f334(f136(x42391,x42392),f334(f334(f154(x42393,x42391),x42394),x42395))),f334(f196(f878(x42393)),f334(f136(x42393,f334(f74(x42391,a871,x42393,x42392),x42394)),x42395))) % 169.19/169.64 [4377]E(f334(f334(f113(f886(x43771,a871)),f334(f334(f3(f886(x43771,a871)),f185(x43771,x43772,x43773)),f334(f254(x43771),f334(f334(f9(x43771,f886(x43771,a871),a871),f336(x43771)),f334(f334(f3(f886(x43771,a871)),x43774),f185(x43771,x43772,x43775)))))),f334(f254(x43771),f334(f334(f9(x43771,f886(x43771,a871),a871),f336(x43771)),f334(f334(f104(f886(x43771,a871)),x43774),f185(x43771,x43772,x43775))))),f185(x43771,x43772,f77(x43771,f881(x43772),x43773,x43775,x43774))) % 169.19/169.64 [4452]E(f334(f156(f878(f885(x44521,x44522)),x44522,f116(f885(x44521,x44522)),f334(f334(f9(x44522,f886(f878(x44522),f878(f885(x44521,x44522))),f886(f878(x44522),f878(f885(x44521,x44522)))),f334(f334(f10(f886(f878(f885(x44521,x44522)),f878(f885(x44521,x44522))),f886(f886(f878(x44522),f878(f885(x44521,x44522))),f886(f878(x44522),f878(f885(x44521,x44522)))),x44522),f10(f878(f885(x44521,x44522)),f878(f885(x44521,x44522)),f878(x44522))),f334(f334(f10(f885(x44521,x44522),f886(f878(f885(x44521,x44522)),f878(f885(x44521,x44522))),x44522),f151(f885(x44521,x44522))),f334(f269(x44521,x44522),x44523)))),f334(f183(x44521,x44522),x44524))),x44525),f334(f334(f183(x44521,x44522),f334(f334(f151(x44521),x44523),x44524)),x44525)) % 169.19/169.64 [3923]E(f334(f334(f159(x39231,f334(f334(f159(x39231,x39232),x39233),x39234)),x39233),x39235),f334(f334(f159(x39231,x39232),x39233),x39235)) % 169.19/169.64 [3977]E(f334(f265(x39771,x39772),f334(f334(f312(f885(x39771,x39772)),f334(f334(f269(x39771,x39772),x39773),x39774)),x39775)),f334(f334(f312(x39772),x39774),f334(f265(x39771,x39772),x39775))) % 169.19/169.64 [3978]E(f334(f267(x39781,x39782),f334(f334(f312(f885(x39781,x39782)),f334(f334(f269(x39781,x39782),x39783),x39784)),x39785)),f334(f334(f312(x39781),x39783),f334(f267(x39781,x39782),x39785))) % 169.19/169.64 [4027]E(f123(x40271,x40272,f334(x40273,x40274),f334(f334(f9(x40271,a102,f879(f881(x40272))),x40275),x40274)),f334(f203(x40271,x40272,x40273,x40275),x40274)) % 169.19/169.64 [4057]E(f334(f334(f3(f886(f885(x40571,x40572),a871)),f334(f334(f271(x40571,x40572),x40573),x40574)),f334(f334(f271(x40571,x40572),x40575),x40574)),f334(f334(f271(x40571,x40572),f334(f334(f3(f886(x40571,a871)),x40573),x40575)),x40574)) % 169.19/169.64 [4058]E(f334(f334(f113(f886(f885(x40581,x40582),a871)),f334(f334(f271(x40581,x40582),x40583),x40584)),f334(f334(f271(x40581,x40582),x40585),x40584)),f334(f334(f271(x40581,x40582),f334(f334(f113(f886(x40581,a871)),x40583),x40585)),x40584)) % 169.19/169.64 [4059]E(f334(f334(f104(f886(f885(x40591,x40592),a871)),f334(f334(f271(x40591,x40592),x40593),x40594)),f334(f334(f271(x40591,x40592),x40595),x40594)),f334(f334(f271(x40591,x40592),f334(f334(f104(f886(x40591,a871)),x40593),x40595)),x40594)) % 169.19/169.64 [4120]E(f334(f334(f104(f886(x41201,a871)),f334(f334(f43(x41202,f886(x41201,a871)),x41203),x41204)),f334(f334(f43(x41202,f886(x41201,a871)),x41205),x41204)),f334(f334(f43(x41202,f886(x41201,a871)),f334(f334(f113(f886(x41202,a871)),x41203),x41205)),x41204)) % 169.19/169.64 [4121]E(f334(f334(f113(f886(x41211,a871)),f334(f334(f44(x41212,f886(x41211,a871)),x41213),x41214)),f334(f334(f44(x41212,f886(x41211,a871)),x41215),x41214)),f334(f334(f44(x41212,f886(x41211,a871)),f334(f334(f113(f886(x41212,a871)),x41213),x41215)),x41214)) % 169.19/169.64 [4135]E(f334(f334(f43(x41351,f886(x41352,a871)),x41353),f334(f334(f10(f886(x41352,a871),f886(x41352,a871),x41351),f334(f113(f886(x41352,a871)),x41354)),x41355)),f334(f334(f113(f886(x41352,a871)),x41354),f334(f334(f43(x41351,f886(x41352,a871)),x41353),x41355))) % 169.19/169.64 [4136]E(f334(f334(f44(x41361,f886(x41362,a871)),x41363),f334(f334(f10(f886(x41362,a871),f886(x41362,a871),x41361),f334(f3(f886(x41362,a871)),x41364)),x41365)),f334(f334(f3(f886(x41362,a871)),x41364),f334(f334(f43(x41361,f886(x41362,a871)),x41363),x41365))) % 169.19/169.64 [4137]E(f334(f334(f44(x41371,f886(x41372,a871)),x41373),f334(f334(f10(f886(x41372,a871),f886(x41372,a871),x41371),f334(f104(f886(x41372,a871)),x41374)),x41375)),f334(f334(f104(f886(x41372,a871)),x41374),f334(f334(f44(x41371,f886(x41372,a871)),x41373),x41375))) % 169.19/169.64 [4174]E(f186(x41741,x41742,x41743,f334(f179(x41741,x41742),f334(f169(f885(x41741,x41742)),f334(f334(f183(x41741,x41742),x41744),x41745)))),f188(x41741,x41742,x41743,x41744,x41745)) % 169.19/169.64 [4196]E(f192(f878(x41961),f334(f334(f151(x41961),x41962),x41963),f334(f334(f10(f878(x41961),f878(x41961),a877),f334(f151(x41961),x41964)),f334(f334(f9(a877,x41961,f878(x41961)),f159(x41961,x41963)),x41962)),x41965),f334(f334(f159(x41961,f334(f334(f151(x41961),x41964),x41963)),x41965),x41962)) % 169.19/169.64 [4200]E(f334(f334(f43(x42001,f886(f885(x42002,x42003),a871)),x42004),f334(f334(f10(f886(f885(x42003,x42002),a871),f886(f885(x42002,x42003),a871),x42001),f289(x42003,x42002)),x42005)),f334(f289(x42003,x42002),f334(f334(f43(x42001,f886(f885(x42003,x42002),a871)),x42004),x42005))) % 169.19/169.64 [4201]E(f334(f334(f44(x42011,f886(f885(x42012,x42013),a871)),x42014),f334(f334(f10(f886(f885(x42013,x42012),a871),f886(f885(x42012,x42013),a871),x42011),f289(x42013,x42012)),x42015)),f334(f289(x42013,x42012),f334(f334(f44(x42011,f886(f885(x42013,x42012),a871)),x42014),x42015))) % 169.19/169.64 [4257]E(f185(x42571,x42572,f334(f334(f20(x42571,f881(x42573),f881(x42572)),f334(f334(f10(f886(x42573,x42572),f886(f881(x42573),f881(x42572)),x42571),f207(x42573,x42572)),x42574)),x42575)),f185(x42571,x42573,x42575)) % 169.19/169.64 [4308]P104(f334(f334(f249(f886(x43081,a871)),f334(f334(f3(f886(x43081,a871)),f334(f313(x43082,x43081,x43083),x43084)),f334(f313(x43082,x43081,x43083),x43085))),f334(f313(x43082,x43081,x43083),f334(f334(f3(f886(x43082,a871)),x43084),x43085)))) % 169.19/169.64 [4456]E(f334(f156(f878(f885(x44561,x44562)),x44561,f116(f885(x44561,x44562)),f334(f334(f9(x44561,f886(f878(x44561),f878(f885(x44561,x44562))),f886(f878(x44561),f878(f885(x44561,x44562)))),f334(f334(f10(f886(f878(f885(x44561,x44562)),f878(f885(x44561,x44562))),f886(f886(f878(x44561),f878(f885(x44561,x44562))),f886(f878(x44561),f878(f885(x44561,x44562)))),x44561),f10(f878(f885(x44561,x44562)),f878(f885(x44561,x44562)),f878(x44561))),f334(f334(f10(f885(x44561,x44562),f886(f878(f885(x44561,x44562)),f878(f885(x44561,x44562))),x44561),f151(f885(x44561,x44562))),f334(f334(f9(x44561,x44562,f885(x44561,x44562)),f269(x44561,x44562)),x44563)))),f334(f334(f9(f878(x44561),f878(x44562),f878(f885(x44561,x44562))),f183(x44561,x44562)),x44564))),x44565),f334(f334(f183(x44561,x44562),x44565),f334(f334(f151(x44562),x44563),x44564))) % 169.19/169.64 [4162]E(f334(f334(f113(f886(x41621,a871)),f334(f288(x41622,x41621,x41623),x41624)),f334(f288(x41622,x41621,x41625),x41624)),f334(f288(x41622,x41621,f334(f334(f113(f886(f885(x41622,x41621),a871)),x41623),x41625)),x41624)) % 169.19/169.64 [4203]E(f334(f334(f134(f885(x42031,x42032)),f334(f334(f183(x42031,x42032),x42033),f334(f334(f176(x42032),f334(f196(f878(x42031)),x42033)),x42034))),f334(f334(f183(x42031,x42032),x42035),f334(f334(f138(x42032),f334(f196(f878(x42031)),x42033)),x42034))),f334(f334(f183(x42031,x42032),f334(f334(f134(x42031),x42033),x42035)),x42034)) % 169.19/169.64 [4311]E(f334(f334(f271(x43111,x43112),x43113),f334(f334(f20(x43111,f886(x43112,a871),f886(x43112,a871)),f334(f334(f10(f886(x43112,a871),f886(f886(x43112,a871),f886(x43112,a871)),x43111),f3(f886(x43112,a871))),x43114)),x43115)),f334(f334(f3(f886(f885(x43111,x43112),a871)),f334(f334(f271(x43111,x43112),x43113),x43114)),f334(f334(f271(x43111,x43112),x43113),x43115))) % 169.19/169.64 [4312]E(f334(f334(f271(x43121,x43122),x43123),f334(f334(f20(x43121,f886(x43122,a871),f886(x43122,a871)),f334(f334(f10(f886(x43122,a871),f886(f886(x43122,a871),f886(x43122,a871)),x43121),f113(f886(x43122,a871))),x43124)),x43125)),f334(f334(f113(f886(f885(x43121,x43122),a871)),f334(f334(f271(x43121,x43122),x43123),x43124)),f334(f334(f271(x43121,x43122),x43123),x43125))) % 169.19/169.64 [4313]E(f334(f334(f271(x43131,x43132),x43133),f334(f334(f20(x43131,f886(x43132,a871),f886(x43132,a871)),f334(f334(f10(f886(x43132,a871),f886(f886(x43132,a871),f886(x43132,a871)),x43131),f104(f886(x43132,a871))),x43134)),x43135)),f334(f334(f104(f886(f885(x43131,x43132),a871)),f334(f334(f271(x43131,x43132),x43133),x43134)),f334(f334(f271(x43131,x43132),x43133),x43135))) % 169.19/169.64 [4317]E(f334(f334(f43(x43171,f886(x43172,a871)),x43173),f334(f334(f9(x43171,f886(x43172,a871),f886(x43172,a871)),f334(f334(f10(f886(x43172,a871),f886(f886(x43172,a871),f886(x43172,a871)),x43171),f113(f886(x43172,a871))),x43174)),x43175)),f334(f334(f113(f886(x43172,a871)),f334(f334(f43(x43171,f886(x43172,a871)),x43173),x43174)),x43175)) % 169.19/169.64 [4318]E(f334(f334(f44(x43181,f886(x43182,a871)),x43183),f334(f334(f9(x43181,f886(x43182,a871),f886(x43182,a871)),f334(f334(f10(f886(x43182,a871),f886(f886(x43182,a871),f886(x43182,a871)),x43181),f3(f886(x43182,a871))),x43184)),x43185)),f334(f334(f3(f886(x43182,a871)),f334(f334(f44(x43181,f886(x43182,a871)),x43183),x43184)),x43185)) % 169.19/169.64 [4319]E(f334(f334(f44(x43191,f886(x43192,a871)),x43193),f334(f334(f9(x43191,f886(x43192,a871),f886(x43192,a871)),f334(f334(f10(f886(x43192,a871),f886(f886(x43192,a871),f886(x43192,a871)),x43191),f104(f886(x43192,a871))),x43194)),x43195)),f334(f334(f104(f886(x43192,a871)),f334(f334(f44(x43191,f886(x43192,a871)),x43193),x43194)),x43195)) % 169.19/169.64 [4323]E(f334(f334(f43(x43231,f886(x43232,a871)),x43233),f334(f334(f20(x43231,f886(x43232,a871),f886(x43232,a871)),f334(f334(f10(f886(x43232,a871),f886(f886(x43232,a871),f886(x43232,a871)),x43231),f104(f886(x43232,a871))),x43234)),x43235)),f334(f334(f104(f886(x43232,a871)),f334(f334(f43(x43231,f886(x43232,a871)),x43233),x43234)),f334(f334(f43(x43231,f886(x43232,a871)),x43233),x43235))) % 169.19/169.64 [4324]E(f334(f334(f44(x43241,f886(x43242,a871)),x43243),f334(f334(f20(x43241,f886(x43242,a871),f886(x43242,a871)),f334(f334(f10(f886(x43242,a871),f886(f886(x43242,a871),f886(x43242,a871)),x43241),f113(f886(x43242,a871))),x43244)),x43245)),f334(f334(f113(f886(x43242,a871)),f334(f334(f44(x43241,f886(x43242,a871)),x43243),x43244)),f334(f334(f44(x43241,f886(x43242,a871)),x43243),x43245))) % 169.19/169.64 [4338]E(f334(f334(f43(x43381,f886(x43382,a871)),x43383),f334(f334(f20(x43381,f886(x43382,a871),f886(x43382,a871)),f334(f334(f10(f886(x43382,a871),f886(f886(x43382,a871),f886(x43382,a871)),x43381),f104(f886(x43382,a871))),x43384)),x43385)),f334(f334(f104(f886(x43382,a871)),f42(f886(x43382,a871),f334(f313(x43381,f886(x43382,a871),x43384),x43383))),f42(f886(x43382,a871),f334(f313(x43381,f886(x43382,a871),x43385),x43383)))) % 169.19/169.64 [4339]E(f334(f334(f44(x43391,f886(x43392,a871)),x43393),f334(f334(f20(x43391,f886(x43392,a871),f886(x43392,a871)),f334(f334(f10(f886(x43392,a871),f886(f886(x43392,a871),f886(x43392,a871)),x43391),f113(f886(x43392,a871))),x43394)),x43395)),f334(f334(f113(f886(x43392,a871)),f41(f886(x43392,a871),f334(f313(x43391,f886(x43392,a871),x43394),x43393))),f41(f886(x43392,a871),f334(f313(x43391,f886(x43392,a871),x43395),x43393)))) % 169.19/169.65 [4373]E(f334(f334(f138(x43731),f334(f196(f878(x43731)),f178(x43731,x43732,f334(f334(f154(x43733,x43731),x43734),x43735)))),f334(f334(f154(x43733,x43731),x43734),x43735)),f334(f334(f154(x43733,x43731),x43734),f334(f334(f138(x43733),f334(f196(f878(x43733)),f178(x43733,f334(f74(x43731,a871,x43733,x43732),x43734),x43735))),x43735))) % 169.19/169.65 [4247]E(f334(f334(f134(f885(x42471,x42472)),f334(f334(f183(x42471,x42472),f334(f334(f176(x42471),f334(f196(f878(x42472)),x42473)),x42474)),x42473)),f334(f334(f183(x42471,x42472),f334(f334(f138(x42471),f334(f196(f878(x42472)),x42473)),x42474)),x42475)),f334(f334(f183(x42471,x42472),x42474),f334(f334(f134(x42472),x42473),x42475))) % 169.19/169.65 [4365]E(f86(x43651,f334(f334(f20(x43651,a871,a871),f334(f334(f10(a871,f886(a871,a871),x43651),a332),f334(f334(f9(x43651,f886(x43651,a871),a871),f336(x43651)),x43652))),f334(f334(f9(x43651,x43653,a871),f334(f334(f10(x43653,f886(x43653,a871),x43651),a331),x43654)),x43655))),f334(f78(x43651,x43653,x43652,x43654),x43655)) % 169.19/169.65 [4417]E(f334(f334(f87(a1,x44171),f334(f106(a1),f334(f334(f81(a1),x44172),a100))),f334(f334(f20(a1,x44171,x44171),f334(f334(f9(a1,x44171,f886(x44171,x44171)),f334(f334(f10(a871,f886(x44171,f886(x44171,x44171)),a1),f99(x44171)),a201)),f192(x44171,x44173,x44174,x44175))),f334(f334(f10(a877,x44171,a1),x44174),f334(f334(f9(a1,a877,a877),f334(f334(f10(a877,f886(a877,a877),a1),f81(a877)),a107)),x44175)))),f192(x44171,x44173,x44174,f334(f334(f81(a877),f334(f106(a877),x44172)),x44175))) % 169.19/169.65 [4453]E(f334(f179(x44531,x44532),f334(f334(f154(f885(x44531,x44533),f885(x44531,x44532)),f334(f273(x44531,x44533,f885(x44531,x44532)),f334(f334(f9(x44531,f886(x44533,x44532),f886(x44533,f885(x44531,x44532))),f334(f334(f10(f886(x44532,f885(x44531,x44532)),f886(f886(x44533,x44532),f886(x44533,f885(x44531,x44532))),x44531),f10(x44532,f885(x44531,x44532),x44533)),f269(x44531,x44532))),x44534))),x44535)),f334(f74(f881(x44533),f881(x44532),x44531,f334(f207(x44533,x44532),x44534)),f334(f179(x44531,x44533),x44535))) % 169.19/169.65 [4410]E(f185(x44101,x44102,f334(f334(f20(x44101,f881(x44102),f881(x44102)),f334(f334(f20(x44101,f881(x44102),f886(f881(x44102),f881(x44102))),f334(f334(f10(a871,f886(f881(x44102),f886(f881(x44102),f881(x44102))),x44101),f99(f881(x44102))),x44103)),x44104)),x44105)),f334(f334(f113(f886(x44101,a871)),f334(f334(f104(f886(x44101,a871)),f185(x44101,x44102,x44104)),f334(f254(x44101),x44103))),f334(f334(f104(f886(x44101,a871)),f185(x44101,x44102,x44105)),f334(f254(x44101),f334(f334(f10(a871,a871,x44101),a329),x44103))))) % 169.19/169.65 [4451]E(f334(f334(f87(a1,x44511),f334(f106(a1),f334(f334(f81(a1),x44512),a100))),f334(f334(f20(a1,x44511,x44511),f334(f334(f9(a1,x44511,f886(x44511,x44511)),f334(f334(f10(a871,f886(x44511,f886(x44511,x44511)),a1),f99(x44511)),a201)),f334(f191(x44511,x44513,x44514),x44515))),f334(f334(f20(a1,x44511,x44511),f334(f334(f10(a877,f886(x44511,x44511),a1),x44514),f334(f334(f9(a1,a877,a877),f334(f334(f10(a877,f886(a877,a877),a1),f81(a877)),a107)),x44515))),f334(f334(f10(a877,x44511,a1),f191(x44511,x44513,x44514)),f334(f334(f9(a1,a877,a877),f334(f334(f10(a877,f886(a877,a877),a1),f81(a877)),a107)),x44515))))),f334(f191(x44511,x44513,x44514),f334(f334(f81(a877),f334(f106(a877),x44512)),x44515))) % 169.19/169.65 [4485]E(f334(f254(f885(x44851,x44852)),f334(f273(x44851,x44852,a871),f334(f334(f10(f886(x44852,f886(x44853,a871)),f886(x44852,a871),x44851),f334(f10(f886(x44853,a871),a871,x44852),f88(x44853))),f334(f334(f9(x44851,f886(x44852,f886(x44853,a871)),f886(x44852,f886(x44853,a871))),f334(f334(f10(f886(f886(x44853,a871),f886(x44853,a871)),f886(f886(x44852,f886(x44853,a871)),f886(x44852,f886(x44853,a871))),x44851),f10(f886(x44853,a871),f886(x44853,a871),x44852)),f334(f334(f10(f886(x44853,f886(a871,a871)),f886(f886(x44853,a871),f886(x44853,a871)),x44851),f20(x44853,a871,a871)),f334(f334(f10(f886(x44853,a871),f886(x44853,f886(a871,a871)),x44851),f334(f10(a871,f886(a871,a871),x44853),a332)),f334(f334(f9(x44851,f886(f885(x44851,x44853),a871),f886(x44853,a871)),f334(f334(f10(f886(x44853,f886(f886(f885(x44851,x44853),a871),a871)),f886(f886(f885(x44851,x44853),a871),f886(x44853,a871)),x44851),f9(x44853,f886(f885(x44851,x44853),a871),a871)),f334(f334(f10(f886(x44853,f885(x44851,x44853)),f886(x44853,f886(f886(f885(x44851,x44853),a871),a871)),x44851),f334(f10(f885(x44851,x44853),f886(f886(f885(x44851,x44853),a871),a871),x44853),f336(f885(x44851,x44853)))),f269(x44851,x44853)))),x44854))))),f334(f334(f9(x44852,f886(f885(x44853,x44852),a871),f886(x44853,a871)),f334(f334(f10(f886(x44853,f886(f886(f885(x44853,x44852),a871),a871)),f886(f886(f885(x44853,x44852),a871),f886(x44853,a871)),x44852),f9(x44853,f886(f885(x44853,x44852),a871),a871)),f334(f334(f10(f886(x44853,f885(x44853,x44852)),f886(x44853,f886(f886(f885(x44853,x44852),a871),a871)),x44852),f334(f10(f885(x44853,x44852),f886(f886(f885(x44853,x44852),a871),a871),x44853),f336(f885(x44853,x44852)))),f334(f9(x44853,x44852,f885(x44853,x44852)),f269(x44853,x44852))))),x44855))))),f334(f334(f291(x44851,x44853,x44852),x44854),x44855)) % 169.19/169.65 [4570]~E(f31(x45701,x45702,x45703),f29(x45704,x45705,x45706)) % 169.19/169.65 [4573]~E(f30(x45731,x45732,x45733),f29(x45734,x45735,x45736)) % 169.19/169.65 [4574]~E(f30(x45741,x45742,x45743),f31(x45744,x45745,x45746)) % 169.19/169.65 [4012]E(f130(x40121,x40122,x40123,x40124,f127(x40122,x40125,x40126)),f334(f334(x40124,x40125),x40126)) % 169.19/169.65 [4088]E(f232(x40881,x40882,x40883,x40884,f229(x40881,x40882,x40885,x40886)),f334(f334(x40884,x40885),x40886)) % 169.19/169.65 [4089]E(f233(x40891,x40892,x40893,x40894,f229(x40891,x40892,x40895,x40896)),f334(f334(x40894,x40895),x40896)) % 169.19/169.65 [4231]E(f188(x42311,x42312,f186(x42311,x42312,x42313,x42314),x42315,x42316),f186(x42311,x42312,x42313,f188(x42311,x42312,x42314,x42315,x42316))) % 169.19/169.65 [4354]E(f334(f74(f885(x43541,x43542),x43542,f885(x43543,x43544),f272(x43541,x43542)),f274(x43543,x43541,x43544,x43542,x43545,x43546)),f334(f74(x43544,x43542,f885(x43543,x43544),x43546),f272(x43543,x43544))) % 169.19/169.65 [4355]E(f334(f74(f885(x43551,x43552),x43551,f885(x43553,x43554),f268(x43551,x43552)),f274(x43553,x43551,x43554,x43552,x43555,x43556)),f334(f74(x43553,x43551,f885(x43553,x43554),x43555),f268(x43553,x43554))) % 169.19/169.65 [3952]E(f334(f334(f74(x39521,x39522,x39523,x39524),x39525),x39526),f334(x39524,f334(x39525,x39526))) % 169.19/169.65 [4150]E(f234(x41501,x41502,x41503,x41504,f229(x41501,x41502,x41505,x41506)),f334(f334(f81(a877),f334(f334(f81(a877),f334(x41503,x41505)),f334(x41504,x41506))),f334(a115,f2(a877)))) % 169.19/169.65 [3744]E(f334(f334(f273(x37441,x37442,x37443),x37444),f334(f334(f269(x37441,x37442),x37445),x37446)),f334(f334(x37444,x37445),x37446)) % 169.19/169.65 [3806]E(f334(f334(f334(f10(x38061,x38062,x38063),x38064),x38065),x38066),f334(x38064,f334(x38065,x38066))) % 169.19/169.65 [3807]E(f334(f334(f334(f9(x38071,x38072,x38073),x38074),x38075),x38076),f334(f334(x38074,x38076),x38075)) % 169.19/169.65 [3825]E(f334(f334(f334(f20(x38251,x38252,x38253),x38254),x38255),x38256),f334(f334(x38254,x38256),f334(x38255,x38256))) % 169.19/169.65 [3847]E(f334(f156(x38471,x38472,x38473,x38474),f334(f334(f151(x38472),x38475),x38476)),f334(f334(x38474,x38475),x38476)) % 169.19/169.65 [3888]E(f170(f885(x38881,x38882),f334(f334(f247(a877),x38883),x38884),f334(f334(f269(x38881,x38882),x38885),x38886)),f334(f334(f183(x38881,x38882),f170(x38881,x38883,x38885)),f170(x38882,x38884,x38886))) % 169.19/169.65 [3956]E(f334(f334(f151(f885(x39561,x39562)),f334(f334(f269(x39561,x39562),x39563),x39564)),f334(f334(f183(x39561,x39562),x39565),x39566)),f334(f334(f183(x39561,x39562),f334(f334(f151(x39561),x39563),x39565)),f334(f334(f151(x39562),x39564),x39566))) % 169.19/169.65 [3958]E(f334(f334(f154(x39581,x39582),x39583),f334(f334(f159(x39581,x39584),x39585),x39586)),f334(f334(f159(x39582,f334(f334(f154(x39581,x39582),x39583),x39584)),x39585),f334(x39583,x39586))) % 169.19/169.65 [4001]E(f334(f142(x40011,x40012,x40013,x40014),f334(f334(f151(x40012),x40015),x40016)),f334(f142(x40011,x40012,x40013,f334(f334(x40013,x40014),x40015)),x40016)) % 169.19/169.65 [4028]E(f276(x40281,x40282,x40283,x40284,f334(f334(f269(x40281,x40282),x40285),x40286)),f334(f334(x40284,x40285),x40286)) % 169.19/169.65 [4113]E(f334(f334(f44(x41131,f886(x41132,a871)),x41133),f334(f74(x41134,f886(x41132,a871),x41131,x41135),x41136)),f334(f334(f44(x41134,f886(x41132,a871)),f334(f313(x41131,x41134,x41136),x41133)),x41135)) % 169.19/169.65 [4165]E(f334(f334(f154(x41651,x41652),x41653),f334(f334(f154(x41654,x41651),x41655),x41656)),f334(f334(f154(x41654,x41652),f334(f74(x41651,x41652,x41654,x41653),x41655)),x41656)) % 169.19/169.65 [4167]E(f334(f334(f207(x41671,x41672),x41673),f334(f334(f207(x41674,x41671),x41675),x41676)),f334(f334(f207(x41674,x41672),f334(f74(x41671,x41672,x41674,x41673),x41675)),x41676)) % 169.19/169.65 [4172]E(f334(f313(x41721,x41722,f334(f74(x41723,x41722,x41721,x41724),x41725)),x41726),f334(f313(x41723,x41722,x41724),f334(f313(x41721,x41723,x41725),x41726))) % 169.19/169.65 [4173]E(f334(f314(x41731,x41732,f334(f74(x41733,x41732,x41731,x41734),x41735)),x41736),f334(f314(x41731,x41733,x41735),f334(f314(x41733,x41732,x41734),x41736))) % 169.19/169.65 [4202]E(f186(x42021,x42022,x42023,f334(f334(f334(f73(x42021,f881(x42022)),x42024),x42025),f334(f241(x42022),x42026))),f334(f334(f334(f73(x42021,f881(x42022)),f186(x42021,x42022,x42023,x42024)),x42025),f334(f241(x42022),x42026))) % 169.19/169.65 [4204]E(f334(f142(x42041,x42042,x42043,f334(f142(x42041,x42042,x42043,x42044),x42045)),x42046),f334(f142(x42041,x42042,x42043,x42044),f334(f334(f134(x42042),x42045),x42046))) % 169.19/169.65 [4344]E(f334(f274(x43441,x43441,x43442,x43443,f35(x43441),x43444),f334(f334(f269(x43441,x43442),x43445),x43446)),f334(f334(f269(x43441,x43443),x43445),f334(x43444,x43446))) % 169.19/169.65 [4345]E(f334(f274(x43451,x43452,x43453,x43453,x43454,f35(x43453)),f334(f334(f269(x43451,x43453),x43455),x43456)),f334(f334(f269(x43452,x43453),f334(x43454,x43455)),x43456)) % 169.19/169.65 [4435]E(f334(f334(f154(f885(x44351,x44352),f885(x44351,x44353)),f334(f273(x44351,x44352,f885(x44351,x44353)),f334(f334(f9(x44351,f886(x44352,x44353),f886(x44352,f885(x44351,x44353))),f334(f334(f10(f886(x44353,f885(x44351,x44353)),f886(f886(x44352,x44353),f886(x44352,f885(x44351,x44353))),x44351),f10(x44353,f885(x44351,x44353),x44352)),f269(x44351,x44353))),x44354))),f334(f334(f183(x44351,x44352),x44355),x44356)),f334(f334(f183(x44351,x44353),x44355),f334(f334(f154(x44352,x44353),x44354),x44356))) % 169.19/169.65 [3812]E(f97(x38121,x38122,x38123,f334(f334(f334(f93(x38121),x38124),x38125),x38126)),f334(f334(f334(x38123,x38124),x38125),x38126)) % 169.19/169.65 [3813]E(f98(x38131,x38132,x38133,f334(f334(f334(f93(x38131),x38134),x38135),x38136)),f334(f334(f334(x38133,x38134),x38135),x38136)) % 169.19/169.65 [4011]E(f334(f334(f74(x40111,x40112,x40113,f334(f18(x40112,x40111),x40114)),x40115),x40116),x40114) % 169.19/169.65 [4047]E(f334(f313(x40471,x40472,x40473),f334(f313(x40474,x40471,x40475),x40476)),f334(f313(x40474,x40472,f334(f334(f10(x40471,x40472,x40474),x40473),x40475)),x40476)) % 169.19/169.65 [4053]E(f334(f334(f43(x40531,f886(x40532,a871)),f334(f313(x40533,x40531,x40534),x40535)),x40536),f334(f334(f43(x40533,f886(x40532,a871)),x40535),f334(f334(f10(x40531,f886(x40532,a871),x40533),x40536),x40534))) % 169.19/169.65 [4054]E(f334(f334(f44(x40541,f886(x40542,a871)),f334(f313(x40543,x40541,x40544),x40545)),x40546),f334(f334(f44(x40543,f886(x40542,a871)),x40545),f334(f334(f10(x40541,f886(x40542,a871),x40543),x40546),x40544))) % 169.19/169.65 [4055]E(f334(f334(f43(x40551,f886(x40552,a871)),x40553),f334(f334(f10(x40554,f886(x40552,a871),x40551),x40555),x40556)),f334(f334(f43(x40554,f886(x40552,a871)),f334(f313(x40551,x40554,x40556),x40553)),x40555)) % 169.19/169.65 [4056]E(f334(f334(f44(x40561,f886(x40562,a871)),x40563),f334(f334(f10(x40564,f886(x40562,a871),x40561),x40565),x40566)),f334(f334(f44(x40564,f886(x40562,a871)),f334(f313(x40561,x40564,x40566),x40563)),x40565)) % 169.19/169.65 [4115]E(f334(f334(f44(x41151,f886(x41152,a871)),x41153),f334(f334(f10(f886(x41154,a871),f886(x41152,a871),x41151),f313(x41154,x41152,x41155)),x41156)),f334(f313(x41154,x41152,x41155),f334(f334(f44(x41151,f886(x41154,a871)),x41153),x41156))) % 169.19/169.65 [4116]E(f334(f334(f44(x41161,f886(x41162,a871)),x41163),f334(f334(f10(f886(x41164,a871),f886(x41162,a871),x41161),f288(x41164,x41162,x41165)),x41166)),f334(f288(x41164,x41162,x41165),f334(f334(f44(x41161,f886(x41164,a871)),x41163),x41166))) % 169.19/169.65 [4117]E(f334(f334(f43(x41171,f886(x41172,a871)),x41173),f334(f334(f10(f886(x41174,a871),f886(x41172,a871),x41171),f314(x41172,x41174,x41175)),x41176)),f334(f314(x41172,x41174,x41175),f334(f334(f43(x41171,f886(x41174,a871)),x41173),x41176))) % 169.19/169.65 [4118]E(f334(f334(f44(x41181,f886(x41182,a871)),x41183),f334(f334(f10(f886(x41184,a871),f886(x41182,a871),x41181),f314(x41182,x41184,x41185)),x41186)),f334(f314(x41182,x41184,x41185),f334(f334(f44(x41181,f886(x41184,a871)),x41183),x41186))) % 169.19/169.65 [4210]E(f334(f142(x42101,x42102,f334(f9(x42102,x42101,x42101),x42103),x42104),f334(f169(x42102),f334(f334(f151(x42102),x42105),x42106))),f334(f334(x42103,x42105),f334(f142(x42101,x42102,f334(f9(x42102,x42101,x42101),x42103),x42104),f334(f169(x42102),x42106)))) % 169.19/169.65 [4270]E(f334(f334(f20(f885(x42701,x42702),x42702,x42703),f334(f334(f10(x42704,f886(x42702,x42703),f885(x42701,x42702)),x42705),f334(f334(f10(x42701,x42704,f885(x42701,x42702)),x42706),f268(x42701,x42702)))),f272(x42701,x42702)),f334(f273(x42701,x42702,x42703),f334(f334(f10(x42704,f886(x42702,x42703),x42701),x42705),x42706))) % 169.19/169.65 [4277]E(f334(f142(x42771,x42772,f334(f9(x42772,x42771,x42771),x42773),f334(f142(x42771,x42772,f334(f9(x42772,x42771,x42771),x42773),x42774),f334(f169(x42772),x42775))),f334(f169(x42772),x42776)),f334(f142(x42771,x42772,f334(f9(x42772,x42771,x42771),x42773),x42774),f334(f169(x42772),f334(f334(f134(x42772),x42776),x42775)))) % 169.19/169.65 [4279]E(f334(f334(f154(f885(x42791,x42792),f885(x42793,x42792)),f334(f273(x42791,x42792,f885(x42793,x42792)),f334(f334(f10(x42793,f886(x42792,f885(x42793,x42792)),x42791),f269(x42793,x42792)),x42794))),f334(f334(f183(x42791,x42792),x42795),x42796)),f334(f334(f183(x42793,x42792),f334(f334(f154(x42791,x42793),x42794),x42795)),x42796)) % 169.19/169.65 [4327]P104(f334(f334(f249(f886(x43271,a871)),f334(f288(x43272,x43271,x43273),f334(f334(f43(x43274,f886(x43272,a871)),x43275),x43276))),f334(f334(f43(x43274,f886(x43271,a871)),x43275),f334(f334(f10(f886(x43272,a871),f886(x43271,a871),x43274),f288(x43272,x43271,x43273)),x43276)))) % 169.19/169.65 [4128]E(f334(f334(f183(x41281,x41282),f334(f334(f159(x41281,x41283),x41284),f334(f268(x41281,x41282),x41285))),f334(f334(f159(x41282,x41286),x41284),f334(f272(x41281,x41282),x41285))),f334(f334(f159(f885(x41281,x41282),f334(f334(f183(x41281,x41282),x41283),x41286)),x41284),x41285)) % 169.19/169.65 [4191]E(f334(f334(f113(f886(f885(x41911,x41912),a871)),f334(f334(f291(x41911,x41913,x41912),x41914),x41915)),f334(f334(f291(x41911,x41913,x41912),x41914),x41916)),f334(f334(f291(x41911,x41913,x41912),x41914),f334(f334(f113(f886(f885(x41913,x41912),a871)),x41915),x41916))) % 169.19/169.65 [4290]E(f334(f334(f312(f885(x42901,x42902)),f334(f334(f269(x42901,x42902),x42903),x42904)),f334(f334(f113(f886(f885(x42901,x42902),a871)),f334(f334(f271(x42901,x42902),x42905),f334(f18(f886(x42902,a871),x42901),f334(f334(f312(x42902),x42904),x42906)))),f334(f334(f271(x42901,x42902),f334(f334(f312(x42901),x42903),x42905)),f334(f18(f886(x42902,a871),x42901),x42906)))),f334(f334(f271(x42901,x42902),f334(f334(f312(x42901),x42903),x42905)),f334(f18(f886(x42902,a871),x42901),f334(f334(f312(x42902),x42904),x42906)))) % 169.19/169.65 [4368]E(f334(f334(f104(f886(x43681,a871)),f334(f314(x43681,x43682,f334(f74(f885(x43682,x43683),x43682,x43681,f268(x43682,x43683)),x43684)),x43685)),f334(f314(x43681,x43683,f334(f74(f885(x43682,x43683),x43683,x43681,f272(x43682,x43683)),x43684)),x43686)),f334(f314(x43681,f885(x43682,x43683),x43684),f334(f334(f271(x43682,x43683),x43685),f334(f18(f886(x43683,a871),x43682),x43686)))) % 169.19/169.65 [4112]E(f334(f334(f334(f73(x41121,x41122),f334(f334(f334(f73(x41121,x41122),x41123),x41124),x41125)),x41124),x41126),f334(f334(f334(f73(x41121,x41122),x41123),x41124),x41126)) % 169.19/169.65 [4216]E(f334(f334(f113(f886(f885(x42161,x42162),a871)),f334(f334(f291(x42161,x42163,x42162),x42164),x42165)),f334(f334(f291(x42161,x42163,x42162),x42166),x42165)),f334(f334(f291(x42161,x42163,x42162),f334(f334(f113(f886(f885(x42161,x42163),a871)),x42164),x42166)),x42165)) % 169.19/169.65 [4352]E(f334(f334(f43(x43521,f886(x43522,a871)),x43523),f334(f334(f9(x43521,f886(x43524,f886(x43522,a871)),f886(x43522,a871)),f334(f334(f10(f886(x43524,a871),f886(f886(x43524,f886(x43522,a871)),f886(x43522,a871)),x43521),f43(x43524,f886(x43522,a871))),x43525)),x43526)),f334(f334(f43(x43524,f886(x43522,a871)),f334(f334(f44(x43521,f886(x43524,a871)),x43523),x43525)),x43526)) % 169.19/169.65 [4353]E(f334(f334(f44(x43531,f886(x43532,a871)),x43533),f334(f334(f9(x43531,f886(x43534,f886(x43532,a871)),f886(x43532,a871)),f334(f334(f10(f886(x43534,a871),f886(f886(x43534,f886(x43532,a871)),f886(x43532,a871)),x43531),f44(x43534,f886(x43532,a871))),x43535)),x43536)),f334(f334(f44(x43534,f886(x43532,a871)),f334(f334(f44(x43531,f886(x43534,a871)),x43533),x43535)),x43536)) % 169.19/169.65 [4405]E(f334(f273(x44051,x44052,f885(x44053,x44054)),f334(f334(f9(x44051,f886(x44052,x44054),f886(x44052,f885(x44053,x44054))),f334(f334(f10(f886(x44054,f885(x44053,x44054)),f886(f886(x44052,x44054),f886(x44052,f885(x44053,x44054))),x44051),f10(x44054,f885(x44053,x44054),x44052)),f334(f334(f10(x44053,f886(x44054,f885(x44053,x44054)),x44051),f269(x44053,x44054)),x44055))),x44056)),f274(x44051,x44053,x44052,x44054,x44055,x44056)) % 169.19/169.65 [4326]E(f334(f334(f334(f73(x43261,f881(x43262)),f189(x43261,x43262,x43263,f334(f334(f3(f886(x43261,a871)),x43264),f334(f334(f312(x43261),x43265),f195(f886(x43261,a871)))))),x43265),x43266),f334(f334(f334(f73(x43261,f881(x43262)),f189(x43261,x43262,x43263,x43264)),x43265),x43266)) % 169.19/169.65 [4430]E(f334(f313(x44301,x44302,f334(f334(f20(x44301,x44302,x44302),f334(f334(f20(x44301,x44302,f886(x44302,x44302)),f334(f334(f10(a871,f886(x44302,f886(x44302,x44302)),x44301),f99(x44302)),x44303)),x44304)),x44305)),x44306),f334(f334(f113(f886(x44302,a871)),f334(f313(x44301,x44302,x44304),f334(f334(f104(f886(x44301,a871)),x44306),f334(f254(x44301),x44303)))),f334(f313(x44301,x44302,x44305),f334(f334(f104(f886(x44301,a871)),x44306),f334(f254(x44301),f334(f334(f10(a871,a871,x44301),a329),x44303)))))) % 169.19/169.65 [4441]E(f334(f313(x44411,f885(x44412,x44413),f334(f334(f20(x44411,x44413,f885(x44412,x44413)),f334(f334(f10(x44412,f886(x44413,f885(x44412,x44413)),x44411),f269(x44412,x44413)),x44414)),x44415)),x44416),f334(f334(f271(x44412,x44413),f334(f313(x44411,x44412,x44414),x44416)),f334(f334(f10(f886(x44411,a871),f886(x44413,a871),x44412),f313(x44411,x44413,x44415)),f334(f334(f9(x44412,f886(x44411,a871),f886(x44411,a871)),f334(f334(f10(f886(x44411,a871),f886(f886(x44411,a871),f886(x44411,a871)),x44412),f104(f886(x44411,a871))),f334(f334(f10(f886(x44412,a871),f886(x44411,a871),x44412),f314(x44411,x44412,x44414)),f334(f334(f9(x44412,f886(x44412,a871),f886(x44412,a871)),f312(x44412)),f195(f886(x44412,a871)))))),x44416)))) % 169.19/169.65 [4387]E(f334(f272(x43871,x43872),f334(f274(x43873,x43871,x43874,x43872,x43875,x43876),x43877)),f334(x43876,f334(f272(x43873,x43874),x43877))) % 169.19/169.65 [4388]E(f334(f268(x43881,x43882),f334(f274(x43883,x43881,x43884,x43882,x43885,x43886),x43887)),f334(x43885,f334(f268(x43883,x43884),x43887))) % 169.19/169.65 [4090]E(f334(f334(f183(x40901,x40902),f334(f334(f159(x40901,x40903),x40904),x40905)),f334(f334(f159(x40902,x40906),x40904),x40907)),f334(f334(f159(f885(x40901,x40902),f334(f334(f183(x40901,x40902),x40903),x40906)),x40904),f334(f334(f269(x40901,x40902),x40905),x40907))) % 169.19/169.65 [4159]E(f334(f334(f334(f275(x41591,x41592,x41593,x41594),x41595),x41596),x41597),f334(f334(f273(x41592,x41593,x41594),x41596),f334(x41595,x41597))) % 169.19/169.65 [4171]E(f334(f334(f334(f275(x41711,x41712,x41713,x41714),x41715),x41716),x41717),f334(f334(x41716,f334(f268(x41712,x41713),f334(x41715,x41717))),f334(f272(x41712,x41713),f334(x41715,x41717)))) % 169.19/169.65 [4206]E(f188(x42061,x42062,f334(f334(f334(f73(x42061,f881(x42062)),x42063),x42064),f334(f241(x42062),x42065)),x42066,x42067),f188(x42061,x42062,x42063,f334(f334(f151(x42061),x42064),x42066),f334(f334(f151(x42062),x42065),x42067))) % 169.19/169.65 [4225]E(f334(f74(x42251,x42252,x42253,x42254),f334(f74(x42255,x42251,x42253,x42256),x42257)),f334(f74(x42255,x42252,x42253,f334(f74(x42251,x42252,x42255,x42254),x42256)),x42257)) % 169.19/169.65 [4286]E(f334(f74(f881(x42861),f881(x42862),x42863,f334(f207(x42861,x42862),x42864)),f334(f334(f334(f73(x42863,f881(x42861)),x42865),x42866),f334(f241(x42861),x42867))),f334(f334(f334(f73(x42863,f881(x42862)),f334(f74(f881(x42861),f881(x42862),x42863,f334(f207(x42861,x42862),x42864)),x42865)),x42866),f334(f241(x42862),f334(x42864,x42867)))) % 169.19/169.65 [4412]E(f334(f274(x44121,x44122,x44123,x44123,x44124,f35(x44123)),f334(f274(x44121,x44121,x44125,x44123,f35(x44121),x44126),x44127)),f334(f334(f269(x44122,x44123),f334(x44124,f334(f268(x44121,x44125),x44127))),f334(x44126,f334(f272(x44121,x44125),x44127)))) % 169.19/169.65 [4413]E(f334(f274(x44131,x44131,x44132,x44133,f35(x44131),x44134),f334(f274(x44135,x44131,x44132,x44132,x44136,f35(x44132)),x44137)),f334(f334(f269(x44131,x44133),f334(x44136,f334(f268(x44135,x44132),x44137))),f334(x44134,f334(f272(x44135,x44132),x44137)))) % 169.19/169.65 [4428]E(f334(f274(x44281,x44282,x44283,x44283,x44284,f35(x44283)),f334(f274(x44285,x44281,x44283,x44283,x44286,f35(x44283)),x44287)),f334(f274(x44285,x44282,x44283,x44283,f334(f74(x44281,x44282,x44285,x44284),x44286),f35(x44283)),x44287)) % 169.19/169.65 [4429]E(f334(f274(x44291,x44291,x44292,x44293,f35(x44291),x44294),f334(f274(x44291,x44291,x44295,x44292,f35(x44291),x44296),x44297)),f334(f274(x44291,x44291,x44295,x44293,f35(x44291),f334(f74(x44292,x44293,x44295,x44294),x44296)),x44297)) % 169.19/169.65 [4438]E(f334(f274(x44381,x44382,x44383,x44383,x44384,f35(x44383)),f334(f274(x44381,x44381,x44385,x44383,f35(x44381),x44386),x44387)),f334(f274(x44382,x44382,x44385,x44383,f35(x44382),x44386),f334(f274(x44381,x44382,x44385,x44385,x44384,f35(x44385)),x44387))) % 169.19/169.65 [4125]E(f334(f334(f291(x41251,x41252,x41253),f334(f334(f291(x41251,x41254,x41252),x41255),x41256)),x41257),f334(f334(f291(x41251,x41254,x41253),x41255),f334(f334(f291(x41254,x41252,x41253),x41256),x41257))) % 169.19/169.65 [4197]E(f334(f334(f273(x41971,x41972,x41973),f334(f74(x41974,f886(x41972,x41973),x41971,x41975),x41976)),x41977),f334(f334(x41975,f334(x41976,f334(f268(x41971,x41972),x41977))),f334(f272(x41971,x41972),x41977))) % 169.19/169.65 [4250]E(f334(f74(x42501,x42502,x42503,x42504),f334(f334(f334(f73(x42503,x42501),x42505),x42506),x42507)),f334(f334(f334(f73(x42503,x42502),f334(f74(x42501,x42502,x42503,x42504),x42505)),x42506),f334(x42504,x42507))) % 169.19/169.65 [4282]E(f334(f142(x42821,x42822,f334(f9(x42822,x42821,x42821),x42823),x42824),f334(f169(x42822),f334(f334(f154(x42825,x42822),x42826),x42827))),f334(f142(x42821,x42825,f334(f9(x42825,x42821,x42821),f334(f74(x42822,f886(x42821,x42821),x42825,x42823),x42826)),x42824),f334(f169(x42825),x42827))) % 169.19/169.65 [4226]E(f334(f334(f44(x42261,f886(f885(x42262,x42263),a871)),x42264),f334(f334(f10(f886(f885(x42265,x42263),a871),f886(f885(x42262,x42263),a871),x42261),f334(f291(x42262,x42265,x42263),x42266)),x42267)),f334(f334(f291(x42262,x42265,x42263),x42266),f334(f334(f44(x42261,f886(f885(x42265,x42263),a871)),x42264),x42267))) % 169.19/169.65 [4374]E(f334(f334(f44(x43741,f886(f885(x43742,x43743),a871)),x43744),f334(f334(f9(x43741,f886(f885(x43745,x43743),a871),f886(f885(x43742,x43743),a871)),f334(f334(f10(f886(f885(x43742,x43745),a871),f886(f886(f885(x43745,x43743),a871),f886(f885(x43742,x43743),a871)),x43741),f291(x43742,x43745,x43743)),x43746)),x43747)),f334(f334(f291(x43742,x43745,x43743),f334(f334(f44(x43741,f886(f885(x43742,x43745),a871)),x43744),x43746)),x43747)) % 169.19/169.65 [4375]E(f334(f142(x43751,x43752,f334(f334(f9(x43751,f886(x43752,x43753),f886(x43752,x43751)),f334(f334(f10(f886(x43753,x43751),f886(f886(x43752,x43753),f886(x43752,x43751)),x43751),f10(x43753,x43751,x43752)),x43754)),x43755),x43756),x43757),f334(f142(x43751,x43753,x43754,x43756),f334(f334(f154(x43752,x43753),x43755),x43757))) % 169.19/169.65 [4439]E(f334(f334(f43(x44391,f886(x44392,a871)),x44393),f334(f334(f10(f886(x44394,f886(x44392,a871)),f886(x44392,a871),x44391),f334(f43(x44394,f886(x44392,a871)),x44395)),f334(f334(f9(x44391,f886(x44394,f886(x44392,a871)),f886(x44394,f886(x44392,a871))),f334(f334(f10(f886(f886(x44392,a871),f886(x44392,a871)),f886(f886(x44394,f886(x44392,a871)),f886(x44394,f886(x44392,a871))),x44391),f10(f886(x44392,a871),f886(x44392,a871),x44394)),f334(f334(f10(f886(x44392,a871),f886(f886(x44392,a871),f886(x44392,a871)),x44391),f113(f886(x44392,a871))),x44396))),x44397))),f334(f334(f113(f886(x44392,a871)),f334(f334(f43(x44391,f886(x44392,a871)),x44393),x44396)),f334(f334(f43(x44394,f886(x44392,a871)),x44395),x44397))) % 169.19/169.65 [4440]E(f334(f334(f44(x44401,f886(x44402,a871)),x44403),f334(f334(f10(f886(x44404,f886(x44402,a871)),f886(x44402,a871),x44401),f334(f44(x44404,f886(x44402,a871)),x44405)),f334(f334(f9(x44401,f886(x44404,f886(x44402,a871)),f886(x44404,f886(x44402,a871))),f334(f334(f10(f886(f886(x44402,a871),f886(x44402,a871)),f886(f886(x44404,f886(x44402,a871)),f886(x44404,f886(x44402,a871))),x44401),f10(f886(x44402,a871),f886(x44402,a871),x44404)),f334(f334(f10(f886(x44402,a871),f886(f886(x44402,a871),f886(x44402,a871)),x44401),f104(f886(x44402,a871))),x44406))),x44407))),f334(f334(f104(f886(x44402,a871)),f334(f334(f44(x44401,f886(x44402,a871)),x44403),x44406)),f334(f334(f44(x44404,f886(x44402,a871)),x44405),x44407))) % 169.19/169.65 [4433]E(f205(x44331,x44332,f334(f334(f334(x44333,x44334),x44335),x44336),f334(f334(f9(x44331,f885(a102,a102),f886(a102,f879(x44332))),f334(f334(f9(x44331,a102,f886(f885(a102,a102),f886(a102,f879(x44332)))),f334(f334(f9(x44331,a102,f886(a102,f886(f885(a102,a102),f886(a102,f879(x44332))))),x44337),x44334)),x44335)),x44336)),f334(f334(f334(f218(x44331,x44332,x44333,x44337),x44334),x44335),x44336)) % 169.19/169.65 [4446]E(f206(x44461,x44462,f334(f334(f334(x44463,x44464),x44465),x44466),f334(f334(f9(x44461,f885(a102,a102),f886(a102,f879(x44462))),f334(f334(f9(x44461,a102,f886(f885(a102,a102),f886(a102,f879(x44462)))),f334(f334(f9(x44461,a102,f886(a102,f886(f885(a102,a102),f886(a102,f879(x44462))))),x44467),x44464)),x44465)),x44466)),f220(x44461,x44462,x44463,x44467,x44464,x44465,x44466)) % 169.19/169.65 [4437]E(f203(x44371,x44372,f334(f334(f334(x44373,x44374),x44375),x44376),f334(f334(f9(x44371,f885(a102,a102),f886(a102,f879(f881(x44372)))),f334(f334(f9(x44371,a102,f886(f885(a102,a102),f886(a102,f879(f881(x44372))))),f334(f334(f9(x44371,a102,f886(a102,f886(f885(a102,a102),f886(a102,f879(f881(x44372)))))),x44377),x44374)),x44375)),x44376)),f334(f334(f334(f214(x44371,x44372,x44373,x44377),x44374),x44375),x44376)) % 169.19/169.65 [4448]E(f204(x44481,x44482,f334(f334(f334(x44483,x44484),x44485),x44486),f334(f334(f9(x44481,f885(a102,a102),f886(a102,f879(f881(x44482)))),f334(f334(f9(x44481,a102,f886(f885(a102,a102),f886(a102,f879(f881(x44482))))),f334(f334(f9(x44481,a102,f886(a102,f886(f885(a102,a102),f886(a102,f879(f881(x44482)))))),x44487),x44484)),x44485)),x44486)),f216(x44481,x44482,x44483,x44487,x44484,x44485,x44486)) % 169.19/169.65 [4346]E(f334(f274(x43461,x43462,x43463,x43464,x43465,x43466),f334(f334(f269(x43461,x43463),x43467),x43468)),f334(f334(f269(x43462,x43464),f334(x43465,x43467)),f334(x43466,x43468))) % 169.19/169.65 [4450]E(f334(f334(f154(f885(x44501,x44502),f885(x44503,x44504)),f334(f273(x44501,x44502,f885(x44503,x44504)),f334(f334(f9(x44501,f886(x44502,x44504),f886(x44502,f885(x44503,x44504))),f334(f334(f10(f886(x44504,f885(x44503,x44504)),f886(f886(x44502,x44504),f886(x44502,f885(x44503,x44504))),x44501),f10(x44504,f885(x44503,x44504),x44502)),f334(f334(f10(x44503,f886(x44504,f885(x44503,x44504)),x44501),f269(x44503,x44504)),x44505))),x44506))),f334(f334(f183(x44501,x44502),x44507),x44508)),f334(f334(f183(x44503,x44504),f334(f334(f154(x44501,x44503),x44505),x44507)),f334(f334(f154(x44502,x44504),x44506),x44508))) % 169.19/169.65 [4454]E(f334(f334(f154(f885(x44541,x44542),x44543),f334(f273(x44541,x44542,x44543),f334(f334(f10(f886(x44542,f885(x44541,x44544)),f886(x44542,x44543),x44541),f334(f10(f885(x44541,x44544),x44543,x44542),x44545)),f334(f334(f9(x44541,f886(x44542,x44544),f886(x44542,f885(x44541,x44544))),f334(f334(f10(f886(x44544,f885(x44541,x44544)),f886(f886(x44542,x44544),f886(x44542,f885(x44541,x44544))),x44541),f10(x44544,f885(x44541,x44544),x44542)),f269(x44541,x44544))),x44546)))),f334(f334(f183(x44541,x44542),x44547),x44548)),f334(f334(f154(f885(x44541,x44544),x44543),x44545),f334(f334(f183(x44541,x44544),x44547),f334(f334(f154(x44542,x44544),x44546),x44548)))) % 169.19/169.65 [4379]E(f334(f334(f154(f885(x43791,x43792),x43793),f334(f273(x43791,x43792,x43793),f334(f334(f10(f886(x43792,f885(x43794,x43792)),f886(x43792,x43793),x43791),f334(f10(f885(x43794,x43792),x43793,x43792),x43795)),f334(f334(f10(x43794,f886(x43792,f885(x43794,x43792)),x43791),f269(x43794,x43792)),x43796)))),f334(f334(f183(x43791,x43792),x43797),x43798)),f334(f334(f154(f885(x43794,x43792),x43793),x43795),f334(f334(f183(x43794,x43792),f334(f334(f154(x43791,x43794),x43796),x43797)),x43798))) % 169.19/169.65 [4337]E(f334(f334(f273(x43371,x43372,x43373),f334(f334(f10(f886(x43372,f885(x43374,x43375)),f886(x43372,x43373),x43371),f334(f10(f885(x43374,x43375),x43373,x43372),f334(f273(x43374,x43375,x43373),x43376))),x43377)),x43378),f334(f334(f273(x43374,x43375,x43373),x43376),f334(f334(f273(x43371,x43372,f885(x43374,x43375)),x43377),x43378))) % 169.19/169.65 [4455]E(f334(f334(f44(f885(x44551,x44552),f886(f885(x44553,x44554),a871)),f334(f334(f271(x44551,x44552),x44555),f334(f18(f886(x44552,a871),x44551),x44556))),f334(f273(x44551,x44552,f886(f885(x44553,x44554),a871)),f334(f334(f9(x44551,f886(x44552,f886(x44553,f886(x44554,a871))),f886(x44552,f886(f885(x44553,x44554),a871))),f334(f334(f10(f886(f886(x44553,f886(x44554,a871)),f886(f885(x44553,x44554),a871)),f886(f886(x44552,f886(x44553,f886(x44554,a871))),f886(x44552,f886(f885(x44553,x44554),a871))),x44551),f10(f886(x44553,f886(x44554,a871)),f886(f885(x44553,x44554),a871),x44552)),f334(f334(f10(f886(x44553,a871),f886(f886(x44553,f886(x44554,a871)),f886(f885(x44553,x44554),a871)),x44551),f271(x44553,x44554)),x44557))),f334(f334(f10(f886(x44554,a871),f886(x44553,f886(x44554,a871)),x44552),f18(f886(x44554,a871),x44553)),x44558)))),f334(f334(f271(x44553,x44554),f334(f334(f44(x44551,f886(x44553,a871)),x44555),x44557)),f334(f18(f886(x44554,a871),x44553),f334(f334(f44(x44552,f886(x44554,a871)),x44556),x44558)))) % 169.19/169.65 [4393]E(f334(f334(f275(x43931,x43932,x43933,x43934),f334(f334(f275(x43931,x43935,x43936,f885(x43932,x43933)),x43937),x43938)),x43939),f334(f334(f275(x43931,x43935,x43936,x43934),x43937),f334(f334(f9(x43935,f886(x43932,f886(x43933,x43934)),f886(x43936,x43934)),f334(f334(f10(f886(x43936,f885(x43932,x43933)),f886(f886(x43932,f886(x43933,x43934)),f886(x43936,x43934)),x43935),f275(x43936,x43932,x43933,x43934)),x43938)),x43939))) % 169.19/169.65 [4425]E(f334(f74(f885(x44251,x44252),f885(x44253,x44254),f885(x44255,x44256),f274(x44251,x44253,x44252,x44254,x44257,x44258)),f274(x44255,x44251,x44256,x44252,x44259,x442510)),f274(x44255,x44253,x44256,x44254,f334(f74(x44251,x44253,x44255,x44257),x44259),f334(f74(x44252,x44254,x44256,x44258),x442510))) % 169.19/169.65 [4431]E(f334(f274(x44311,x44312,x44313,x44314,x44315,x44316),f334(f274(x44317,x44311,x44318,x44313,x44319,x443110),x443111)),f334(f274(x44317,x44312,x44318,x44314,f334(f74(x44311,x44312,x44317,x44315),x44319),f334(f74(x44313,x44314,x44318,x44316),x443110)),x443111)) % 169.19/169.65 [4609]~E(a543,a561)+~P1(a5000) % 169.19/169.65 [4611]~E(f340(x46111),x46111)+~P1(a5000) % 169.19/169.65 [4613]~P91(x46131)+E(f92(x46131),a331) % 169.19/169.65 [4614]~P25(x46141)+P25(f881(x46141)) % 169.19/169.65 [4615]~P58(x46151)+P58(f881(x46151)) % 169.19/169.65 [4616]~P102(x46161)+P102(f878(x46161)) % 169.19/169.65 [4619]~P141(x46191)+~E(f79(x46191),f2(x46191)) % 169.19/169.65 [4621]~E(x46211,f2(a102))+E(f334(a22,x46211),f2(a1)) % 169.19/169.65 [4622]~E(x46221,f2(a1))+E(f83(a1,x46221),f2(a1)) % 169.19/169.65 [4629]~P142(x46291)+P32(x46291,f2(x46291)) % 169.19/169.65 [4631]~P107(x46311)+P30(x46311,f116(x46311)) % 169.19/169.65 [4641]P104(x46411)+P104(f334(a329,x46411)) % 169.19/169.65 [4684]~P142(x46841)+~P32(x46841,f79(x46841)) % 169.19/169.65 [4731]~P104(x47311)+~P104(f334(a329,x47311)) % 169.19/169.65 [4754]E(f334(a107,x47541),f2(a877))+~P104(f334(a201,x47541)) % 169.19/169.65 [4820]~P65(x48201)+P12(x48201,x48201,f82(x48201)) % 169.19/169.65 [4821]~P93(x48211)+P11(x48211,x48211,f82(x48211)) % 169.19/169.65 [4822]~P100(x48221)+P11(x48221,x48221,f113(x48221)) % 169.19/169.65 [4823]~P101(x48231)+P11(x48231,x48231,f104(x48231)) % 169.19/169.65 [4824]~P107(x48241)+P11(x48241,x48241,f247(x48241)) % 169.19/169.65 [4825]~P107(x48251)+P11(x48251,x48251,f248(x48251)) % 169.19/169.65 [4626]~E(x46261,f2(a877))+E(f334(f103(a1),x46261),f2(a1)) % 169.19/169.65 [4634]~P92(x46341)+E(f334(f106(x46341),a84),f2(x46341)) % 169.19/169.65 [4637]~E(f562(x46371),f2(a877))+E(f334(f166(a877),x46371),f2(a877)) % 169.19/169.65 [4638]~P106(x46381)+E(f251(x46381,f249(x46381)),f247(x46381)) % 169.19/169.65 [4639]~P106(x46391)+E(f252(x46391,f249(x46391)),f248(x46391)) % 169.19/169.65 [4640]~P86(x46401)+E(f83(x46401,f2(x46401)),f2(x46401)) % 169.19/169.65 [4649]~P142(x46491)+E(f334(f103(x46491),f79(a877)),f79(x46491)) % 169.19/169.65 [4650]~P142(x46501)+E(f334(f103(x46501),f2(a877)),f2(x46501)) % 169.19/169.65 [4651]~P137(x46511)+E(f334(f105(x46511),f79(a1)),f79(x46511)) % 169.19/169.65 [4652]~P137(x46521)+E(f334(f105(x46521),f2(a1)),f2(x46521)) % 169.19/169.65 [4653]E(x46531,f2(a877))+~E(f334(f103(a1),x46531),f2(a1)) % 169.19/169.65 [4678]~P79(x46781)+E(f334(f80(x46781),f195(x46781)),f257(x46781)) % 169.19/169.65 [4679]~P67(x46791)+E(f334(f80(x46791),f2(x46791)),f2(x46791)) % 169.19/169.65 [4680]~P79(x46801)+E(f334(f80(x46801),f257(x46801)),f195(x46801)) % 169.19/169.65 [4681]~P120(x46811)+E(f334(f76(x46811),f79(x46811)),f79(x46811)) % 169.19/169.65 [4682]~P83(x46821)+E(f334(f76(x46821),f2(x46821)),f2(x46821)) % 169.19/169.65 [4683]~P78(x46831)+E(f334(f166(x46831),f116(x46831)),f2(x46831)) % 169.19/169.65 [4704]~P38(x47041)+P41(f334(f173(a1),x47041)) % 169.19/169.65 [4736]~P92(x47361)+E(f334(f80(x47361),f79(x47361)),f334(f106(x47361),a100)) % 169.19/169.65 [4753]~P92(x47531)+P32(x47531,f334(f106(x47531),a84)) % 169.19/169.65 [4770]~P58(x47701)+E(f334(f173(x47701),f57(x47701)),f257(f886(x47701,a871))) % 169.19/169.65 [4780]P38(x47801)+~P41(f334(f173(a1),x47801)) % 169.19/169.65 [4781]~P58(x47811)+P104(f334(f137(x47811),f57(x47811))) % 169.19/169.65 [4826]E(f334(f103(a1),f334(a107,x48261)),x48261)+P104(f334(a201,x48261)) % 169.19/169.65 [4895]~P112(x48951)+E(f260(x48951,f79(x48951),f82(x48951)),f259(x48951)) % 169.19/169.65 [4925]~P92(x49251)+~P32(x49251,f334(f106(x49251),a100)) % 169.19/169.65 [4935]E(f334(a28,x49351),f198(a873))+P104(f334(a25,f334(a26,x49351))) % 169.19/169.65 [5068]E(f334(f76(a1),x50681),x50681)+P104(f334(f334(f250(a1),x50681),f2(a1))) % 169.19/169.65 [5089]~E(f334(a107,x50891),f2(a877))+P104(f334(f334(f249(a1),x50891),f2(a1))) % 169.19/169.65 [5151]~P104(f334(a201,x51511))+P104(f334(f334(f250(a1),x51511),f2(a1))) % 169.19/169.65 [5191]~P137(x51911)+P104(f334(f334(f336(x51911),f79(x51911)),f112(x51911))) % 169.19/169.65 [5192]~P142(x51921)+P104(f334(f334(f336(x51921),f79(x51921)),f193(x51921))) % 169.19/169.65 [5193]~P137(x51931)+P104(f334(f334(f336(x51931),f2(x51931)),f112(x51931))) % 169.19/169.65 [5194]~P142(x51941)+P104(f334(f334(f336(x51941),f2(x51941)),f193(x51941))) % 169.19/169.65 [5195]~P119(x51951)+P104(f334(f334(f249(x51951),f2(x51951)),f79(x51951))) % 169.19/169.65 [5196]~P119(x51961)+P104(f334(f334(f250(x51961),f2(x51961)),f79(x51961))) % 169.19/169.65 [5198]E(f334(f241(a873),f363(x51981)),f334(a28,x51981))+~P104(f334(a25,f334(a26,x51981))) % 169.19/169.65 [5199]E(f334(f241(a873),f429(x51991)),f334(a28,x51991))+~P104(f334(a25,f334(a26,x51991))) % 169.19/169.65 [5254]E(x52541,f2(a877))+~P104(f334(f334(f249(a877),x52541),f2(a877))) % 169.19/169.65 [5299]E(f334(a107,x52991),f2(a877))+~P104(f334(f334(f249(a1),x52991),f2(a1))) % 169.19/169.65 [5365]P104(f334(a201,x53651))+~P104(f334(f334(f250(a1),x53651),f2(a1))) % 169.19/169.65 [5370]~P107(x53701)+P12(x53701,f878(x53701),f148(x53701,x53701,f7(x53701))) % 169.19/169.65 [5387]P41(x53871)+~P104(f334(f334(f249(a1),f2(a1)),f341(x53871))) % 169.19/169.65 [5393]E(f334(f76(a1),x53931),f334(f80(a1),x53931))+~P104(f334(f334(f250(a1),x53931),f2(a1))) % 169.19/169.65 [5565]~P119(x55651)+~P104(f334(f334(f249(x55651),f79(x55651)),f2(x55651))) % 169.19/169.65 [5566]~P119(x55661)+~P104(f334(f334(f250(x55661),f79(x55661)),f2(x55661))) % 169.19/169.65 [5576]~E(x55761,f2(a877))+P104(f334(f334(f249(a1),f334(f103(a1),x55761)),f2(a1))) % 169.19/169.65 [5577]~E(x55771,f2(a1))+P104(f334(f334(f250(a1),f334(f76(a1),x55771)),f79(a1))) % 169.19/169.65 [5698]~P78(x56981)+E(f142(x56981,x56981,f81(x56981),f2(x56981)),f166(x56981)) % 169.19/169.65 [5870]~P94(x58701)+P21(a877,x58701,f103(x58701),f257(f886(a877,a871))) % 169.19/169.65 [6064]E(x60641,f2(a877))+~P104(f334(f334(f249(a1),f334(f103(a1),x60641)),f2(a1))) % 169.19/169.65 [6065]E(x60651,f2(a1))+~P104(f334(f334(f250(a1),f334(f76(a1),x60651)),f79(a1))) % 169.19/169.65 [6862]~P104(f334(f334(f250(a1),x68621),f2(a1)))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x68621),x68621)),f2(a1))) % 169.19/169.65 [7408]P104(f334(f334(f250(a1),x74081),f2(a1)))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),x74081),x74081)),f2(a1))) % 169.19/169.65 [7961]E(x79611,f334(a5,f2(a877)))+P104(f334(f334(f250(a877),f334(f334(f3(a877),f334(a21,x79611)),f334(a115,f2(a877)))),f334(a21,x79611))) % 169.19/169.65 [8707]~P104(f334(f334(f250(a1),x87071),f2(a1)))+P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x87071),x87071)),a100)),f2(a1))) % 169.19/169.65 [8793]~P104(f334(f334(f250(a1),x87931),f2(a1)))+P104(f334(f334(f250(a1),f334(f334(f81(a1),f334(f334(f81(a1),f79(a1)),x87931)),x87931)),f2(a1))) % 169.19/169.65 [9105]P104(f334(f334(f250(a1),x91051),f2(a1)))+~P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x91051),x91051)),a100)),f2(a1))) % 169.19/169.65 [9166]P104(f334(f334(f250(a1),x91661),f2(a1)))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),f334(f334(f81(a1),f79(a1)),x91661)),x91661)),f2(a1))) % 169.19/169.65 [4724]~E(a84,x47241)+E(f334(f334(f81(a1),x47241),x47241),a84) % 169.19/169.65 [4725]~E(x47251,a84)+E(f334(f334(f81(a1),x47251),x47251),a84) % 169.19/169.65 [4739]E(x47391,f2(a1))+E(f334(f334(f40(a1),x47391),x47391),f79(a1)) % 169.19/169.65 [4871]E(x48711,a84)+~E(f334(f334(f81(a1),x48711),x48711),a84) % 169.19/169.65 [4872]E(a84,x48721)+~E(f334(f334(f81(a1),x48721),x48721),a84) % 169.19/169.65 [4885]~P28(x48851)+E(f41(x48851,f195(f886(x48851,a871))),f195(x48851)) % 169.19/169.65 [4886]~P28(x48861)+E(f41(x48861,f257(f886(x48861,a871))),f257(x48861)) % 169.19/169.65 [4887]~P28(x48871)+E(f42(x48871,f195(f886(x48871,a871))),f257(x48871)) % 169.19/169.65 [4888]~P28(x48881)+E(f42(x48881,f257(f886(x48881,a871))),f195(x48881)) % 169.19/169.65 [4889]~P107(x48891)+E(f139(x48891,f195(f886(x48891,a871))),f116(x48891)) % 169.19/169.65 [5026]E(x50261,f2(a877))+P104(f334(f334(f250(a877),f2(a877)),x50261)) % 169.19/169.65 [5045]~P29(x50451)+P104(f334(f334(f249(a1),f2(a1)),x50451)) % 169.19/169.65 [5080]~E(f334(f106(a877),x50801),f2(a877))+P104(f334(f334(f249(a1),x50801),a84)) % 169.19/169.65 [5085]P41(x50851)+P104(f334(f334(f336(a1),f341(x50851)),x50851)) % 169.19/169.65 [5086]E(x50861,f334(a5,f2(a877)))+P104(f334(f334(f249(a102),f79(a102)),x50861)) % 169.19/169.65 [5125]P104(f334(a201,x51251))+P104(f334(f334(f249(a1),f2(a1)),x51251)) % 169.19/169.65 [5173]E(f334(f103(a1),f334(a107,x51731)),f2(a1))+P104(f334(f334(f249(a1),f2(a1)),x51731)) % 169.19/169.65 [5240]E(f334(f103(a1),f334(f106(a877),x52401)),f334(f106(a1),x52401))+P104(f334(a201,f334(f106(a1),x52401))) % 169.19/169.65 [5260]E(f334(f106(a877),x52601),f2(a877))+~P104(f334(a201,f334(f106(a1),x52601))) % 169.19/169.65 [5261]E(f334(f106(a877),x52611),f2(a877))+~P104(f334(f334(f249(a1),x52611),a84)) % 169.19/169.65 [5296]P29(x52961)+~P104(f334(f334(f249(a1),f2(a1)),x52961)) % 169.19/169.65 [5373]E(f334(a115,f732(x53731)),x53731)+~P104(f334(f334(f250(a877),f2(a877)),x53731)) % 169.19/169.65 [5381]E(f334(a115,f334(f106(a877),x53811)),f79(a877))+~P104(f334(a201,f334(f106(a1),x53811))) % 169.19/169.65 [5389]E(f334(f103(a1),f859(x53891)),x53891)+~P104(f334(f334(f250(a1),f2(a1)),x53891)) % 169.19/169.65 [5396]~E(x53961,f334(a5,f2(a877)))+~P104(f334(f334(f249(a102),f79(a102)),x53961)) % 169.19/169.65 [5403]E(f334(f103(a1),f334(f106(a877),x54031)),f2(a1))+~P104(f334(a201,f334(f106(a1),x54031))) % 169.19/169.65 [5429]E(f334(f166(a877),x54291),f2(a877))+P104(f334(f334(f336(a877),f562(x54291)),f334(f173(a877),x54291))) % 169.19/169.65 [5450]E(f334(f103(a1),f334(a107,x54501)),x54501)+~P104(f334(f334(f249(a1),f2(a1)),x54501)) % 169.19/169.65 [5459]~P104(f334(a201,x54591))+~P104(f334(f334(f249(a1),f2(a1)),x54591)) % 169.19/169.65 [5558]E(f334(f334(f81(a877),f79(a877)),f334(f106(a877),x55581)),f79(a877))+~P104(f334(f334(f250(a1),x55581),a84)) % 169.19/169.65 [5618]E(x56181,f2(a877))+~P104(f334(f334(f250(a877),x56181),f334(a115,f2(a877)))) % 169.19/169.65 [5657]E(f334(f334(f3(a877),f334(f106(a877),x56571)),f79(a877)),f2(a877))+~P104(f334(f334(f249(a1),x56571),a84)) % 169.19/169.65 [5658]E(f334(f334(f81(a877),f334(f106(a877),x56581)),f79(a877)),f79(a877))+~P104(f334(f334(f250(a1),x56581),a84)) % 169.19/169.65 [5668]~P41(x56681)+E(f334(f39(a877),f334(f313(a1,a877,a107),x56681)),f334(f39(a1),x56681)) % 169.19/169.65 [5699]~P107(x56991)+E(f251(x56991,f334(f9(x56991,x56991,a871),f249(x56991))),f248(x56991)) % 169.19/169.65 [5700]~P107(x57001)+E(f252(x57001,f334(f9(x57001,x57001,a871),f249(x57001))),f247(x57001)) % 169.19/169.65 [5710]E(f46(a877,f334(a115,f2(a877)),f334(f106(a877),x57101)),f334(a115,f2(a877)))+~P104(f334(a201,f334(f106(a1),x57101))) % 169.19/169.65 [5719]~P104(f334(f334(f250(a1),f2(a1)),x57191))+P104(f334(f334(f249(a1),f79(a1)),x57191)) % 169.19/169.65 [5720]P104(f334(f334(f250(a1),f2(a1)),x57201))+~P104(f334(f334(f249(a1),f79(a1)),x57201)) % 169.19/169.65 [5731]E(f334(a115,f334(f334(f3(a877),x57311),f79(a877))),x57311)+~P104(f334(f334(f250(a877),f2(a877)),x57311)) % 169.19/169.65 [5789]P104(f334(f334(f250(a877),f2(a877)),f859(x57891)))+~P104(f334(f334(f250(a1),f2(a1)),x57891)) % 169.19/169.65 [5848]E(f46(a1,f334(f106(a1),a100),x58481),f334(f334(f3(a1),x58481),f79(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x58481)) % 169.19/169.65 [5882]~P104(f334(f334(f250(a1),a84),x58821))+P104(f334(f334(f250(a877),f2(a877)),f334(f106(a877),x58821))) % 169.19/169.65 [5932]P104(f334(f334(f250(a877),f2(a877)),f334(a107,x59321)))+~P104(f334(f334(f250(a1),f2(a1)),x59321)) % 169.19/169.65 [5983]~P104(f334(f334(f250(a877),f2(a877)),x59831))+P104(f334(f334(f250(a1),f2(a1)),f334(f103(a1),x59831))) % 169.19/169.65 [6018]~P104(f334(f334(f250(a877),f2(a877)),f334(a107,x60181)))+P104(f334(f334(f250(a1),f2(a1)),x60181)) % 169.19/169.65 [6032]~P41(x60321)+E(f334(f313(a877,a1,f103(a1)),f334(f313(a1,a877,a107),x60321)),x60321) % 169.19/169.65 [6045]P104(f334(f334(f250(a1),a84),x60451))+~P104(f334(f334(f250(a877),f2(a877)),f334(f106(a877),x60451))) % 169.19/169.65 [6093]~P58(x60931)+E(f334(f334(f151(f881(x60931)),f198(x60931)),f334(f334(f154(x60931,f881(x60931)),f241(x60931)),f57(x60931))),f57(f881(x60931))) % 169.19/169.65 [6104]P104(f334(f334(f250(a877),f2(a877)),x61041))+~P104(f334(f334(f250(a1),f2(a1)),f334(f103(a1),x61041))) % 169.19/169.65 [6219]E(f334(f313(a877,a1,f103(a1)),f334(f255(a877),f334(a107,x62191))),f334(f304(a1,f2(a1)),x62191))+~P104(f334(f334(f249(a1),f2(a1)),x62191)) % 169.19/169.65 [6235]~P119(x62351)+P104(f334(f334(f250(x62351),f2(x62351)),f334(f334(f81(x62351),f79(x62351)),f79(x62351)))) % 169.19/169.65 [6286]P104(f334(f334(f250(a877),f334(a115,f2(a877))),f334(a107,x62861)))+~P104(f334(f334(f250(a1),f79(a1)),x62861)) % 169.19/169.65 [6380]E(x63801,f2(a1))+P104(f334(f50(f2(a1),x63801),f334(f334(f269(a1,a1),f2(a1)),f2(a1)))) % 169.19/169.65 [6547]~P104(f334(f334(f250(a877),f334(a115,f2(a877))),f334(a107,x65471)))+P104(f334(f334(f250(a1),f79(a1)),x65471)) % 169.19/169.65 [6972]~P114(x69721)+P39(x69721,f334(f254(f885(x69721,x69721)),f334(f273(x69721,x69721,a871),f250(x69721)))) % 169.19/169.65 [5605]E(f334(f106(a877),f334(f334(f3(a1),x56051),a100)),f334(a115,f334(f106(a877),x56051)))+P104(f334(a201,f334(f106(a1),x56051))) % 169.19/169.65 [5621]~P38(x56211)+E(f334(f334(f154(a877,a1),f103(a1)),f334(f334(f154(a1,a877),a107),x56211)),x56211) % 169.19/169.65 [5737]E(f334(f80(a1),f334(f103(a1),f334(a115,f860(x57371)))),x57371)+~P104(f334(f334(f250(a1),x57371),f2(a1))) % 169.19/169.65 [5747]E(f334(f334(f81(a877),f79(a877)),f334(f106(a877),x57471)),f334(f106(a877),f334(f334(f3(a1),x57471),a100)))+P104(f334(f334(f250(a1),x57471),a84)) % 169.19/169.65 [5791]E(f334(f334(f40(a1),f334(f106(a1),a100)),x57911),f334(f106(a1),a100))+~P104(f334(f334(f250(a1),f2(a1)),x57911)) % 169.19/169.65 [5878]E(f334(f334(f3(a877),f334(f106(a877),x58781)),f79(a877)),f334(f106(a877),f334(f334(f81(a1),x58781),a100)))+P104(f334(f334(f249(a1),x58781),a84)) % 169.19/169.65 [5879]E(f334(f334(f81(a877),f334(f106(a877),x58791)),f79(a877)),f334(f106(a877),f334(f334(f3(a1),x58791),a100)))+P104(f334(f334(f250(a1),x58791),a84)) % 169.19/169.65 [5920]E(f334(a107,f334(f334(f81(a1),f79(a1)),x59201)),f334(a115,f334(a107,x59201)))+~P104(f334(f334(f249(a1),f2(a1)),x59201)) % 169.19/169.65 [5956]E(f334(a115,f334(f334(f3(a877),x59561),f334(a115,f2(a877)))),x59561)+~P104(f334(f334(f250(a877),f2(a877)),x59561)) % 169.19/169.65 [6164]E(f46(a877,f334(a115,f2(a877)),f334(f106(a877),x61641)),f334(a107,f46(a1,f79(a1),f334(f106(a1),x61641))))+P104(f334(a201,f334(f106(a1),x61641))) % 169.19/169.65 [6209]~P104(f334(f334(f249(a1),a84),x62091))+P104(f334(f334(f249(a1),a84),f334(f334(f81(a1),x62091),x62091))) % 169.19/169.65 [6210]~P104(f334(f334(f250(a1),a100),x62101))+P104(f334(f334(f249(a1),a100),f334(f334(f81(a1),x62101),x62101))) % 169.19/169.65 [6211]~P104(f334(f334(f250(a1),a84),x62111))+P104(f334(f334(f250(a1),a84),f334(f334(f81(a1),x62111),x62111))) % 169.19/169.65 [6212]~P104(f334(f334(f250(a1),a100),x62121))+P104(f334(f334(f250(a1),a100),f334(f334(f81(a1),x62121),x62121))) % 169.19/169.65 [6213]~P104(f334(f334(f92(a1),a84),x62131))+P104(f334(f334(f92(a1),a84),f334(f334(f81(a1),x62131),x62131))) % 169.19/169.65 [6393]~P104(f334(f63(x63931),f257(f886(x63931,a871))))+P104(f334(f63(f881(x63931)),f257(f886(f881(x63931),a871)))) % 169.19/169.65 [6480]~P104(f334(f334(f249(a1),f2(a1)),x64801))+P104(f334(f334(f250(a1),f2(a1)),f334(f334(f81(a1),f79(a1)),x64801))) % 169.19/169.65 [6487]E(f334(f268(a1,a1),f48(f79(a1),f334(f106(a1),x64871))),f334(f334(f40(a1),f79(a1)),f334(f106(a1),x64871)))+~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x64871))) % 169.19/169.65 [6507]E(f334(f272(a1,a1),f48(f79(a1),f334(f106(a1),x65071))),f46(a1,f79(a1),f334(f106(a1),x65071)))+~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x65071))) % 169.19/169.65 [6519]P104(f334(f63(x65191),f257(f886(x65191,a871))))+~P104(f334(f63(f881(x65191)),f257(f886(f881(x65191),a871)))) % 169.19/169.65 [6548]P104(f334(f334(f249(a1),a84),x65481))+~P104(f334(f334(f249(a1),a84),f334(f334(f81(a1),x65481),x65481))) % 169.19/169.65 [6549]P104(f334(f334(f250(a1),a84),x65491))+~P104(f334(f334(f250(a1),a84),f334(f334(f81(a1),x65491),x65491))) % 169.19/169.65 [6550]P104(f334(f334(f250(a1),a100),x65501))+~P104(f334(f334(f249(a1),a100),f334(f334(f81(a1),x65501),x65501))) % 169.19/169.65 [6551]P104(f334(f334(f250(a1),a100),x65511))+~P104(f334(f334(f250(a1),a100),f334(f334(f81(a1),x65511),x65511))) % 169.19/169.65 [6552]P104(f334(f334(f92(a1),a84),x65521))+~P104(f334(f334(f92(a1),a84),f334(f334(f81(a1),x65521),x65521))) % 169.19/169.65 [6866]~P104(f334(f63(x68661),f257(f886(x68661,a871))))+P104(f334(f334(f250(a877),f2(a877)),f334(f39(x68661),f257(f886(x68661,a871))))) % 169.19/169.65 [7450]P104(f334(f63(a877),x74501))+~P104(f334(f63(a1),f334(f313(a877,a1,f103(a1)),x74501))) % 169.19/169.65 [5533]~E(a100,x55331)+E(f334(f334(f3(a1),f334(f334(f81(a1),x55331),x55331)),a100),a100) % 169.19/169.65 [5534]~E(x55341,a100)+E(f334(f334(f3(a1),f334(f334(f81(a1),x55341),x55341)),a100),a100) % 169.19/169.65 [6038]E(x60381,a100)+~E(f334(f334(f3(a1),f334(f334(f81(a1),x60381),x60381)),a100),a100) % 169.19/169.65 [6039]E(a100,x60391)+~E(f334(f334(f3(a1),f334(f334(f81(a1),x60391),x60391)),a100),a100) % 169.19/169.65 [6449]~E(f334(f106(a877),x64491),f2(a877))+P104(f334(a201,f334(f106(a1),f334(f334(f81(a1),x64491),a100)))) % 169.19/169.65 [6792]~P104(f334(a201,f334(f106(a1),x67921)))+P104(f334(a201,f334(f106(a1),f334(f334(f81(a1),x67921),x67921)))) % 169.19/169.65 [6793]~P104(f334(f334(f249(a1),x67931),a84))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x67931),x67931)),a84)) % 169.19/169.65 [6794]~P104(f334(f334(f249(a1),x67941),a100))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x67941),x67941)),a100)) % 169.19/169.65 [6795]~P104(f334(f334(f250(a1),x67951),a84))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x67951),x67951)),a84)) % 169.19/169.65 [6796]~P104(f334(f334(f249(a1),x67961),a100))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x67961),x67961)),a100)) % 169.19/169.65 [6797]~P104(f334(f334(f92(a1),x67971),a84))+P104(f334(f334(f92(a1),f334(f334(f81(a1),x67971),x67971)),a84)) % 169.19/169.65 [7117]E(f334(f106(a877),x71171),f2(a877))+~P104(f334(a201,f334(f106(a1),f334(f334(f81(a1),x71171),a100)))) % 169.19/169.65 [7359]~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x73591)))+P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),f334(f334(f81(a1),x73591),x73591)))) % 169.19/169.65 [7360]P104(f334(a201,f334(f106(a1),x73601)))+~P104(f334(a201,f334(f106(a1),f334(f334(f81(a1),x73601),x73601)))) % 169.19/169.65 [7361]P104(f334(f334(f249(a1),x73611),a84))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),x73611),x73611)),a84)) % 169.19/169.65 [7362]P104(f334(f334(f249(a1),x73621),a100))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),x73621),x73621)),a100)) % 169.19/169.65 [7363]P104(f334(f334(f249(a1),x73631),a100))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),x73631),x73631)),a100)) % 169.19/169.65 [7364]P104(f334(f334(f250(a1),x73641),a84))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),x73641),x73641)),a84)) % 169.19/169.65 [7365]P104(f334(f334(f92(a1),x73651),a84))+~P104(f334(f334(f92(a1),f334(f334(f81(a1),x73651),x73651)),a84)) % 169.19/169.65 [7732]E(f334(a110,f709(x77321)),x77321)+~P104(f334(f334(f336(f886(f885(a877,a877),a871)),x77321),a101)) % 169.19/169.65 [6366]~P92(x63661)+E(f334(f106(x63661),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f79(x63661)) % 169.19/169.65 [6844]~P104(f334(a201,f334(f106(a1),x68441)))+E(f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),x68441),x68441)),a100)),f2(a877)) % 169.19/169.65 [7907]~P104(f334(f334(f250(a1),f334(f106(a1),x79071)),f2(a1)))+E(f334(f268(a1,a1),f334(a52,f51(f334(f80(a1),f79(a1)),f334(f80(a1),f334(f106(a1),x79071))))),f334(f334(f40(a1),f79(a1)),f334(f106(a1),x79071))) % 169.19/169.65 [7920]~P104(f334(f334(f250(a1),f334(f106(a1),x79201)),f2(a1)))+E(f334(f272(a1,a1),f334(a52,f51(f334(f80(a1),f79(a1)),f334(f80(a1),f334(f106(a1),x79201))))),f46(a1,f79(a1),f334(f106(a1),x79201))) % 169.19/169.65 [7967]~P104(f334(f334(f249(a1),a84),x79671))+P104(f334(f334(f249(a1),a84),f334(f334(f3(a1),f334(f334(f81(a1),x79671),x79671)),a100))) % 169.19/169.65 [7968]~P104(f334(f334(f249(a1),a100),x79681))+P104(f334(f334(f249(a1),a100),f334(f334(f3(a1),f334(f334(f81(a1),x79681),x79681)),a100))) % 169.19/169.65 [7969]~P104(f334(f334(f249(a1),a84),x79691))+P104(f334(f334(f250(a1),a84),f334(f334(f3(a1),f334(f334(f81(a1),x79691),x79691)),a100))) % 169.19/169.65 [7970]~P104(f334(f334(f250(a1),a100),x79701))+P104(f334(f334(f250(a1),a100),f334(f334(f3(a1),f334(f334(f81(a1),x79701),x79701)),a100))) % 169.19/169.65 [7971]~P104(f334(f334(f92(a1),a100),x79711))+P104(f334(f334(f92(a1),a100),f334(f334(f3(a1),f334(f334(f81(a1),x79711),x79711)),a100))) % 169.19/169.65 [8271]~P92(x82711)+~P32(x82711,f334(f106(x82711),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))) % 169.19/169.65 [8447]P104(f334(f334(f249(a1),a84),x84471))+~P104(f334(f334(f249(a1),a84),f334(f334(f3(a1),f334(f334(f81(a1),x84471),x84471)),a100))) % 169.19/169.65 [8448]P104(f334(f334(f249(a1),a84),x84481))+~P104(f334(f334(f250(a1),a84),f334(f334(f3(a1),f334(f334(f81(a1),x84481),x84481)),a100))) % 169.19/169.65 [8449]P104(f334(f334(f249(a1),a100),x84491))+~P104(f334(f334(f249(a1),a100),f334(f334(f3(a1),f334(f334(f81(a1),x84491),x84491)),a100))) % 169.19/169.65 [8450]P104(f334(f334(f250(a1),a100),x84501))+~P104(f334(f334(f250(a1),a100),f334(f334(f3(a1),f334(f334(f81(a1),x84501),x84501)),a100))) % 169.19/169.65 [8451]P104(f334(f334(f92(a1),a100),x84511))+~P104(f334(f334(f92(a1),a100),f334(f334(f3(a1),f334(f334(f81(a1),x84511),x84511)),a100))) % 169.19/169.65 [8751]E(f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),x87511),x87511)),a100)),f334(f334(f87(a877,a877),f334(f106(a877),x87511)),f334(f334(f10(a877,a877,a877),a115),f334(f334(f20(a877,a877,a877),f81(a877)),f7(a877)))))+P104(f334(a201,f334(f106(a1),x87511))) % 169.19/169.65 [9563]E(x95631,f195(f886(f885(a877,a877),a871)))+P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x95631),f195(f886(f885(a877,a877),a871)))),a37)) % 169.19/169.65 [8682]~P104(f334(a201,f334(f106(a1),x86821)))+P104(f334(a201,f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),x86821),x86821)),a100)))) % 169.19/169.65 [8683]~P104(f334(f334(f250(a1),x86831),a84))+P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x86831),x86831)),a100)),a84)) % 169.19/169.65 [8684]~P104(f334(f334(f249(a1),x86841),a100))+P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x86841),x86841)),a100)),a100)) % 169.19/169.65 [8685]~P104(f334(f334(f250(a1),x86851),a84))+P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x86851),x86851)),a100)),a84)) % 169.19/169.65 [8686]~P104(f334(f334(f250(a1),x86861),a100))+P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x86861),x86861)),a100)),a100)) % 169.19/169.65 [8687]~P104(f334(f334(f92(a1),x86871),a100))+P104(f334(f334(f92(a1),f334(f334(f3(a1),f334(f334(f81(a1),x86871),x86871)),a100)),a100)) % 169.19/169.65 [8786]~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x87861)))+P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),x87861),x87861)),a100)))) % 169.19/169.65 [8943]~P92(x89431)+E(f334(f334(f81(x89431),f79(x89431)),f79(x89431)),f334(f106(x89431),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))) % 169.19/169.65 [9089]P104(f334(a201,f334(f106(a1),x90891)))+~P104(f334(a201,f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90891),x90891)),a100)))) % 169.19/169.65 [9090]P104(f334(f334(f249(a1),x90901),a100))+~P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90901),x90901)),a100)),a100)) % 169.19/169.65 [9091]P104(f334(f334(f250(a1),x90911),a84))+~P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90911),x90911)),a100)),a84)) % 169.19/169.65 [9092]P104(f334(f334(f250(a1),x90921),a84))+~P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90921),x90921)),a100)),a84)) % 169.19/169.65 [9093]P104(f334(f334(f250(a1),x90931),a100))+~P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90931),x90931)),a100)),a100)) % 169.19/169.65 [9094]P104(f334(f334(f92(a1),x90941),a100))+~P104(f334(f334(f92(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90941),x90941)),a100)),a100)) % 169.19/169.65 [9609]~P104(f334(f63(f885(a877,a877)),x96091))+P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),f195(f886(f885(a877,a877),a871))),x96091)),a70)) % 169.19/169.65 [9401]~P142(x94011)+E(f334(f334(f259(x94011),f79(x94011)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f79(x94011)) % 169.19/169.65 [9402]~P142(x94021)+E(f334(f334(f259(x94021),f2(x94021)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f2(x94021)) % 169.19/169.65 [9837]~P104(f334(f334(f250(a877),f79(a877)),x98371))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f40(a877),x98371),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.65 [9847]~P104(f334(f334(f250(a877),f2(a877)),x98471))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f40(a877),f334(f334(f81(a877),x98471),f79(a877))),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.65 [9889]~E(f46(a877,x98891,f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f79(a877))+P104(f334(f334(f250(a877),f2(a877)),f46(a877,x98891,f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.65 [9908]E(f46(a877,x99081,f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f79(a877))+~P104(f334(f334(f250(a877),f2(a877)),f46(a877,x99081,f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.65 [4657]~P39(x46571,x46572)+P55(x46571,x46572) % 169.19/169.65 [4658]~P44(x46581,x46582)+P55(x46581,x46582) % 169.19/169.65 [4617]~E(x46171,x46172)+E(f281(x46171,x46172),f79(a102)) % 169.19/169.65 [4620]E(f225(x46201,x46202),x46201)+~E(x46202,f2(a877)) % 169.19/169.65 [4625]P40(x46251,x46252)+~E(x46252,f198(x46251)) % 169.19/169.65 [4628]~E(x46282,f116(x46281))+E(f152(x46281,x46282),f116(x46281)) % 169.19/169.65 [4632]~P40(x46322,x46321)+E(x46321,f198(x46322)) % 169.19/169.65 [4648]~E(f152(x46482,x46481),f116(x46482))+E(x46481,f116(x46482)) % 169.19/169.65 [4662]~P24(x46622)+P24(f886(x46621,x46622)) % 169.19/169.65 [4663]~P105(x46632)+P105(f886(x46631,x46632)) % 169.19/169.65 [4664]~P106(x46642)+P106(f886(x46641,x46642)) % 169.19/169.65 [4665]~P108(x46652)+P108(f886(x46651,x46652)) % 169.19/169.65 [4666]~P63(x46662)+P63(f886(x46661,x46662)) % 169.19/169.65 [4667]~P79(x46672)+P79(f886(x46671,x46672)) % 169.19/169.65 [4668]~P80(x46682)+P80(f886(x46681,x46682)) % 169.19/169.65 [4669]~P95(x46692)+P95(f886(x46691,x46692)) % 169.19/169.65 [4670]~P95(x46702)+P100(f886(x46701,x46702)) % 169.19/169.65 [4671]~P98(x46712)+P96(f886(x46711,x46712)) % 169.19/169.65 [4672]~P113(x46722)+P113(f886(x46721,x46722)) % 169.19/169.65 [4673]~P98(x46732)+P97(f886(x46731,x46732)) % 169.19/169.65 [4674]~P28(x46742)+P28(f886(x46741,x46742)) % 169.19/169.65 [4675]~P95(x46752)+P101(f886(x46751,x46752)) % 169.19/169.65 [4676]~P99(x46762)+P99(f886(x46761,x46762)) % 169.19/169.65 [4677]~P98(x46772)+P98(f886(x46771,x46772)) % 169.19/169.65 [4689]E(x46891,x46892)+~E(f334(a26,x46891),f334(a26,x46892)) % 169.19/169.65 [4691]E(x46911,x46912)+~E(f334(a115,x46911),f334(a115,x46912)) % 169.19/169.65 [4692]E(x46921,x46922)+~E(f334(a110,x46921),f334(a110,x46922)) % 169.19/169.65 [4693]E(x46931,x46932)+~E(f334(a5,x46931),f334(a5,x46932)) % 169.19/169.65 [4695]E(x46951,x46952)+~E(f334(a21,x46951),f334(a21,x46952)) % 169.19/169.65 [4799]~P26(x47991)+E(f46(x47991,x47992,x47992),f2(x47991)) % 169.19/169.65 [4833]~P39(x48331,x48332)+P39(f878(x48331),f145(x48331,x48332)) % 169.19/169.65 [4834]~P39(x48341,x48342)+P39(f878(x48341),f146(x48341,x48342)) % 169.19/169.65 [4930]~P39(x49301,x49302)+P39(f886(x49301,a871),f325(x49301,x49302)) % 169.19/169.65 [4931]~P39(x49311,x49312)+P39(f886(x49311,a871),f326(x49311,x49312)) % 169.19/169.65 [5051]~P29(x50511)+P41(f305(a1,x50511,x50512)) % 169.19/169.65 [5154]~P39(x51541,x51542)+P57(x51541,f69(x51541,x51541,x51542)) % 169.19/169.65 [5662]~P75(x56621)+P21(x56621,x56621,f80(x56621),x56622) % 169.19/169.65 [4643]~E(x46432,f116(x46431))+E(f334(f168(x46431),x46432),f116(x46431)) % 169.19/169.65 [4644]~E(x46442,f116(x46441))+E(f334(f169(x46441),x46442),f116(x46441)) % 169.19/169.65 [4699]E(x46991,f334(a107,x46992))+~E(f334(f103(a1),x46991),x46992) % 169.19/169.65 [4702]E(x47021,f116(x47022))+~E(f334(f168(x47022),x47021),f116(x47022)) % 169.19/169.65 [4703]E(x47031,f116(x47032))+~E(f334(f169(x47032),x47031),f116(x47032)) % 169.19/169.65 [4721]~P92(x47211)+E(f334(f106(x47211),x47212),f334(f105(x47211),x47212)) % 169.19/169.65 [4728]~E(x47282,f198(x47281))+E(f240(x47281,x47282),f195(f886(x47281,a871))) % 169.19/169.65 [4730]~P25(x47301)+P104(f334(f63(x47301),x47302)) % 169.19/169.65 [4737]E(x47371,f198(x47372))+E(f334(f241(x47372),f362(x47372,x47371)),x47371) % 169.19/169.65 [4738]E(x47381,f198(x47382))+E(f334(f241(x47382),f450(x47382,x47381)),x47381) % 169.19/169.65 [4740]~E(f572(x47402,x47401),f116(x47401))+E(f181(x47401,x47402),f116(f878(x47401))) % 169.19/169.65 [4749]~E(x47492,f116(x47491))+E(f334(f173(x47491),x47492),f195(f886(x47491,a871))) % 169.19/169.65 [4750]~E(x47502,f116(x47501))+E(f195(f886(x47501,a871)),f334(f173(x47501),x47502)) % 169.19/169.65 [4752]E(x47521,x47522)+~E(f334(f103(a1),x47521),f334(f103(a1),x47522)) % 169.19/169.65 [4755]E(f223(x47551,x47552),f2(a877))+P104(f334(f63(x47551),x47552)) % 169.19/169.65 [4775]~P120(x47751)+E(f83(x47751,f83(x47751,x47752)),f83(x47751,x47752)) % 169.19/169.65 [4788]~P77(x47881)+E(f334(f334(f259(x47881),x47882),f79(a877)),x47882) % 169.19/169.65 [4789]~P115(x47891)+E(f334(f334(f259(x47891),x47892),f79(a877)),x47892) % 169.19/169.65 [4793]E(x47931,x47932)+E(f281(x47931,x47932),f334(f334(f81(a102),x47932),f79(a102))) % 169.19/169.65 [4796]E(f334(f39(x47961),x47962),f2(a877))+P104(f334(f63(x47961),x47962)) % 169.19/169.65 [4800]~E(f152(x48001,x48002),x48002)+P104(f334(f137(x48001),x48002)) % 169.19/169.65 [4803]~P67(x48031)+E(f334(f334(f3(x48031),x48032),f2(x48031)),x48032) % 169.19/169.65 [4804]~P77(x48041)+E(f334(f334(f82(x48041),x48042),f79(x48041)),x48042) % 169.19/169.65 [4805]~P68(x48051)+E(f334(f334(f82(x48051),x48052),f79(x48051)),x48052) % 169.19/169.65 [4806]~P115(x48061)+E(f334(f334(f82(x48061),x48062),f79(x48061)),x48062) % 169.19/169.65 [4807]~P115(x48071)+E(f334(f334(f81(x48071),x48072),f2(x48071)),x48072) % 169.19/169.65 [4808]~P78(x48081)+E(f334(f334(f81(x48081),x48082),f2(x48081)),x48082) % 169.19/169.65 [4809]~P72(x48091)+E(f334(f334(f81(x48091),x48092),f2(x48091)),x48092) % 169.19/169.65 [4810]~P117(x48101)+E(f334(f334(f292(x48101),x48102),f79(x48101)),x48102) % 169.19/169.65 [4811]~P26(x48111)+E(f334(f334(f40(x48111),x48112),f79(x48111)),x48112) % 169.19/169.65 [4812]~P97(x48121)+E(f334(f334(f113(x48121),x48122),f195(x48121)),x48122) % 169.19/169.65 [4813]~P96(x48131)+E(f334(f334(f104(x48131),x48132),f257(x48131)),x48132) % 169.19/169.65 [4814]~P115(x48141)+E(f334(f334(f259(x48141),x48142),f2(a877)),f79(x48141)) % 169.19/169.65 [4815]~P112(x48151)+E(f334(f334(f259(x48151),x48152),f2(a877)),f79(x48151)) % 169.19/169.65 [4816]~E(x48162,f195(f886(x48161,a871)))+E(f334(f39(x48161),x48162),f2(a877)) % 169.19/169.65 [4827]~P26(x48271)+E(f46(x48271,x48272,f2(x48271)),x48272) % 169.19/169.65 [4835]~P115(x48351)+E(f334(f334(f82(x48351),x48352),f2(x48351)),f2(x48351)) % 169.19/169.65 [4836]~P130(x48361)+E(f334(f334(f82(x48361),x48362),f2(x48361)),f2(x48361)) % 169.19/169.65 [4837]~P118(x48371)+E(f334(f334(f292(x48371),x48372),f2(x48371)),f2(x48371)) % 169.19/169.65 [4838]~P26(x48381)+E(f334(f334(f40(x48381),x48382),f2(x48381)),f2(x48381)) % 169.19/169.65 [4839]~P96(x48391)+E(f334(f334(f113(x48391),x48392),f257(x48391)),f257(x48391)) % 169.19/169.65 [4840]~P97(x48401)+E(f334(f334(f104(x48401),x48402),f195(x48401)),f195(x48401)) % 169.19/169.65 [4841]E(x48411,f198(x48412))+~E(f240(x48412,x48411),f195(f886(x48412,a871))) % 169.19/169.65 [4843]~P26(x48431)+E(f46(x48431,x48432,f79(x48431)),f2(x48431)) % 169.19/169.65 [4844]~P26(x48441)+E(f46(x48441,f2(x48441),x48442),f2(x48441)) % 169.19/169.65 [4873]E(x48731,f2(a877))+E(f56(x48732,x48731,f116(x48732)),f116(f878(x48732))) % 169.19/169.65 [4897]P39(x48971,x48972)+~E(f713(x48972,x48971),f195(f886(x48971,a871))) % 169.19/169.65 [4898]E(x48981,f116(x48982))+~E(f334(f173(x48982),x48981),f195(f886(x48982,a871))) % 169.19/169.65 [4899]E(x48991,f116(x48992))+~E(f195(f886(x48992,a871)),f334(f173(x48992),x48991)) % 169.19/169.65 [4902]~E(x49021,x49022)+P104(f334(f334(a331,x49021),x49022)) % 169.19/169.65 [4912]P104(x49121)+P104(f334(f334(a337,x49121),x49122)) % 169.19/169.65 [4913]E(x49131,f116(x49132))+E(f334(f334(f165(x49132),x49131),f2(a877)),f334(f141(x49132),x49131)) % 169.19/169.65 [4916]E(f152(x49161,x49162),x49162)+~P104(f334(f137(x49161),x49162)) % 169.19/169.65 [4921]~P104(x49212)+P104(f334(f334(a337,x49211),x49212)) % 169.19/169.65 [4922]~P104(x49222)+P104(f334(f334(a333,x49221),x49222)) % 169.19/169.65 [4923]~P104(x49231)+P104(f334(f334(a333,x49231),x49232)) % 169.19/169.65 [4933]~E(f573(x49332,x49331),f580(x49332,x49331))+P104(f334(f137(x49331),x49332)) % 169.19/169.65 [4941]E(f334(f254(x49411),x49412),f195(f886(x49411,a871)))+P104(f334(x49412,f563(x49412))) % 169.19/169.65 [4942]E(f195(f886(x49421,a871)),f334(f254(x49421),x49422))+P104(f334(x49422,f564(x49422))) % 169.19/169.65 [5008]~P120(x50081)+E(f334(f334(f82(x50081),x50082),f83(x50081,x50082)),f334(f76(x50081),x50082)) % 169.19/169.65 [5019]~E(x50191,f2(a1))+E(f47(x50191,x50192),f334(f334(f269(a1,a1),f2(a1)),f2(a1))) % 169.19/169.65 [5050]~P55(x50501,x50502)+P55(x50501,f334(f289(x50501,x50501),x50502)) % 169.19/169.65 [5069]~E(f334(a28,x50691),f334(f241(a873),x50692))+P104(f334(a25,f334(a26,x50691))) % 169.19/169.65 [5074]E(x50741,x50742)+~P104(f334(f334(a331,x50741),x50742)) % 169.19/169.65 [5078]~P104(f334(a25,x50782))+P104(f334(a25,f33(x50781,x50782))) % 169.19/169.65 [5087]P104(x50871)+~P104(f334(f334(a332,x50872),x50871)) % 169.19/169.65 [5088]P104(x50881)+~P104(f334(f334(a332,x50881),x50882)) % 169.19/169.65 [5093]~P113(x50931)+P104(f334(f334(f249(x50931),x50932),f257(x50931))) % 169.19/169.65 [5097]E(x50971,x50972)+~E(f334(x50971,f451(x50972,x50971)),f334(x50972,f451(x50972,x50971))) % 169.19/169.65 [5127]E(x51271,f2(a877))+E(f225(x51271,f46(a877,x51272,x51271)),f225(x51272,x51271)) % 169.19/169.65 [5132]~P107(x51321)+P30(x51321,f334(f334(f151(x51321),x51322),f116(x51321))) % 169.19/169.65 [5134]E(x51341,f2(a1))+P104(f334(f50(x51342,x51341),f47(x51342,x51341))) % 169.19/169.65 [5152]~E(x51521,x51522)+P104(f334(f334(f250(a877),x51521),f334(a115,x51522))) % 169.19/169.65 [5162]~E(x51621,f2(a877))+P104(f334(f334(f250(a877),x51621),f334(a115,x51622))) % 169.19/169.65 [5172]P104(f334(x51721,x51722))+P104(f334(f334(f249(a1),f2(a1)),f342(x51721))) % 169.19/169.65 [5208]P104(f334(a25,x52081))+~P104(f334(a25,f33(x52082,x52081))) % 169.19/169.65 [5210]P104(f334(a25,x52101))+~P104(f334(a25,f34(x52102,x52101))) % 169.19/169.65 [5212]P104(f334(a25,x52121))+~P104(f334(a25,f34(x52121,x52122))) % 169.19/169.65 [5244]P55(x52441,x52442)+~P55(x52441,f334(f289(x52441,x52441),x52442)) % 169.19/169.65 [5247]~E(f46(a877,x52472,x52471),f2(a877))+E(f334(f334(f82(a877),x52471),f343(x52471,x52472)),x52472) % 169.19/169.65 [5248]~E(f46(a1,x52482,x52481),f2(a1))+E(f334(f334(f82(a1),x52481),f344(x52481,x52482)),x52482) % 169.19/169.65 [5275]~P104(f334(x52751,x52752))+P104(f334(f334(f249(a1),f2(a1)),f825(x52751))) % 169.19/169.65 [5287]E(f334(f334(f3(a877),f334(a107,x52871)),f334(a107,x52872)),f334(a107,x52871))+~P104(f334(a201,x52872)) % 169.19/169.65 [5320]E(f282(x53201,x53202),f79(a102))+~P104(f334(f334(f249(a102),x53201),f79(a102))) % 169.19/169.65 [5415]E(f334(f334(f165(x54151),x54152),f573(x54152,x54151)),f334(f334(f165(x54151),x54152),f580(x54152,x54151)))+P104(f334(f137(x54151),x54152)) % 169.19/169.65 [5460]~P104(f334(x54601,f91(x54602,x54601)))+P104(f334(x54601,f574(x54602,x54601))) % 169.19/169.65 [5523]P57(x55231,x55232)+~P104(f334(f322(x55231,x55232),f704(x55232,x55231))) % 169.19/169.65 [5669]~E(f334(a115,f46(a877,x56691,x56692)),x56692)+E(f46(a877,f334(a115,x56691),x56692),f2(a877)) % 169.19/169.65 [5726]P39(x57261,x57262)+P104(f334(f334(f336(x57261),f758(x57262,x57261)),f759(x57262,x57261))) % 169.19/169.65 [5733]~P92(x57331)+P104(f334(f334(f336(x57331),f334(f106(x57331),x57332)),f112(x57331))) % 169.19/169.65 [5734]~P137(x57341)+P104(f334(f334(f336(x57341),f334(f103(x57341),x57342)),f112(x57341))) % 169.19/169.65 [5735]~P142(x57351)+P104(f334(f334(f336(x57351),f334(f103(x57351),x57352)),f193(x57351))) % 169.19/169.65 [5736]~P137(x57361)+P104(f334(f334(f336(x57361),f334(f105(x57361),x57362)),f112(x57361))) % 169.19/169.65 [5881]E(f334(a115,f46(a877,x58811,x58812)),x58812)+E(f46(a877,f334(a115,x58811),x58812),f334(a115,f46(a877,x58811,x58812))) % 169.19/169.65 [6298]P39(x62981,x62982)+~P104(f334(f334(f336(x62981),f672(x62982,x62981)),f323(x62981,x62982))) % 169.19/169.65 [6332]~P119(x63321)+~P104(f334(f334(f250(x63321),f334(f103(x63321),x63322)),f2(x63321))) % 169.19/169.65 [6333]~P83(x63331)+~P104(f334(f334(f250(x63331),f334(f76(x63331),x63332)),f2(x63331))) % 169.19/169.65 [6422]P104(f334(f334(f250(a1),x64221),f46(a1,x64222,x64221)))+~P104(f334(f334(f250(a1),x64221),f2(a1))) % 169.19/169.65 [6521]E(f334(f334(f312(a877),f334(a115,x65211)),f305(a877,x65212,x65211)),f305(a877,x65212,f334(a115,x65211)))+~P104(f334(f334(f249(a877),x65212),f334(a115,x65211))) % 169.19/169.65 [6608]~P107(x66081)+P30(x66081,f150(x66081,x66081,f7(x66081),x66082)) % 169.19/169.65 [6736]E(f334(f168(x67361),x67362),x67362)+~P104(f334(f334(f249(a877),f334(f196(f878(x67361)),x67362)),f79(a877))) % 169.19/169.65 [6756]~P83(x67561)+P104(f334(f334(f249(x67561),f334(f80(x67561),f334(f76(x67561),x67562))),f2(x67561))) % 169.19/169.65 [6789]~P39(x67891,x67892)+P39(x67891,f334(f334(f291(x67891,x67891,x67891),x67892),f310(x67891,x67892))) % 169.19/169.65 [7010]~P104(f334(f334(f250(a1),x70102),f2(a1)))+P104(f334(f334(f249(a1),f46(a1,x70101,x70102)),f2(a1))) % 169.19/169.65 [7404]~P142(x74041)+E(f197(x74041,f334(f334(f9(x74041,x74041,x74041),f81(x74041)),f79(x74041)),x74042,f2(x74041)),f334(f103(x74041),x74042)) % 169.19/169.65 [7433]~P124(x74331)+~P104(f334(f334(f250(x74331),f334(f334(f82(x74331),x74332),x74332)),f2(x74331))) % 169.19/169.65 [9998]~P120(x99981)+~P104(f334(f334(f250(x99981),f334(f334(f259(x99981),x99982),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f2(x99981))) % 169.19/169.65 [4700]~E(x47002,f116(x47001))+E(f334(f196(f878(x47001)),x47002),f2(a877)) % 169.19/169.65 [4741]~E(x47411,f2(a877))+E(f334(f334(f81(a877),x47411),x47412),x47412) % 169.19/169.65 [4742]~E(x47422,f2(a877))+E(f334(f334(f82(a877),x47421),x47422),f2(a877)) % 169.19/169.65 [4744]~E(x47441,f2(a877))+E(f334(f334(f82(a877),x47441),x47442),f2(a877)) % 169.19/169.65 [4745]~E(x47452,f2(a1))+E(f334(f334(f40(a1),x47451),x47452),f2(a1)) % 169.19/169.65 [4746]~E(x47462,f2(a877))+E(f334(f334(f259(a877),x47461),x47462),f79(a877)) % 169.19/169.65 [4756]E(x47561,f116(x47562))+~E(f334(f196(f878(x47562)),x47561),f2(a877)) % 169.19/169.65 [4758]~P93(x47581)+E(f334(f334(f82(x47581),x47582),x47582),x47582) % 169.19/169.65 [4759]~P95(x47591)+E(f334(f334(f113(x47591),x47592),x47592),x47592) % 169.19/169.65 [4761]~P100(x47611)+E(f334(f334(f113(x47611),x47612),x47612),x47612) % 169.19/169.65 [4762]~P95(x47621)+E(f334(f334(f104(x47621),x47622),x47622),x47622) % 169.19/169.65 [4764]~P101(x47641)+E(f334(f334(f104(x47641),x47642),x47642),x47642) % 169.19/169.65 [4766]~P107(x47661)+E(f334(f334(f247(x47661),x47662),x47662),x47662) % 169.19/169.65 [4768]~P107(x47681)+E(f334(f334(f248(x47681),x47682),x47682),x47682) % 169.19/169.65 [4787]~P67(x47871)+E(f334(f334(f3(x47871),x47872),x47872),f2(x47871)) % 169.19/169.65 [4801]~P79(x48011)+E(f334(f80(x48011),f334(f80(x48011),x48012)),x48012) % 169.19/169.65 [4802]~P67(x48021)+E(f334(f80(x48021),f334(f80(x48021),x48022)),x48022) % 169.19/169.65 [4819]~E(x48192,f2(a877))+E(f334(f334(f259(a877),x48191),x48192),f334(a115,f2(a877))) % 169.19/169.65 [4852]~P77(x48521)+E(f334(f334(f82(x48521),f79(x48521)),x48522),x48522) % 169.19/169.65 [4853]~P68(x48531)+E(f334(f334(f82(x48531),f79(x48531)),x48532),x48532) % 169.19/169.65 [4854]~P115(x48541)+E(f334(f334(f82(x48541),f79(x48541)),x48542),x48542) % 169.19/169.65 [4855]~P115(x48551)+E(f334(f334(f81(x48551),f2(x48551)),x48552),x48552) % 169.19/169.65 [4856]~P78(x48561)+E(f334(f334(f81(x48561),f2(x48561)),x48562),x48562) % 169.19/169.65 [4857]~P72(x48571)+E(f334(f334(f81(x48571),f2(x48571)),x48572),x48572) % 169.19/169.65 [4858]~P97(x48581)+E(f334(f334(f113(x48581),f195(x48581)),x48582),x48582) % 169.19/169.65 [4859]~P96(x48591)+E(f334(f334(f104(x48591),f257(x48591)),x48592),x48592) % 169.19/169.65 [4878]~P115(x48781)+E(f334(f334(f82(x48781),f2(x48781)),x48782),f2(x48781)) % 169.19/169.65 [4879]~P130(x48791)+E(f334(f334(f82(x48791),f2(x48791)),x48792),f2(x48791)) % 169.19/169.65 [4880]~P117(x48801)+E(f334(f334(f292(x48801),f2(x48801)),x48802),f2(x48801)) % 169.19/169.65 [4881]~P26(x48811)+E(f334(f334(f40(x48811),f2(x48811)),x48812),f2(x48811)) % 169.19/169.65 [4882]~P77(x48821)+E(f334(f334(f259(x48821),f79(x48821)),x48822),f79(x48821)) % 169.19/169.65 [4883]~P96(x48831)+E(f334(f334(f113(x48831),f257(x48831)),x48832),f257(x48831)) % 169.19/169.65 [4884]~P97(x48841)+E(f334(f334(f104(x48841),f195(x48841)),x48842),f195(x48841)) % 169.19/169.65 [4892]E(x48921,f116(x48922))+E(f144(x48922,f334(f169(x48922),x48921)),f334(f141(x48922),x48921)) % 169.19/169.65 [4893]E(x48931,f116(x48932))+E(f334(f141(x48932),f334(f169(x48932),x48931)),f144(x48932,x48931)) % 169.19/169.65 [4894]E(x48941,f2(a877))+~E(f334(f334(f81(a877),x48942),x48941),x48942) % 169.19/169.65 [4900]~P92(x49001)+E(f334(f105(x49001),f334(f106(a1),x49002)),f334(f106(x49001),x49002)) % 169.19/169.65 [4901]~P137(x49011)+E(f334(f105(x49011),f334(f103(a1),x49012)),f334(f103(x49011),x49012)) % 169.19/169.65 [4908]E(x49081,f79(a877))+~E(f334(f334(f82(a877),x49082),x49081),f79(a877)) % 169.19/169.65 [4909]E(x49091,f79(a877))+~E(f334(f334(f82(a877),x49091),x49092),f79(a877)) % 169.19/169.65 [4910]E(x49101,f2(a877))+~E(f334(f334(f81(a877),x49102),x49101),f2(a877)) % 169.19/169.65 [4911]E(x49111,f2(a877))+~E(f334(f334(f81(a877),x49111),x49112),f2(a877)) % 169.19/169.65 [4926]~P83(x49261)+E(f334(f76(x49261),f334(f80(x49261),x49262)),f334(f76(x49261),x49262)) % 169.19/169.65 [4927]~P120(x49271)+E(f334(f76(x49271),f334(f103(x49271),x49272)),f334(f103(x49271),x49272)) % 169.19/169.65 [4928]~P83(x49281)+E(f334(f76(x49281),f334(f76(x49281),x49282)),f334(f76(x49281),x49282)) % 169.19/169.65 [4929]~P72(x49291)+E(f334(f166(x49291),f334(f169(x49291),x49292)),f334(f166(x49291),x49292)) % 169.19/169.65 [4934]~E(x49341,f334(a115,f2(a877)))+E(f334(f334(f259(a877),x49341),x49342),f334(a115,f2(a877))) % 169.19/169.65 [4944]~P67(x49441)+E(f334(f334(f3(x49441),f2(x49441)),x49442),f334(f80(x49441),x49442)) % 169.19/169.65 [4945]~E(x49452,f2(a877))+E(f139(a877,f334(f304(a877,x49451),x49452)),f116(a877)) % 169.19/169.65 [4954]~P92(x49541)+E(f334(f334(f81(x49541),x49542),f334(f106(x49541),a84)),x49542) % 169.19/169.65 [4955]E(x49551,f2(a1))+E(f48(f334(f76(a1),x49552),f334(f76(a1),x49551)),f54(x49552,x49551)) % 169.19/169.65 [4971]~E(x49711,x49712)+P104(f334(f334(f249(a877),x49711),x49712)) % 169.19/169.65 [4978]~E(x49781,f2(a102))+E(f334(f334(f81(a877),f334(a21,x49781)),x49782),x49782) % 169.19/169.65 [4988]~P29(x49881)+P29(f334(f334(f259(a1),x49881),x49882)) % 169.19/169.65 [4989]~P67(x49891)+E(f334(f334(f81(x49891),x49892),f334(f80(x49891),x49892)),f2(x49891)) % 169.19/169.65 [4990]~P79(x49901)+E(f334(f334(f113(x49901),x49902),f334(f80(x49901),x49902)),f257(x49901)) % 169.19/169.65 [4991]~P79(x49911)+E(f334(f334(f104(x49911),x49912),f334(f80(x49911),x49912)),f195(x49911)) % 169.19/169.65 [5016]E(x50161,f2(a877))+~E(f334(f80(a1),f334(f103(a1),x50162)),f334(f103(a1),x50161)) % 169.19/169.65 [5017]E(x50171,f2(a877))+~E(f334(f80(a1),f334(f103(a1),x50171)),f334(f103(a1),x50172)) % 169.19/169.65 [5027]E(f202(x50271,x50272),f2(a1))+P104(f334(f334(f249(a1),x50272),x50271)) % 169.19/169.65 [5028]E(f180(x50281,x50282),f116(a1))+P104(f334(f334(f249(a1),x50281),x50282)) % 169.19/169.65 [5041]E(x50411,f334(a115,f2(a877)))+~E(f334(f334(f82(a877),x50412),x50411),f334(a115,f2(a877))) % 169.19/169.65 [5042]E(x50421,f334(a115,f2(a877)))+~E(f334(f334(f82(a877),x50421),x50422),f334(a115,f2(a877))) % 169.19/169.65 [5043]~P105(x50431)+P104(f334(f334(f249(x50431),x50432),x50432)) % 169.19/169.65 [5044]~P91(x50441)+P104(f334(f334(f92(x50441),x50442),x50442)) % 169.19/169.65 [5047]~P92(x50471)+E(f334(f334(f82(x50471),x50472),f334(f106(x50471),a100)),f334(f80(x50471),x50472)) % 169.19/169.65 [5065]~P92(x50651)+E(f334(f80(x50651),f334(f106(x50651),x50652)),f334(f106(x50651),f334(f80(a1),x50652))) % 169.19/169.65 [5066]~P137(x50661)+E(f334(f80(x50661),f334(f105(x50661),x50662)),f334(f105(x50661),f334(f80(a1),x50662))) % 169.19/169.65 [5098]~E(x50981,f334(a115,x50982))+P104(f334(f334(f250(a877),f2(a877)),x50981)) % 169.19/169.65 [5115]~P107(x51151)+E(f334(f80(f886(x51151,a871)),f334(f303(x51151),x51152)),f334(f306(x51151),x51152)) % 169.19/169.65 [5116]~P107(x51161)+E(f334(f80(f886(x51161,a871)),f334(f255(x51161),x51162)),f334(f256(x51161),x51162)) % 169.19/169.65 [5117]~P107(x51171)+E(f334(f80(f886(x51171,a871)),f334(f306(x51171),x51172)),f334(f303(x51171),x51172)) % 169.19/169.65 [5118]~P107(x51181)+E(f334(f80(f886(x51181,a871)),f334(f256(x51181),x51182)),f334(f255(x51181),x51182)) % 169.19/169.65 [5126]~E(f334(f103(a1),x51262),x51261)+P104(f334(f334(f249(a1),f2(a1)),x51261)) % 169.19/169.65 [5133]~E(x51332,f2(a1))+E(f54(x51331,x51332),f334(f334(f269(a1,a1),f2(a1)),f334(f76(a1),x51331))) % 169.19/169.65 [5135]~P24(x51351)+P104(f334(f334(f249(x51351),f195(x51351)),x51352)) % 169.19/169.65 [5167]E(x51671,x51672)+~E(f334(f334(f81(a1),x51671),x51671),f334(f334(f81(a1),x51672),x51672)) % 169.19/169.65 [5171]~P104(f334(x51711,x51712))+P104(f334(x51711,f334(a107,f825(x51711)))) % 169.19/169.65 [5197]~P120(x51971)+E(f334(f334(f82(x51971),f83(x51971,x51972)),f334(f76(x51971),x51972)),x51972) % 169.19/169.65 [5206]~E(x52062,f2(a877))+E(f86(f885(a877,a877),f49(x52061,x52062)),f334(f334(f269(a877,a877),f2(a877)),x52061)) % 169.19/169.65 [5217]~E(x52171,x52172)+~P104(f334(f334(f250(a877),x52171),x52172)) % 169.19/169.65 [5218]~E(x52181,x52182)+~P104(f334(f334(f250(a1),x52181),x52182)) % 169.19/169.65 [5221]~P142(x52211)+E(f334(f334(f81(x52211),f79(x52211)),f334(f103(x52211),x52212)),f334(f103(x52211),f334(a115,x52212))) % 169.19/169.65 [5225]~E(x52251,f2(a877))+~P104(f334(f334(f250(a877),x52252),x52251)) % 169.19/169.65 [5241]E(f152(x52411,x52412),x52412)+~E(f334(f196(f878(x52411)),f152(x52411,x52412)),f334(f196(f878(x52411)),x52412)) % 169.19/169.65 [5242]E(f334(f39(x52421),f334(f173(x52421),x52422)),f334(f196(f878(x52421)),x52422))+~P104(f334(f137(x52421),x52422)) % 169.19/169.65 [5252]~P104(f334(x52521,f826(x52521)))+P104(f334(x52521,f334(f103(a1),x52522))) % 169.19/169.65 [5263]E(f282(x52631,x52632),f79(a102))+~P104(f334(f334(f250(a102),x52632),x52631)) % 169.19/169.65 [5264]E(f180(x52641,x52642),f116(a1))+~P104(f334(f334(f250(a1),x52642),x52641)) % 169.19/169.65 [5265]E(f125(x52651,x52652),f118(a1))+~P104(f334(f334(f250(a1),x52651),x52652)) % 169.19/169.65 [5268]~P108(x52681)+E(f305(x52681,x52682,x52682),f334(f334(f312(x52681),x52682),f195(f886(x52681,a871)))) % 169.19/169.65 [5290]~E(f334(f334(f3(a877),x52901),x52902),f2(a877))+P104(f334(f334(f249(a877),x52901),x52902)) % 169.19/169.65 [5291]~E(f334(f334(f3(a1),x52911),x52912),f2(a1))+P104(f334(f334(f92(a1),x52911),x52912)) % 169.19/169.65 [5317]~E(x53172,f2(a877))+E(f56(x53171,x53172,f116(x53171)),f334(f334(f151(f878(x53171)),f116(x53171)),f116(f878(x53171)))) % 169.19/169.65 [5321]~P105(x53211)+~P104(f334(f334(f250(x53211),x53212),x53212)) % 169.19/169.65 [5324]~E(f46(a1,x53241,x53242),f2(a1))+E(f46(a1,x53241,f334(f80(a1),x53242)),f2(a1)) % 169.19/169.65 [5326]~E(f46(a1,x53261,x53262),f2(a1))+E(f46(a1,f334(f80(a1),x53261),x53262),f2(a1)) % 169.19/169.65 [5335]E(f334(f304(a877,x53351),f334(a115,x53352)),f195(f886(a877,a871)))+P104(f334(f334(f249(a877),x53351),x53352)) % 169.19/169.65 [5356]E(f139(a877,f334(f304(a877,x53561),x53562)),f116(a877))+P104(f334(f334(f250(a877),x53561),x53562)) % 169.19/169.65 [5361]~E(f334(f39(x53611),f334(f173(x53611),x53612)),f334(f196(f878(x53611)),x53612))+P104(f334(f137(x53611),x53612)) % 169.19/169.65 [5366]~P104(f334(f137(x53661),x53662))+P104(f334(f137(x53661),f334(f168(x53661),x53662))) % 169.19/169.65 [5367]~P104(f334(f137(x53671),x53672))+P104(f334(f137(x53671),f334(f172(x53671),x53672))) % 169.19/169.65 [5368]~P104(f334(f137(x53681),x53682))+P104(f334(f137(x53681),f334(f169(x53681),x53682))) % 169.19/169.65 [5375]P104(f334(x53751,x53752))+~P104(f334(x53751,f334(a107,f342(x53751)))) % 169.19/169.65 [5376]P104(f334(f334(f249(a877),x53762),x53761))+P104(f334(f334(f249(a877),x53761),x53762)) % 169.19/169.65 [5377]P104(f334(f334(f249(a1),x53772),x53771))+P104(f334(f334(f249(a1),x53771),x53772)) % 169.19/169.65 [5379]~P83(x53791)+P104(f334(f334(f249(x53791),x53792),f334(f76(x53791),x53792))) % 169.19/169.65 [5382]P104(f334(x53821,f856(x53821)))+~P104(f334(x53821,f334(f103(a1),x53822))) % 169.19/169.65 [5407]E(f334(f334(f3(a877),x54071),x54072),f2(a877))+~P104(f334(f334(f249(a877),x54071),x54072)) % 169.19/169.65 [5408]E(f334(f334(f3(a1),x54081),x54082),f2(a1))+~P104(f334(f334(f92(a1),x54081),x54082)) % 169.19/169.65 [5409]E(f334(f334(f40(a877),x54091),x54092),f2(a877))+~P104(f334(f334(f250(a877),x54091),x54092)) % 169.19/169.65 [5427]E(f46(a877,x54271,x54272),x54271)+~P104(f334(f334(f250(a877),x54271),x54272)) % 169.19/169.65 [5436]E(f46(a1,x54361,f334(f80(a1),x54362)),f293(x54361,x54362))+P104(f334(f334(f249(a1),f2(a1)),x54362)) % 169.19/169.65 [5448]E(f334(f334(f3(a1),x54481),x54482),f202(x54481,x54482))+~P104(f334(f334(f249(a1),x54482),x54481)) % 169.19/169.65 [5467]P104(f334(f334(f249(a1),f2(a1)),f826(x54671)))+P104(f334(x54671,f334(f103(a1),x54672))) % 169.19/169.65 [5479]~P58(x54791)+P104(f334(f334(f336(x54791),x54792),f334(f173(x54791),f57(x54791)))) % 169.19/169.65 [5481]~P119(x54811)+P104(f334(f334(f249(x54811),f2(x54811)),f334(f103(x54811),x54812))) % 169.19/169.65 [5482]~P83(x54821)+P104(f334(f334(f249(x54821),f2(x54821)),f334(f76(x54821),x54822))) % 169.19/169.65 [5509]E(f334(f334(f81(a877),x55091),f696(x55092,x55091)),x55092)+~P104(f334(f334(f249(a877),x55091),x55092)) % 169.19/169.65 [5524]E(f305(a1,x55241,x55242),f195(f886(a1,a871)))+~P104(f334(f334(f250(a1),x55242),x55241)) % 169.19/169.65 [5527]~P120(x55271)+E(f334(f334(f82(x55271),f334(f76(x55271),x55272)),f334(f76(x55271),x55272)),f334(f334(f82(x55271),x55272),x55272)) % 169.19/169.65 [5532]E(f139(a877,f334(f304(a877,x55321),f334(a115,x55322))),f116(a877))+P104(f334(f334(f249(a877),x55321),x55322)) % 169.19/169.65 [5536]E(f334(f334(f40(a1),x55361),x55362),f294(x55361,x55362))+~P104(f334(f334(f249(a1),f2(a1)),x55362)) % 169.19/169.65 [5556]P104(f334(f137(x55561),x55562))+~P104(f334(f137(x55561),f334(f168(x55561),x55562))) % 169.19/169.65 [5557]P104(f334(f137(x55571),x55572))+~P104(f334(f137(x55571),f334(f169(x55571),x55572))) % 169.19/169.65 [5578]P104(f334(f63(a877),x55781))+P104(f334(f334(f336(a877),f827(x55781,x55782)),x55781)) % 169.19/169.65 [5579]P104(f334(f63(a877),x55791))+P104(f334(f334(f336(a877),f830(x55791,x55792)),x55791)) % 169.19/169.65 [5582]P104(f334(f334(f250(a877),x55822),f334(a115,x55821)))+P104(f334(f334(f250(a877),x55821),x55822)) % 169.19/169.65 [5583]E(f46(a1,x55831,x55832),f293(x55831,x55832))+~P104(f334(f334(f249(a1),f2(a1)),x55832)) % 169.19/169.65 [5586]E(f139(a877,f334(f304(a877,x55861),x55862)),f116(a877))+~P104(f334(f334(f249(a877),x55862),x55861)) % 169.19/169.65 [5587]~P75(x55871)+E(f334(f313(x55871,x55871,f80(x55871)),f334(f303(x55871),x55872)),f334(f256(x55871),f334(f80(x55871),x55872))) % 169.19/169.65 [5588]~P75(x55881)+E(f334(f313(x55881,x55881,f80(x55881)),f334(f255(x55881),x55882)),f334(f306(x55881),f334(f80(x55881),x55882))) % 169.19/169.65 [5589]~P75(x55891)+E(f334(f313(x55891,x55891,f80(x55891)),f334(f306(x55891),x55892)),f334(f255(x55891),f334(f80(x55891),x55892))) % 169.19/169.65 [5590]~P75(x55901)+E(f334(f313(x55901,x55901,f80(x55901)),f334(f256(x55901),x55902)),f334(f303(x55901),f334(f80(x55901),x55902))) % 169.19/169.65 [5601]E(x56011,f195(f886(x56012,a871)))+P104(f334(f334(f336(x56012),f364(x56011,x56012)),x56011)) % 169.19/169.65 [5602]E(x56021,f195(f886(x56022,a871)))+P104(f334(f334(f336(x56022),f397(x56021,x56022)),x56021)) % 169.19/169.65 [5613]~P104(f334(f334(f250(a877),x56131),x56132))+P104(f334(f334(f249(a877),x56131),x56132)) % 169.19/169.65 [5614]~P104(f334(f334(f250(a1),x56141),x56142))+P104(f334(f334(f249(a1),x56141),x56142)) % 169.19/169.65 [5630]E(f48(x56301,x56302),f334(f334(f269(a1,a1),f2(a1)),x56301))+~P104(f334(f334(f250(a1),x56301),x56302)) % 169.19/169.65 [5632]E(f224(f334(f80(a1),x56321),f334(f80(a1),x56322)),f224(x56321,x56322))+~P104(f334(f334(f250(a1),x56322),f2(a1))) % 169.19/169.65 [5643]E(x56431,x56432)+~E(f334(a5,f334(a115,f334(a21,x56431))),f334(a5,f334(a115,f334(a21,x56432)))) % 169.19/169.65 [5648]E(f48(x56481,x56482),f334(f334(f269(a1,a1),f2(a1)),x56481))+~P104(f334(f334(f249(a1),x56482),f2(a1))) % 169.19/169.65 [5675]E(f46(a877,f334(f106(a877),x56751),f334(f106(a877),x56752)),f2(a877))+~P104(f334(a201,f334(f106(a1),x56751))) % 169.19/169.65 [5690]P104(f334(f334(f249(a1),f2(a1)),f856(x56901)))+~P104(f334(x56901,f334(f103(a1),x56902))) % 169.19/169.65 [5724]P41(f305(a1,x57241,x57242))+~P104(f334(f334(f249(a1),f2(a1)),x57241)) % 169.19/169.65 [5729]~P104(f334(f63(x57291),x57292))+P104(f334(f63(f886(x57291,a871)),f334(f311(x57291),x57292))) % 169.19/169.65 [5742]E(f334(f334(f81(a1),x57421),f334(f103(a1),f861(x57422,x57421))),x57422)+~P104(f334(f334(f249(a1),x57421),x57422)) % 169.19/169.65 [5750]P104(f334(f334(f249(a877),x57501),x57502))+P104(f334(f334(f249(a877),f334(a115,x57502)),x57501)) % 169.19/169.65 [5795]E(f334(f334(f40(a877),f334(f106(a877),x57951)),f334(f106(a877),x57952)),f2(a877))+~P104(f334(a201,f334(f106(a1),x57951))) % 169.19/169.65 [5796]E(f334(f334(f82(a877),f334(f106(a877),x57961)),f334(f106(a877),x57962)),f2(a877))+~P104(f334(f334(f250(a1),x57961),a84)) % 169.19/169.65 [5798]P104(f334(f334(f249(a877),x57981),f334(a115,x57982)))+~P104(f334(f334(f249(a877),x57981),x57982)) % 169.19/169.65 [5800]P104(f334(f334(f250(a877),x58001),f334(a115,x58002)))+~P104(f334(f334(f249(a877),x58001),x58002)) % 169.19/169.65 [5802]P104(f334(f334(f250(a877),x58021),f334(a115,x58022)))+~P104(f334(f334(f250(a877),x58021),x58022)) % 169.19/169.65 [5805]~E(x58051,x58052)+P104(f334(f334(f250(a1),x58051),f334(f334(f81(a1),x58052),f79(a1)))) % 169.19/169.65 [5808]E(f46(a1,x58081,x58082),f2(a1))+E(f334(f334(f3(a1),x58082),f46(a1,x58081,x58082)),f46(a1,f334(f80(a1),x58081),x58082)) % 169.19/169.65 [5817]E(x58171,f116(x58172))+P104(f334(f334(f336(x58172),f144(x58172,x58171)),f334(f173(x58172),x58171))) % 169.19/169.65 [5829]E(f86(f885(a877,a877),f49(x58291,x58292)),f334(f334(f269(a877,a877),f2(a877)),x58291))+~P104(f334(f334(f250(a877),x58291),x58292)) % 169.19/169.65 [5862]E(f334(f334(f3(a877),f334(f106(a877),x58621)),f334(f106(a877),x58622)),f334(f106(a877),x58621))+~P104(f334(f334(f250(a1),x58622),a84)) % 169.19/169.65 [5863]E(f334(f334(f81(a877),f334(f106(a877),x58631)),f334(f106(a877),x58632)),f334(f106(a877),x58632))+~P104(f334(f334(f250(a1),x58631),a84)) % 169.19/169.65 [5868]E(f334(a115,f334(f334(f81(a877),x58681),f715(x58682,x58681))),x58682)+~P104(f334(f334(f250(a877),x58681),x58682)) % 169.19/169.65 [5891]P104(f334(x58911,x58912))+~P104(f334(x58911,f334(a90,f708(x58912,x58911)))) % 169.19/169.65 [5899]~P104(f334(f334(f250(a877),x58991),f334(a115,x58992)))+P104(f334(f334(f249(a877),x58991),x58992)) % 169.19/169.65 [5945]E(f334(f334(f312(a877),x59451),f334(f304(a877,x59452),x59451)),f334(f304(a877,x59452),f334(a115,x59451)))+~P104(f334(f334(f249(a877),x59452),x59451)) % 169.19/169.65 [5949]E(x59491,f116(x59492))+E(f334(f334(f134(x59492),f117(x59492,x59491)),f334(f334(f151(x59492),f144(x59492,x59491)),f116(x59492))),x59491) % 169.19/169.65 [5963]P104(f334(f63(x59631),x59632))+~P104(f334(f334(f250(a877),f2(a877)),f334(f39(x59631),x59632))) % 169.19/169.65 [5965]~E(x59651,f195(f886(x59652,a871)))+~P104(f334(f334(f250(a877),f2(a877)),f334(f39(x59652),x59651))) % 169.19/169.65 [5977]~P104(f334(f334(f250(a877),x59771),x59772))+P104(f334(f334(f249(a877),f334(a115,x59771)),x59772)) % 169.19/169.65 [5984]~P107(x59841)+E(f150(x59841,x59841,f7(x59841),f152(x59841,x59842)),f139(x59841,f334(f173(x59841),x59842))) % 169.19/169.65 [5987]E(x59871,f116(x59872))+P104(f334(f334(f336(x59872),f334(f141(x59872),x59871)),f334(f173(x59872),x59871))) % 169.19/169.65 [5993]~P119(x59931)+P104(f334(f334(f250(x59931),x59932),f334(f334(f81(x59931),x59932),f79(x59931)))) % 169.19/169.65 [5995]~P83(x59951)+P104(f334(f334(f249(x59951),f334(f80(x59951),x59952)),f334(f76(x59951),x59952))) % 169.19/169.65 [6025]P104(f334(f63(a877),x60251))+~P104(f334(f334(f249(a877),f830(x60251,x60252)),x60252)) % 169.19/169.65 [6026]P104(f334(f63(a877),x60261))+~P104(f334(f334(f250(a877),f827(x60261,x60262)),x60262)) % 169.19/169.65 [6029]~P104(f334(f63(f885(x60291,x60291)),x60292))+P104(f334(f63(x60291),f334(f287(x60291),x60292))) % 169.19/169.65 [6085]~P104(f334(f334(f250(a877),x60852),f334(a115,x60851)))+~P104(f334(f334(f250(a877),x60851),x60852)) % 169.19/169.65 [6086]~P108(x60861)+E(f334(f334(f104(f886(x60861,a871)),f334(f303(x60861),x60862)),f334(f256(x60861),x60862)),f334(f334(f312(x60861),x60862),f195(f886(x60861,a871)))) % 169.19/169.65 [6099]P104(f334(f63(x60991),x60992))+~P104(f334(f63(f886(x60991,a871)),f334(f311(x60991),x60992))) % 169.19/169.65 [6123]P104(f334(f334(f249(a877),f334(a115,x61231)),f334(a115,x61232)))+~P104(f334(f334(f249(a877),x61231),x61232)) % 169.19/169.65 [6124]P104(f334(f334(f249(a877),f334(a21,x61241)),f334(a21,x61242)))+~P104(f334(f334(f249(a102),x61241),x61242)) % 169.19/169.65 [6125]P104(f334(f334(f249(a102),f334(a5,x61251)),f334(a5,x61252)))+~P104(f334(f334(f249(a877),x61251),x61252)) % 169.19/169.65 [6127]P104(f334(f334(f250(a877),f334(a115,x61271)),f334(a115,x61272)))+~P104(f334(f334(f250(a877),x61271),x61272)) % 169.19/169.65 [6128]P104(f334(f334(f250(a877),f334(a21,x61281)),f334(a21,x61282)))+~P104(f334(f334(f250(a102),x61281),x61282)) % 169.19/169.65 [6129]P104(f334(f334(f250(a102),f334(a5,x61291)),f334(a5,x61292)))+~P104(f334(f334(f250(a877),x61291),x61292)) % 169.19/169.65 [6132]E(x61321,x61322)+~E(f334(f313(a877,a1,f103(a1)),x61321),f334(f313(a877,a1,f103(a1)),x61322)) % 169.19/169.65 [6148]P104(f334(f334(f249(a877),x61481),x61482))+~P104(f334(f334(f249(a877),f334(a115,x61481)),x61482)) % 169.19/169.65 [6151]P104(f334(f334(f250(a877),x61511),x61512))+~P104(f334(f334(f249(a877),f334(a115,x61511)),x61512)) % 169.19/169.65 [6152]P104(f334(f334(f250(a877),x61521),x61522))+~P104(f334(f334(f250(a877),f334(a115,x61521)),x61522)) % 169.19/169.65 [6167]E(f46(a1,x61671,x61672),f2(a1))+E(f334(f334(f3(a1),f46(a1,x61671,x61672)),x61672),f46(a1,x61671,f334(f80(a1),x61672))) % 169.19/169.65 [6238]E(f334(f39(f886(x62381,a871)),f334(f311(x62381),x62382)),f334(f334(f259(a877),f334(a115,f334(a115,f2(a877)))),f334(f39(x62381),x62382)))+~P104(f334(f63(x62381),x62382)) % 169.19/169.65 [6241]E(x62411,f116(x62412))+E(f334(f334(f165(x62412),x62411),f334(f334(f3(a877),f334(f196(f878(x62412)),x62411)),f79(a877))),f144(x62412,x62411)) % 169.19/169.65 [6266]E(x62661,f116(x62662))+E(f334(f334(f134(x62662),f334(f172(x62662),x62661)),f334(f334(f151(x62662),f334(f141(x62662),x62661)),f116(x62662))),f334(f168(x62662),x62661)) % 169.19/169.65 [6295]~P104(f334(f63(x62951),f41(f886(x62951,a871),x62952)))+P104(f334(f63(f886(x62951,a871)),x62952)) % 169.19/169.65 [6317]P104(f334(f334(f249(a877),f334(f106(a877),x63171)),f334(f106(a877),x63172)))+~P104(f334(f334(f249(a1),x63171),a84)) % 169.19/169.65 [6334]~P104(f334(f334(f250(a1),x63341),x63342))+P104(f334(f334(f249(a1),x63341),f334(f334(f3(a1),x63342),f79(a1)))) % 169.19/169.65 [6335]~P104(f334(f334(f249(a1),x63351),x63352))+P104(f334(f334(f250(a1),x63351),f334(f334(f81(a1),x63352),f79(a1)))) % 169.19/169.65 [6336]~P104(f334(f334(f250(a1),x63361),x63362))+P104(f334(f334(f250(a1),x63361),f334(f334(f81(a1),x63362),f79(a1)))) % 169.19/169.65 [6338]~P104(f334(f334(f249(a1),x63381),x63382))+P104(f334(f334(f249(a877),f334(f106(a877),x63381)),f334(f106(a877),x63382))) % 169.19/169.65 [6339]~P104(f334(f334(f249(a1),x63391),x63392))+P104(f334(f334(f249(a1),f334(f106(a1),x63391)),f334(f106(a1),x63392))) % 169.19/169.65 [6341]~P104(f334(f334(f249(a877),x63411),x63412))+P104(f334(f334(f249(a1),f334(f103(a1),x63411)),f334(f103(a1),x63412))) % 169.19/169.65 [6342]~P104(f334(f334(f250(a1),x63421),x63422))+P104(f334(f334(f250(a1),f334(f106(a1),x63421)),f334(f106(a1),x63422))) % 169.19/169.65 [6344]~P104(f334(f334(f250(a877),x63441),x63442))+P104(f334(f334(f250(a1),f334(f103(a1),x63441)),f334(f103(a1),x63442))) % 169.19/169.65 [6345]~P104(f334(f334(f92(a1),x63451),x63452))+P104(f334(f334(f92(a1),f334(f106(a1),x63451)),f334(f106(a1),x63452))) % 169.19/169.65 [6363]~P104(f334(f334(f249(a877),x63631),x63632))+~P104(f334(f334(f249(a877),f334(a115,x63632)),x63631)) % 169.19/169.65 [6408]~P104(f334(f334(f249(a877),f334(a115,x64081)),f334(a115,x64082)))+P104(f334(f334(f249(a877),x64081),x64082)) % 169.19/169.65 [6409]~P104(f334(f334(f249(a102),f334(a5,x64091)),f334(a5,x64092)))+P104(f334(f334(f249(a877),x64091),x64092)) % 169.19/169.65 [6410]~P104(f334(f334(f249(a877),f334(a21,x64101)),f334(a21,x64102)))+P104(f334(f334(f249(a102),x64101),x64102)) % 169.19/169.65 [6412]~P104(f334(f334(f250(a877),f334(a115,x64121)),f334(a115,x64122)))+P104(f334(f334(f250(a877),x64121),x64122)) % 169.19/169.65 [6413]~P104(f334(f334(f250(a102),f334(a5,x64131)),f334(a5,x64132)))+P104(f334(f334(f250(a877),x64131),x64132)) % 169.19/169.65 [6414]~P104(f334(f334(f250(a877),f334(a107,x64141)),f334(a107,x64142)))+P104(f334(f334(f250(a1),x64141),x64142)) % 169.19/169.65 [6415]~P104(f334(f334(f250(a877),f334(a21,x64151)),f334(a21,x64152)))+P104(f334(f334(f250(a102),x64151),x64152)) % 169.19/169.65 [6455]~P104(f334(f334(f250(a877),f334(a107,x64552)),f334(a107,x64551)))+P104(f334(f334(f250(a1),f2(a1)),x64551)) % 169.19/169.65 [6486]P104(f334(f334(f249(a1),f2(a1)),f46(a1,x64861,x64862)))+~P104(f334(f334(f250(a1),f2(a1)),x64862)) % 169.19/169.65 [6643]P39(x66431,x66432)+~E(f334(f334(f291(x66431,x66431,x66431),x66432),x66432),f195(f886(f885(x66431,x66431),a871))) % 169.19/169.65 [6655]~P39(x66551,x66552)+P39(x66551,f334(f334(f291(x66551,x66551,x66551),x66552),x66552)) % 169.19/169.65 [6666]P104(f334(f334(f249(a1),x66661),x66662))+~P104(f334(f334(f250(a1),x66661),f334(f334(f81(a1),x66662),f79(a1)))) % 169.19/169.65 [6667]P104(f334(f334(f250(a1),x66671),x66672))+~P104(f334(f334(f249(a1),x66671),f334(f334(f3(a1),x66672),f79(a1)))) % 169.19/169.65 [6670]P104(f334(f334(f249(a877),x66701),x66702))+~P104(f334(f334(f249(a1),f334(f103(a1),x66701)),f334(f103(a1),x66702))) % 169.19/169.65 [6671]P104(f334(f334(f249(a1),x66711),x66712))+~P104(f334(f334(f249(a1),f334(f106(a1),x66711)),f334(f106(a1),x66712))) % 169.19/169.65 [6673]P104(f334(f334(f250(a877),x66731),x66732))+~P104(f334(f334(f250(a1),f334(f103(a1),x66731)),f334(f103(a1),x66732))) % 169.19/169.65 [6674]P104(f334(f334(f250(a1),x66741),x66742))+~P104(f334(f334(f250(a877),f334(f106(a877),x66741)),f334(f106(a877),x66742))) % 169.19/169.65 [6675]P104(f334(f334(f250(a1),x66751),x66752))+~P104(f334(f334(f250(a1),f334(f106(a1),x66751)),f334(f106(a1),x66752))) % 169.19/169.65 [6676]P104(f334(f334(f92(a1),x66761),x66762))+~P104(f334(f334(f92(a1),f334(f106(a1),x66761)),f334(f106(a1),x66762))) % 169.19/169.65 [6769]~E(f645(x67692,x67691),f116(x67691))+E(f334(f142(f878(x67691),f878(x67691),f134(x67691),f116(x67691)),x67692),f116(x67691)) % 169.19/169.65 [6770]~E(f646(x67702,x67701),f116(x67701))+E(f334(f142(f878(x67701),f878(x67701),f134(x67701),f116(x67701)),x67702),f116(x67701)) % 169.19/169.65 [6777]~P28(x67771)+E(f334(f142(x67771,x67771,f113(x67771),f195(x67771)),x67772),f41(x67771,f334(f173(x67771),x67772))) % 169.19/169.65 [6778]~P28(x67781)+E(f334(f142(x67781,x67781,f104(x67781),f257(x67781)),x67782),f42(x67781,f334(f173(x67781),x67782))) % 169.19/169.65 [6790]E(x67901,f2(a102))+E(f334(f334(f81(a877),f334(a21,f334(f334(f3(a102),x67901),f79(a102)))),f334(a115,x67902)),f334(f334(f81(a877),f334(a21,x67901)),x67902)) % 169.19/169.65 [6840]P104(f334(f334(f250(a1),f334(f334(f3(a1),x68401),x68402)),f2(a1)))+~P104(f334(f334(f250(a1),x68401),x68402)) % 169.19/169.65 [6868]~P107(x68681)+E(f334(f334(f113(f886(x68681,a871)),f334(f334(f312(x68681),x68682),f195(f886(x68681,a871)))),f334(f306(x68681),x68682)),f334(f256(x68681),x68682)) % 169.19/169.65 [6943]~P57(x69431,x69432)+P39(x69431,f334(f254(f885(x69431,x69431)),f334(f273(x69431,x69431,a871),x69432))) % 169.19/169.65 [6944]~P57(x69441,x69442)+P55(x69441,f334(f254(f885(x69441,x69441)),f334(f273(x69441,x69441,a871),x69442))) % 169.19/169.65 [6945]E(x69451,f195(f886(x69452,a871)))+~P104(f334(f334(f249(f886(x69452,a871)),x69451),f195(f886(x69452,a871)))) % 169.19/169.65 [7026]~P104(f334(f334(f250(a877),f2(a877)),x70262))+P104(f334(f334(f249(a877),f46(a877,x70261,x70262)),x70262)) % 169.19/169.65 [7027]~P104(f334(f334(f249(a1),f2(a1)),x70271))+P104(f334(f334(f249(a1),f46(a1,x70271,x70272)),x70271)) % 169.19/169.65 [7028]~P104(f334(f334(f250(a877),f2(a877)),x70282))+P104(f334(f334(f250(a877),f46(a877,x70281,x70282)),x70282)) % 169.19/169.65 [7030]~P104(f334(f334(f250(a1),f2(a1)),x70302))+P104(f334(f334(f250(a1),f46(a1,x70301,x70302)),x70302)) % 169.19/169.65 [7106]~P108(x71061)+E(f334(f334(f3(f886(x71061,a871)),f334(f334(f312(x71061),x71062),f195(f886(x71061,a871)))),f334(f255(x71061),x71062)),f334(f334(f312(x71061),x71062),f195(f886(x71061,a871)))) % 169.19/169.65 [7179]~P51(x71791,x71792)+P49(x71791,f257(f886(x71791,a871)),f334(f254(f885(x71791,x71791)),f334(f273(x71791,x71791,a871),x71792))) % 169.19/169.65 [7180]P104(f334(x71801,x71802))+P104(f334(f334(f336(f886(f885(a877,a877),a871)),f708(x71802,x71801)),a101)) % 169.19/169.65 [7225]E(f334(f334(f134(a877),f139(a877,f334(f304(a877,x72251),x72252))),f334(f334(f151(a877),x72252),f116(a877))),f139(a877,f334(f304(a877,x72251),f334(a115,x72252))))+~P104(f334(f334(f249(a877),x72251),x72252)) % 169.19/169.65 [7369]E(x73691,f2(a877))+~E(f334(f142(a877,a877,f81(a877),x73691),x73692),f2(a877)) % 169.19/169.65 [7394]~P104(f334(f334(f250(a1),f334(f334(f3(a1),x73941),x73942)),f2(a1)))+P104(f334(f334(f250(a1),x73941),x73942)) % 169.19/169.65 [7424]P39(x74241,x74242)+~P39(x74241,f334(f334(f291(x74241,x74241,x74241),x74242),x74242)) % 169.19/169.65 [7453]~P104(f334(f334(f249(a877),f334(a115,x74531)),x74532))+P104(f192(a871,a246,f334(f249(a877),x74531),x74532)) % 169.19/169.65 [7611]P21(a877,a877,f334(f334(f9(a877,a877,a877),f3(a877)),x76111),x76112)+P104(f334(f334(f336(a877),f716(x76111,x76112)),x76112)) % 169.19/169.65 [7667]E(f334(f334(f334(f67(a877,x76671,f81(a877)),f334(f18(a877,x76671),f79(a877))),f2(a877)),x76672),f334(f39(x76671),x76672))+~P104(f334(f63(x76671),x76672)) % 169.19/169.65 [7709]P21(a877,a877,f334(f334(f9(a877,a877,a877),f3(a877)),x77091),x77092)+~P104(f334(f334(f249(a877),x77091),f716(x77091,x77092))) % 169.19/169.65 [7767]P39(x77671,x77672)+P104(f334(f334(f249(f886(x77671,a871)),f713(x77672,x77671)),f334(f288(x77671,x77671,x77672),f713(x77672,x77671)))) % 169.19/169.65 [7772]P57(x77721,x77722)+~P39(x77721,f334(f254(f885(x77721,x77721)),f334(f273(x77721,x77721,a871),x77722))) % 169.19/169.65 [7840]P104(f334(f334(f249(a877),f334(a115,x78401)),x78402))+~P104(f192(a871,a246,f334(f249(a877),x78401),x78402)) % 169.19/169.65 [7895]P104(f334(f334(f336(f885(a877,a877)),f334(f334(f269(a877,a877),x78951),x78952)),f310(a877,a324)))+~P104(f334(f334(f249(a877),x78951),x78952)) % 169.19/169.65 [7992]P51(x79921,x79922)+~P49(x79921,f257(f886(x79921,a871)),f334(f254(f885(x79921,x79921)),f334(f273(x79921,x79921,a871),x79922))) % 169.19/169.65 [8047]~P104(f334(f137(x80471),x80472))+P104(f334(f137(f886(x80471,a871)),f334(f334(f154(f878(x80471),f886(x80471,a871)),f173(x80471)),f55(x80471,x80472)))) % 169.19/169.65 [8248]~P39(x82481,f334(f289(x82481,x82481),x82482))+P39(x82481,f334(f289(x82481,x82481),f334(f334(f291(x82481,x82481,x82481),x82482),f310(x82481,x82482)))) % 169.19/169.65 [8367]P104(f334(f63(f885(x83671,x83671)),f334(f334(f291(x83671,x83671,x83671),x83672),f310(x83671,x83672))))+~P104(f334(f63(f885(x83671,x83671)),x83672)) % 169.19/169.65 [8398]E(x83981,f2(a1))+P104(f334(f50(x83982,x83981),f334(f334(f269(a1,a1),f334(f334(f40(a1),x83982),x83981)),f46(a1,x83982,x83981)))) % 169.19/169.65 [8409]~P104(f334(f334(f336(f885(a877,a877)),f334(f334(f269(a877,a877),x84091),x84092)),f310(a877,a324)))+P104(f334(f334(f249(a877),x84091),x84092)) % 169.19/169.65 [8424]~P78(x84241)+E(f334(f142(x84241,x84241,f334(f9(x84241,x84241,x84241),f81(x84241)),f2(x84241)),f334(f169(x84241),x84242)),f334(f142(x84241,x84241,f81(x84241),f2(x84241)),x84242)) % 169.19/169.65 [8592]~P107(x85921)+E(f334(f142(f878(x85921),x85921,f334(f9(x85921,f878(x85921),f878(x85921)),f148(x85921,x85921,f7(x85921))),f116(x85921)),x85922),f150(x85921,x85921,f7(x85921),x85922)) % 169.19/169.65 [8692]~P55(x86921,f334(f254(f885(x86921,x86921)),f334(f273(x86921,x86921,a871),x86922)))+P55(x86921,f334(f254(f885(x86921,x86921)),f334(f273(x86921,x86921,a871),f258(x86921,x86921,x86922)))) % 169.19/169.65 [8706]P104(f334(f334(f336(f885(a877,a877)),f334(f334(f269(a877,a877),x87061),x87062)),f334(f334(f291(a877,a877,a877),a324),f310(a877,a324))))+~P104(f334(f334(f250(a877),x87061),x87062)) % 169.19/169.65 [8749]~P104(f334(f63(f885(x87491,x87491)),f334(f334(f291(x87491,x87491,x87491),x87492),f310(x87491,x87492))))+P104(f334(f63(f885(x87491,x87491)),x87492)) % 169.19/169.65 [8800]~P55(x88001,f334(f254(f885(x88001,x88001)),f334(f273(x88001,x88001,a871),f258(x88001,x88001,x88002))))+P55(x88001,f334(f254(f885(x88001,x88001)),f334(f273(x88001,x88001,a871),x88002))) % 169.19/169.65 [8993]P55(x89931,x89932)+P104(f334(f334(f336(f885(x89931,x89931)),f334(f334(f269(x89931,x89931),f753(x89932,x89931)),f753(x89932,x89931))),f334(f334(f291(x89931,x89931,x89931),x89932),f310(x89931,x89932)))) % 169.19/169.65 [8994]P55(x89941,x89942)+P104(f334(f334(f336(f885(x89941,x89941)),f334(f334(f269(x89941,x89941),f764(x89942,x89941)),f764(x89942,x89941))),f334(f334(f291(x89941,x89941,x89941),x89942),f310(x89941,x89942)))) % 169.19/169.65 [9108]~P104(f334(f334(f336(f885(a877,a877)),f334(f334(f269(a877,a877),x91081),x91082)),f334(f334(f291(a877,a877,a877),a324),f310(a877,a324))))+P104(f334(f334(f250(a877),x91081),x91082)) % 169.19/169.65 [5111]~P92(x51111)+E(f334(f334(f81(x51111),f334(f106(x51111),a84)),x51112),x51112) % 169.19/169.65 [5140]~P64(x51401)+E(f334(f334(f81(x51401),f334(f80(x51401),x51402)),x51402),f2(x51401)) % 169.19/169.65 [5141]~P67(x51411)+E(f334(f334(f81(x51411),f334(f80(x51411),x51412)),x51412),f2(x51411)) % 169.19/169.65 [5142]~P79(x51421)+E(f334(f334(f113(x51421),f334(f80(x51421),x51422)),x51422),f257(x51421)) % 169.19/169.65 [5143]~P79(x51431)+E(f334(f334(f104(x51431),f334(f80(x51431),x51432)),x51432),f195(x51431)) % 169.19/169.65 [5175]~P92(x51751)+E(f334(f334(f82(x51751),f334(f106(x51751),a100)),x51752),f334(f80(x51751),x51752)) % 169.19/169.65 [5349]~P111(x53491)+E(f334(f334(f82(x53491),f334(f80(x53491),f79(x53491))),x53492),f334(f80(x53491),x53492)) % 169.19/169.65 [5392]E(f334(f76(a1),x53921),f79(a1))+~E(f334(f76(a1),f334(f334(f82(a1),x53921),x53922)),f79(a1)) % 169.19/169.65 [5484]~P92(x54841)+E(f334(f334(f81(x54841),f79(x54841)),f334(f106(x54841),x54842)),f334(f106(x54841),f334(f334(f3(a1),x54842),a100))) % 169.19/169.65 [5537]~P95(x55371)+E(f12(x55371,f334(f334(f312(x55371),x55372),f195(f886(x55371,a871)))),x55372) % 169.19/169.65 [5538]~P28(x55381)+E(f41(x55381,f334(f334(f312(x55381),x55382),f195(f886(x55381,a871)))),x55382) % 169.19/169.65 [5539]~P95(x55391)+E(f13(x55391,f334(f334(f312(x55391),x55392),f195(f886(x55391,a871)))),x55392) % 169.19/169.65 [5540]~P28(x55401)+E(f42(x55401,f334(f334(f312(x55401),x55402),f195(f886(x55401,a871)))),x55402) % 169.19/169.65 [5541]~P107(x55411)+E(f16(x55411,f334(f334(f312(x55411),x55412),f195(f886(x55411,a871)))),x55412) % 169.19/169.65 [5542]~P107(x55421)+E(f17(x55421,f334(f334(f312(x55421),x55422),f195(f886(x55421,a871)))),x55422) % 169.19/169.65 [5564]E(f334(f334(f81(a877),x55641),f334(f334(f3(a877),x55642),x55641)),x55642)+P104(f334(f334(f250(a877),x55642),x55641)) % 169.19/169.65 [5596]E(x55961,f116(x55962))+P104(f334(f334(f250(a877),f2(a877)),f334(f196(f878(x55962)),x55961))) % 169.19/169.65 [5721]~P107(x57211)+E(f14(x57211,f247(x57211),f334(f334(f312(x57211),x57212),f195(f886(x57211,a871)))),x57212) % 169.19/169.65 [5722]~P107(x57221)+E(f15(x57221,f248(x57221),f334(f334(f312(x57221),x57222),f195(f886(x57221,a871)))),x57222) % 169.19/169.65 [5785]E(f334(f334(f3(a877),x57851),f334(f334(f3(a877),x57851),x57852)),x57852)+~P104(f334(f334(f249(a877),x57852),x57851)) % 169.19/169.65 [5786]E(f334(f334(f81(a877),x57861),f334(f334(f3(a877),x57862),x57861)),x57862)+~P104(f334(f334(f249(a877),x57861),x57862)) % 169.19/169.65 [5807]E(f46(a877,f334(f334(f3(a877),x58071),x58072),x58072),f46(a877,x58071,x58072))+P104(f334(f334(f250(a877),x58071),x58072)) % 169.19/169.65 [5818]E(f334(f80(a1),f334(f334(f40(a1),x58181),f334(f80(a1),x58182))),f294(x58181,x58182))+P104(f334(f334(f249(a1),f2(a1)),x58182)) % 169.19/169.65 [5820]~E(x58202,f2(a877))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f259(a877),x58201),x58202))) % 169.19/169.65 [5871]~P92(x58711)+E(f334(f334(f81(x58711),f334(f80(x58711),f79(x58711))),f334(f106(x58711),x58712)),f334(f106(x58711),f334(f334(f81(a1),x58712),a100))) % 169.19/169.65 [5872]E(f334(f334(f259(a877),f334(f106(a877),x58721)),x58722),f334(f334(f259(a877),f2(a877)),x58722))+~P104(f334(a201,f334(f106(a1),x58721))) % 169.19/169.65 [5969]E(f334(f141(a877),f139(a877,f334(f304(a877,x59691),x59692))),x59691)+~P104(f334(f334(f250(a877),x59691),x59692)) % 169.19/169.65 [5988]E(f334(f334(f82(a877),f334(f106(a877),x59881)),f334(f106(a877),x59882)),f334(f106(a877),f334(f334(f82(a1),x59881),x59882)))+P104(f334(f334(f250(a1),x59881),a84)) % 169.19/169.65 [5994]~P124(x59941)+P104(f334(f334(f249(x59941),f2(x59941)),f334(f334(f82(x59941),x59942),x59942))) % 169.19/169.65 [6006]E(f334(f334(f3(a877),f334(a115,x60061)),x60062),f334(a115,f334(f334(f3(a877),x60061),x60062)))+~P104(f334(f334(f249(a877),x60062),x60061)) % 169.19/169.65 [6009]E(f46(a877,f334(f334(f3(a877),x60091),x60092),x60092),f46(a877,x60091,x60092))+~P104(f334(f334(f249(a877),x60092),x60091)) % 169.19/169.65 [6060]E(f334(f334(f259(a877),f334(a107,x60601)),x60602),f334(a107,f334(f334(f259(a1),x60601),x60602)))+~P104(f334(f334(f249(a1),f2(a1)),x60601)) % 169.19/169.65 [6076]P104(f334(f137(x60761),x60762))+P104(f334(f334(f250(a877),f573(x60762,x60761)),f334(f196(f878(x60761)),x60762))) % 169.19/169.65 [6077]P104(f334(f137(x60771),x60772))+P104(f334(f334(f250(a877),f580(x60772,x60771)),f334(f196(f878(x60771)),x60772))) % 169.19/169.65 [6092]~E(x60921,f116(x60922))+~P104(f334(f334(f250(a877),f2(a877)),f334(f196(f878(x60922)),x60921))) % 169.19/169.65 [6106]E(f144(a877,f139(a877,f334(f304(a877,x61061),x61062))),f334(f334(f3(a877),x61062),f79(a877)))+~P104(f334(f334(f250(a877),x61061),x61062)) % 169.19/169.65 [6109]E(f334(f334(f81(a1),x61091),f334(f103(a1),f334(a115,f862(x61092,x61091)))),x61092)+~P104(f334(f334(f250(a1),x61091),x61092)) % 169.19/169.65 [6116]E(x61161,f2(a877))+E(f334(f334(f82(a877),x61162),f334(f334(f259(a877),x61162),f334(f334(f3(a877),x61161),f79(a877)))),f334(f334(f259(a877),x61162),x61161)) % 169.19/169.65 [6142]E(f334(f334(f82(a877),f334(a107,x61421)),f334(a107,x61422)),f334(a107,f334(f334(f82(a1),x61421),x61422)))+~P104(f334(f334(f249(a1),f2(a1)),x61421)) % 169.19/169.65 [6143]E(f334(f334(f40(a877),f334(a107,x61431)),f334(a107,x61432)),f334(a107,f334(f334(f40(a1),x61431),x61432)))+~P104(f334(f334(f249(a1),f2(a1)),x61431)) % 169.19/169.65 [6157]~P115(x61571)+E(f334(f334(f81(x61571),x61572),x61572),f334(f334(f82(x61571),f334(f334(f81(x61571),f79(x61571)),f79(x61571))),x61572)) % 169.19/169.65 [6174]E(f334(f334(f3(a1),f334(f103(a1),x61741)),f334(f103(a1),x61742)),f334(f103(a1),f334(f334(f3(a877),x61741),x61742)))+~P104(f334(f334(f249(a877),x61742),x61741)) % 169.19/169.65 [6176]E(f334(f334(f269(a1,a1),f334(f106(a1),a100)),f334(f334(f81(a1),x61761),x61762)),f51(x61761,x61762))+~P104(f334(f334(f249(a1),x61762),f2(a1))) % 169.19/169.65 [6216]E(f181(x62161,x62162),f116(f878(x62161)))+P104(f334(f334(f336(f878(x62161)),f572(x62162,x62161)),f334(f173(f878(x62161)),x62162))) % 169.19/169.65 [6225]E(f119(a1,f334(f126(a1),x62251),f125(x62252,f334(f334(f81(a1),x62251),f79(a1)))),f125(x62252,x62251))+P104(f334(f334(f250(a1),x62252),x62251)) % 169.19/169.65 [6301]E(f334(f334(f151(a1),x63011),f180(f334(f334(f81(a1),x63011),f79(a1)),x63012)),f180(x63011,x63012))+~P104(f334(f334(f249(a1),x63011),x63012)) % 169.19/169.65 [6337]~P104(f334(f334(f250(a877),x63372),x63371))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f3(a877),x63371),x63372))) % 169.19/169.65 [6368]~P104(f334(f334(f250(a877),x63681),f334(a107,x63682)))+P104(f334(f334(f250(a1),f334(f103(a1),x63681)),x63682)) % 169.19/169.65 [6399]~P107(x63991)+E(f334(f334(f113(f886(x63991,a871)),f334(f255(x63991),x63992)),f334(f334(f312(x63991),x63992),f195(f886(x63991,a871)))),f334(f303(x63991),x63992)) % 169.19/169.65 [6400]~P104(f334(f334(f249(a1),f2(a1)),x64001))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f259(a1),x64001),x64002))) % 169.19/169.65 [6403]~P104(f334(f334(f250(a877),f2(a877)),x64031))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f259(a877),x64031),x64032))) % 169.19/169.65 [6431]~E(f334(x64311,f2(a877)),f2(a877))+E(f334(f334(f8(a877,a877),x64311),f305(a877,f334(a115,f2(a877)),x64312)),f334(f334(f8(a877,a877),x64311),f305(a877,f2(a877),x64312))) % 169.19/169.65 [6494]~P92(x64941)+E(f334(f334(f82(x64941),f334(f334(f81(x64941),f79(x64941)),f79(x64941))),f334(f106(x64941),x64942)),f334(f106(x64941),f334(f334(f81(a1),x64942),x64942))) % 169.19/169.65 [6510]E(f334(f334(f312(a1),x65101),f305(a1,f334(f334(f81(a1),x65101),f79(a1)),x65102)),f305(a1,x65101,x65102))+P104(f334(f334(f250(a1),x65102),x65101)) % 169.19/169.65 [6511]P104(f334(f334(f250(a877),x65111),f334(a107,x65112)))+~P104(f334(f334(f250(a1),f334(f103(a1),x65111)),x65112)) % 169.19/169.65 [6610]E(f334(a107,f334(f334(f40(a1),f334(f106(a1),x66101)),f334(f106(a1),x66102))),f334(f334(f40(a877),f334(f106(a877),x66101)),f334(f106(a877),x66102)))+P104(f334(a201,f334(f106(a1),x66101))) % 169.19/169.65 [6668]P104(f334(f334(f250(a877),x66681),x66682))+~P104(f334(f334(f250(a877),f2(a877)),f334(f334(f3(a877),x66682),x66681))) % 169.19/169.65 [6712]P104(f334(f334(f250(a877),f2(a877)),x67121))+~P104(f334(f334(f250(a877),f2(a877)),f334(f334(f82(a877),x67122),x67121))) % 169.19/169.65 [6713]P104(f334(f334(f250(a877),f2(a877)),x67131))+~P104(f334(f334(f250(a877),f2(a877)),f334(f334(f82(a877),x67131),x67132))) % 169.19/169.65 [6730]~P104(f334(f334(f249(a1),x67301),f2(a1)))+E(f334(f334(f82(a877),f334(a107,f334(f80(a1),x67301))),f334(a107,f334(f80(a1),x67302))),f334(a107,f334(f334(f82(a1),x67301),x67302))) % 169.19/169.65 [6788]~E(x67882,f195(f886(x67881,a871)))+P104(f334(f334(f249(f886(x67881,a871)),x67882),f334(f80(f886(x67881,a871)),x67882))) % 169.19/169.65 [6851]~P92(x68511)+E(f334(f334(f81(x68511),f334(f334(f81(x68511),f2(x68511)),f334(f106(x68511),x68512))),f334(f106(x68511),x68512)),f334(f106(x68511),f334(f334(f81(a1),x68512),x68512))) % 169.19/169.65 [6908]~P104(f334(f334(f250(a1),x69081),x69082))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x69081),f79(a1))),x69082)) % 169.19/169.65 [6973]E(x69731,f2(a877))+~P104(f334(f334(f249(a1),f334(f103(a1),x69732)),f334(f80(a1),f334(f103(a1),x69731)))) % 169.19/169.65 [6974]E(x69741,f2(a877))+~P104(f334(f334(f249(a1),f334(f103(a1),x69741)),f334(f80(a1),f334(f103(a1),x69742)))) % 169.19/169.65 [7077]E(f334(f334(f269(a1,a1),f334(f106(a1),a100)),f334(f334(f81(a1),x70771),x70772)),f51(x70771,x70772))+~P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),x70771),x70772))) % 169.19/169.65 [7119]~P22(x71191,x71192)+P39(x71191,f334(f268(f886(f885(x71191,x71191),a871),f886(f885(x71191,x71191),a871)),x71192)) % 169.19/169.65 [7137]~P104(f334(f334(f249(a877),f334(a115,f2(a877))),x71371))+P104(f334(f334(f249(a877),f334(a115,f2(a877))),f334(f334(f259(a877),x71371),x71372))) % 169.19/169.65 [7310]~P104(f334(f334(f249(a1),x73101),x73102))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x73101),x73101)),f334(f334(f81(a1),x73102),x73102))) % 169.19/169.65 [7315]~P104(f334(f334(f250(a1),x73151),x73152))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x73151),x73151)),f334(f334(f81(a1),x73152),x73152))) % 169.19/169.65 [7316]~P104(f334(f334(f92(a1),x73161),x73162))+P104(f334(f334(f92(a1),f334(f334(f81(a1),x73161),x73161)),f334(f334(f81(a1),x73162),x73162))) % 169.19/169.65 [7371]~P104(f334(f334(f250(a877),f2(a877)),x73711))+P104(f334(f334(f250(a877),f334(f334(f3(a877),x73711),f334(a115,x73712))),x73711)) % 169.19/169.65 [7406]P104(f334(f334(f249(a877),f334(a115,f2(a877))),x74061))+~P104(f334(f334(f249(a877),f334(a115,f2(a877))),f334(f334(f82(a877),x74062),x74061))) % 169.19/169.65 [7407]P104(f334(f334(f249(a877),f334(a115,f2(a877))),x74071))+~P104(f334(f334(f249(a877),f334(a115,f2(a877))),f334(f334(f82(a877),x74071),x74072))) % 169.19/169.65 [7411]P104(f334(f334(f249(a877),f334(f334(f165(a877),x74111),x74112)),f334(f166(a877),x74111)))+~P104(f334(f334(f250(a877),x74112),f334(f196(f878(a877)),x74111))) % 169.19/169.65 [7452]P104(f334(f334(f250(a1),x74521),x74522))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),x74521),f79(a1))),x74522)) % 169.19/169.65 [7496]P104(f334(f63(x74961),f257(f886(x74961,a871))))+~P104(f334(f63(f886(x74962,x74961)),f257(f886(f886(x74962,x74961),a871)))) % 169.19/169.65 [7497]P104(f334(f63(x74971),f257(f886(x74971,a871))))+~P104(f334(f63(f884(x74972,x74971)),f257(f886(f884(x74972,x74971),a871)))) % 169.19/169.65 [7498]P104(f334(f63(x74981),f257(f886(x74981,a871))))+~P104(f334(f63(f884(x74981,x74982)),f257(f886(f884(x74981,x74982),a871)))) % 169.19/169.65 [7540]E(x75401,f195(f886(x75402,a871)))+~P104(f334(f334(f249(f886(x75402,a871)),x75401),f334(f80(f886(x75402,a871)),x75401))) % 169.19/169.65 [7677]E(f334(f142(f878(x76771),f878(x76771),f134(x76771),f116(x76771)),x76772),f116(x76771))+P104(f334(f334(f336(f878(x76771)),f645(x76772,x76771)),f334(f173(f878(x76771)),x76772))) % 169.19/169.65 [7678]E(f334(f142(f878(x76781),f878(x76781),f134(x76781),f116(x76781)),x76782),f116(x76781))+P104(f334(f334(f336(f878(x76781)),f646(x76782,x76781)),f334(f173(f878(x76781)),x76782))) % 169.19/169.65 [7912]P104(f334(f334(f249(a1),x79121),x79122))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),x79121),x79121)),f334(f334(f81(a1),x79122),x79122))) % 169.19/169.65 [7917]P104(f334(f334(f250(a1),x79171),x79172))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),x79171),x79171)),f334(f334(f81(a1),x79172),x79172))) % 169.19/169.65 [7918]P104(f334(f334(f92(a1),x79181),x79182))+~P104(f334(f334(f92(a1),f334(f334(f81(a1),x79181),x79181)),f334(f334(f81(a1),x79182),x79182))) % 169.19/169.65 [8012]~P115(x80121)+E(f334(f334(f82(x80121),f334(f334(f81(x80121),f79(x80121)),f79(x80121))),f334(f334(f8(a877,x80121),f103(x80121)),f305(a877,f79(a877),x80122))),f334(f334(f82(x80121),f334(f103(x80121),x80122)),f334(f334(f81(x80121),f334(f103(x80121),x80122)),f79(x80121)))) % 169.19/169.65 [8061]P104(f334(f334(f336(a877),x80611),x80612))+~P104(f334(f334(f336(a1),f334(f103(a1),x80611)),f334(f313(a877,a1,f103(a1)),x80612))) % 169.19/169.65 [8219]~P104(f334(f63(x82191),x82192))+E(f334(f313(a877,x82191,f674(x82192,x82191)),f334(f254(a877),f334(f334(f9(a877,a877,a871),f250(a877)),f666(x82192,x82191)))),x82192) % 169.19/169.65 [8496]P50(x84961,x84962)+P104(f334(f334(f336(f885(x84961,x84961)),f334(f334(f269(x84961,x84961),f525(x84962,x84961)),f525(x84962,x84961))),x84962)) % 169.19/169.65 [8633]~P92(x86331)+E(f334(f334(f3(x86331),f79(x86331)),f334(f106(x86331),x86332)),f334(f106(x86331),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f80(a1),x86332)))) % 169.19/169.65 [8746]~P104(f334(f334(f250(f886(a877,a871)),x87461),x87462))+P104(f334(f334(f250(f886(a1,a871)),f334(f313(a877,a1,f103(a1)),x87461)),f334(f313(a877,a1,f103(a1)),x87462))) % 169.19/169.65 [8774]~P104(f334(f334(f250(a1),x87741),x87742))+P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x87741),x87741)),a100)),f334(f334(f81(a1),x87742),x87742))) % 169.19/169.65 [8776]~P104(f334(f334(f250(a1),x87761),x87762))+P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x87761),x87761)),a100)),f334(f334(f81(a1),x87762),x87762))) % 169.19/169.65 [8846]~P104(f334(f334(f336(a877),x88461),f334(f173(a877),x88462)))+P104(f334(f334(f249(a877),x88461),f334(f142(a877,a877,f81(a877),f2(a877)),x88462))) % 169.19/169.65 [8898]P20(a872,x88981,f334(f334(f312(f876(a872)),f94(f334(a26,x88982))),f195(f886(f876(a872),a871))))+~P20(a872,f334(f334(f312(f876(a872)),f94(f334(a26,x88982))),x88981),f334(f334(f312(f876(a872)),f94(f334(f245(a873),f334(a28,x88982)))),f195(f886(f876(a872),a871)))) % 169.19/169.65 [8939]P46(x89391,x89392)+~P104(f334(f334(f336(f885(x89391,x89391)),f334(f334(f269(x89391,x89391),f494(x89392,x89391)),f494(x89392,x89391))),x89392)) % 169.19/169.65 [9074]~P104(f334(f334(f249(f886(a1,a871)),f334(f313(a877,a1,f103(a1)),x90741)),f334(f313(a877,a1,f103(a1)),x90742)))+P104(f334(f334(f249(f886(a877,a871)),x90741),x90742)) % 169.19/169.65 [9075]~P104(f334(f334(f250(f886(a1,a871)),f334(f313(a877,a1,f103(a1)),x90751)),f334(f313(a877,a1,f103(a1)),x90752)))+P104(f334(f334(f250(f886(a877,a871)),x90751),x90752)) % 169.19/169.65 [9155]P104(f334(f334(f250(a1),x91551),x91552))+~P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x91551),x91551)),a100)),f334(f334(f81(a1),x91552),x91552))) % 169.19/169.65 [9157]P104(f334(f334(f250(a1),x91571),x91572))+~P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x91571),x91571)),a100)),f334(f334(f81(a1),x91572),x91572))) % 169.19/169.65 [10018]~P102(x100181)+E(f119(f878(x100181),f334(f126(f878(x100181)),f116(x100181)),f334(f334(f334(f99(f879(f878(x100181))),f334(f334(f250(a1),f2(a1)),x100182)),f334(f121(f885(x100181,f878(x100181)),f878(x100181),f131(x100181,f878(x100181),f132(x100181,f334(f334(f3(a1),x100182),f79(a1))),f132(f878(x100181),f334(f334(f3(a1),x100182),f79(a1))))),f334(f273(x100181,f878(x100181),f879(f878(x100181))),f334(f334(f10(f886(f878(x100181),f878(x100181)),f886(f878(x100181),f879(f878(x100181))),x100181),f334(f10(f878(x100181),f879(f878(x100181)),f878(x100181)),f126(f878(x100181)))),f151(x100181))))),f118(f878(x100181)))),f132(f878(x100181),x100182)) % 169.19/169.65 [10039]~P104(f334(f63(x100391),x100392))+E(f334(f196(f878(x100391)),f91(f878(x100391),f334(f334(f20(f878(x100391),a871,a871),f334(f334(f10(a871,f886(a871,a871),f878(x100391)),a332),f334(f334(f9(f878(x100391),f886(x100391,a871),a871),f334(f334(f10(f886(x100391,a871),f886(f886(x100391,a871),a871),f878(x100391)),a331),f173(x100391))),x100392))),f137(x100391)))),f223(x100391,x100392)) % 169.19/169.65 [6105]E(f334(f334(f81(a877),f334(f334(f3(a877),x61051),x61052)),x61052),x61051)+~P104(f334(f334(f249(a877),x61052),x61051)) % 169.19/169.65 [6170]E(f334(f334(f40(a877),f334(f334(f82(a877),x61701),x61702)),x61702),x61701)+~P104(f334(f334(f250(a877),f2(a877)),x61702)) % 169.19/169.65 [6171]E(f334(f334(f40(a877),f334(f334(f82(a877),x61711),x61712)),x61711),x61712)+~P104(f334(f334(f250(a877),f2(a877)),x61711)) % 169.19/169.65 [6175]~P72(x61751)+E(f334(f334(f8(a877,x61751),f334(f165(x61751),x61752)),f334(f304(a877,f2(a877)),f334(f196(f878(x61751)),x61752))),f334(f166(x61751),x61752)) % 169.19/169.65 [6293]E(f46(a877,f334(a115,f334(f334(f82(a877),x62931),x62932)),x62931),f79(a877))+~P104(f334(f334(f250(a877),f79(a877)),x62931)) % 169.19/169.65 [6299]E(f334(a115,f334(f334(f81(a877),f334(f106(a877),x62991)),x62992)),f334(f334(f81(a877),f79(a877)),x62992))+~P104(f334(a201,f334(f106(a1),x62991))) % 169.19/169.65 [6326]E(f334(a107,f334(f334(f259(a1),f334(f106(a1),x63261)),x63262)),f334(f334(f259(a877),f334(f106(a877),x63261)),x63262))+P104(f334(a201,f334(f106(a1),x63261))) % 169.19/169.65 [6564]E(f334(f334(f3(a877),x65641),f334(f106(a877),f334(f334(f81(a1),x65642),a100))),f334(f334(f3(a877),f334(a115,x65641)),f334(f106(a877),x65642)))+~P104(f334(f334(f250(a1),a84),x65642)) % 169.19/169.65 [6642]E(x66421,f2(a877))+E(f334(a115,f334(f334(f81(a877),f334(f334(f3(a877),x66421),f79(a877))),x66422)),f334(f334(f81(a877),x66421),x66422)) % 169.19/169.65 [6682]E(x66821,f2(a1))+P104(f334(f334(f250(a1),f2(a1)),f334(f334(f259(a1),f334(f76(a1),x66821)),x66822))) % 169.19/169.65 [6697]~E(x66972,f2(a877))+P104(f334(f334(f250(a1),f2(a1)),f334(f334(f259(a1),f334(f76(a1),x66971)),x66972))) % 169.19/169.65 [6734]E(x67341,f2(a877))+E(f334(f334(f81(a877),x67342),f334(f334(f82(a877),f334(f334(f3(a877),x67341),f79(a877))),x67342)),f334(f334(f82(a877),x67341),x67342)) % 169.19/169.65 [6782]~P104(f334(f334(f249(a1),x67821),x67822))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x67821),a100)),x67822)) % 169.19/169.65 [6911]E(f334(f334(f151(a877),x69111),f139(a877,f334(f304(a877,f334(a115,x69111)),x69112))),f139(a877,f334(f304(a877,x69111),x69112)))+~P104(f334(f334(f250(a877),x69111),x69112)) % 169.19/169.65 [7110]E(x71101,x71102)+~E(f334(f334(f3(a1),f334(f334(f81(a1),x71101),x71101)),a100),f334(f334(f3(a1),f334(f334(f81(a1),x71102),x71102)),a100)) % 169.19/169.65 [7113]E(x71131,f116(x71132))+E(f278(x71132,f334(f334(f154(x71132,f885(a102,x71132)),f334(f269(a102,x71132),f79(a102))),x71131)),f285(x71132,x71131)) % 169.19/169.65 [7340]P104(f334(f334(f249(a1),x73401),x73402))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),x73401),a100)),x73402)) % 169.19/169.65 [7820]~P104(f334(f334(f250(a877),x78201),x78202))+P104(f334(f334(f336(f885(a877,a877)),f334(f334(f269(a877,a877),x78201),x78202)),a253)) % 169.19/169.65 [8038]~P104(f334(f334(f250(a102),f2(a102)),x80381))+P104(f334(f334(f250(a102),f334(f268(a102,f885(a102,a102)),f334(f279(x80381),x80382))),x80381)) % 169.19/169.65 [8345]~P83(x83451)+P104(f334(f334(f249(x83451),f334(f76(x83451),f334(f166(x83451),x83452))),f334(f166(x83451),f334(f334(f154(x83451,x83451),f76(x83451)),x83452)))) % 169.19/169.65 [8369]P104(f334(f334(f250(a877),x83691),x83692))+~P104(f334(f334(f336(f885(a877,a877)),f334(f334(f269(a877,a877),x83691),x83692)),a253)) % 169.19/169.65 [8516]E(f334(f334(f269(x85161,x85161),f776(x85162,x85161)),f776(x85162,x85161)),x85162)+~P104(f334(f334(f336(f885(x85161,x85161)),x85162),f310(x85161,f195(f886(f885(x85161,x85161),a871))))) % 169.19/169.65 [8557]E(f334(f304(a877,x85571),f334(f334(f81(a877),x85571),f334(f39(a877),x85572))),x85572)+~P104(f334(f334(f249(f886(a877,a871)),x85572),f334(f304(a877,x85571),f334(f334(f81(a877),x85571),f334(f39(a877),x85572))))) % 169.19/169.65 [8885]E(f334(f334(f40(a1),f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),x88851),x88851)),a100))),f334(f106(a1),f334(f334(f81(a1),x88852),x88852))),f334(f334(f40(a1),f334(f106(a1),x88851)),f334(f106(a1),x88852)))+~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x88852))) % 169.19/169.65 [9004]E(f178(f878(x90041),f334(f334(f10(a871,a871,f878(x90041)),a329),f334(f334(f9(f878(x90041),f878(x90041),a871),a331),f116(x90041))),x90042),f181(x90041,f181(x90041,x90042)))+~P30(a877,f334(f169(a877),f334(f334(f154(f878(x90041),a877),f196(f878(x90041))),x90042))) % 169.19/169.65 [9007]E(f334(f334(f40(a1),f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90071),x90071)),a100))),f334(f106(a1),f334(f334(f81(a1),x90072),x90072))),f334(f334(f40(a1),f334(f334(f81(a1),f334(f106(a1),x90071)),f79(a1))),f334(f106(a1),x90072)))+P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x90072))) % 169.19/169.65 [9818]P104(f334(a201,x98182))+E(f334(f334(f87(a1,a877),f334(f334(f3(a1),x98181),x98182)),f334(f334(f20(a1,a877,a877),f334(f334(f9(a1,a877,f886(a877,a877)),f334(f334(f10(a871,f886(a877,f886(a877,a877)),a1),f99(a877)),a201)),f2(a877))),a107)),f334(f334(f3(a877),f334(a107,x98181)),f334(a107,x98182))) % 169.19/169.65 [9826]E(f334(f334(f87(a1,a877),f334(f106(a1),f334(f334(f81(a1),x98261),f334(f80(a1),x98262)))),f334(f334(f20(a1,a877,a877),f334(f334(f9(a1,a877,f886(a877,a877)),f334(f334(f10(a871,f886(a877,f886(a877,a877)),a1),f99(a877)),a201)),f2(a877))),a107)),f334(f334(f3(a877),f334(f106(a877),x98261)),f334(f106(a877),x98262)))+P104(f334(f334(f250(a1),x98262),a84)) % 169.19/169.65 [9827]~P22(x98271,x98272)+P104(f334(f334(f249(f886(f885(x98271,x98271),a871)),f334(f334(f291(x98271,x98271,x98271),f334(f268(f886(f885(x98271,x98271),a871),f886(f885(x98271,x98271),a871)),x98272)),f334(f272(f886(f885(x98271,x98271),a871),f886(f885(x98271,x98271),a871)),x98272))),f334(f268(f886(f885(x98271,x98271),a871),f886(f885(x98271,x98271),a871)),x98272))) % 169.19/169.65 [9890]~E(f334(f39(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,f886(a877,a871),a871),f336(a877)),x98901))),f334(f334(f9(a877,a877,a871),f250(a877)),f334(a115,x98902))))),f2(a877))+~P104(f334(f334(f336(a877),f2(a877)),x98901)) % 169.19/169.65 [9946]E(f46(a1,f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),x99461),x99461)),a100)),f334(f106(a1),f334(f334(f81(a1),x99462),x99462))),f334(f334(f81(a1),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f46(a1,f334(f106(a1),x99461),f334(f106(a1),x99462)))),f79(a1)))+~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x99462))) % 169.19/169.65 [9955]E(f46(a1,f334(f106(a1),f334(f334(f3(a1),f334(f334(f81(a1),x99551),x99551)),a100)),f334(f106(a1),f334(f334(f81(a1),x99552),x99552))),f334(f334(f3(a1),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f46(a1,f334(f334(f81(a1),f334(f106(a1),x99551)),f79(a1)),f334(f106(a1),x99552)))),f79(a1)))+P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x99552))) % 169.19/169.65 [10007]~P28(x100071)+E(f41(x100071,f334(f254(x100071),f334(f334(f10(f886(x100071,a871),a871,x100071),f89(x100071)),f334(f334(f10(f886(x100071,a871),f886(x100071,a871),x100071),f334(f20(x100071,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100071),a337),f334(f334(f9(x100071,f886(x100071,a871),a871),f336(x100071)),x100072)))),f249(x100071))))),f42(x100071,x100072)) % 169.19/169.65 [10032]~P39(x100321,x100322)+P57(x100321,f334(f334(f9(x100321,f886(f885(x100321,x100321),a871),f886(x100321,a871)),f334(f334(f10(f886(x100321,f886(f886(f885(x100321,x100321),a871),a871)),f886(f886(f885(x100321,x100321),a871),f886(x100321,a871)),x100321),f9(x100321,f886(f885(x100321,x100321),a871),a871)),f334(f334(f10(f886(x100321,f885(x100321,x100321)),f886(x100321,f886(f886(f885(x100321,x100321),a871),a871)),x100321),f334(f10(f885(x100321,x100321),f886(f886(f885(x100321,x100321),a871),a871),x100321),f336(f885(x100321,x100321)))),f269(x100321,x100321)))),x100322)) % 169.19/169.65 [10033]~P6(x100331,f257(f886(x100331,a871)),x100332)+P5(x100331,f334(f334(f9(x100331,f886(f885(x100331,x100331),a871),f886(x100331,a871)),f334(f334(f10(f886(x100331,f886(f886(f885(x100331,x100331),a871),a871)),f886(f886(f885(x100331,x100331),a871),f886(x100331,a871)),x100331),f9(x100331,f886(f885(x100331,x100331),a871),a871)),f334(f334(f10(f886(x100331,f885(x100331,x100331)),f886(x100331,f886(f886(f885(x100331,x100331),a871),a871)),x100331),f334(f10(f885(x100331,x100331),f886(f886(f885(x100331,x100331),a871),a871),x100331),f336(f885(x100331,x100331)))),f269(x100331,x100331)))),x100332)) % 169.19/169.65 [10070]P39(x100701,x100702)+~P57(x100701,f334(f334(f9(x100701,f886(f885(x100701,x100701),a871),f886(x100701,a871)),f334(f334(f10(f886(x100701,f886(f886(f885(x100701,x100701),a871),a871)),f886(f886(f885(x100701,x100701),a871),f886(x100701,a871)),x100701),f9(x100701,f886(f885(x100701,x100701),a871),a871)),f334(f334(f10(f886(x100701,f885(x100701,x100701)),f886(x100701,f886(f886(f885(x100701,x100701),a871),a871)),x100701),f334(f10(f885(x100701,x100701),f886(f886(f885(x100701,x100701),a871),a871),x100701),f336(f885(x100701,x100701)))),f269(x100701,x100701)))),x100702)) % 169.19/169.65 [10071]P6(x100711,f257(f886(x100711,a871)),x100712)+~P5(x100711,f334(f334(f9(x100711,f886(f885(x100711,x100711),a871),f886(x100711,a871)),f334(f334(f10(f886(x100711,f886(f886(f885(x100711,x100711),a871),a871)),f886(f886(f885(x100711,x100711),a871),f886(x100711,a871)),x100711),f9(x100711,f886(f885(x100711,x100711),a871),a871)),f334(f334(f10(f886(x100711,f885(x100711,x100711)),f886(x100711,f886(f886(f885(x100711,x100711),a871),a871)),x100711),f334(f10(f885(x100711,x100711),f886(f886(f885(x100711,x100711),a871),a871),x100711),f336(f885(x100711,x100711)))),f269(x100711,x100711)))),x100712)) % 169.19/169.65 [7291]E(f334(f334(f81(a877),f334(f106(a877),f334(f334(f3(a1),x72911),a100))),x72912),f334(a115,f334(f334(f81(a877),f334(f106(a877),x72911)),x72912)))+P104(f334(a201,f334(f106(a1),x72911))) % 169.19/169.65 [7736]~P92(x77361)+E(f334(f334(f81(x77361),f334(f334(f81(x77361),f79(x77361)),f334(f106(x77361),x77362))),f334(f106(x77361),x77362)),f334(f106(x77361),f334(f334(f3(a1),f334(f334(f81(a1),x77362),x77362)),a100))) % 169.19/169.65 [8371]~P104(f334(f334(f249(a1),x83711),x83712))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x83711),x83711)),f334(f334(f3(a1),f334(f334(f81(a1),x83712),x83712)),a100))) % 169.19/169.65 [8373]~P104(f334(f334(f249(a1),x83731),x83732))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x83731),x83731)),f334(f334(f3(a1),f334(f334(f81(a1),x83732),x83732)),a100))) % 169.19/169.65 [8778]P104(f334(f334(f249(a1),x87781),x87782))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),x87781),x87781)),f334(f334(f3(a1),f334(f334(f81(a1),x87782),x87782)),a100))) % 169.19/169.65 [8780]P104(f334(f334(f249(a1),x87801),x87802))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),x87801),x87801)),f334(f334(f3(a1),f334(f334(f81(a1),x87802),x87802)),a100))) % 169.19/169.65 [9062]~P104(f334(f334(f249(a1),x90621),x90622))+P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90621),x90621)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x90622),x90622)),a100))) % 169.19/169.65 [9064]~P104(f334(f334(f250(a1),x90641),x90642))+P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90641),x90641)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x90642),x90642)),a100))) % 169.19/169.65 [9065]~P104(f334(f334(f92(a1),x90651),x90652))+P104(f334(f334(f92(a1),f334(f334(f3(a1),f334(f334(f81(a1),x90651),x90651)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x90652),x90652)),a100))) % 169.19/169.65 [9316]P104(f334(f334(f249(a1),x93161),x93162))+~P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),x93161),x93161)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x93162),x93162)),a100))) % 169.19/169.65 [9318]P104(f334(f334(f250(a1),x93181),x93182))+~P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),x93181),x93181)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x93182),x93182)),a100))) % 169.19/169.65 [9319]P104(f334(f334(f92(a1),x93191),x93192))+~P104(f334(f334(f92(a1),f334(f334(f3(a1),f334(f334(f81(a1),x93191),x93191)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),x93192),x93192)),a100))) % 169.19/169.65 [9351]~P104(f334(f63(x93511),x93512))+P104(f334(f63(f886(x93511,a871)),f334(f254(f886(x93511,a871)),f334(f334(f9(f886(x93511,a871),f886(x93511,a871),a871),f249(f886(x93511,a871))),x93512)))) % 169.19/169.65 [9396]~E(f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),x93961),f195(f886(f885(a877,a877),a871)))),f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),x93962),f195(f886(f885(a877,a877),a871)))))+P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),x93961),x93962)),a111)) % 169.19/169.65 [9478]E(f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),x94781),f195(f886(f885(a877,a877),a871)))),f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),x94782),f195(f886(f885(a877,a877),a871)))))+~P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),x94781),x94782)),a111)) % 169.19/169.65 [9511]P104(f334(f334(f249(a1),f2(a1)),f791(x95111,x95112)))+E(f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x95111)),f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x95112))) % 169.19/169.65 [10017]~P28(x100171)+E(f42(x100171,f334(f254(x100171),f334(f334(f10(f886(x100171,a871),a871,x100171),f89(x100171)),f334(f334(f10(f886(x100171,a871),f886(x100171,a871),x100171),f334(f20(x100171,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100171),a337),f334(f334(f9(x100171,f886(x100171,a871),a871),f336(x100171)),x100172)))),f334(f9(x100171,x100171,a871),f249(x100171)))))),f41(x100171,x100172)) % 169.19/169.65 [10038]P104(f334(f334(f336(a877),f2(a877)),x100381))+E(f334(f39(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,f886(a877,a871),a871),f334(f334(f10(a877,f886(f886(a877,a871),a871),a877),f336(a877)),a115)),x100381))),f334(f334(f9(a877,a877,a871),f250(a877)),x100382)))),f334(f39(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,f886(a877,a871),a871),f336(a877)),x100381))),f334(f334(f9(a877,a877,a871),f250(a877)),f334(a115,x100382)))))) % 169.19/169.65 [7605]~P92(x76051)+E(f334(f334(f82(x76051),x76052),f334(f106(x76051),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),x76052) % 169.19/169.65 [7865]~P92(x78651)+E(f334(f334(f81(x78651),f334(f106(x78651),x78652)),f79(x78651)),f334(f106(x78651),f334(f334(f81(a1),x78652),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))) % 169.19/169.65 [8010]P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x80102)))+E(f334(f334(f259(a1),x80101),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),x80102),x80102)),a100))),f79(a1)) % 169.19/169.65 [9375]~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x93752)))+E(f334(f334(f259(a1),x93751),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),x93752),x93752)),a100))),f334(f334(f87(a1,a1),f334(f334(f259(a1),x93751),f334(f106(a877),x93752))),f334(f334(f20(a1,a1,a1),f334(f334(f10(a1,f886(a1,a1),a1),f82(a1)),f334(f82(a1),x93751))),f7(a1)))) % 169.19/169.65 [9732]~P104(f334(f334(f249(a877),f801(x97322,x97321)),f334(x97321,f801(x97322,x97321))))+P104(f334(f63(a877),f334(f254(a877),f334(f334(f9(a877,a877,a871),f334(f334(f10(a877,f886(a877,a871),a877),f249(a877)),x97321)),x97322)))) % 169.19/169.65 [9880]~P104(f334(f334(f249(a877),f334(f106(a877),x98801)),f334(a115,x98802)))+P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x98801),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),f249(a877)),a107)),x98802)))) % 169.19/169.65 [9881]~P104(f334(f334(f250(a877),f334(f106(a877),x98811)),f334(a115,x98812)))+P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x98811),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),f250(a877)),a107)),x98812)))) % 169.19/169.65 [9930]P104(f334(f334(f249(a877),f334(f106(a877),x99301)),f334(a115,x99302)))+~P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x99301),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),f249(a877)),a107)),x99302)))) % 169.19/169.65 [9931]P104(f334(f334(f250(a877),f334(f106(a877),x99311)),f334(a115,x99312)))+~P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x99311),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),f250(a877)),a107)),x99312)))) % 169.19/169.65 [9961]~P104(f334(f334(f249(a877),f334(a115,x99612)),f334(f106(a877),x99611)))+P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x99611),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f10(a877,a871,a1),f334(f249(a877),x99612)),a107))))) % 169.19/169.65 [9962]~P104(f334(f334(f250(a877),f334(a115,x99622)),f334(f106(a877),x99621)))+P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x99621),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f10(a877,a871,a1),f334(f250(a877),x99622)),a107))))) % 169.19/169.65 [10005]P104(f334(f334(f249(a877),f334(a115,x100051)),f334(f106(a877),x100052)))+~P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x100052),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f10(a877,a871,a1),f334(f249(a877),x100051)),a107))))) % 169.19/169.65 [10006]P104(f334(f334(f250(a877),f334(a115,x100061)),f334(f106(a877),x100062)))+~P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x100062),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f10(a877,a871,a1),f334(f250(a877),x100061)),a107))))) % 169.19/169.65 [10077]~P104(f334(f334(f336(a877),f2(a877)),x100771))+E(f334(a115,f334(f39(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,f886(a877,a871),a871),f334(f334(f10(a877,f886(f886(a877,a871),a871),a877),f336(a877)),a115)),x100771))),f334(f334(f9(a877,a877,a871),f250(a877)),x100772))))),f334(f39(a877),f334(f254(a877),f334(f334(f20(a877,a871,a871),f334(f334(f10(a871,f886(a871,a871),a877),a332),f334(f334(f9(a877,f886(a877,a871),a871),f336(a877)),x100771))),f334(f334(f9(a877,a877,a871),f250(a877)),f334(a115,x100772)))))) % 169.19/169.65 [8541]~P92(x85411)+E(f334(f334(f82(x85411),f334(f106(x85411),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),x85412),x85412) % 169.19/169.65 [8601]~P92(x86011)+E(f334(f334(f81(x86011),f79(x86011)),f334(f106(x86011),x86012)),f334(f106(x86011),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),x86012))) % 169.19/169.65 [8658]~P92(x86581)+E(f334(f334(f3(x86581),f334(f106(x86581),x86582)),f79(x86581)),f334(f106(x86581),f334(f334(f81(a1),x86582),f334(f80(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [8796]~P104(f334(f334(f250(a877),f334(f106(a877),a84)),x87962))+E(f334(f334(f3(a877),x87961),f334(f334(f3(a877),x87962),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f3(a877),f334(a115,x87961)),x87962)) % 169.19/169.65 [9412]~P115(x94121)+E(f334(f334(f82(x94121),x94122),x94122),f334(f334(f259(x94121),x94122),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [9413]~P77(x94131)+E(f334(f334(f259(x94131),x94132),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f82(x94131),x94132),x94132)) % 169.19/169.65 [9415]~P92(x94151)+E(f334(f334(f82(x94151),x94152),f334(f106(x94151),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f81(x94151),x94152),x94152)) % 169.19/169.65 [9650]~P137(x96501)+E(f334(f334(f259(x96501),f334(f80(x96501),x96502)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f259(x96501),x96502),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [9651]~P120(x96511)+E(f334(f334(f259(x96511),f334(f76(x96511),x96512)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f259(x96511),x96512),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [9647]~P92(x96471)+E(f334(f334(f82(x96471),f334(f106(x96471),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x96472),f334(f334(f81(x96471),x96472),x96472)) % 169.19/169.65 [9772]~P120(x97721)+E(f334(f76(x97721),f334(f334(f259(x97721),x97722),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x97721),x97722),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [9834]~P120(x98341)+P104(f334(f334(f249(x98341),f2(x98341)),f334(f334(f259(x98341),x98342),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.65 [9996]~E(f334(a115,x99962),f334(f106(a877),x99961))+P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x99961),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),a331),a107)),x99962))))) % 169.19/169.65 [9997]~E(f334(f106(a877),x99971),f334(a115,x99972))+P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x99971),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),a331),a107)),x99972))))) % 169.19/169.65 [10041]E(f334(a115,x100411),f334(f106(a877),x100412))+~P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x100412),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),a331),a107)),x100411))))) % 169.19/169.65 [10042]E(f334(f106(a877),x100421),f334(a115,x100422))+~P104(f334(f334(f87(a1,a871),f334(f106(a1),f334(f334(f81(a1),x100421),a100))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a337),f334(f334(f10(a871,a871,a1),a329),a201))),f334(f334(f9(a1,a877,a871),f334(f334(f10(a877,f886(a877,a871),a1),a331),a107)),x100422))))) % 169.19/169.65 [9832]~P92(x98321)+E(f334(f334(f259(x98321),f334(f106(x98321),a100)),f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x98322)),f79(x98321)) % 169.19/169.65 [9833]~P137(x98331)+E(f334(f334(f259(x98331),f334(f80(x98331),f79(x98331))),f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x98332)),f79(x98331)) % 169.19/169.65 [9836]~P77(x98361)+E(f334(f334(f259(x98361),x98362),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),a100))),f334(f334(f82(x98361),f334(f334(f82(x98361),x98362),x98362)),x98362)) % 169.19/169.65 [10021]~P104(f334(f334(f249(a1),f2(a1)),x100212))+E(f46(a1,f334(f334(f81(a1),f79(a1)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100211)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100212)),f334(f334(f81(a1),f79(a1)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f46(a1,x100211,x100212)))) % 169.19/169.65 [10044]~P104(f334(f334(f249(a1),f2(a1)),x100442))+E(f334(f334(f40(a1),f334(f334(f81(a1),f79(a1)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100441))),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100442)),f334(f334(f40(a1),x100441),x100442)) % 169.19/169.65 [10046]~P104(f334(f334(f249(a1),x100462),f2(a1)))+E(f334(f334(f40(a1),f334(f334(f81(a1),f79(a1)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100461))),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100462)),f334(f334(f40(a1),f334(f334(f81(a1),x100461),f79(a1))),x100462)) % 169.19/169.65 [10047]~P104(f334(f334(f249(a1),x100472),f2(a1)))+E(f46(a1,f334(f334(f81(a1),f79(a1)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100471)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100472)),f334(f334(f3(a1),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f46(a1,f334(f334(f81(a1),x100471),f79(a1)),x100472))),f79(a1))) % 169.19/169.65 [9921]~P92(x99211)+E(f334(f334(f259(x99211),f334(f106(x99211),a100)),f334(a115,f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99212))),f334(f106(x99211),a100)) % 169.19/169.65 [9923]~P137(x99231)+E(f334(f334(f259(x99231),f334(f80(x99231),f79(x99231))),f334(a115,f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99232))),f334(f80(x99231),f79(x99231))) % 169.19/169.65 [5148]~P20(x51481,x51482,x51483)+P23(x51481,x51482,x51483) % 169.19/169.65 [8076]~E(x80762,x80763)+P36(x80761,x80761,a331,x80762,x80763) % 169.19/169.65 [8614]E(x86141,x86142)+~P36(x86143,x86143,a331,x86141,x86142) % 169.19/169.65 [4791]E(f170(x47911,x47912,x47913),f116(x47911))+~E(x47912,f2(a877)) % 169.19/169.65 [4957]~E(f170(x49572,x49571,x49573),f116(x49572))+E(x49571,f2(a877)) % 169.19/169.65 [5153]~P39(x51531,x51533)+P39(x51531,f328(x51531,x51532,x51533)) % 169.19/169.65 [5329]P31(x53291,x53292,x53293)+~P31(x53291,f334(a115,x53292),x53293) % 169.19/169.65 [5416]~P6(x54161,x54162,x54163)+P6(f878(x54161),f161(x54161,x54162),f158(x54161,x54163)) % 169.19/169.65 [5417]~P49(x54171,x54172,x54173)+P49(f878(x54171),f161(x54171,x54172),f158(x54171,x54173)) % 169.19/169.65 [5529]P52(x55291,x55292,x55293)+~E(f733(x55293,x55292,x55291),f734(x55293,x55292,x55291)) % 169.19/169.65 [5530]P53(x55301,x55302,x55303)+~E(f756(x55303,x55302,x55301),f757(x55303,x55302,x55301)) % 169.19/169.65 [6469]P23(x64691,x64692,x64693)+~P31(x64691,f583(x64693,x64692,x64691),f604(x64693,x64692,x64691)) % 169.19/169.65 [4697]~E(x46971,f198(x46972))+~E(x46971,f334(f241(x46972),x46973)) % 169.19/169.65 [4747]~E(f334(f169(x47472),x47471),x47473)+E(x47471,f334(f169(x47472),x47473)) % 169.19/169.65 [4748]~E(x47482,f334(f169(x47481),x47483))+E(f334(f169(x47481),x47482),x47483) % 169.19/169.65 [4797]E(x47971,x47972)+~E(f334(f241(x47973),x47971),f334(f241(x47973),x47972)) % 169.19/169.65 [4798]E(x47981,x47982)+~E(f334(f169(x47983),x47981),f334(f169(x47983),x47982)) % 169.19/169.65 [5004]~P5(x50043,x50041)+P104(f334(f334(x50041,x50042),x50042)) % 169.19/169.65 [5005]~P51(x50053,x50051)+P104(f334(f334(x50051,x50052),x50052)) % 169.19/169.65 [5007]~P57(x50071,x50072)+P104(f334(f322(x50071,x50072),x50073)) % 169.19/169.65 [5070]~P39(x50701,x50702)+P39(f878(x50701),f334(f143(x50701,x50702),x50703)) % 169.19/169.65 [5075]~P104(f334(x50752,x50753))+~E(f334(f254(x50751),x50752),f195(f886(x50751,a871))) % 169.19/169.65 [5076]~P104(f334(x50762,x50763))+~E(f195(f886(x50761,a871)),f334(f254(x50761),x50762)) % 169.19/169.65 [5090]E(x50901,f2(a877))+E(f144(x50902,f170(x50902,x50901,x50903)),x50903) % 169.19/169.65 [5108]~P104(f334(x51081,x51083))+P104(f334(x51081,f91(x51082,x51081))) % 169.19/169.65 [5120]E(x51201,f2(a877))+E(f334(f141(x51202),f170(x51202,x51201,x51203)),x51203) % 169.19/169.65 [5233]~E(x52332,x52333)+P104(f334(f334(f336(x52331),x52332),f334(a331,x52333))) % 169.19/169.65 [5245]~E(x52452,f2(a877))+E(f334(f173(x52451),f170(x52451,x52452,x52453)),f195(f886(x52451,a871))) % 169.19/169.65 [5292]E(f334(f169(x52921),x52922),f334(f334(f151(x52921),x52923),f116(x52921)))+~E(x52922,f334(f334(f151(x52921),x52923),f116(x52921))) % 169.19/169.65 [5293]~E(x52933,f334(f334(f151(x52931),x52932),f116(x52931)))+E(f334(f334(f151(x52931),x52932),f116(x52931)),f334(f169(x52931),x52933)) % 169.19/169.65 [5322]~E(x53223,f334(f18(f881(x53222),x53221),f198(x53222)))+E(f185(x53221,x53222,x53223),f195(f886(x53221,a871))) % 169.19/169.65 [5344]~P35(x53441,x53442,x53443)+P35(x53441,x53442,f334(f169(x53441),x53443)) % 169.19/169.65 [5345]~P33(x53451,x53452,x53453)+P33(x53451,x53452,f334(f169(x53451),x53453)) % 169.19/169.65 [5348]E(f334(f39(x53481),f730(x53482,x53483,x53481)),x53482)+~E(f334(f39(x53481),x53483),f334(a115,x53482)) % 169.19/169.65 [5354]~P39(x53541,x53543)+P104(f334(f334(f336(x53541),x53542),f323(x53541,x53543))) % 169.19/169.65 [5358]~E(f334(f169(x53582),x53581),f334(f334(f151(x53582),x53583),f116(x53582)))+E(x53581,f334(f334(f151(x53582),x53583),f116(x53582))) % 169.19/169.65 [5359]~E(f334(f334(f151(x53592),x53593),f116(x53592)),f334(f169(x53592),x53591))+E(x53591,f334(f334(f151(x53592),x53593),f116(x53592))) % 169.19/169.65 [5374]E(x53741,f334(f18(f881(x53742),x53743),f198(x53742)))+~E(f185(x53743,x53742,x53741),f195(f886(x53743,a871))) % 169.19/169.65 [5380]E(f86(f885(a877,a877),f49(x53801,x53802)),x53803)+~P104(f334(f49(x53801,x53802),x53803)) % 169.19/169.65 [5388]~E(x53883,f334(f241(x53881),x53882))+P104(f334(f334(f336(x53881),x53882),f240(x53881,x53883))) % 169.19/169.65 [5420]P35(x54201,x54202,x54203)+~P35(x54201,x54202,f334(f169(x54201),x54203)) % 169.19/169.65 [5421]P33(x54211,x54212,x54213)+~P33(x54211,x54212,f334(f169(x54211),x54213)) % 169.19/169.65 [5483]~E(x54832,f116(x54831))+P104(f334(f334(f336(f878(x54831)),x54832),f161(x54831,x54833))) % 169.19/169.65 [5490]~P49(x54901,x54902,x54903)+P49(x54901,x54902,f334(f289(x54901,x54901),x54903)) % 169.19/169.65 [5491]~P53(x54911,x54912,x54913)+P53(x54911,x54912,f334(f289(x54911,x54911),x54913)) % 169.19/169.65 [5510]~P26(x55101)+E(f46(x55101,f46(x55101,x55102,x55103),x55103),f46(x55101,x55102,x55103)) % 169.19/169.65 [5607]E(x56071,x56072)+~P104(f334(f334(f336(x56073),x56071),f334(a331,x56072))) % 169.19/169.65 [5653]~P142(x56531)+E(f197(x56531,x56532,f2(a877),x56533),x56533) % 169.19/169.65 [5673]P49(x56731,x56732,x56733)+~P49(x56731,x56732,f334(f289(x56731,x56731),x56733)) % 169.19/169.65 [5674]P53(x56741,x56742,x56743)+~P53(x56741,x56742,f334(f289(x56741,x56741),x56743)) % 169.19/169.65 [5678]~P107(x56782)+E(f150(x56781,x56782,x56783,f116(x56781)),f116(x56781)) % 169.19/169.65 [5691]E(f171(x56911,x56912,f152(x56911,x56913)),f152(x56911,f171(x56911,x56912,x56913)))+~P104(f334(f137(x56911),x56913)) % 169.19/169.65 [5697]E(x56971,f334(f241(x56972),x56973))+~P104(f334(f334(f336(x56972),x56973),f240(x56972,x56971))) % 169.19/169.65 [5783]~P104(f334(a25,x57833))+P104(f334(a25,f30(x57831,x57832,x57833))) % 169.19/169.65 [5794]E(f334(f136(x57941,x57942),x57943),f116(x57941))+P104(f334(x57942,f581(x57943,x57942,x57941))) % 169.19/169.65 [5937]~P104(f334(f137(x59371),x59373))+P104(f334(f137(x59371),f171(x59371,x59372,x59373))) % 169.19/169.65 [5938]~P104(f334(f137(x59381),x59382))+P104(f334(f137(x59381),f177(x59381,x59382,x59383))) % 169.19/169.65 [5939]~P104(f334(f137(x59391),x59393))+P104(f334(f137(x59391),f178(x59391,x59392,x59393))) % 169.19/169.65 [5940]~P104(f334(f137(x59401),x59403))+P104(f334(f137(x59401),f140(x59401,x59402,x59403))) % 169.19/169.65 [5941]~P145(x59411,x59413,x59412)+P104(f334(x59411,f46(a1,x59412,x59413))) % 169.19/169.65 [5960]~P35(x59603,x59601,x59602)+P104(f334(x59601,f735(x59602,x59601,x59603))) % 169.19/169.65 [5961]~P37(x59613,x59611,x59612)+P104(f334(x59611,f803(x59612,x59611,x59613))) % 169.19/169.65 [5982]E(f334(f136(x59821,x59822),x59823),f178(x59821,x59822,x59823))+P104(f334(x59822,f658(x59823,x59822,x59821))) % 169.19/169.65 [6021]~P104(f334(f137(x60211),x60213))+P104(f334(f137(f878(x60211)),f56(x60211,x60212,x60213))) % 169.19/169.65 [6043]P104(f334(a25,f29(x60431,x60432,x60433)))+~P104(f334(a25,f334(a26,x60432))) % 169.19/169.65 [6055]~P108(x60551)+E(f334(f334(f104(f886(x60551,a871)),f334(f303(x60551),x60552)),f308(x60551,x60552,x60553)),f195(f886(x60551,a871))) % 169.19/169.65 [6056]~P108(x60561)+E(f334(f334(f104(f886(x60561,a871)),f334(f303(x60561),x60562)),f307(x60561,x60562,x60563)),f195(f886(x60561,a871))) % 169.19/169.65 [6057]~P108(x60571)+E(f334(f334(f104(f886(x60571,a871)),f334(f255(x60571),x60572)),f305(x60571,x60572,x60573)),f195(f886(x60571,a871))) % 169.19/169.65 [6204]P104(f334(a25,x62041))+~P104(f334(a25,f30(x62042,x62043,x62041))) % 169.19/169.65 [6206]P104(f334(a25,x62061))+~P104(f334(a25,f31(x62062,x62063,x62061))) % 169.19/169.65 [6208]P104(f334(a25,x62081))+~P104(f334(a25,f31(x62082,x62081,x62083))) % 169.19/169.65 [6289]E(f334(f136(x62891,x62892),x62893),x62893)+~P104(f334(x62892,f632(x62893,x62892,x62891))) % 169.19/169.65 [6291]E(f334(f334(f312(x62911),f821(x62912,x62913,x62911)),f730(x62912,x62913,x62911)),x62913)+~E(f334(f39(x62911),x62913),f334(a115,x62912)) % 169.19/169.65 [6306]P145(x63061,x63062,x63063)+~P104(f334(x63061,f46(a1,x63063,x63062))) % 169.19/169.65 [6353]P33(x63531,x63532,x63533)+~P104(f334(x63532,f795(x63533,x63532,x63531))) % 169.19/169.65 [6354]P33(x63541,x63542,x63543)+~P104(f334(x63542,f799(x63542,x63543,x63541))) % 169.19/169.65 [6355]P33(x63551,x63552,x63553)+~P104(f334(x63552,f800(x63553,x63552,x63551))) % 169.19/169.65 [6357]E(f178(x63571,x63572,x63573),x63573)+~P104(f334(x63572,f644(x63573,x63572,x63571))) % 169.19/169.65 [6395]~P104(f334(a25,f29(x63952,x63951,x63953)))+P104(f334(a25,f334(a26,x63951))) % 169.19/169.65 [6438]~P104(f334(x64382,f584(x64383,x64382,x64381)))+P104(f334(f262(x64381,x64382),x64383)) % 169.19/169.65 [6439]~P104(f334(x64392,f660(x64393,x64392,x64391)))+P104(f334(f160(x64391,x64392),x64393)) % 169.19/169.65 [6683]~P104(f334(f322(x66831,x66832),f484(x66833,x66832,x66831)))+P104(f334(f322(x66831,x66832),x66833)) % 169.19/169.65 [6684]~P104(f334(f322(x66841,x66842),f498(x66843,x66842,x66841)))+P104(f334(f322(x66841,x66842),x66843)) % 169.19/169.65 [7292]~P26(x72921)+E(f334(f334(f81(x72921),f334(f334(f82(x72921),x72922),f334(f334(f40(x72921),x72923),x72922))),f46(x72921,x72923,x72922)),x72923) % 169.19/169.65 [7759]E(f334(f334(f269(x77591,x77591),f545(x77592,x77593,x77591)),f545(x77592,x77593,x77591)),x77593)+~P104(f334(f334(f336(f885(x77591,x77591)),x77593),f266(x77591,x77592))) % 169.19/169.65 [7873]~P104(f334(f334(f336(x78731),f673(x78733,x78732,x78731)),f323(x78731,x78733)))+P104(f334(f334(f336(x78731),x78732),f323(x78731,x78733))) % 169.19/169.65 [7874]~P104(f334(f334(f336(x78741),f737(x78743,x78742,x78741)),f323(x78741,x78743)))+P104(f334(f334(f336(x78741),x78742),f323(x78741,x78743))) % 169.19/169.65 [7875]~P104(f334(f334(f336(x78751),f746(x78753,x78752,x78751)),f323(x78751,x78753)))+P104(f334(f334(f336(x78751),x78752),f323(x78751,x78753))) % 169.19/169.65 [8057]~P26(x80571)+E(f334(f334(f81(x80571),f334(f334(f82(x80571),f334(f334(f40(x80571),x80572),x80573)),x80573)),f46(x80571,x80572,x80573)),x80572) % 169.19/169.65 [8102]~E(f334(f39(x81021),x81022),f334(a115,x81023))+~P104(f334(f334(f336(x81021),f821(x81023,x81022,x81021)),f730(x81023,x81022,x81021))) % 169.19/169.65 [8708]P104(f334(f334(f249(f886(f885(x87081,x87081),a871)),f310(x87081,x87082)),f310(x87081,x87083)))+~P104(f334(f334(f249(f886(f885(x87081,x87081),a871)),x87082),f310(x87081,x87083))) % 169.19/169.65 [8974]E(x89741,f116(x89742))+~P104(f334(f334(f336(f885(f878(x89742),f878(x89742))),f334(f334(f269(f878(x89742),f878(x89742)),x89741),f116(x89742))),f158(x89742,x89743))) % 169.19/169.65 [8998]E(x89981,f116(x89982))+~P104(f334(f334(f336(f885(f878(x89982),f878(x89982))),f334(f334(f269(f878(x89982),f878(x89982)),f116(x89982)),x89981)),f158(x89982,x89983))) % 169.19/169.65 [9120]E(f334(f334(f151(x91201),f623(x91202,x91203,x91201)),f624(x91202,x91203,x91201)),x91203)+~P104(f334(f334(f336(f885(f878(x91201),f878(x91201))),f334(f334(f269(f878(x91201),f878(x91201)),f116(x91201)),x91203)),f147(x91201,x91202))) % 169.19/169.65 [9344]~P124(x93441)+~P104(f334(f334(f250(x93441),f334(f334(f81(x93441),f334(f334(f82(x93441),x93442),x93442)),f334(f334(f82(x93441),x93443),x93443))),f2(x93441))) % 169.19/169.65 [9391]P104(f334(f63(x93911),x93912))+~P104(f334(f334(f336(f885(f886(x93911,a871),f886(x93911,a871))),f334(f334(f269(f886(x93911,a871),f886(x93911,a871)),x93913),x93912)),f309(x93911))) % 169.19/169.65 [9673]~P47(x96731,x96732,x96733)+P104(f334(f334(f249(a1),f334(f334(f74(f885(a1,a1),a1,x96731,f268(a1,a1)),f221(x96731)),f238(x96731,x96732,f235(x96731,x96733)))),f2(a1))) % 169.19/169.65 [9674]~P48(x96741,x96742,x96743)+P104(f334(f334(f250(a1),f334(f334(f74(f885(a1,a1),a1,x96741,f268(a1,a1)),f221(x96741)),f238(x96741,x96742,f235(x96741,x96743)))),f2(a1))) % 169.19/169.65 [9802]P48(x98021,x98022,x98023)+~P104(f334(f334(f250(a1),f334(f334(f74(f885(a1,a1),a1,x98021,f268(a1,a1)),f221(x98021)),f238(x98021,x98022,f235(x98021,x98023)))),f2(a1))) % 169.19/169.65 [9803]P47(x98031,x98032,x98033)+~P104(f334(f334(f249(a1),f334(f334(f74(f885(a1,a1),a1,x98031,f268(a1,a1)),f221(x98031)),f238(x98031,x98032,f235(x98031,x98033)))),f2(a1))) % 169.19/169.65 [10122]~P120(x101221)+~P104(f334(f334(f250(x101221),f334(f334(f81(x101221),f334(f334(f259(x101221),x101222),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x101221),x101223),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f2(x101221))) % 169.19/169.65 [4778]~E(x47783,f116(x47781))+E(f334(f334(f134(x47781),x47782),x47783),x47782) % 169.19/169.65 [4779]~E(x47792,f116(x47791))+E(f334(f334(f134(x47791),x47792),x47793),x47793) % 169.19/169.65 [4786]~E(x47862,f2(a877))+E(f334(f334(f176(x47861),x47862),x47863),f116(x47861)) % 169.19/169.65 [4792]~E(x47923,f116(x47921))+E(f334(f334(f176(x47921),x47922),x47923),f116(x47921)) % 169.19/169.65 [4832]~E(x48321,x48323)+E(x48321,f334(f334(f134(x48322),f116(x48322)),x48323)) % 169.19/169.65 [4919]~P24(x49192)+E(f334(f195(f886(x49191,x49192)),x49193),f195(x49192)) % 169.19/169.65 [4920]~P113(x49202)+E(f334(f257(f886(x49201,x49202)),x49203),f257(x49202)) % 169.19/169.65 [4939]E(x49391,f116(x49392))+~E(f334(f334(f134(x49392),x49393),x49391),x49393) % 169.19/169.65 [4940]E(x49401,f116(x49402))+~E(f334(f334(f134(x49402),x49401),x49403),x49403) % 169.19/169.65 [4948]E(x49481,f116(x49482))+~E(f334(f334(f134(x49482),x49483),x49481),f116(x49482)) % 169.19/169.65 [4949]E(x49491,f116(x49492))+~E(f334(f334(f134(x49492),x49491),x49493),f116(x49492)) % 169.19/169.65 [4974]~E(x49742,f2(a877))+E(f334(f334(f82(a877),x49741),x49742),f334(f334(f82(a877),x49743),x49742)) % 169.19/169.65 [4976]~E(x49761,f2(a877))+E(f334(f334(f82(a877),x49761),x49762),f334(f334(f82(a877),x49761),x49763)) % 169.19/169.65 [5029]~P115(x50291)+E(f334(f334(f82(x50291),x50292),x50293),f334(f334(f82(x50291),x50293),x50292)) % 169.19/169.65 [5030]~P115(x50301)+E(f334(f334(f81(x50301),x50302),x50303),f334(f334(f81(x50301),x50303),x50302)) % 169.19/169.65 [5031]~P95(x50311)+E(f334(f334(f113(x50311),x50312),x50313),f334(f334(f113(x50311),x50313),x50312)) % 169.19/169.65 [5033]~P100(x50331)+E(f334(f334(f113(x50331),x50332),x50333),f334(f334(f113(x50331),x50333),x50332)) % 169.19/169.65 [5034]~P95(x50341)+E(f334(f334(f104(x50341),x50342),x50343),f334(f334(f104(x50341),x50343),x50342)) % 169.19/169.65 [5036]~P101(x50361)+E(f334(f334(f104(x50361),x50362),x50363),f334(f334(f104(x50361),x50363),x50362)) % 169.19/169.65 [5038]~P107(x50381)+E(f334(f334(f247(x50381),x50382),x50383),f334(f334(f247(x50381),x50383),x50382)) % 169.19/169.65 [5040]~P107(x50401)+E(f334(f334(f248(x50401),x50402),x50403),f334(f334(f248(x50401),x50403),x50402)) % 169.19/169.65 [5103]E(f46(a877,x51031,x51032),f2(a877))+~E(x51031,f334(f334(f82(a877),x51032),x51033)) % 169.19/169.65 [5104]E(f46(a1,x51041,x51042),f2(a1))+~E(x51041,f334(f334(f82(a1),x51042),x51043)) % 169.19/169.65 [5165]E(x51651,x51652)+~E(f334(f334(f81(a877),x51653),x51651),f334(f334(f81(a877),x51653),x51652)) % 169.19/169.65 [5166]E(x51661,x51662)+~E(f334(f334(f81(a877),x51661),x51663),f334(f334(f81(a877),x51662),x51663)) % 169.19/169.65 [5176]~P64(x51761)+E(f334(f334(f81(x51761),x51762),f334(f80(x51761),x51763)),f334(f334(f3(x51761),x51762),x51763)) % 169.19/169.65 [5177]~P67(x51771)+E(f334(f334(f81(x51771),x51772),f334(f80(x51771),x51773)),f334(f334(f3(x51771),x51772),x51773)) % 169.19/169.65 [5178]~P111(x51781)+E(f334(f334(f81(x51781),x51782),f334(f80(x51781),x51783)),f334(f334(f3(x51781),x51782),x51783)) % 169.19/169.65 [5179]~P79(x51791)+E(f334(f334(f104(x51791),x51792),f334(f80(x51791),x51793)),f334(f334(f3(x51791),x51792),x51793)) % 169.19/169.65 [5180]~P67(x51801)+E(f334(f334(f3(x51801),x51802),f334(f80(x51801),x51803)),f334(f334(f81(x51801),x51802),x51803)) % 169.19/169.65 [5226]~P104(f334(x52263,x52262))+P104(f334(f334(f336(x52261),x52262),x52263)) % 169.19/169.65 [5228]~P72(x52282)+E(f334(f334(f8(x52281,x52282),x52283),f195(f886(x52281,a871))),f2(x52282)) % 169.19/169.65 [5230]~P68(x52302)+E(f334(f334(f11(x52301,x52302),x52303),f195(f886(x52301,a871))),f79(x52302)) % 169.19/169.65 [5280]~E(x52802,f334(f334(f81(a877),x52801),x52803))+P104(f334(f334(f249(a877),x52801),x52802)) % 169.19/169.65 [5283]~E(x52832,f195(f886(x52831,a871)))+E(f334(f334(f62(x52831),x52832),x52833),f195(f886(f886(x52831,a871),a871))) % 169.19/169.65 [5284]~E(x52842,f195(f886(x52841,a871)))+E(f195(f886(f886(x52841,a871),a871)),f334(f334(f62(x52841),x52842),x52843)) % 169.19/169.65 [5363]~E(f334(f265(x53632,x53633),x53631),f195(f886(x53633,a871)))+E(x53631,f195(f886(f885(x53632,x53633),a871))) % 169.19/169.65 [5364]~E(f334(f267(x53642,x53643),x53641),f195(f886(x53642,a871)))+E(x53641,f195(f886(f885(x53642,x53643),a871))) % 169.19/169.65 [5394]E(f334(f265(x53941,x53942),x53943),f195(f886(x53942,a871)))+~E(x53943,f195(f886(f885(x53941,x53942),a871))) % 169.19/169.65 [5395]E(f334(f267(x53951,x53952),x53953),f195(f886(x53951,a871)))+~E(x53953,f195(f886(f885(x53951,x53952),a871))) % 169.19/169.65 [5398]E(f284(x53981,x53982,x53983),f334(f334(f3(a102),x53982),x53983))+P104(f334(f334(f250(a102),x53982),x53983)) % 169.19/169.65 [5414]P104(f334(x54141,x54142))+~P104(f334(f334(f336(x54143),x54142),x54141)) % 169.19/169.65 [5453]E(x54531,x54532)+~E(f334(f80(f886(x54533,a871)),x54531),f334(f80(f886(x54533,a871)),x54532)) % 169.19/169.65 [5458]E(f316(x54581,x54582,x54583),f198(f878(a330)))+~P104(f334(f334(f250(a1),x54582),x54583)) % 169.19/169.65 [5463]~E(x54631,f195(f886(x54632,a871)))+~P104(f334(f334(f336(x54632),x54633),x54631)) % 169.19/169.65 [5492]~E(x54922,f334(f334(f81(a1),x54921),f334(f103(a1),x54923)))+P104(f334(f334(f249(a1),x54921),x54922)) % 169.19/169.65 [5508]E(f334(f334(f312(x55081),x55082),x55083),x55083)+~P104(f334(f334(f336(x55081),x55082),x55083)) % 169.19/169.65 [5519]E(x55191,f195(f886(x55192,a871)))+~E(f334(f334(f62(x55192),x55191),x55193),f195(f886(f886(x55192,a871),a871))) % 169.19/169.65 [5520]E(x55201,f195(f886(x55202,a871)))+~E(f195(f886(f886(x55202,a871),a871)),f334(f334(f62(x55202),x55201),x55203)) % 169.19/169.65 [5526]~P109(x55261)+E(f334(f334(f82(x55261),f334(f80(x55261),x55262)),f334(f80(x55261),x55263)),f334(f334(f82(x55261),x55262),x55263)) % 169.19/169.65 [5528]~P59(x55281)+E(f334(f334(f292(x55281),f334(f80(x55281),x55282)),f334(f80(x55281),x55283)),f334(f334(f292(x55281),x55282),x55283)) % 169.19/169.65 [5560]~P104(f334(x55603,x55602))+P104(f334(f334(f336(x55601),x55602),f334(f254(x55601),x55603))) % 169.19/169.65 [5581]E(x55811,f2(a877))+E(f334(f173(x55812),f170(x55812,x55811,x55813)),f334(f334(f312(x55812),x55813),f195(f886(x55812,a871)))) % 169.19/169.65 [5600]E(f171(x56001,x56002,x56003),x56003)+P104(f334(f334(f336(x56001),x56002),f334(f173(x56001),x56003))) % 169.19/169.65 [5682]~P104(f334(f137(x56821),x56823))+P104(f334(f137(x56821),f334(f136(x56821,x56822),x56823))) % 169.19/169.65 [5727]~P26(x57271)+E(f334(f334(f40(x57271),f46(x57271,x57272,x57273)),x57273),f2(x57271)) % 169.19/169.65 [5746]E(f177(x57461,f334(f334(f151(x57461),x57462),f116(x57461)),x57463),f116(x57461))+P104(f334(f334(f336(a877),f2(a877)),x57463)) % 169.19/169.65 [5752]E(x57521,f2(a877))+E(f334(f172(x57522),f170(x57522,x57521,x57523)),f170(x57522,f334(f334(f3(a877),x57521),f79(a877)),x57523)) % 169.19/169.65 [5804]E(f334(f334(f151(x58041),x58042),x58043),f140(x58041,x58042,x58043))+P104(f334(f334(f336(x58041),x58042),f334(f173(x58041),x58043))) % 169.19/169.65 [5813]E(x58131,x58132)+~E(f334(f334(f82(a877),f334(a115,x58133)),x58131),f334(f334(f82(a877),f334(a115,x58133)),x58132)) % 169.19/169.65 [5814]~E(x58142,f334(f334(f81(a1),x58141),f334(f103(a1),f334(a115,x58143))))+P104(f334(f334(f250(a1),x58141),x58142)) % 169.19/169.65 [5919]~E(x59193,f116(x59191))+E(f334(f334(f334(f190(f878(x59191),f878(x59191)),x59192),f168(x59191)),x59193),f116(x59191)) % 169.19/169.65 [5923]P104(f334(x59231,x59232))+~P104(f334(f334(f336(x59233),x59232),f334(f254(x59233),x59231))) % 169.19/169.65 [5955]E(x59551,x59552)+~E(f334(f334(f312(x59553),x59551),f195(f886(x59553,a871))),f334(f334(f312(x59553),x59552),f195(f886(x59553,a871)))) % 169.19/169.65 [5966]~P108(x59661)+E(f334(f334(f104(f886(x59661,a871)),f334(f255(x59661),x59662)),f334(f304(x59661,x59662),x59663)),f195(f886(x59661,a871))) % 169.19/169.65 [6008]E(f140(x60081,x60082,x60083),x60083)+~P104(f334(f334(f336(x60081),x60082),f334(f173(x60081),x60083))) % 169.19/169.65 [6028]~P75(x60281)+E(f334(f313(x60281,x60281,f80(x60281)),f334(f304(x60281,x60282),x60283)),f307(x60281,f334(f80(x60281),x60283),f334(f80(x60281),x60282))) % 169.19/169.65 [6037]E(f334(f196(f878(x60371)),f171(x60371,x60372,x60373)),f334(f196(f878(x60371)),x60373))+P104(f334(f334(f336(x60371),x60372),f334(f173(x60371),x60373))) % 169.19/169.65 [6091]~P108(x60911)+E(f334(f334(f104(f886(x60911,a871)),f334(f304(x60911,x60912),x60913)),f334(f256(x60911),x60913)),f195(f886(x60911,a871))) % 169.19/169.65 [6114]~P75(x61141)+E(f334(f313(x61141,x61141,f80(x61141)),f308(x61141,x61142,x61143)),f308(x61141,f334(f80(x61141),x61143),f334(f80(x61141),x61142))) % 169.19/169.65 [6115]~P75(x61151)+E(f334(f313(x61151,x61151,f80(x61151)),f305(x61151,x61152,x61153)),f305(x61151,f334(f80(x61151),x61153),f334(f80(x61151),x61152))) % 169.19/169.65 [6172]E(f177(x61721,f334(f334(f151(x61721),x61722),f116(x61721)),x61723),f334(f334(f151(x61721),x61722),f116(x61721)))+~P104(f334(f334(f336(a877),f2(a877)),x61723)) % 169.19/169.65 [6179]~P75(x61791)+E(f334(f313(x61791,x61791,f80(x61791)),f307(x61791,x61792,x61793)),f334(f304(x61791,f334(f80(x61791),x61793)),f334(f80(x61791),x61792))) % 169.19/169.65 [6199]~P27(x61991)+E(f46(x61991,f334(f80(x61991),f46(x61991,x61992,x61993)),x61993),f46(x61991,f334(f80(x61991),x61992),x61993)) % 169.19/169.65 [6304]~P104(f334(f63(f885(x63042,x63041)),x63043))+P104(f334(f63(x63041),f334(f265(x63042,x63041),x63043))) % 169.19/169.65 [6305]~P104(f334(f63(f885(x63051,x63052)),x63053))+P104(f334(f63(x63051),f334(f267(x63051,x63052),x63053))) % 169.19/169.65 [6310]~P108(x63101)+E(f334(f334(f104(f886(x63101,a871)),f308(x63101,x63102,x63103)),f334(f256(x63101),x63103)),f195(f886(x63101,a871))) % 169.19/169.65 [6311]~P108(x63111)+E(f334(f334(f104(f886(x63111,a871)),f305(x63111,x63112,x63113)),f334(f306(x63111),x63113)),f195(f886(x63111,a871))) % 169.19/169.65 [6312]~P108(x63121)+E(f334(f334(f104(f886(x63121,a871)),f307(x63121,x63122,x63123)),f334(f306(x63121),x63123)),f195(f886(x63121,a871))) % 169.19/169.65 [6378]E(f334(f334(f165(x63781),x63782),f582(x63782,x63783,x63781)),x63783)+~P104(f334(f334(f336(x63781),x63783),f334(f173(x63781),x63782))) % 169.19/169.65 [6520]E(x65201,f116(x65202))+~E(f334(f334(f334(f190(f878(x65202),f878(x65202)),x65203),f168(x65202)),x65201),f116(x65202)) % 169.19/169.65 [6621]~P104(f334(f63(f885(x66212,x66211)),x66213))+P104(f334(f63(f885(x66211,x66212)),f334(f289(x66212,x66211),x66213))) % 169.19/169.65 [6771]P53(x67711,x67712,x67713)+P104(f334(f334(f336(x67711),f757(x67713,x67712,x67711)),x67712)) % 169.19/169.65 [6772]P53(x67721,x67722,x67723)+P104(f334(f334(f336(x67721),f756(x67723,x67722,x67721)),x67722)) % 169.19/169.65 [6784]P104(f334(f322(x67841,x67842),x67843))+P104(f334(f334(x67842,f484(x67843,x67842,x67841)),x67843)) % 169.19/169.65 [6785]P104(f334(f322(x67851,x67852),x67853))+P104(f334(f334(x67852,f498(x67853,x67852,x67851)),x67853)) % 169.19/169.65 [6816]E(f334(f196(f878(x68161)),f171(x68161,x68162,x68163)),f334(f334(f3(a877),f334(f196(f878(x68161)),x68163)),f79(a877)))+~P104(f334(f334(f336(x68161),x68162),f334(f173(x68161),x68163))) % 169.19/169.65 [6856]P104(f334(f262(x68561,x68562),x68563))+P104(f334(f334(f336(x68561),f584(x68563,x68562,x68561)),x68563)) % 169.19/169.65 [6867]~P104(f334(f63(f885(x68672,x68671)),f334(f289(x68671,x68672),x68673)))+P104(f334(f63(f885(x68671,x68672)),x68673)) % 169.19/169.65 [6923]~P104(f334(f334(f336(x69231),x69232),f334(f173(x69231),f117(x69231,x69233))))+P104(f334(f334(f336(x69231),x69232),f334(f173(x69231),x69233))) % 169.19/169.65 [6928]P23(x69281,x69282,x69283)+P104(f334(f334(f336(f876(x69281)),f604(x69283,x69282,x69281)),x69283)) % 169.19/169.65 [6956]E(f334(f136(x69561,x69562),x69563),x69563)+P104(f334(f334(f336(x69561),f632(x69563,x69562,x69561)),f334(f173(x69561),x69563))) % 169.19/169.65 [6971]E(f334(f136(x69711,x69712),x69713),f116(x69711))+P104(f334(f334(f336(x69711),f581(x69713,x69712,x69711)),f334(f173(x69711),x69713))) % 169.19/169.65 [6994]P33(x69941,x69942,x69943)+P104(f334(f334(f336(x69941),f795(x69943,x69942,x69941)),f334(f173(x69941),x69943))) % 169.19/169.65 [6995]P33(x69951,x69952,x69953)+P104(f334(f334(f336(x69951),f800(x69953,x69952,x69951)),f334(f173(x69951),x69953))) % 169.19/169.65 [6996]P33(x69961,x69962,x69963)+P104(f334(f334(f336(x69961),f799(x69962,x69963,x69961)),f334(f173(x69961),x69963))) % 169.19/169.65 [6999]E(f178(x69991,x69992,x69993),x69993)+P104(f334(f334(f336(x69991),f644(x69993,x69992,x69991)),f334(f173(x69991),x69993))) % 169.19/169.65 [7078]P104(f334(f160(x70781,x70782),x70783))+P104(f334(f334(f336(x70781),f660(x70783,x70782,x70781)),f334(f173(x70781),x70783))) % 169.19/169.65 [7087]~P35(x70871,x70873,x70872)+P104(f334(f334(f336(x70871),f735(x70872,x70873,x70871)),f334(f173(x70871),x70872))) % 169.19/169.65 [7088]~P37(x70881,x70883,x70882)+P104(f334(f334(f336(x70881),f803(x70882,x70883,x70881)),f334(f173(x70881),x70882))) % 169.19/169.65 [7123]P104(f334(f334(f336(x71231),x71232),f453(x71233,x71232,x71231)))+~P104(f334(f334(f336(x71231),x71232),f41(f886(x71231,a871),x71233))) % 169.19/169.65 [7124]~P72(x71241)+E(f334(f334(f81(x71241),f334(f334(f8(a877,x71241),x71242),f334(f255(a877),x71243))),f334(x71242,x71243)),f334(f334(f8(a877,x71241),x71242),f334(f255(a877),f334(a115,x71243)))) % 169.19/169.65 [7213]~P35(x72132,x72131,x72133)+P104(f334(x72131,f334(f334(f165(x72132),x72133),f750(x72133,x72131,x72132)))) % 169.19/169.65 [7226]~P104(f334(f334(f336(x72261),x72262),f454(x72262,x72263,x72261)))+P104(f334(f334(f336(x72261),x72262),f42(f886(x72261,a871),x72263))) % 169.19/169.65 [7256]~P72(x72561)+E(f334(f334(f81(x72561),f334(f334(f8(a877,x72561),x72562),f334(f303(a877),x72563))),f334(x72562,f334(a115,x72563))),f334(f334(f8(a877,x72561),x72562),f334(f303(a877),f334(a115,x72563)))) % 169.19/169.65 [7392]P104(f334(f334(f336(f878(x73921)),x73922),f161(x73921,x73923)))+P104(f334(f334(f336(x73921),f621(x73923,x73922,x73921)),f334(f173(x73921),x73922))) % 169.19/169.65 [7409]~P104(f334(f334(f336(f878(x74091)),x74092),f161(x74091,f323(x74091,x74093))))+P104(f334(f334(f336(f878(x74091)),x74092),f323(f878(x74091),f157(x74091,x74093)))) % 169.19/169.65 [7434]~P104(f334(f334(f336(f878(x74341)),x74342),f323(f878(x74341),f157(x74341,x74343))))+P104(f334(f334(f336(f878(x74341)),x74342),f161(x74341,f323(x74341,x74343)))) % 169.19/169.65 [7470]E(f334(f334(f334(f190(f878(x74701),f878(x74701)),x74702),f168(x74701)),x74703),x74703)+~P104(f334(f334(f249(a877),f334(f196(f878(x74701)),x74703)),f79(a877))) % 169.19/169.65 [7505]E(f334(f334(f134(x75051),f761(x75052,x75053,x75051)),f334(f334(f151(x75051),x75053),f781(x75052,x75053,x75051))),x75052)+~P104(f334(f334(f336(x75051),x75053),f334(f173(x75051),x75052))) % 169.19/169.65 [7506]E(f334(f334(f134(x75061),f782(x75062,x75063,x75061)),f334(f334(f151(x75061),x75063),f783(x75062,x75063,x75061))),x75062)+~P104(f334(f334(f336(x75061),x75063),f334(f173(x75061),x75062))) % 169.19/169.65 [7507]E(f334(f334(f134(x75071),f784(x75072,x75073,x75071)),f334(f334(f151(x75071),x75073),f785(x75072,x75073,x75071))),x75072)+~P104(f334(f334(f336(x75071),x75073),f334(f173(x75071),x75072))) % 169.19/169.65 [7531]~P21(x75311,x75312,x75313,f257(f886(x75311,a871)))+P21(f878(x75311),f878(x75312),f334(f154(x75311,x75312),x75313),f257(f886(f878(x75311),a871))) % 169.19/169.65 [7680]E(x76801,f334(f334(f81(a877),f334(f334(f82(a877),f334(f268(a877,a877),x76802)),x76803)),f334(f272(a877,a877),x76802)))+~P104(f334(f49(x76801,x76803),x76802)) % 169.19/169.65 [7688]P21(x76881,x76882,x76883,f257(f886(x76881,a871)))+~P21(f878(x76881),f878(x76882),f334(f154(x76881,x76882),x76883),f257(f886(f878(x76881),a871))) % 169.19/169.65 [7731]P104(f334(f334(f336(f886(x77311,a871)),f454(x77312,x77313,x77311)),x77313))+P104(f334(f334(f336(x77311),x77312),f42(f886(x77311,a871),x77313))) % 169.19/169.65 [7823]P104(f334(f334(f336(f878(x78231)),x78232),f161(x78231,x78233)))+~P104(f334(f334(f336(x78231),f621(x78233,x78232,x78231)),x78233)) % 169.19/169.65 [7922]P33(x79221,x79222,x79223)+~P104(f334(x79222,f334(f334(f165(x79221),x79223),f796(x79223,x79222,x79221)))) % 169.19/169.65 [7946]E(x79461,x79462)+~E(f334(f334(f9(x79463,f886(x79463,a871),a871),f336(x79463)),x79461),f334(f334(f9(x79463,f886(x79463,a871),a871),f336(x79463)),x79462)) % 169.19/169.65 [7952]~P104(f334(f334(f336(f885(x79521,x79521)),x79523),f266(x79521,x79522)))+P104(f334(f334(f336(x79521),f545(x79522,x79523,x79521)),x79522)) % 169.19/169.65 [7954]~P104(f334(f334(f336(x79541),x79543),f41(f886(x79541,a871),x79542)))+P104(f334(f334(f336(f886(x79541,a871)),f453(x79542,x79543,x79541)),x79542)) % 169.19/169.65 [8129]~P104(f334(f334(f336(x81291),x81292),f334(f173(x81291),f782(x81293,x81292,x81291))))+~P104(f334(f334(f336(x81291),x81292),f334(f173(x81291),x81293))) % 169.19/169.65 [8130]~P104(f334(f334(f336(x81301),x81302),f334(f173(x81301),f785(x81303,x81302,x81301))))+~P104(f334(f334(f336(x81301),x81302),f334(f173(x81301),x81303))) % 169.19/169.65 [8218]E(f334(f243(f881(f878(a330)),f878(a330),f316(x82181,x82182,f334(f334(f81(a1),x82183),f79(a1))),f241(f878(a330))),f334(x82181,x82183)),f316(x82181,x82182,x82183))+P104(f334(f334(f250(a1),x82182),x82183)) % 169.19/169.65 [8318]E(x83181,f116(x83182))+P104(f334(f334(f336(x83182),f334(f268(x83182,f885(a102,a102)),f334(f285(x83182,x83181),x83183))),f334(f173(x83182),x83181))) % 169.19/169.65 [8414]~P66(x84141)+E(f334(f142(x84141,x84141,f334(f9(x84141,x84141,x84141),f81(x84141)),x84142),f334(f169(x84141),x84143)),f334(f142(x84141,x84141,f81(x84141),x84142),x84143)) % 169.19/169.65 [8891]~P107(x88911)+E(f334(f173(x88911),f149(x88911,x88911,f7(x88911),x88912,x88913)),f334(f334(f312(x88911),x88912),f334(f173(x88911),x88913))) % 169.19/169.65 [8903]P104(f334(f334(f250(a877),f2(a877)),f765(x89031,x89032,x89033)))+~P104(f334(f334(f336(f885(x89033,x89033)),x89032),f334(f334(f291(x89033,x89033,x89033),x89031),f310(x89033,x89031)))) % 169.19/169.65 [9177]~P55(x91771,x91772)+~P104(f334(f334(f336(f885(x91771,x91771)),f334(f334(f269(x91771,x91771),x91773),x91773)),f334(f334(f291(x91771,x91771,x91771),x91772),f310(x91771,x91772)))) % 169.19/169.65 [9299]~E(f334(f334(f104(f886(f885(x92991,x92991),a871)),f334(f289(x92991,x92991),x92992)),f310(x92991,x92992)),f195(f886(f885(x92991,x92991),a871)))+~P104(f334(f334(f336(f885(x92991,x92991)),f334(f334(f269(x92991,x92991),x92993),x92993)),f334(f334(f291(x92991,x92991,x92991),x92992),f310(x92991,x92992)))) % 169.19/169.65 [9474]~P104(f334(f63(x94741),x94742))+P104(f334(f334(f249(a877),f334(f39(x94741),f334(f334(f3(f886(x94741,a871)),x94742),f334(f334(f312(x94741),x94743),f195(f886(x94741,a871)))))),f334(f39(x94741),x94742))) % 169.19/169.65 [5092]~E(x50923,f116(x50921))+E(f144(x50921,f334(f334(f151(x50921),x50922),x50923)),x50922) % 169.19/169.65 [5100]~E(x51003,f116(x51001))+E(f117(x51001,f334(f334(f151(x51001),x51002),x51003)),f116(x51001)) % 169.19/169.65 [5129]E(x51291,f116(x51292))+E(f144(x51292,f334(f334(f151(x51292),x51293),x51291)),f144(x51292,x51291)) % 169.19/169.65 [5131]E(x51311,f116(x51312))+E(f144(x51312,f334(f334(f134(x51312),x51313),x51311)),f144(x51312,x51311)) % 169.19/169.65 [5137]~E(x51373,f116(x51371))+E(f144(x51371,f334(f334(f134(x51371),x51372),x51373)),f144(x51371,x51372)) % 169.19/169.65 [5138]~E(x51383,f116(x51381))+E(f117(x51381,f334(f334(f134(x51381),x51382),x51383)),f117(x51381,x51382)) % 169.19/169.65 [5170]E(x51701,f116(x51702))+E(f334(f141(x51702),f334(f334(f134(x51702),x51701),x51703)),f334(f141(x51702),x51701)) % 169.19/169.65 [5200]~E(x52002,f116(x52001))+E(f334(f141(x52001),f334(f334(f134(x52001),x52002),x52003)),f334(f141(x52001),x52003)) % 169.19/169.65 [5255]~P95(x52551)+E(f334(f334(f113(x52551),x52552),f334(f334(f104(x52551),x52552),x52553)),x52552) % 169.19/169.65 [5256]~P95(x52561)+E(f334(f334(f104(x52561),x52562),f334(f334(f113(x52561),x52562),x52563)),x52562) % 169.19/169.65 [5257]~P107(x52571)+E(f334(f334(f247(x52571),x52572),f334(f334(f248(x52571),x52572),x52573)),x52572) % 169.19/169.65 [5258]~P107(x52581)+E(f334(f334(f248(x52581),x52582),f334(f334(f247(x52581),x52582),x52583)),x52582) % 169.19/169.65 [5278]~P26(x52781)+E(f46(x52781,f334(f334(f82(x52781),x52782),x52783),x52783),f2(x52781)) % 169.19/169.65 [5279]~P26(x52791)+E(f46(x52791,f334(f334(f82(x52791),x52792),x52793),x52792),f2(x52791)) % 169.19/169.65 [5357]~P64(x53571)+E(f334(f80(x53571),f334(f334(f3(x53571),x53572),x53573)),f334(f334(f3(x53571),x53573),x53572)) % 169.19/169.65 [5418]E(x54181,f116(x54182))+E(f117(x54182,f334(f334(f151(x54182),x54183),x54181)),f334(f334(f151(x54182),x54183),f117(x54182,x54181))) % 169.19/169.65 [5419]E(x54191,f116(x54192))+E(f117(x54192,f334(f334(f134(x54192),x54193),x54191)),f334(f334(f134(x54192),x54193),f117(x54192,x54191))) % 169.19/169.65 [5422]~P28(x54221)+E(f41(x54221,f334(f334(f312(x54221),x54222),x54223)),f334(f334(f113(x54221),x54222),f41(x54221,x54223))) % 169.19/169.65 [5423]~P28(x54231)+E(f42(x54231,f334(f334(f312(x54231),x54232),x54233)),f334(f334(f104(x54231),x54232),f42(x54231,x54233))) % 169.19/169.65 [5468]~P93(x54681)+E(f334(f334(f82(x54681),x54682),f334(f334(f82(x54681),x54682),x54683)),f334(f334(f82(x54681),x54682),x54683)) % 169.19/169.65 [5469]~P95(x54691)+E(f334(f334(f113(x54691),x54692),f334(f334(f113(x54691),x54692),x54693)),f334(f334(f113(x54691),x54692),x54693)) % 169.19/169.65 [5471]~P100(x54711)+E(f334(f334(f113(x54711),x54712),f334(f334(f113(x54711),x54712),x54713)),f334(f334(f113(x54711),x54712),x54713)) % 169.19/169.65 [5472]~P95(x54721)+E(f334(f334(f104(x54721),x54722),f334(f334(f104(x54721),x54722),x54723)),f334(f334(f104(x54721),x54722),x54723)) % 169.19/169.65 [5474]~P101(x54741)+E(f334(f334(f104(x54741),x54742),f334(f334(f104(x54741),x54742),x54743)),f334(f334(f104(x54741),x54742),x54743)) % 169.19/169.65 [5476]~P107(x54761)+E(f334(f334(f247(x54761),x54762),f334(f334(f247(x54761),x54762),x54763)),f334(f334(f247(x54761),x54762),x54763)) % 169.19/169.65 [5478]~P107(x54781)+E(f334(f334(f248(x54781),x54782),f334(f334(f248(x54781),x54782),x54783)),f334(f334(f248(x54781),x54782),x54783)) % 169.19/169.65 [5486]~P26(x54861)+E(f46(x54861,f334(f334(f81(x54861),x54862),x54863),x54863),f46(x54861,x54862,x54863)) % 169.19/169.65 [5487]~P26(x54871)+E(f46(x54871,f334(f334(f81(x54871),x54872),x54873),x54872),f46(x54871,x54873,x54872)) % 169.19/169.65 [5493]~P109(x54931)+E(f334(f334(f82(x54931),x54932),f334(f80(x54931),x54933)),f334(f80(x54931),f334(f334(f82(x54931),x54932),x54933))) % 169.19/169.65 [5494]~P59(x54941)+E(f334(f334(f292(x54941),x54942),f334(f80(x54941),x54943)),f334(f80(x54941),f334(f334(f292(x54941),x54942),x54943))) % 169.19/169.65 [5495]~P78(x54951)+E(f334(f334(f81(x54951),x54952),f334(f166(x54951),x54953)),f334(f166(x54951),f334(f334(f151(x54951),x54952),x54953))) % 169.19/169.65 [5525]~P109(x55251)+E(f334(f334(f82(x55251),f334(f80(x55251),x55252)),x55253),f334(f334(f82(x55251),x55252),f334(f80(x55251),x55253))) % 169.19/169.65 [5531]~P6(x55311,x55312,x55313)+E(f41(f886(x55311,a871),f334(f334(f62(x55311),x55312),x55313)),x55312) % 169.19/169.65 [5592]~P112(x55921)+E(f334(f334(f82(x55921),x55922),f334(f334(f259(x55921),x55922),x55923)),f334(f334(f259(x55921),x55922),f334(a115,x55923))) % 169.19/169.65 [5593]~P115(x55931)+E(f334(f334(f82(x55931),x55932),f334(f334(f259(x55931),x55932),x55933)),f334(f334(f259(x55931),x55932),f334(a115,x55933))) % 169.19/169.65 [5603]~P67(x56031)+E(f334(f334(f81(x56031),f334(f80(x56031),x56032)),f334(f334(f81(x56031),x56032),x56033)),x56033) % 169.19/169.65 [5626]~P142(x56261)+E(f334(f334(f259(x56261),f334(f103(x56261),x56262)),x56263),f334(f103(x56261),f334(f334(f259(a877),x56262),x56263))) % 169.19/169.65 [5627]~P137(x56271)+E(f334(f334(f259(x56271),f334(f105(x56271),x56272)),x56273),f334(f105(x56271),f334(f334(f259(a1),x56272),x56273))) % 169.19/169.65 [5633]~P83(x56331)+E(f334(f76(x56331),f334(f334(f3(x56331),x56332),x56333)),f334(f76(x56331),f334(f334(f3(x56331),x56333),x56332))) % 169.19/169.65 [5635]~P120(x56351)+E(f334(f334(f82(x56351),f83(x56351,x56352)),f83(x56351,x56353)),f83(x56351,f334(f334(f82(x56351),x56352),x56353))) % 169.19/169.65 [5639]E(x56391,f116(x56392))+E(f334(f334(f134(x56392),f334(f172(x56392),x56391)),x56393),f334(f172(x56392),f334(f334(f134(x56392),x56391),x56393))) % 169.19/169.65 [5644]~E(x56442,f334(a115,f334(f334(f81(a877),x56441),x56443)))+P104(f334(f334(f250(a877),x56441),x56442)) % 169.19/169.65 [5645]~P109(x56451)+E(f334(f334(f82(x56451),f334(f80(x56451),x56452)),x56453),f334(f80(x56451),f334(f334(f82(x56451),x56452),x56453))) % 169.19/169.65 [5646]~P117(x56461)+E(f334(f334(f292(x56461),f334(f80(x56461),x56462)),x56463),f334(f80(x56461),f334(f334(f292(x56461),x56462),x56463))) % 169.19/169.65 [5647]~P120(x56471)+E(f334(f334(f259(x56471),f334(f76(x56471),x56472)),x56473),f334(f76(x56471),f334(f334(f259(x56471),x56472),x56473))) % 169.19/169.65 [5745]E(f412(x57451,x57452,x57453),f425(x57451,x57452,x57453))+E(f334(f334(f104(f886(x57453,a871)),x57452),x57451),f195(f886(x57453,a871))) % 169.19/169.65 [5760]~P72(x57602)+E(f334(f334(f8(x57601,x57602),f334(f18(x57602,x57601),f2(x57602))),x57603),f2(x57602)) % 169.19/169.65 [5761]~P68(x57612)+E(f334(f334(f11(x57611,x57612),f334(f18(x57612,x57611),f79(x57612))),x57613),f79(x57612)) % 169.19/169.65 [5763]~P92(x57631)+E(f334(f334(f3(x57631),f334(f106(x57631),x57632)),f334(f106(x57631),x57633)),f334(f106(x57631),f334(f334(f3(a1),x57632),x57633))) % 169.19/169.65 [5766]~P142(x57661)+E(f334(f334(f82(x57661),f334(f103(x57661),x57662)),f334(f103(x57661),x57663)),f334(f103(x57661),f334(f334(f82(a877),x57662),x57663))) % 169.19/169.65 [5767]~P142(x57671)+E(f334(f334(f81(x57671),f334(f103(x57671),x57672)),f334(f103(x57671),x57673)),f334(f103(x57671),f334(f334(f81(a877),x57672),x57673))) % 169.19/169.65 [5768]~P137(x57681)+E(f334(f334(f3(x57681),f334(f105(x57681),x57682)),f334(f105(x57681),x57683)),f334(f105(x57681),f334(f334(f3(a1),x57682),x57683))) % 169.19/169.65 [5769]~P137(x57691)+E(f334(f334(f82(x57691),f334(f105(x57691),x57692)),f334(f105(x57691),x57693)),f334(f105(x57691),f334(f334(f82(a1),x57692),x57693))) % 169.19/169.65 [5770]~P137(x57701)+E(f334(f334(f81(x57701),f334(f105(x57701),x57702)),f334(f105(x57701),x57703)),f334(f105(x57701),f334(f334(f81(a1),x57702),x57703))) % 169.19/169.65 [5771]~P92(x57711)+E(f334(f334(f82(x57711),f334(f106(x57711),x57712)),f334(f106(x57711),x57713)),f334(f106(x57711),f334(f334(f82(a1),x57712),x57713))) % 169.19/169.65 [5772]~P92(x57721)+E(f334(f334(f81(x57721),f334(f106(x57721),x57722)),f334(f106(x57721),x57723)),f334(f106(x57721),f334(f334(f81(a1),x57722),x57723))) % 169.19/169.65 [5821]~E(x58213,x58212)+P104(f334(f334(f249(f886(x58211,a871)),x58212),x58213)) % 169.19/169.65 [5827]~E(x58272,x58273)+P104(f334(f334(f249(f886(x58271,a871)),x58272),x58273)) % 169.19/169.65 [5832]~P67(x58321)+E(f334(f334(f81(x58321),f334(f80(x58321),x58322)),f334(f80(x58321),x58323)),f334(f80(x58321),f334(f334(f81(x58321),x58323),x58322))) % 169.19/169.65 [5833]~P64(x58331)+E(f334(f334(f81(x58331),f334(f80(x58331),x58332)),f334(f80(x58331),x58333)),f334(f80(x58331),f334(f334(f81(x58331),x58332),x58333))) % 169.19/169.65 [5834]~P79(x58341)+E(f334(f334(f104(x58341),f334(f80(x58341),x58342)),f334(f80(x58341),x58343)),f334(f80(x58341),f334(f334(f113(x58341),x58342),x58343))) % 169.19/169.65 [5835]~P79(x58351)+E(f334(f334(f113(x58351),f334(f80(x58351),x58352)),f334(f80(x58351),x58353)),f334(f80(x58351),f334(f334(f104(x58351),x58352),x58353))) % 169.19/169.65 [5836]~P73(x58361)+E(f334(f334(f248(x58361),f334(f80(x58361),x58362)),f334(f80(x58361),x58363)),f334(f80(x58361),f334(f334(f247(x58361),x58362),x58363))) % 169.19/169.65 [5837]~P73(x58371)+E(f334(f334(f247(x58371),f334(f80(x58371),x58372)),f334(f80(x58371),x58373)),f334(f80(x58371),f334(f334(f248(x58371),x58372),x58373))) % 169.19/169.65 [5838]~P120(x58381)+E(f334(f334(f82(x58381),f334(f76(x58381),x58382)),f334(f76(x58381),x58383)),f334(f76(x58381),f334(f334(f82(x58381),x58382),x58383))) % 169.19/169.65 [5839]~P61(x58391)+E(f334(f334(f292(x58391),f334(f76(x58391),x58392)),f334(f76(x58391),x58393)),f334(f76(x58391),f334(f334(f292(x58391),x58392),x58393))) % 169.19/169.65 [5840]~P78(x58401)+E(f334(f334(f81(x58401),f334(f166(x58401),x58402)),f334(f166(x58401),x58403)),f334(f166(x58401),f334(f334(f134(x58401),x58402),x58403))) % 169.19/169.65 [5841]E(x58411,f195(f886(x58412,a871)))+~E(f334(f334(f113(f886(x58412,a871)),x58413),x58411),f195(f886(x58412,a871))) % 169.19/169.65 [5842]E(x58421,f195(f886(x58422,a871)))+~E(f334(f334(f113(f886(x58422,a871)),x58421),x58423),f195(f886(x58422,a871))) % 169.19/169.65 [5843]~P146(x58431,x58433,x58432)+P104(f334(x58431,f334(f334(f40(a1),x58432),x58433))) % 169.19/169.65 [5893]~P104(f334(f63(x58931),x58933))+P104(f334(f63(x58931),f334(f334(f312(x58931),x58932),x58933))) % 169.19/169.65 [5894]~P104(f334(f137(x58941),x58943))+P104(f334(f137(x58941),f334(f334(f176(x58941),x58942),x58943))) % 169.19/169.65 [5895]~P104(f334(f137(x58951),x58953))+P104(f334(f137(x58951),f334(f334(f138(x58951),x58952),x58953))) % 169.19/169.65 [5924]~P95(x59241)+P104(f334(f334(f249(x59241),x59242),f334(f334(f113(x59241),x59243),x59242))) % 169.19/169.65 [5925]~P100(x59251)+P104(f334(f334(f249(x59251),x59252),f334(f334(f113(x59251),x59253),x59252))) % 169.19/169.65 [5926]~P95(x59261)+P104(f334(f334(f249(x59261),x59262),f334(f334(f113(x59261),x59262),x59263))) % 169.19/169.65 [5927]~P100(x59271)+P104(f334(f334(f249(x59271),x59272),f334(f334(f113(x59271),x59272),x59273))) % 169.19/169.65 [5928]~P107(x59281)+P104(f334(f334(f249(x59281),x59282),f334(f334(f248(x59281),x59283),x59282))) % 169.19/169.65 [5929]~P107(x59291)+P104(f334(f334(f249(x59291),x59292),f334(f334(f248(x59291),x59292),x59293))) % 169.19/169.65 [5943]~E(x59431,f2(a877))+E(f334(f334(f40(a877),f334(f334(f82(a877),x59431),x59432)),f334(f334(f82(a877),x59431),x59433)),f2(a877)) % 169.19/169.65 [6023]~P92(x60231)+E(f334(f334(f3(x60231),f334(f106(x60231),x60232)),f334(f106(x60231),x60233)),f334(f106(x60231),f334(f334(f81(a1),x60232),f334(f80(a1),x60233)))) % 169.19/169.65 [6078]E(x60781,f2(a877))+E(f334(f334(f40(a877),f334(f334(f82(a877),x60781),x60782)),f334(f334(f82(a877),x60781),x60783)),f334(f334(f40(a877),x60782),x60783)) % 169.19/169.65 [6112]E(f152(x61121,f334(f334(f151(x61121),x61122),x61123)),f334(f334(f151(x61121),x61122),f152(x61121,x61123)))+P104(f334(f334(f336(x61121),x61122),f334(f173(x61121),x61123))) % 169.19/169.65 [6146]P146(x61461,x61462,x61463)+~P104(f334(x61461,f334(f334(f40(a1),x61463),x61462))) % 169.19/169.65 [6221]E(x62211,f116(x62212))+E(f334(f334(f151(x62212),f334(f141(x62212),x62211)),f334(f334(f176(x62212),x62213),f334(f172(x62212),x62211))),f334(f334(f176(x62212),f334(a115,x62213)),x62211)) % 169.19/169.65 [6228]E(f334(f334(f3(f886(x62281,a871)),x62282),x62283),x62282)+~E(f334(f334(f104(f886(x62281,a871)),x62282),x62283),f195(f886(x62281,a871))) % 169.19/169.65 [6242]E(f152(x62421,f334(f334(f151(x62421),x62422),x62423)),f152(x62421,x62423))+~P104(f334(f334(f336(x62421),x62422),f334(f173(x62421),x62423))) % 169.19/169.65 [6274]~P104(f334(f334(f249(a877),x62741),x62743))+P104(f334(f334(f249(a877),x62741),f334(f334(f81(a877),x62742),x62743))) % 169.19/169.65 [6276]~P104(f334(f334(f249(a877),x62761),x62762))+P104(f334(f334(f249(a877),x62761),f334(f334(f81(a877),x62762),x62763))) % 169.19/169.65 [6278]~P104(f334(f334(f250(a877),x62781),x62783))+P104(f334(f334(f250(a877),x62781),f334(f334(f81(a877),x62782),x62783))) % 169.19/169.65 [6280]~P104(f334(f334(f250(a877),x62801),x62802))+P104(f334(f334(f250(a877),x62801),f334(f334(f81(a877),x62802),x62803))) % 169.19/169.65 [6318]P104(f334(f63(x63181),x63182))+~P104(f334(f63(x63181),f334(f334(f312(x63181),x63183),x63182))) % 169.19/169.65 [6319]P104(f334(f137(x63191),x63192))+~P104(f334(f137(x63191),f334(f334(f151(x63191),x63193),x63192))) % 169.19/169.65 [6320]P104(f334(f137(x63201),x63202))+~P104(f334(f137(x63201),f334(f334(f134(x63201),x63203),x63202))) % 169.19/169.65 [6321]P104(f334(f137(x63211),x63212))+~P104(f334(f137(x63211),f334(f334(f134(x63211),x63212),x63213))) % 169.19/169.65 [6367]~P115(x63671)+E(f334(f334(f81(x63671),x63672),f334(f334(f82(x63671),x63673),x63672)),f334(f334(f82(x63671),f334(f334(f81(x63671),x63673),f79(x63671))),x63672)) % 169.19/169.65 [6416]~E(x64161,x64162)+~P104(f334(f334(f250(f886(x64163,a871)),x64161),x64162)) % 169.19/169.65 [6460]P104(f334(f334(f336(x64601),x64602),x64603))+P104(f334(f334(f336(x64601),x64602),f334(f80(f886(x64601,a871)),x64603))) % 169.19/169.65 [6466]E(f144(x64661,f334(f334(f138(x64661),x64662),x64663)),f144(x64661,x64663))+~P104(f334(f334(f250(a877),x64662),f334(f196(f878(x64661)),x64663))) % 169.19/169.65 [6467]E(f334(f334(f176(x64671),x64672),f117(x64671,x64673)),f334(f334(f176(x64671),x64672),x64673))+~P104(f334(f334(f250(a877),x64672),f334(f196(f878(x64671)),x64673))) % 169.19/169.65 [6522]E(f334(f334(f334(f190(f878(x65221),f878(x65221)),x65222),f168(x65221)),x65223),x65223)+~E(f46(a877,x65222,f334(f196(f878(x65221)),x65223)),f2(a877)) % 169.19/169.65 [6529]~P6(x65291,x65293,x65292)+E(f334(f334(f291(x65291,x65291,x65291),f334(f289(x65291,x65291),x65292)),x65292),x65292) % 169.19/169.65 [6571]~E(f334(f334(f113(f886(x65711,a871)),x65712),x65713),x65713)+P104(f334(f334(f249(f886(x65711,a871)),x65712),x65713)) % 169.19/169.65 [6576]~P52(x65761,x65761,x65763)+P52(x65761,x65761,f334(f334(f190(f885(x65761,x65761),a871),x65762),x65763)) % 169.19/169.65 [6578]~P104(f334(f334(f336(x65781),x65783),f334(f173(x65781),x65782)))+P104(f334(f334(f250(a877),f2(a877)),f334(f196(f878(x65781)),x65782))) % 169.19/169.65 [6604]~P83(x66041)+E(f334(f76(x66041),f334(f334(f81(x66041),f334(f76(x66041),x66042)),f334(f76(x66041),x66043))),f334(f334(f81(x66041),f334(f76(x66041),x66042)),f334(f76(x66041),x66043))) % 169.19/169.65 [6614]E(f334(f334(f40(a877),f334(f334(f82(a877),x66141),x66142)),f334(f334(f82(a877),x66141),x66143)),f334(f334(f40(a877),x66142),x66143))+~P104(f334(f334(f250(a877),f2(a877)),x66141)) % 169.19/169.65 [6750]~P104(f334(f63(x67501),x67503))+E(f334(f334(f66(x67501,f886(x67501,a871),f312(x67501)),x67502),x67503),f334(f334(f113(f886(x67501,a871)),x67503),x67502)) % 169.19/169.65 [6809]E(f334(f334(f113(f886(x68091,a871)),x68092),x68093),x68092)+~P104(f334(f334(f249(f886(x68091,a871)),x68093),x68092)) % 169.19/169.65 [6811]E(f334(f334(f113(f886(x68111,a871)),x68112),x68113),x68113)+~P104(f334(f334(f249(f886(x68111,a871)),x68112),x68113)) % 169.19/169.65 [6812]E(f334(f334(f104(f886(x68121,a871)),x68122),x68123),x68123)+~P104(f334(f334(f249(f886(x68121,a871)),x68123),x68122)) % 169.19/169.65 [6813]E(f334(f334(f104(f886(x68131,a871)),x68132),x68133),x68132)+~P104(f334(f334(f249(f886(x68131,a871)),x68132),x68133)) % 169.19/169.65 [6865]~P104(f334(f137(x68651),x68652))+E(f334(f334(f3(f886(x68651,a871)),f334(f173(x68651),x68652)),f334(f334(f312(x68651),x68653),f195(f886(x68651,a871)))),f334(f173(x68651),f171(x68651,x68653,x68652))) % 169.19/169.65 [6918]P39(x69181,x69182)+~P39(x69181,f334(f334(f190(f885(x69181,x69181),a871),x69183),x69182)) % 169.19/169.65 [6982]P104(f334(f50(x69821,x69822),f334(a52,x69823)))+~P104(f334(f50(f334(f80(a1),x69821),f334(f80(a1),x69822)),x69823)) % 169.19/169.65 [6987]E(f334(f334(f3(f886(x69871,a871)),f334(f334(f312(x69871),x69872),x69873)),f334(f334(f312(x69871),x69872),f195(f886(x69871,a871)))),x69873)+P104(f334(f334(f336(x69871),x69872),x69873)) % 169.19/169.65 [7008]E(f334(f334(f104(f886(x70081,a871)),f334(f173(x70081),x70082)),f334(f173(x70081),x70083)),f195(f886(x70081,a871)))+~P104(f334(f137(x70081),f334(f334(f134(x70081),x70082),x70083))) % 169.19/169.65 [7024]~P104(f334(f334(f336(x70241),x70242),f334(f173(x70241),x70243)))+~P104(f334(f137(x70241),f334(f334(f151(x70241),x70242),x70243))) % 169.19/169.65 [7094]P33(x70941,x70942,x70943)+P104(f334(f334(f250(a877),f796(x70943,x70942,x70941)),f334(f196(f878(x70941)),x70943))) % 169.19/169.65 [7104]E(f334(f334(f104(f886(x71041,a871)),x71042),x71043),f195(f886(x71041,a871)))+P104(f334(f334(f336(x71041),f412(x71043,x71042,x71041)),x71042)) % 169.19/169.65 [7105]E(f334(f334(f104(f886(x71051,a871)),x71052),x71053),f195(f886(x71051,a871)))+P104(f334(f334(f336(x71051),f425(x71053,x71052,x71051)),x71053)) % 169.19/169.65 [7109]E(f117(x71091,f334(f334(f176(x71091),x71092),x71093)),f334(f334(f176(x71091),f334(f334(f3(a877),x71092),f79(a877))),x71093))+~P104(f334(f334(f249(a877),x71092),f334(f196(f878(x71091)),x71093))) % 169.19/169.65 [7168]~P35(x71683,x71682,x71681)+P104(f334(f334(f250(a877),f750(x71681,x71682,x71683)),f334(f196(f878(x71683)),x71681))) % 169.19/169.65 [7186]P104(f334(f334(f250(a877),f2(a877)),x71861))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x71862),x71861)),f334(f334(f82(a877),x71863),x71861))) % 169.19/169.65 [7187]P104(f334(f334(f250(a877),f2(a877)),x71871))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x71871),x71872)),f334(f334(f82(a877),x71871),x71873))) % 169.19/169.65 [7190]~P104(f334(f334(f336(x71901),x71902),x71903))+~P104(f334(f334(f336(x71901),x71902),f334(f80(f886(x71901,a871)),x71903))) % 169.19/169.65 [7197]~P104(f334(f334(f250(f886(x71971,a871)),x71972),x71973))+P104(f334(f334(f249(f886(x71971,a871)),x71972),x71973)) % 169.19/169.65 [7299]~P104(f334(f334(f249(a877),x72993),x72992))+P104(f334(f334(f249(a877),f334(f334(f3(a877),x72991),x72992)),f334(f334(f3(a877),x72991),x72993))) % 169.19/169.65 [7300]~P104(f334(f334(f249(a877),x73001),x73003))+P104(f334(f334(f249(a877),f334(f334(f3(a877),x73001),x73002)),f334(f334(f3(a877),x73003),x73002))) % 169.19/169.65 [7302]~P104(f334(f334(f249(a877),x73022),x73023))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x73021),x73022)),f334(f334(f82(a877),x73021),x73023))) % 169.19/169.65 [7304]~P104(f334(f334(f249(a877),x73041),x73043))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x73041),x73042)),f334(f334(f82(a877),x73043),x73042))) % 169.19/169.65 [7305]~P104(f334(f334(f249(a877),x73052),x73053))+P104(f334(f334(f249(a877),f334(f334(f81(a877),x73051),x73052)),f334(f334(f81(a877),x73051),x73053))) % 169.19/169.65 [7306]~P104(f334(f334(f249(a877),x73061),x73063))+P104(f334(f334(f249(a877),f334(f334(f81(a877),x73061),x73062)),f334(f334(f81(a877),x73063),x73062))) % 169.19/169.65 [7307]~P104(f334(f334(f249(a877),x73071),x73073))+P104(f334(f334(f249(a877),f334(f334(f40(a877),x73071),x73072)),f334(f334(f40(a877),x73073),x73072))) % 169.19/169.65 [7308]~P104(f334(f334(f249(a1),x73082),x73083))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x73081),x73082)),f334(f334(f81(a1),x73081),x73083))) % 169.19/169.65 [7311]~P104(f334(f334(f250(a877),x73112),x73113))+P104(f334(f334(f250(a877),f334(f334(f81(a877),x73111),x73112)),f334(f334(f81(a877),x73111),x73113))) % 169.19/169.65 [7312]~P104(f334(f334(f250(a877),x73121),x73123))+P104(f334(f334(f250(a877),f334(f334(f81(a877),x73121),x73122)),f334(f334(f81(a877),x73123),x73122))) % 169.19/169.65 [7313]~P104(f334(f334(f250(a1),x73131),x73133))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x73131),x73132)),f334(f334(f81(a1),x73133),x73132))) % 169.19/169.65 [7391]E(x73911,x73912)+~P104(f334(f334(f336(x73913),x73911),f334(f334(f312(x73913),x73912),f195(f886(x73913,a871))))) % 169.19/169.65 [7393]~E(f334(f334(f104(f886(x73931,a871)),x73932),x73933),f195(f886(x73931,a871)))+P104(f334(f334(f249(f886(x73931,a871)),x73932),f334(f80(f886(x73931,a871)),x73933))) % 169.19/169.65 [7400]P104(f334(f334(f336(f886(x74001,a871)),x74002),f334(f311(x74001),x74003)))+~P104(f334(f334(f249(f886(x74001,a871)),x74002),x74003)) % 169.19/169.65 [7405]P104(f334(f334(f336(x74051),f417(x74052,x74053,x74051)),x74053))+P104(f334(f334(f249(f886(x74051,a871)),x74053),x74052)) % 169.19/169.65 [7454]E(f334(f334(f151(x74541),f334(f334(f165(x74541),x74542),x74543)),f334(f334(f138(x74541),f334(a115,x74543)),x74542)),f334(f334(f138(x74541),x74543),x74542))+~P104(f334(f334(f250(a877),x74543),f334(f196(f878(x74541)),x74542))) % 169.19/169.65 [7481]P104(f334(f334(f336(f885(x74811,x74811)),x74812),f310(x74811,x74813)))+~P104(f334(f334(f336(f885(x74811,x74811)),x74812),x74813)) % 169.19/169.65 [7491]~P104(f334(f334(f336(f886(x74911,a871)),x74912),f334(f311(x74911),x74913)))+P104(f334(f334(f249(f886(x74911,a871)),x74912),x74913)) % 169.19/169.65 [7537]P104(f334(f334(f249(f886(x75371,a871)),x75372),f41(f886(x75371,a871),x75373)))+~P104(f334(f334(f336(f886(x75371,a871)),x75372),x75373)) % 169.19/169.65 [7562]~P137(x75621)+E(f334(f334(f82(x75621),f334(f334(f259(x75621),f334(f80(x75621),f79(x75621))),x75622)),f334(f334(f259(x75621),x75623),x75622)),f334(f334(f259(x75621),f334(f80(x75621),x75623)),x75622)) % 169.19/169.65 [7584]E(f334(f334(f165(x75841),x75842),f334(f334(f3(a877),f334(f196(f878(x75841)),x75842)),f334(a115,x75843))),f334(f334(f165(x75841),f334(f169(x75841),x75842)),x75843))+~P104(f334(f334(f250(a877),x75843),f334(f196(f878(x75841)),x75842))) % 169.19/169.65 [7601]~E(f334(f334(f104(f886(x76011,a871)),f427(x76013,x76012,x76011)),x76013),f195(f886(x76011,a871)))+E(f334(f334(f104(f886(x76011,a871)),f41(f886(x76011,a871),x76012)),x76013),f195(f886(x76011,a871))) % 169.19/169.65 [7662]~P104(f334(f334(f336(x76623),x76622),f334(f173(x76623),x76621)))+P104(f334(f334(f250(a877),f582(x76621,x76622,x76623)),f334(f196(f878(x76623)),x76621))) % 169.19/169.65 [7670]P104(f334(f334(f336(x76701),f334(f334(f165(x76701),x76702),x76703)),f334(f173(x76701),x76702)))+~P104(f334(f334(f250(a877),x76703),f334(f196(f878(x76701)),x76702))) % 169.19/169.65 [7770]~P104(f334(x77702,f650(x77703,x77702,x77701)))+E(f334(f334(f138(x77701),f334(f196(f878(x77701)),f178(x77701,x77702,x77703))),x77703),f116(x77701)) % 169.19/169.65 [7781]P104(f334(f334(f249(f886(f878(x77811),a871)),f161(x77811,x77812)),f161(x77811,x77813)))+~P104(f334(f334(f249(f886(x77811,a871)),x77812),x77813)) % 169.19/169.65 [7782]P104(f334(f334(f249(f886(f878(x77821),a871)),f160(x77821,x77822)),f160(x77821,x77823)))+~P104(f334(f334(f249(f886(x77821,a871)),x77822),x77823)) % 169.19/169.65 [7809]E(f334(f334(f104(f886(x78091,a871)),f41(f886(x78091,a871),x78092)),x78093),f195(f886(x78091,a871)))+P104(f334(f334(f336(f886(x78091,a871)),f427(x78093,x78092,x78091)),x78092)) % 169.19/169.65 [7812]~P104(f334(f334(f336(f886(x78121,a871)),x78123),x78122))+P104(f334(f334(f249(f886(x78121,a871)),f42(f886(x78121,a871),x78122)),x78123)) % 169.19/169.65 [7814]E(f334(f334(f104(f886(x78141,a871)),x78142),x78143),f195(f886(x78141,a871)))+~P104(f334(f334(f249(f886(x78141,a871)),x78142),f334(f80(f886(x78141,a871)),x78143))) % 169.19/169.65 [7860]E(f334(f334(f3(a877),f334(f334(f81(a877),f334(f166(a877),x78601)),x78602)),f334(f334(f165(a877),x78601),x78603)),f334(f166(a877),f334(f334(f159(a877,x78601),x78603),x78602)))+~P104(f334(f334(f250(a877),x78603),f334(f196(f878(a877)),x78601))) % 169.19/169.65 [7910]P104(f334(f334(f249(a877),x79101),x79102))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),x79103),x79101)),f334(f334(f81(a877),x79103),x79102))) % 169.19/169.65 [7913]P104(f334(f334(f250(a877),x79131),x79132))+~P104(f334(f334(f250(a877),f334(f334(f81(a877),x79133),x79131)),f334(f334(f81(a877),x79133),x79132))) % 169.19/169.65 [7914]P104(f334(f334(f250(a877),x79141),x79142))+~P104(f334(f334(f250(a877),f334(f334(f82(a877),x79143),x79141)),f334(f334(f82(a877),x79143),x79142))) % 169.19/169.65 [7915]P104(f334(f334(f250(a877),x79151),x79152))+~P104(f334(f334(f250(a877),f334(f334(f82(a877),x79151),x79153)),f334(f334(f82(a877),x79152),x79153))) % 169.19/169.65 [7944]P104(f334(f334(f250(a877),f2(a877)),x79441))+~P104(f334(f334(f250(a877),f334(f334(f82(a877),x79442),x79441)),f334(f334(f82(a877),x79443),x79441))) % 169.19/169.65 [7945]P104(f334(f334(f250(a877),f2(a877)),x79451))+~P104(f334(f334(f250(a877),f334(f334(f82(a877),x79451),x79452)),f334(f334(f82(a877),x79451),x79453))) % 169.19/169.65 [7984]~P104(f334(f334(f336(x79841),f417(x79843,x79842,x79841)),x79843))+P104(f334(f334(f249(f886(x79841,a871)),x79842),x79843)) % 169.19/169.65 [8020]E(f261(x80201,x80202,x80203),x80202)+~P104(f334(f334(f249(f886(x80201,a871)),x80203),f334(f334(f312(x80201),x80202),f195(f886(x80201,a871))))) % 169.19/169.65 [8070]~P104(f334(f137(x80701),x80703))+E(f334(f136(x80701,f334(f334(f10(a871,a871,x80701),a329),f334(a331,x80702))),x80703),f171(x80701,x80702,x80703)) % 169.19/169.65 [8093]E(f334(f334(f138(x80931),f334(f196(f878(x80931)),f178(x80931,x80932,x80933))),x80933),f116(x80931))+P104(f334(f334(f336(x80931),f650(x80933,x80932,x80931)),f334(f173(x80931),x80933))) % 169.19/169.65 [8097]E(f334(f334(f134(x80971),f334(f334(f176(x80971),x80972),x80973)),f334(f334(f151(x80971),f334(f334(f165(x80971),x80973),x80972)),f116(x80971))),f334(f334(f176(x80971),f334(a115,x80972)),x80973))+~P104(f334(f334(f250(a877),x80972),f334(f196(f878(x80971)),x80973))) % 169.19/169.65 [8158]E(f334(f136(x81581,f334(f334(f10(a871,a871,x81581),a329),f334(a331,x81582))),x81583),x81583)+P104(f334(f334(f336(x81581),x81582),f334(f173(x81581),x81583))) % 169.19/169.65 [8165]P104(f334(f334(f249(f886(f886(x81651,a871),a871)),f262(x81651,x81652)),f262(x81651,x81653)))+~P104(f334(f334(f249(f886(x81651,a871)),x81652),x81653)) % 169.19/169.65 [8209]~P104(f334(f137(x82091),x82093))+P104(f334(f137(x82091),f334(f334(f334(f190(f878(x82091),f878(x82091)),x82092),f168(x82091)),x82093))) % 169.19/169.65 [8215]~P104(f334(f334(f250(a877),x82152),x82153))+P104(f334(f334(f250(a877),f334(f334(f82(a877),f334(a115,x82151)),x82152)),f334(f334(f82(a877),f334(a115,x82151)),x82153))) % 169.19/169.65 [8237]P104(f334(f334(f249(f886(f886(x82371,a871),a871)),f334(f311(x82371),x82372)),f334(f311(x82371),x82373)))+~P104(f334(f334(f249(f886(x82371,a871)),x82372),x82373)) % 169.19/169.65 [8397]~P104(f334(f334(f249(f886(x83971,a871)),x83973),x83972))+P104(f334(f334(f249(f886(x83971,a871)),f334(f80(f886(x83971,a871)),x83972)),f334(f80(f886(x83971,a871)),x83973))) % 169.19/169.65 [8427]E(f334(f313(a877,a877,f334(f334(f9(a877,a877,a877),f3(a877)),x84271)),f334(f304(a877,x84272),x84273)),f334(f304(a877,f334(f334(f3(a877),x84272),x84271)),f334(f334(f3(a877),x84273),x84271)))+~P104(f334(f334(f250(a877),x84271),x84273)) % 169.19/169.65 [8455]~P78(x84551)+E(f334(f334(f81(x84551),x84552),f334(f142(x84551,x84551,f81(x84551),f2(x84551)),x84553)),f334(f142(x84551,x84551,f81(x84551),x84552),x84553)) % 169.19/169.65 [8528]~P83(x85281)+P104(f334(f334(f249(x85281),f334(f76(x85281),f334(f334(f3(x85281),x85282),x85283))),f334(f334(f81(x85281),f334(f76(x85281),x85282)),f334(f76(x85281),x85283)))) % 169.19/169.65 [8529]~P83(x85291)+P104(f334(f334(f249(x85291),f334(f76(x85291),f334(f334(f81(x85291),x85292),x85293))),f334(f334(f81(x85291),f334(f76(x85291),x85292)),f334(f76(x85291),x85293)))) % 169.19/169.65 [8539]E(f334(f334(f81(a1),f334(f334(f82(a1),x85391),f46(a1,f334(f334(f40(a1),x85392),x85391),x85393))),f46(a1,x85392,x85391)),f46(a1,x85392,f334(f334(f82(a1),x85391),x85393)))+~P104(f334(f334(f250(a1),f2(a1)),x85393)) % 169.19/169.65 [8545]E(f334(f334(f134(x85451),f334(f334(f176(x85451),x85452),x85453)),f334(f334(f151(x85451),f334(f141(x85451),f334(f334(f138(x85451),x85452),x85453))),f116(x85451))),f334(f334(f176(x85451),f334(a115,x85452)),x85453))+~P104(f334(f334(f250(a877),x85452),f334(f196(f878(x85451)),x85453))) % 169.19/169.65 [8564]E(f334(f280(x85641,f334(f334(f154(x85641,f885(a102,x85641)),f334(f269(a102,x85641),f79(a102))),x85642)),f334(a5,x85643)),f334(f334(f165(x85641),x85642),x85643))+~P104(f334(f334(f250(a877),x85643),f334(f196(f878(x85641)),x85642))) % 169.19/169.65 [8630]P104(f334(f334(f336(f885(x86301,x86301)),x86302),f334(f334(f291(x86301,x86301,x86301),x86303),f310(x86301,x86303))))+~P104(f334(f334(f336(f885(x86301,x86301)),x86302),x86303)) % 169.19/169.65 [8647]P104(f334(f334(f249(a877),x86471),x86472))+~P104(f334(f334(f249(a877),f334(f334(f82(a877),f334(a115,x86473)),x86471)),f334(f334(f82(a877),f334(a115,x86473)),x86472))) % 169.19/169.65 [8663]P104(f334(f334(f249(f886(x86631,a871)),x86632),x86633))+~P104(f334(f334(f249(f886(x86631,a871)),f334(f80(f886(x86631,a871)),x86633)),f334(f80(f886(x86631,a871)),x86632))) % 169.19/169.65 [8681]P104(f334(f137(x86811),x86812))+~P104(f334(f137(x86811),f334(f334(f334(f190(f878(x86811),f878(x86811)),x86813),f168(x86811)),x86812))) % 169.19/169.65 [8741]E(f334(f313(f885(x87411,x87412),x87412,f272(x87411,x87412)),f334(f173(f885(x87411,x87412)),x87413)),f187(x87411,x87412,f334(f179(x87411,x87412),x87413)))+~P104(f334(f137(x87411),f334(f334(f154(f885(x87411,x87412),x87411),f268(x87411,x87412)),x87413))) % 169.19/169.65 [8750]E(f334(f288(x87501,x87501,f310(x87501,x87502)),x87503),x87503)+~P104(f334(f334(f249(f886(x87501,a871)),f334(f288(x87501,x87501,x87502),x87503)),x87503)) % 169.19/169.65 [8792]~P107(x87921)+P30(x87921,f334(f136(x87921,f334(f334(f9(x87921,x87921,a871),a331),f334(x87922,x87923))),x87923)) % 169.19/169.65 [8798]~P104(f334(f334(f249(a877),x87981),x87982))+P104(f334(f334(f249(a877),x87981),f334(f142(a877,a877,f81(a877),x87982),x87983))) % 169.19/169.65 [8875]~P104(f334(f334(f336(f885(x88751,x88751)),x88752),f310(x88751,x88753)))+P104(f334(f334(f336(f885(x88751,x88751)),x88752),f334(f334(f190(f885(x88751,x88751),a871),f763(x88753,x88752,x88751)),x88753))) % 169.19/169.65 [8963]~P78(x89631)+E(f334(f334(f81(x89631),x89632),f334(f142(x89631,x89631,f334(f9(x89631,x89631,x89631),f81(x89631)),f2(x89631)),f334(f169(x89631),x89633))),f334(f142(x89631,x89631,f81(x89631),x89632),x89633)) % 169.19/169.65 [9223]P52(x92231,x92232,x92233)+P104(f334(f334(f336(f885(x92231,x92232)),f334(f334(f269(x92231,x92232),f754(x92233,x92232,x92231)),f734(x92233,x92232,x92231))),x92233)) % 169.19/169.65 [9224]P52(x92241,x92242,x92243)+P104(f334(f334(f336(f885(x92241,x92242)),f334(f334(f269(x92241,x92242),f754(x92243,x92242,x92241)),f733(x92243,x92242,x92241))),x92243)) % 169.19/169.65 [9286]~P104(f334(f334(f336(f885(x92861,x92861)),x92862),f334(f334(f291(x92861,x92861,x92861),x92863),f310(x92861,x92863))))+P104(f334(f334(f336(f885(x92861,x92861)),x92862),f334(f334(f190(f885(x92861,x92861),a871),f765(x92863,x92862,x92861)),x92863))) % 169.19/169.65 [9287]~P104(f334(x92871,f334(f334(f165(x92872),x92873),f334(f196(f878(x92872)),f178(x92872,x92871,x92873)))))+~P104(f334(f334(f250(a877),f334(f196(f878(x92872)),f178(x92872,x92871,x92873))),f334(f196(f878(x92872)),x92873))) % 169.19/169.65 [9373]~P104(f334(f334(f249(f886(x93731,a871)),x93732),x93733))+P104(f334(f334(f249(f886(x93731,a871)),f334(f334(f9(x93731,f886(x93731,a871),a871),f336(x93731)),x93732)),f334(f334(f9(x93731,f886(x93731,a871),a871),f336(x93731)),x93733))) % 169.19/169.65 [9424]~P104(f334(f334(f336(f885(f886(x94241,a871),f886(x94241,a871))),f334(f334(f269(f886(x94241,a871),f886(x94241,a871)),x94242),x94243)),f309(x94241)))+P104(f334(f334(f250(f886(x94241,a871)),x94242),x94243)) % 169.19/169.65 [9448]P53(x94481,x94482,x94483)+~P104(f334(f334(f336(f885(x94481,x94481)),f334(f334(f269(x94481,x94481),f757(x94483,x94482,x94481)),f756(x94483,x94482,x94481))),x94483)) % 169.19/169.65 [9449]P53(x94491,x94492,x94493)+~P104(f334(f334(f336(f885(x94491,x94491)),f334(f334(f269(x94491,x94491),f756(x94493,x94492,x94491)),f757(x94493,x94492,x94491))),x94493)) % 169.19/169.65 [9484]~P104(f334(f334(f336(f885(f878(x94841),f878(x94841))),f334(f334(f269(f878(x94841),f878(x94841)),x94842),x94842)),f147(x94841,x94843)))+P104(f334(f334(f336(f885(x94841,x94841)),f334(f334(f269(x94841,x94841),f626(x94842,x94843,x94841)),f626(x94842,x94843,x94841))),x94843)) % 169.19/169.65 [9532]P104(f334(f334(f249(f886(x95321,a871)),x95322),x95323))+~P104(f334(f334(f249(f886(x95321,a871)),f334(f334(f9(x95321,f886(x95321,a871),a871),f336(x95321)),x95322)),f334(f334(f9(x95321,f886(x95321,a871),a871),f336(x95321)),x95323))) % 169.19/169.65 [9613]E(f334(f334(f3(a877),f334(f334(f8(a877,a877),x96131),f334(f255(a877),x96132))),f334(f334(f8(a877,a877),x96133),f334(f255(a877),x96132))),f334(f334(f8(a877,a877),f334(f334(f20(a877,a877,a877),f334(f334(f10(a877,f886(a877,a877),a877),f3(a877)),x96131)),x96133)),f334(f255(a877),x96132)))+~P104(f334(f334(f249(a877),f334(x96133,f511(x96132,x96131,x96133))),f334(x96131,f511(x96132,x96131,x96133)))) % 169.19/169.65 [9915]E(f334(f254(f885(x99151,x99152)),f334(f273(x99151,x99152,a871),f334(f334(f9(x99151,f886(x99152,f881(x99152)),f886(x99152,a871)),f334(f334(f10(f886(f881(x99152),a871),f886(f886(x99152,f881(x99152)),f886(x99152,a871)),x99151),f10(f881(x99152),a871,x99152)),f334(f334(f10(f881(x99152),f886(f881(x99152),a871),x99151),a331),f334(f179(x99151,x99152),x99153)))),f241(x99152)))),f334(f173(f885(x99151,x99152)),x99153))+~P104(f334(f137(x99151),f334(f334(f154(f885(x99151,x99152),x99151),f268(x99151,x99152)),x99153))) % 169.19/169.65 [5679]~P67(x56791)+E(f334(f334(f3(x56791),f334(f334(f81(x56791),x56792),x56793)),x56793),x56792) % 169.19/169.65 [5680]~P67(x56801)+E(f334(f334(f81(x56801),f334(f334(f3(x56801),x56802),x56803)),x56803),x56802) % 169.19/169.65 [5901]~P67(x59011)+E(f334(f334(f81(x59011),x59012),f334(f334(f81(x59011),f334(f80(x59011),x59012)),x59013)),x59013) % 169.19/169.65 [5985]~P77(x59851)+E(f334(f334(f82(x59851),f334(f334(f259(x59851),x59852),x59853)),x59852),f334(f334(f259(x59851),x59852),f334(a115,x59853))) % 169.19/169.65 [5986]~P115(x59861)+E(f334(f334(f82(x59861),f334(f334(f259(x59861),x59862),x59863)),x59862),f334(f334(f259(x59861),x59862),f334(a115,x59863))) % 169.19/169.65 [6196]~P120(x61961)+E(f334(f76(x61961),f334(f334(f259(x61961),f334(f80(x61961),x61962)),x61963)),f334(f76(x61961),f334(f334(f259(x61961),x61962),x61963))) % 169.19/169.65 [6248]~P77(x62481)+E(f334(f334(f82(x62481),f334(f334(f259(x62481),x62482),x62483)),x62482),f334(f334(f82(x62481),x62482),f334(f334(f259(x62481),x62482),x62483))) % 169.19/169.65 [6309]E(f334(f334(f3(a102),f334(f334(f81(a102),x63091),x63092)),x63093),f284(x63091,x63092,x63093))+~P104(f334(f334(f250(a102),x63092),x63093)) % 169.19/169.65 [6330]~E(f334(f334(f138(x63301),x63303),x63302),f116(x63301))+P104(f334(f334(f249(a877),f334(f196(f878(x63301)),x63302)),x63303)) % 169.19/169.65 [6465]E(f334(f334(f82(a877),f334(f106(a877),x64651)),f334(f334(f82(a877),f334(f106(a877),x64652)),x64653)),f2(a877))+~P104(f334(f334(f250(a1),x64651),a84)) % 169.19/169.65 [6481]~P59(x64811)+E(f334(f334(f259(x64811),f334(f334(f292(x64811),f79(x64811)),x64812)),x64813),f334(f334(f292(x64811),f79(x64811)),f334(f334(f259(x64811),x64812),x64813))) % 169.19/169.65 [6558]E(f334(f334(f3(a877),f334(f334(f81(a877),x65581),x65582)),x65583),f334(f334(f3(a877),x65581),f334(f334(f3(a877),x65583),x65582)))+~P104(f334(f334(f249(a877),x65582),x65583)) % 169.19/169.65 [6560]E(f334(f334(f3(a877),f334(f334(f81(a877),x65601),x65602)),x65603),f334(f334(f81(a877),x65601),f334(f334(f3(a877),x65602),x65603)))+~P104(f334(f334(f249(a877),x65603),x65602)) % 169.19/169.65 [6595]~P95(x65951)+P104(f334(f334(f249(x65951),f334(f334(f104(x65951),x65952),x65953)),x65953)) % 169.19/169.65 [6596]~P101(x65961)+P104(f334(f334(f249(x65961),f334(f334(f104(x65961),x65962),x65963)),x65963)) % 169.19/169.65 [6597]~P95(x65971)+P104(f334(f334(f249(x65971),f334(f334(f104(x65971),x65972),x65973)),x65972)) % 169.19/169.65 [6598]~P101(x65981)+P104(f334(f334(f249(x65981),f334(f334(f104(x65981),x65982),x65983)),x65982)) % 169.19/169.65 [6599]~P107(x65991)+P104(f334(f334(f249(x65991),f334(f334(f247(x65991),x65992),x65993)),x65993)) % 169.19/169.65 [6600]~P107(x66001)+P104(f334(f334(f249(x66001),f334(f334(f247(x66001),x66002),x66003)),x66002)) % 169.19/169.65 [6613]E(f334(f334(f40(a1),f334(f334(f40(a1),x66131),x66132)),x66133),f334(f334(f40(a1),x66131),f334(f334(f82(a1),x66132),x66133)))+~P104(f334(f334(f250(a1),f2(a1)),x66133)) % 169.19/169.65 [6664]~P115(x66641)+E(f334(f334(f81(x66641),f334(f334(f82(x66641),x66642),x66643)),x66643),f334(f334(f82(x66641),f334(f334(f81(x66641),x66642),f79(x66641))),x66643)) % 169.19/169.65 [6665]~P92(x66651)+E(f334(f334(f82(x66651),f334(f80(x66651),f334(f106(x66651),x66652))),x66653),f334(f334(f82(x66651),f334(f106(x66651),f334(f80(a1),x66652))),x66653)) % 169.19/169.65 [6737]~P78(x67371)+E(f334(f166(x67371),f334(f334(f154(x67372,x67371),f334(f18(x67371,x67372),f2(x67371))),x67373)),f2(x67371)) % 169.19/169.65 [6753]E(f334(f334(f81(a877),f334(f106(a877),x67531)),f334(f334(f81(a877),f334(f106(a877),x67532)),x67533)),f334(f334(f81(a877),f334(f106(a877),x67532)),x67533))+~P104(f334(a201,f334(f106(a1),x67531))) % 169.19/169.65 [6767]~P28(x67671)+E(f41(x67671,f334(f334(f312(x67671),x67672),f334(f334(f312(x67671),x67673),f195(f886(x67671,a871))))),f334(f334(f113(x67671),x67672),x67673)) % 169.19/169.65 [6768]~P28(x67681)+E(f42(x67681,f334(f334(f312(x67681),x67682),f334(f334(f312(x67681),x67683),f195(f886(x67681,a871))))),f334(f334(f104(x67681),x67682),x67683)) % 169.19/169.65 [6791]E(f334(f334(f176(x67911),x67912),x67913),x67913)+~P104(f334(f334(f249(a877),f334(f196(f878(x67911)),x67913)),x67912)) % 169.19/169.65 [6804]E(f334(f334(f138(x68041),x68042),x68043),f116(x68041))+~P104(f334(f334(f249(a877),f334(f196(f878(x68041)),x68043)),x68042)) % 169.19/169.65 [6815]E(f334(f334(f81(a877),f334(f334(f3(a877),x68151),x68152)),x68153),f334(f334(f3(a877),f334(f334(f81(a877),x68151),x68153)),x68152))+~P104(f334(f334(f249(a877),x68152),x68151)) % 169.19/169.65 [6829]~P104(f334(f334(f250(a877),x68291),x68293))+P104(f334(f334(f250(a877),f334(f334(f3(a877),x68291),x68292)),x68293)) % 169.19/169.65 [6857]~P107(x68571)+E(f171(x68571,x68572,f334(f334(f148(x68571,x68571,f7(x68571)),x68572),x68573)),x68573) % 169.19/169.65 [6946]E(f334(f334(f3(a877),f334(f334(f81(a877),x69461),x69462)),f334(a115,x69463)),f334(f334(f3(a877),x69461),f334(a115,f334(f334(f3(a877),x69463),x69462))))+~P104(f334(f334(f249(a877),x69462),x69463)) % 169.19/169.65 [6947]~P120(x69471)+P104(f334(f334(f249(x69471),f2(x69471)),f334(f334(f259(x69471),f334(f76(x69471),x69472)),x69473))) % 169.19/169.65 [6992]P20(x69921,x69922,x69923)+~P104(f334(f334(f249(f886(f876(x69921),a871)),x69923),x69922)) % 169.19/169.65 [7035]~P104(f334(f63(x70351),x70352))+P104(f334(f63(x70351),f334(f334(f3(f886(x70351,a871)),x70352),x70353))) % 169.19/169.65 [7036]~P104(f334(f63(x70361),x70363))+P104(f334(f63(x70361),f334(f334(f104(f886(x70361,a871)),x70362),x70363))) % 169.19/169.65 [7037]~P104(f334(f63(x70371),x70372))+P104(f334(f63(x70371),f334(f334(f104(f886(x70371,a871)),x70372),x70373))) % 169.19/169.65 [7176]~P39(x71761,x71763)+P39(x71761,f334(f334(f104(f886(f885(x71761,x71761),a871)),x71762),x71763)) % 169.19/169.65 [7177]~P39(x71771,x71772)+P39(x71771,f334(f334(f104(f886(f885(x71771,x71771),a871)),x71772),x71773)) % 169.19/169.65 [7295]~P95(x72951)+E(f12(x72951,f334(f173(x72951),f334(f334(f151(x72951),x72952),x72953))),f334(f142(x72951,x72951,f113(x72951),x72952),x72953)) % 169.19/169.65 [7296]~P95(x72961)+E(f13(x72961,f334(f173(x72961),f334(f334(f151(x72961),x72962),x72963))),f334(f142(x72961,x72961,f104(x72961),x72962),x72963)) % 169.19/169.65 [7297]~P107(x72971)+E(f16(x72971,f334(f173(x72971),f334(f334(f151(x72971),x72972),x72973))),f334(f142(x72971,x72971,f247(x72971),x72972),x72973)) % 169.19/169.65 [7298]~P107(x72981)+E(f17(x72981,f334(f173(x72981),f334(f334(f151(x72981),x72982),x72983))),f334(f142(x72981,x72981,f248(x72981),x72982),x72983)) % 169.19/169.65 [7358]~P104(f334(f63(x73581),x73582))+P104(f334(f334(f249(a877),f334(f39(x73581),x73582)),f334(f39(x73581),f334(f334(f312(x73581),x73583),x73582)))) % 169.19/169.65 [7366]E(f334(f334(f113(f886(a877,a871)),f334(f304(a877,x73661),x73662)),f334(f304(a877,x73662),f334(f334(f81(a877),x73662),x73663))),f334(f304(a877,x73661),f334(f334(f81(a877),x73662),x73663)))+~P104(f334(f334(f249(a877),x73661),x73662)) % 169.19/169.65 [7376]P104(f334(f334(f249(a877),x73761),x73762))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),x73763),x73761)),x73762)) % 169.19/169.65 [7377]P104(f334(f334(f249(a877),x73771),x73772))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),x73771),x73773)),x73772)) % 169.19/169.65 [7378]P104(f334(f334(f250(a877),x73781),x73782))+~P104(f334(f334(f250(a877),f334(f334(f81(a877),x73781),x73783)),x73782)) % 169.19/169.65 [7418]~P107(x74181)+E(f14(x74181,f247(x74181),f334(f173(x74181),f334(f334(f151(x74181),x74182),x74183))),f334(f142(x74181,x74181,f247(x74181),x74182),x74183)) % 169.19/169.65 [7419]~P107(x74191)+E(f15(x74191,f248(x74191),f334(f173(x74191),f334(f334(f151(x74191),x74192),x74193))),f334(f142(x74191,x74191,f248(x74191),x74192),x74193)) % 169.19/169.65 [7423]~E(x74232,f195(f886(f885(x74231,x74231),a871)))+P104(f334(f334(f249(f886(f885(x74231,x74231),a871)),x74232),x74233)) % 169.19/169.65 [7532]E(f334(f334(f113(f886(x75321,a871)),x75322),f334(f334(f3(f886(x75321,a871)),x75323),x75322)),x75323)+~P104(f334(f334(f249(f886(x75321,a871)),x75322),x75323)) % 169.19/169.65 [7533]~P104(f334(f334(f249(a877),x75331),f334(f334(f81(a877),x75333),x75332)))+P104(f334(f334(f249(a877),f334(f334(f3(a877),x75331),x75332)),x75333)) % 169.19/169.65 [7534]~P104(f334(f334(f250(a877),x75341),f334(f334(f3(a877),x75343),x75342)))+P104(f334(f334(f250(a877),f334(f334(f81(a877),x75341),x75342)),x75343)) % 169.19/169.65 [7591]E(x75911,f116(x75912))+E(f334(f141(x75912),f334(f334(f334(f190(f878(x75912),f878(x75912)),x75913),f168(x75912)),x75911)),f334(f334(f165(x75912),x75911),f46(a877,x75913,f334(f196(f878(x75912)),x75911)))) % 169.19/169.65 [7600]E(f334(f334(f312(x76001),x76002),f334(f334(f3(f886(x76001,a871)),x76003),f334(f334(f312(x76001),x76002),f195(f886(x76001,a871))))),x76003)+~P104(f334(f334(f336(x76001),x76002),x76003)) % 169.19/169.65 [7761]P104(f334(f334(f249(a877),x77611),f334(f334(f81(a877),x77612),x77613)))+~P104(f334(f334(f249(a877),f334(f334(f3(a877),x77611),x77613)),x77612)) % 169.19/169.65 [7762]P104(f334(f334(f250(a877),x77621),f334(f334(f3(a877),x77622),x77623)))+~P104(f334(f334(f250(a877),f334(f334(f81(a877),x77621),x77623)),x77622)) % 169.19/169.65 [7785]P104(f334(f63(x77851),x77852))+~P104(f334(f63(x77851),f334(f334(f113(f886(x77851,a871)),x77853),x77852))) % 169.19/169.65 [7786]P104(f334(f63(x77861),x77862))+~P104(f334(f63(x77861),f334(f334(f113(f886(x77861,a871)),x77862),x77863))) % 169.19/169.65 [7859]~P46(x78591,x78593)+P104(f334(f334(f336(f885(x78591,x78591)),f334(f334(f269(x78591,x78591),x78592),x78592)),x78593)) % 169.19/169.65 [7993]E(f334(f334(f165(a877),f139(a877,f334(f304(a877,x79931),x79932))),x79933),f334(f334(f81(a877),x79931),x79933))+~P104(f334(f334(f250(a877),f334(f334(f81(a877),x79931),x79933)),x79932)) % 169.19/169.65 [8059]E(f334(f334(f176(a877),x80591),f139(a877,f334(f304(a877,x80592),x80593))),f139(a877,f334(f304(a877,x80592),f334(f334(f81(a877),x80592),x80591))))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),x80592),x80591)),x80593)) % 169.19/169.65 [8112]~P92(x81121)+E(f334(f334(f259(x81121),x81122),f334(f106(a877),f334(f334(f81(a1),x81123),x81123))),f334(f334(f87(x81121,x81121),f334(f334(f259(x81121),x81122),f334(f106(a877),x81123))),f334(f334(f20(x81121,x81121,x81121),f82(x81121)),f7(x81121)))) % 169.19/169.65 [8377]E(f334(f334(f134(x83771),f334(f334(f176(x83771),x83772),x83773)),f334(f334(f151(x83771),f334(f334(f165(x83771),x83773),x83772)),f334(f334(f138(x83771),f334(a115,x83772)),x83773))),x83773)+~P104(f334(f334(f250(a877),x83772),f334(f196(f878(x83771)),x83773))) % 169.19/169.65 [8384]P104(f334(f334(f249(f886(x83841,a871)),f322(x83841,x83842)),f322(x83841,x83843)))+~P104(f334(f334(f249(f886(x83841,f886(x83841,a871))),x83843),x83842)) % 169.19/169.65 [8386]~P53(x83861,x83862,x83863)+P53(x83861,x83862,f334(f334(f3(f886(f885(x83861,x83861),a871)),x83863),f310(x83861,f195(f886(f885(x83861,x83861),a871))))) % 169.19/169.65 [8403]P104(f334(f334(f249(f886(x84031,a871)),f323(x84031,x84032)),f323(x84031,x84033)))+~P104(f334(f334(f249(f886(f885(x84031,x84031),a871)),x84033),x84032)) % 169.19/169.65 [8410]~P124(x84101)+P104(f334(f334(f249(x84101),f2(x84101)),f334(f334(f81(x84101),f334(f334(f82(x84101),x84102),x84102)),f334(f334(f82(x84101),x84103),x84103)))) % 169.19/169.65 [8443]P104(f334(f334(f249(f886(x84431,a871)),f334(f287(x84431),x84432)),f334(f287(x84431),x84433)))+~P104(f334(f334(f249(f886(f885(x84431,x84431),a871)),x84432),x84433)) % 169.19/169.65 [8473]~P50(x84731,x84732)+~P104(f334(f334(f336(f885(x84731,x84731)),f334(f334(f269(x84731,x84731),x84733),x84733)),x84732)) % 169.19/169.65 [8475]~P39(x84751,x84752)+~P104(f334(f334(f336(f885(x84751,x84751)),f334(f334(f269(x84751,x84751),x84753),x84753)),x84752)) % 169.19/169.65 [8530]P104(f334(f334(f249(f886(x85301,a871)),f41(f886(x85301,a871),x85302)),f41(f886(x85301,a871),x85303)))+~P104(f334(f334(f249(f886(f886(x85301,a871),a871)),x85302),x85303)) % 169.19/169.65 [8531]P104(f334(f334(f249(f886(x85311,a871)),f42(f886(x85311,a871),x85312)),f42(f886(x85311,a871),x85313)))+~P104(f334(f334(f249(f886(f886(x85311,a871),a871)),x85313),x85312)) % 169.19/169.65 [8583]~P6(x85831,x85833,x85832)+P104(f334(f334(f249(f886(f885(x85831,x85831),a871)),x85832),f334(f334(f271(x85831,x85831),x85833),f334(f18(f886(x85831,a871),x85831),x85833)))) % 169.19/169.65 [8584]~P49(x85841,x85843,x85842)+P104(f334(f334(f249(f886(f885(x85841,x85841),a871)),x85842),f334(f334(f271(x85841,x85841),x85843),f334(f18(f886(x85841,a871),x85841),x85843)))) % 169.19/169.65 [8631]~P83(x86311)+P104(f334(f334(f249(x86311),f334(f334(f3(x86311),f334(f76(x86311),x86312)),f334(f76(x86311),x86313))),f334(f76(x86311),f334(f334(f3(x86311),x86313),x86312)))) % 169.19/169.65 [8632]~P83(x86321)+P104(f334(f334(f249(x86321),f334(f334(f3(x86321),f334(f76(x86321),x86322)),f334(f76(x86321),x86323))),f334(f76(x86321),f334(f334(f3(x86321),x86322),x86323)))) % 169.19/169.65 [8661]P104(f334(f334(f249(f886(f885(x86611,x86611),a871)),f310(x86611,x86612)),f310(x86611,x86613)))+~P104(f334(f334(f249(f886(f885(x86611,x86611),a871)),x86612),x86613)) % 169.19/169.65 [8816]P53(x88161,x88162,x88163)+~P53(x88161,x88162,f334(f334(f3(f886(f885(x88161,x88161),a871)),x88163),f310(x88161,f195(f886(f885(x88161,x88161),a871))))) % 169.19/169.65 [8834]P104(f334(f334(f249(f886(f885(f878(x88341),f878(x88341)),a871)),f158(x88341,x88342)),f158(x88341,x88343)))+~P104(f334(f334(f249(f886(f885(x88341,x88341),a871)),x88342),x88343)) % 169.19/169.65 [8835]P104(f334(f334(f249(f886(f885(f878(x88351),f878(x88351)),a871)),f157(x88351,x88352)),f157(x88351,x88353)))+~P104(f334(f334(f249(f886(f885(x88351,x88351),a871)),x88352),x88353)) % 169.19/169.65 [8854]~P49(x88541,x88543,x88542)+P104(f334(f334(f249(f886(f885(x88541,x88541),a871)),x88542),f334(f334(f291(x88541,x88541,x88541),f334(f289(x88541,x88541),x88542)),x88542))) % 169.19/169.65 [8904]~P104(f334(f137(x89041),x89042))+E(f334(f136(x89041,f334(f334(f9(x89041,f886(x89041,a871),a871),f336(x89041)),f334(f173(x89041),f177(x89041,x89042,x89043)))),x89042),f177(x89041,x89042,x89043)) % 169.19/169.65 [8961]E(x89611,x89612)+~P104(f334(f334(f336(f885(x89613,x89613)),f334(f334(f269(x89613,x89613),x89611),x89612)),f310(x89613,f195(f886(f885(x89613,x89613),a871))))) % 169.19/169.65 [9041]P104(f334(f334(f336(x90411),x90412),f323(x90411,x90413)))+P104(f334(f334(f336(f885(x90411,x90411)),f334(f334(f269(x90411,x90411),f673(x90413,x90412,x90411)),x90412)),x90413)) % 169.19/169.65 [9042]P104(f334(f334(f336(x90421),x90422),f323(x90421,x90423)))+P104(f334(f334(f336(f885(x90421,x90421)),f334(f334(f269(x90421,x90421),f737(x90423,x90422,x90421)),x90422)),x90423)) % 169.19/169.65 [9043]P104(f334(f334(f336(x90431),x90432),f323(x90431,x90433)))+P104(f334(f334(f336(f885(x90431,x90431)),f334(f334(f269(x90431,x90431),f746(x90433,x90432,x90431)),x90432)),x90433)) % 169.19/169.65 [9129]~P104(f334(f334(f336(f878(x91291)),x91293),f161(x91291,x91292)))+P104(f334(f160(x91291,f334(f334(f9(x91291,f886(x91291,a871),a871),f336(x91291)),x91292)),x91293)) % 169.19/169.65 [9150]P104(f334(x91503,x91502))+E(f334(f254(x91501),f334(f334(f20(x91501,a871,a871),f334(f334(f10(a871,f886(a871,a871),x91501),a332),f334(a331,x91502))),x91503)),f195(f886(x91501,a871))) % 169.19/169.65 [9168]~P83(x91681)+P104(f334(f334(f249(x91681),f334(f76(x91681),f334(f334(f3(x91681),f334(f76(x91681),x91682)),f334(f76(x91681),x91683)))),f334(f76(x91681),f334(f334(f3(x91681),x91682),x91683)))) % 169.19/169.65 [9182]~P104(f334(x91823,x91822))+E(f334(f254(x91821),f334(f334(f20(x91821,a871,a871),f334(f334(f10(a871,f886(a871,a871),x91821),a332),f334(a331,x91822))),x91823)),f334(f334(f312(x91821),x91822),f195(f886(x91821,a871)))) % 169.19/169.65 [9189]~P104(f334(f334(f336(f886(x91891,a871)),x91893),f334(f311(x91891),x91892)))+P104(f334(f262(x91891,f334(f334(f9(x91891,f886(x91891,a871),a871),f336(x91891)),x91892)),x91893)) % 169.19/169.65 [9222]P39(x92221,x92222)+P104(f334(f334(f336(f885(x92221,x92221)),f334(f334(f269(x92221,x92221),f334(f683(x92222,x92221),f334(a115,x92223))),f334(f683(x92222,x92221),x92223))),x92222)) % 169.19/169.65 [9353]P104(f334(f334(f336(f878(x93531)),x93532),f161(x93531,x93533)))+~P104(f334(f160(x93531,f334(f334(f9(x93531,f886(x93531,a871),a871),f336(x93531)),x93533)),x93532)) % 169.19/169.65 [9365]P104(f334(f334(f336(f886(x93651,a871)),x93652),f334(f311(x93651),x93653)))+~P104(f334(f262(x93651,f334(f334(f9(x93651,f886(x93651,a871),a871),f336(x93651)),x93653)),x93652)) % 169.19/169.65 [9420]P104(f334(f334(f336(x94201),f334(f280(x94201,x94202),x94203)),f334(f173(x94201),f334(f334(f154(f885(a102,x94201),x94201),f272(a102,x94201)),x94202))))+~P104(f334(f334(f250(a102),x94203),f334(f166(a102),f334(f334(f154(f885(a102,x94201),a102),f268(a102,x94201)),x94202)))) % 169.19/169.65 [9467]P104(f334(f334(f249(f886(f885(f878(x94671),f878(x94671)),a871)),f158(x94671,x94672)),f334(f334(f271(f878(x94671),f878(x94671)),f161(x94671,x94673)),f334(f18(f886(f878(x94671),a871),f878(x94671)),f161(x94671,x94673)))))+~P104(f334(f334(f249(f886(f885(x94671,x94671),a871)),x94672),f334(f334(f271(x94671,x94671),x94673),f334(f18(f886(x94671,a871),x94671),x94673)))) % 169.19/169.65 [9487]P104(f334(f334(f336(x94871),f334(f268(x94871,f885(a102,a102)),f334(f278(x94871,x94872),x94873))),f334(f173(x94871),f334(f334(f154(f885(a102,x94871),x94871),f272(a102,x94871)),x94872))))+~P104(f334(f334(f250(a102),f2(a102)),f334(f166(a102),f334(f334(f154(f885(a102,x94871),a102),f268(a102,x94871)),x94872)))) % 169.19/169.65 [9501]~P104(f334(f334(f249(f886(f885(x95011,x95011),a871)),x95012),f334(f334(f271(x95011,x95011),x95013),f334(f18(f886(x95011,a871),x95011),x95013))))+P104(f334(f334(f249(f886(f885(x95011,x95011),a871)),f334(f334(f291(x95011,x95011,x95011),x95012),f310(x95011,x95012))),f334(f334(f271(x95011,x95011),x95013),f334(f18(f886(x95011,a871),x95011),x95013)))) % 169.19/169.65 [9805]~P39(x98051,x98052)+~P104(f334(f334(f336(f885(x98051,x98051)),f334(f334(f269(x98051,x98051),f334(x98053,f334(a115,f685(x98052,x98051,x98053)))),f334(x98053,f685(x98052,x98051,x98053)))),x98052)) % 169.19/169.65 [9806]~P39(x98061,x98062)+~P104(f334(f334(f336(f885(x98061,x98061)),f334(f334(f269(x98061,x98061),f334(x98063,f334(a115,f751(x98063,x98062,x98061)))),f334(x98063,f751(x98063,x98062,x98061)))),x98062)) % 169.19/169.65 [10055]P104(f334(f334(f249(f886(f885(f886(x100551,a871),f886(x100551,a871)),a871)),f334(f334(f291(f886(x100551,a871),f886(x100551,a871),f886(x100551,a871)),f325(x100551,x100552)),f334(f334(f113(f886(f885(f886(x100551,a871),f886(x100551,a871)),a871)),f325(x100551,x100553)),f334(f334(f312(f885(f886(x100551,a871),f886(x100551,a871))),f334(f334(f269(f886(x100551,a871),f886(x100551,a871)),f195(f886(x100551,a871))),f195(f886(x100551,a871)))),f195(f886(f885(f886(x100551,a871),f886(x100551,a871)),a871)))))),f325(x100551,x100552)))+~P104(f334(f334(f249(f886(f885(x100551,x100551),a871)),f334(f334(f291(x100551,x100551,x100551),x100552),x100553)),x100552)) % 169.19/169.65 [10056]P104(f334(f334(f249(f886(f885(f886(x100561,a871),f886(x100561,a871)),a871)),f334(f334(f291(f886(x100561,a871),f886(x100561,a871),f886(x100561,a871)),f326(x100561,x100562)),f334(f334(f113(f886(f885(f886(x100561,a871),f886(x100561,a871)),a871)),f326(x100561,x100563)),f334(f334(f312(f885(f886(x100561,a871),f886(x100561,a871))),f334(f334(f269(f886(x100561,a871),f886(x100561,a871)),f195(f886(x100561,a871))),f195(f886(x100561,a871)))),f195(f886(f885(f886(x100561,a871),f886(x100561,a871)),a871)))))),f326(x100561,x100562)))+~P104(f334(f334(f249(f886(f885(x100561,x100561),a871)),f334(f334(f291(x100561,x100561,x100561),x100562),x100563)),x100562)) % 169.19/169.65 [7294]~P104(f334(f334(f249(a877),x72942),x72941))+E(f334(f334(f3(a877),f334(a115,f334(f334(f3(a877),x72941),x72942))),x72943),f334(f334(f3(a877),f334(a115,x72941)),f334(f334(f81(a877),x72942),x72943))) % 169.19/169.65 [7333]~P26(x73331)+E(f334(f334(f81(x73331),f46(x73331,x73332,x73333)),f334(f334(f82(x73331),f334(f334(f40(x73331),x73332),x73333)),x73333)),x73332) % 169.19/169.65 [7538]E(f334(f334(f82(a877),f334(f106(a877),x75381)),f334(f334(f82(a877),f334(f106(a877),x75382)),x75383)),f334(f334(f82(a877),f334(f106(a877),f334(f334(f82(a1),x75381),x75382))),x75383))+P104(f334(f334(f250(a1),x75381),a84)) % 169.19/169.65 [8002]~P104(f334(f334(f249(a877),x80023),x80022))+P104(f334(f334(f249(a877),x80021),f334(f334(f3(a877),f334(f334(f81(a877),x80022),x80021)),x80023))) % 169.19/169.65 [8199]~P104(f334(f334(f249(a877),x81991),x81992))+E(f334(f334(f134(a877),f139(a877,f334(f304(a877,x81991),x81992))),f139(a877,f334(f304(a877,x81992),f334(f334(f81(a877),x81992),x81993)))),f139(a877,f334(f304(a877,x81991),f334(f334(f81(a877),x81992),x81993)))) % 169.19/169.65 [8452]~P104(f334(f63(x84521),x84522))+E(f334(a115,f334(f39(x84521),f334(f334(f3(f886(x84521,a871)),x84522),f334(f334(f312(x84521),x84523),f195(f886(x84521,a871)))))),f334(f39(x84521),f334(f334(f312(x84521),x84523),x84522))) % 169.19/169.65 [8493]~P104(f334(f63(x84931),x84932))+E(f334(f334(f81(a877),f79(a877)),f334(f39(x84931),f334(f334(f3(f886(x84931,a871)),x84932),f334(f334(f312(x84931),x84933),f195(f886(x84931,a871)))))),f334(f39(x84931),f334(f334(f312(x84931),x84933),x84932))) % 169.19/169.65 [8670]E(f334(f334(f3(a877),f334(f39(x86701),x86702)),f334(f39(x86701),f334(f334(f104(f886(x86701,a871)),x86702),x86703))),f334(f39(x86701),f334(f334(f3(f886(x86701,a871)),x86702),x86703)))+~P104(f334(f63(x86701),f334(f334(f104(f886(x86701,a871)),x86702),x86703))) % 169.19/169.65 [8900]~P29(f334(x89002,f490(x89002,x89003,x89001)))+E(f334(f103(a1),f334(f334(f8(x89001,a877),f334(f334(f10(a1,a877,x89001),a107),x89002)),x89003)),f334(f334(f8(x89001,a1),x89002),x89003)) % 169.19/169.65 [8901]~P29(f334(x89012,f491(x89012,x89013,x89011)))+E(f334(f103(a1),f334(f334(f11(x89011,a877),f334(f334(f10(a1,a877,x89011),a107),x89012)),x89013)),f334(f334(f11(x89011,a1),x89012),x89013)) % 169.19/169.65 [8946]~P104(f334(f63(x89461),x89463))+P104(f334(f334(f249(a877),f334(f334(f3(a877),f334(f39(x89461),x89462)),f334(f39(x89461),x89463))),f334(f39(x89461),f334(f334(f3(f886(x89461,a871)),x89462),x89463)))) % 169.19/169.65 [8969]P104(f334(f334(f336(x89691),f490(x89692,x89693,x89691)),x89693))+E(f334(f103(a1),f334(f334(f8(x89691,a877),f334(f334(f10(a1,a877,x89691),a107),x89692)),x89693)),f334(f334(f8(x89691,a1),x89692),x89693)) % 169.19/169.65 [8970]P104(f334(f334(f336(x89701),f491(x89702,x89703,x89701)),x89703))+E(f334(f103(a1),f334(f334(f11(x89701,a877),f334(f334(f10(a1,a877,x89701),a107),x89702)),x89703)),f334(f334(f11(x89701,a1),x89702),x89703)) % 169.19/169.65 [9033]E(f86(x90331,f334(f334(f9(x90331,f886(x90331,a871),a871),f336(x90331)),f334(f334(f3(f886(x90331,a871)),x90332),f334(f334(f312(x90331),x90333),f195(f886(x90331,a871)))))),f261(x90331,x90333,x90332))+P104(f334(f334(f249(f886(x90331,a871)),x90332),f334(f334(f312(x90331),x90333),f195(f886(x90331,a871))))) % 169.19/169.65 [9366]E(f334(f334(f154(f878(x93661),x93661),f334(f334(f9(f878(x93661),a877,x93661),f165(x93661)),x93662)),f334(f136(f878(x93661),f334(f334(f10(a877,a871,f878(x93661)),f334(f250(a877),x93662)),f196(f878(x93661)))),x93663)),f334(f334(f165(f878(x93661)),f181(x93661,x93663)),x93662))+~P104(f334(f334(f250(a877),x93662),f334(f196(f878(f878(x93661))),f181(x93661,x93663)))) % 169.19/169.65 [9437]E(f334(f136(x94371,x94372),x94373),f178(x94371,x94372,x94373))+P104(f334(f334(f336(x94371),f658(x94373,x94372,x94371)),f334(f173(x94371),f334(f334(f138(x94371),f334(f196(f878(x94371)),f178(x94371,x94372,x94373))),x94373)))) % 169.19/169.65 [9572]E(f334(f334(f138(x95721),f334(f196(f878(x95721)),f178(x95721,x95722,x95723))),x95723),f116(x95721))+~P104(f334(x95722,f334(f141(x95721),f334(f334(f138(x95721),f334(f196(f878(x95721)),f178(x95721,x95722,x95723))),x95723)))) % 169.19/169.65 [9665]~P104(f334(f334(f336(f885(x96651,x96651)),x96652),f310(x96651,x96653)))+P104(f334(f334(f336(f885(x96651,x96651)),x96652),f334(f334(f44(a877,f886(f885(x96651,x96651),a871)),f257(f886(a877,a871))),f334(f334(f9(a877,f886(f885(x96651,x96651),a871),f886(f885(x96651,x96651),a871)),f190(f885(x96651,x96651),a871)),x96653)))) % 169.19/169.65 [9722]~P104(f334(f334(f249(f886(x97221,a871)),f334(f334(f44(a877,f886(x97221,a871)),f334(f304(a877,f2(a877)),f540(x97223,x97222,x97221))),x97222)),x97223))+P104(f334(f334(f249(f886(x97221,a871)),f334(f334(f44(a877,f886(x97221,a871)),f257(f886(a877,a871))),x97222)),x97223)) % 169.19/169.65 [9780]~P104(f334(f334(f250(a1),f2(a1)),x97803))+P104(f334(f334(f250(a1),x97801),f334(f334(f81(a1),x97802),f334(f334(f82(a1),f334(f334(f81(a1),f334(f76(a1),f334(f334(f3(a1),x97802),x97801))),f79(a1))),x97803)))) % 169.19/169.65 [9792]~P39(x97921,f334(f334(f113(f886(f885(x97921,x97921),a871)),x97922),x97923))+P39(x97921,f334(f334(f113(f886(f885(x97921,x97921),a871)),f334(f334(f113(f886(f885(x97921,x97921),a871)),f334(f334(f291(x97921,x97921,x97921),x97922),x97922)),f334(f334(f291(x97921,x97921,x97921),x97923),x97922))),x97923)) % 169.19/169.65 [9871]P39(x98711,f334(f334(f113(f886(f885(x98711,x98711),a871)),x98712),x98713))+~P39(x98711,f334(f334(f113(f886(f885(x98711,x98711),a871)),f334(f334(f113(f886(f885(x98711,x98711),a871)),f334(f334(f291(x98711,x98711,x98711),x98712),x98712)),f334(f334(f291(x98711,x98711,x98711),x98713),x98712))),x98713)) % 169.19/169.65 [9440]~P137(x94401)+E(f334(f105(x94401),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x94402),x94403)),f195(f886(f885(a877,a877),a871)))))),f334(f334(f3(x94401),f334(f103(x94401),x94402)),f334(f103(x94401),x94403))) % 169.19/169.65 [9519]P104(f334(x95193,x95192))+E(f334(f254(x95191),f334(f334(f20(x95191,a871,a871),f334(f334(f10(a871,f886(a871,a871),x95191),a332),f334(f334(f9(x95191,x95191,a871),a331),x95192))),x95193)),f195(f886(x95191,a871))) % 169.19/169.65 [9521]~P104(f334(x95213,x95212))+E(f334(f254(x95211),f334(f334(f20(x95211,a871,a871),f334(f334(f10(a871,f886(a871,a871),x95211),a332),f334(f334(f9(x95211,x95211,a871),a331),x95212))),x95213)),f334(f334(f312(x95211),x95212),f195(f886(x95211,a871)))) % 169.19/169.65 [9758]E(x97581,x97582)+P104(f334(f334(f258(x97583,x97583,f334(f334(f10(f886(x97583,a871),f886(x97583,a871),x97583),f334(f10(a871,a871,x97583),a329)),a331)),x97581),x97582)) % 169.19/169.65 [9849]~E(x98491,x98492)+~P104(f334(f334(f258(x98493,x98493,f334(f334(f10(f886(x98493,a871),f886(x98493,a871),x98493),f334(f10(a871,a871,x98493),a329)),a331)),x98491),x98492)) % 169.19/169.65 [9863]~P104(f334(f63(x98631),x98633))+E(f334(f334(f66(x98631,f886(x98631,a871),f334(f334(f10(f886(x98631,a871),f886(f886(x98631,a871),f886(x98631,a871)),x98631),f334(f9(f886(x98631,a871),f886(x98631,a871),f886(x98631,a871)),f3(f886(x98631,a871)))),f334(f334(f9(x98631,f886(x98631,a871),f886(x98631,a871)),f312(x98631)),f195(f886(x98631,a871))))),x98632),x98633),f334(f334(f3(f886(x98631,a871)),x98632),x98633)) % 169.19/169.65 [9895]~P104(f334(f334(f250(a1),f2(a1)),x98953))+P104(f334(f334(f250(a1),f334(f334(f3(a1),x98951),f334(f334(f82(a1),f334(f334(f81(a1),f334(f76(a1),f334(f334(f3(a1),x98951),x98952))),f79(a1))),x98953))),x98952)) % 169.19/169.65 [10118]~P104(f334(f334(f336(x101181),x101183),f323(x101181,x101182)))+P104(f334(f322(x101181,f334(f334(f9(x101181,f886(f885(x101181,x101181),a871),f886(x101181,a871)),f334(f334(f10(f886(x101181,f886(f886(f885(x101181,x101181),a871),a871)),f886(f886(f885(x101181,x101181),a871),f886(x101181,a871)),x101181),f9(x101181,f886(f885(x101181,x101181),a871),a871)),f334(f334(f10(f886(x101181,f885(x101181,x101181)),f886(x101181,f886(f886(f885(x101181,x101181),a871),a871)),x101181),f334(f10(f885(x101181,x101181),f886(f886(f885(x101181,x101181),a871),a871),x101181),f336(f885(x101181,x101181)))),f269(x101181,x101181)))),x101182)),x101183)) % 169.19/169.65 [10131]P104(f334(f334(f336(x101311),x101312),f323(x101311,x101313)))+~P104(f334(f322(x101311,f334(f334(f9(x101311,f886(f885(x101311,x101311),a871),f886(x101311,a871)),f334(f334(f10(f886(x101311,f886(f886(f885(x101311,x101311),a871),a871)),f886(f886(f885(x101311,x101311),a871),f886(x101311,a871)),x101311),f9(x101311,f886(f885(x101311,x101311),a871),a871)),f334(f334(f10(f886(x101311,f885(x101311,x101311)),f886(x101311,f886(f886(f885(x101311,x101311),a871),a871)),x101311),f334(f10(f885(x101311,x101311),f886(f886(f885(x101311,x101311),a871),a871),x101311),f336(f885(x101311,x101311)))),f269(x101311,x101311)))),x101313)),x101312)) % 169.19/169.65 [9720]~P104(f334(f63(x97201),f334(f254(x97201),x97203)))+P104(f334(f63(x97201),f334(f254(x97201),f334(f334(f20(x97201,a871,a871),f334(f334(f10(a871,f886(a871,a871),x97201),a332),x97202)),x97203)))) % 169.19/169.65 [9721]~P104(f334(f63(x97211),f334(f254(x97211),x97212)))+P104(f334(f63(x97211),f334(f254(x97211),f334(f334(f20(x97211,a871,a871),f334(f334(f10(a871,f886(a871,a871),x97211),a332),x97212)),x97213)))) % 169.19/169.65 [9824]P104(f334(f63(x98241),f334(f254(x98241),x98242)))+~P104(f334(f63(x98241),f334(f254(x98241),f334(f334(f20(x98241,a871,a871),f334(f334(f10(a871,f886(a871,a871),x98241),a333),x98243)),x98242)))) % 169.19/169.65 [9825]P104(f334(f63(x98251),f334(f254(x98251),x98252)))+~P104(f334(f63(x98251),f334(f254(x98251),f334(f334(f20(x98251,a871,a871),f334(f334(f10(a871,f886(a871,a871),x98251),a333),x98252)),x98253)))) % 169.19/169.65 [10103]~P104(f334(f63(x101031),x101032))+P104(f334(f63(f878(x101031)),f334(f254(f878(x101031)),f334(f334(f20(f878(x101031),a871,a871),f334(f334(f10(a871,f886(a871,a871),f878(x101031)),a332),f334(f334(f9(f878(x101031),f886(x101031,a871),a871),f334(f334(f10(f886(x101031,a871),f886(f886(x101031,a871),a871),f878(x101031)),f249(f886(x101031,a871))),f173(x101031))),x101032))),f334(f334(f9(f878(x101031),a877,a871),f334(f334(f10(a877,f886(a877,a871),f878(x101031)),a331),f196(f878(x101031)))),x101033))))) % 169.19/169.65 [10104]~P104(f334(f63(x101041),x101042))+P104(f334(f63(f878(x101041)),f334(f254(f878(x101041)),f334(f334(f20(f878(x101041),a871,a871),f334(f334(f10(a871,f886(a871,a871),f878(x101041)),a332),f334(f334(f9(f878(x101041),f886(x101041,a871),a871),f334(f334(f10(f886(x101041,a871),f886(f886(x101041,a871),a871),f878(x101041)),f249(f886(x101041,a871))),f173(x101041))),x101042))),f334(f334(f9(f878(x101041),a877,a871),f334(f334(f10(a877,f886(a877,a871),f878(x101041)),f249(a877)),f196(f878(x101041)))),x101043))))) % 169.19/169.65 [9838]~P115(x98381)+E(f334(f334(f259(x98381),x98382),f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x98383)),f334(f334(f82(x98381),f334(f334(f259(x98381),x98382),x98383)),f334(f334(f259(x98381),x98382),x98383))) % 169.19/169.65 [9876]~P77(x98761)+E(f334(f334(f259(x98761),f334(f334(f259(x98761),x98762),x98763)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f259(x98761),x98762),f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x98763))) % 169.19/169.65 [9922]~P137(x99221)+E(f334(f334(f259(x99221),f334(f80(x99221),x99222)),f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99223)),f334(f334(f259(x99221),x99222),f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99223))) % 169.19/169.65 [10062]~P120(x100621)+P104(f334(f334(f249(x100621),f2(x100621)),f334(f334(f81(x100621),f334(f334(f259(x100621),x100622),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x100621),x100623),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))))) % 169.19/169.65 [9932]~P115(x99321)+E(f334(f334(f259(x99321),x99322),f334(a115,f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99323))),f334(f334(f82(x99321),x99322),f334(f334(f82(x99321),f334(f334(f259(x99321),x99322),x99323)),f334(f334(f259(x99321),x99322),x99323)))) % 169.19/169.65 [9981]~P77(x99811)+E(f334(f334(f82(x99811),x99812),f334(f334(f259(x99811),f334(f334(f259(x99811),x99812),x99813)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x99811),x99812),f334(a115,f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99813)))) % 169.19/169.65 [10020]~P120(x100201)+P104(f334(f334(f249(x100201),f2(x100201)),f334(f334(f259(x100201),x100202),f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100203)))) % 169.19/169.65 [10084]~P92(x100841)+E(f334(f334(f3(x100841),f334(f334(f81(x100841),f334(f334(f259(x100841),x100842),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x100841),x100843),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f334(f334(f82(x100841),f334(f334(f82(x100841),f334(f106(x100841),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100842)),x100843)),f334(f334(f259(x100841),f334(f334(f3(x100841),x100842),x100843)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [10085]~P92(x100851)+E(f334(f334(f81(x100851),f334(f334(f81(x100851),f334(f334(f259(x100851),x100852),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x100851),x100853),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f334(f334(f82(x100851),f334(f334(f82(x100851),f334(f106(x100851),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x100852)),x100853)),f334(f334(f259(x100851),f334(f334(f81(x100851),x100852),x100853)),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [4717]E(x47171,x47172)+~E(f34(x47173,x47171),f34(x47174,x47172)) % 169.19/169.65 [4718]E(x47181,x47182)+~E(f34(x47181,x47183),f34(x47182,x47184)) % 169.19/169.65 [4719]E(x47191,x47192)+~E(f33(x47193,x47191),f33(x47194,x47192)) % 169.19/169.65 [4720]E(x47201,x47202)+~E(f33(x47201,x47203),f33(x47202,x47204)) % 169.19/169.65 [7803]P21(x78031,x78032,x78033,x78034)+~E(f762(x78034,x78033,x78032,x78031),f786(x78034,x78033,x78032,x78031)) % 169.19/169.65 [8091]P36(x80911,x80912,x80913,x80914,f116(x80912))+~E(x80914,f116(x80911)) % 169.19/169.65 [8092]P36(x80921,x80922,x80923,f116(x80921),x80924)+~E(x80924,f116(x80922)) % 169.19/169.65 [8304]~P21(x83041,f881(x83042),x83044,f185(x83041,x83042,x83044))+P21(x83041,f881(x83042),f186(x83041,x83042,x83043,x83044),f185(x83041,x83042,x83044)) % 169.19/169.65 [8507]~P21(x85071,f881(x85072),f186(x85071,x85072,x85074,x85073),f185(x85071,x85072,x85073))+P21(x85071,f881(x85072),x85073,f185(x85071,x85072,x85073)) % 169.19/169.65 [8621]~P36(x86212,x86213,x86214,x86211,f116(x86213))+E(x86211,f116(x86212)) % 169.19/169.65 [8622]~P36(x86223,x86222,x86224,f116(x86223),x86221)+E(x86221,f116(x86222)) % 169.19/169.65 [5096]~P13(x50963,x50961,x50964)+E(f334(f334(x50961,x50962),x50962),x50962) % 169.19/169.65 [5355]P104(f334(x53552,x53554))+E(f334(f136(x53551,x53552),f170(x53551,x53553,x53554)),f116(x53551)) % 169.19/169.65 [5391]~E(x53914,f195(f886(x53911,a871)))+E(f334(f313(x53911,x53912,x53913),x53914),f195(f886(x53912,a871))) % 169.19/169.65 [5631]~P104(f334(x56312,x56314))+E(f334(f136(x56311,x56312),f170(x56311,x56313,x56314)),f170(x56311,x56313,x56314)) % 169.19/169.65 [5660]~E(f334(f313(x56602,x56603,x56604),x56601),f195(f886(x56603,a871)))+E(x56601,f195(f886(x56602,a871))) % 169.19/169.65 [5944]~P107(x59442)+E(f334(f334(f148(x59441,x59442,x59443),x59444),f116(x59441)),f334(f334(f151(x59441),x59444),f116(x59441))) % 169.19/169.65 [5981]E(f334(x59811,x59812),f198(x59813))+P104(f334(f334(f336(x59814),x59812),f185(x59814,x59813,x59811))) % 169.19/169.65 [6303]~E(x63031,f195(f886(x63032,a871)))+~P104(f334(f64(x63032,x63033,x63031),x63034)) % 169.19/169.65 [6324]~P56(x63241,x63243,x63244,x63242)+P104(f334(f63(x63241),x63242)) % 169.19/169.65 [6325]~P56(x63251,x63253,x63252,x63254)+P104(f334(f63(x63251),x63252)) % 169.19/169.65 [6331]~P56(x63312,x63313,x63314,x63311)+~E(x63311,f195(f886(x63312,a871))) % 169.19/169.65 [6362]~P108(x63621)+E(f334(f334(f104(f886(x63621,a871)),f334(f304(x63621,x63622),x63623)),f305(x63621,x63623,x63624)),f195(f886(x63621,a871))) % 169.19/169.65 [6389]~P104(f334(f334(x63893,x63894),x63892))+P104(f334(f334(f336(x63891),x63892),f295(x63891,x63893,x63894))) % 169.19/169.65 [6390]~P104(f334(f334(x63903,x63904),x63902))+P104(f334(f334(f336(x63901),x63902),f296(x63901,x63903,x63904))) % 169.19/169.65 [6391]~P104(f334(f334(x63913,x63912),x63914))+P104(f334(f334(f336(x63911),x63912),f297(x63911,x63913,x63914))) % 169.19/169.65 [6392]~P104(f334(f334(x63923,x63922),x63924))+P104(f334(f334(f336(x63921),x63922),f300(x63921,x63923,x63924))) % 169.19/169.65 [6533]~P108(x65331)+E(f334(f334(f104(f886(x65331,a871)),f308(x65331,x65332,x65333)),f305(x65331,x65333,x65334)),f195(f886(x65331,a871))) % 169.19/169.65 [6534]~P108(x65341)+E(f334(f334(f104(f886(x65341,a871)),f305(x65341,x65342,x65343)),f308(x65341,x65343,x65344)),f195(f886(x65341,a871))) % 169.19/169.65 [6535]~P108(x65351)+E(f334(f334(f104(f886(x65351,a871)),f305(x65351,x65352,x65353)),f307(x65351,x65353,x65354)),f195(f886(x65351,a871))) % 169.19/169.65 [6536]~P108(x65361)+E(f334(f334(f104(f886(x65361,a871)),f307(x65361,x65362,x65363)),f308(x65361,x65363,x65364)),f195(f886(x65361,a871))) % 169.19/169.65 [6537]~P108(x65371)+E(f334(f334(f104(f886(x65371,a871)),f307(x65371,x65372,x65373)),f307(x65371,x65373,x65374)),f195(f886(x65371,a871))) % 169.19/169.65 [6574]P104(f334(f334(x65741,x65742),f679(x65742,x65741)))+~P104(f334(f263(x65743,x65744,x65741),x65742)) % 169.19/169.65 [6622]~E(f334(x66221,x66222),f198(x66223))+~P104(f334(f334(f336(x66224),x66222),f185(x66224,x66223,x66221))) % 169.19/169.65 [6651]~P107(x66512)+E(f334(f173(x66511),f150(x66511,x66512,x66513,x66514)),f334(f173(x66511),x66514)) % 169.19/169.65 [6702]~P142(x67021)+E(f197(x67021,x67022,f334(a115,x67023),x67024),f197(x67021,x67022,x67023,f334(x67022,x67024))) % 169.19/169.65 [6762]~P104(f334(f334(f336(x67624),x67623),f295(x67624,x67621,x67622)))+P104(f334(f334(x67621,x67622),x67623)) % 169.19/169.65 [6763]~P104(f334(f334(f336(x67634),x67633),f296(x67634,x67631,x67632)))+P104(f334(f334(x67631,x67632),x67633)) % 169.19/169.65 [6764]~P104(f334(f334(f336(x67644),x67642),f297(x67644,x67641,x67643)))+P104(f334(f334(x67641,x67642),x67643)) % 169.19/169.65 [6765]~P104(f334(f334(f336(x67654),x67652),f300(x67654,x67651,x67653)))+P104(f334(f334(x67651,x67652),x67653)) % 169.19/169.65 [6842]E(f334(f39(f884(x68421,x68422)),f321(x68421,x68422,x68423,x68424)),f2(a877))+P104(f334(f63(x68422),x68424)) % 169.19/169.65 [6843]E(f334(f39(f884(x68431,x68432)),f321(x68431,x68432,x68433,x68434)),f2(a877))+P104(f334(f63(x68431),x68433)) % 169.19/169.65 [7044]~P11(x70444,x70441,x70442)+E(f334(f74(x70441,x70441,x70441,f334(x70442,x70443)),f334(x70442,x70443)),f334(x70442,x70443)) % 169.19/169.65 [7923]~E(x79232,x79233)+P104(f334(f334(f336(f885(x79231,x79231)),f334(f334(f269(x79231,x79231),x79232),x79233)),f310(x79231,x79234))) % 169.19/169.65 [7951]~P21(x79511,x79512,x79513,f257(f886(x79511,a871)))+E(f334(f78(x79511,x79512,f257(f886(x79511,a871)),x79513),f334(x79513,x79514)),x79514) % 169.19/169.65 [8042]~P104(f334(f334(f336(f878(x80421)),f334(f334(f151(x80421),x80424),x80422)),f161(x80421,x80423)))+P104(f334(f334(f336(f878(x80421)),x80422),f161(x80421,x80423))) % 169.19/169.65 [8043]~P104(f334(f334(f336(f878(x80431)),f334(f334(f134(x80431),x80434),x80432)),f161(x80431,x80433)))+P104(f334(f334(f336(f878(x80431)),x80432),f161(x80431,x80433))) % 169.19/169.65 [8044]~P104(f334(f334(f336(f878(x80441)),f334(f334(f134(x80441),x80442),x80444)),f161(x80441,x80443)))+P104(f334(f334(f336(f878(x80441)),x80442),f161(x80441,x80443))) % 169.19/169.65 [8055]~P107(x80551)+P30(x80551,f334(f334(f154(x80552,x80551),x80553),f150(x80552,x80551,x80553,x80554))) % 169.19/169.65 [8152]P21(x81524,x81523,x81521,x81522)+E(f334(x81521,f762(x81522,x81521,x81523,x81524)),f334(x81521,f786(x81522,x81521,x81523,x81524))) % 169.19/169.65 [8164]E(f186(x81641,x81642,x81643,x81644),f186(x81641,x81642,x81644,x81643))+~E(f334(f334(f104(f886(x81641,a871)),f185(x81641,x81642,x81643)),f185(x81641,x81642,x81644)),f195(f886(x81641,a871))) % 169.19/169.65 [8267]~P21(x82672,x82671,x82674,x82673)+P21(x82671,x82672,f78(x82672,x82671,x82673,x82674),f334(f313(x82672,x82671,x82674),x82673)) % 169.19/169.65 [8401]P39(f885(x84012,x84014),f286(x84012,x84014,x84011,x84013))+P104(f334(x84011,f681(x84012,x84013,x84014,x84011))) % 169.19/169.65 [8514]E(x85141,x85142)+~P104(f334(f334(f336(f885(x85143,x85143)),f334(f334(f269(x85143,x85143),x85141),x85142)),f266(x85143,x85144))) % 169.19/169.65 [8575]~P104(f334(f63(f884(x85753,x85751)),f321(x85753,x85751,x85754,x85752)))+P104(f334(f63(x85751),x85752)) % 169.19/169.65 [8576]~P104(f334(f63(f884(x85761,x85763)),f321(x85761,x85763,x85762,x85764)))+P104(f334(f63(x85761),x85762)) % 169.19/169.65 [8753]P39(f885(x87531,x87532),f286(x87531,x87532,x87533,x87534))+~P39(x87532,f334(x87534,f681(x87531,x87534,x87532,x87533))) % 169.19/169.65 [9291]E(f334(f334(f159(x92911,x92912),f608(x92913,x92914,x92912,x92911)),f609(x92913,x92914,x92912,x92911)),x92914)+~P104(f334(f334(f336(f885(f878(x92911),f878(x92911))),f334(f334(f269(f878(x92911),f878(x92911)),x92912),x92914)),f157(x92911,x92913))) % 169.19/169.65 [9296]~P104(f334(f334(f336(f885(f878(x92961),f878(x92961))),f334(f334(f269(f878(x92961),f878(x92961)),x92962),x92963)),f145(x92961,x92964)))+P104(f334(f334(f336(f885(f878(x92961),f878(x92961))),f334(f334(f269(f878(x92961),f878(x92961)),x92962),x92963)),f147(x92961,x92964))) % 169.19/169.65 [9399]P104(f334(f63(x93991),x93992))+~P104(f334(f334(f336(f885(f886(x93991,a871),f886(x93991,a871))),f334(f334(f269(f886(x93991,a871),f886(x93991,a871)),x93993),x93992)),f326(x93991,x93994))) % 169.19/169.65 [9400]P104(f334(f63(x94001),x94002))+~P104(f334(f334(f336(f885(f886(x94001,a871),f886(x94001,a871))),f334(f334(f269(f886(x94001,a871),f886(x94001,a871)),x94002),x94003)),f326(x94001,x94004))) % 169.19/169.65 [9403]~E(x94031,f195(f886(x94032,a871)))+~P104(f334(f334(f336(f885(f886(x94032,a871),f886(x94032,a871))),f334(f334(f269(f886(x94032,a871),f886(x94032,a871)),x94033),x94031)),f326(x94032,x94034))) % 169.19/169.65 [10031]P9(x100311,x100312,x100313,x100314)+~P104(f334(f334(f273(x100311,x100311,a871),f334(f334(f9(x100311,f886(x100311,x100312),f886(x100311,a871)),f334(f334(f10(f886(x100312,a871),f886(f886(x100311,x100312),f886(x100311,a871)),x100311),f10(x100312,a871,x100311)),f334(f334(f10(x100312,f886(x100312,a871),x100311),a331),x100314))),x100314)),f594(x100314,x100313,x100312,x100311))) % 169.19/169.65 [4995]~E(x49954,f116(x49951))+E(f334(f334(f154(x49951,x49952),x49953),x49954),f116(x49952)) % 169.19/169.65 [4996]~E(x49964,f198(x49961))+E(f334(f334(f207(x49961,x49962),x49963),x49964),f198(x49962)) % 169.19/169.65 [4997]~E(x49972,f116(x49971))+E(f334(f334(f159(x49971,x49972),x49973),x49974),f116(x49971)) % 169.19/169.65 [5235]E(x52351,f198(x52352))+~E(f334(f334(f207(x52352,x52353),x52354),x52351),f198(x52353)) % 169.19/169.65 [5236]E(x52361,f116(x52362))+~E(f334(f334(f154(x52362,x52363),x52364),x52361),f116(x52363)) % 169.19/169.65 [5237]E(x52371,f116(x52372))+~E(f334(f334(f159(x52372,x52371),x52373),x52374),f116(x52372)) % 169.19/169.65 [5270]E(x52701,x52702)+~E(f334(f334(f134(x52703),x52704),x52701),f334(f334(f134(x52703),x52704),x52702)) % 169.19/169.65 [5271]E(x52711,x52712)+~E(f334(f334(f134(x52713),x52711),x52714),f334(f334(f134(x52713),x52712),x52714)) % 169.19/169.65 [5428]P104(f334(x54283,x54282))+E(f171(x54281,x54282,f334(f136(x54281,x54283),x54284)),f334(f136(x54281,x54283),x54284)) % 169.19/169.65 [5431]~P104(f334(x54312,x54313))+P35(x54311,x54312,f334(f334(f151(x54311),x54313),x54314)) % 169.19/169.65 [5440]E(x54401,x54402)+~E(f139(a877,f334(f304(a877,x54401),x54403)),f334(f334(f151(a877),x54402),x54404)) % 169.19/169.65 [5488]~P22(x54882,x54883)+P22(x54881,f334(f334(f75(x54882,x54881),x54883),x54884)) % 169.19/169.65 [5489]~P39(x54892,x54893)+P39(x54891,f334(f334(f290(x54892,x54891),x54893),x54894)) % 169.19/169.65 [5615]~P35(x56151,x56152,x56154)+P35(x56151,x56152,f334(f334(f151(x56151),x56153),x56154)) % 169.19/169.65 [5616]~P35(x56161,x56162,x56164)+P35(x56161,x56162,f334(f334(f134(x56161),x56163),x56164)) % 169.19/169.65 [5617]~P35(x56171,x56172,x56173)+P35(x56171,x56172,f334(f334(f134(x56171),x56173),x56174)) % 169.19/169.65 [5703]~E(x57031,f116(x57032))+~E(f334(f334(f134(x57032),x57033),f334(f334(f151(x57032),x57034),f116(x57032))),x57031) % 169.19/169.65 [5728]~P33(x57283,x57281,f334(f334(f151(x57283),x57282),x57284))+P104(f334(x57281,x57282)) % 169.19/169.65 [5738]E(f144(x57381,x57382),x57383)+~E(f334(f334(f134(x57381),x57384),f334(f334(f151(x57381),x57383),f116(x57381))),x57382) % 169.19/169.65 [5739]E(f117(x57391,x57392),x57393)+~E(f334(f334(f134(x57391),x57393),f334(f334(f151(x57391),x57394),f116(x57391))),x57392) % 169.19/169.65 [5849]~E(f139(a877,f334(f304(a877,x58491),x58492)),f334(f334(f151(a877),x58493),x58494))+P104(f334(f334(f250(a877),x58491),x58492)) % 169.19/169.65 [5857]P33(x58571,x58572,x58573)+~P33(x58571,x58572,f334(f334(f151(x58571),x58574),x58573)) % 169.19/169.65 [5858]P33(x58581,x58582,x58583)+~P33(x58581,x58582,f334(f334(f134(x58581),x58584),x58583)) % 169.19/169.65 [5859]P33(x58591,x58592,x58593)+~P33(x58591,x58592,f334(f334(f134(x58591),x58593),x58594)) % 169.19/169.65 [6046]E(x60461,f334(f334(f134(x60462),f334(f169(x60462),x60463)),f334(f334(f151(x60462),x60464),f116(x60462))))+~E(f334(f169(x60462),x60461),f334(f334(f151(x60462),x60464),x60463)) % 169.19/169.65 [6223]~P108(x62231)+E(f334(f334(f104(f886(x62231,a871)),f334(f304(x62231,x62232),x62233)),f334(f304(x62231,x62233),x62234)),f195(f886(x62231,a871))) % 169.19/169.65 [6234]E(f334(f334(f165(x62341),f170(x62341,x62342,x62343)),x62344),x62343)+~P104(f334(f334(f250(a877),x62344),x62342)) % 169.19/169.65 [6261]~P72(x62611)+E(f334(f166(x62611),f334(f334(f154(a1,x62611),x62612),f180(x62613,x62614))),f334(f334(f8(a1,x62611),x62612),f334(f173(a1),f180(x62613,x62614)))) % 169.19/169.65 [6262]~P72(x62621)+E(f334(f334(f8(a1,x62621),x62622),f334(f173(a1),f180(x62623,x62624))),f334(f166(x62621),f334(f334(f154(a1,x62621),x62622),f180(x62623,x62624)))) % 169.19/169.65 [6404]~E(x64042,f334(f334(f134(x64041),f334(f169(x64041),x64044)),f334(f334(f151(x64041),x64043),f116(x64041))))+E(f334(f169(x64041),x64042),f334(f334(f151(x64041),x64043),x64044)) % 169.19/169.65 [6420]~P15(x64202,x64203,x64204,x64201)+E(f334(x64201,f195(f886(x64202,a871))),f35(x64203)) % 169.19/169.65 [6446]~P108(x64461)+E(f334(f334(f104(f886(x64461,a871)),f308(x64461,x64462,x64463)),f334(f304(x64461,x64463),x64464)),f195(f886(x64461,a871))) % 169.19/169.65 [6652]E(x66521,f195(f886(x66522,a871)))+~E(f321(x66523,x66522,x66524,x66521),f195(f886(f884(x66523,x66522),a871))) % 169.19/169.65 [6653]E(x66531,f195(f886(x66532,a871)))+~E(f321(x66532,x66533,x66531,x66534),f195(f886(f884(x66532,x66533),a871))) % 169.19/169.65 [6721]~P107(x67212)+E(f334(f196(f878(x67211)),f150(x67211,x67212,x67213,x67214)),f334(f196(f878(x67211)),x67214)) % 169.19/169.65 [6733]~P104(f334(f264(x67333,x67334,x67331),x67332))+P104(f334(f334(x67331,f680(x67332,x67331)),x67332)) % 169.19/169.65 [6773]~P104(f334(f63(x67732),x67734))+P104(f334(f63(x67731),f334(f313(x67732,x67731,x67733),x67734))) % 169.19/169.65 [7004]~P21(x70042,x70041,x70043,x70044)+E(f334(f39(x70041),f334(f313(x70042,x70041,x70043),x70044)),f334(f39(x70042),x70044)) % 169.19/169.65 [7023]E(f334(f313(x70231,x70232,x70233),f334(f314(x70231,x70232,x70233),x70234)),x70234)+~E(f334(f313(x70231,x70232,x70233),f257(f886(x70231,a871))),f257(f886(x70232,a871))) % 169.19/169.65 [7432]~P21(x74321,x74322,x74323,f257(f886(x74321,a871)))+E(f334(f314(x74321,x74322,x74323),f334(f313(x74321,x74322,x74323),x74324)),x74324) % 169.19/169.65 [7719]E(x77191,x77192)+~P104(f334(f334(f336(x77193),x77191),f334(f173(x77193),f170(x77193,x77194,x77192)))) % 169.19/169.65 [7728]~E(x77281,f2(a877))+~P104(f334(f334(f336(x77282),x77283),f334(f173(x77282),f170(x77282,x77281,x77284)))) % 169.19/169.65 [7764]P104(f334(x77641,x77642))+~P104(f334(f334(f336(x77643),x77642),f334(f173(x77643),f178(x77643,x77641,x77644)))) % 169.19/169.65 [7870]~P104(f334(f334(f336(f878(x78701)),f334(f334(f151(x78701),x78702),x78704)),f161(x78701,x78703)))+P104(f334(f334(f336(x78701),x78702),x78703)) % 169.19/169.65 [7998]~P104(f334(f334(f336(x79981),x79982),f334(f173(x79981),f171(x79981,x79984,x79983))))+P104(f334(f334(f336(x79981),x79982),f334(f173(x79981),x79983))) % 169.19/169.65 [8000]~P104(f334(f334(f336(x80001),x80002),f334(f173(x80001),f177(x80001,x80003,x80004))))+P104(f334(f334(f336(x80001),x80002),f334(f173(x80001),x80003))) % 169.19/169.65 [8001]~P104(f334(f334(f336(x80011),x80012),f334(f173(x80011),f178(x80011,x80014,x80013))))+P104(f334(f334(f336(x80011),x80012),f334(f173(x80011),x80013))) % 169.19/169.65 [8011]E(f334(f196(f878(x80111)),x80112),x80113)+~P104(f334(f334(f336(f878(x80111)),x80112),f334(f173(f878(x80111)),f56(x80111,x80113,x80114)))) % 169.19/169.65 [8103]P104(f334(x81033,x81032))+E(f334(f136(x81031,f334(f334(f10(a871,a871,x81031),a329),f334(a331,x81032))),f334(f136(x81031,x81033),x81034)),f334(f136(x81031,x81033),x81034)) % 169.19/169.65 [8216]E(f334(f334(f165(x82161),f178(x82161,x82162,x82163)),x82164),f334(f334(f165(x82161),x82163),x82164))+~P104(f334(f334(f250(a877),x82164),f334(f196(f878(x82161)),f178(x82161,x82162,x82163)))) % 169.19/169.65 [8302]~P72(x83021)+E(f334(f334(f8(a877,x83021),f334(f334(f10(a877,x83021,a877),x83022),a115)),f334(f304(a877,x83023),x83024)),f334(f334(f8(a877,x83021),x83022),f334(f304(a877,f334(a115,x83023)),f334(a115,x83024)))) % 169.19/169.65 [8311]~P72(x83111)+E(f334(f334(f8(a877,x83111),f334(f334(f10(a877,x83111,a877),x83112),a115)),f305(a877,x83113,x83114)),f334(f334(f8(a877,x83111),x83112),f305(a877,f334(a115,x83113),f334(a115,x83114)))) % 169.19/169.65 [8436]~P21(x84361,x84363,x84364,f257(f886(x84361,a871)))+P21(x84361,f886(x84362,x84363),f334(f334(f10(x84363,f886(x84362,x84363),x84361),f18(x84363,x84362)),x84364),f257(f886(x84361,a871))) % 169.19/169.65 [8519]~P21(x85192,x85191,x85194,x85193)+E(f334(f313(x85191,x85192,f78(x85192,x85191,x85193,x85194)),f334(f313(x85192,x85191,x85194),x85193)),x85193) % 169.19/169.65 [8577]~P104(f334(f334(f336(f885(x85771,x85771)),f334(f334(f269(x85771,x85771),x85772),x85774)),f266(x85771,x85773)))+P104(f334(f334(f336(x85771),x85772),x85773)) % 169.19/169.65 [8666]E(f334(f334(f334(f73(x86661,f881(x86662)),f334(f18(f881(x86662),x86661),f198(x86662))),x86663),f334(f241(x86662),f486(x86663,x86664,x86662,x86661))),x86664)+~E(f185(x86661,x86662,x86664),f334(f334(f312(x86661),x86663),f195(f886(x86661,a871)))) % 169.19/169.65 [8788]~E(f334(f334(f8(x87881,a877),x87884),x87883),f334(a115,x87882))+P104(f334(f334(f336(x87881),f850(x87882,x87883,x87884,x87881)),x87883)) % 169.19/169.65 [8808]~E(f334(f334(f8(x88084,a877),x88081),x88083),f334(a115,x88082))+P104(f334(f334(f250(a877),f2(a877)),f334(x88081,f850(x88082,x88083,x88081,x88084)))) % 169.19/169.65 [8819]~P104(f334(f63(x88192),x88194))+P104(f334(f334(f249(a877),f334(f39(x88191),f334(f313(x88192,x88191,x88193),x88194))),f334(f39(x88192),x88194))) % 169.19/169.65 [8820]E(f334(f334(f269(x88201,x88202),f789(x88203,x88204,x88202,x88201)),f790(x88203,x88204,x88202,x88201)),x88204)+~P104(f334(f334(f336(f885(x88201,x88202)),x88204),f334(f289(x88202,x88201),x88203))) % 169.19/169.65 [8828]P21(x88281,x88282,x88283,x88284)+P104(f334(f334(f336(x88281),f762(x88284,x88283,x88282,x88281)),x88284)) % 169.19/169.65 [8829]P21(x88291,x88292,x88293,x88294)+P104(f334(f334(f336(x88291),f786(x88294,x88293,x88292,x88291)),x88294)) % 169.19/169.65 [8890]P9(x88901,x88902,x88903,x88904)+P104(f334(f334(f336(f885(x88901,x88901)),f594(x88904,x88903,x88902,x88901)),x88903)) % 169.19/169.65 [8950]P104(f334(x89501,x89502))+~P104(f334(x89501,f334(f334(f269(x89503,x89504),f495(x89504,x89503,x89501)),f496(x89504,x89503,x89501)))) % 169.19/169.65 [8964]E(f334(f196(f878(x89641)),x89642),f334(f196(f878(x89641)),x89643))+~P104(f334(f334(f336(f885(f878(x89641),f878(x89641))),f334(f334(f269(f878(x89641),f878(x89641)),x89642),x89643)),f145(x89641,x89644))) % 169.19/169.65 [8967]E(f334(f196(f878(x89671)),x89672),f334(f196(f878(x89671)),x89673))+~P104(f334(f334(f336(f885(f878(x89671),f878(x89671))),f334(f334(f269(f878(x89671),f878(x89671)),x89672),x89673)),f158(x89671,x89674))) % 169.19/169.65 [8968]E(f334(f196(f878(x89681)),x89682),f334(f196(f878(x89681)),x89683))+~P104(f334(f334(f336(f885(f878(x89681),f878(x89681))),f334(f334(f269(f878(x89681),f878(x89681)),x89682),x89683)),f157(x89681,x89684))) % 169.19/169.65 [9037]P104(f334(f334(f249(a877),f155(x90371,x90372,x90373)),f155(x90371,x90374,x90373)))+P104(f334(f334(f336(x90371),f622(x90374,x90372,x90373,x90371)),f334(f173(x90371),x90373))) % 169.19/169.65 [9040]E(f334(f196(f878(x90401)),x90402),f334(f196(f878(x90401)),x90403))+~P104(f334(f334(f336(f885(f878(x90401),f878(x90401))),f334(f334(f269(f878(x90401),f878(x90401)),x90402),x90403)),f310(f878(x90401),f157(x90401,x90404)))) % 169.19/169.65 [9266]~P21(x92661,x92662,x92663,x92664)+~P104(f334(f334(f250(a877),f334(f39(x92662),f334(f313(x92661,x92662,x92663),x92664))),f334(f39(x92661),x92664))) % 169.19/169.65 [9307]~P104(f334(f334(f336(f885(f878(x93071),f878(x93071))),f334(f334(f269(f878(x93071),f878(x93071)),x93072),x93073)),f157(x93071,x93074)))+P104(f334(f334(f336(f885(f878(x93071),f878(x93071))),f334(f334(f269(f878(x93071),f878(x93071)),x93072),x93073)),f158(x93071,f310(x93071,x93074)))) % 169.19/169.65 [9311]~P104(f334(f334(f336(f885(f878(x93111),f878(x93111))),f334(f334(f269(f878(x93111),f878(x93111)),x93112),x93113)),f158(x93111,x93114)))+P104(f334(f334(f336(f885(f878(x93111),f878(x93111))),f334(f334(f269(f878(x93111),f878(x93111)),x93112),x93113)),f310(f878(x93111),f157(x93111,x93114)))) % 169.19/169.65 [9328]P104(f334(f334(f336(f885(x93281,x93281)),f334(f334(f269(x93281,x93281),x93282),x93283)),f310(x93281,x93284)))+~P104(f334(f334(f336(f885(x93281,x93281)),f334(f334(f269(x93281,x93281),x93282),x93283)),f334(f334(f291(x93281,x93281,x93281),x93284),f310(x93281,x93284)))) % 169.19/169.65 [9502]E(f334(f334(f134(x95021),f612(x95022,x95023,x95024,x95021)),f334(f334(f151(x95021),f613(x95022,x95023,x95024,x95021)),f615(x95022,x95023,x95024,x95021))),x95024)+~P104(f334(f334(f336(f885(f878(x95021),f878(x95021))),f334(f334(f269(f878(x95021),f878(x95021)),x95024),x95023)),f157(x95021,x95022))) % 169.19/169.65 [9503]E(f334(f334(f134(x95031),f612(x95032,x95033,x95034,x95031)),f334(f334(f151(x95031),f614(x95032,x95033,x95034,x95031)),f615(x95032,x95033,x95034,x95031))),x95033)+~P104(f334(f334(f336(f885(f878(x95031),f878(x95031))),f334(f334(f269(f878(x95031),f878(x95031)),x95034),x95033)),f157(x95031,x95032))) % 169.19/169.65 [9579]P104(f334(f334(f336(f885(x95791,x95791)),f334(f334(f269(x95791,x95791),x95792),f778(x95793,x95794,x95792,x95791))),f310(x95791,x95793)))+~P104(f334(f334(f336(f885(x95791,x95791)),f334(f334(f269(x95791,x95791),x95792),x95794)),f334(f334(f291(x95791,x95791,x95791),x95793),f310(x95791,x95793)))) % 169.19/169.65 [9648]P104(f334(f334(f249(a877),f155(x96481,x96482,x96483)),f155(x96481,x96484,x96483)))+~P104(f334(f334(f250(a877),f334(x96482,f622(x96484,x96482,x96483,x96481))),f334(x96484,f622(x96484,x96482,x96483,x96481)))) % 169.19/169.65 [9716]P104(f334(f334(f336(f885(x97161,x97161)),f334(f334(f269(x97161,x97161),f777(x97162,x97163,x97164,x97161)),x97163)),f310(x97161,x97162)))+~P104(f334(f334(f336(f885(x97161,x97161)),f334(f334(f269(x97161,x97161),x97164),x97163)),f334(f334(f291(x97161,x97161,x97161),x97162),f310(x97161,x97162)))) % 169.19/169.65 [5251]~E(x52512,x52513)+E(f171(x52511,x52512,f334(f334(f151(x52511),x52513),x52514)),x52514) % 169.19/169.65 [5383]P104(f334(x53832,x53833))+E(f178(x53831,x53832,f334(f334(f151(x53831),x53833),x53834)),f116(x53831)) % 169.19/169.65 [5452]~P80(x54522)+E(f334(f334(f80(f886(x54521,x54522)),x54523),x54524),f334(f80(x54522),f334(x54523,x54524))) % 169.19/169.65 [5464]~E(x54642,f2(a877))+E(f334(f334(f138(x54641),x54642),f334(f334(f151(x54641),x54643),x54644)),f334(f334(f151(x54641),x54643),x54644)) % 169.19/169.65 [5465]P104(f334(x54652,x54653))+E(f334(f136(x54651,x54652),f334(f334(f151(x54651),x54653),x54654)),f334(f136(x54651,x54652),x54654)) % 169.19/169.65 [5598]~E(x55982,x55984)+P104(f334(f334(f334(f312(x55981),x55982),x55983),x55984)) % 169.19/169.65 [5606]E(x56061,f116(x56062))+E(f144(x56063,f334(f334(f154(x56062,x56063),x56064),x56061)),f334(x56064,f144(x56062,x56061))) % 169.19/169.65 [5620]~E(x56201,f65(x56202,x56204))+E(f334(x56201,f334(f334(f312(x56202),x56203),f195(f886(x56202,a871)))),x56203) % 169.19/169.65 [5655]E(x56551,f116(x56552))+E(f334(f141(x56553),f334(f334(f154(x56552,x56553),x56554),x56551)),f334(x56554,f334(f141(x56552),x56551))) % 169.19/169.65 [5758]~P104(f334(x57583,x57584))+P104(f334(f334(f334(f312(x57581),x57582),x57583),x57584)) % 169.19/169.65 [5874]~P14(x58742,x58744,x58741)+E(f334(x58741,f334(f334(f312(x58742),x58743),f195(f886(x58742,a871)))),x58743) % 169.19/169.65 [5898]~E(x58982,x58983)+P104(f334(f334(f336(x58981),x58982),f334(f334(f312(x58981),x58983),x58984))) % 169.19/169.65 [5902]~P115(x59021)+E(f334(f334(f82(x59021),x59022),f334(f334(f82(x59021),x59023),x59024)),f334(f334(f82(x59021),x59023),f334(f334(f82(x59021),x59022),x59024))) % 169.19/169.65 [5903]~P115(x59031)+E(f334(f334(f81(x59031),x59032),f334(f334(f81(x59031),x59033),x59034)),f334(f334(f81(x59031),x59033),f334(f334(f81(x59031),x59032),x59034))) % 169.19/169.65 [5904]~P95(x59041)+E(f334(f334(f113(x59041),x59042),f334(f334(f113(x59041),x59043),x59044)),f334(f334(f113(x59041),x59043),f334(f334(f113(x59041),x59042),x59044))) % 169.19/169.65 [5906]~P100(x59061)+E(f334(f334(f113(x59061),x59062),f334(f334(f113(x59061),x59063),x59064)),f334(f334(f113(x59061),x59063),f334(f334(f113(x59061),x59062),x59064))) % 169.19/169.65 [5907]~P95(x59071)+E(f334(f334(f104(x59071),x59072),f334(f334(f104(x59071),x59073),x59074)),f334(f334(f104(x59071),x59073),f334(f334(f104(x59071),x59072),x59074))) % 169.19/169.65 [5909]~P101(x59091)+E(f334(f334(f104(x59091),x59092),f334(f334(f104(x59091),x59093),x59094)),f334(f334(f104(x59091),x59093),f334(f334(f104(x59091),x59092),x59094))) % 169.19/169.65 [5911]~P107(x59111)+E(f334(f334(f247(x59111),x59112),f334(f334(f247(x59111),x59113),x59114)),f334(f334(f247(x59111),x59113),f334(f334(f247(x59111),x59112),x59114))) % 169.19/169.65 [5913]~P107(x59131)+E(f334(f334(f248(x59131),x59132),f334(f334(f248(x59131),x59133),x59134)),f334(f334(f248(x59131),x59133),f334(f334(f248(x59131),x59132),x59134))) % 169.19/169.65 [5918]E(x59181,x59182)+E(f171(x59183,x59181,f334(f334(f151(x59183),x59182),x59184)),f334(f334(f151(x59183),x59182),f171(x59183,x59181,x59184))) % 169.19/169.65 [5931]~P104(f334(x59312,x59313))+E(f334(f136(x59311,x59312),f334(f334(f151(x59311),x59313),x59314)),f334(f334(f151(x59311),x59313),f334(f136(x59311,x59312),x59314))) % 169.19/169.65 [6066]~P104(f334(x60662,x60663))+E(f178(x60661,x60662,f334(f334(f151(x60661),x60663),x60664)),f334(f334(f151(x60661),x60663),f178(x60661,x60662,x60664))) % 169.19/169.65 [6117]P20(x61171,x61172,x61173)+~P20(x61171,x61172,f334(f334(f312(f876(x61171)),x61174),x61173)) % 169.19/169.65 [6130]E(x61301,f195(f886(x61302,a871)))+E(f334(f334(f43(x61302,f886(x61303,a871)),x61301),f334(f18(f886(x61303,a871),x61302),x61304)),x61304) % 169.19/169.65 [6131]E(x61311,f195(f886(x61312,a871)))+E(f334(f334(f44(x61312,f886(x61313,a871)),x61311),f334(f18(f886(x61313,a871),x61312),x61314)),x61314) % 169.19/169.65 [6140]~E(x61404,f195(f886(x61402,a871)))+E(f334(f334(f271(x61401,x61402),x61403),f334(f18(f886(x61402,a871),x61401),x61404)),f195(f886(f885(x61401,x61402),a871))) % 169.19/169.65 [6141]~E(x61413,f195(f886(x61411,a871)))+E(f334(f334(f271(x61411,x61412),x61413),f334(f18(f886(x61412,a871),x61411),x61414)),f195(f886(f885(x61411,x61412),a871))) % 169.19/169.65 [6187]E(x61871,f2(a877))+E(f334(f334(f138(x61872),x61871),f334(f334(f151(x61872),x61873),x61874)),f334(f334(f138(x61872),f334(f334(f3(a877),x61871),f79(a877))),x61874)) % 169.19/169.65 [6217]E(x62171,f195(f886(x62172,a871)))+E(f334(f313(x62172,x62173,f334(f18(x62173,x62172),x62174)),x62171),f334(f334(f312(x62173),x62174),f195(f886(x62173,a871)))) % 169.19/169.65 [6220]E(f334(f314(x62201,x62202,f334(f18(x62202,x62201),x62203)),x62204),f195(f886(x62201,a871)))+P104(f334(f334(f336(x62202),x62203),x62204)) % 169.19/169.65 [6287]~E(x62873,f195(f886(x62871,a871)))+E(f334(f334(f43(x62871,f886(x62872,a871)),x62873),f334(f18(f886(x62872,a871),x62871),x62874)),f257(f886(x62872,a871))) % 169.19/169.65 [6288]~E(x62883,f195(f886(x62881,a871)))+E(f334(f334(f44(x62881,f886(x62882,a871)),x62883),f334(f18(f886(x62882,a871),x62881),x62884)),f195(f886(x62882,a871))) % 169.19/169.65 [6290]~P26(x62901)+E(f46(x62901,f334(f334(f82(x62901),x62902),x62903),f334(f334(f82(x62901),x62902),x62904)),f334(f334(f82(x62901),x62902),f46(x62901,x62903,x62904))) % 169.19/169.65 [6456]E(f334(f314(x64561,x64562,f334(f18(x64562,x64561),x64563)),x64564),f257(f886(x64561,a871)))+~P104(f334(f334(f336(x64562),x64563),x64564)) % 169.19/169.65 [6479]~P104(f334(f334(f336(x64791),x64792),x64794))+P104(f334(f334(f336(x64791),x64792),f334(f334(f312(x64791),x64793),x64794))) % 169.19/169.65 [6484]P104(f334(x64841,x64842))+~P104(f334(f160(x64843,x64841),f334(f334(f151(x64843),x64842),x64844))) % 169.19/169.65 [6493]~E(x64933,f334(f334(f3(a877),f334(f196(f878(x64931)),x64932)),f79(a877)))+E(f117(x64931,f334(f334(f159(x64931,x64932),x64933),x64934)),f117(x64931,x64932)) % 169.19/169.65 [6512]~P107(x65121)+E(f334(f334(f104(f886(x65121,a871)),f334(f303(x65121),x65122)),f305(x65121,x65123,x65124)),f305(x65121,x65123,f334(f334(f247(x65121),x65122),x65124))) % 169.19/169.65 [6513]~P107(x65131)+E(f334(f334(f104(f886(x65131,a871)),f334(f256(x65131),x65132)),f305(x65131,x65133,x65134)),f305(x65131,f334(f334(f248(x65131),x65132),x65133),x65134)) % 169.19/169.65 [6528]E(f334(f334(f104(f886(x65281,a871)),x65282),f334(f334(f312(x65281),x65283),x65284)),f334(f334(f104(f886(x65281,a871)),x65282),x65284))+P104(f334(f334(f336(x65281),x65283),x65282)) % 169.19/169.65 [6540]E(f171(x65401,x65402,f334(f334(f134(x65401),x65403),x65404)),f334(f334(f134(x65401),x65403),f171(x65401,x65402,x65404)))+P104(f334(f334(f336(x65401),x65402),f334(f173(x65401),x65403))) % 169.19/169.65 [6544]~P77(x65441)+E(f334(f334(f82(x65441),f334(f334(f259(x65441),x65442),x65443)),f334(f334(f259(x65441),x65442),x65444)),f334(f334(f259(x65441),x65442),f334(f334(f81(a877),x65443),x65444))) % 169.19/169.65 [6545]~P115(x65451)+E(f334(f334(f82(x65451),f334(f334(f259(x65451),x65452),x65453)),f334(f334(f259(x65451),x65452),x65454)),f334(f334(f259(x65451),x65452),f334(f334(f81(a877),x65453),x65454))) % 169.19/169.65 [6581]~P115(x65811)+E(f334(f334(f81(x65811),f334(f334(f82(x65811),x65812),x65813)),f334(f334(f82(x65811),x65812),x65814)),f334(f334(f82(x65811),x65812),f334(f334(f81(x65811),x65813),x65814))) % 169.19/169.65 [6582]~P99(x65821)+E(f334(f334(f104(x65821),f334(f334(f113(x65821),x65822),x65823)),f334(f334(f113(x65821),x65822),x65824)),f334(f334(f113(x65821),x65822),f334(f334(f104(x65821),x65823),x65824))) % 169.19/169.65 [6583]~P99(x65831)+E(f334(f334(f113(x65831),f334(f334(f104(x65831),x65832),x65833)),f334(f334(f104(x65831),x65832),x65834)),f334(f334(f104(x65831),x65832),f334(f334(f113(x65831),x65833),x65834))) % 169.19/169.65 [6584]~P107(x65841)+E(f334(f334(f248(x65841),f334(f334(f247(x65841),x65842),x65843)),f334(f334(f247(x65841),x65842),x65844)),f334(f334(f247(x65841),x65842),f334(f334(f248(x65841),x65843),x65844))) % 169.19/169.65 [6585]~P107(x65851)+E(f334(f334(f247(x65851),f334(f334(f248(x65851),x65852),x65853)),f334(f334(f248(x65851),x65852),x65854)),f334(f334(f248(x65851),x65852),f334(f334(f247(x65851),x65853),x65854))) % 169.19/169.65 [6616]~P26(x66161)+E(f46(x66161,f334(f334(f82(x66161),x66162),x66163),f334(f334(f82(x66161),x66164),x66163)),f334(f334(f82(x66161),f46(x66161,x66162,x66164)),x66163)) % 169.19/169.65 [6619]~E(f334(f196(f878(x66191)),x66193),f334(f196(f878(x66192)),x66194))+E(f334(f334(f154(f885(x66191,x66192),x66192),f272(x66191,x66192)),f334(f334(f183(x66191,x66192),x66193),x66194)),x66194) % 169.19/169.65 [6620]~E(f334(f196(f878(x66201)),x66203),f334(f196(f878(x66202)),x66204))+E(f334(f334(f154(f885(x66201,x66202),x66201),f268(x66201,x66202)),f334(f334(f183(x66201,x66202),x66203),x66204)),x66203) % 169.19/169.65 [6626]P104(f334(f160(x66261,x66262),x66263))+~P104(f334(f160(x66261,x66262),f334(f334(f151(x66261),x66264),x66263))) % 169.19/169.65 [6627]P104(f334(f160(x66271,x66272),x66273))+~P104(f334(f160(x66271,x66272),f334(f334(f134(x66271),x66274),x66273))) % 169.19/169.65 [6628]P104(f334(f160(x66281,x66282),x66283))+~P104(f334(f160(x66281,x66282),f334(f334(f134(x66281),x66283),x66284))) % 169.19/169.65 [6633]~P27(x66331)+E(f46(x66331,f334(f334(f3(x66331),x66332),f46(x66331,x66333,x66334)),x66334),f46(x66331,f334(f334(f3(x66331),x66332),x66333),x66334)) % 169.19/169.65 [6634]~P26(x66341)+E(f46(x66341,f334(f334(f82(x66341),x66342),f46(x66341,x66343,x66344)),x66344),f46(x66341,f334(f334(f82(x66341),x66342),x66343),x66344)) % 169.19/169.65 [6636]~P26(x66361)+E(f46(x66361,f334(f334(f81(x66361),x66362),f46(x66361,x66363,x66364)),x66364),f46(x66361,f334(f334(f81(x66361),x66362),x66363),x66364)) % 169.19/169.65 [6715]~P107(x67151)+E(f334(f334(f104(f886(x67151,a871)),f305(x67151,x67152,x67153)),f334(f303(x67151),x67154)),f305(x67151,x67152,f334(f334(f247(x67151),x67153),x67154))) % 169.19/169.65 [6716]~P107(x67161)+E(f334(f334(f104(f886(x67161,a871)),f305(x67161,x67162,x67163)),f334(f256(x67161),x67164)),f305(x67161,f334(f334(f248(x67161),x67162),x67164),x67163)) % 169.19/169.65 [6719]~E(f334(f196(f878(x67191)),x67193),f334(f196(f878(x67192)),x67194))+E(f334(f334(f183(x67191,x67192),f334(f169(x67191),x67193)),f334(f169(x67192),x67194)),f334(f169(f885(x67191,x67192)),f334(f334(f183(x67191,x67192),x67193),x67194))) % 169.19/169.65 [6729]E(x67291,f334(f334(f3(a877),f334(f196(f878(x67292)),x67293)),f79(a877)))+E(f117(x67292,f334(f334(f159(x67292,x67293),x67291),x67294)),f334(f334(f159(x67292,f117(x67292,x67293)),x67291),x67294)) % 169.19/169.65 [6744]~P104(f334(f137(x67442),x67444))+P104(f334(f137(f885(x67441,x67442)),f334(f334(f183(x67441,x67442),x67443),x67444))) % 169.19/169.65 [6745]~P104(f334(f137(x67451),x67453))+P104(f334(f137(f885(x67451,x67452)),f334(f334(f183(x67451,x67452),x67453),x67454))) % 169.19/169.65 [7007]E(f334(f334(f40(a877),x70071),x70072),x70073)+~P104(f334(f49(x70071,x70072),f334(f334(f269(a877,a877),x70073),x70074))) % 169.19/169.65 [7031]E(f46(a877,x70311,x70312),x70313)+~P104(f334(f49(x70311,x70312),f334(f334(f269(a877,a877),x70314),x70313))) % 169.19/169.65 [7034]P104(f334(f137(x70341),x70342))+~P104(f334(f137(x70343),f334(f334(f154(x70341,x70343),x70344),x70342))) % 169.19/169.65 [7042]~P20(x70421,x70422,f334(f334(f312(f876(x70421)),x70423),x70424))+P20(x70421,x70422,f334(f334(f312(f876(x70421)),x70423),f195(f886(f876(x70421),a871)))) % 169.19/169.65 [7118]E(f171(x71181,x71182,f334(f334(f134(x71181),x71183),x71184)),f334(f334(f134(x71181),f171(x71181,x71182,x71183)),x71184))+~P104(f334(f334(f336(x71181),x71182),f334(f173(x71181),x71183))) % 169.19/169.65 [7208]~P27(x72081)+E(f46(x72081,f334(f334(f3(x72081),f46(x72081,x72082,x72083)),x72084),x72083),f46(x72081,f334(f334(f3(x72081),x72082),x72084),x72083)) % 169.19/169.65 [7211]~P26(x72111)+E(f46(x72111,f334(f334(f82(x72111),f46(x72111,x72112,x72113)),x72114),x72113),f46(x72111,f334(f334(f82(x72111),x72112),x72114),x72113)) % 169.19/169.65 [7212]~P26(x72121)+E(f46(x72121,f334(f334(f81(x72121),f46(x72121,x72122,x72123)),x72124),x72123),f46(x72121,f334(f334(f81(x72121),x72122),x72124),x72123)) % 169.19/169.65 [7402]~E(x74021,f334(f334(f151(x74022),x74023),x74024))+~P104(f334(f334(f249(a877),f334(f196(f878(x74022)),x74021)),f334(f196(f878(x74022)),x74024))) % 169.19/169.65 [7478]~E(f334(f179(x74781,x74782),x74783),f334(f179(x74781,x74782),x74784))+E(f334(f313(f885(x74781,x74782),x74781,f268(x74781,x74782)),f334(f173(f885(x74781,x74782)),x74783)),f334(f313(f885(x74781,x74782),x74781,f268(x74781,x74782)),f334(f173(f885(x74781,x74782)),x74784))) % 169.19/169.65 [7612]P21(x76121,x76122,x76123,f334(f173(x76121),x76124))+~P104(f334(f137(x76122),f334(f334(f154(x76121,x76122),x76123),x76124))) % 169.19/169.65 [7686]~P104(f334(f334(f249(f886(x76861,a871)),x76862),x76864))+P104(f334(f334(f249(f886(x76861,a871)),x76862),f334(f334(f312(x76861),x76863),x76864))) % 169.19/169.65 [7720]~P27(x77201)+E(f46(x77201,f334(f334(f3(x77201),f46(x77201,x77202,x77203)),f46(x77201,x77204,x77203)),x77203),f46(x77201,f334(f334(f3(x77201),x77202),x77204),x77203)) % 169.19/169.65 [7721]~P26(x77211)+E(f46(x77211,f334(f334(f82(x77211),f46(x77211,x77212,x77213)),f46(x77211,x77214,x77213)),x77213),f46(x77211,f334(f334(f82(x77211),x77212),x77214),x77213)) % 169.19/169.65 [7722]~P26(x77221)+E(f46(x77221,f334(f334(f81(x77221),f46(x77221,x77222,x77223)),f46(x77221,x77224,x77223)),x77223),f46(x77221,f334(f334(f81(x77221),x77222),x77224),x77223)) % 169.19/169.65 [7827]~E(f334(x78274,f499(x78274,x78273,x78271,x78272)),f195(f886(x78272,a871)))+E(f334(f334(f44(x78271,f886(x78272,a871)),x78273),x78274),f195(f886(x78272,a871))) % 169.19/169.65 [7828]~E(f334(x78284,f500(x78284,x78283,x78281,x78282)),f257(f886(x78282,a871)))+E(f334(f334(f43(x78281,f886(x78282,a871)),x78283),x78284),f257(f886(x78282,a871))) % 169.19/169.65 [7829]~E(f334(x78294,f501(x78294,x78293,x78292,x78291)),f257(f886(x78292,a871)))+E(f334(f334(f43(x78291,f886(x78292,a871)),x78293),x78294),f257(f886(x78292,a871))) % 169.19/169.65 [7830]~E(f334(x78304,f523(x78304,x78303,x78302,x78301)),f195(f886(x78302,a871)))+E(f334(f334(f44(x78301,f886(x78302,a871)),x78303),x78304),f195(f886(x78302,a871))) % 169.19/169.65 [8217]P104(f334(x82171,x82172))+~P104(f334(f334(f336(x82173),x82172),f334(f334(f104(f886(x82173,a871)),x82174),f334(f254(x82173),x82171)))) % 169.19/169.65 [8256]~P104(f334(f334(f249(f886(x82561,a871)),x82563),x82564))+P104(f334(f334(f249(f886(x82561,a871)),f334(f334(f312(x82561),x82562),x82563)),f334(f334(f312(x82561),x82562),x82564))) % 169.19/169.65 [8428]P104(f334(x84282,x84283))+E(f334(f334(f138(x84281),f334(f196(f878(x84281)),f178(x84281,x84282,f334(f334(f151(x84281),x84283),x84284)))),f334(f334(f151(x84281),x84283),x84284)),f334(f334(f151(x84281),x84283),x84284)) % 169.19/169.65 [8533]~P104(f334(f334(f250(a877),f334(x85334,x85332)),f334(x85334,x85333)))+P104(f334(f334(f336(f885(x85331,x85331)),f334(f334(f269(x85331,x85331),x85332),x85333)),f334(f334(f290(a877,x85331),a253),x85334))) % 169.19/169.65 [8624]~P104(f334(x86242,f728(x86244,x86242,x86243,x86241)))+E(f178(x86241,x86242,f334(f334(f134(x86241),x86243),x86244)),f334(f334(f134(x86241),x86243),f178(x86241,x86242,x86244))) % 169.19/169.65 [8693]P21(f878(x86931),f878(x86932),f334(f154(x86931,x86932),x86933),x86934)+~P21(x86931,x86932,x86933,f41(f886(x86931,a871),f334(f313(f878(x86931),f886(x86931,a871),f173(x86931)),x86934))) % 169.19/169.65 [8760]~P104(f334(x87602,x87603))+E(f334(f334(f138(x87601),f334(f196(f878(x87601)),f178(x87601,x87602,f334(f334(f151(x87601),x87603),x87604)))),f334(f334(f151(x87601),x87603),x87604)),f334(f334(f138(x87601),f334(f196(f878(x87601)),f178(x87601,x87602,x87604))),x87604)) % 169.19/169.65 [8799]~E(x87992,x87993)+E(f334(f136(x87991,f334(f334(f10(a871,a871,x87991),a329),f334(a331,x87992))),f334(f334(f151(x87991),x87993),x87994)),f334(f136(x87991,f334(f334(f10(a871,a871,x87991),a329),f334(a331,x87992))),x87994)) % 169.19/169.65 [8809]E(f334(f334(f44(x88091,f886(x88092,a871)),x88093),x88094),f195(f886(x88092,a871)))+P104(f334(f334(f336(x88091),f499(x88094,x88093,x88091,x88092)),x88093)) % 169.19/169.65 [8810]E(f334(f334(f43(x88101,f886(x88102,a871)),x88103),x88104),f257(f886(x88102,a871)))+P104(f334(f334(f336(x88101),f500(x88104,x88103,x88101,x88102)),x88103)) % 169.19/169.65 [8811]E(f334(f334(f43(x88111,f886(x88112,a871)),x88113),x88114),f257(f886(x88112,a871)))+P104(f334(f334(f336(x88111),f501(x88114,x88113,x88112,x88111)),x88113)) % 169.19/169.65 [8812]E(f334(f334(f44(x88121,f886(x88122,a871)),x88123),x88124),f195(f886(x88122,a871)))+P104(f334(f334(f336(x88121),f523(x88124,x88123,x88122,x88121)),x88123)) % 169.19/169.65 [8848]P104(f334(f334(f250(a877),f334(x88481,x88482)),f334(x88481,x88483)))+~P104(f334(f334(f336(f885(x88484,x88484)),f334(f334(f269(x88484,x88484),x88482),x88483)),f334(f334(f290(a877,x88484),a253),x88481))) % 169.19/169.65 [8869]E(f178(x88691,x88692,f334(f334(f134(x88691),x88693),x88694)),f334(f334(f134(x88691),x88693),f178(x88691,x88692,x88694)))+P104(f334(f334(f336(x88691),f728(x88694,x88692,x88693,x88691)),f334(f173(x88691),x88693))) % 169.19/169.65 [9026]P104(f334(f334(f336(x90261),f546(x90262,x90263,x90264,x90261)),x90263))+~P104(f334(f334(f336(f886(x90261,a871)),x90264),f334(f334(f62(x90261),x90263),x90262))) % 169.19/169.65 [9029]E(x90291,x90292)+~P104(f334(f334(f336(f885(x90293,x90293)),f334(f334(f269(x90293,x90293),x90291),x90292)),f334(f334(f190(f885(x90293,x90293),a871),f2(a877)),x90294))) % 169.19/169.65 [9107]E(f334(f288(x91071,x91071,x91072),f334(f334(f312(x91071),f546(x91072,x91073,x91074,x91071)),f195(f886(x91071,a871)))),x91074)+~P104(f334(f334(f336(f886(x91071,a871)),x91074),f334(f334(f62(x91071),x91073),x91072))) % 169.19/169.65 [9113]~P104(f334(f334(f336(f885(x91131,x91131)),f334(f334(f269(x91131,x91131),x91133),x91132)),f310(x91131,x91134)))+P104(f334(f334(f336(f885(x91131,x91131)),f334(f334(f269(x91131,x91131),x91132),x91133)),f310(x91131,f334(f289(x91131,x91131),x91134)))) % 169.19/169.65 [9125]~P26(x91251)+E(f334(f334(f81(x91251),f334(f334(f81(x91251),f334(f334(f82(x91251),x91252),f334(f334(f40(x91251),x91253),x91252))),f46(x91251,x91253,x91252))),x91254),f334(f334(f81(x91251),x91253),x91254)) % 169.19/169.65 [9135]~P104(f334(f334(f336(x91351),x91353),x91354))+P104(f334(f334(f336(f886(x91351,a871)),f334(f288(x91351,x91351,x91352),f334(f334(f312(x91351),x91353),f195(f886(x91351,a871))))),f334(f334(f62(x91351),x91354),x91352))) % 169.19/169.65 [9146]P104(f334(f334(f336(f885(x91461,x91461)),f334(f334(f269(x91461,x91461),x91462),x91463)),f310(x91461,x91464)))+~P104(f334(f334(f336(f885(x91461,x91461)),f334(f334(f269(x91461,x91461),x91463),x91462)),f310(x91461,f334(f289(x91461,x91461),x91464)))) % 169.19/169.65 [9230]E(f334(f334(f159(x92301,f334(f169(x92301),x92302)),f334(f334(f3(a877),f334(f334(f3(a877),f334(f196(f878(x92301)),x92302)),x92303)),f79(a877))),x92304),f334(f169(x92301),f334(f334(f159(x92301,x92302),x92303),x92304)))+~P104(f334(f334(f250(a877),x92303),f334(f196(f878(x92301)),x92302))) % 169.19/169.65 [9233]~P104(f334(x92332,f721(x92334,x92332,x92333,x92331)))+E(f334(f334(f138(x92331),f334(f196(f878(x92331)),f178(x92331,x92332,f334(f334(f134(x92331),x92333),x92334)))),f334(f334(f134(x92331),x92333),x92334)),f334(f334(f138(x92331),f334(f196(f878(x92331)),f178(x92331,x92332,x92334))),x92334)) % 169.19/169.65 [9272]~P21(x92722,x92721,x92723,f257(f886(x92722,a871)))+P104(f334(f334(f249(f886(x92721,a871)),f334(f313(x92722,x92721,x92723),f334(f80(f886(x92722,a871)),x92724))),f334(f80(f886(x92721,a871)),f334(f313(x92722,x92721,x92723),x92724)))) % 169.19/169.65 [9282]~P28(x92821)+E(f334(f142(x92821,x92822,f334(f9(x92822,x92821,x92821),f334(f334(f10(x92821,f886(x92821,x92821),x92822),f104(x92821)),x92823)),f257(x92821)),x92824),f334(f334(f43(x92822,x92821),f334(f173(x92822),x92824)),x92823)) % 169.19/169.65 [9283]~P28(x92831)+E(f334(f142(x92831,x92832,f334(f9(x92832,x92831,x92831),f334(f334(f10(x92831,f886(x92831,x92831),x92832),f113(x92831)),x92833)),f195(x92831)),x92834),f334(f334(f44(x92832,x92831),f334(f173(x92832),x92834)),x92833)) % 169.19/169.65 [9293]E(f334(f334(f138(x92931),f334(f196(f878(x92931)),f178(x92931,x92932,f334(f334(f134(x92931),x92933),x92934)))),f334(f334(f134(x92931),x92933),x92934)),f334(f334(f138(x92931),f334(f196(f878(x92931)),f178(x92931,x92932,x92934))),x92934))+P104(f334(f334(f336(x92931),f721(x92934,x92932,x92933,x92931)),f334(f173(x92931),x92933))) % 169.19/169.65 [9360]~P104(f334(f334(f336(f885(f878(x93604),f878(x93604))),f334(f334(f269(f878(x93604),f878(x93604)),x93603),x93602)),f157(x93604,x93601)))+P104(f334(f334(f250(a877),f608(x93601,x93602,x93603,x93604)),f334(f196(f878(x93604)),x93603))) % 169.19/169.65 [9361]~P26(x93611)+E(f334(f334(f81(x93611),f334(f334(f81(x93611),f334(f334(f82(x93611),f334(f334(f40(x93611),x93612),x93613)),x93613)),f46(x93611,x93612,x93613))),x93614),f334(f334(f81(x93611),x93612),x93614)) % 169.19/169.65 [9387]~P104(f334(f334(f336(f885(f878(x93871),f878(x93871))),f334(f334(f269(f878(x93871),f878(x93871)),x93872),x93873)),f334(f289(f878(x93871),f878(x93871)),f157(x93871,x93874))))+P104(f334(f334(f336(f885(f878(x93871),f878(x93871))),f334(f334(f269(f878(x93871),f878(x93871)),x93872),x93873)),f157(x93871,f334(f289(x93871,x93871),x93874)))) % 169.19/169.65 [9388]P104(f334(f334(f336(f885(f878(x93881),f878(x93881))),f334(f334(f269(f878(x93881),f878(x93881)),x93882),x93883)),f334(f289(f878(x93881),f878(x93881)),f157(x93881,x93884))))+~P104(f334(f334(f336(f885(f878(x93881),f878(x93881))),f334(f334(f269(f878(x93881),f878(x93881)),x93882),x93883)),f157(x93881,f334(f289(x93881,x93881),x93884)))) % 169.19/169.65 [9422]~P104(f334(f334(f336(x94221),x94223),f334(f267(x94221,x94222),x94224)))+P104(f334(f334(f336(f885(x94221,x94222)),f334(f334(f269(x94221,x94222),x94223),f692(x94224,x94222,x94223,x94221))),x94224)) % 169.19/169.65 [9423]~P104(f334(f334(f336(x94231),x94233),f334(f267(x94231,x94232),x94234)))+P104(f334(f334(f336(f885(x94231,x94232)),f334(f334(f269(x94231,x94232),x94233),f694(x94234,x94232,x94233,x94231))),x94234)) % 169.19/169.65 [9527]~P104(f334(f63(f881(x95271)),f334(f313(x95272,f881(x95271),x95273),f257(f886(x95272,a871)))))+P104(f334(f63(f881(x95271)),f334(f313(x95272,f881(x95271),f186(x95272,x95271,x95273,f334(f179(x95272,x95271),x95274))),f257(f886(x95272,a871))))) % 169.19/169.65 [9574]~P104(f334(f334(f336(f885(x95741,x95741)),f334(f334(f269(x95741,x95741),x95742),x95744)),f334(f334(f291(x95741,x95741,x95741),x95743),f310(x95741,x95743))))+P104(f334(f334(f336(f885(x95741,x95741)),f334(f334(f269(x95741,x95741),x95742),f777(x95743,x95744,x95742,x95741))),x95743)) % 169.19/169.65 [9743]~P104(f334(f334(f336(f885(x97432,x97431)),x97434),f334(f289(x97431,x97432),x97433)))+P104(f334(f334(f336(f885(x97431,x97432)),f334(f334(f269(x97431,x97432),f790(x97433,x97434,x97431,x97432)),f789(x97433,x97434,x97431,x97432))),x97433)) % 169.19/169.65 [9771]~P104(f334(f334(f336(f885(f878(x97711),f878(x97711))),f334(f334(f269(f878(x97711),f878(x97711)),x97714),x97713)),f157(x97711,x97712)))+P104(f334(f334(f336(f885(x97711,x97711)),f334(f334(f269(x97711,x97711),f613(x97712,x97713,x97714,x97711)),f614(x97712,x97713,x97714,x97711))),x97712)) % 169.19/169.65 [9865]~P104(f334(f334(f336(f885(f878(x98651),f878(x98651))),f334(f334(f269(f878(x98651),f878(x98651)),x98652),x98654)),f157(x98651,x98653)))+P104(f334(f334(f336(f885(x98651,x98651)),f334(f334(f269(x98651,x98651),f334(f334(f165(x98651),x98652),f608(x98653,x98654,x98652,x98651))),f609(x98653,x98654,x98652,x98651))),x98653)) % 169.19/169.65 [9887]~P104(f334(f63(x98872),x98874))+E(f334(f334(f334(f67(f886(x98871,a871),x98872,f113(f886(x98871,a871))),f334(f334(f9(x98872,f886(x98871,a871),f886(x98871,a871)),f334(f334(f10(x98871,f886(f886(x98871,a871),f886(x98871,a871)),x98872),f312(x98871)),x98873)),f195(f886(x98871,a871)))),f195(f886(x98871,a871))),x98874),f334(f313(x98872,x98871,x98873),x98874)) % 169.19/169.65 [9982]~P21(x99821,x99822,x99823,f257(f886(x99821,a871)))+P104(f334(f334(f249(f886(x99821,a871)),f334(f314(x99821,x99822,x99823),f334(f334(f312(x99822),x99824),f195(f886(x99822,a871))))),f334(f334(f312(x99821),f86(x99821,f334(f334(f9(x99821,x99822,a871),f334(f334(f10(x99822,f886(x99822,a871),x99821),a331),x99823)),x99824))),f195(f886(x99821,a871))))) % 169.19/169.65 [5664]~E(f334(f334(f134(x56641),x56642),x56644),x56643)+E(f334(f334(f176(x56641),f334(f196(f878(x56641)),x56642)),x56643),x56642) % 169.19/169.65 [5665]~E(f334(f334(f134(x56652),x56653),x56651),x56654)+E(x56651,f334(f334(f138(x56652),f334(f196(f878(x56652)),x56653)),x56654)) % 169.19/169.65 [5676]~E(x56764,f2(a877))+E(f334(f334(f165(x56761),f334(f334(f151(x56761),x56762),x56763)),x56764),x56762) % 169.19/169.65 [6200]~P115(x62001)+E(f334(f334(f259(x62001),f334(f334(f259(x62001),x62002),x62003)),x62004),f334(f334(f259(x62001),x62002),f334(f334(f82(a877),x62003),x62004))) % 169.19/169.65 [6201]~P77(x62011)+E(f334(f334(f259(x62011),f334(f334(f259(x62011),x62012),x62013)),x62014),f334(f334(f259(x62011),x62012),f334(f334(f82(a877),x62013),x62014))) % 169.19/169.65 [6218]E(x62181,f2(a877))+E(f334(f334(f165(x62182),f334(f334(f151(x62182),x62183),x62184)),x62181),f334(f334(f165(x62182),x62184),f334(f334(f3(a877),x62181),f79(a877)))) % 169.19/169.65 [6244]~P117(x62441)+E(f334(f334(f292(x62441),f334(f334(f82(x62441),x62442),x62443)),x62444),f334(f334(f82(x62441),x62442),f334(f334(f292(x62441),x62443),x62444))) % 169.19/169.65 [6246]~P65(x62461)+E(f334(f334(f82(x62461),f334(f334(f82(x62461),x62462),x62463)),x62464),f334(f334(f82(x62461),x62462),f334(f334(f82(x62461),x62463),x62464))) % 169.19/169.65 [6247]~P115(x62471)+E(f334(f334(f82(x62471),f334(f334(f82(x62471),x62472),x62473)),x62474),f334(f334(f82(x62471),x62472),f334(f334(f82(x62471),x62473),x62474))) % 169.19/169.65 [6249]~P115(x62491)+E(f334(f334(f81(x62491),f334(f334(f81(x62491),x62492),x62493)),x62494),f334(f334(f81(x62491),x62492),f334(f334(f81(x62491),x62493),x62494))) % 169.19/169.65 [6250]~P66(x62501)+E(f334(f334(f81(x62501),f334(f334(f81(x62501),x62502),x62503)),x62504),f334(f334(f81(x62501),x62502),f334(f334(f81(x62501),x62503),x62504))) % 169.19/169.65 [6251]~P95(x62511)+E(f334(f334(f113(x62511),f334(f334(f113(x62511),x62512),x62513)),x62514),f334(f334(f113(x62511),x62512),f334(f334(f113(x62511),x62513),x62514))) % 169.19/169.65 [6253]~P100(x62531)+E(f334(f334(f113(x62531),f334(f334(f113(x62531),x62532),x62533)),x62534),f334(f334(f113(x62531),x62532),f334(f334(f113(x62531),x62533),x62534))) % 169.19/169.65 [6254]~P95(x62541)+E(f334(f334(f104(x62541),f334(f334(f104(x62541),x62542),x62543)),x62544),f334(f334(f104(x62541),x62542),f334(f334(f104(x62541),x62543),x62544))) % 169.19/169.65 [6256]~P101(x62561)+E(f334(f334(f104(x62561),f334(f334(f104(x62561),x62562),x62563)),x62564),f334(f334(f104(x62561),x62562),f334(f334(f104(x62561),x62563),x62564))) % 169.19/169.65 [6258]~P107(x62581)+E(f334(f334(f247(x62581),f334(f334(f247(x62581),x62582),x62583)),x62584),f334(f334(f247(x62581),x62582),f334(f334(f247(x62581),x62583),x62584))) % 169.19/169.65 [6260]~P107(x62601)+E(f334(f334(f248(x62601),f334(f334(f248(x62601),x62602),x62603)),x62604),f334(f334(f248(x62601),x62602),f334(f334(f248(x62601),x62603),x62604))) % 169.19/169.65 [6271]~P26(x62711)+E(f46(x62711,f334(f334(f81(x62711),x62712),f334(f334(f82(x62711),x62713),x62714)),x62714),f46(x62711,x62712,x62714)) % 169.19/169.65 [6272]~P26(x62721)+E(f46(x62721,f334(f334(f81(x62721),x62722),f334(f334(f82(x62721),x62723),x62724)),x62723),f46(x62721,x62722,x62723)) % 169.19/169.65 [6405]E(f334(f334(f165(x64051),f334(f334(f176(x64051),x64052),x64053)),x64054),f334(f334(f165(x64051),x64053),x64054))+~P104(f334(f334(f250(a877),x64054),x64052)) % 169.19/169.65 [6579]~P115(x65791)+E(f334(f334(f82(x65791),f334(f334(f82(x65791),x65792),x65793)),x65794),f334(f334(f82(x65791),f334(f334(f82(x65791),x65792),x65794)),x65793)) % 169.19/169.65 [6580]~P115(x65801)+E(f334(f334(f81(x65801),f334(f334(f81(x65801),x65802),x65803)),x65804),f334(f334(f81(x65801),f334(f334(f81(x65801),x65802),x65804)),x65803)) % 169.19/169.65 [6639]~P142(x66392)+E(f334(f334(f8(x66391,x66392),f334(f18(x66392,x66391),x66393)),x66394),f334(f334(f82(x66392),f334(f103(x66392),f334(f39(x66391),x66394))),x66393)) % 169.19/169.65 [6807]E(f334(f334(f104(f886(x68071,a871)),f334(f334(f312(x68071),x68072),x68073)),x68074),f334(f334(f104(f886(x68071,a871)),x68073),x68074))+P104(f334(f334(f336(x68071),x68072),x68074)) % 169.19/169.65 [6877]~P75(x68771)+E(f334(f334(f247(x68771),f334(f334(f3(x68771),x68772),x68773)),f334(f334(f3(x68771),x68774),x68773)),f334(f334(f3(x68771),f334(f334(f247(x68771),x68772),x68774)),x68773)) % 169.19/169.65 [6878]~P75(x68781)+E(f334(f334(f248(x68781),f334(f334(f3(x68781),x68782),x68783)),f334(f334(f3(x68781),x68784),x68783)),f334(f334(f3(x68781),f334(f334(f248(x68781),x68782),x68784)),x68783)) % 169.19/169.65 [6880]~P116(x68801)+E(f334(f334(f81(x68801),f334(f334(f82(x68801),x68802),x68803)),f334(f334(f82(x68801),x68804),x68803)),f334(f334(f82(x68801),f334(f334(f81(x68801),x68802),x68804)),x68803)) % 169.19/169.65 [6881]~P81(x68811)+E(f334(f334(f247(x68811),f334(f334(f81(x68811),x68812),x68813)),f334(f334(f81(x68811),x68814),x68813)),f334(f334(f81(x68811),f334(f334(f247(x68811),x68812),x68814)),x68813)) % 169.19/169.65 [6882]~P81(x68821)+E(f334(f334(f248(x68821),f334(f334(f81(x68821),x68822),x68823)),f334(f334(f81(x68821),x68824),x68823)),f334(f334(f81(x68821),f334(f334(f248(x68821),x68822),x68824)),x68823)) % 169.19/169.65 [6883]~P117(x68831)+E(f334(f334(f3(x68831),f334(f334(f292(x68831),x68832),x68833)),f334(f334(f292(x68831),x68834),x68833)),f334(f334(f292(x68831),f334(f334(f3(x68831),x68832),x68834)),x68833)) % 169.19/169.65 [6884]~P117(x68841)+E(f334(f334(f81(x68841),f334(f334(f292(x68841),x68842),x68843)),f334(f334(f292(x68841),x68844),x68843)),f334(f334(f292(x68841),f334(f334(f81(x68841),x68842),x68844)),x68843)) % 169.19/169.65 [6885]~P68(x68851)+E(f334(f334(f82(x68851),f334(f334(f259(x68851),x68852),x68853)),f334(f334(f259(x68851),x68854),x68853)),f334(f334(f259(x68851),f334(f334(f82(x68851),x68852),x68854)),x68853)) % 169.19/169.65 [6886]~P115(x68861)+E(f334(f334(f82(x68861),f334(f334(f259(x68861),x68862),x68863)),f334(f334(f259(x68861),x68864),x68863)),f334(f334(f259(x68861),f334(f334(f82(x68861),x68862),x68864)),x68863)) % 169.19/169.65 [6887]~P59(x68871)+E(f334(f334(f292(x68871),f334(f334(f259(x68871),x68872),x68873)),f334(f334(f259(x68871),x68874),x68873)),f334(f334(f259(x68871),f334(f334(f292(x68871),x68872),x68874)),x68873)) % 169.19/169.65 [6888]~P99(x68881)+E(f334(f334(f104(x68881),f334(f334(f113(x68881),x68882),x68883)),f334(f334(f113(x68881),x68884),x68883)),f334(f334(f113(x68881),f334(f334(f104(x68881),x68882),x68884)),x68883)) % 169.19/169.65 [6889]~P99(x68891)+E(f334(f334(f113(x68891),f334(f334(f104(x68891),x68892),x68893)),f334(f334(f104(x68891),x68894),x68893)),f334(f334(f104(x68891),f334(f334(f113(x68891),x68892),x68894)),x68893)) % 169.19/169.65 [6890]~P107(x68901)+E(f334(f334(f248(x68901),f334(f334(f247(x68901),x68902),x68903)),f334(f334(f247(x68901),x68904),x68903)),f334(f334(f247(x68901),f334(f334(f248(x68901),x68902),x68904)),x68903)) % 169.19/169.65 [6891]~P107(x68911)+E(f334(f334(f247(x68911),f334(f334(f248(x68911),x68912),x68913)),f334(f334(f248(x68911),x68914),x68913)),f334(f334(f248(x68911),f334(f334(f247(x68911),x68912),x68914)),x68913)) % 169.19/169.65 [6892]~P115(x68921)+E(f334(f334(f81(x68921),f334(f334(f82(x68921),x68922),x68923)),f334(f334(f82(x68921),x68924),x68923)),f334(f334(f82(x68921),f334(f334(f81(x68921),x68922),x68924)),x68923)) % 169.19/169.65 [6924]E(f334(f334(f159(x69241,x69242),x69243),x69244),x69242)+~P104(f334(f334(f249(a877),f334(f196(f878(x69241)),x69242)),x69243)) % 169.19/169.65 [6949]~P104(f334(x69493,x69494))+P104(f334(f334(f334(f113(f886(x69491,a871)),x69492),x69493),x69494)) % 169.19/169.65 [6951]~P104(f334(x69512,x69514))+P104(f334(f334(f334(f113(f886(x69511,a871)),x69512),x69513),x69514)) % 169.19/169.65 [6970]E(f334(f334(f165(x69701),f334(f334(f134(x69701),x69702),x69703)),x69704),f334(f334(f165(x69701),x69702),x69704))+~P104(f334(f334(f250(a877),x69704),f334(f196(f878(x69701)),x69702))) % 169.19/169.65 [6980]E(f334(f334(f3(f886(x69801,a871)),f334(f334(f312(x69801),x69802),x69803)),x69804),f334(f334(f3(f886(x69801,a871)),x69803),x69804))+~P104(f334(f334(f336(x69801),x69802),x69804)) % 169.19/169.65 [7021]~E(f139(a877,f334(f304(a877,x70211),x70212)),f334(f334(f151(a877),x70214),x70213))+E(f139(a877,f334(f304(a877,f334(f334(f81(a877),x70211),f79(a877))),x70212)),x70213) % 169.19/169.65 [7092]E(x70921,f2(a877))+E(f334(f334(f151(x70922),x70923),f334(f334(f176(x70922),f334(f334(f3(a877),x70921),f79(a877))),x70924)),f334(f334(f176(x70922),x70921),f334(f334(f151(x70922),x70923),x70924))) % 169.19/169.65 [7192]E(f334(f334(f165(x71921),x71922),f334(f334(f3(a877),x71923),f334(f196(f878(x71921)),x71924))),f334(f334(f165(x71921),f334(f334(f134(x71921),x71924),x71922)),x71923))+P104(f334(f334(f250(a877),x71923),f334(f196(f878(x71921)),x71924))) % 169.19/169.65 [7222]E(f334(f334(f104(f886(x72221,a871)),x72222),f334(f334(f312(x72221),x72223),x72224)),f334(f334(f312(x72221),x72223),f334(f334(f104(f886(x72221,a871)),x72222),x72224)))+~P104(f334(f334(f336(x72221),x72223),x72222)) % 169.19/169.65 [7257]E(f334(f334(f165(x72571),f334(f334(f159(x72571,x72572),x72573),x72574)),x72573),x72574)+~P104(f334(f334(f250(a877),x72573),f334(f196(f878(x72571)),x72572))) % 169.19/169.65 [7279]E(x72791,f195(f886(x72792,a871)))+E(f334(f313(f885(x72793,x72792),x72793,f268(x72793,x72792)),f334(f334(f271(x72793,x72792),x72794),f334(f18(f886(x72792,a871),x72793),x72791))),x72794) % 169.19/169.65 [7280]E(x72801,f195(f886(x72802,a871)))+E(f334(f313(f885(x72802,x72803),x72803,f272(x72802,x72803)),f334(f334(f271(x72802,x72803),x72801),f334(f18(f886(x72803,a871),x72802),x72804))),x72804) % 169.19/169.65 [7349]E(f334(f334(f3(f886(x73491,a871)),f334(f334(f312(x73491),x73492),x73493)),x73494),f334(f334(f312(x73491),x73492),f334(f334(f3(f886(x73491,a871)),x73493),x73494)))+P104(f334(f334(f336(x73491),x73492),x73494)) % 169.19/169.65 [7386]~E(x73864,f195(f886(x73862,a871)))+E(f334(f313(f885(x73861,x73862),x73861,f268(x73861,x73862)),f334(f334(f271(x73861,x73862),x73863),f334(f18(f886(x73862,a871),x73861),x73864))),f195(f886(x73861,a871))) % 169.19/169.65 [7387]~E(x73873,f195(f886(x73871,a871)))+E(f334(f313(f885(x73871,x73872),x73872,f272(x73871,x73872)),f334(f334(f271(x73871,x73872),x73873),f334(f18(f886(x73872,a871),x73871),x73874))),f195(f886(x73872,a871))) % 169.19/169.65 [7443]~P104(f334(f334(f336(x74431),x74432),x74434))+P104(f334(f334(f336(x74431),x74432),f334(f334(f113(f886(x74431,a871)),x74433),x74434))) % 169.19/169.65 [7446]~P104(f334(f334(f336(x74461),x74462),x74463))+P104(f334(f334(f336(x74461),x74462),f334(f334(f113(f886(x74461,a871)),x74463),x74464))) % 169.19/169.65 [7465]E(f334(f334(f104(f886(x74651,a871)),f334(f334(f312(x74651),x74652),x74653)),x74654),f334(f334(f312(x74651),x74652),f334(f334(f104(f886(x74651,a871)),x74653),x74654)))+~P104(f334(f334(f336(x74651),x74652),x74654)) % 169.19/169.65 [7743]P104(f334(x77431,x77432))+~P104(f334(f334(f334(f104(f886(x77433,a871)),x77434),x77431),x77432)) % 169.19/169.65 [7744]P104(f334(x77441,x77442))+~P104(f334(f334(f334(f104(f886(x77443,a871)),x77441),x77444),x77442)) % 169.19/169.65 [7747]E(f334(f334(f8(x77471,a877),x77472),f334(f334(f3(f886(x77471,a871)),x77473),f334(f334(f312(x77471),x77474),f195(f886(x77471,a871))))),f334(f334(f8(x77471,a877),x77472),x77473))+P104(f334(f334(f336(x77471),x77474),x77473)) % 169.19/169.65 [7752]~P72(x77521)+E(f334(f166(x77521),f334(f334(f154(a877,x77521),x77522),f139(a877,f334(f304(a877,x77523),x77524)))),f334(f334(f8(a877,x77521),x77522),f334(f173(a877),f139(a877,f334(f304(a877,x77523),x77524))))) % 169.19/169.65 [7753]~P72(x77531)+E(f334(f334(f8(a877,x77531),x77532),f334(f173(a877),f139(a877,f334(f304(a877,x77533),x77534)))),f334(f166(x77531),f334(f334(f154(a877,x77531),x77532),f139(a877,f334(f304(a877,x77533),x77534))))) % 169.19/169.65 [7863]~E(x78633,x78634)+P104(f334(f64(x78631,x78632,f334(f334(f312(x78631),x78633),f195(f886(x78631,a871)))),x78634)) % 169.19/169.65 [7959]P104(f334(f334(f336(x79591),x79592),f334(f173(x79591),x79593)))+~P104(f334(f334(f336(x79591),x79592),f334(f173(x79591),f334(f334(f176(x79591),x79594),x79593)))) % 169.19/169.65 [7960]P104(f334(f334(f336(x79601),x79602),f334(f173(x79601),x79603)))+~P104(f334(f334(f336(x79601),x79602),f334(f173(x79601),f334(f334(f138(x79601),x79604),x79603)))) % 169.19/169.65 [8032]P104(f334(f334(f336(x80321),x80322),x80323))+~P104(f334(f334(f336(x80321),x80322),f334(f334(f3(f886(x80321,a871)),x80323),x80324))) % 169.19/169.65 [8034]P104(f334(f334(f336(x80341),x80342),x80343))+~P104(f334(f334(f336(x80341),x80342),f334(f334(f104(f886(x80341,a871)),x80344),x80343))) % 169.19/169.65 [8037]P104(f334(f334(f336(x80371),x80372),x80373))+~P104(f334(f334(f336(x80371),x80372),f334(f334(f104(f886(x80371,a871)),x80373),x80374))) % 169.19/169.65 [8052]E(f334(f334(f134(x80521),f334(f334(f176(x80521),x80522),x80523)),f334(f334(f151(x80521),x80524),f334(f334(f138(x80521),f334(a115,x80522)),x80523))),f334(f334(f159(x80521,x80523),x80522),x80524))+~P104(f334(f334(f250(a877),x80522),f334(f196(f878(x80521)),x80523))) % 169.19/169.65 [8075]P104(f334(f334(f336(x80751),x80752),x80753))+~P104(f334(f334(f249(f886(x80751,a871)),f334(f334(f312(x80751),x80752),x80754)),x80753)) % 169.19/169.65 [8108]~P104(f334(f334(f336(x81081),x81082),x81083))+~P104(f334(f334(f336(x81081),x81082),f334(f334(f3(f886(x81081,a871)),x81084),x81083))) % 169.19/169.65 [8140]~P104(f334(f334(f250(a877),x81404),f334(f196(f878(x81401)),x81403)))+P104(f334(f334(f336(x81401),x81402),f334(f173(x81401),f334(f334(f159(x81401,x81403),x81404),x81402)))) % 169.19/169.65 [8194]E(f334(f334(f165(x81941),f334(f334(f138(x81941),x81942),x81943)),x81944),f334(f334(f165(x81941),x81943),f334(f334(f81(a877),x81942),x81944)))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),x81942),x81944)),f334(f196(f878(x81941)),x81943))) % 169.19/169.65 [8204]~P142(x82042)+E(f334(f334(f8(x82041,x82042),f334(f334(f10(a877,x82042,x82041),f103(x82042)),x82043)),x82044),f334(f103(x82042),f334(f334(f8(x82041,a877),x82043),x82044))) % 169.19/169.65 [8205]~P137(x82052)+E(f334(f334(f8(x82051,x82052),f334(f334(f10(a1,x82052,x82051),f105(x82052)),x82053)),x82054),f334(f105(x82052),f334(f334(f8(x82051,a1),x82053),x82054))) % 169.19/169.65 [8258]~P62(x82582)+E(f334(f334(f11(x82581,x82582),f334(f334(f10(x82582,x82582,x82581),f76(x82582)),x82583)),x82584),f334(f76(x82582),f334(f334(f11(x82581,x82582),x82583),x82584))) % 169.19/169.65 [8259]~P64(x82592)+E(f334(f334(f8(x82591,x82592),f334(f334(f10(x82592,x82592,x82591),f80(x82592)),x82593)),x82594),f334(f80(x82592),f334(f334(f8(x82591,x82592),x82593),x82594))) % 169.19/169.65 [8261]E(f334(f334(f8(x82611,a877),x82612),f334(f334(f3(f886(x82611,a871)),x82613),f334(f334(f312(x82611),x82614),f195(f886(x82611,a871))))),f334(f334(f3(a877),f334(f334(f8(x82611,a877),x82612),x82613)),f334(x82612,x82614)))+~P104(f334(f334(f336(x82611),x82614),x82613)) % 169.19/169.65 [8281]P104(f334(f334(f249(f886(x82811,a871)),x82812),x82813))+~P104(f334(f334(f249(f886(x82811,a871)),f334(f334(f312(x82811),x82814),x82812)),x82813)) % 169.19/169.65 [8482]E(f334(f334(f179(x84821,x84822),x84823),x84824),f198(x84822))+P104(f334(f334(f336(x84821),x84824),f334(f313(f885(x84821,x84822),x84821,f268(x84821,x84822)),f334(f173(f885(x84821,x84822)),x84823)))) % 169.19/169.65 [8483]P39(x84831,x84832)+~P39(x84831,f334(f334(f312(f885(x84831,x84831)),f334(f334(f269(x84831,x84831),x84833),x84834)),x84832)) % 169.19/169.65 [8484]P55(x84841,x84842)+~P55(x84841,f334(f334(f312(f885(x84841,x84841)),f334(f334(f269(x84841,x84841),x84843),x84844)),x84842)) % 169.19/169.65 [8490]~P107(x84901)+E(f334(f334(f148(x84901,x84901,f7(x84901)),x84902),f334(f334(f148(x84901,x84901,f7(x84901)),x84903),x84904)),f334(f334(f148(x84901,x84901,f7(x84901)),x84903),f334(f334(f148(x84901,x84901,f7(x84901)),x84902),x84904))) % 169.19/169.65 [8500]E(x85001,x85002)+~P104(f334(f64(x85003,x85004,f334(f334(f312(x85003),x85001),f195(f886(x85003,a871)))),x85002)) % 169.19/169.65 [8510]E(f334(f334(f134(x85101),f334(f334(f176(x85101),x85102),x85103)),f334(f334(f176(x85101),x85104),f334(f334(f138(x85101),x85102),x85103))),f334(f334(f176(x85101),f334(f334(f81(a877),x85102),x85104)),x85103))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),x85102),x85104)),f334(f196(f878(x85101)),x85103))) % 169.19/169.65 [8547]P104(f334(f63(x85471),x85472))+~E(x85472,f334(f313(a877,x85471,x85473),f334(f254(a877),f334(f334(f9(a877,a877,a871),f250(a877)),x85474)))) % 169.19/169.65 [8567]~P87(x85671)+E(f334(f142(x85671,x85671,f81(x85671),f334(f334(f81(x85671),x85672),x85673)),x85674),f334(f334(f81(x85671),x85672),f334(f142(x85671,x85671,f81(x85671),x85673),x85674))) % 169.19/169.65 [8602]P104(f334(f334(f249(f886(x86021,a871)),f334(f267(x86021,x86022),x86023)),f334(f267(x86021,x86022),x86024)))+~P104(f334(f334(f249(f886(f885(x86021,x86022),a871)),x86023),x86024)) % 169.19/169.65 [8615]~P104(f334(f334(f249(a877),x86152),x86154))+P104(f334(f334(f249(f886(x86151,a871)),f334(f173(x86151),f334(f334(f176(x86151),x86152),x86153))),f334(f173(x86151),f334(f334(f176(x86151),x86154),x86153)))) % 169.19/169.65 [8616]~P104(f334(f334(f249(a877),x86164),x86162))+P104(f334(f334(f249(f886(x86161,a871)),f334(f173(x86161),f334(f334(f138(x86161),x86162),x86163))),f334(f173(x86161),f334(f334(f138(x86161),x86164),x86163)))) % 169.19/169.65 [8668]~P104(f334(f63(x86681),f334(f334(f3(f886(x86681,a871)),x86682),x86684)))+P104(f334(f63(x86681),f334(f334(f3(f886(x86681,a871)),x86682),f334(f334(f312(x86681),x86683),x86684)))) % 169.19/169.65 [8704]P104(f334(f334(f336(f885(x87041,x87041)),x87042),f310(x87041,x87043)))+~P104(f334(f334(f336(f885(x87041,x87041)),x87042),f334(f334(f190(f885(x87041,x87041),a871),x87044),x87043))) % 169.19/169.65 [8781]~P104(f334(f63(x87811),f334(f334(f3(f886(x87811,a871)),x87812),f334(f334(f312(x87811),x87814),x87813))))+P104(f334(f63(x87811),f334(f334(f3(f886(x87811,a871)),x87812),x87813))) % 169.19/169.65 [8928]~E(f334(f334(f179(x89281,x89282),x89283),x89284),f198(x89282))+~P104(f334(f334(f336(x89281),x89284),f334(f313(f885(x89281,x89282),x89281,f268(x89281,x89282)),f334(f173(f885(x89281,x89282)),x89283)))) % 169.19/169.65 [8987]~P95(x89871)+P104(f334(f334(f249(x89871),f334(f334(f113(x89871),x89872),f334(f334(f104(x89871),x89873),x89874))),f334(f334(f104(x89871),f334(f334(f113(x89871),x89872),x89873)),f334(f334(f113(x89871),x89872),x89874)))) % 169.19/169.65 [8988]~P107(x89881)+P104(f334(f334(f249(x89881),f334(f334(f248(x89881),x89882),f334(f334(f247(x89881),x89883),x89884))),f334(f334(f247(x89881),f334(f334(f248(x89881),x89882),x89883)),f334(f334(f248(x89881),x89882),x89884)))) % 169.19/169.65 [9131]E(x91311,x91312)+~P104(f334(f334(f336(f885(x91313,x91313)),f334(f334(f269(x91313,x91313),x91311),x91312)),f334(f173(f885(x91313,x91313)),f334(f334(f183(x91313,x91313),x91314),x91314)))) % 169.19/169.65 [9161]~P104(f334(f334(f336(f885(x91611,x91611)),f334(f334(f269(x91611,x91611),x91613),x91612)),f310(x91611,x91614)))+~P39(x91611,f334(f334(f312(f885(x91611,x91611)),f334(f334(f269(x91611,x91611),x91612),x91613)),x91614)) % 169.19/169.65 [9162]~P104(f334(f334(f336(f885(x91621,x91621)),f334(f334(f269(x91621,x91621),x91623),x91622)),f310(x91621,x91624)))+~P55(x91621,f334(f334(f312(f885(x91621,x91621)),f334(f334(f269(x91621,x91621),x91622),x91623)),x91624)) % 169.19/169.65 [9167]E(x91671,x91672)+E(f334(f136(x91673,f334(f334(f10(a871,a871,x91673),a329),f334(a331,x91671))),f334(f334(f151(x91673),x91672),x91674)),f334(f334(f151(x91673),x91672),f334(f136(x91673,f334(f334(f10(a871,a871,x91673),a329),f334(a331,x91671))),x91674))) % 169.19/169.65 [9211]~P95(x92111)+P104(f334(f334(f249(x92111),f334(f334(f113(x92111),f334(f334(f104(x92111),x92112),x92113)),f334(f334(f104(x92111),x92112),x92114))),f334(f334(f104(x92111),x92112),f334(f334(f113(x92111),x92113),x92114)))) % 169.19/169.65 [9212]~P107(x92121)+P104(f334(f334(f249(x92121),f334(f334(f248(x92121),f334(f334(f247(x92121),x92122),x92123)),f334(f334(f247(x92121),x92122),x92124))),f334(f334(f247(x92121),x92122),f334(f334(f248(x92121),x92123),x92124)))) % 169.19/169.65 [9278]~E(f334(f313(x92782,x92781,x92783),f257(f886(x92782,a871))),f257(f886(x92781,a871)))+P104(f334(f334(f249(f886(x92781,a871)),f334(f80(f886(x92781,a871)),f334(f313(x92782,x92781,x92783),x92784))),f334(f313(x92782,x92781,x92783),f334(f80(f886(x92782,a871)),x92784)))) % 169.19/169.65 [9588]P104(f334(f334(f336(f885(x95881,x95881)),f334(f334(f269(x95881,x95881),x95882),x95883)),f334(f289(x95881,x95881),f334(f334(f291(x95881,x95881,x95881),x95884),f310(x95881,x95884)))))+~P104(f334(f334(f336(f885(x95881,x95881)),f334(f334(f269(x95881,x95881),x95882),x95883)),f334(f334(f291(x95881,x95881,x95881),f334(f289(x95881,x95881),x95884)),f310(x95881,f334(f289(x95881,x95881),x95884))))) % 169.19/169.65 [9589]~P104(f334(f334(f336(f885(x95891,x95891)),f334(f334(f269(x95891,x95891),x95892),x95893)),f334(f289(x95891,x95891),f334(f334(f291(x95891,x95891,x95891),x95894),f310(x95891,x95894)))))+P104(f334(f334(f336(f885(x95891,x95891)),f334(f334(f269(x95891,x95891),x95892),x95893)),f334(f334(f291(x95891,x95891,x95891),f334(f289(x95891,x95891),x95894)),f310(x95891,f334(f289(x95891,x95891),x95894))))) % 169.19/169.65 [9610]~P104(f334(f334(f336(x96102),x96104),f334(f265(x96101,x96102),x96103)))+P104(f334(f334(f336(f885(x96101,x96102)),f334(f334(f269(x96101,x96102),f690(x96103,x96101,x96104,x96102)),x96104)),x96103)) % 169.19/169.65 [9611]~P104(f334(f334(f336(x96112),x96114),f334(f265(x96111,x96112),x96113)))+P104(f334(f334(f336(f885(x96111,x96112)),f334(f334(f269(x96111,x96112),f691(x96113,x96111,x96114,x96112)),x96114)),x96113)) % 169.19/169.65 [9636]~P104(f334(f334(f336(x96361),x96364),f334(f334(f113(f886(x96361,a871)),x96362),x96363)))+P104(f334(f334(f334(f113(f886(x96361,a871)),f334(f334(f9(x96361,f886(x96361,a871),a871),f336(x96361)),x96362)),f334(f334(f9(x96361,f886(x96361,a871),a871),f336(x96361)),x96363)),x96364)) % 169.19/169.65 [9637]~P104(f334(f334(f336(x96371),x96374),f334(f334(f104(f886(x96371,a871)),x96372),x96373)))+P104(f334(f334(f334(f104(f886(x96371,a871)),f334(f334(f9(x96371,f886(x96371,a871),a871),f336(x96371)),x96372)),f334(f334(f9(x96371,f886(x96371,a871),a871),f336(x96371)),x96373)),x96374)) % 169.19/169.65 [9714]~P104(f334(f334(f336(f885(x97141,x97141)),f334(f334(f269(x97141,x97141),x97144),x97143)),f334(f334(f291(x97141,x97141,x97141),x97142),f310(x97141,x97142))))+P104(f334(f334(f336(f885(x97141,x97141)),f334(f334(f269(x97141,x97141),f778(x97142,x97143,x97144,x97141)),x97143)),x97142)) % 169.19/169.65 [9759]P104(f334(f334(f336(x97591),x97592),f334(f334(f113(f886(x97591,a871)),x97593),x97594)))+~P104(f334(f334(f334(f113(f886(x97591,a871)),f334(f334(f9(x97591,f886(x97591,a871),a871),f336(x97591)),x97593)),f334(f334(f9(x97591,f886(x97591,a871),a871),f336(x97591)),x97594)),x97592)) % 169.19/169.65 [9760]P104(f334(f334(f336(x97601),x97602),f334(f334(f104(f886(x97601,a871)),x97603),x97604)))+~P104(f334(f334(f334(f104(f886(x97601,a871)),f334(f334(f9(x97601,f886(x97601,a871),a871),f336(x97601)),x97603)),f334(f334(f9(x97601,f886(x97601,a871),a871),f336(x97601)),x97604)),x97602)) % 169.19/169.65 [10036]P34(x100361,f334(f334(f9(x100361,f886(f885(x100361,x100361),a871),f886(x100361,a871)),f334(f334(f10(f886(x100361,f886(f886(f885(x100361,x100361),a871),a871)),f886(f886(f885(x100361,x100361),a871),f886(x100361,a871)),x100361),f9(x100361,f886(f885(x100361,x100361),a871),a871)),f334(f334(f10(f886(x100361,f885(x100361,x100361)),f886(x100361,f886(f886(f885(x100361,x100361),a871),a871)),x100361),f334(f10(f885(x100361,x100361),f886(f886(f885(x100361,x100361),a871),a871),x100361),f336(f885(x100361,x100361)))),f269(x100361,x100361)))),x100362),x100363,x100364)+~P104(f334(f334(f336(f885(f878(x100361),f878(x100361))),f334(f334(f269(f878(x100361),f878(x100361)),x100363),x100364)),f158(x100361,x100362))) % 169.19/169.65 [10040]P56(x100401,f334(f334(f9(x100401,f886(f885(x100401,x100401),a871),f886(x100401,a871)),f334(f334(f10(f886(x100401,f886(f886(f885(x100401,x100401),a871),a871)),f886(f886(f885(x100401,x100401),a871),f886(x100401,a871)),x100401),f9(x100401,f886(f885(x100401,x100401),a871),a871)),f334(f334(f10(f886(x100401,f885(x100401,x100401)),f886(x100401,f886(f886(f885(x100401,x100401),a871),a871)),x100401),f334(f10(f885(x100401,x100401),f886(f886(f885(x100401,x100401),a871),a871),x100401),f336(f885(x100401,x100401)))),f269(x100401,x100401)))),x100402),x100403,x100404)+~P104(f334(f334(f336(f885(f886(x100401,a871),f886(x100401,a871))),f334(f334(f269(f886(x100401,a871),f886(x100401,a871)),x100403),x100404)),f326(x100401,x100402))) % 169.19/169.65 [10069]E(x100691,x100692)+~E(f334(f334(f9(x100693,f886(f885(x100693,x100694),a871),f886(x100694,a871)),f334(f334(f10(f886(x100694,f886(f886(f885(x100693,x100694),a871),a871)),f886(f886(f885(x100693,x100694),a871),f886(x100694,a871)),x100693),f9(x100694,f886(f885(x100693,x100694),a871),a871)),f334(f334(f10(f886(x100694,f885(x100693,x100694)),f886(x100694,f886(f886(f885(x100693,x100694),a871),a871)),x100693),f334(f10(f885(x100693,x100694),f886(f886(f885(x100693,x100694),a871),a871),x100694),f336(f885(x100693,x100694)))),f269(x100693,x100694)))),x100691),f334(f334(f9(x100693,f886(f885(x100693,x100694),a871),f886(x100694,a871)),f334(f334(f10(f886(x100694,f886(f886(f885(x100693,x100694),a871),a871)),f886(f886(f885(x100693,x100694),a871),f886(x100694,a871)),x100693),f9(x100694,f886(f885(x100693,x100694),a871),a871)),f334(f334(f10(f886(x100694,f885(x100693,x100694)),f886(x100694,f886(f886(f885(x100693,x100694),a871),a871)),x100693),f334(f10(f885(x100693,x100694),f886(f886(f885(x100693,x100694),a871),a871),x100694),f336(f885(x100693,x100694)))),f269(x100693,x100694)))),x100692)) % 169.19/169.65 [10072]~P34(x100721,f334(f334(f9(x100721,f886(f885(x100721,x100721),a871),f886(x100721,a871)),f334(f334(f10(f886(x100721,f886(f886(f885(x100721,x100721),a871),a871)),f886(f886(f885(x100721,x100721),a871),f886(x100721,a871)),x100721),f9(x100721,f886(f885(x100721,x100721),a871),a871)),f334(f334(f10(f886(x100721,f885(x100721,x100721)),f886(x100721,f886(f886(f885(x100721,x100721),a871),a871)),x100721),f334(f10(f885(x100721,x100721),f886(f886(f885(x100721,x100721),a871),a871),x100721),f336(f885(x100721,x100721)))),f269(x100721,x100721)))),x100724),x100722,x100723)+P104(f334(f334(f336(f885(f878(x100721),f878(x100721))),f334(f334(f269(f878(x100721),f878(x100721)),x100722),x100723)),f158(x100721,x100724))) % 169.19/169.65 [10073]~P56(x100731,f334(f334(f9(x100731,f886(f885(x100731,x100731),a871),f886(x100731,a871)),f334(f334(f10(f886(x100731,f886(f886(f885(x100731,x100731),a871),a871)),f886(f886(f885(x100731,x100731),a871),f886(x100731,a871)),x100731),f9(x100731,f886(f885(x100731,x100731),a871),a871)),f334(f334(f10(f886(x100731,f885(x100731,x100731)),f886(x100731,f886(f886(f885(x100731,x100731),a871),a871)),x100731),f334(f10(f885(x100731,x100731),f886(f886(f885(x100731,x100731),a871),a871),x100731),f336(f885(x100731,x100731)))),f269(x100731,x100731)))),x100734),x100732,x100733)+P104(f334(f334(f336(f885(f886(x100731,a871),f886(x100731,a871))),f334(f334(f269(f886(x100731,a871),f886(x100731,a871)),x100732),x100733)),f326(x100731,x100734))) % 169.19/169.65 [7516]~P92(x75161)+E(f334(f334(f82(x75161),f334(f106(x75161),x75162)),f334(f334(f82(x75161),f334(f106(x75161),x75163)),x75164)),f334(f334(f82(x75161),f334(f106(x75161),f334(f334(f82(a1),x75162),x75163))),x75164)) % 169.19/169.65 [7517]~P92(x75171)+E(f334(f334(f81(x75171),f334(f106(x75171),x75172)),f334(f334(f3(x75171),f334(f106(x75171),x75173)),x75174)),f334(f334(f3(x75171),f334(f106(x75171),f334(f334(f81(a1),x75172),x75173))),x75174)) % 169.19/169.65 [7518]~P92(x75181)+E(f334(f334(f81(x75181),f334(f106(x75181),x75182)),f334(f334(f81(x75181),f334(f106(x75181),x75183)),x75184)),f334(f334(f81(x75181),f334(f106(x75181),f334(f334(f81(a1),x75182),x75183))),x75184)) % 169.19/169.65 [7563]~P142(x75631)+E(f334(f166(x75631),f334(f334(f154(x75632,x75631),f334(f18(x75631,x75632),x75633)),x75634)),f334(f334(f82(x75631),f334(f103(x75631),f334(f196(f878(x75632)),x75634))),x75633)) % 169.19/169.65 [7799]E(f334(f280(x77991,f334(f334(f151(f885(a102,x77991)),x77992),x77993)),x77994),f334(f272(a102,x77991),x77992))+~P104(f334(f334(f250(a102),x77994),f334(f268(a102,x77991),x77992))) % 169.19/169.65 [7841]~P92(x78411)+E(f334(f334(f81(x78411),f334(f106(x78411),x78412)),f334(f334(f3(x78411),x78413),f334(f106(x78411),x78414))),f334(f334(f81(x78411),f334(f106(x78411),f334(f334(f81(a1),x78412),f334(f80(a1),x78414)))),x78413)) % 169.19/169.65 [7972]E(f334(f280(x79721,x79722),f334(f334(f3(a102),x79723),f334(f268(a102,x79721),x79724))),f334(f280(x79721,f334(f334(f151(f885(a102,x79721)),x79724),x79722)),x79723))+P104(f334(f334(f250(a102),x79723),f334(f268(a102,x79721),x79724))) % 169.19/169.65 [8405]~P104(f334(f334(f336(x84051),x84052),f334(f173(x84051),f117(x84051,x84054))))+P104(f334(f334(f336(x84051),x84052),f334(f173(x84051),f117(x84051,f334(f334(f134(x84051),x84053),x84054))))) % 169.19/169.65 [8406]~P104(f334(f334(f336(x84061),x84062),f334(f173(x84061),f117(x84061,x84063))))+P104(f334(f334(f336(x84061),x84062),f334(f173(x84061),f117(x84061,f334(f334(f134(x84061),x84063),x84064))))) % 169.19/169.65 [8423]E(f334(f334(f113(f886(x84231,a871)),f334(f334(f104(f886(x84231,a871)),x84232),x84233)),x84234),f334(f334(f104(f886(x84231,a871)),x84232),f334(f334(f113(f886(x84231,a871)),x84233),x84234)))+~P104(f334(f334(f249(f886(x84231,a871)),x84234),x84232)) % 169.19/169.65 [8717]~E(f334(f334(f113(f886(x87171,a871)),f334(f334(f104(f886(x87171,a871)),x87173),x87174)),x87172),f334(f334(f104(f886(x87171,a871)),x87173),f334(f334(f113(f886(x87171,a871)),x87174),x87172)))+P104(f334(f334(f249(f886(x87171,a871)),x87172),x87173)) % 169.19/169.65 [8992]~P104(f334(f334(f249(f886(x89921,a871)),x89922),f334(f334(f113(f886(x89921,a871)),x89923),x89924)))+P104(f334(f334(f249(f886(x89921,a871)),f334(f334(f3(f886(x89921,a871)),x89922),x89923)),x89924)) % 169.19/169.65 [9109]P104(f334(f334(f249(f886(x91091,a871)),x91092),f334(f334(f113(f886(x91091,a871)),x91093),x91094)))+~P104(f334(f334(f249(f886(x91091,a871)),f334(f334(f3(f886(x91091,a871)),x91092),x91093)),x91094)) % 169.19/169.65 [9192]~P83(x91921)+E(f334(f76(x91921),f334(f334(f8(x91922,x91921),f334(f334(f10(x91921,x91921,x91922),f76(x91921)),x91923)),x91924)),f334(f334(f8(x91922,x91921),f334(f334(f10(x91921,x91921,x91922),f76(x91921)),x91923)),x91924)) % 169.19/169.65 [9352]~P83(x93521)+P104(f334(f334(f249(x93521),f2(x93521)),f334(f334(f8(x93522,x93521),f334(f334(f10(x93521,x93521,x93522),f76(x93521)),x93523)),x93524))) % 169.19/169.65 [9356]~P64(x93561)+E(f334(f166(x93561),f334(f334(f154(x93562,x93561),f334(f74(x93561,x93561,x93562,f80(x93561)),x93563)),x93564)),f334(f80(x93561),f334(f166(x93561),f334(f334(f154(x93562,x93561),x93563),x93564)))) % 169.19/169.65 [9486]~P83(x94861)+P104(f334(f334(f249(x94861),f334(f76(x94861),f334(f334(f8(x94862,x94861),x94863),x94864))),f334(f334(f8(x94862,x94861),f334(f334(f10(x94861,x94861,x94862),f76(x94861)),x94863)),x94864))) % 169.19/169.65 [9513]~E(f334(f334(f81(a877),x95131),x95134),f334(f334(f81(a877),x95133),x95132))+P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),f334(f334(f269(a877,a877),x95131),x95132)),f334(f334(f269(a877,a877),x95133),x95134))),a111)) % 169.19/169.65 [9514]~P104(f334(f334(f250(a877),x95141),x95143))+P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),f334(f334(f269(a877,a877),x95141),x95142)),f334(f334(f269(a877,a877),x95143),x95144))),a36)) % 169.19/169.65 [9515]~P104(f334(f334(f250(a877),x95151),x95153))+P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),f334(f334(f269(a877,a877),x95151),x95152)),f334(f334(f269(a877,a877),x95153),x95154))),a71)) % 169.19/169.65 [9661]E(f334(f334(f81(a877),x96611),x96612),f334(f334(f81(a877),x96613),x96614))+~P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),f334(f334(f269(a877,a877),x96611),x96614)),f334(f334(f269(a877,a877),x96613),x96612))),a111)) % 169.19/169.65 [9688]E(f334(f334(f165(x96881),f334(f334(f138(x96881),f334(f196(f878(x96881)),f178(x96881,x96882,x96883))),x96883)),x96884),f334(f334(f165(x96881),x96883),f334(f334(f81(a877),x96884),f334(f196(f878(x96881)),f178(x96881,x96882,x96883)))))+~P104(f334(f334(f250(a877),x96884),f334(f196(f878(x96881)),f334(f334(f138(x96881),f334(f196(f878(x96881)),f178(x96881,x96882,x96883))),x96883)))) % 169.19/169.65 [9705]~P104(f334(f334(f336(x97052),x97054),f334(f334(f43(x97051,f886(x97052,a871)),f257(f886(x97051,a871))),x97053)))+P104(f334(f334(f334(f43(x97051,f886(x97052,a871)),f257(f886(x97051,a871))),f334(f334(f10(f886(x97052,a871),f886(x97052,a871),x97051),f334(f9(x97052,f886(x97052,a871),a871),f336(x97052))),x97053)),x97054)) % 169.19/169.65 [9706]~P104(f334(f334(f336(x97062),x97064),f334(f334(f44(x97061,f886(x97062,a871)),f257(f886(x97061,a871))),x97063)))+P104(f334(f334(f334(f44(x97061,f886(x97062,a871)),f257(f886(x97061,a871))),f334(f334(f10(f886(x97062,a871),f886(x97062,a871),x97061),f334(f9(x97062,f886(x97062,a871),a871),f336(x97062))),x97063)),x97064)) % 169.19/169.65 [9787]~P104(f334(f50(x97871,x97872),f334(f334(f269(a1,a1),x97874),x97873)))+P104(f334(f50(f334(f80(a1),x97871),x97872),f334(f334(f269(a1,a1),f334(f334(f334(f99(a1),f334(f334(a331,x97873),f2(a1))),f334(f80(a1),x97874)),f334(f334(f3(a1),f334(f80(a1),x97874)),f79(a1)))),f334(f334(f334(f99(a1),f334(f334(a331,x97873),f2(a1))),f2(a1)),f334(f334(f3(a1),x97872),x97873))))) % 169.19/169.65 [9797]P104(f334(f334(f336(x97971),x97972),f334(f334(f43(x97973,f886(x97971,a871)),f257(f886(x97973,a871))),x97974)))+~P104(f334(f334(f334(f43(x97973,f886(x97971,a871)),f257(f886(x97973,a871))),f334(f334(f10(f886(x97971,a871),f886(x97971,a871),x97973),f334(f9(x97971,f886(x97971,a871),a871),f336(x97971))),x97974)),x97972)) % 169.19/169.65 [9798]P104(f334(f334(f336(x97981),x97982),f334(f334(f44(x97983,f886(x97981,a871)),f257(f886(x97983,a871))),x97984)))+~P104(f334(f334(f334(f44(x97983,f886(x97981,a871)),f257(f886(x97983,a871))),f334(f334(f10(f886(x97981,a871),f886(x97981,a871),x97983),f334(f9(x97981,f886(x97981,a871),a871),f336(x97981))),x97984)),x97982)) % 169.19/169.65 [9810]E(f334(f334(f44(a877,f886(x98101,a871)),f257(f886(a877,a871))),x98102),f334(f334(f44(a877,f886(x98101,a871)),f257(f886(a877,a871))),x98103))+~E(f334(f334(f44(a877,f886(x98101,a871)),f334(f304(a877,f2(a877)),f537(x98102,x98104,x98103,x98101))),x98103),f334(f334(f44(a877,f886(x98101,a871)),f334(f304(a877,f2(a877)),f334(f334(f81(a877),f537(x98102,x98104,x98103,x98101)),x98104))),x98102)) % 169.19/169.65 [10129]~P104(f334(f334(f249(f886(f885(x101291,x101292),a871)),x101293),x101294))+P104(f334(f334(f249(f886(x101291,f886(x101292,a871))),f334(f334(f9(x101291,f886(f885(x101291,x101292),a871),f886(x101292,a871)),f334(f334(f10(f886(x101292,f886(f886(f885(x101291,x101292),a871),a871)),f886(f886(f885(x101291,x101292),a871),f886(x101292,a871)),x101291),f9(x101292,f886(f885(x101291,x101292),a871),a871)),f334(f334(f10(f886(x101292,f885(x101291,x101292)),f886(x101292,f886(f886(f885(x101291,x101292),a871),a871)),x101291),f334(f10(f885(x101291,x101292),f886(f886(f885(x101291,x101292),a871),a871),x101292),f336(f885(x101291,x101292)))),f269(x101291,x101292)))),x101293)),f334(f334(f9(x101291,f886(f885(x101291,x101292),a871),f886(x101292,a871)),f334(f334(f10(f886(x101292,f886(f886(f885(x101291,x101292),a871),a871)),f886(f886(f885(x101291,x101292),a871),f886(x101292,a871)),x101291),f9(x101292,f886(f885(x101291,x101292),a871),a871)),f334(f334(f10(f886(x101292,f885(x101291,x101292)),f886(x101292,f886(f886(f885(x101291,x101292),a871),a871)),x101291),f334(f10(f885(x101291,x101292),f886(f886(f885(x101291,x101292),a871),a871),x101292),f336(f885(x101291,x101292)))),f269(x101291,x101292)))),x101294))) % 169.19/169.65 [10146]P104(f334(f334(f249(f886(f885(x101461,x101462),a871)),x101463),x101464))+~P104(f334(f334(f249(f886(x101461,f886(x101462,a871))),f334(f334(f9(x101461,f886(f885(x101461,x101462),a871),f886(x101462,a871)),f334(f334(f10(f886(x101462,f886(f886(f885(x101461,x101462),a871),a871)),f886(f886(f885(x101461,x101462),a871),f886(x101462,a871)),x101461),f9(x101462,f886(f885(x101461,x101462),a871),a871)),f334(f334(f10(f886(x101462,f885(x101461,x101462)),f886(x101462,f886(f886(f885(x101461,x101462),a871),a871)),x101461),f334(f10(f885(x101461,x101462),f886(f886(f885(x101461,x101462),a871),a871),x101462),f336(f885(x101461,x101462)))),f269(x101461,x101462)))),x101463)),f334(f334(f9(x101461,f886(f885(x101461,x101462),a871),f886(x101462,a871)),f334(f334(f10(f886(x101462,f886(f886(f885(x101461,x101462),a871),a871)),f886(f886(f885(x101461,x101462),a871),f886(x101462,a871)),x101461),f9(x101462,f886(f885(x101461,x101462),a871),a871)),f334(f334(f10(f886(x101462,f885(x101461,x101462)),f886(x101462,f886(f886(f885(x101461,x101462),a871),a871)),x101461),f334(f10(f885(x101461,x101462),f886(f886(f885(x101461,x101462),a871),a871),x101462),f336(f885(x101461,x101462)))),f269(x101461,x101462)))),x101464))) % 169.19/169.65 [9236]~P104(f334(f334(f336(f885(x92361,x92361)),x92362),f310(x92361,x92364)))+P104(f334(f334(f336(f885(x92361,x92361)),x92362),f310(x92361,f334(f334(f113(f886(f885(x92361,x92361),a871)),x92363),x92364)))) % 169.19/169.65 [9237]~P104(f334(f334(f336(f885(x92371,x92371)),x92372),f310(x92371,x92373)))+P104(f334(f334(f336(f885(x92371,x92371)),x92372),f310(x92371,f334(f334(f113(f886(f885(x92371,x92371),a871)),x92373),x92374)))) % 169.19/169.65 [9580]~E(f334(f173(x95801),x95804),f185(x95801,x95802,x95803))+E(f334(f179(x95801,x95802),f334(f334(f154(x95801,f885(x95801,x95802)),f334(f334(f20(x95801,x95802,f885(x95801,x95802)),f269(x95801,x95802)),f334(f334(f10(f881(x95802),x95802,x95801),f245(x95802)),x95803))),x95804)),x95803) % 169.19/169.65 [9901]~P104(f334(f334(f249(a877),f334(f334(f81(a877),x99011),x99014)),f334(f334(f81(a877),x99013),x99012)))+P104(f334(f334(f249(a1),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99011),x99012)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99013),x99014)),f195(f886(f885(a877,a877),a871))))))) % 169.19/169.65 [9902]~P104(f334(f334(f250(a877),f334(f334(f81(a877),x99021),x99024)),f334(f334(f81(a877),x99023),x99022)))+P104(f334(f334(f250(a1),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99021),x99022)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99023),x99024)),f195(f886(f885(a877,a877),a871))))))) % 169.19/169.65 [9979]P104(f334(f334(f249(a877),f334(f334(f81(a877),x99791),x99792)),f334(f334(f81(a877),x99793),x99794)))+~P104(f334(f334(f249(a1),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99791),x99794)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99793),x99792)),f195(f886(f885(a877,a877),a871))))))) % 169.19/169.65 [9980]P104(f334(f334(f250(a877),f334(f334(f81(a877),x99801),x99802)),f334(f334(f81(a877),x99803),x99804)))+~P104(f334(f334(f250(a1),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99801),x99804)),f195(f886(f885(a877,a877),a871)))))),f334(a90,f334(f288(f885(a877,a877),f885(a877,a877),a111),f334(f334(f312(f885(a877,a877)),f334(f334(f269(a877,a877),x99803),x99802)),f195(f886(f885(a877,a877),a871))))))) % 169.19/169.65 [10022]P104(f334(f334(f249(f886(x100221,a871)),f334(f334(f44(a877,f886(x100221,a871)),f257(f886(a877,a871))),x100222)),f334(f334(f44(a877,f886(x100221,a871)),f257(f886(a877,a871))),x100223)))+~P104(f334(f334(f249(f886(x100221,a871)),f334(f334(f44(a877,f886(x100221,a871)),f334(f304(a877,f2(a877)),f538(x100223,x100224,x100222,x100221))),x100222)),f334(f334(f44(a877,f886(x100221,a871)),f334(f304(a877,f2(a877)),f334(f334(f81(a877),f538(x100223,x100224,x100222,x100221)),x100224))),x100223))) % 169.19/169.65 [10119]~P104(f334(f334(f336(x101192),x101194),f334(f265(x101191,x101192),x101193)))+P104(f334(f264(x101191,x101192,f334(f334(f9(x101191,f886(f885(x101191,x101192),a871),f886(x101192,a871)),f334(f334(f10(f886(x101192,f886(f886(f885(x101191,x101192),a871),a871)),f886(f886(f885(x101191,x101192),a871),f886(x101192,a871)),x101191),f9(x101192,f886(f885(x101191,x101192),a871),a871)),f334(f334(f10(f886(x101192,f885(x101191,x101192)),f886(x101192,f886(f886(f885(x101191,x101192),a871),a871)),x101191),f334(f10(f885(x101191,x101192),f886(f886(f885(x101191,x101192),a871),a871),x101192),f336(f885(x101191,x101192)))),f269(x101191,x101192)))),x101193)),x101194)) % 169.19/169.65 [10120]~P104(f334(f334(f336(x101201),x101204),f334(f267(x101201,x101202),x101203)))+P104(f334(f263(x101201,x101202,f334(f334(f9(x101201,f886(f885(x101201,x101202),a871),f886(x101202,a871)),f334(f334(f10(f886(x101202,f886(f886(f885(x101201,x101202),a871),a871)),f886(f886(f885(x101201,x101202),a871),f886(x101202,a871)),x101201),f9(x101202,f886(f885(x101201,x101202),a871),a871)),f334(f334(f10(f886(x101202,f885(x101201,x101202)),f886(x101202,f886(f886(f885(x101201,x101202),a871),a871)),x101201),f334(f10(f885(x101201,x101202),f886(f886(f885(x101201,x101202),a871),a871),x101202),f336(f885(x101201,x101202)))),f269(x101201,x101202)))),x101203)),x101204)) % 169.19/169.65 [10132]P104(f334(f334(f336(x101321),x101322),f334(f265(x101323,x101321),x101324)))+~P104(f334(f264(x101323,x101321,f334(f334(f9(x101323,f886(f885(x101323,x101321),a871),f886(x101321,a871)),f334(f334(f10(f886(x101321,f886(f886(f885(x101323,x101321),a871),a871)),f886(f886(f885(x101323,x101321),a871),f886(x101321,a871)),x101323),f9(x101321,f886(f885(x101323,x101321),a871),a871)),f334(f334(f10(f886(x101321,f885(x101323,x101321)),f886(x101321,f886(f886(f885(x101323,x101321),a871),a871)),x101323),f334(f10(f885(x101323,x101321),f886(f886(f885(x101323,x101321),a871),a871),x101321),f336(f885(x101323,x101321)))),f269(x101323,x101321)))),x101324)),x101322)) % 169.19/169.65 [10133]P104(f334(f334(f336(x101331),x101332),f334(f267(x101331,x101333),x101334)))+~P104(f334(f263(x101331,x101333,f334(f334(f9(x101331,f886(f885(x101331,x101333),a871),f886(x101333,a871)),f334(f334(f10(f886(x101333,f886(f886(f885(x101331,x101333),a871),a871)),f886(f886(f885(x101331,x101333),a871),f886(x101333,a871)),x101331),f9(x101333,f886(f885(x101331,x101333),a871),a871)),f334(f334(f10(f886(x101333,f885(x101331,x101333)),f886(x101333,f886(f886(f885(x101331,x101333),a871),a871)),x101331),f334(f10(f885(x101331,x101333),f886(f886(f885(x101331,x101333),a871),a871),x101333),f336(f885(x101331,x101333)))),f269(x101331,x101333)))),x101334)),x101332)) % 169.19/169.65 [9820]P104(f334(f160(x98201,x98202),x98203))+~P104(f334(f160(x98201,f334(f334(f20(x98201,a871,a871),f334(f334(f10(a871,f886(a871,a871),x98201),a332),x98204)),x98202)),x98203)) % 169.19/169.65 [9821]P104(f334(f160(x98211,x98212),x98213))+~P104(f334(f160(x98211,f334(f334(f20(x98211,a871,a871),f334(f334(f10(a871,f886(a871,a871),x98211),a332),x98212)),x98214)),x98213)) % 169.19/169.65 [9903]~P115(x99031)+E(f334(f334(f82(x99031),f334(f334(f81(x99031),f79(x99031)),f79(x99031))),f334(f334(f8(a877,x99031),f334(f334(f10(x99031,x99031,a877),f334(f81(x99031),x99032)),f334(f334(f9(a877,x99031,x99031),f334(f334(f10(x99031,f886(x99031,x99031),a877),f82(x99031)),f103(x99031))),x99033))),f334(f255(a877),x99034))),f334(f334(f82(x99031),f334(f103(x99031),x99034)),f334(f334(f81(x99031),x99032),f334(f334(f81(x99031),x99032),f334(f334(f82(x99031),f334(f103(x99031),f334(f334(f3(a877),x99034),f79(a877)))),x99033))))) % 169.19/169.65 [10043]P104(f334(x100431,f688(x100432,x100433,x100434,x100431)))+P39(x100432,f334(f254(f885(x100432,x100432)),f334(f273(x100432,x100432,a871),f334(f334(f10(f886(x100432,a871),f886(x100432,a871),x100432),f334(f20(x100432,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100432),a332),x100431))),f334(f334(f9(x100432,f886(x100432,x100432),f886(x100432,a871)),f334(f334(f10(f886(x100432,a871),f886(f886(x100432,x100432),f886(x100432,a871)),x100432),f10(x100432,a871,x100432)),a331)),x100433))))) % 169.19/169.65 [10057]~P104(f334(f334(f250(a877),f334(x100574,f334(x100573,f688(x100571,x100573,x100574,x100572)))),f334(x100574,f688(x100571,x100573,x100574,x100572))))+P39(x100571,f334(f254(f885(x100571,x100571)),f334(f273(x100571,x100571,a871),f334(f334(f10(f886(x100571,a871),f886(x100571,a871),x100571),f334(f20(x100571,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100571),a332),x100572))),f334(f334(f9(x100571,f886(x100571,x100571),f886(x100571,a871)),f334(f334(f10(f886(x100571,a871),f886(f886(x100571,x100571),f886(x100571,a871)),x100571),f10(x100571,a871,x100571)),a331)),x100573))))) % 169.19/169.65 [10159]~P104(f334(f334(f336(f885(x101591,x101591)),f334(f334(f269(x101591,x101591),x101593),x101594)),f334(f334(f113(f886(f885(x101591,x101591),a871)),x101592),f310(x101591,f195(f886(f885(x101591,x101591),a871))))))+P104(f334(f334(f334(f334(f113(f886(x101591,f886(x101591,a871))),f334(f334(f9(x101591,f886(f885(x101591,x101591),a871),f886(x101591,a871)),f334(f334(f10(f886(x101591,f886(f886(f885(x101591,x101591),a871),a871)),f886(f886(f885(x101591,x101591),a871),f886(x101591,a871)),x101591),f9(x101591,f886(f885(x101591,x101591),a871),a871)),f334(f334(f10(f886(x101591,f885(x101591,x101591)),f886(x101591,f886(f886(f885(x101591,x101591),a871),a871)),x101591),f334(f10(f885(x101591,x101591),f886(f886(f885(x101591,x101591),a871),a871),x101591),f336(f885(x101591,x101591)))),f269(x101591,x101591)))),x101592)),a331),x101593),x101594)) % 169.19/169.65 [10169]P104(f334(f334(f336(f885(x101691,x101691)),f334(f334(f269(x101691,x101691),x101692),x101693)),f334(f334(f113(f886(f885(x101691,x101691),a871)),x101694),f310(x101691,f195(f886(f885(x101691,x101691),a871))))))+~P104(f334(f334(f334(f334(f113(f886(x101691,f886(x101691,a871))),f334(f334(f9(x101691,f886(f885(x101691,x101691),a871),f886(x101691,a871)),f334(f334(f10(f886(x101691,f886(f886(f885(x101691,x101691),a871),a871)),f886(f886(f885(x101691,x101691),a871),f886(x101691,a871)),x101691),f9(x101691,f886(f885(x101691,x101691),a871),a871)),f334(f334(f10(f886(x101691,f885(x101691,x101691)),f886(x101691,f886(f886(f885(x101691,x101691),a871),a871)),x101691),f334(f10(f885(x101691,x101691),f886(f886(f885(x101691,x101691),a871),a871),x101691),f336(f885(x101691,x101691)))),f269(x101691,x101691)))),x101694)),a331),x101692),x101693)) % 169.19/169.65 [10116]E(f334(f334(f151(f878(x101161)),f334(f334(f151(x101161),x101162),f334(f142(f878(x101161),f878(x101161),f134(x101161),f116(x101161)),f334(f334(f154(f878(x101161),f878(x101161)),f156(f878(x101161),x101161,f116(x101161),f334(f334(f10(f878(x101161),f886(f878(x101161),f878(x101161)),x101161),f18(f878(x101161),f878(x101161))),f334(f334(f9(x101161,f878(x101161),f878(x101161)),f151(x101161)),f116(x101161))))),x101163)))),f181(x101161,f334(f334(f151(f878(x101161)),x101164),f334(f142(f878(f878(x101161)),f878(f878(x101161)),f134(f878(x101161)),f116(f878(x101161))),f334(f334(f154(f878(x101161),f878(f878(x101161))),f156(f878(f878(x101161)),x101161,f116(f878(x101161)),f334(f18(f886(f878(x101161),f878(f878(x101161))),x101161),f334(f334(f9(f878(x101161),f878(f878(x101161)),f878(f878(x101161))),f151(f878(x101161))),f116(f878(x101161)))))),x101163))))),f181(x101161,f334(f334(f151(f878(x101161)),f334(f334(f151(x101161),x101162),x101164)),x101163)))+~P104(f334(f322(f878(f878(x101161)),f182(x101161)),f334(f334(f151(f878(x101161)),f334(f334(f151(x101161),x101162),x101164)),x101163))) % 169.19/169.65 [10158]~P104(f334(f63(x101582),f334(f254(x101582),x101584)))+P104(f334(f63(x101581),f334(f254(x101581),f334(f334(f10(f886(x101582,a871),a871,x101581),f88(x101582)),f334(f334(f9(x101581,f886(x101582,a871),f886(x101582,a871)),f334(f334(f10(f886(x101582,f886(a871,a871)),f886(f886(x101582,a871),f886(x101582,a871)),x101581),f20(x101582,a871,a871)),f334(f334(f10(f886(x101582,a871),f886(x101582,f886(a871,a871)),x101581),f334(f10(a871,f886(a871,a871),x101582),a332)),f334(f334(f9(x101581,f886(x101582,x101581),f886(x101582,a871)),f334(f334(f10(f886(x101581,a871),f886(f886(x101582,x101581),f886(x101582,a871)),x101581),f10(x101581,a871,x101582)),a331)),x101583)))),x101584))))) % 169.19/169.65 [5309]E(x53091,x53092)+~E(f127(x53093,x53094,x53091),f127(x53093,x53095,x53092)) % 169.19/169.65 [5310]E(x53101,x53102)+~E(f127(x53103,x53101,x53104),f127(x53103,x53102,x53105)) % 169.19/169.65 [5311]E(x53111,x53112)+~E(f170(x53113,x53111,x53114),f170(x53113,x53112,x53115)) % 169.19/169.65 [5689]E(f334(f334(f312(x56891),x56892),f185(x56891,x56893,x56894)),f185(x56891,x56893,x56894))+~E(f334(x56894,x56892),f334(f241(x56893),x56895)) % 169.19/169.65 [6096]P104(f334(f264(x60961,x60962,x60963),x60964))+~P104(f334(f334(x60963,x60965),x60964)) % 169.19/169.65 [6098]P104(f334(f263(x60981,x60982,x60983),x60984))+~P104(f334(f334(x60983,x60984),x60985)) % 169.19/169.65 [6101]~E(f334(x61014,x61012),f334(f241(x61013),x61015))+P104(f334(f334(f336(x61011),x61012),f185(x61011,x61013,x61014))) % 169.19/169.65 [6102]~E(f334(x61024,x61025),f334(f241(x61021),x61022))+P104(f334(f334(f336(x61021),x61022),f187(x61023,x61021,x61024))) % 169.19/169.65 [6569]~E(x65695,f2(a102))+E(f334(f204(x65691,x65692,x65693,x65694),x65695),f128(x65692)) % 169.19/169.65 [6570]~E(x65705,f2(a102))+E(f334(f206(x65701,x65702,x65703,x65704),x65705),f118(x65702)) % 169.19/169.65 [6704]~E(x67043,f2(a102))+E(f334(f283(x67041,x67042,x67043,x67044),x67045),f334(f269(x67041,x67042),x67045)) % 169.19/169.65 [6776]~E(f334(x67764,x67765),f198(x67762))+E(f334(f243(f881(x67761),x67762,f198(x67761),x67763),f334(x67764,x67765)),f198(x67761)) % 169.19/169.65 [7397]E(f334(x73971,x73972),f198(x73973))+~E(f334(f186(x73974,x73973,x73975,x73971),x73972),f198(x73973)) % 169.19/169.65 [7398]E(f334(x73981,x73982),f198(x73983))+~E(f334(f186(x73984,x73983,x73981,x73985),x73982),f198(x73983)) % 169.19/169.65 [7435]E(f334(f186(x74351,x74352,x74353,x74354),x74355),f334(x74353,x74355))+P104(f334(f334(f336(x74351),x74355),f185(x74351,x74352,x74354))) % 169.19/169.65 [7436]E(f334(f186(x74361,x74362,x74363,x74364),x74365),f334(x74364,x74365))+P104(f334(f334(f336(x74361),x74365),f185(x74361,x74362,x74363))) % 169.19/169.65 [7757]~P16(x77574,x77571,x77572,x77575)+E(f334(f74(x77571,x77571,x77571,f334(x77572,x77573)),f334(x77572,x77573)),f334(x77572,x77573)) % 169.19/169.65 [7801]E(f334(f186(x78011,x78012,x78013,x78014),x78015),f334(x78014,x78015))+~P104(f334(f334(f336(x78011),x78015),f185(x78011,x78012,x78014))) % 169.19/169.65 [8141]~P12(x81415,x81411,x81412)+E(f334(f74(x81411,x81411,x81411,f334(x81412,x81413)),f334(x81412,x81414)),f334(f74(x81411,x81411,x81411,f334(x81412,x81414)),f334(x81412,x81413))) % 169.19/169.65 [8465]P104(f334(f334(f336(f885(x84651,x84651)),f334(f334(f269(x84651,x84651),x84652),x84653)),f328(x84651,x84654,x84655)))+~P104(f334(f334(f250(a877),f334(x84654,x84652)),f334(x84654,x84653))) % 169.19/169.65 [8553]~P104(f334(f334(f336(x85534),x85533),f298(x85534,x85531,x85532,x85535)))+P104(f334(f334(x85531,x85532),x85533)) % 169.19/169.65 [8554]~P104(f334(f334(f336(x85544),x85543),f301(x85544,x85541,x85542,x85545)))+P104(f334(f334(x85541,x85542),x85543)) % 169.19/169.65 [8555]~P104(f334(f334(f336(x85554),x85552),f298(x85554,x85551,x85555,x85553)))+P104(f334(f334(x85551,x85552),x85553)) % 169.19/169.65 [8556]~P104(f334(f334(f336(x85564),x85562),f301(x85564,x85561,x85565,x85563)))+P104(f334(f334(x85561,x85562),x85563)) % 169.19/169.65 [8694]~P54(x86942,x86941,x86945,x86943,x86944)+E(f334(f313(x86941,x86942,x86943),x86944),f257(f886(x86942,a871))) % 169.19/169.65 [9121]~P36(x91211,x91212,x91213,x91214,x91215)+P36(x91211,x91212,x91213,f334(f169(x91211),x91214),f334(f169(x91212),x91215)) % 169.19/169.65 [9123]~P36(x91231,x91232,x91233,f334(f169(x91231),x91234),x91235)+P36(x91231,x91232,x91233,x91234,f334(f169(x91232),x91235)) % 169.19/169.65 [9124]~P36(x91241,x91242,x91243,x91244,f334(f169(x91242),x91245))+P36(x91241,x91242,x91243,f334(f169(x91241),x91244),x91245) % 169.19/169.65 [9130]P36(x91301,x91302,x91303,x91304,x91305)+~P36(x91301,x91302,x91303,f334(f169(x91301),x91304),f334(f169(x91302),x91305)) % 169.19/169.65 [9504]P104(f334(f334(f336(f885(f878(x95041),f878(x95041))),f334(f334(f269(f878(x95041),f878(x95041)),f334(f334(f151(x95041),x95042),x95043)),f334(f334(f151(x95041),x95042),x95044))),f157(x95041,x95045)))+~P104(f334(f334(f336(f885(f878(x95041),f878(x95041))),f334(f334(f269(f878(x95041),f878(x95041)),x95043),x95044)),f157(x95041,x95045))) % 169.19/169.65 [9505]P104(f334(f334(f336(f885(f878(x95051),f878(x95051))),f334(f334(f269(f878(x95051),f878(x95051)),f334(f334(f134(x95051),x95052),x95053)),f334(f334(f134(x95051),x95052),x95054))),f147(x95051,x95055)))+~P104(f334(f334(f336(f885(f878(x95051),f878(x95051))),f334(f334(f269(f878(x95051),f878(x95051)),x95053),x95054)),f147(x95051,x95055))) % 169.19/169.65 [9695]E(f334(f334(f151(x96951),f587(x96952,x96953,x96954,x96955,x96951)),f591(x96952,x96953,x96954,x96955,x96951)),x96955)+~P104(f334(f334(f336(f885(f878(x96951),f878(x96951))),f334(f334(f269(f878(x96951),f878(x96951)),x96955),f334(f334(f151(x96951),x96954),x96953))),f158(x96951,x96952))) % 169.19/169.65 [9717]E(f334(f334(f151(x97171),f588(x97172,x97173,x97174,x97175,x97171)),f589(x97172,x97173,x97174,x97175,x97171)),x97173)+~P104(f334(f334(f336(f885(f878(x97171),f878(x97171))),f334(f334(f269(f878(x97171),f878(x97171)),f334(f334(f151(x97171),x97175),x97174)),x97173)),f158(x97171,x97172))) % 169.19/169.65 [9877]~P104(f334(f334(f336(f885(f878(x98771),f878(x98771))),f334(f334(f269(f878(x98771),f878(x98771)),f334(f334(f151(x98771),x98775),x98772)),x98774)),f158(x98771,x98773)))+P104(f334(f334(f336(f885(f878(x98771),f878(x98771))),f334(f334(f269(f878(x98771),f878(x98771)),x98772),f589(x98773,x98774,x98772,x98775,x98771))),f158(x98771,x98773))) % 169.19/169.65 [9947]~P104(f334(f334(f336(f885(f878(x99471),f878(x99471))),f334(f334(f269(f878(x99471),f878(x99471)),x99475),f334(f334(f151(x99471),x99474),x99473))),f158(x99471,x99472)))+P104(f334(f334(f336(f885(f878(x99471),f878(x99471))),f334(f334(f269(f878(x99471),f878(x99471)),f591(x99472,x99473,x99474,x99475,x99471)),x99473)),f158(x99471,x99472))) % 169.19/169.65 [10111]P104(f334(f334(f336(f885(x101111,x101111)),f334(f334(f269(x101111,x101111),f334(x101112,f334(f334(f81(a877),x101113),x101114))),f334(x101112,x101113))),f310(x101111,x101115)))+~P104(f334(f334(f336(f885(x101111,x101111)),f334(f334(f269(x101111,x101111),f334(x101112,f334(a115,f755(x101114,x101113,x101115,x101112,x101111)))),f334(x101112,f755(x101114,x101113,x101115,x101112,x101111)))),f310(x101111,x101115))) % 169.19/169.65 [5272]E(x52721,x52722)+~E(f334(f334(f151(x52723),x52724),x52721),f334(f334(f151(x52723),x52725),x52722)) % 169.19/169.65 [5273]E(x52731,x52732)+~E(f334(f334(f151(x52733),x52731),x52734),f334(f334(f151(x52733),x52732),x52735)) % 169.19/169.65 [5327]P104(f334(x53271,x53272))+~E(f334(f136(x53273,x53271),x53274),f334(f334(f151(x53273),x53272),x53275)) % 169.19/169.65 [5328]P104(f334(x53281,x53282))+~E(f334(f334(f151(x53283),x53282),x53284),f334(f136(x53283,x53281),x53285)) % 169.19/169.65 [5485]~E(f334(f334(f138(x54851),x54853),x54852),f334(f334(f151(x54851),x54854),x54855))+E(f334(f334(f165(x54851),x54852),x54853),x54854) % 169.19/169.65 [5619]~P11(x56194,x56195,x56191)+E(f334(f334(x56191,x56192),f334(f334(x56191,x56192),x56193)),f334(f334(x56191,x56192),x56193)) % 169.19/169.65 [6154]~E(x61544,f2(a102))+E(f334(f334(f120(x61541,x61542,x61543),x61544),x61545),f334(f334(f269(f878(x61542),x61541),f116(x61542)),x61545)) % 169.19/169.65 [6227]~P107(x62272)+~E(f334(f334(f148(x62271,x62272,x62273),x62274),x62275),f116(x62271)) % 169.19/169.65 [6606]E(x66061,x66062)+~E(f334(f334(f134(x66063),x66064),f334(f334(f151(x66063),x66061),f116(x66063))),f334(f334(f134(x66063),x66065),f334(f334(f151(x66063),x66062),f116(x66063)))) % 169.19/169.65 [6607]E(x66071,x66072)+~E(f334(f334(f134(x66073),x66071),f334(f334(f151(x66073),x66074),f116(x66073))),f334(f334(f134(x66073),x66072),f334(f334(f151(x66073),x66075),f116(x66073)))) % 169.19/169.65 [6860]E(f334(f189(x68601,x68602,x68603,x68604),x68605),f198(x68602))+P104(f334(f334(f336(x68601),x68605),x68604)) % 169.19/169.65 [6922]E(f334(f334(f312(x69221),f334(x69222,x69223)),f334(f313(x69224,x69221,x69222),x69225)),f334(f313(x69224,x69221,x69222),x69225))+~P104(f334(f334(f336(x69224),x69223),x69225)) % 169.19/169.65 [6929]~P104(f334(x69294,f334(x69293,x69295)))+P104(f334(f334(f314(x69291,x69292,x69293),x69294),x69295)) % 169.19/169.65 [6932]~P104(f334(f334(x69323,x69325),x69324))+P104(f334(f334(f258(x69321,x69322,x69323),x69324),x69325)) % 169.19/169.65 [7025]~E(f334(f313(x70251,x70252,x70253),x70254),x70255)+E(f334(f313(f886(x70251,a871),f886(x70252,a871),f313(x70251,x70252,x70253)),f334(f311(x70251),x70254)),f334(f311(x70252),x70255)) % 169.19/169.65 [7055]E(f334(f189(x70551,x70552,x70553,x70554),x70555),f334(x70553,x70555))+~P104(f334(f334(f336(x70551),x70555),x70554)) % 169.19/169.65 [7357]P21(x73571,x73572,x73573,x73574)+~P21(x73571,x73572,x73573,f334(f334(f312(x73571),x73575),x73574)) % 169.19/169.65 [7425]P104(f334(x74251,x74252))+~P104(f334(f334(f95(x74253,x74254,x74251),x74255),x74252)) % 169.19/169.65 [7469]~P104(f334(f334(f336(x74694),x74693),x74695))+P104(f334(f334(f336(x74691),f334(x74692,x74693)),f334(f313(x74694,x74691,x74692),x74695))) % 169.19/169.65 [7492]~P107(x74922)+E(f150(x74921,x74922,x74923,f334(f136(x74921,x74924),x74925)),f334(f136(x74921,x74924),f150(x74921,x74922,x74923,x74925))) % 169.19/169.65 [7525]P104(f334(x75251,f334(x75252,x75253)))+~P104(f334(f334(f314(x75254,x75255,x75252),x75251),x75253)) % 169.19/169.65 [7528]P104(f334(f334(x75281,x75282),x75283))+~P104(f334(f334(f258(x75284,x75285,x75281),x75283),x75282)) % 169.19/169.65 [7529]P104(f334(f334(x75291,x75292),x75293))+~P104(f334(f334(f95(x75294,x75291,x75295),x75292),x75293)) % 169.19/169.65 [7593]~P104(f334(f334(f336(x75933),f334(x75934,x75932)),x75935))+P104(f334(f334(f336(x75931),x75932),f334(f314(x75931,x75933,x75934),x75935))) % 169.19/169.65 [7987]~P104(f334(f334(f336(x79875),x79873),f334(f314(x79875,x79871,x79872),x79874)))+P104(f334(f334(f336(x79871),f334(x79872,x79873)),x79874)) % 169.19/169.65 [8206]~E(x82063,f334(f334(f334(f73(x82061,f881(x82062)),f334(f18(f881(x82062),x82061),f198(x82062))),x82064),f334(f241(x82062),x82065)))+E(f185(x82061,x82062,x82063),f334(f334(f312(x82061),x82064),f195(f886(x82061,a871)))) % 169.19/169.65 [8286]~P12(x82862,x82861,x82863)+E(f334(f142(x82861,x82862,f334(f9(x82862,x82861,x82861),x82863),x82864),f152(x82862,x82865)),f334(f334(f66(x82862,x82861,x82863),x82864),f334(f173(x82862),x82865))) % 169.19/169.65 [8305]E(f334(x83051,f617(x83052,x83051,x83053,x83054)),x83054)+~P104(f334(f334(f336(x83055),x83054),f334(f313(x83053,x83055,x83051),x83052))) % 169.19/169.65 [8600]~E(x86002,f334(f334(f151(x86001),x86004),x86005))+P104(f334(f334(f336(f885(f878(x86001),f878(x86001))),f334(f334(f269(f878(x86001),f878(x86001)),f116(x86001)),x86002)),f147(x86001,x86003))) % 169.19/169.65 [8651]~P36(x86511,x86513,x86515,x86512,x86514)+E(f334(f196(f878(x86511)),x86512),f334(f196(f878(x86513)),x86514)) % 169.19/169.65 [8662]P104(f334(f334(f249(f886(x86621,a871)),f334(f334(f43(x86622,f886(x86621,a871)),x86623),x86624)),f334(x86624,x86625)))+~P104(f334(f334(f336(x86622),x86625),x86623)) % 169.19/169.65 [8710]~P54(x87101,x87102,x87103,x87105,x87104)+E(f334(f313(x87101,x87102,x87103),f257(f886(x87101,a871))),x87104) % 169.19/169.65 [8915]E(f334(f334(f334(f73(x89151,f881(x89152)),f189(x89151,x89152,x89153,x89154)),x89155),f198(x89152)),f189(x89151,x89152,x89153,x89154))+P104(f334(f334(f336(x89151),x89155),x89154)) % 169.19/169.65 [8920]E(f334(f136(x89201,x89202),f738(x89203,x89204,x89205,x89202,x89201)),x89203)+~E(f334(f136(x89201,x89202),x89205),f334(f334(f151(x89201),x89204),x89203)) % 169.19/169.65 [8921]E(f334(f136(x89211,x89212),f739(x89213,x89212,x89214,x89215,x89211)),x89214)+~E(f334(f334(f151(x89211),x89215),x89214),f334(f136(x89211,x89212),x89213)) % 169.19/169.65 [8922]E(f334(x89221,f565(x89222,x89223,x89221,x89224,x89225)),x89222)+~E(f334(f334(f207(x89225,x89224),x89221),x89223),f334(f241(x89224),x89222)) % 169.19/169.65 [8925]E(f334(f241(x89251),f565(x89252,x89253,x89254,x89255,x89251)),x89253)+~E(f334(f334(f207(x89251,x89255),x89254),x89253),f334(f241(x89255),x89252)) % 169.19/169.65 [9013]E(f334(f196(f878(x90131)),x90132),x90133)+~P104(f334(f334(f336(f885(f878(x90131),f878(x90131))),f334(f334(f269(f878(x90131),f878(x90131)),x90134),x90132)),f334(f143(x90131,x90135),x90133))) % 169.19/169.65 [9014]E(f334(f196(f878(x90141)),x90142),x90143)+~P104(f334(f334(f336(f885(f878(x90141),f878(x90141))),f334(f334(f269(f878(x90141),f878(x90141)),x90142),x90144)),f334(f143(x90141,x90145),x90143))) % 169.19/169.65 [9080]P104(f334(f334(f336(x90801),f617(x90802,x90803,x90801,x90804)),x90802))+~P104(f334(f334(f336(x90805),x90804),f334(f313(x90801,x90805,x90803),x90802))) % 169.19/169.65 [9234]E(f334(f313(x92341,x92342,x92343),f630(x92344,x92343,x92341,x92345,x92342)),x92345)+~P104(f334(f334(f249(f886(x92342,a871)),x92345),f334(f313(x92341,x92342,x92343),x92344))) % 169.19/169.65 [9477]E(f334(x94771,f611(x94772,x94771,x94773,x94774,x94775)),f334(f241(x94775),x94774))+~P104(f334(f334(f336(x94775),x94774),f187(x94773,x94775,f189(x94773,x94775,x94771,x94772)))) % 169.19/169.65 [9520]P104(f334(f334(f336(f885(f878(x95201),f878(x95201))),f334(f334(f269(f878(x95201),f878(x95201)),f334(f334(f151(x95201),x95202),x95203)),f334(f334(f151(x95201),x95202),x95204))),f310(f878(x95201),f157(x95201,x95205))))+~P104(f334(f334(f336(f885(f878(x95201),f878(x95201))),f334(f334(f269(f878(x95201),f878(x95201)),x95203),x95204)),f310(f878(x95201),f157(x95201,x95205)))) % 169.19/169.65 [9551]~E(f334(x95513,f559(x95515,x95514,x95513,x95512,x95511)),f334(x95515,f559(x95515,x95514,x95513,x95512,x95511)))+E(f334(f334(f154(x95511,x95512),x95513),x95514),f334(f334(f154(x95511,x95512),x95515),x95514)) % 169.19/169.65 [9627]~E(f334(f136(x96271,x96275),x96274),f334(f334(f151(x96271),x96273),x96272))+E(f334(f334(f134(x96271),f741(x96272,x96273,x96274,x96275,x96271)),f334(f334(f151(x96271),x96273),f738(x96272,x96273,x96274,x96275,x96271))),x96274) % 169.19/169.65 [9628]~E(f334(f334(f151(x96281),x96285),x96284),f334(f136(x96281,x96283),x96282))+E(f334(f334(f134(x96281),f740(x96282,x96283,x96284,x96285,x96281)),f334(f334(f151(x96281),x96285),f739(x96282,x96283,x96284,x96285,x96281))),x96282) % 169.19/169.65 [9632]E(f334(f334(f154(x96321,x96322),x96323),x96324),f334(f334(f154(x96321,x96322),x96325),x96324))+P104(f334(f334(f336(x96321),f559(x96323,x96324,x96325,x96322,x96321)),f334(f173(x96321),x96324))) % 169.19/169.65 [9662]~P104(f334(f334(f336(x96625),x96624),f334(f288(x96621,x96625,x96623),x96622)))+P104(f334(f334(f336(x96621),f539(x96622,x96623,x96621,x96624,x96625)),x96622)) % 169.19/169.65 [9663]~P104(f334(f334(f336(x96635),x96634),f334(f288(x96631,x96635,x96633),x96632)))+P104(f334(f334(f336(x96631),f552(x96632,x96633,x96631,x96634,x96635)),x96632)) % 169.19/169.65 [9689]~P104(f334(f334(f249(f886(x96895,a871)),x96894),f334(f313(x96891,x96895,x96893),x96892)))+P104(f334(f334(f249(f886(x96891,a871)),f630(x96892,x96893,x96891,x96894,x96895)),x96892)) % 169.19/169.65 [9740]~P104(f334(f334(f336(x97405),x97404),f187(x97401,x97405,f189(x97401,x97405,x97403,x97402))))+P104(f334(f334(f336(x97401),f611(x97402,x97403,x97401,x97404,x97405)),x97402)) % 169.19/169.65 [10135]E(x101351,f2(a102))+E(f334(f243(f885(f878(x101352),x101353),f885(x101352,x101353),f334(f334(f269(f878(x101352),x101353),f116(x101352)),x101354),f334(f273(x101352,x101353,f885(f878(x101352),x101353)),f334(f334(f9(x101352,f886(x101353,f885(f878(x101352),x101353)),f886(x101353,f885(f878(x101352),x101353))),f334(f334(f10(f886(f885(f878(x101352),x101353),f885(f878(x101352),x101353)),f886(f886(x101353,f885(f878(x101352),x101353)),f886(x101353,f885(f878(x101352),x101353))),x101352),f10(f885(f878(x101352),x101353),f885(f878(x101352),x101353),x101353)),f334(f334(f10(f886(f878(x101352),f886(x101353,f885(f878(x101352),x101353))),f886(f885(f878(x101352),x101353),f885(f878(x101352),x101353)),x101352),f273(f878(x101352),x101353,f885(f878(x101352),x101353))),f334(f334(f10(f886(f878(x101352),f878(x101352)),f886(f878(x101352),f886(x101353,f885(f878(x101352),x101353))),x101352),f334(f10(f878(x101352),f886(x101353,f885(f878(x101352),x101353)),f878(x101352)),f269(f878(x101352),x101353))),f151(x101352))))),f334(f120(x101353,x101352,x101355),f334(f334(f3(a102),x101351),f79(a102)))))),f334(x101355,x101354)),f334(f334(f120(x101353,x101352,x101355),x101351),x101354)) % 169.19/169.65 [5498]~E(f334(x54983,x54984),x54985)+E(f334(f334(f334(f73(x54981,x54982),x54983),x54984),x54985),x54983) % 169.19/169.65 [5942]E(f334(x59421,x59422),x59423)+~E(f334(f334(f334(f73(x59424,x59425),x59421),x59422),x59423),x59421) % 169.19/169.65 [6033]E(x60331,x60332)+~E(f334(f272(x60333,x60334),f334(f334(f269(x60333,x60334),x60335),x60331)),x60332) % 169.19/169.65 [6034]E(x60341,x60342)+~E(f334(f268(x60343,x60344),f334(f334(f269(x60343,x60344),x60341),x60345)),x60342) % 169.19/169.65 [6302]~E(x63023,f334(f334(f134(x63021),x63024),f334(f334(f151(x63021),x63022),x63025)))+P104(f334(f334(f336(x63021),x63022),f334(f173(x63021),x63023))) % 169.19/169.65 [6691]E(f334(f313(x66911,x66912,f334(f18(x66912,x66911),x66913)),x66914),f334(f334(f312(x66912),x66913),f195(f886(x66912,a871))))+~P104(f334(f334(f336(x66911),x66915),x66914)) % 169.19/169.65 [6761]E(f334(f334(f113(f886(x67611,a871)),f334(f173(x67611),x67612)),f334(f173(x67611),x67613)),f334(f173(x67611),x67614))+~E(f167(x67611,x67615,x67614),f334(f334(f269(f878(x67611),f878(x67611)),x67612),x67613)) % 169.19/169.65 [6864]~P107(x68642)+E(f334(f196(f878(x68641)),f334(f334(f148(x68641,x68642,x68643),x68644),x68645)),f334(a115,f334(f196(f878(x68641)),x68645))) % 169.19/169.65 [6876]~P107(x68762)+E(f334(f173(x68761),f334(f334(f148(x68761,x68762,x68763),x68764),x68765)),f334(f334(f312(x68761),x68764),f334(f173(x68761),x68765))) % 169.19/169.65 [7146]~P115(x71461)+E(f334(f334(f82(x71461),f334(f334(f82(x71461),x71462),x71463)),f334(f334(f82(x71461),x71464),x71465)),f334(f334(f82(x71461),f334(f334(f82(x71461),x71462),x71464)),f334(f334(f82(x71461),x71463),x71465))) % 169.19/169.65 [7147]~P115(x71471)+E(f334(f334(f81(x71471),f334(f334(f81(x71471),x71472),x71473)),f334(f334(f81(x71471),x71474),x71475)),f334(f334(f81(x71471),f334(f334(f81(x71471),x71472),x71474)),f334(f334(f81(x71471),x71473),x71475))) % 169.19/169.65 [7148]~P59(x71481)+E(f334(f334(f292(x71481),f334(f334(f82(x71481),x71482),x71483)),f334(f334(f82(x71481),x71484),x71485)),f334(f334(f82(x71481),f334(f334(f292(x71481),x71482),x71484)),f334(f334(f292(x71481),x71483),x71485))) % 169.19/169.65 [7162]~P107(x71621)+E(f308(x71621,f334(f334(f248(x71621),x71622),x71623),f334(f334(f247(x71621),x71624),x71625)),f334(f334(f104(f886(x71621,a871)),f308(x71621,x71622,x71624)),f308(x71621,x71623,x71625))) % 169.19/169.65 [7163]~P107(x71631)+E(f305(x71631,f334(f334(f248(x71631),x71632),x71633),f334(f334(f247(x71631),x71634),x71635)),f334(f334(f104(f886(x71631,a871)),f305(x71631,x71632,x71634)),f305(x71631,x71633,x71635))) % 169.19/169.65 [7164]~P107(x71641)+E(f307(x71641,f334(f334(f248(x71641),x71642),x71643),f334(f334(f247(x71641),x71644),x71645)),f334(f334(f104(f886(x71641,a871)),f307(x71641,x71642,x71644)),f307(x71641,x71643,x71645))) % 169.19/169.65 [7165]~P107(x71651)+E(f334(f334(f104(f886(x71651,a871)),f334(f304(x71651,x71652),x71653)),f334(f304(x71651,x71654),x71655)),f334(f304(x71651,f334(f334(f248(x71651),x71652),x71654)),f334(f334(f247(x71651),x71653),x71655))) % 169.19/169.65 [7281]~P104(f334(x72811,f485(x72813,x72812,x72811)))+P104(f334(x72811,f334(f334(f269(x72812,x72813),x72814),x72815))) % 169.19/169.65 [7370]~E(f334(x73703,x73704),f198(x73702))+E(f187(x73701,x73702,f334(f334(f334(f73(x73701,f881(x73702)),x73703),x73704),f334(f241(x73702),x73705))),f334(f334(f312(x73702),x73705),f187(x73701,x73702,x73703))) % 169.19/169.65 [7389]~E(x73892,f334(x73894,x73895))+P104(f334(f334(f336(x73891),x73892),f334(f313(x73893,x73891,x73894),f257(f886(x73893,a871))))) % 169.19/169.65 [7447]~E(f334(x74473,x74474),f198(x74472))+E(f334(f334(f3(f886(x74471,a871)),f185(x74471,x74472,x74473)),f334(f334(f312(x74471),x74474),x74475)),f334(f334(f3(f886(x74471,a871)),f185(x74471,x74472,x74473)),x74475)) % 169.19/169.65 [7466]~P12(x74663,x74662,x74664)+P12(x74661,x74662,f334(f334(f10(x74663,f886(x74662,x74662),x74661),x74664),x74665)) % 169.19/169.65 [7467]~P11(x74673,x74672,x74674)+P11(x74671,x74672,f334(f334(f10(x74673,f886(x74672,x74672),x74671),x74674),x74675)) % 169.19/169.65 [7609]~P21(x76091,x76092,x76093,x76094)+P21(x76091,x76092,x76093,f334(f334(f3(f886(x76091,a871)),x76094),x76095)) % 169.19/169.65 [7766]~P104(f334(f334(x77663,x77664),x77665))+P104(f334(f334(f273(x77661,x77662,a871),x77663),f334(f334(f269(x77661,x77662),x77664),x77665))) % 169.19/169.65 [7876]~P104(f334(x78762,x78764))+~E(f334(f334(f138(x78761),f334(f196(f878(x78761)),f178(x78761,x78762,x78763))),x78763),f334(f334(f151(x78761),x78764),x78765)) % 169.19/169.65 [7896]P21(x78961,x78962,x78963,x78964)+~P21(x78961,x78962,x78963,f334(f334(f113(f886(x78961,a871)),x78965),x78964)) % 169.19/169.65 [7897]P21(x78971,x78972,x78973,x78974)+~P21(x78971,x78972,x78973,f334(f334(f113(f886(x78971,a871)),x78974),x78975)) % 169.19/169.65 [7943]~P107(x79432)+E(f334(f334(f148(x79431,x79432,x79433),x79434),f150(x79431,x79432,x79433,x79435)),f150(x79431,x79432,x79433,f334(f334(f151(x79431),x79434),x79435))) % 169.19/169.65 [8101]~P31(x81011,f334(a115,x81012),f334(f334(f334(f93(x81011),x81013),f334(a26,x81014)),x81015))+P31(x81011,x81012,f334(f334(f334(f93(x81011),x81013),f334(f245(a873),f334(a28,x81014))),x81015)) % 169.19/169.65 [8233]P31(x82331,f334(a115,x82332),f334(f334(f334(f93(x82331),x82333),f334(a26,x82334)),x82335))+~P31(x82331,x82332,f334(f334(f334(f93(x82331),x82333),f334(f245(a873),f334(a28,x82334))),x82335)) % 169.19/169.65 [8262]~P11(x82622,x82621,x82623)+E(f334(f142(x82621,x82622,f334(f9(x82622,x82621,x82621),x82623),x82624),x82625),f334(f334(f66(x82622,x82621,x82623),x82624),f334(f173(x82622),x82625))) % 169.19/169.65 [8291]~E(f334(f334(f138(x82911),f334(f196(f878(x82911)),f178(x82911,x82912,x82913))),x82913),f334(f334(f151(x82911),x82914),x82915))+E(f334(f334(f134(x82911),f178(x82911,x82912,x82913)),f334(f334(f151(x82911),x82914),x82915)),x82913) % 169.19/169.65 [8315]P104(f334(f334(x83151,x83152),x83153))+~P104(f334(f334(f273(x83154,x83155,a871),x83151),f334(f334(f269(x83154,x83155),x83152),x83153))) % 169.19/169.65 [8376]~E(f334(f334(f179(x83761,x83762),x83765),x83763),f334(f241(x83762),x83764))+P104(f334(f334(f336(f885(x83761,x83762)),f334(f334(f269(x83761,x83762),x83763),x83764)),f334(f173(f885(x83761,x83762)),x83765))) % 169.19/169.65 [8765]P104(f334(f334(f249(f886(x87651,a871)),f334(f313(x87652,x87651,x87653),x87654)),f334(f313(x87652,x87651,x87653),x87655)))+~P104(f334(f334(f249(f886(x87652,a871)),x87654),x87655)) % 169.19/169.65 [8766]P104(f334(f334(f249(f886(x87661,a871)),f334(f314(x87661,x87662,x87663),x87664)),f334(f314(x87661,x87662,x87663),x87665)))+~P104(f334(f334(f249(f886(x87662,a871)),x87664),x87665)) % 169.19/169.65 [8841]E(x88411,f2(a102))+E(f334(f334(f275(x88412,x88413,x88412,f885(x88413,x88412)),f334(x88414,x88415)),f283(x88413,x88412,f334(f334(f3(a102),x88411),f79(a102)),x88414)),f334(f283(x88413,x88412,x88411,x88414),x88415)) % 169.19/169.65 [9338]E(f334(f241(x93381),f550(x93382,x93383,x93384,x93381,x93385)),f334(f334(f179(x93385,x93381),x93382),x93384))+~P104(f334(f334(f336(f885(x93385,x93381)),f334(f334(f269(x93385,x93381),x93384),x93383)),f334(f173(f885(x93385,x93381)),x93382))) % 169.19/169.65 [9441]~P20(x94411,x94412,f334(f334(f312(f876(x94411)),f334(f334(f334(f93(x94411),x94413),f334(f245(a873),f334(a28,x94414))),x94415)),f195(f886(f876(x94411),a871))))+P20(x94411,x94412,f334(f334(f312(f876(x94411)),f334(f334(f334(f93(x94411),x94413),f334(a26,x94414)),x94415)),f195(f886(f876(x94411),a871)))) % 169.19/169.65 [9469]~P104(f334(f63(x94693),f334(f313(x94692,x94693,x94695),f257(f886(x94692,a871)))))+P104(f334(f63(x94691),f334(f313(x94692,x94691,f334(f334(f10(x94693,x94691,x94692),x94694),x94695)),f257(f886(x94692,a871))))) % 169.19/169.65 [9490]P104(f334(f334(f249(f886(f886(x94901,a871),a871)),f334(f313(f886(x94902,a871),f886(x94901,a871),f313(x94902,x94901,x94903)),f334(f311(x94902),x94904))),f334(f311(x94901),x94905)))+~P104(f334(f334(f249(f886(x94901,a871)),f334(f313(x94902,x94901,x94903),x94904)),x94905)) % 169.19/169.65 [9500]~P104(f334(f63(f881(x95001)),f334(f313(x95002,f881(x95001),x95003),f257(f886(x95002,a871)))))+P104(f334(f63(f881(x95001)),f334(f313(x95002,f881(x95001),f334(f334(f334(f73(x95002,f881(x95001)),x95003),x95004),f334(f241(x95001),x95005))),f257(f886(x95002,a871))))) % 169.19/169.65 [9560]E(x95601,x95602)+~P104(f334(f68(x95603,x95604,x95605,x95601,f195(f886(x95603,a871))),x95602)) % 169.19/169.65 [9575]E(f334(f334(f269(x95751,x95752),f703(x95753,x95754,x95755,x95752,x95751)),f706(x95753,x95754,x95755,x95752,x95751)),x95755)+~P104(f334(f334(f336(f885(x95751,x95752)),x95755),f334(f334(f271(x95751,x95752),x95754),x95753))) % 169.19/169.65 [9667]P104(f334(f334(f336(x96671),f703(x96672,x96673,x96674,x96675,x96671)),x96673))+~P104(f334(f334(f336(f885(x96671,x96675)),x96674),f334(f334(f271(x96671,x96675),x96673),x96672))) % 169.19/169.65 [9776]P20(x97765,x97764,f334(f334(f312(f876(x97765)),f334(f334(f334(f93(x97765),x97761),x97763),x97762)),f195(f886(f876(x97765),a871))))+P104(f334(f334(x97761,f557(x97762,x97763,x97764,x97765,x97761)),f558(x97762,x97763,x97764,x97765,x97761))) % 169.19/169.65 [9828]P104(f334(f334(f336(x98281),f706(x98282,x98283,x98284,x98281,x98285)),f334(x98282,f703(x98282,x98283,x98284,x98281,x98285))))+~P104(f334(f334(f336(f885(x98285,x98281)),x98284),f334(f334(f271(x98285,x98281),x98283),x98282))) % 169.19/169.65 [9853]P104(f334(f334(f336(f885(x98531,x98531)),f334(f334(f269(x98531,x98531),x98532),f779(x98533,x98534,x98535,x98532,x98531))),x98533))+~P104(f334(f334(f336(f885(x98531,x98531)),f334(f334(f269(x98531,x98531),x98532),x98535)),f334(f334(f190(f885(x98531,x98531),a871),f334(a115,x98534)),x98533))) % 169.19/169.65 [9854]P104(f334(f334(f336(f885(x98541,x98541)),f334(f334(f269(x98541,x98541),x98542),f780(x98543,x98544,x98545,x98542,x98541))),x98543))+~P104(f334(f334(f336(f885(x98541,x98541)),f334(f334(f269(x98541,x98541),x98542),x98545)),f334(f334(f190(f885(x98541,x98541),a871),f334(a115,x98544)),x98543))) % 169.19/169.65 [9872]~P104(f334(f334(f336(f885(f878(x98721),f878(x98721))),f334(f334(f269(f878(x98721),f878(x98721)),f334(f334(f151(x98721),x98722),x98725)),x98724)),f158(x98721,x98723)))+P104(f334(f334(f336(f885(x98721,x98721)),f334(f334(f269(x98721,x98721),x98722),f588(x98723,x98724,x98725,x98722,x98721))),x98723)) % 169.19/169.65 [9874]~P20(x98741,x98742,f334(f334(f312(f876(x98741)),f334(f334(f334(f93(x98741),f95(x98741,x98743,x98744)),x98745),x98743)),f195(f886(f876(x98741),a871))))+P20(x98741,x98742,f334(f334(f312(f876(x98741)),f334(f334(f334(f93(x98741),x98743),f33(x98744,x98745)),f95(x98741,x98743,f334(f74(a871,a871,a872,a329),x98744)))),f195(f886(f876(x98741),a871)))) % 169.19/169.65 [9875]~P23(x98751,x98752,f334(f334(f312(f876(x98751)),f334(f334(f334(f93(x98751),f95(x98751,x98753,x98754)),x98755),x98753)),f195(f886(f876(x98751),a871))))+P23(x98751,x98752,f334(f334(f312(f876(x98751)),f334(f334(f334(f93(x98751),x98753),f33(x98754,x98755)),f95(x98751,x98753,f334(f74(a871,a871,a872,a329),x98754)))),f195(f886(f876(x98751),a871)))) % 169.19/169.65 [10136]P20(x101361,x101362,f334(f334(f312(f876(x101361)),f334(f334(f334(f93(x101361),x101363),x101364),x101365)),f195(f886(f876(x101361),a871))))+~P20(x101361,x101362,f334(f334(f312(f876(x101361)),f334(f334(f334(f93(x101361),f334(f18(f886(a872,a871),x101361),f334(f334(f9(a872,a872,a871),a331),f558(x101365,x101364,x101362,x101361,x101363)))),x101364),f334(f18(f886(a872,a871),x101361),f334(x101365,f557(x101365,x101364,x101362,x101361,x101363))))),f195(f886(f876(x101361),a871)))) % 169.19/169.65 [6375]P104(f334(x63752,x63754))+E(f178(x63751,x63752,f334(f334(f134(x63751),x63753),f334(f334(f151(x63751),x63754),x63755))),f178(x63751,x63752,x63753)) % 169.19/169.65 [6425]~P63(x64252)+E(f334(f334(f334(f3(f886(x64251,x64252)),x64253),x64254),x64255),f334(f334(f3(x64252),f334(x64253,x64255)),f334(x64254,x64255))) % 169.19/169.65 [6427]~P95(x64272)+E(f334(f334(f334(f113(f886(x64271,x64272)),x64273),x64274),x64275),f334(f334(f113(x64272),f334(x64273,x64275)),f334(x64274,x64275))) % 169.19/169.65 [6429]~P95(x64292)+E(f334(f334(f334(f104(f886(x64291,x64292)),x64293),x64294),x64295),f334(f334(f104(x64292),f334(x64293,x64295)),f334(x64294,x64295))) % 169.19/169.65 [6447]E(x64471,x64472)+E(f334(f334(f165(x64473),f334(f334(f159(x64473,x64474),x64471),x64475)),x64472),f334(f334(f165(x64473),x64474),x64472)) % 169.19/169.65 [6709]~E(x67094,f195(f886(x67093,a871)))+E(f334(f334(f3(f886(x67091,a871)),x67092),f334(f334(f44(x67093,f886(x67091,a871)),x67094),x67095)),x67092) % 169.19/169.65 [6710]~E(x67104,f195(f886(x67103,a871)))+E(f334(f334(f113(f886(x67101,a871)),x67102),f334(f334(f44(x67103,f886(x67101,a871)),x67104),x67105)),x67102) % 169.19/169.65 [6711]~E(x67114,f195(f886(x67113,a871)))+E(f334(f334(f104(f886(x67111,a871)),x67112),f334(f334(f43(x67113,f886(x67111,a871)),x67114),x67115)),x67112) % 169.19/169.65 [6725]~E(x67254,f195(f886(x67253,a871)))+E(f334(f334(f312(x67251),x67252),f334(f334(f44(x67253,f886(x67251,a871)),x67254),x67255)),f334(f334(f312(x67251),x67252),f195(f886(x67251,a871)))) % 169.19/169.65 [7514]E(f334(f334(f165(x75141),f334(f334(f154(x75142,x75141),x75143),x75144)),x75145),f334(x75143,f334(f334(f165(x75142),x75144),x75145)))+~P104(f334(f334(f250(a877),x75145),f334(f196(f878(x75142)),x75144))) % 169.19/169.65 [7581]E(f334(f334(f113(f886(x75811,a871)),f334(x75812,x75813)),f334(f334(f44(x75814,f886(x75811,a871)),x75815),x75812)),f334(f334(f44(x75814,f886(x75811,a871)),x75815),x75812))+~P104(f334(f334(f336(x75814),x75813),x75815)) % 169.19/169.65 [7582]E(f334(f334(f104(f886(x75821,a871)),f334(x75822,x75823)),f334(f334(f43(x75824,f886(x75821,a871)),x75825),x75822)),f334(f334(f43(x75824,f886(x75821,a871)),x75825),x75822))+~P104(f334(f334(f336(x75824),x75823),x75825)) % 169.19/169.65 [8179]~E(x81793,f195(f886(x81791,a871)))+E(f334(f334(f44(x81791,f886(x81792,a871)),x81793),f334(f334(f10(f886(x81792,a871),f886(x81792,a871),x81791),f334(f312(x81792),x81794)),x81795)),f195(f886(x81792,a871))) % 169.19/169.65 [8184]~P104(f334(f334(f336(x81844),x81843),x81845))+P104(f334(f334(f249(f886(x81841,a871)),f334(x81842,x81843)),f334(f334(f44(x81844,f886(x81841,a871)),x81845),x81842))) % 169.19/169.65 [8314]~E(f334(x83144,x83142),x83145)+P104(f334(f334(f336(x83141),x83142),f334(f314(x83141,x83143,x83144),f334(f334(f312(x83143),x83145),f195(f886(x83143,a871)))))) % 169.19/169.65 [8358]~P52(x83581,x83582,f334(f289(x83582,x83581),x83583))+E(f334(f334(f104(f886(x83581,a871)),f334(f288(x83582,x83581,x83583),x83584)),f334(f288(x83582,x83581,x83583),x83585)),f334(f288(x83582,x83581,x83583),f334(f334(f104(f886(x83582,a871)),x83584),x83585))) % 169.19/169.65 [8432]E(x84321,f2(a102))+E(f334(f121(x84322,x84323,f334(x84324,f334(f334(f3(a102),x84321),f79(a102)))),f334(f334(f9(x84322,a102,f879(x84323)),x84325),x84321)),f334(f206(x84322,x84323,x84324,x84325),x84321)) % 169.19/169.65 [8472]E(x84721,f195(f886(x84722,a871)))+E(f334(f334(f44(x84722,f886(x84723,a871)),x84721),f334(f334(f10(f886(x84723,a871),f886(x84723,a871),x84722),f334(f312(x84723),x84724)),x84725)),f334(f334(f312(x84723),x84724),f334(f334(f44(x84722,f886(x84723,a871)),x84721),x84725))) % 169.19/169.65 [8520]~P21(x85202,x85201,x85203,f257(f886(x85202,a871)))+E(f334(f334(f3(f886(x85201,a871)),f334(f313(x85202,x85201,x85203),x85204)),f334(f313(x85202,x85201,x85203),x85205)),f334(f313(x85202,x85201,x85203),f334(f334(f3(f886(x85202,a871)),x85204),x85205))) % 169.19/169.65 [8521]~P21(x85212,x85211,x85213,f257(f886(x85212,a871)))+E(f334(f334(f104(f886(x85211,a871)),f334(f313(x85212,x85211,x85213),x85214)),f334(f313(x85212,x85211,x85213),x85215)),f334(f313(x85212,x85211,x85213),f334(f334(f104(f886(x85212,a871)),x85214),x85215))) % 169.19/169.65 [8586]~P104(f334(f334(f69(x85861,x85862,x85865),x85863),x85864))+P104(f334(f334(f336(f885(x85861,x85862)),f334(f334(f269(x85861,x85862),x85863),x85864)),x85865)) % 169.19/169.65 [8618]P104(f334(f334(f336(x86181),x86182),f334(f265(x86183,x86181),x86184)))+~P104(f334(f334(f336(f885(x86183,x86181)),f334(f334(f269(x86183,x86181),x86185),x86182)),x86184)) % 169.19/169.65 [8620]P104(f334(f334(f336(x86201),x86202),f334(f267(x86201,x86203),x86204)))+~P104(f334(f334(f336(f885(x86201,x86203)),f334(f334(f269(x86201,x86203),x86202),x86205)),x86204)) % 169.19/169.65 [8752]P104(f334(f334(f69(x87521,x87522,x87523),x87524),x87525))+~P104(f334(f334(f336(f885(x87521,x87522)),f334(f334(f269(x87521,x87522),x87524),x87525)),x87523)) % 169.19/169.65 [8787]E(f334(x87871,x87872),x87873)+~P104(f334(f334(f336(x87874),x87872),f334(f314(x87874,x87875,x87871),f334(f334(f312(x87875),x87873),f195(f886(x87875,a871)))))) % 169.19/169.65 [9010]P104(f334(f334(f336(f885(x90101,x90102)),f334(f334(f269(x90101,x90102),x90103),x90104)),f334(f289(x90102,x90101),x90105)))+~P104(f334(f334(f336(f885(x90102,x90101)),f334(f334(f269(x90102,x90101),x90104),x90103)),x90105)) % 169.19/169.65 [9028]~P104(f334(f334(x90281,x90285),x90284))+P104(f334(f334(x90281,f334(f272(x90282,x90283),f334(f334(f269(x90282,x90283),x90284),x90285))),f334(f268(x90282,x90283),f334(f334(f269(x90282,x90283),x90284),x90285)))) % 169.19/169.65 [9057]~P104(f334(f334(f336(f885(x90572,x90571)),f334(f334(f269(x90572,x90571),x90574),x90573)),f334(f289(x90571,x90572),x90575)))+P104(f334(f334(f336(f885(x90571,x90572)),f334(f334(f269(x90571,x90572),x90573),x90574)),x90575)) % 169.19/169.65 [9087]~P104(f334(f334(f336(f885(x90873,x90871)),f334(f334(f269(x90873,x90871),x90875),x90872)),x90874))+P104(f334(f334(f336(x90871),x90872),f334(f288(x90873,x90871,x90874),f334(f334(f312(x90873),x90875),f195(f886(x90873,a871)))))) % 169.19/169.65 [9133]P104(f334(f334(f336(f885(x91331,x91332)),f334(f334(f269(x91331,x91332),x91333),x91334)),x91335))+~P104(f334(f334(f336(x91332),x91334),f334(f288(x91331,x91332,x91335),f334(f334(f312(x91331),x91333),f195(f886(x91331,a871)))))) % 169.19/169.65 [9153]E(f334(f334(f334(f73(x91531,f881(x91532)),f189(x91531,x91532,x91533,x91534)),x91535),f198(x91532)),f189(x91531,x91532,x91533,f334(f334(f3(f886(x91531,a871)),x91534),f334(f334(f312(x91531),x91535),f195(f886(x91531,a871))))))+~P104(f334(f334(f336(x91531),x91535),x91534)) % 169.19/169.65 [9219]~P72(x92191)+E(f334(f334(f8(a877,x92191),x92192),f305(a877,f334(f334(f81(a877),x92193),x92194),f334(f334(f81(a877),x92195),x92194))),f334(f334(f8(a877,x92191),f334(f334(f10(a877,x92191,a877),x92192),f334(f334(f9(a877,a877,a877),f81(a877)),x92194))),f305(a877,x92193,x92195))) % 169.19/169.65 [9238]~P72(x92381)+E(f334(f334(f8(a877,x92381),x92382),f334(f304(a877,f334(f334(f81(a877),x92383),x92384)),f334(f334(f81(a877),x92385),x92384))),f334(f334(f8(a877,x92381),f334(f334(f10(a877,x92381,a877),x92382),f334(f334(f9(a877,a877,a877),f81(a877)),x92384))),f334(f304(a877,x92383),x92385))) % 169.19/169.65 [9288]~P21(x92881,x92882,x92883,f257(f886(x92881,a871)))+E(f334(f334(f154(x92881,x92882),x92883),f334(f136(x92881,f334(f334(f10(a871,a871,x92881),a329),f334(a331,x92884))),x92885)),f334(f136(x92882,f334(f334(f10(a871,a871,x92882),a329),f334(a331,f334(x92883,x92884)))),f334(f334(f154(x92881,x92882),x92883),x92885))) % 169.19/169.65 [9304]~P21(x93041,x93042,x93043,f334(f334(f312(x93041),x93044),f334(f173(x93041),x93045)))+E(f334(f334(f154(x93041,x93042),x93043),f334(f136(x93041,f334(f334(f10(a871,a871,x93041),a329),f334(a331,x93044))),x93045)),f334(f136(x93042,f334(f334(f10(a871,a871,x93042),a329),f334(a331,f334(x93043,x93044)))),f334(f334(f154(x93041,x93042),x93043),x93045))) % 169.19/169.65 [9456]P104(f334(f334(f336(f885(f878(x94561),f878(x94561))),f334(f334(f269(f878(x94561),f878(x94561)),f334(f334(f151(x94561),x94562),x94563)),f334(f334(f151(x94561),x94564),x94563))),f157(x94561,x94565)))+~P104(f334(f334(f336(f885(x94561,x94561)),f334(f334(f269(x94561,x94561),x94562),x94564)),x94565)) % 169.19/169.65 [9558]P20(x95581,x95582,f334(f334(f312(f876(x95581)),f334(f334(f334(f93(x95581),x95583),f334(a26,x95584)),x95585)),f195(f886(f876(x95581),a871))))+~P20(x95581,f334(f334(f312(f876(x95581)),f334(f334(f334(f93(x95581),x95583),f334(a26,x95584)),x95585)),x95582),f334(f334(f312(f876(x95581)),f334(f334(f334(f93(x95581),x95583),f334(f245(a873),f334(a28,x95584))),x95585)),f195(f886(f876(x95581),a871)))) % 169.19/169.65 [9570]E(f334(f334(f312(x95701),f642(x95702,x95703,x95704,x95705,x95701)),f653(x95702,x95703,x95704,x95705,x95701)),f334(f334(f312(x95701),x95704),x95703))+~P104(f334(f64(x95701,x95705,f334(f334(f312(x95701),x95704),x95703)),x95702)) % 169.19/169.65 [9571]E(f334(f334(f312(x95711),f663(x95712,x95713,x95714,x95715,x95711)),f671(x95712,x95713,x95714,x95715,x95711)),f334(f334(f312(x95711),x95714),x95713))+~P104(f334(f64(x95711,x95715,f334(f334(f312(x95711),x95714),x95713)),x95712)) % 169.19/169.65 [9653]P104(f334(f334(f336(x96531),f520(x96532,x96533,x96534,x96535,x96531)),x96534))+P104(f334(f334(f334(f43(x96531,f886(x96535,a871)),x96534),x96533),x96532)) % 169.19/169.65 [9658]P104(f334(f334(f336(x96581),f517(x96582,x96583,x96581,x96584,x96585)),x96583))+P104(f334(f334(f336(x96585),x96584),f334(f334(f43(x96581,f886(x96585,a871)),x96583),x96582))) % 169.19/169.65 [9666]P104(f334(f334(f336(x96661),f518(x96662,x96663,x96661,x96664,x96665)),x96663))+P104(f334(f334(f249(f886(x96665,a871)),x96664),f334(f334(f43(x96661,f886(x96665,a871)),x96663),x96662))) % 169.19/169.65 [9668]P104(f334(f334(x96681,f533(x96682,x96681,x96683,x96684,x96685)),x96682))+~P104(f334(f334(f334(f44(x96685,f886(x96684,a871)),x96683),x96681),x96682)) % 169.19/169.65 [9671]P104(f334(f334(f336(x96711),f533(x96712,x96713,x96714,x96715,x96711)),x96714))+~P104(f334(f334(f334(f44(x96711,f886(x96715,a871)),x96714),x96713),x96712)) % 169.19/169.65 [9672]P49(x96724,f334(f334(f43(x96721,f886(x96724,a871)),x96725),x96723),f334(f334(f43(x96721,f886(f885(x96724,x96724),a871)),x96725),x96722))+P104(f334(f334(f336(x96721),f813(x96722,x96723,x96724,x96725,x96721)),x96725)) % 169.19/169.65 [9682]P104(f334(f334(f336(x96821),f529(x96822,x96823,x96821,x96824,x96825)),x96823))+~P104(f334(f334(f336(x96825),x96824),f334(f334(f44(x96821,f886(x96825,a871)),x96823),x96822))) % 169.19/169.65 [9687]P104(f334(f334(f336(x96871),x96872),f334(x96873,f529(x96873,x96874,x96875,x96872,x96871))))+~P104(f334(f334(f336(x96871),x96872),f334(f334(f44(x96875,f886(x96871,a871)),x96874),x96873))) % 169.19/169.65 [9781]~P104(f334(f334(x97814,f520(x97815,x97814,x97813,x97812,x97811)),x97815))+P104(f334(f334(f334(f43(x97811,f886(x97812,a871)),x97813),x97814),x97815)) % 169.19/169.65 [9784]~P104(f334(f334(f336(x97841),x97842),f334(x97845,f517(x97845,x97844,x97843,x97842,x97841))))+P104(f334(f334(f336(x97841),x97842),f334(f334(f43(x97843,f886(x97841,a871)),x97844),x97845))) % 169.19/169.65 [9788]~P49(x97881,f334(x97884,f813(x97885,x97884,x97881,x97883,x97882)),f334(x97885,f813(x97885,x97884,x97881,x97883,x97882)))+P49(x97881,f334(f334(f43(x97882,f886(x97881,a871)),x97883),x97884),f334(f334(f43(x97882,f886(f885(x97881,x97881),a871)),x97883),x97885)) % 169.19/169.65 [9789]~P104(f334(f334(f249(f886(x97891,a871)),x97892),f334(x97895,f518(x97895,x97894,x97893,x97892,x97891))))+P104(f334(f334(f249(f886(x97891,a871)),x97892),f334(f334(f43(x97893,f886(x97891,a871)),x97894),x97895))) % 169.19/169.65 [9857]~P104(f334(f334(f336(x98571),f642(x98575,x98574,x98573,x98572,x98571)),f653(x98575,x98574,x98573,x98572,x98571)))+~P104(f334(f64(x98571,x98572,f334(f334(f312(x98571),x98573),x98574)),x98575)) % 169.19/169.65 [9858]~P104(f334(f334(f336(x98581),f663(x98585,x98584,x98583,x98582,x98581)),f671(x98585,x98584,x98583,x98582,x98581)))+~P104(f334(f64(x98581,x98582,f334(f334(f312(x98581),x98583),x98584)),x98585)) % 169.19/169.65 [9859]~P104(f334(f334(f336(f885(x98591,x98591)),f334(f334(f269(x98591,x98591),x98592),x98595)),f334(f334(f190(f885(x98591,x98591),a871),f334(a115,x98594)),x98593)))+P104(f334(f334(f336(f885(x98591,x98591)),f334(f334(f269(x98591,x98591),x98592),f775(x98593,x98594,x98595,x98592,x98591))),f334(f334(f190(f885(x98591,x98591),a871),x98594),x98593))) % 169.19/169.65 [9866]P104(f334(f68(x98661,x98661,x98662,f642(x98663,x98664,x98665,x98662,x98661),f653(x98663,x98664,x98665,x98662,x98661)),x98663))+~P104(f334(f64(x98661,x98662,f334(f334(f312(x98661),x98665),x98664)),x98663)) % 169.19/169.65 [9867]P104(f334(f68(x98671,x98671,x98672,f663(x98673,x98674,x98675,x98672,x98671),f671(x98673,x98674,x98675,x98672,x98671)),x98673))+~P104(f334(f64(x98671,x98672,f334(f334(f312(x98671),x98675),x98674)),x98673)) % 169.19/169.65 [9879]~P107(x98791)+P30(x98791,f334(f334(f154(x98792,x98791),x98793),f334(f136(x98792,f334(f334(f9(x98792,x98791,a871),f334(f334(f10(x98791,f886(x98791,a871),x98792),a331),x98793)),f334(x98794,x98795))),x98795))) % 169.19/169.65 [9919]~P104(f334(f334(f336(x99192),x99195),f334(f288(x99191,x99192,x99194),x99193)))+P104(f334(f334(f336(f885(x99191,x99192)),f334(f334(f269(x99191,x99192),f539(x99193,x99194,x99191,x99195,x99192)),x99195)),x99194)) % 169.19/169.65 [9920]~P104(f334(f334(f336(x99202),x99205),f334(f288(x99201,x99202,x99204),x99203)))+P104(f334(f334(f336(f885(x99201,x99202)),f334(f334(f269(x99201,x99202),f552(x99203,x99204,x99201,x99205,x99202)),x99205)),x99204)) % 169.19/169.65 [9940]~P104(f334(f334(f336(f885(x99401,x99401)),f334(f334(f269(x99401,x99401),x99405),x99404)),f334(f334(f190(f885(x99401,x99401),a871),f334(a115,x99403)),x99402)))+P104(f334(f334(f336(f885(x99401,x99401)),f334(f334(f269(x99401,x99401),f775(x99402,x99403,x99404,x99405,x99401)),x99404)),x99402)) % 169.19/169.65 [9943]~P104(f334(f334(f336(f885(x99431,x99431)),f334(f334(f269(x99431,x99431),x99435),x99434)),f334(f334(f190(f885(x99431,x99431),a871),f334(a115,x99433)),x99432)))+P104(f334(f334(f336(f885(x99431,x99431)),f334(f334(f269(x99431,x99431),f779(x99432,x99433,x99434,x99435,x99431)),x99434)),f334(f334(f190(f885(x99431,x99431),a871),x99433),x99432))) % 169.19/169.65 [9944]~P104(f334(f334(f336(f885(x99441,x99441)),f334(f334(f269(x99441,x99441),x99445),x99444)),f334(f334(f190(f885(x99441,x99441),a871),f334(a115,x99443)),x99442)))+P104(f334(f334(f336(f885(x99441,x99441)),f334(f334(f269(x99441,x99441),f780(x99442,x99443,x99444,x99445,x99441)),x99444)),f334(f334(f190(f885(x99441,x99441),a871),x99443),x99442))) % 169.19/169.65 [9945]~P104(f334(f334(f336(f885(f878(x99451),f878(x99451))),f334(f334(f269(f878(x99451),f878(x99451)),x99455),f334(f334(f151(x99451),x99454),x99453))),f158(x99451,x99452)))+P104(f334(f334(f336(f885(x99451,x99451)),f334(f334(f269(x99451,x99451),f587(x99452,x99453,x99454,x99455,x99451)),x99454)),x99452)) % 169.19/169.65 [7108]E(x71081,f198(x71082))+E(f185(x71083,x71082,f334(f334(f334(f73(x71083,f881(x71082)),x71084),x71085),x71081)),f334(f334(f312(x71083),x71085),f185(x71083,x71082,x71084))) % 169.19/169.65 [7602]~E(x76023,f195(f886(x76022,a871)))+E(f334(f334(f113(f886(x76021,a871)),f334(f334(f44(x76022,f886(x76021,a871)),x76023),x76024)),x76025),x76025) % 169.19/169.65 [7603]~E(x76033,f195(f886(x76032,a871)))+E(f334(f334(f104(f886(x76031,a871)),f334(f334(f43(x76032,f886(x76031,a871)),x76033),x76034)),x76035),x76035) % 169.19/169.65 [7958]~E(x79585,f198(x79582))+E(f185(x79581,x79582,f334(f334(f334(f73(x79581,f881(x79582)),x79583),x79584),x79585)),f334(f334(f3(f886(x79581,a871)),f185(x79581,x79582,x79583)),f334(f334(f312(x79581),x79584),f195(f886(x79581,a871))))) % 169.19/169.65 [8026]~E(x80263,f195(f886(x80262,a871)))+E(f334(f334(f3(f886(x80261,a871)),f334(f334(f43(x80262,f886(x80261,a871)),x80263),x80264)),x80265),f334(f334(f3(f886(x80261,a871)),f257(f886(x80261,a871))),x80265)) % 169.19/169.65 [8151]E(f334(f334(f159(x81511,f334(f334(f134(x81511),x81512),x81513)),x81514),x81515),f334(f334(f134(x81511),f334(f334(f159(x81511,x81512),x81514),x81515)),x81513))+~P104(f334(f334(f250(a877),x81514),f334(f196(f878(x81511)),x81512))) % 169.19/169.65 [8266]P104(f334(f334(f336(x82661),x82665),f334(f173(x82661),x82663)))+E(f334(f334(f179(x82661,x82662),f334(f334(f183(x82661,x82662),x82663),f334(f334(f154(x82661,x82662),x82664),x82663))),x82665),f198(x82662)) % 169.19/169.65 [8385]~P104(f334(f334(f336(x83851),x83855),f334(f173(x83851),x83853)))+E(f334(f334(f179(x83851,x83852),f334(f334(f183(x83851,x83852),x83853),f334(f334(f154(x83851,x83852),x83854),x83853))),x83855),f334(f241(x83852),f334(x83854,x83855))) % 169.19/169.65 [8422]E(f334(f334(f165(x84221),f334(f334(f154(a877,x84221),x84222),f139(a877,f334(f304(a877,x84223),x84224)))),x84225),f334(x84222,f334(f334(f81(a877),x84223),x84225)))+~P104(f334(f334(f250(a877),x84225),f334(f334(f3(a877),x84224),x84223))) % 169.19/169.65 [8437]E(x84371,f2(a102))+E(f123(x84372,x84373,f334(x84374,f334(f334(f3(a102),x84371),f79(a102))),f334(f334(f9(x84372,a102,f879(f881(x84373))),x84375),x84371)),f334(f204(x84372,x84373,x84374,x84375),x84371)) % 169.19/169.65 [8462]~E(x84623,f195(f886(x84621,a871)))+E(f334(f334(f43(x84621,f886(x84622,a871)),x84623),f334(f334(f10(f886(x84622,a871),f886(x84622,a871),x84621),f334(f3(f886(x84622,a871)),x84624)),x84625)),f257(f886(x84622,a871))) % 169.19/169.65 [8463]~E(x84633,f195(f886(x84631,a871)))+E(f334(f334(f43(x84631,f886(x84632,a871)),x84633),f334(f334(f10(f886(x84632,a871),f886(x84632,a871),x84631),f334(f104(f886(x84632,a871)),x84634)),x84635)),f257(f886(x84632,a871))) % 169.19/169.65 [8464]~E(x84643,f195(f886(x84641,a871)))+E(f334(f334(f44(x84641,f886(x84642,a871)),x84643),f334(f334(f10(f886(x84642,a871),f886(x84642,a871),x84641),f334(f113(f886(x84642,a871)),x84644)),x84645)),f195(f886(x84642,a871))) % 169.19/169.65 [8466]~P143(x84662)+E(f334(f334(f8(x84661,x84662),f334(f334(f10(x84662,x84662,x84661),f334(f82(x84662),x84663)),x84664)),x84665),f334(f334(f82(x84662),x84663),f334(f334(f8(x84661,x84662),x84664),x84665))) % 169.19/169.65 [8737]E(x87371,f195(f886(x87372,a871)))+E(f334(f334(f43(x87372,f886(x87373,a871)),x87371),f334(f334(f10(f886(x87373,a871),f886(x87373,a871),x87372),f334(f3(f886(x87373,a871)),x87374)),x87375)),f334(f334(f3(f886(x87373,a871)),x87374),f334(f334(f44(x87372,f886(x87373,a871)),x87371),x87375))) % 169.19/169.65 [8738]E(x87381,f195(f886(x87382,a871)))+E(f334(f334(f43(x87382,f886(x87383,a871)),x87381),f334(f334(f10(f886(x87383,a871),f886(x87383,a871),x87382),f334(f104(f886(x87383,a871)),x87384)),x87385)),f334(f334(f104(f886(x87383,a871)),x87384),f334(f334(f43(x87382,f886(x87383,a871)),x87381),x87385))) % 169.19/169.65 [8739]E(x87391,f195(f886(x87392,a871)))+E(f334(f334(f44(x87392,f886(x87393,a871)),x87391),f334(f334(f10(f886(x87393,a871),f886(x87393,a871),x87392),f334(f113(f886(x87393,a871)),x87394)),x87395)),f334(f334(f113(f886(x87393,a871)),x87394),f334(f334(f44(x87392,f886(x87393,a871)),x87391),x87395))) % 169.19/169.65 [8934]~P104(f334(f334(f250(a877),f334(x89344,x89342)),f334(x89344,x89343)))+P104(f334(f334(f336(f885(x89341,x89341)),f334(f334(f269(x89341,x89341),x89342),x89343)),f153(x89341,f334(f334(f151(f886(x89341,a877)),x89344),x89345)))) % 169.19/169.65 [9186]~P21(x91862,x91861,x91863,f334(f334(f113(f886(x91862,a871)),x91864),x91865))+E(f334(f334(f104(f886(x91861,a871)),f334(f313(x91862,x91861,x91863),f334(f334(f3(f886(x91862,a871)),x91864),x91865))),f334(f313(x91862,x91861,x91863),f334(f334(f3(f886(x91862,a871)),x91865),x91864))),f195(f886(x91861,a871))) % 169.19/169.65 [9452]~P104(f334(f334(f249(f886(x94523,a871)),f334(f288(x94521,x94523,x94524),x94522)),x94525))+P104(f334(f334(f249(f886(x94521,a871)),x94522),f334(f80(f886(x94521,a871)),f334(f288(x94523,x94521,f334(f289(x94521,x94523),x94524)),f334(f80(f886(x94523,a871)),x94525))))) % 169.19/169.65 [9476]~P21(x94761,x94762,x94763,f334(f334(f312(x94761),x94764),x94765))+~P104(f334(f334(f336(x94762),f334(x94763,x94764)),f334(f313(x94761,x94762,x94763),f334(f334(f3(f886(x94761,a871)),x94765),f334(f334(f312(x94761),x94764),f195(f886(x94761,a871))))))) % 169.19/169.65 [9524]P104(f334(f334(f249(f886(x95241,a871)),f334(f288(x95242,x95241,x95243),x95244)),x95245))+~P104(f334(f334(f249(f886(x95242,a871)),x95244),f334(f80(f886(x95242,a871)),f334(f288(x95241,x95242,f334(f289(x95242,x95241),x95243)),f334(f80(f886(x95241,a871)),x95245))))) % 169.19/169.65 [9598]~P83(x95981)+P104(f334(f334(f249(x95981),f334(f76(x95981),f334(f334(f3(x95981),f334(f334(f81(x95981),x95982),x95983)),f334(f334(f81(x95981),x95984),x95985)))),f334(f334(f81(x95981),f334(f76(x95981),f334(f334(f3(x95981),x95982),x95984))),f334(f76(x95981),f334(f334(f3(x95981),x95983),x95985))))) % 169.19/169.65 [9702]P104(f334(f334(f336(x97021),f530(x97022,x97023,x97024,x97021,x97025)),x97024))+P104(f334(f334(f249(f886(x97025,a871)),f334(f334(f44(x97021,f886(x97025,a871)),x97024),x97023)),x97022)) % 169.19/169.65 [9897]~P104(f334(f334(f249(f886(x98971,a871)),f334(x98974,f530(x98975,x98974,x98973,x98972,x98971))),x98975))+P104(f334(f334(f249(f886(x98971,a871)),f334(f334(f44(x98972,f886(x98971,a871)),x98973),x98974)),x98975)) % 169.19/169.65 [8566]E(f334(f334(f134(x85661),x85662),f334(f334(f159(x85661,x85663),f334(f334(f3(a877),x85664),f334(f196(f878(x85661)),x85662))),x85665)),f334(f334(f159(x85661,f334(f334(f134(x85661),x85662),x85663)),x85664),x85665))+P104(f334(f334(f250(a877),x85664),f334(f196(f878(x85661)),x85662))) % 169.19/169.65 [8594]~P139(x85941)+E(f334(f334(f81(x85941),f334(f334(f82(x85941),x85942),x85943)),f334(f334(f81(x85941),f334(f334(f82(x85941),x85944),x85943)),x85945)),f334(f334(f81(x85941),f334(f334(f82(x85941),f334(f334(f81(x85941),x85942),x85944)),x85943)),x85945)) % 169.19/169.65 [9143]~P143(x91431)+E(f334(f166(x91431),f334(f334(f154(x91432,x91431),f334(f334(f10(x91431,x91431,x91432),f334(f82(x91431),x91433)),x91434)),x91435)),f334(f334(f82(x91431),x91433),f334(f166(x91431),f334(f334(f154(x91432,x91431),x91434),x91435)))) % 169.19/169.65 [9303]E(f334(f196(f878(x93031)),f334(f334(f176(x93031),f334(f334(f247(a877),f334(f196(f878(x93031)),x93032)),f334(f196(f878(x93033)),x93034))),x93032)),f334(f196(f878(x93033)),f334(f334(f176(x93033),f334(f334(f247(a877),f334(f196(f878(x93031)),x93032)),f334(f196(f878(x93033)),x93034))),x93034)))+P104(f334(x93035,f334(f334(f183(x93031,x93033),x93032),x93034))) % 169.19/169.65 [9535]~P143(x95352)+E(f334(f334(f8(x95351,x95352),f334(f334(f9(x95351,x95352,x95352),f334(f334(f10(x95352,f886(x95352,x95352),x95351),f82(x95352)),x95353)),x95354)),x95355),f334(f334(f82(x95352),f334(f334(f8(x95351,x95352),x95353),x95355)),x95354)) % 169.19/169.65 [9536]~P60(x95362)+E(f334(f334(f8(x95361,x95362),f334(f334(f9(x95361,x95362,x95362),f334(f334(f10(x95362,f886(x95362,x95362),x95361),f292(x95362)),x95363)),x95364)),x95365),f334(f334(f292(x95362),f334(f334(f8(x95361,x95362),x95363),x95365)),x95364)) % 169.19/169.65 [9543]~P64(x95432)+E(f334(f334(f8(x95431,x95432),f334(f334(f20(x95431,x95432,x95432),f334(f334(f10(x95432,f886(x95432,x95432),x95431),f3(x95432)),x95433)),x95434)),x95435),f334(f334(f3(x95432),f334(f334(f8(x95431,x95432),x95433),x95435)),f334(f334(f8(x95431,x95432),x95434),x95435))) % 169.19/169.65 [9544]~P72(x95442)+E(f334(f334(f8(x95441,x95442),f334(f334(f20(x95441,x95442,x95442),f334(f334(f10(x95442,f886(x95442,x95442),x95441),f81(x95442)),x95443)),x95444)),x95445),f334(f334(f81(x95442),f334(f334(f8(x95441,x95442),x95443),x95445)),f334(f334(f8(x95441,x95442),x95444),x95445))) % 169.19/169.65 [9545]~P68(x95452)+E(f334(f334(f11(x95451,x95452),f334(f334(f20(x95451,x95452,x95452),f334(f334(f10(x95452,f886(x95452,x95452),x95451),f82(x95452)),x95453)),x95454)),x95455),f334(f334(f82(x95452),f334(f334(f11(x95451,x95452),x95453),x95455)),f334(f334(f11(x95451,x95452),x95454),x95455))) % 169.19/169.65 [9583]~E(x95833,f195(f886(x95831,a871)))+E(f334(f334(f43(x95831,f886(x95832,a871)),x95833),f334(f334(f9(x95831,f886(x95832,a871),f886(x95832,a871)),f334(f334(f10(f886(x95832,a871),f886(f886(x95832,a871),f886(x95832,a871)),x95831),f3(f886(x95832,a871))),x95834)),x95835)),f257(f886(x95832,a871))) % 169.19/169.65 [9584]~E(x95843,f195(f886(x95841,a871)))+E(f334(f334(f43(x95841,f886(x95842,a871)),x95843),f334(f334(f9(x95841,f886(x95842,a871),f886(x95842,a871)),f334(f334(f10(f886(x95842,a871),f886(f886(x95842,a871),f886(x95842,a871)),x95841),f104(f886(x95842,a871))),x95844)),x95845)),f257(f886(x95842,a871))) % 169.19/169.65 [9585]~E(x95853,f195(f886(x95851,a871)))+E(f334(f334(f44(x95851,f886(x95852,a871)),x95853),f334(f334(f9(x95851,f886(x95852,a871),f886(x95852,a871)),f334(f334(f10(f886(x95852,a871),f886(f886(x95852,a871),f886(x95852,a871)),x95851),f113(f886(x95852,a871))),x95854)),x95855)),f195(f886(x95852,a871))) % 169.19/169.65 [9606]E(x96061,f195(f886(x96062,a871)))+E(f334(f334(f43(x96062,f886(x96063,a871)),x96061),f334(f334(f9(x96062,f886(x96063,a871),f886(x96063,a871)),f334(f334(f10(f886(x96063,a871),f886(f886(x96063,a871),f886(x96063,a871)),x96062),f3(f886(x96063,a871))),x96064)),x96065)),f334(f334(f3(f886(x96063,a871)),f334(f334(f43(x96062,f886(x96063,a871)),x96061),x96064)),x96065)) % 169.19/169.65 [9607]E(x96071,f195(f886(x96072,a871)))+E(f334(f334(f43(x96072,f886(x96073,a871)),x96071),f334(f334(f9(x96072,f886(x96073,a871),f886(x96073,a871)),f334(f334(f10(f886(x96073,a871),f886(f886(x96073,a871),f886(x96073,a871)),x96072),f104(f886(x96073,a871))),x96074)),x96075)),f334(f334(f104(f886(x96073,a871)),f334(f334(f43(x96072,f886(x96073,a871)),x96071),x96074)),x96075)) % 169.19/169.65 [9608]E(x96081,f195(f886(x96082,a871)))+E(f334(f334(f44(x96082,f886(x96083,a871)),x96081),f334(f334(f9(x96082,f886(x96083,a871),f886(x96083,a871)),f334(f334(f10(f886(x96083,a871),f886(f886(x96083,a871),f886(x96083,a871)),x96082),f113(f886(x96083,a871))),x96084)),x96085)),f334(f334(f113(f886(x96083,a871)),f334(f334(f44(x96082,f886(x96083,a871)),x96081),x96084)),x96085)) % 169.19/169.65 [9193]~P104(f334(f334(f249(a877),x91931),x91934))+E(f334(f334(f3(a877),f334(f334(f81(a877),f334(f334(f82(a877),x91931),x91932)),x91933)),f334(f334(f81(a877),f334(f334(f82(a877),x91934),x91932)),x91935)),f334(f334(f3(a877),x91933),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x91934),x91931)),x91932)),x91935))) % 169.19/169.65 [9762]~P143(x97621)+E(f334(f166(x97621),f334(f334(f154(x97622,x97621),f334(f334(f9(x97622,x97621,x97621),f334(f334(f10(x97621,f886(x97621,x97621),x97622),f82(x97621)),x97623)),x97624)),x97625)),f334(f334(f82(x97621),f334(f166(x97621),f334(f334(f154(x97622,x97621),x97623),x97625))),x97624)) % 169.19/169.65 [9768]~P64(x97681)+E(f334(f166(x97681),f334(f334(f154(x97682,x97681),f334(f334(f20(x97682,x97681,x97681),f334(f334(f10(x97681,f886(x97681,x97681),x97682),f3(x97681)),x97683)),x97684)),x97685)),f334(f334(f3(x97681),f334(f166(x97681),f334(f334(f154(x97682,x97681),x97683),x97685))),f334(f166(x97681),f334(f334(f154(x97682,x97681),x97684),x97685)))) % 169.19/169.65 [9769]~P72(x97691)+E(f334(f166(x97691),f334(f334(f154(x97692,x97691),f334(f334(f20(x97692,x97691,x97691),f334(f334(f10(x97691,f886(x97691,x97691),x97692),f81(x97691)),x97693)),x97694)),x97695)),f334(f334(f81(x97691),f334(f166(x97691),f334(f334(f154(x97692,x97691),x97693),x97695))),f334(f166(x97691),f334(f334(f154(x97692,x97691),x97694),x97695)))) % 169.19/169.65 [9910]P104(f334(x99101,f334(f334(f183(x99102,x99103),x99104),x99105)))+~P104(f334(x99101,f334(f334(f183(x99102,x99103),f334(f334(f176(x99102),f334(f334(f247(a877),f334(f196(f878(x99102)),x99104)),f334(f196(f878(x99103)),x99105))),x99104)),f334(f334(f176(x99103),f334(f334(f247(a877),f334(f196(f878(x99102)),x99104)),f334(f196(f878(x99103)),x99105))),x99105)))) % 169.19/169.65 [10145]~P104(f334(f334(f336(f885(x101452,x101451)),f334(f334(f269(x101452,x101451),x101454),x101455)),f334(f289(x101451,x101452),x101453)))+P104(f334(f334(f258(x101451,x101452,f334(f334(f9(x101451,f886(f885(x101451,x101452),a871),f886(x101452,a871)),f334(f334(f10(f886(x101452,f886(f886(f885(x101451,x101452),a871),a871)),f886(f886(f885(x101451,x101452),a871),f886(x101452,a871)),x101451),f9(x101452,f886(f885(x101451,x101452),a871),a871)),f334(f334(f10(f886(x101452,f885(x101451,x101452)),f886(x101452,f886(f886(f885(x101451,x101452),a871),a871)),x101451),f334(f10(f885(x101451,x101452),f886(f886(f885(x101451,x101452),a871),a871),x101452),f336(f885(x101451,x101452)))),f269(x101451,x101452)))),x101453)),x101454),x101455)) % 169.19/169.65 [10154]P104(f334(f334(f336(f885(x101541,x101542)),f334(f334(f269(x101541,x101542),x101543),x101544)),f334(f289(x101542,x101541),x101545)))+~P104(f334(f334(f258(x101542,x101541,f334(f334(f9(x101542,f886(f885(x101542,x101541),a871),f886(x101541,a871)),f334(f334(f10(f886(x101541,f886(f886(f885(x101542,x101541),a871),a871)),f886(f886(f885(x101542,x101541),a871),f886(x101541,a871)),x101542),f9(x101541,f886(f885(x101542,x101541),a871),a871)),f334(f334(f10(f886(x101541,f885(x101542,x101541)),f886(x101541,f886(f886(f885(x101542,x101541),a871),a871)),x101542),f334(f10(f885(x101542,x101541),f886(f886(f885(x101542,x101541),a871),a871),x101541),f336(f885(x101542,x101541)))),f269(x101542,x101541)))),x101545)),x101543),x101544)) % 169.19/169.65 [9421]~P104(f334(f334(f249(a877),x94214),x94211))+E(f334(f334(f3(a877),f334(f334(f81(a877),f334(f334(f82(a877),x94211),x94212)),x94213)),f334(f334(f81(a877),f334(f334(f82(a877),x94214),x94212)),x94215)),f334(f334(f3(a877),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x94211),x94214)),x94212)),x94213)),x94215)) % 169.19/169.65 [10163]P20(x101631,x101632,f334(f313(a874,f876(x101631),f334(f334(f20(a874,f886(x101631,f886(a872,a871)),f876(x101631)),f334(f334(f20(a874,a873,f886(f886(x101631,f886(a872,a871)),f876(x101631))),f334(f334(f10(f886(x101631,f886(a872,a871)),f886(a873,f886(f886(x101631,f886(a872,a871)),f876(x101631))),a874),f93(x101631)),x101633)),a26)),x101634)),x101635))+~P20(x101631,f334(f334(f113(f886(f876(x101631),a871)),x101632),f334(f313(a874,f876(x101631),f334(f334(f20(a874,f886(x101631,f886(a872,a871)),f876(x101631)),f334(f334(f20(a874,a873,f886(f886(x101631,f886(a872,a871)),f876(x101631))),f334(f334(f10(f886(x101631,f886(a872,a871)),f886(a873,f886(f886(x101631,f886(a872,a871)),f876(x101631))),a874),f93(x101631)),x101633)),a26)),x101634)),x101635)),f334(f313(a874,f876(x101631),f334(f334(f20(a874,f886(x101631,f886(a872,a871)),f876(x101631)),f334(f334(f20(a874,a873,f886(f886(x101631,f886(a872,a871)),f876(x101631))),f334(f334(f10(f886(x101631,f886(a872,a871)),f886(a873,f886(f886(x101631,f886(a872,a871)),f876(x101631))),a874),f93(x101631)),x101633)),f334(f334(f10(f881(a873),a873,a874),f245(a873)),a28))),x101634)),x101635)) % 169.19/169.65 [10164]P23(x101641,x101642,f334(f313(a874,f876(x101641),f334(f334(f20(a874,f886(x101641,f886(a872,a871)),f876(x101641)),f334(f334(f20(a874,a873,f886(f886(x101641,f886(a872,a871)),f876(x101641))),f334(f334(f10(f886(x101641,f886(a872,a871)),f886(a873,f886(f886(x101641,f886(a872,a871)),f876(x101641))),a874),f93(x101641)),x101643)),a26)),x101644)),x101645))+~P23(x101641,f334(f334(f113(f886(f876(x101641),a871)),x101642),f334(f313(a874,f876(x101641),f334(f334(f20(a874,f886(x101641,f886(a872,a871)),f876(x101641)),f334(f334(f20(a874,a873,f886(f886(x101641,f886(a872,a871)),f876(x101641))),f334(f334(f10(f886(x101641,f886(a872,a871)),f886(a873,f886(f886(x101641,f886(a872,a871)),f876(x101641))),a874),f93(x101641)),x101643)),a26)),x101644)),x101645)),f334(f313(a874,f876(x101641),f334(f334(f20(a874,f886(x101641,f886(a872,a871)),f876(x101641)),f334(f334(f20(a874,a873,f886(f886(x101641,f886(a872,a871)),f876(x101641))),f334(f334(f10(f886(x101641,f886(a872,a871)),f886(a873,f886(f886(x101641,f886(a872,a871)),f876(x101641))),a874),f93(x101641)),x101643)),f334(f334(f10(f881(a873),a873,a874),f245(a873)),a28))),x101644)),x101645)) % 169.19/169.65 [5300]E(x53001,x53002)+~E(f29(x53003,x53004,x53001),f29(x53005,x53006,x53002)) % 169.19/169.65 [5301]E(x53011,x53012)+~E(f29(x53013,x53011,x53014),f29(x53015,x53012,x53016)) % 169.19/169.65 [5302]E(x53021,x53022)+~E(f29(x53021,x53023,x53024),f29(x53022,x53025,x53026)) % 169.19/169.65 [5303]E(x53031,x53032)+~E(f31(x53033,x53034,x53031),f31(x53035,x53036,x53032)) % 169.19/169.65 [5304]E(x53041,x53042)+~E(f31(x53043,x53041,x53044),f31(x53045,x53042,x53046)) % 169.19/169.65 [5305]E(x53051,x53052)+~E(f31(x53051,x53053,x53054),f31(x53052,x53055,x53056)) % 169.19/169.65 [5306]E(x53061,x53062)+~E(f30(x53063,x53064,x53061),f30(x53065,x53066,x53062)) % 169.19/169.65 [5307]E(x53071,x53072)+~E(f30(x53073,x53071,x53074),f30(x53075,x53072,x53076)) % 169.19/169.65 [5308]E(x53081,x53082)+~E(f30(x53081,x53083,x53084),f30(x53082,x53085,x53086)) % 169.19/169.65 [7289]E(x72891,x72892)+~E(f229(x72893,x72894,x72895,x72891),f229(x72893,x72894,x72896,x72892)) % 169.19/169.65 [7290]E(x72901,x72902)+~E(f229(x72903,x72904,x72901,x72905),f229(x72903,x72904,x72902,x72906)) % 169.19/169.65 [6752]E(f334(f186(x67521,x67522,x67523,x67524),x67525),f334(f241(x67522),x67526))+~E(f334(x67524,x67525),f334(f241(x67522),x67526)) % 169.19/169.65 [6896]E(f334(f243(f881(x68961),x68962,f198(x68961),x68963),f334(x68964,x68965)),f334(x68963,x68966))+~E(f334(x68964,x68965),f334(f241(x68962),x68966)) % 169.19/169.65 [8408]~P15(x84085,x84081,x84082,x84086)+E(f334(f74(x84081,x84081,x84081,f334(x84082,x84083)),f334(x84082,x84084)),f334(f74(x84081,x84081,x84081,f334(x84082,x84084)),f334(x84082,x84083))) % 169.19/169.65 [8635]~P54(x86354,x86355,x86352,x86351,x86356)+E(f334(x86351,f334(x86352,x86353)),x86353) % 169.19/169.65 [8785]P21(x87851,x87852,x87853,x87854)+~P21(x87851,x87855,f334(f74(x87852,x87855,x87851,x87856),x87853),x87854) % 169.19/169.65 [8868]~P21(x88684,x88682,f334(f74(x88681,x88682,x88684,x88683),x88685),x88686)+P21(x88681,x88682,x88683,f334(f313(x88684,x88681,x88685),x88686)) % 169.19/169.65 [9546]P104(f334(f63(x95461),x95462))+~P104(f334(f68(x95461,x95463,x95464,x95465,x95462),x95466)) % 169.19/169.65 [9554]~P104(f334(f334(f336(x95544),x95543),f299(x95544,x95541,x95545,x95542,x95546)))+P104(f334(f334(x95541,x95542),x95543)) % 169.19/169.65 [9555]~P104(f334(f334(f336(x95554),x95553),f302(x95554,x95555,x95551,x95552,x95556)))+P104(f334(f334(x95551,x95552),x95553)) % 169.19/169.65 [9556]~P104(f334(f334(f336(x95564),x95562),f299(x95564,x95565,x95561,x95566,x95563)))+P104(f334(f334(x95561,x95562),x95563)) % 169.19/169.65 [9557]~P104(f334(f334(f336(x95574),x95572),f302(x95574,x95571,x95575,x95576,x95573)))+P104(f334(f334(x95571,x95572),x95573)) % 169.19/169.65 [5810]E(x58101,x58102)+~E(f334(f334(f269(x58103,x58104),x58105),x58101),f334(f334(f269(x58103,x58104),x58106),x58102)) % 169.19/169.65 [5812]E(x58121,x58122)+~E(f334(f334(f269(x58123,x58124),x58121),x58125),f334(f334(f269(x58123,x58124),x58122),x58126)) % 169.19/169.65 [5936]~P12(x59365,x59366,x59361)+E(f334(f334(x59361,x59362),f334(f334(x59361,x59363),x59364)),f334(f334(x59361,x59363),f334(f334(x59361,x59362),x59364))) % 169.19/169.65 [7351]~P34(x73514,x73511,f334(f334(f151(x73514),x73512),x73515),f334(f334(f151(x73514),x73513),x73516))+P104(f334(f334(x73511,x73512),x73513)) % 169.19/169.65 [7716]P34(x77161,x77162,x77163,x77164)+~P34(x77161,x77162,f334(f334(f151(x77161),x77165),x77163),f334(f334(f151(x77161),x77166),x77164)) % 169.19/169.65 [8728]~P54(x87285,x87281,x87282,x87286,x87284)+P104(f334(f334(f336(x87281),f334(x87282,x87283)),x87284)) % 169.19/169.65 [8896]E(f334(f77(x88961,x88962,x88963,x88964,x88965),x88966),f334(x88963,x88966))+P104(f334(f334(f336(x88961),x88966),x88965)) % 169.19/169.65 [8918]~E(x89183,f334(f334(f151(x89181),x89185),x89186))+P104(f334(f334(f336(f885(f878(x89181),f878(x89181))),f334(f334(f269(f878(x89181),f878(x89181)),x89182),f334(f334(f134(x89181),x89182),x89183))),f147(x89181,x89184))) % 169.19/169.65 [8924]E(f334(f77(x89241,x89242,x89243,x89244,x89245),x89246),f334(x89244,x89246))+~P104(f334(f334(f336(x89241),x89246),x89245)) % 169.19/169.65 [8929]E(f334(f188(x89291,x89292,x89293,x89294,x89295),x89296),f334(x89293,x89296))+P104(f334(f334(f336(x89291),x89296),f334(f173(x89291),x89294))) % 169.19/169.65 [9147]~P36(x91471,x91472,x91473,x91475,x91476)+P36(x91471,x91472,x91473,f334(f334(f176(x91471),x91474),x91475),f334(f334(f176(x91472),x91474),x91476)) % 169.19/169.65 [9148]~P36(x91481,x91482,x91483,x91485,x91486)+P36(x91481,x91482,x91483,f334(f334(f138(x91481),x91484),x91485),f334(f334(f138(x91482),x91484),x91486)) % 169.19/169.65 [9618]~P19(x96184,x96182,x96185,x96183,x96186,x96181)+E(f334(x96181,f195(f886(x96182,a871))),x96183) % 169.19/169.65 [9860]~E(f334(x98604,f334(f268(x98601,x98603),x98605)),f334(x98606,f334(f268(x98601,x98603),x98605)))+E(f334(f274(x98601,x98602,x98603,x98603,x98604,f35(x98603)),x98605),f334(f274(x98601,x98602,x98603,x98603,x98606,f35(x98603)),x98605)) % 169.19/169.65 [9861]~E(f334(x98614,f334(f272(x98611,x98612),x98615)),f334(x98616,f334(f272(x98611,x98612),x98615)))+E(f334(f274(x98611,x98611,x98612,x98613,f35(x98611),x98614),x98615),f334(f274(x98611,x98611,x98612,x98613,f35(x98611),x98616),x98615)) % 169.19/169.65 [9906]~E(f334(f274(x99062,x99066,x99063,x99063,x99061,f35(x99063)),x99064),f334(f274(x99062,x99066,x99063,x99063,x99065,f35(x99063)),x99064))+E(f334(x99061,f334(f268(x99062,x99063),x99064)),f334(x99065,f334(f268(x99062,x99063),x99064))) % 169.19/169.65 [9907]~E(f334(f274(x99072,x99072,x99073,x99076,f35(x99072),x99071),x99074),f334(f274(x99072,x99072,x99073,x99076,f35(x99072),x99075),x99074))+E(f334(x99071,f334(f272(x99072,x99073),x99074)),f334(x99075,f334(f272(x99072,x99073),x99074))) % 169.19/169.65 [8824]P104(f334(f334(f336(x88241),x88242),x88243))+~P104(f334(f334(f336(f885(x88241,x88244)),f334(f334(f269(x88241,x88244),x88242),x88245)),f334(f334(f271(x88241,x88244),x88243),x88246))) % 169.19/169.65 [8838]P104(f334(f334(f336(x88381),x88382),f334(x88383,x88384)))+~P104(f334(f334(f336(f885(x88385,x88381)),f334(f334(f269(x88385,x88381),x88384),x88382)),f334(f334(f271(x88385,x88381),x88386),x88383))) % 169.19/169.65 [8926]~E(f334(f196(f878(x89261)),x89264),f334(f196(f878(x89262)),x89265))+E(f188(x89261,x89262,x89263,x89264,f334(f334(f134(x89262),x89265),x89266)),f188(x89261,x89262,x89263,x89264,x89265)) % 169.19/169.65 [8927]~E(f334(f196(f878(x89271)),x89274),f334(f196(f878(x89272)),x89276))+E(f188(x89271,x89272,x89273,f334(f334(f134(x89271),x89274),x89275),x89276),f188(x89271,x89272,x89273,x89274,x89276)) % 169.19/169.65 [9165]P104(f334(f334(f336(x91651),x91654),f185(x91651,x91652,x91656)))+E(f186(x91651,x91652,f334(f334(f334(f73(x91651,f881(x91652)),x91653),x91654),f334(f241(x91652),x91655)),x91656),f334(f334(f334(f73(x91651,f881(x91652)),f186(x91651,x91652,x91653,x91656)),x91654),f334(f241(x91652),x91655))) % 169.19/169.65 [9259]P104(f334(f334(f336(f885(x92591,x92591)),f334(f334(f269(x92591,x92591),f334(x92592,x92593)),f334(x92592,x92594))),x92595))+~P104(f334(f334(f336(f885(x92596,x92596)),f334(f334(f269(x92596,x92596),x92593),x92594)),f334(f334(f290(x92591,x92596),x92595),x92592))) % 169.19/169.65 [9276]~P104(f334(f334(f336(f885(x92764,x92764)),f334(f334(f269(x92764,x92764),f334(x92766,x92762)),f334(x92766,x92763))),x92765))+P104(f334(f334(f336(f885(x92761,x92761)),f334(f334(f269(x92761,x92761),x92762),x92763)),f334(f334(f290(x92764,x92761),x92765),x92766))) % 169.19/169.65 [9909]E(f334(f334(f269(x99091,x99092),f793(x99093,x99094,x99095,x99096,x99092,x99091)),f797(x99093,x99094,x99095,x99096,x99092,x99091)),x99096)+~P104(f334(f334(f336(f885(x99091,x99092)),x99096),f334(f334(f291(x99091,x99095,x99092),x99094),x99093))) % 169.19/169.65 [10108]~P104(f334(f334(f336(f885(x101081,x101086)),x101085),f334(f334(f291(x101081,x101082,x101086),x101084),x101083)))+P104(f334(f334(f336(f885(x101081,x101082)),f334(f334(f269(x101081,x101082),f793(x101083,x101084,x101082,x101085,x101086,x101081)),f798(x101083,x101084,x101082,x101085,x101086,x101081))),x101084)) % 169.19/169.65 [10109]~P104(f334(f334(f336(f885(x101096,x101092)),x101095),f334(f334(f291(x101096,x101091,x101092),x101094),x101093)))+P104(f334(f334(f336(f885(x101091,x101092)),f334(f334(f269(x101091,x101092),f798(x101093,x101094,x101091,x101095,x101092,x101096)),f797(x101093,x101094,x101091,x101095,x101092,x101096))),x101093)) % 169.19/169.65 [6215]~E(x62156,x62154)+E(f334(f334(f334(f334(f73(x62151,x62152),x62153),x62154),x62155),x62156),x62155) % 169.19/169.65 [6265]E(x62651,x62652)+E(f334(f334(f334(f334(f73(x62653,x62654),x62655),x62652),x62656),x62651),f334(x62655,x62651)) % 169.19/169.65 [7787]~P28(x77872)+E(f334(f334(f43(x77871,x77872),x77873),f334(f334(f9(x77871,x77874,x77872),x77875),x77876)),f334(f334(f334(f43(x77871,f886(x77874,x77872)),x77873),x77875),x77876)) % 169.19/169.65 [7788]~P28(x77882)+E(f334(f334(f44(x77881,x77882),x77883),f334(f334(f9(x77881,x77884,x77882),x77885),x77886)),f334(f334(f334(f44(x77881,f886(x77884,x77882)),x77883),x77885),x77886)) % 169.19/169.65 [8549]E(f334(f334(f44(x85491,f886(x85492,a871)),x85493),f334(f334(f10(f886(x85492,a871),f886(x85492,a871),x85491),f334(f312(x85492),x85494)),x85495)),f334(f334(f312(x85492),x85494),f334(f334(f44(x85491,f886(x85492,a871)),x85493),x85495)))+~P104(f334(f334(f336(x85491),x85496),x85493)) % 169.19/169.65 [8972]~P28(x89722)+E(f334(f334(f43(x89721,x89722),x89723),f334(f334(f10(f886(x89724,x89722),x89722,x89721),f334(f43(x89724,x89722),x89725)),f334(f9(x89724,x89721,x89722),x89726))),f334(f334(f43(x89724,x89722),x89725),f334(f334(f10(f886(x89721,x89722),x89722,x89724),f334(f43(x89721,x89722),x89723)),x89726))) % 169.19/169.65 [8973]~P28(x89732)+E(f334(f334(f44(x89731,x89732),x89733),f334(f334(f10(f886(x89734,x89732),x89732,x89731),f334(f44(x89734,x89732),x89735)),f334(f9(x89734,x89731,x89732),x89736))),f334(f334(f44(x89734,x89732),x89735),f334(f334(f10(f886(x89731,x89732),x89732,x89734),f334(f44(x89731,x89732),x89733)),x89736))) % 169.19/169.65 [9174]P104(f334(f334(f336(x91741),x91742),f334(f173(x91741),x91743)))+~P104(f334(f334(f336(f885(x91744,x91741)),f334(f334(f269(x91744,x91741),x91745),x91742)),f334(f173(f885(x91744,x91741)),f334(f334(f183(x91744,x91741),x91746),x91743)))) % 169.19/169.65 [9175]P104(f334(f334(f336(x91751),x91752),f334(f173(x91751),x91753)))+~P104(f334(f334(f336(f885(x91751,x91754)),f334(f334(f269(x91751,x91754),x91752),x91755)),f334(f173(f885(x91751,x91754)),f334(f334(f183(x91751,x91754),x91753),x91756)))) % 169.19/169.65 [9273]P104(f334(f334(f249(f886(x92731,a871)),f334(f288(x92732,x92731,x92733),x92734)),x92735))+~P104(f334(f334(f249(f886(f885(x92732,x92731),a871)),x92733),f334(f334(f271(x92732,x92731),x92736),f334(f18(f886(x92731,a871),x92732),x92735)))) % 169.19/169.65 [9455]P104(f334(f334(f336(f885(f878(x94551),f878(x94551))),f334(f334(f269(f878(x94551),f878(x94551)),f334(f334(f151(x94551),x94552),x94553)),f334(f334(f151(x94551),x94554),x94555))),f147(x94551,x94556)))+~P104(f334(f334(f336(f885(x94551,x94551)),f334(f334(f269(x94551,x94551),x94552),x94554)),x94556)) % 169.19/169.65 [9905]E(f334(f334(f269(x99051,x99052),f724(x99053,x99054,x99055,x99052,x99051,x99056)),f725(x99053,x99054,x99055,x99052,x99051,x99056)),x99056)+P104(f334(f334(f336(x99055),x99054),f334(f334(f273(x99051,x99052,f886(x99055,a871)),x99053),x99056))) % 169.19/169.65 [9911]E(f334(f334(f269(x99111,x99112),f726(x99113,x99114,x99112,x99111,x99115,x99116)),f727(x99113,x99114,x99112,x99111,x99115,x99116)),x99113)+~P104(f334(f334(f336(x99116),x99115),f334(f334(f273(x99111,x99112,f886(x99116,a871)),x99114),x99113))) % 169.19/169.65 [10068]P104(f334(f334(f336(x100681),x100682),f334(f334(x100683,f726(x100684,x100683,x100685,x100686,x100682,x100681)),f727(x100684,x100683,x100685,x100686,x100682,x100681))))+~P104(f334(f334(f336(x100681),x100682),f334(f334(f273(x100686,x100685,f886(x100681,a871)),x100683),x100684))) % 169.19/169.65 [10086]~P104(f334(f334(f336(x100861),x100862),f334(f334(x100865,f724(x100865,x100862,x100861,x100864,x100863,x100866)),f725(x100865,x100862,x100861,x100864,x100863,x100866))))+P104(f334(f334(f336(x100861),x100862),f334(f334(f273(x100863,x100864,f886(x100861,a871)),x100865),x100866))) % 169.19/169.65 [7905]P104(f334(f334(f336(x79051),x79054),x79056))+E(f189(x79051,x79052,f334(f334(f334(f73(x79051,f881(x79052)),x79053),x79054),x79055),x79056),f189(x79051,x79052,x79053,x79056)) % 169.19/169.65 [7981]P104(f334(f334(f336(x79811),x79814),x79816))+E(f334(f313(x79811,x79812,f334(f334(f334(f73(x79811,x79812),x79813),x79814),x79815)),x79816),f334(f313(x79811,x79812,x79813),x79816)) % 169.19/169.65 [8009]P104(f334(f334(f336(x80091),x80094),f334(f173(x80091),x80096)))+E(f334(f334(f154(x80091,x80092),f334(f334(f334(f73(x80091,x80092),x80093),x80094),x80095)),x80096),f334(f334(f154(x80091,x80092),x80093),x80096)) % 169.19/169.65 [8454]E(x84541,x84542)+E(f334(f334(f159(x84543,f334(f334(f159(x84543,x84544),x84541),x84545)),x84542),x84546),f334(f334(f159(x84543,f334(f334(f159(x84543,x84544),x84542),x84546)),x84541),x84545)) % 169.19/169.65 [8978]~P104(f334(f334(f336(x89783),x89786),x89785))+E(f334(f334(f312(x89781),x89782),f334(f313(x89783,x89781,x89784),f334(f334(f3(f886(x89783,a871)),x89785),f334(f334(f312(x89783),x89786),f195(f886(x89783,a871)))))),f334(f313(x89783,x89781,f334(f334(f334(f73(x89783,x89781),x89784),x89786),x89782)),x89785)) % 169.19/169.65 [9724]E(f188(x97241,x97242,x97243,f334(f334(f134(x97241),x97244),f334(f334(f151(x97241),x97245),f116(x97241))),x97246),f334(f334(f334(f73(x97241,f881(x97242)),f188(x97241,x97242,x97243,x97244,x97246)),x97245),f334(f241(x97242),f334(f334(f165(x97242),x97246),f334(f196(f878(x97241)),x97244)))))+~P104(f334(f334(f250(a877),f334(f196(f878(x97241)),x97244)),f334(f196(f878(x97242)),x97246))) % 169.19/169.65 [8767]~E(x87673,x87676)+E(f334(f334(f179(x87671,x87672),f334(f334(f151(f885(x87671,x87672)),f334(f334(f269(x87671,x87672),x87673),x87674)),x87675)),x87676),f334(f241(x87672),x87674)) % 169.19/169.65 [8794]E(x87941,x87942)+E(f334(f334(f179(x87943,x87944),f334(f334(f151(f885(x87943,x87944)),f334(f334(f269(x87943,x87944),x87941),x87945)),x87946)),x87942),f334(f334(f179(x87943,x87944),x87946),x87942)) % 169.19/169.65 [9051]~P104(f334(f334(x90514,x90515),x90516))+P104(f334(f334(f334(f334(f113(f886(x90511,f886(x90512,a871))),x90513),x90514),x90515),x90516)) % 169.19/169.65 [9053]~P104(f334(f334(x90533,x90535),x90536))+P104(f334(f334(f334(f334(f113(f886(x90531,f886(x90532,a871))),x90533),x90534),x90535),x90536)) % 169.19/169.65 [9325]P104(f334(f334(x93251,x93252),x93253))+~P104(f334(f334(f334(f334(f104(f886(x93254,f886(x93255,a871))),x93256),x93251),x93252),x93253)) % 169.19/169.65 [9326]P104(f334(f334(x93261,x93262),x93263))+~P104(f334(f334(f334(f334(f104(f886(x93264,f886(x93265,a871))),x93261),x93266),x93262),x93263)) % 169.19/169.65 [9746]~P72(x97462)+E(f334(f334(f8(x97461,x97462),f334(f334(f9(x97461,f886(x97463,a871),x97462),f334(f334(f10(f886(x97463,x97462),f886(f886(x97463,a871),x97462),x97461),f8(x97463,x97462)),x97464)),x97465)),x97466),f334(f334(f8(f885(x97461,x97463),x97462),f334(f273(x97461,x97463,x97462),x97464)),f334(f334(f271(x97461,x97463),x97466),f334(f18(f886(x97463,a871),x97461),x97465)))) % 169.19/169.65 [9747]~P68(x97472)+E(f334(f334(f11(x97471,x97472),f334(f334(f9(x97471,f886(x97473,a871),x97472),f334(f334(f10(f886(x97473,x97472),f886(f886(x97473,a871),x97472),x97471),f11(x97473,x97472)),x97474)),x97475)),x97476),f334(f334(f11(f885(x97471,x97473),x97472),f334(f273(x97471,x97473,x97472),x97474)),f334(f334(f271(x97471,x97473),x97476),f334(f18(f886(x97473,a871),x97471),x97475)))) % 169.19/169.65 [9888]~P72(x98882)+E(f334(f334(f8(x98881,x98882),f334(f334(f9(x98881,f886(x98883,a871),x98882),f334(f334(f10(f886(x98883,x98882),f886(f886(x98883,a871),x98882),x98881),f8(x98883,x98882)),f334(f9(x98883,x98881,x98882),x98884))),x98885)),x98886),f334(f334(f8(x98883,x98882),f334(f334(f9(x98883,f886(x98881,a871),x98882),f334(f334(f10(f886(x98881,x98882),f886(f886(x98881,a871),x98882),x98883),f8(x98881,x98882)),x98884)),x98886)),x98885)) % 169.19/169.65 [9587]~P104(f334(f334(f336(x95871),x95875),x95874))+E(f334(f334(f334(f73(x95871,f881(x95872)),f189(x95871,x95872,x95873,f334(f334(f3(f886(x95871,a871)),x95874),f334(f334(f312(x95871),x95875),f195(f886(x95871,a871)))))),x95875),x95876),f189(x95871,x95872,f334(f334(f334(f73(x95871,f881(x95872)),x95873),x95875),x95876),x95874)) % 169.19/169.65 [10167]~P104(f334(f334(f336(f885(x101671,x101672)),f334(f334(f269(x101671,x101672),x101675),x101676)),f334(f334(f113(f886(f885(x101671,x101672),a871)),x101673),x101674)))+P104(f334(f334(f334(f334(f113(f886(x101671,f886(x101672,a871))),f334(f334(f9(x101671,f886(f885(x101671,x101672),a871),f886(x101672,a871)),f334(f334(f10(f886(x101672,f886(f886(f885(x101671,x101672),a871),a871)),f886(f886(f885(x101671,x101672),a871),f886(x101672,a871)),x101671),f9(x101672,f886(f885(x101671,x101672),a871),a871)),f334(f334(f10(f886(x101672,f885(x101671,x101672)),f886(x101672,f886(f886(f885(x101671,x101672),a871),a871)),x101671),f334(f10(f885(x101671,x101672),f886(f886(f885(x101671,x101672),a871),a871),x101672),f336(f885(x101671,x101672)))),f269(x101671,x101672)))),x101673)),f334(f334(f9(x101671,f886(f885(x101671,x101672),a871),f886(x101672,a871)),f334(f334(f10(f886(x101672,f886(f886(f885(x101671,x101672),a871),a871)),f886(f886(f885(x101671,x101672),a871),f886(x101672,a871)),x101671),f9(x101672,f886(f885(x101671,x101672),a871),a871)),f334(f334(f10(f886(x101672,f885(x101671,x101672)),f886(x101672,f886(f886(f885(x101671,x101672),a871),a871)),x101671),f334(f10(f885(x101671,x101672),f886(f886(f885(x101671,x101672),a871),a871),x101672),f336(f885(x101671,x101672)))),f269(x101671,x101672)))),x101674)),x101675),x101676)) % 169.19/169.65 [10168]~P104(f334(f334(f336(f885(x101681,x101682)),f334(f334(f269(x101681,x101682),x101685),x101686)),f334(f334(f104(f886(f885(x101681,x101682),a871)),x101683),x101684)))+P104(f334(f334(f334(f334(f104(f886(x101681,f886(x101682,a871))),f334(f334(f9(x101681,f886(f885(x101681,x101682),a871),f886(x101682,a871)),f334(f334(f10(f886(x101682,f886(f886(f885(x101681,x101682),a871),a871)),f886(f886(f885(x101681,x101682),a871),f886(x101682,a871)),x101681),f9(x101682,f886(f885(x101681,x101682),a871),a871)),f334(f334(f10(f886(x101682,f885(x101681,x101682)),f886(x101682,f886(f886(f885(x101681,x101682),a871),a871)),x101681),f334(f10(f885(x101681,x101682),f886(f886(f885(x101681,x101682),a871),a871),x101682),f336(f885(x101681,x101682)))),f269(x101681,x101682)))),x101683)),f334(f334(f9(x101681,f886(f885(x101681,x101682),a871),f886(x101682,a871)),f334(f334(f10(f886(x101682,f886(f886(f885(x101681,x101682),a871),a871)),f886(f886(f885(x101681,x101682),a871),f886(x101682,a871)),x101681),f9(x101682,f886(f885(x101681,x101682),a871),a871)),f334(f334(f10(f886(x101682,f885(x101681,x101682)),f886(x101682,f886(f886(f885(x101681,x101682),a871),a871)),x101681),f334(f10(f885(x101681,x101682),f886(f886(f885(x101681,x101682),a871),a871),x101682),f336(f885(x101681,x101682)))),f269(x101681,x101682)))),x101684)),x101685),x101686)) % 169.19/169.65 [10174]P104(f334(f334(f336(f885(x101741,x101742)),f334(f334(f269(x101741,x101742),x101743),x101744)),f334(f334(f113(f886(f885(x101741,x101742),a871)),x101745),x101746)))+~P104(f334(f334(f334(f334(f113(f886(x101741,f886(x101742,a871))),f334(f334(f9(x101741,f886(f885(x101741,x101742),a871),f886(x101742,a871)),f334(f334(f10(f886(x101742,f886(f886(f885(x101741,x101742),a871),a871)),f886(f886(f885(x101741,x101742),a871),f886(x101742,a871)),x101741),f9(x101742,f886(f885(x101741,x101742),a871),a871)),f334(f334(f10(f886(x101742,f885(x101741,x101742)),f886(x101742,f886(f886(f885(x101741,x101742),a871),a871)),x101741),f334(f10(f885(x101741,x101742),f886(f886(f885(x101741,x101742),a871),a871),x101742),f336(f885(x101741,x101742)))),f269(x101741,x101742)))),x101745)),f334(f334(f9(x101741,f886(f885(x101741,x101742),a871),f886(x101742,a871)),f334(f334(f10(f886(x101742,f886(f886(f885(x101741,x101742),a871),a871)),f886(f886(f885(x101741,x101742),a871),f886(x101742,a871)),x101741),f9(x101742,f886(f885(x101741,x101742),a871),a871)),f334(f334(f10(f886(x101742,f885(x101741,x101742)),f886(x101742,f886(f886(f885(x101741,x101742),a871),a871)),x101741),f334(f10(f885(x101741,x101742),f886(f886(f885(x101741,x101742),a871),a871),x101742),f336(f885(x101741,x101742)))),f269(x101741,x101742)))),x101746)),x101743),x101744)) % 169.19/169.65 [10175]P104(f334(f334(f336(f885(x101751,x101752)),f334(f334(f269(x101751,x101752),x101753),x101754)),f334(f334(f104(f886(f885(x101751,x101752),a871)),x101755),x101756)))+~P104(f334(f334(f334(f334(f104(f886(x101751,f886(x101752,a871))),f334(f334(f9(x101751,f886(f885(x101751,x101752),a871),f886(x101752,a871)),f334(f334(f10(f886(x101752,f886(f886(f885(x101751,x101752),a871),a871)),f886(f886(f885(x101751,x101752),a871),f886(x101752,a871)),x101751),f9(x101752,f886(f885(x101751,x101752),a871),a871)),f334(f334(f10(f886(x101752,f885(x101751,x101752)),f886(x101752,f886(f886(f885(x101751,x101752),a871),a871)),x101751),f334(f10(f885(x101751,x101752),f886(f886(f885(x101751,x101752),a871),a871),x101752),f336(f885(x101751,x101752)))),f269(x101751,x101752)))),x101755)),f334(f334(f9(x101751,f886(f885(x101751,x101752),a871),f886(x101752,a871)),f334(f334(f10(f886(x101752,f886(f886(f885(x101751,x101752),a871),a871)),f886(f886(f885(x101751,x101752),a871),f886(x101752,a871)),x101751),f9(x101752,f886(f885(x101751,x101752),a871),a871)),f334(f334(f10(f886(x101752,f885(x101751,x101752)),f886(x101752,f886(f886(f885(x101751,x101752),a871),a871)),x101751),f334(f10(f885(x101751,x101752),f886(f886(f885(x101751,x101752),a871),a871),x101752),f336(f885(x101751,x101752)))),f269(x101751,x101752)))),x101756)),x101753),x101754)) % 169.19/169.65 [10161]~P104(f334(f334(f336(f885(x101612,x101613)),f334(f334(f269(x101612,x101613),x101615),x101616)),f334(f334(f43(x101611,f886(f885(x101612,x101613),a871)),f257(f886(x101611,a871))),x101614)))+P104(f334(f334(f334(f334(f43(x101611,f886(x101612,f886(x101613,a871))),f257(f886(x101611,a871))),f334(f334(f10(f886(f885(x101612,x101613),a871),f886(x101612,f886(x101613,a871)),x101611),f334(f9(x101612,f886(f885(x101612,x101613),a871),f886(x101613,a871)),f334(f334(f10(f886(x101613,f886(f886(f885(x101612,x101613),a871),a871)),f886(f886(f885(x101612,x101613),a871),f886(x101613,a871)),x101612),f9(x101613,f886(f885(x101612,x101613),a871),a871)),f334(f334(f10(f886(x101613,f885(x101612,x101613)),f886(x101613,f886(f886(f885(x101612,x101613),a871),a871)),x101612),f334(f10(f885(x101612,x101613),f886(f886(f885(x101612,x101613),a871),a871),x101613),f336(f885(x101612,x101613)))),f269(x101612,x101613))))),x101614)),x101615),x101616)) % 169.19/169.65 [10162]~P104(f334(f334(f336(f885(x101622,x101623)),f334(f334(f269(x101622,x101623),x101625),x101626)),f334(f334(f44(x101621,f886(f885(x101622,x101623),a871)),f257(f886(x101621,a871))),x101624)))+P104(f334(f334(f334(f334(f44(x101621,f886(x101622,f886(x101623,a871))),f257(f886(x101621,a871))),f334(f334(f10(f886(f885(x101622,x101623),a871),f886(x101622,f886(x101623,a871)),x101621),f334(f9(x101622,f886(f885(x101622,x101623),a871),f886(x101623,a871)),f334(f334(f10(f886(x101623,f886(f886(f885(x101622,x101623),a871),a871)),f886(f886(f885(x101622,x101623),a871),f886(x101623,a871)),x101622),f9(x101623,f886(f885(x101622,x101623),a871),a871)),f334(f334(f10(f886(x101623,f885(x101622,x101623)),f886(x101623,f886(f886(f885(x101622,x101623),a871),a871)),x101622),f334(f10(f885(x101622,x101623),f886(f886(f885(x101622,x101623),a871),a871),x101623),f336(f885(x101622,x101623)))),f269(x101622,x101623))))),x101624)),x101625),x101626)) % 169.19/169.65 [10171]P104(f334(f334(f336(f885(x101711,x101712)),f334(f334(f269(x101711,x101712),x101713),x101714)),f334(f334(f43(x101715,f886(f885(x101711,x101712),a871)),f257(f886(x101715,a871))),x101716)))+~P104(f334(f334(f334(f334(f43(x101715,f886(x101711,f886(x101712,a871))),f257(f886(x101715,a871))),f334(f334(f10(f886(f885(x101711,x101712),a871),f886(x101711,f886(x101712,a871)),x101715),f334(f9(x101711,f886(f885(x101711,x101712),a871),f886(x101712,a871)),f334(f334(f10(f886(x101712,f886(f886(f885(x101711,x101712),a871),a871)),f886(f886(f885(x101711,x101712),a871),f886(x101712,a871)),x101711),f9(x101712,f886(f885(x101711,x101712),a871),a871)),f334(f334(f10(f886(x101712,f885(x101711,x101712)),f886(x101712,f886(f886(f885(x101711,x101712),a871),a871)),x101711),f334(f10(f885(x101711,x101712),f886(f886(f885(x101711,x101712),a871),a871),x101712),f336(f885(x101711,x101712)))),f269(x101711,x101712))))),x101716)),x101713),x101714)) % 169.19/169.65 [10172]P104(f334(f334(f336(f885(x101721,x101722)),f334(f334(f269(x101721,x101722),x101723),x101724)),f334(f334(f44(x101725,f886(f885(x101721,x101722),a871)),f257(f886(x101725,a871))),x101726)))+~P104(f334(f334(f334(f334(f44(x101725,f886(x101721,f886(x101722,a871))),f257(f886(x101725,a871))),f334(f334(f10(f886(f885(x101721,x101722),a871),f886(x101721,f886(x101722,a871)),x101725),f334(f9(x101721,f886(f885(x101721,x101722),a871),f886(x101722,a871)),f334(f334(f10(f886(x101722,f886(f886(f885(x101721,x101722),a871),a871)),f886(f886(f885(x101721,x101722),a871),f886(x101722,a871)),x101721),f9(x101722,f886(f885(x101721,x101722),a871),a871)),f334(f334(f10(f886(x101722,f885(x101721,x101722)),f886(x101722,f886(f886(f885(x101721,x101722),a871),a871)),x101721),f334(f10(f885(x101721,x101722),f886(f886(f885(x101721,x101722),a871),a871),x101722),f336(f885(x101721,x101722)))),f269(x101721,x101722))))),x101726)),x101723),x101724)) % 169.19/169.65 [7462]E(f334(x74621,f334(x74622,x74623)),f334(x74624,x74623))+~E(f334(f74(x74625,x74626,x74627,x74621),x74622),x74624) % 169.19/169.65 [9617]~P18(x96173,x96174,x96171,x96175,x96176,x96177)+E(f334(f334(x96171,x96172),x96172),x96172) % 169.19/169.65 [9985]~E(f334(f243(f881(x99857),x99851,f198(x99857),x99855),f334(x99854,x99853)),f334(f241(x99857),x99852))+E(f334(f241(x99851),f598(x99852,x99853,x99854,x99855,x99856,x99857,x99851)),f334(x99854,x99853)) % 169.19/169.65 [9986]~E(f334(f243(f881(x99866),x99867,f198(x99866),x99861),f334(x99864,x99863)),f334(f241(x99866),x99862))+E(f334(x99861,f598(x99862,x99863,x99864,x99861,x99865,x99866,x99867)),f334(f241(x99866),x99862)) % 169.19/169.65 [6035]~E(f334(f334(f154(x60351,x60355),x60356),x60352),f334(f334(f154(x60353,x60355),x60357),x60354))+E(f334(f196(f878(x60351)),x60352),f334(f196(f878(x60353)),x60354)) % 169.19/169.65 [7539]E(x75391,x75392)+~E(f334(f334(f334(f73(x75393,f881(x75394)),x75395),x75396),f334(f241(x75394),x75391)),f334(f334(f334(f73(x75393,f881(x75394)),x75397),x75396),f334(f241(x75394),x75392))) % 169.19/169.65 [8486]E(f334(x84861,f334(x84862,x84863)),f334(x84864,x84863))+~E(f334(f74(x84865,x84866,x84867,x84861),x84862),f334(f74(x84866,x84866,x84867,f35(x84866)),x84864)) % 169.19/169.65 [8813]~P36(x88134,x88135,x88131,f334(f334(f151(x88134),x88132),x88136),f334(f334(f151(x88135),x88133),x88137))+P104(f334(f334(x88131,x88132),x88133)) % 169.19/169.65 [9181]P36(x91811,x91812,x91813,x91814,x91815)+~P36(x91811,x91812,x91813,f334(f334(f151(x91811),x91816),x91814),f334(f334(f151(x91812),x91817),x91815)) % 169.19/169.65 [9785]P104(f334(f334(x97851,x97852),f684(x97853,x97852,x97854,x97851)))+~P104(f334(f334(f270(x97855,x97856,x97857,x97851,x97854),x97852),x97853)) % 169.19/169.65 [9807]P104(f334(f334(x98071,f684(x98072,x98073,x98071,x98074)),x98072))+~P104(f334(f334(f270(x98075,x98076,x98077,x98074,x98071),x98073),x98072)) % 169.19/169.65 [6081]E(x60811,x60812)+~E(f334(f334(f334(f93(x60813),x60814),x60815),x60811),f334(f334(f334(f93(x60813),x60816),x60817),x60812)) % 169.19/169.65 [6082]E(x60821,x60822)+~E(f334(f334(f334(f93(x60823),x60824),x60821),x60825),f334(f334(f334(f93(x60823),x60826),x60822),x60827)) % 169.19/169.65 [6083]E(x60831,x60832)+~E(f334(f334(f334(f93(x60833),x60831),x60834),x60835),f334(f334(f334(f93(x60833),x60832),x60836),x60837)) % 169.19/169.65 [8932]~P16(x89326,x89321,x89323,x89327)+E(f334(f74(x89321,x89321,x89322,f334(x89323,x89324)),f334(f74(x89321,x89321,x89322,f334(x89323,x89324)),x89325)),f334(f74(x89321,x89321,x89322,f334(x89323,x89324)),x89325)) % 169.19/169.65 [9279]~P36(x92793,x92792,x92794,f334(f334(f154(x92791,x92793),x92795),x92796),x92797)+P36(x92791,x92792,f334(f334(f10(x92793,f886(x92792,a871),x92791),x92794),x92795),x92796,x92797) % 169.19/169.65 [9300]P36(x93001,x93002,x93003,f334(f334(f154(x93004,x93001),x93005),x93006),x93007)+~P36(x93004,x93002,f334(f334(f10(x93001,f886(x93002,a871),x93004),x93003),x93005),x93006,x93007) % 169.19/169.65 [9704]E(f188(x97041,x97042,f334(f334(f334(f73(x97041,f881(x97042)),x97043),x97044),f334(f241(x97042),x97045)),x97046,x97047),f334(f334(f334(f73(x97041,f881(x97042)),f188(x97041,x97042,x97043,x97046,x97047)),x97044),f334(f241(x97042),x97045)))+P104(f334(f334(f336(x97041),x97044),f334(f173(x97041),x97046))) % 169.19/169.65 [8931]~P104(f334(f334(f336(x89311),x89312),f334(f334(x89315,x89316),x89317)))+P104(f334(f334(f336(x89311),x89312),f334(f334(f273(x89313,x89314,f886(x89311,a871)),x89315),f334(f334(f269(x89313,x89314),x89316),x89317)))) % 169.19/169.65 [9207]P104(f334(f334(f334(x92071,x92072),x92073),x92074))+~P104(f334(f334(f334(f273(x92075,x92076,f886(x92077,a871)),x92071),f334(f334(f269(x92075,x92076),x92072),x92073)),x92074)) % 169.19/169.65 [9339]P104(f334(f334(f336(x93391),f334(f334(x93392,x93393),x93394)),f334(f313(f885(x93395,x93396),x93391,f334(f273(x93395,x93396,x93391),x93392)),x93397)))+~P104(f334(f334(f336(f885(x93395,x93396)),f334(f334(f269(x93395,x93396),x93393),x93394)),x93397)) % 169.19/169.65 [9664]P104(f334(f334(f336(f885(f878(x96641),f878(x96641))),f334(f334(f269(f878(x96641),f878(x96641)),f334(f334(f134(x96641),x96642),f334(f334(f151(x96641),x96643),x96644))),f334(f334(f134(x96641),x96642),f334(f334(f151(x96641),x96645),x96646)))),f147(x96641,x96647)))+~P104(f334(f334(f336(f885(x96641,x96641)),f334(f334(f269(x96641,x96641),x96643),x96645)),x96647)) % 169.19/169.65 [9726]~P36(x97261,x97263,x97264,x97266,f334(f334(f154(x97262,x97263),x97265),x97267))+P36(x97261,x97262,f334(f334(f9(x97261,f886(x97262,x97263),f886(x97262,a871)),f334(f334(f10(f886(x97263,a871),f886(f886(x97262,x97263),f886(x97262,a871)),x97261),f10(x97263,a871,x97262)),x97264)),x97265),x97266,x97267) % 169.19/169.65 [9811]P36(x98111,x98112,x98113,x98114,f334(f334(f154(x98115,x98112),x98116),x98117))+~P36(x98111,x98115,f334(f334(f9(x98111,f886(x98115,x98112),f886(x98115,a871)),f334(f334(f10(f886(x98112,a871),f886(f886(x98115,x98112),f886(x98115,a871)),x98111),f10(x98112,a871,x98115)),x98113)),x98116),x98114,x98117) % 169.19/169.65 [9199]E(x91991,x91992)+E(f334(f334(f334(f73(x91993,x91994),f334(f334(f334(f73(x91993,x91994),x91995),x91991),x91996)),x91992),x91997),f334(f334(f334(f73(x91993,x91994),f334(f334(f334(f73(x91993,x91994),x91995),x91992),x91997)),x91991),x91996)) % 169.19/169.65 [9430]E(f188(x94301,x94302,f334(f334(f334(f73(x94301,f881(x94302)),x94303),x94304),f334(f241(x94302),x94305)),x94306,x94307),f188(x94301,x94302,x94303,x94306,x94307))+~P104(f334(f334(f336(x94301),x94304),f334(f173(x94301),f334(f334(f176(x94301),f334(f196(f878(x94302)),x94307)),x94306)))) % 169.19/169.65 [9737]E(f188(x97371,x97372,f334(f334(f334(f73(x97371,f881(x97372)),x97373),x97374),f334(f241(x97372),x97375)),x97376,x97377),f334(f334(f334(f73(x97371,f881(x97372)),f188(x97371,x97372,x97373,x97376,x97377)),x97374),f334(f241(x97372),x97375)))+P104(f334(f334(f336(x97371),x97374),f334(f173(x97371),f334(f334(f176(x97371),f334(f196(f878(x97372)),x97377)),x97376)))) % 169.19/169.65 [10097]P104(f334(f334(f336(x100971),f522(x100972,x100973,x100974,x100975,x100976,x100977,x100971)),x100975))+P104(f334(f334(f334(f334(f43(x100971,f886(x100977,f886(x100976,a871))),x100975),x100974),x100973),x100972)) % 169.19/169.65 [10098]P104(f334(f334(f336(x100981),f534(x100982,x100983,x100984,x100985,x100986,x100987,x100981)),x100985))+~P104(f334(f334(f334(f334(f44(x100981,f886(x100987,f886(x100986,a871))),x100985),x100984),x100983),x100982)) % 169.19/169.65 [10125]P104(f334(f334(f334(x101251,f534(x101252,x101253,x101251,x101254,x101255,x101256,x101257)),x101253),x101252))+~P104(f334(f334(f334(f334(f44(x101257,f886(x101256,f886(x101255,a871))),x101254),x101251),x101253),x101252)) % 169.19/169.65 [10143]~P104(f334(f334(f334(x101435,f522(x101437,x101436,x101435,x101434,x101433,x101432,x101431)),x101436),x101437))+P104(f334(f334(f334(f334(f43(x101431,f886(x101432,f886(x101433,a871))),x101434),x101435),x101436),x101437)) % 169.19/169.65 [10160]~P104(f334(f334(f336(f885(x101601,x101603)),f334(f334(f269(x101601,x101603),x101606),x101607)),f334(f334(f291(x101601,x101602,x101603),x101604),x101605)))+P104(f334(f334(f270(x101601,x101602,x101603,f334(f334(f9(x101601,f886(f885(x101601,x101602),a871),f886(x101602,a871)),f334(f334(f10(f886(x101602,f886(f886(f885(x101601,x101602),a871),a871)),f886(f886(f885(x101601,x101602),a871),f886(x101602,a871)),x101601),f9(x101602,f886(f885(x101601,x101602),a871),a871)),f334(f334(f10(f886(x101602,f885(x101601,x101602)),f886(x101602,f886(f886(f885(x101601,x101602),a871),a871)),x101601),f334(f10(f885(x101601,x101602),f886(f886(f885(x101601,x101602),a871),a871),x101602),f336(f885(x101601,x101602)))),f269(x101601,x101602)))),x101604),f334(f334(f9(x101602,f886(f885(x101602,x101603),a871),f886(x101603,a871)),f334(f334(f10(f886(x101603,f886(f886(f885(x101602,x101603),a871),a871)),f886(f886(f885(x101602,x101603),a871),f886(x101603,a871)),x101602),f9(x101603,f886(f885(x101602,x101603),a871),a871)),f334(f334(f10(f886(x101603,f885(x101602,x101603)),f886(x101603,f886(f886(f885(x101602,x101603),a871),a871)),x101602),f334(f10(f885(x101602,x101603),f886(f886(f885(x101602,x101603),a871),a871),x101603),f336(f885(x101602,x101603)))),f269(x101602,x101603)))),x101605)),x101606),x101607)) % 169.19/169.65 [10170]P104(f334(f334(f336(f885(x101701,x101702)),f334(f334(f269(x101701,x101702),x101703),x101704)),f334(f334(f291(x101701,x101705,x101702),x101706),x101707)))+~P104(f334(f334(f270(x101701,x101705,x101702,f334(f334(f9(x101701,f886(f885(x101701,x101705),a871),f886(x101705,a871)),f334(f334(f10(f886(x101705,f886(f886(f885(x101701,x101705),a871),a871)),f886(f886(f885(x101701,x101705),a871),f886(x101705,a871)),x101701),f9(x101705,f886(f885(x101701,x101705),a871),a871)),f334(f334(f10(f886(x101705,f885(x101701,x101705)),f886(x101705,f886(f886(f885(x101701,x101705),a871),a871)),x101701),f334(f10(f885(x101701,x101705),f886(f886(f885(x101701,x101705),a871),a871),x101705),f336(f885(x101701,x101705)))),f269(x101701,x101705)))),x101706),f334(f334(f9(x101705,f886(f885(x101705,x101702),a871),f886(x101702,a871)),f334(f334(f10(f886(x101702,f886(f886(f885(x101705,x101702),a871),a871)),f886(f886(f885(x101705,x101702),a871),f886(x101702,a871)),x101705),f9(x101702,f886(f885(x101705,x101702),a871),a871)),f334(f334(f10(f886(x101702,f885(x101705,x101702)),f886(x101702,f886(f886(f885(x101705,x101702),a871),a871)),x101705),f334(f10(f885(x101705,x101702),f886(f886(f885(x101705,x101702),a871),a871),x101702),f336(f885(x101705,x101702)))),f269(x101705,x101702)))),x101707)),x101703),x101704)) % 169.19/169.65 [10107]~P143(x101072)+E(f334(f334(f8(x101071,x101072),f334(f334(f9(x101071,f886(x101073,a871),x101072),f334(f334(f10(f886(x101073,x101072),f886(f886(x101073,a871),x101072),x101071),f8(x101073,x101072)),f334(f334(f9(x101071,f886(x101073,x101072),f886(x101073,x101072)),f334(f334(f10(f886(x101072,x101072),f886(f886(x101073,x101072),f886(x101073,x101072)),x101071),f10(x101072,x101072,x101073)),f334(f334(f10(x101072,f886(x101072,x101072),x101071),f82(x101072)),x101074))),x101075))),x101076)),x101077),f334(f334(f82(x101072),f334(f334(f8(x101071,x101072),x101074),x101077)),f334(f334(f8(x101073,x101072),x101075),x101076))) % 169.19/169.65 [9235]~P15(x92357,x92351,x92353,x92358)+E(f334(f74(x92351,x92351,x92352,f334(x92353,x92354)),f334(f74(x92351,x92351,x92352,f334(x92353,x92355)),x92356)),f334(f74(x92351,x92351,x92352,f334(x92353,x92355)),f334(f74(x92351,x92351,x92352,f334(x92353,x92354)),x92356))) % 169.19/169.65 [10165]E(f334(f334(f269(x101651,x101652),f334(x101653,f618(x101654,x101655,x101653,x101656,x101657,x101658,x101652,x101651))),f334(x101655,f619(x101654,x101655,x101653,x101656,x101657,x101658,x101652,x101651))),x101658)+~P104(f334(f334(f336(f885(x101651,x101652)),x101658),f334(f313(f885(x101657,x101656),f885(x101651,x101652),f274(x101657,x101651,x101656,x101652,x101653,x101655)),x101654))) % 169.19/169.65 [10179]~P104(f334(f334(f336(f885(x101798,x101797)),x101796),f334(f313(f885(x101791,x101792),f885(x101798,x101797),f274(x101791,x101798,x101792,x101797,x101795,x101794)),x101793)))+P104(f334(f334(f336(f885(x101791,x101792)),f334(f334(f269(x101791,x101792),f618(x101793,x101794,x101795,x101792,x101791,x101796,x101797,x101798)),f619(x101793,x101794,x101795,x101792,x101791,x101796,x101797,x101798))),x101793)) % 169.19/169.65 [9654]P104(f334(f334(f336(f885(f885(x96541,x96542),f885(x96541,x96542))),f334(f334(f269(f885(x96541,x96542),f885(x96541,x96542)),f334(f334(f269(x96541,x96542),x96543),x96544)),f334(f334(f269(x96541,x96542),x96545),x96546))),f327(x96541,x96542,x96547,x96548)))+~P104(f334(f334(f336(f885(x96541,x96541)),f334(f334(f269(x96541,x96541),x96543),x96545)),x96547)) % 169.19/169.65 [10153]E(f334(f142(x101531,x101532,f334(f9(x101532,x101531,x101531),x101533),f334(x101534,x101535)),x101536),f334(x101534,f334(f142(x101537,x101532,f334(f9(x101532,x101537,x101537),x101538),x101535),x101536)))+P104(f334(f334(f336(x101532),f707(x101535,x101538,x101534,x101533,x101537,x101531,x101536,x101532)),f334(f173(x101532),x101536))) % 169.19/169.65 [10173]~E(f334(f74(x101731,x101731,x101737,f334(x101733,f707(x101735,x101738,x101734,x101733,x101737,x101731,x101736,x101732))),x101734),f334(f74(x101737,x101731,x101737,x101734),f334(x101738,f707(x101735,x101738,x101734,x101733,x101737,x101731,x101736,x101732))))+E(f334(f142(x101731,x101732,f334(f9(x101732,x101731,x101731),x101733),f334(x101734,x101735)),x101736),f334(x101734,f334(f142(x101737,x101732,f334(f9(x101732,x101737,x101737),x101738),x101735),x101736))) % 169.19/169.65 [8492]E(f334(x84921,f334(x84922,x84923)),f334(x84924,f334(x84925,x84923)))+~E(f334(f74(x84926,x84927,x84928,x84921),x84922),f334(f74(x84929,x84927,x84928,x84924),x84925)) % 169.19/169.65 [10037]P104(f334(f334(f336(f885(x100371,x100372)),f334(f334(f269(x100371,x100372),f334(x100373,x100374)),f334(x100375,x100376))),f334(f313(f885(x100377,x100378),f885(x100371,x100372),f274(x100377,x100371,x100378,x100372,x100373,x100375)),x100379)))+~P104(f334(f334(f336(f885(x100377,x100378)),f334(f334(f269(x100377,x100378),x100374),x100376)),x100379)) % 169.19/169.65 [8761]~E(f334(x87614,f334(x87615,x87616)),f334(x87619,f334(x876110,x876111)))+E(f334(f334(f74(x87611,x87612,x87613,x87614),x87615),x87616),f334(f334(f74(x87617,x87612,x87618,x87619),x876110),x876111)) % 169.19/169.65 [4623]~P107(x46231)+~P101(x46231)+E(f104(x46231),f247(x46231)) % 169.19/169.65 [4624]~P107(x46241)+~P100(x46241)+E(f113(x46241),f248(x46241)) % 169.19/169.65 [4870]~P120(x48701)+~P92(x48701)+E(f334(f76(x48701),f334(f106(x48701),a100)),f79(x48701)) % 169.19/169.65 [5150]E(x51501,f2(a1))+E(f83(a1,x51501),f334(f80(a1),f79(a1)))+P104(f334(f334(f250(a1),f2(a1)),x51501)) % 169.19/169.65 [5369]E(x53691,f2(a1))+E(f83(a1,x53691),f79(a1))+~P104(f334(f334(f250(a1),f2(a1)),x53691)) % 169.19/169.65 [7355]~P41(x73551)+P104(f334(f63(a1),x73551))+~P104(f334(f63(a877),f334(f313(a1,a877,a107),x73551))) % 169.19/169.65 [8591]~P2(a5000)+~P104(f334(f334(f336(f885(a874,a873)),x85911),f334(f173(f885(a874,a873)),a27)))+P104(f334(f334(f273(a874,a873,a871),f334(f18(f886(a873,a871),a874),a25)),x85911)) % 169.19/169.65 [9616]E(x96161,f195(f886(f885(a877,a877),a871)))+~P104(f334(f63(f885(a877,a877)),x96161))+P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),f195(f886(f885(a877,a877),a871))),x96161)),a38)) % 169.19/169.65 [9786]E(x97861,f2(a877))+E(x97861,f334(a115,f2(a877)))+~P104(f334(f334(f250(a877),x97861),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [10065]E(x100651,f2(a102))+E(f334(f334(f81(a1),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(a22,f334(f334(f40(a102),x100651),f334(f106(a102),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))))),f79(a1)),f334(a22,x100651))+E(f46(a102,x100651,f334(f106(a102),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f2(a102)) % 169.19/169.65 [9916]E(x99161,f2(a102))+~E(f46(a102,x99161,f334(f106(a102),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f2(a102))+E(f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(a22,f334(f334(f40(a102),x99161),f334(f106(a102),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f334(a22,x99161)) % 169.19/169.65 [4698]~P55(x46981,x46982)+P44(x46981,x46982)+~P45(a871) % 169.19/169.65 [4635]~P142(x46351)+P32(x46351,x46352)+~E(x46352,f2(x46351)) % 169.19/169.65 [4636]~P107(x46361)+P30(x46361,x46362)+~E(x46362,f116(x46361)) % 169.19/169.65 [4645]~P120(x46451)+~E(x46452,f2(x46451))+E(f83(x46451,x46452),f2(x46451)) % 169.19/169.65 [4646]~P86(x46461)+~E(x46462,f2(x46461))+E(f83(x46461,x46462),f2(x46461)) % 169.19/169.65 [4654]~P142(x46542)+~P32(x46542,x46541)+E(x46541,f2(x46542)) % 169.19/169.65 [4688]~P120(x46882)+~E(f83(x46882,x46881),f2(x46882))+E(x46881,f2(x46882)) % 169.19/169.65 [4705]~P25(x47052)+~P25(x47051)+P25(f886(x47051,x47052)) % 169.19/169.65 [4706]~P25(x47062)+~P25(x47061)+P25(f884(x47061,x47062)) % 169.19/169.65 [4707]~P25(x47072)+~P25(x47071)+P25(f885(x47071,x47072)) % 169.19/169.65 [4708]~P29(x47082)+~P29(x47081)+P29(f202(x47081,x47082)) % 169.19/169.65 [4709]~P144(x47092)+~P144(x47091)+P144(f885(x47091,x47092)) % 169.19/169.65 [4710]~P58(x47102)+~P58(x47101)+P58(f886(x47101,x47102)) % 169.19/169.65 [4711]~P58(x47112)+~P58(x47111)+P58(f884(x47111,x47112)) % 169.19/169.65 [4712]~P58(x47122)+~P58(x47121)+P58(f885(x47121,x47122)) % 169.19/169.65 [4713]~P58(x47131)+~P91(x47132)+P91(f886(x47131,x47132)) % 169.19/169.65 [4714]~P102(x47142)+~P102(x47141)+P102(f885(x47141,x47142)) % 169.19/169.65 [4842]~P107(x48421)+~P30(x48421,x48422)+P30(x48421,f152(x48421,x48422)) % 169.19/169.65 [5081]~P29(x50812)+~P29(x50811)+P29(f46(a1,x50811,x50812)) % 169.19/169.65 [4656]~P73(x46561)+~E(x46562,f2(x46561))+E(f334(f80(x46561),x46562),x46562) % 169.19/169.65 [4660]~P137(x46601)+~E(x46602,f2(a1))+E(f334(f105(x46601),x46602),f2(x46601)) % 169.19/169.65 [4661]~P89(x46611)+~E(x46612,f2(a1))+E(f334(f105(x46611),x46612),f2(x46611)) % 169.19/169.65 [4685]~P67(x46851)+~E(f2(x46851),x46852)+E(f334(f80(x46851),x46852),f2(x46851)) % 169.19/169.65 [4686]~P67(x46861)+~E(x46862,f2(x46861))+E(f334(f80(x46861),x46862),f2(x46861)) % 169.19/169.65 [4687]~P83(x46871)+~E(x46872,f2(x46871))+E(f334(f76(x46871),x46872),f2(x46871)) % 169.19/169.65 [4716]~P73(x47162)+E(x47161,f2(x47162))+~E(f334(f80(x47162),x47161),x47161) % 169.19/169.65 [4722]E(x47221,f334(a107,x47222))+~E(x47221,f2(a877))+~E(x47222,f334(f103(a1),x47221)) % 169.19/169.65 [4723]E(f334(a107,x47231),x47232)+~E(x47232,f2(a877))+~E(x47231,f334(f103(a1),x47232)) % 169.19/169.65 [4727]~P89(x47272)+E(x47271,f2(a1))+~E(f334(f105(x47272),x47271),f2(x47272)) % 169.19/169.65 [4732]~P67(x47322)+E(x47321,f2(x47322))+~E(f334(f80(x47322),x47321),f2(x47322)) % 169.19/169.65 [4733]~P83(x47332)+E(x47331,f2(x47332))+~E(f334(f76(x47332),x47331),f2(x47332)) % 169.19/169.65 [4734]~P67(x47341)+E(f2(x47341),x47342)+~E(f334(f80(x47341),x47342),f2(x47341)) % 169.19/169.65 [4875]~P2(a5000)+~E(f334(a28,x48752),f334(f241(a873),x48751))+P104(f334(a25,x48751)) % 169.19/169.65 [4917]~P107(x49171)+~P30(x49171,x49172)+P30(x49171,f334(f172(x49171),x49172)) % 169.19/169.65 [4943]~P104(x49432)+~P104(x49431)+P104(f334(f334(a332,x49431),x49432)) % 169.19/169.65 [4977]~E(f79(a877),f2(a877))+E(f334(f39(x49771),x49772),f2(a877))+~P104(f334(f63(x49771),x49772)) % 169.19/169.65 [5010]~P112(x50101)+~P143(x50101)+E(f334(f334(f259(x50101),f2(x50101)),f334(a115,x50102)),f2(x50101)) % 169.19/169.65 [5048]~P107(x50481)+P30(x50481,f139(x50481,x50482))+~P104(f334(f63(x50481),x50482)) % 169.19/169.65 [5049]~P107(x50491)+P30(x50491,f714(x50492,x50491))+~P104(f334(f63(x50491),x50492)) % 169.19/169.65 [5071]~P107(x50711)+E(f334(f173(x50711),f139(x50711,x50712)),x50712)+~P104(f334(f63(x50711),x50712)) % 169.19/169.65 [5072]~P107(x50721)+E(f334(f173(x50721),f714(x50722,x50721)),x50722)+~P104(f334(f63(x50721),x50722)) % 169.19/169.65 [5102]P104(x51021)+P104(x51022)+~P104(f334(f334(a333,x51022),x51021)) % 169.19/169.65 [5114]E(x51141,f195(f886(x51142,a871)))+~E(f334(f39(x51142),x51141),f2(a877))+~P104(f334(f63(x51142),x51141)) % 169.19/169.65 [5119]P104(x51191)+~P104(x51192)+~P104(f334(f334(a337,x51192),x51191)) % 169.19/169.65 [5168]~P71(x51681)+E(f334(f76(x51681),x51682),x51682)+P104(f334(f334(f250(x51681),x51682),f2(x51681))) % 169.19/169.65 [5238]~P58(x52382)+~P104(f334(f59(x52382),x52381))+P104(f334(x52381,f634(x52381,x52382))) % 169.19/169.65 [5239]~P58(x52392)+~P104(f334(f59(x52392),x52391))+P104(f334(x52391,f656(x52391,x52392))) % 169.19/169.65 [5267]~P104(f334(a25,x52672))+~P104(f334(a25,x52671))+P104(f334(a25,f34(x52671,x52672))) % 169.19/169.65 [5276]E(x52761,f116(x52762))+P104(f334(f137(x52762),f117(x52762,x52761)))+~P104(f334(f137(x52762),x52761)) % 169.19/169.65 [5281]~P107(x52811)+~P104(f334(f63(x52811),x52812))+P104(f334(f137(x52811),f139(x52811,x52812))) % 169.19/169.65 [5282]~P107(x52821)+~P104(f334(f63(x52821),x52822))+P104(f334(f137(x52821),f714(x52822,x52821))) % 169.19/169.65 [5288]~P137(x52881)+E(f334(f103(x52881),f334(a107,x52882)),f334(f105(x52881),x52882))+P104(f334(f334(f250(a1),x52882),f2(a1))) % 169.19/169.65 [5319]P5(x53192,x53191)+E(f334(x53191,f544(x53191)),f334(x53191,f547(x53191)))+P104(f334(f334(x53191,f544(x53191)),f547(x53191))) % 169.19/169.65 [5334]E(f334(f103(a1),f345(x53341,x53342)),x53341)+P104(f334(x53342,f334(a107,x53341)))+~P104(f334(x53342,f2(a877))) % 169.19/169.65 [5346]~P58(x53461)+~P104(f334(x53462,f635(x53462,x53461)))+P104(f334(f60(x53461),x53462)) % 169.19/169.65 [5347]~P58(x53471)+~P104(f334(x53472,f657(x53472,x53471)))+P104(f334(f60(x53471),x53472)) % 169.19/169.65 [5362]~P58(x53622)+~P37(x53622,x53621,f57(x53622))+P104(f334(x53621,f731(x53621,x53622))) % 169.19/169.65 [5378]~P120(x53781)+~E(f83(x53781,x53782),f334(f80(x53781),f79(x53781)))+P104(f334(f334(f250(x53781),x53782),f2(x53781))) % 169.19/169.65 [5454]~E(x54542,f2(a1))+E(f224(x54541,x54542),f334(f334(f269(a1,a1),f2(a1)),f79(a1)))+P104(f334(f334(f250(a1),x54542),f2(a1))) % 169.19/169.65 [5455]~E(x54551,f2(a1))+E(f224(x54551,x54552),f334(f334(f269(a1,a1),f2(a1)),f79(a1)))+P104(f334(f334(f250(a1),x54552),f2(a1))) % 169.19/169.65 [5507]E(f334(f103(a1),f345(x55071,x55072)),x55071)+P104(f334(x55072,f334(a107,x55071)))+P104(f334(f334(f250(a1),x55071),f2(a1))) % 169.19/169.65 [5570]~P120(x55701)+E(f83(x55701,x55702),f334(f80(x55701),f79(x55701)))+~P104(f334(f334(f250(x55701),x55702),f2(x55701))) % 169.19/169.65 [5571]~P83(x55711)+E(f334(f76(x55711),x55712),f334(f80(x55711),x55712))+~P104(f334(f334(f249(x55711),x55712),f2(x55711))) % 169.19/169.65 [5572]~P83(x55721)+E(f334(f76(x55721),x55722),f334(f80(x55721),x55722))+~P104(f334(f334(f250(x55721),x55722),f2(x55721))) % 169.19/169.65 [5573]~P71(x55731)+E(f334(f76(x55731),x55732),f334(f80(x55731),x55732))+~P104(f334(f334(f250(x55731),x55732),f2(x55731))) % 169.19/169.65 [5670]~P104(f334(x56701,f345(x56702,x56701)))+P104(f334(x56701,f334(a107,x56702)))+~P104(f334(x56701,f2(a877))) % 169.19/169.65 [5677]E(x56771,f2(a877))+E(f334(a115,f802(x56772,x56771)),x56771)+~P104(f334(f334(f250(a877),x56771),f334(a115,x56772))) % 169.19/169.65 [5681]P5(x56811,x56812)+~E(f334(x56812,f544(x56812)),f334(x56812,f547(x56812)))+~P104(f334(f334(x56812,f544(x56812)),f547(x56812))) % 169.19/169.65 [5701]~P107(x57011)+P30(x57011,x57012)+P104(f334(f334(f249(a877),f636(x57012,x57011)),f637(x57012,x57011))) % 169.19/169.65 [5702]~P107(x57021)+P30(x57021,x57022)+P104(f334(f334(f249(a877),f643(x57022,x57021)),f652(x57022,x57021))) % 169.19/169.65 [5790]~P83(x57901)+~E(x57902,f2(x57901))+P104(f334(f334(f249(x57901),f334(f76(x57901),x57902)),f2(x57901))) % 169.19/169.65 [5869]~P58(x58692)+~P58(x58691)+E(f61(x58691,x58692,f57(x58691),f57(x58692)),f57(f885(x58691,x58692))) % 169.19/169.65 [5873]~P104(f334(x58731,f345(x58732,x58731)))+P104(f334(x58731,f334(a107,x58732)))+P104(f334(f334(f250(a1),x58732),f2(a1))) % 169.19/169.65 [5896]~P104(f334(x58961,f334(a107,x58962)))+P104(f334(x58961,f2(a877)))+~P104(f334(f334(f250(a1),x58962),f2(a1))) % 169.19/169.65 [6237]~P120(x62371)+~P104(f334(f334(f250(x62371),x62372),f2(x62371)))+P104(f334(f334(f250(x62371),f83(x62371,x62372)),f2(x62371))) % 169.19/169.65 [6350]~P120(x63501)+P104(f334(f334(f249(x63501),f334(f105(x63501),x63502)),f2(x63501)))+~P104(f334(f334(f249(a1),x63502),f2(a1))) % 169.19/169.65 [6351]~P120(x63511)+P104(f334(f334(f250(x63511),f334(f105(x63511),x63512)),f2(x63511)))+~P104(f334(f334(f250(a1),x63512),f2(a1))) % 169.19/169.65 [6358]~P83(x63582)+E(x63581,f2(x63582))+~P104(f334(f334(f249(x63582),f334(f76(x63582),x63581)),f2(x63582))) % 169.19/169.65 [6436]~P137(x64361)+~P104(f334(f334(f336(x64361),x64362),f112(x64361)))+P104(f334(f334(f336(x64361),f334(f80(x64361),x64362)),f112(x64361))) % 169.19/169.65 [6468]~P120(x64681)+~P104(f334(f334(f250(x64681),f83(x64681,x64682)),f2(x64681)))+P104(f334(f334(f250(x64681),x64682),f2(x64681))) % 169.19/169.65 [6637]~P120(x66372)+~P104(f334(f334(f249(x66372),f334(f105(x66372),x66371)),f2(x66372)))+P104(f334(f334(f249(a1),x66371),f2(a1))) % 169.19/169.65 [6638]~P120(x66382)+~P104(f334(f334(f250(x66382),f334(f105(x66382),x66381)),f2(x66382)))+P104(f334(f334(f250(a1),x66381),f2(a1))) % 169.19/169.65 [7139]~P73(x71391)+~P104(f334(f334(f249(x71391),x71392),f2(x71391)))+P104(f334(f334(f249(x71391),f334(f334(f81(x71391),x71392),x71392)),f2(x71391))) % 169.19/169.65 [7140]~P120(x71401)+~P104(f334(f334(f250(x71401),x71402),f2(x71401)))+P104(f334(f334(f250(x71401),f334(f334(f81(x71401),x71402),x71402)),f2(x71401))) % 169.19/169.65 [7141]~P73(x71411)+~P104(f334(f334(f250(x71411),x71412),f2(x71411)))+P104(f334(f334(f250(x71411),f334(f334(f81(x71411),x71412),x71412)),f2(x71411))) % 169.19/169.65 [7710]~P73(x77101)+~P104(f334(f334(f249(x77101),f334(f334(f81(x77101),x77102),x77102)),f2(x77101)))+P104(f334(f334(f249(x77101),x77102),f2(x77101))) % 169.19/169.65 [7711]~P120(x77111)+~P104(f334(f334(f250(x77111),f334(f334(f81(x77111),x77112),x77112)),f2(x77111)))+P104(f334(f334(f250(x77111),x77112),f2(x77111))) % 169.19/169.65 [7712]~P73(x77121)+~P104(f334(f334(f250(x77121),f334(f334(f81(x77121),x77122),x77122)),f2(x77121)))+P104(f334(f334(f250(x77121),x77122),f2(x77121))) % 169.19/169.65 [4772]~E(x47722,f79(a877))+~E(x47721,f79(a877))+E(f334(f334(f82(a877),x47721),x47722),f79(a877)) % 169.19/169.65 [4773]~E(x47732,f79(a1))+~E(x47731,f79(a1))+E(f334(f334(f82(a1),x47731),x47732),f79(a1)) % 169.19/169.65 [4774]~E(x47742,f2(a877))+~E(x47741,f2(a877))+E(f334(f334(f81(a877),x47741),x47742),f2(a877)) % 169.19/169.65 [4828]~P117(x48282)+E(x48281,f2(x48282))+E(f334(f334(f292(x48282),x48281),x48281),f79(x48282)) % 169.19/169.65 [4829]~P26(x48292)+E(x48291,f2(x48292))+E(f334(f334(f40(x48292),x48291),x48291),f79(x48292)) % 169.19/169.65 [4830]~P118(x48302)+E(x48301,f2(x48302))+E(f334(f334(f292(x48302),x48301),x48301),f79(x48302)) % 169.19/169.65 [4848]~P136(x48481)+~E(x48482,f79(x48481))+E(f334(f334(f82(x48481),x48482),x48482),f79(x48481)) % 169.19/169.65 [4849]~P73(x48491)+~E(x48492,f2(x48491))+E(f334(f334(f81(x48491),x48492),x48492),f2(x48491)) % 169.19/169.65 [4850]~P118(x48501)+~E(x48502,f2(x48501))+E(f334(f334(f292(x48501),x48502),x48502),f2(x48501)) % 169.19/169.65 [4896]~E(x48962,f2(a877))+~E(x48961,f2(a877))+E(f334(f80(a1),f334(f103(a1),x48961)),f334(f103(a1),x48962)) % 169.19/169.65 [4914]E(x49141,f79(a877))+E(x49142,f2(a877))+~E(f334(f334(f82(a877),x49142),x49141),x49142) % 169.19/169.65 [4924]E(x49241,f2(a877))+E(x49242,f2(a877))+~E(f334(f334(f82(a877),x49242),x49241),f2(a877)) % 169.19/169.65 [4952]~E(x49522,f2(a877))+~E(x49521,f334(a115,f2(a877)))+E(f334(f334(f81(a877),x49521),x49522),f334(a115,f2(a877))) % 169.19/169.65 [4953]~E(x49531,f2(a877))+~E(x49532,f334(a115,f2(a877)))+E(f334(f334(f81(a877),x49531),x49532),f334(a115,f2(a877))) % 169.19/169.65 [4960]E(x49601,f79(a1))+E(x49602,f334(f106(a1),a100))+~E(f334(f334(f82(a1),x49601),x49602),f79(a1)) % 169.19/169.65 [4961]E(x49611,f79(a1))+E(x49612,f334(f106(a1),a100))+~E(f334(f334(f82(a1),x49612),x49611),f79(a1)) % 169.19/169.65 [4962]E(x49621,f79(a1))+E(x49621,f334(f106(a1),a100))+~E(f334(f334(f82(a1),x49622),x49621),f79(a1)) % 169.19/169.65 [4964]E(x49641,f79(a1))+E(x49641,f334(f106(a1),a100))+~E(f334(f334(f82(a1),x49641),x49642),f79(a1)) % 169.19/169.65 [4981]~P73(x49812)+E(x49811,f2(x49812))+~E(f334(f334(f81(x49812),x49811),x49811),f2(x49812)) % 169.19/169.65 [4987]~E(x49871,f334(f106(a1),a100))+~E(x49872,f334(f106(a1),a100))+E(f334(f334(f82(a1),x49871),x49872),f79(a1)) % 169.19/169.65 [4999]E(x49991,f2(a877))+E(x49992,f2(a877))+~E(f334(f334(f81(a877),x49992),x49991),f334(a115,f2(a877))) % 169.19/169.65 [5009]~P92(x50091)+~P59(x50091)+E(f334(f334(f292(x50091),x50092),f334(f106(x50091),a84)),f2(x50091)) % 169.19/169.65 [5015]~P136(x50151)+~E(x50152,f334(f80(x50151),f79(x50151)))+E(f334(f334(f82(x50151),x50152),x50152),f79(x50151)) % 169.19/169.65 [5020]~P29(x50202)+~P29(x50201)+P29(f334(f334(f82(a1),x50201),x50202)) % 169.19/169.65 [5021]~P29(x50212)+~P29(x50211)+P29(f334(f334(f81(a1),x50211),x50212)) % 169.19/169.65 [5022]~P29(x50222)+~P29(x50221)+P29(f334(f334(f40(a1),x50221),x50222)) % 169.19/169.65 [5024]~E(x50242,f2(a1))+E(x50241,f2(a1))+E(f47(x50241,x50242),f334(f334(f269(a1,a1),f2(a1)),x50241)) % 169.19/169.65 [5046]~E(x50462,f334(a115,f2(a877)))+~E(x50461,f334(a115,f2(a877)))+E(f334(f334(f82(a877),x50461),x50462),f334(a115,f2(a877))) % 169.19/169.65 [5061]E(x50611,f2(a877))+E(x50612,f334(a115,f2(a877)))+~E(f334(f334(f259(a877),x50612),x50611),f334(a115,f2(a877))) % 169.19/169.65 [5062]E(x50621,f2(a877))+E(x50621,f334(a115,f2(a877)))+~E(f334(f334(f81(a877),x50622),x50621),f334(a115,f2(a877))) % 169.19/169.65 [5063]E(x50631,f2(a877))+E(x50631,f334(a115,f2(a877)))+~E(f334(f334(f81(a877),x50631),x50632),f334(a115,f2(a877))) % 169.19/169.65 [5073]~P92(x50731)+~P59(x50731)+E(f334(f334(f292(x50731),x50732),f334(f106(x50731),a100)),f334(f80(x50731),x50732)) % 169.19/169.65 [5094]E(x50941,f334(a107,x50942))+~E(x50941,f2(a877))+P104(f334(f334(f249(a1),f2(a1)),x50942)) % 169.19/169.65 [5095]E(f334(a107,x50951),x50952)+~E(x50952,f2(a877))+P104(f334(f334(f249(a1),f2(a1)),x50951)) % 169.19/169.65 [5110]E(x51101,f334(a115,f2(a877)))+E(x51102,f334(a115,f2(a877)))+~E(f334(f334(f81(a877),x51101),x51102),f334(a115,f2(a877))) % 169.19/169.65 [5121]~E(x51211,f334(a107,x51212))+E(x51211,f2(a877))+P104(f334(f334(f249(a1),f2(a1)),x51212)) % 169.19/169.65 [5122]~E(f334(a107,x51222),x51221)+E(x51221,f2(a877))+P104(f334(f334(f249(a1),f2(a1)),x51222)) % 169.19/169.65 [5144]~P95(x51441)+E(f334(f65(x51441,f113(x51441)),x51442),f12(x51441,x51442))+~P104(f334(f63(x51441),x51442)) % 169.19/169.65 [5145]~P95(x51451)+E(f334(f65(x51451,f104(x51451)),x51452),f13(x51451,x51452))+~P104(f334(f63(x51451),x51452)) % 169.19/169.65 [5146]~P107(x51461)+E(f334(f65(x51461,f247(x51461)),x51462),f16(x51461,x51462))+~P104(f334(f63(x51461),x51462)) % 169.19/169.65 [5147]~P107(x51471)+E(f334(f65(x51471,f248(x51471)),x51472),f17(x51471,x51472))+~P104(f334(f63(x51471),x51472)) % 169.19/169.65 [5149]~P58(x51491)+~P104(f334(x51492,f198(x51491)))+P104(f334(f59(f881(x51491)),x51492)) % 169.19/169.65 [5231]~P58(x52312)+P104(f334(x52311,f198(x52312)))+~P104(f334(f60(f881(x52312)),x52311)) % 169.19/169.65 [5232]E(x52321,x52322)+~E(f334(f334(f3(a877),x52322),x52321),f2(a877))+~E(f334(f334(f3(a877),x52321),x52322),f2(a877)) % 169.19/169.65 [5246]P29(x52461)+~P41(x52462)+~P104(f334(f334(f336(a1),x52461),x52462)) % 169.19/169.65 [5277]~P120(x52771)+~E(f83(x52771,x52772),f79(x52771))+P104(f334(f334(f250(x52771),f2(x52771)),x52772)) % 169.19/169.65 [5289]~P92(x52891)+E(f334(f103(x52891),f334(f106(a877),x52892)),f334(f106(x52891),x52892))+P104(f334(a201,f334(f106(a1),x52892))) % 169.19/169.65 [5295]~P44(x52951,x52952)+P45(a871)+P104(f334(f63(f885(x52951,x52951)),x52952)) % 169.19/169.65 [5371]~P107(x53711)+E(f334(f65(x53711,f247(x53711)),x53712),f14(x53711,f247(x53711),x53712))+~P104(f334(f63(x53711),x53712)) % 169.19/169.65 [5372]~P107(x53721)+E(f334(f65(x53721,f248(x53721)),x53722),f15(x53721,f248(x53721),x53722))+~P104(f334(f63(x53721),x53722)) % 169.19/169.65 [5385]E(x53851,x53852)+P104(f334(f334(f250(a877),x53852),x53851))+P104(f334(f334(f250(a877),x53851),x53852)) % 169.19/169.65 [5386]E(x53861,x53862)+P104(f334(f334(f250(a1),x53862),x53861))+P104(f334(f334(f250(a1),x53861),x53862)) % 169.19/169.65 [5441]~P92(x54411)+E(f334(f103(x54411),f334(f106(a877),x54412)),f2(x54411))+~P104(f334(a201,f334(f106(a1),x54412))) % 169.19/169.65 [5444]~E(x54442,f334(a107,x54441))+E(x54441,f334(f103(a1),x54442))+~P104(f334(f334(f249(a1),f2(a1)),x54441)) % 169.19/169.65 [5445]~E(f334(a107,x54451),x54452)+E(x54451,f334(f103(a1),x54452))+~P104(f334(f334(f249(a1),f2(a1)),x54451)) % 169.19/169.65 [5446]~E(x54461,f334(a107,x54462))+E(f334(f103(a1),x54461),x54462)+~P104(f334(f334(f249(a1),f2(a1)),x54462)) % 169.19/169.65 [5456]E(x54561,f334(a107,x54562))+~E(x54562,f334(f103(a1),x54561))+~P104(f334(f334(f249(a1),f2(a1)),x54562)) % 169.19/169.65 [5457]E(f334(a107,x54571),x54572)+~E(x54571,f334(f103(a1),x54572))+~P104(f334(f334(f249(a1),f2(a1)),x54571)) % 169.19/169.65 [5496]~P83(x54962)+E(x54961,f2(x54962))+P104(f334(f334(f250(x54962),f2(x54962)),f334(f76(x54962),x54961))) % 169.19/169.65 [5563]~P120(x55631)+E(f83(x55631,x55632),f79(x55631))+~P104(f334(f334(f250(x55631),f2(x55631)),x55632)) % 169.19/169.65 [5567]~P92(x55671)+E(f334(f103(x55671),f334(f106(a877),x55672)),f2(x55671))+P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x55672))) % 169.19/169.65 [5574]~P83(x55741)+E(f334(f76(x55741),x55742),x55742)+~P104(f334(f334(f249(x55741),f2(x55741)),x55742)) % 169.19/169.65 [5575]~P83(x55751)+E(f334(f76(x55751),x55752),x55752)+~P104(f334(f334(f250(x55751),f2(x55751)),x55752)) % 169.19/169.65 [5584]E(x55841,f2(a877))+~E(f139(a877,f334(f304(a877,x55842),x55841)),f116(a877))+P104(f334(f334(f249(a877),x55841),x55842)) % 169.19/169.65 [5594]~P72(x55941)+E(f334(f334(f8(x55941,x55941),f7(x55941)),f334(f173(x55941),x55942)),f334(f166(x55941),x55942))+~P104(f334(f137(x55941),x55942)) % 169.19/169.65 [5597]~P137(x55971)+E(f334(f103(x55971),f334(a107,x55972)),f334(f105(x55971),x55972))+~P104(f334(f334(f249(a1),f2(a1)),x55972)) % 169.19/169.65 [5624]E(x56241,x56242)+P104(f334(f334(f250(a877),x56241),x56242))+~P104(f334(f334(f249(a877),x56241),x56242)) % 169.19/169.65 [5625]E(x56251,x56252)+P104(f334(f334(f250(a1),x56251),x56252))+~P104(f334(f334(f249(a1),x56251),x56252)) % 169.19/169.65 [5628]E(x56281,f79(a1))+~E(f334(f334(f82(a1),x56282),x56281),f79(a1))+~P104(f334(f334(f250(a1),f2(a1)),x56282)) % 169.19/169.65 [5629]E(x56291,f79(a1))+~E(f334(f334(f82(a1),x56291),x56292),f79(a1))+~P104(f334(f334(f250(a1),f2(a1)),x56291)) % 169.19/169.65 [5667]~P41(x56672)+P104(f334(f334(f249(a1),f2(a1)),x56671))+~P104(f334(f334(f336(a1),x56671),x56672)) % 169.19/169.65 [5686]~P55(x56861,x56862)+P39(x56861,x56862)+~P104(f334(f63(f885(x56861,x56861)),x56862)) % 169.19/169.65 [5688]~P55(x56881,x56882)+P44(x56881,x56882)+~P104(f334(f63(f885(x56881,x56881)),x56882)) % 169.19/169.65 [5732]E(x57321,f195(f886(x57322,a871)))+~P104(f334(f63(x57322),x57321))+P104(f334(f334(f250(a877),f2(a877)),f334(f39(x57322),x57321))) % 169.19/169.65 [5759]~P104(f334(x57591,x57592))+P104(f334(x57591,f2(a877)))+P104(f334(f334(f250(a877),f832(x57592,x57591)),x57592)) % 169.19/169.65 [5784]E(x57841,f2(a877))+~E(f334(f166(a877),x57842),f2(a877))+~P104(f334(f334(f336(a877),x57841),f334(f173(a877),x57842))) % 169.19/169.65 [5850]E(x58501,x58502)+~P104(f334(f334(f249(a877),x58502),x58501))+~P104(f334(f334(f249(a877),x58501),x58502)) % 169.19/169.65 [5851]E(x58511,x58512)+~P104(f334(f334(f249(a1),x58512),x58511))+~P104(f334(f334(f249(a1),x58511),x58512)) % 169.19/169.65 [5852]E(f334(f39(x58521),x58522),f2(a877))+~P104(f334(f63(x58521),x58522))+P104(f334(f334(f336(x58521),f834(x58522,x58521)),x58522)) % 169.19/169.65 [5861]E(f51(x58611,x58612),f47(x58611,x58612))+P104(f334(f334(f249(a1),f2(a1)),x58611))+~P104(f334(f334(f250(a1),f2(a1)),x58612)) % 169.19/169.65 [5885]~P104(f334(x58851,f868(x58851)))+P104(f334(x58851,f334(a107,x58852)))+~P104(f334(f334(f249(a1),f2(a1)),x58852)) % 169.19/169.65 [5887]P104(f334(f334(f249(a877),x58871),f831(x58872)))+~P104(f334(f63(a877),x58872))+~P104(f334(f334(f336(a877),x58871),x58872)) % 169.19/169.65 [5888]P104(f334(f334(f250(a877),x58881),f828(x58882)))+~P104(f334(f63(a877),x58882))+~P104(f334(f334(f336(a877),x58881),x58882)) % 169.19/169.65 [5917]E(x59171,x59172)+~P104(f334(f334(f250(a877),x59171),f334(a115,x59172)))+P104(f334(f334(f250(a877),x59171),x59172)) % 169.19/169.65 [5951]E(x59511,f334(a115,x59512))+~P104(f334(f334(f249(a877),x59511),f334(a115,x59512)))+P104(f334(f334(f249(a877),x59511),x59512)) % 169.19/169.65 [5964]P104(f334(x59641,f869(x59641)))+~P104(f334(x59641,f334(a107,x59642)))+~P104(f334(f334(f249(a1),f2(a1)),x59642)) % 169.19/169.65 [5978]~P104(f334(x59781,x59782))+~P104(f334(f334(f249(a1),f2(a1)),x59782))+P104(f334(x59781,f334(f103(a1),f857(x59781)))) % 169.19/169.65 [5992]~P83(x59922)+~E(x59921,f2(x59922))+~P104(f334(f334(f250(x59922),f2(x59922)),f334(f76(x59922),x59921))) % 169.19/169.65 [6016]~P55(x60161,x60162)+P39(x60161,f334(f289(x60161,x60161),x60162))+~P104(f334(f63(f885(x60161,x60161)),x60162)) % 169.19/169.65 [6024]~P92(x60241)+E(f334(f103(x60241),f334(f106(a877),x60242)),f334(f106(x60241),x60242))+~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x60242))) % 169.19/169.65 [6027]E(f334(a115,x60271),x60272)+~P104(f334(f334(f250(a877),x60271),x60272))+P104(f334(f334(f250(a877),f334(a115,x60271)),x60272)) % 169.19/169.65 [6041]E(f334(f334(f40(a1),x60411),x60412),f2(a1))+~P104(f334(f334(f249(a1),x60411),f2(a1)))+~P104(f334(f334(f250(a1),x60412),x60411)) % 169.19/169.65 [6054]E(f46(a1,x60541,x60542),x60541)+~P104(f334(f334(f249(a1),x60541),f2(a1)))+~P104(f334(f334(f250(a1),x60542),x60541)) % 169.19/169.65 [6067]E(f48(x60671,x60672),f47(x60671,x60672))+~P104(f334(f334(f249(a1),f2(a1)),x60671))+~P104(f334(f334(f249(a1),f2(a1)),x60672)) % 169.19/169.65 [6075]E(f334(f334(f40(a1),x60751),x60752),f2(a1))+~P104(f334(f334(f249(a1),f2(a1)),x60751))+~P104(f334(f334(f250(a1),x60751),x60752)) % 169.19/169.65 [6087]E(f46(a877,f334(f106(a877),x60871),f334(f106(a877),x60872)),f334(f106(a877),x60871))+P104(f334(a201,f334(f106(a1),x60871)))+~P104(f334(a201,f334(f106(a1),x60872))) % 169.19/169.65 [6089]E(f46(a1,x60891,x60892),x60891)+~P104(f334(f334(f249(a1),f2(a1)),x60891))+~P104(f334(f334(f250(a1),x60891),x60892)) % 169.19/169.65 [6090]E(x60901,x60902)+~P104(f334(f334(f250(a877),x60901),f334(a115,x60902)))+~P104(f334(f334(f249(a877),x60902),x60901)) % 169.19/169.65 [6107]~P73(x61071)+~P104(f334(f334(f249(x61071),x61072),f2(x61071)))+P104(f334(f334(f249(x61071),x61072),f334(f80(x61071),x61072))) % 169.19/169.65 [6108]~P120(x61081)+~P104(f334(f334(f250(x61081),x61082),f2(x61081)))+P104(f334(f334(f250(x61081),x61082),f334(f80(x61081),x61082))) % 169.19/169.65 [6118]~P28(x61181)+E(f334(f334(f66(x61181,x61181,f113(x61181)),f195(x61181)),x61182),f41(x61181,x61182))+~P104(f334(f63(x61181),x61182)) % 169.19/169.65 [6119]~P28(x61191)+E(f334(f334(f66(x61191,x61191,f104(x61191)),f257(x61191)),x61192),f42(x61191,x61192))+~P104(f334(f63(x61191),x61192)) % 169.19/169.65 [6133]~P120(x61331)+~P104(f334(f334(f249(a1),f2(a1)),x61332))+P104(f334(f334(f249(x61331),f2(x61331)),f334(f105(x61331),x61332))) % 169.19/169.65 [6134]~P119(x61341)+~P104(f334(f334(f250(a877),f2(a877)),x61342))+P104(f334(f334(f250(x61341),f2(x61341)),f334(f103(x61341),x61342))) % 169.19/169.65 [6135]~P120(x61351)+~P104(f334(f334(f250(a1),f2(a1)),x61352))+P104(f334(f334(f250(x61351),f2(x61351)),f334(f105(x61351),x61352))) % 169.19/169.65 [6138]~P29(x61382)+~P29(x61381)+E(f334(f313(a877,a1,f103(a1)),f305(a877,f334(a107,x61381),f334(a107,x61382))),f305(a1,x61381,x61382)) % 169.19/169.65 [6144]P104(f334(x61441,x61442))+~P104(f334(f334(f249(a1),f2(a1)),x61442))+~P104(f334(x61441,f334(f103(a1),f858(x61441)))) % 169.19/169.65 [6169]E(f334(f334(f81(a877),f334(f106(a877),x61691)),f334(f106(a877),x61692)),f334(f106(a877),x61691))+P104(f334(f334(f250(a1),x61691),a84))+~P104(f334(f334(f250(a1),x61692),a84)) % 169.19/169.65 [6173]~P120(x61731)+P104(f334(f334(f250(x61731),f2(x61731)),f83(x61731,x61732)))+~P104(f334(f334(f250(x61731),f2(x61731)),x61732)) % 169.19/169.65 [6184]~P75(x61841)+~P104(f334(f334(f249(x61841),x61842),f2(x61841)))+P104(f334(f334(f249(x61841),f2(x61841)),f334(f80(x61841),x61842))) % 169.19/169.65 [6185]~P75(x61851)+~P104(f334(f334(f250(x61851),x61852),f2(x61851)))+P104(f334(f334(f250(x61851),f2(x61851)),f334(f80(x61851),x61852))) % 169.19/169.65 [6188]E(x61881,f257(f886(x61882,a871)))+~E(f334(f39(x61882),x61881),f334(f39(x61882),f257(f886(x61882,a871))))+~P104(f334(f63(x61882),f257(f886(x61882,a871)))) % 169.19/169.65 [6229]~P73(x62291)+P104(f334(f334(f249(x62291),x62292),f2(x62291)))+~P104(f334(f334(f249(x62291),x62292),f334(f80(x62291),x62292))) % 169.19/169.65 [6230]~P120(x62301)+P104(f334(f334(f250(x62301),x62302),f2(x62301)))+~P104(f334(f334(f250(x62301),x62302),f334(f80(x62301),x62302))) % 169.19/169.65 [6239]~P92(x62391)+P104(f334(f334(f336(x62391),f334(f106(x62391),x62392)),f193(x62391)))+~P104(f334(f334(f249(a1),a84),x62392)) % 169.19/169.65 [6270]E(x62701,f2(a877))+~P104(f334(f334(f250(a877),x62701),f334(a115,x62702)))+P104(f334(f334(f250(a877),f802(x62702,x62701)),x62702)) % 169.19/169.65 [6292]~P120(x62921)+~P104(f334(f334(f250(x62921),f2(x62921)),f83(x62921,x62922)))+P104(f334(f334(f250(x62921),f2(x62921)),x62922)) % 169.19/169.65 [6294]~E(f334(f106(a877),x62942),f334(f106(a877),x62941))+P104(f334(f334(f249(a1),f334(f106(a1),x62941)),f2(a1)))+~P104(f334(a201,f334(f106(a1),x62942))) % 169.19/169.65 [6323]E(f334(f268(a1,a1),f51(x63231,x63232)),f334(f334(f40(a1),x63231),x63232))+~P104(f334(f334(f250(a1),x63231),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x63232)) % 169.19/169.65 [6356]E(f334(f272(a1,a1),f51(x63561,x63562)),f46(a1,x63561,x63562))+~P104(f334(f334(f250(a1),x63561),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x63562)) % 169.19/169.65 [6359]~P120(x63592)+~P104(f334(f334(f249(x63592),f2(x63592)),f334(f105(x63592),x63591)))+P104(f334(f334(f249(a1),f2(a1)),x63591)) % 169.19/169.65 [6360]~P119(x63602)+~P104(f334(f334(f250(x63602),f2(x63602)),f334(f103(x63602),x63601)))+P104(f334(f334(f250(a877),f2(a877)),x63601)) % 169.19/169.65 [6361]~P120(x63612)+~P104(f334(f334(f250(x63612),f2(x63612)),f334(f105(x63612),x63611)))+P104(f334(f334(f250(a1),f2(a1)),x63611)) % 169.19/169.65 [6364]E(f334(f268(a1,a1),f48(x63641,x63642)),f334(f334(f40(a1),x63641),x63642))+~P104(f334(f334(f249(a1),f2(a1)),x63642))+~P104(f334(f334(f250(a1),f2(a1)),x63641)) % 169.19/169.65 [6379]E(f334(f272(a1,a1),f48(x63791,x63792)),f46(a1,x63791,x63792))+~P104(f334(f334(f249(a1),f2(a1)),x63792))+~P104(f334(f334(f250(a1),f2(a1)),x63791)) % 169.19/169.65 [6396]~P75(x63961)+P104(f334(f334(f249(x63961),x63962),f2(x63961)))+~P104(f334(f334(f249(x63961),f2(x63961)),f334(f80(x63961),x63962))) % 169.19/169.65 [6397]~P75(x63971)+P104(f334(f334(f250(x63971),x63972),f2(x63971)))+~P104(f334(f334(f250(x63971),f2(x63971)),f334(f80(x63971),x63972))) % 169.19/169.65 [6423]P104(f334(f50(x64231,x64232),f51(x64231,x64232)))+~P104(f334(f334(f250(a1),x64231),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x64232)) % 169.19/169.65 [6448]P104(f334(f50(x64481,x64482),f48(x64481,x64482)))+~P104(f334(f334(f249(a1),f2(a1)),x64481))+~P104(f334(f334(f250(a1),f2(a1)),x64482)) % 169.19/169.65 [6491]~P75(x64911)+P104(f334(f334(f249(x64911),f334(f80(x64911),x64912)),f2(x64911)))+~P104(f334(f334(f249(x64911),f2(x64911)),x64912)) % 169.19/169.65 [6492]~P75(x64921)+P104(f334(f334(f250(x64921),f334(f80(x64921),x64922)),f2(x64921)))+~P104(f334(f334(f250(x64921),f2(x64921)),x64922)) % 169.19/169.65 [6509]E(f334(f334(f3(a877),f334(a107,x65091)),f334(a107,x65092)),f334(a107,f202(x65091,x65092)))+~P104(f334(f334(f249(a1),f2(a1)),x65092))+~P104(f334(f334(f249(a1),f2(a1)),x65091)) % 169.19/169.65 [6526]P104(f334(f334(f249(a1),f2(a1)),f202(x65261,x65262)))+~P104(f334(f334(f249(a1),f2(a1)),x65262))+~P104(f334(f334(f249(a1),f2(a1)),x65261)) % 169.19/169.65 [6563]~P104(f334(x65631,x65632))+P104(f334(x65631,f2(a877)))+P104(f334(x65631,f334(f334(f81(a877),f832(x65632,x65631)),f79(a877)))) % 169.19/169.65 [6644]E(f334(f106(a877),x66441),f334(f106(a877),x66442))+~P104(f334(f334(f249(a1),f334(f106(a1),x66442)),f2(a1)))+~P104(f334(a201,f334(f106(a1),x66441))) % 169.19/169.65 [6654]~E(x66541,f2(a877))+~E(f605(x66542,x66541),f2(a877))+E(f334(f142(a877,a877,f81(a877),x66541),x66542),f2(a877)) % 169.19/169.65 [6679]~P104(f334(f63(x66791),f414(x66792,x66791)))+~P104(f334(f63(f886(x66791,a871)),x66792))+P104(f334(f63(x66791),f41(f886(x66791,a871),x66792))) % 169.19/169.65 [6685]E(x66851,x66852)+P104(f334(f334(f250(a1),x66851),x66852))+~P104(f334(f334(f250(a1),x66851),f334(f334(f81(a1),x66852),f79(a1)))) % 169.19/169.65 [6686]P104(f334(f334(f249(a877),f334(a107,x66861)),f334(a107,x66862)))+~P104(f334(f334(f249(a1),f2(a1)),x66862))+~P104(f334(f334(f249(a1),x66861),x66862)) % 169.19/169.65 [6687]P104(f334(f334(f249(a877),f334(a107,x66871)),f334(a107,x66872)))+~P104(f334(f334(f250(a1),f2(a1)),x66871))+~P104(f334(f334(f249(a1),x66871),x66872)) % 169.19/169.65 [6689]P104(f334(f334(f250(a877),f334(a107,x66891)),f334(a107,x66892)))+~P104(f334(f334(f249(a1),f2(a1)),x66891))+~P104(f334(f334(f250(a1),x66891),x66892)) % 169.19/169.65 [6690]P104(f334(f334(f250(a877),f334(a107,x66901)),f334(a107,x66902)))+~P104(f334(f334(f250(a1),f2(a1)),x66902))+~P104(f334(f334(f250(a1),x66901),x66902)) % 169.19/169.65 [6701]E(f46(a877,f334(a107,x67011),f334(a107,x67012)),f334(a107,f46(a1,x67011,x67012)))+~P104(f334(f334(f249(a1),f2(a1)),x67012))+~P104(f334(f334(f249(a1),f2(a1)),x67011)) % 169.19/169.65 [6723]~P75(x67231)+~P104(f334(f334(f249(x67231),f334(f80(x67231),x67232)),f2(x67231)))+P104(f334(f334(f249(x67231),f2(x67231)),x67232)) % 169.19/169.65 [6724]~P75(x67241)+~P104(f334(f334(f250(x67241),f334(f80(x67241),x67242)),f2(x67241)))+P104(f334(f334(f250(x67241),f2(x67241)),x67242)) % 169.19/169.65 [6739]~P104(f334(f334(f250(a1),a84),x67392))+~P104(f334(f334(f250(a1),x67391),x67392))+P104(f334(f334(f250(a877),f334(f106(a877),x67391)),f334(f106(a877),x67392))) % 169.19/169.65 [6830]~P104(f334(f334(f249(a1),f2(a1)),x68301))+P104(f334(f334(f250(a877),f334(a107,x68301)),x68302))+~P104(f334(f334(f250(a1),x68301),f334(f103(a1),x68302))) % 169.19/169.65 [6847]E(x68471,f2(a1))+E(f46(a1,x68472,x68471),f2(a1))+E(f334(f334(f3(a1),f334(f80(a1),f334(f334(f40(a1),x68472),x68471))),f79(a1)),f334(f334(f40(a1),x68472),f334(f80(a1),x68471))) % 169.19/169.65 [6863]~P104(f334(f334(f249(a1),f2(a1)),x68631))+~P104(f334(f334(f250(a877),f334(a107,x68631)),x68632))+P104(f334(f334(f250(a1),x68631),f334(f103(a1),x68632))) % 169.19/169.65 [6898]~P104(f334(f334(f249(a877),f334(a107,x68981)),f334(a107,x68982)))+~P104(f334(f334(f249(a1),f2(a1)),x68982))+P104(f334(f334(f249(a1),x68981),x68982)) % 169.19/169.65 [6899]~P104(f334(f334(f249(a877),f334(a107,x68991)),f334(a107,x68992)))+~P104(f334(f334(f250(a1),f2(a1)),x68991))+P104(f334(f334(f249(a1),x68991),x68992)) % 169.19/169.65 [6927]P104(f334(f334(f249(a1),x69271),x69272))+~P104(f334(f334(f249(a877),f334(f106(a877),x69271)),f334(f106(a877),x69272)))+P104(f334(f334(f249(a1),x69271),a84)) % 169.19/169.65 [6952]P104(f334(f334(f249(a1),f2(a1)),f46(a1,x69521,x69522)))+~P104(f334(f334(f249(a1),f2(a1)),x69522))+~P104(f334(f334(f249(a1),f2(a1)),x69521)) % 169.19/169.65 [7050]P104(f334(f334(f250(a1),a84),x70501))+~P104(f334(f334(f250(a1),x70502),x70501))+~P104(f334(f334(f250(a877),f334(f106(a877),x70502)),f334(f106(a877),x70501))) % 169.19/169.65 [7101]E(f334(f334(f269(a1,a1),f334(f334(f40(a1),x71011),x71012)),f46(a1,x71011,x71012)),f51(x71011,x71012))+~P104(f334(f334(f250(a1),x71011),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x71012)) % 169.19/169.65 [7122]E(f334(f334(f269(a1,a1),f334(f334(f40(a1),x71221),x71222)),f46(a1,x71221,x71222)),f48(x71221,x71222))+~P104(f334(f334(f249(a1),f2(a1)),x71222))+~P104(f334(f334(f249(a1),f2(a1)),x71221)) % 169.19/169.65 [7173]~P93(x71732)+E(x71731,f116(x71732))+E(f334(f142(x71732,x71732,f82(x71732),f334(f141(x71732),x71731)),f334(f172(x71732),x71731)),f334(f65(x71732,f82(x71732)),f334(f173(x71732),x71731))) % 169.19/169.65 [7286]~E(x72861,f2(a877))+E(f334(f142(a877,a877,f81(a877),x72861),x72862),f2(a877))+P104(f334(f334(f336(a877),f605(x72862,x72861)),f334(f173(a877),x72862))) % 169.19/169.65 [7335]~P104(f334(f334(f249(a1),x73351),f2(a1)))+P104(f334(f334(f249(a1),f334(f334(f40(a1),x73351),x73352)),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x73352)) % 169.19/169.65 [7336]~P104(f334(f334(f250(a1),x73362),f2(a1)))+P104(f334(f334(f249(a1),f334(f334(f40(a1),x73361),x73362)),f2(a1)))+~P104(f334(f334(f249(a1),f2(a1)),x73361)) % 169.19/169.65 [7337]~P104(f334(f334(f250(a1),x73372),f2(a1)))+P104(f334(f334(f250(a1),f334(f334(f40(a1),x73371),x73372)),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x73371)) % 169.19/169.65 [7339]~P104(f334(f334(f250(a1),x73391),f2(a1)))+P104(f334(f334(f250(a1),f334(f334(f40(a1),x73391),x73392)),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x73392)) % 169.19/169.65 [7345]P104(f334(f334(f336(f886(x73451,a871)),f414(x73452,x73451)),x73452))+~P104(f334(f63(f886(x73451,a871)),x73452))+P104(f334(f63(x73451),f41(f886(x73451,a871),x73452))) % 169.19/169.65 [7440]P21(x74401,x74401,x74402,f257(f886(x74401,a871)))+~E(f334(f313(x74401,x74401,x74402),f257(f886(x74401,a871))),f257(f886(x74401,a871)))+~P104(f334(f63(x74401),f257(f886(x74401,a871)))) % 169.19/169.65 [7567]~P21(x75671,x75671,x75672,f257(f886(x75671,a871)))+E(f334(f313(x75671,x75671,x75672),f257(f886(x75671,a871))),f257(f886(x75671,a871)))+~P104(f334(f63(x75671),f257(f886(x75671,a871)))) % 169.19/169.65 [7704]E(f334(f334(f40(a1),x77041),x77042),f334(f106(a1),a100))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),x77041),x77042)),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x77041)) % 169.19/169.65 [7763]~P104(f334(f334(f250(a1),x77632),f2(a1)))+~P104(f334(f334(f250(a1),f334(f334(f40(a1),x77631),x77632)),f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x77631)) % 169.19/169.65 [7768]E(f334(f334(f81(a1),x77681),x77682),f46(a1,x77681,x77682))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),x77681),x77682)),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x77681)) % 169.19/169.65 [7771]P104(f334(f334(f250(a1),x77711),f2(a1)))+~P104(f334(f334(f250(a1),f334(f334(f40(a1),x77711),x77712)),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x77712)) % 169.19/169.65 [8154]~P58(x81541)+~P104(f334(f60(f881(x81541)),x81542))+P104(f334(f60(x81541),f334(f334(f10(f881(x81541),a871,x81541),x81542),f241(x81541)))) % 169.19/169.65 [8459]~P107(x84591)+P30(x84591,x84592)+~P104(f334(f334(f249(x84591),f334(f334(f165(x84591),x84592),f636(x84592,x84591))),f334(f334(f165(x84591),x84592),f637(x84592,x84591)))) % 169.19/169.65 [8460]~P107(x84601)+P30(x84601,x84602)+~P104(f334(f334(f249(x84601),f334(f334(f165(x84601),x84602),f643(x84602,x84601))),f334(f334(f165(x84601),x84602),f652(x84602,x84601)))) % 169.19/169.65 [8605]~P58(x86051)+P104(f334(f59(f881(x86051)),x86052))+~P104(f334(f59(x86051),f334(f334(f10(f881(x86051),a871,x86051),x86052),f241(x86051)))) % 169.19/169.65 [9734]~P58(x97341)+~P58(x97342)+E(f334(f334(f154(f878(x97341),f886(x97342,x97341)),f334(f334(f10(f886(x97342,f881(x97341)),f886(x97342,x97341),f878(x97341)),f74(f881(x97341),x97341,x97342,f245(x97341))),f334(f334(f10(f878(f885(x97342,x97341)),f886(x97342,f881(x97341)),f878(x97341)),f179(x97342,x97341)),f334(f183(x97342,x97341),f57(x97342))))),f56(x97341,f334(f196(f878(x97342)),f57(x97342)),f57(x97341))),f57(f886(x97342,x97341))) % 169.19/169.65 [5725]E(x57251,f2(a1))+~E(f46(a1,x57252,x57251),f2(a1))+E(f334(f334(f40(a1),x57252),f334(f80(a1),x57251)),f334(f80(a1),f334(f334(f40(a1),x57252),x57251))) % 169.19/169.65 [5743]~P41(x57432)+~P41(x57431)+P41(f334(f334(f113(f886(a1,a871)),x57431),x57432)) % 169.19/169.65 [5744]~P41(x57442)+~P41(x57441)+P41(f334(f334(f104(f886(a1,a871)),x57441),x57442)) % 169.19/169.65 [5762]~P92(x57621)+~P59(x57621)+E(f334(f80(x57621),f334(f334(f292(x57621),f79(x57621)),x57622)),f334(f334(f292(x57621),f334(f106(x57621),a100)),x57622)) % 169.19/169.65 [5877]E(x58771,f2(a1))+~E(f46(a1,x58772,x58771),f2(a1))+E(f334(f334(f40(a1),f334(f80(a1),x58772)),x58771),f334(f80(a1),f334(f334(f40(a1),x58772),x58771))) % 169.19/169.65 [6010]~P107(x60101)+P30(x60101,x60102)+P104(f334(f334(f250(a877),f637(x60102,x60101)),f334(f196(f878(x60101)),x60102))) % 169.19/169.65 [6011]~P107(x60111)+P30(x60111,x60112)+P104(f334(f334(f250(a877),f652(x60112,x60111)),f334(f196(f878(x60111)),x60112))) % 169.19/169.65 [6165]~P92(x61651)+~E(f334(f106(x61651),x61652),f2(x61651))+P32(x61651,f334(f106(x61651),f334(f334(f81(a1),x61652),f334(f80(a1),a84)))) % 169.19/169.65 [6166]~P92(x61661)+~E(f334(f106(x61661),x61662),f2(x61661))+P32(x61661,f334(f106(x61661),f334(f334(f81(a1),a84),f334(f80(a1),x61662)))) % 169.19/169.65 [6168]E(f334(a52,f48(f334(f80(a1),x61681),f334(f80(a1),x61682))),f47(x61681,x61682))+P104(f334(f334(f249(a1),f2(a1)),x61681))+P104(f334(f334(f250(a1),f2(a1)),x61682)) % 169.19/169.65 [6300]~E(x63002,f2(a877))+~E(x63001,f2(a877))+P104(f334(f334(f249(a1),f334(f103(a1),x63001)),f334(f80(a1),f334(f103(a1),x63002)))) % 169.19/169.65 [6327]E(f334(f334(f81(a877),f334(f106(a877),x63271)),f334(f106(a877),x63272)),f334(f106(a877),f334(f334(f81(a1),x63271),x63272)))+P104(f334(f334(f250(a1),x63271),a84))+P104(f334(f334(f250(a1),x63272),a84)) % 169.19/169.65 [6457]~P73(x64571)+~P104(f334(f334(f249(x64571),f2(x64571)),x64572))+P104(f334(f334(f249(x64571),f334(f80(x64571),x64572)),x64572)) % 169.19/169.65 [6458]~P73(x64581)+~P104(f334(f334(f250(x64581),f2(x64581)),x64582))+P104(f334(f334(f250(x64581),f334(f80(x64581),x64582)),x64582)) % 169.19/169.65 [6630]E(f334(f334(f3(a877),f334(a107,x66301)),f334(a107,x66302)),f334(a107,f334(f334(f3(a1),x66301),x66302)))+~P104(f334(f334(f249(a1),f2(a1)),x66302))+~P104(f334(f334(f249(a1),x66302),x66301)) % 169.19/169.65 [6662]E(f334(a107,f46(a1,f334(f106(a1),x66621),f334(f106(a1),x66622))),f46(a877,f334(f106(a877),x66621),f334(f106(a877),x66622)))+P104(f334(a201,f334(f106(a1),x66621)))+P104(f334(a201,f334(f106(a1),x66622))) % 169.19/169.65 [6680]~P73(x66801)+P104(f334(f334(f249(x66801),f2(x66801)),x66802))+~P104(f334(f334(f249(x66801),f334(f80(x66801),x66802)),x66802)) % 169.19/169.65 [6681]~P73(x66811)+P104(f334(f334(f250(x66811),f2(x66811)),x66812))+~P104(f334(f334(f250(x66811),f334(f80(x66811),x66812)),x66812)) % 169.19/169.65 [6693]~P73(x66931)+~P104(f334(f334(f249(x66931),f2(x66931)),x66932))+P104(f334(f334(f249(x66931),f2(x66931)),f334(f334(f81(x66931),x66932),x66932))) % 169.19/169.65 [6695]~P73(x66951)+~P104(f334(f334(f250(x66951),f2(x66951)),x66952))+P104(f334(f334(f250(x66951),f2(x66951)),f334(f334(f81(x66951),x66952),x66952))) % 169.19/169.65 [6707]E(f334(f334(f81(a877),f334(a107,x67071)),f334(a107,x67072)),f334(a107,f334(f334(f81(a1),x67071),x67072)))+~P104(f334(f334(f249(a1),f2(a1)),x67072))+~P104(f334(f334(f249(a1),f2(a1)),x67071)) % 169.19/169.65 [6718]E(x67181,f2(a877))+P104(f334(f334(f250(a877),f2(a877)),x67182))+~P104(f334(f334(f250(a877),f2(a877)),f334(f334(f259(a877),x67182),x67181))) % 169.19/169.65 [6748]~P92(x67481)+E(f334(f106(x67481),x67482),f2(x67481))+~P32(x67481,f334(f106(x67481),f334(f334(f81(a1),a84),f334(f80(a1),x67482)))) % 169.19/169.65 [6749]~P92(x67491)+E(f334(f106(x67491),x67492),f2(x67491))+~P32(x67491,f334(f106(x67491),f334(f334(f81(a1),x67492),f334(f80(a1),a84)))) % 169.19/169.65 [6808]~P104(f334(f63(x68081),x68082))+~P104(f334(f63(x68081),f257(f886(x68081,a871))))+P104(f334(f63(x68081),f334(f80(f886(x68081,a871)),x68082))) % 169.19/169.65 [6831]~P104(f334(f334(f250(a1),f2(a1)),x68312))+~P104(f334(f334(f249(a1),x68312),x68311))+P104(f334(f334(f250(a1),f2(a1)),f334(f334(f40(a1),x68311),x68312))) % 169.19/169.65 [6832]~P104(f334(f334(f249(a1),x68321),f2(a1)))+~P104(f334(f334(f250(a1),x68322),f2(a1)))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f40(a1),x68321),x68322))) % 169.19/169.65 [6871]~P104(f334(f334(f249(a1),f2(a1)),x68712))+~P104(f334(f334(f249(a1),f2(a1)),x68711))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f82(a1),x68711),x68712))) % 169.19/169.65 [6872]~P104(f334(f334(f249(a1),f2(a1)),x68722))+~P104(f334(f334(f249(a1),f2(a1)),x68721))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),x68721),x68722))) % 169.19/169.65 [6873]~P104(f334(f334(f249(a1),f2(a1)),x68732))+~P104(f334(f334(f249(a1),f2(a1)),x68731))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f40(a1),x68731),x68732))) % 169.19/169.65 [6874]~P104(f334(f334(f249(a1),f2(a1)),x68741))+~P104(f334(f334(f250(a1),f2(a1)),x68742))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f40(a1),x68741),x68742))) % 169.19/169.65 [6875]~P104(f334(f334(f250(a877),f2(a877)),x68752))+~P104(f334(f334(f250(a877),f2(a877)),x68751))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f82(a877),x68751),x68752))) % 169.19/169.65 [6940]E(x69401,f2(a1))+E(f46(a1,x69402,x69401),f2(a1))+E(f334(f334(f3(a1),f334(f80(a1),f334(f334(f40(a1),x69402),x69401))),f79(a1)),f334(f334(f40(a1),f334(f80(a1),x69402)),x69401)) % 169.19/169.65 [6993]P104(f334(f334(f250(a877),f2(a877)),x69931))+P104(f334(f334(f250(a877),f2(a877)),x69932))+~P104(f334(f334(f250(a877),f2(a877)),f334(f334(f81(a877),x69932),x69931))) % 169.19/169.65 [6997]~P73(x69971)+P104(f334(f334(f249(x69971),f2(x69971)),x69972))+~P104(f334(f334(f249(x69971),f2(x69971)),f334(f334(f81(x69971),x69972),x69972))) % 169.19/169.65 [6998]~P73(x69981)+P104(f334(f334(f250(x69981),f2(x69981)),x69982))+~P104(f334(f334(f250(x69981),f2(x69981)),f334(f334(f81(x69981),x69982),x69982))) % 169.19/169.65 [7051]~P104(f334(f63(x70511),x70512))+P104(f334(f63(x70511),f257(f886(x70511,a871))))+~P104(f334(f63(x70511),f334(f80(f886(x70511,a871)),x70512))) % 169.19/169.65 [7114]P104(f334(f334(f249(a1),x71141),f2(a1)))+~P104(f334(f334(f250(a1),x71142),f2(a1)))+~P104(f334(f334(f249(a1),f2(a1)),f334(f334(f40(a1),x71141),x71142))) % 169.19/169.65 [7120]~P104(f334(f334(f250(a1),f2(a1)),x71201))+P104(f334(f334(f249(a1),x71201),x71202))+~P104(f334(f334(f250(a1),f2(a1)),f334(f334(f40(a1),x71202),x71201))) % 169.19/169.65 [7121]~P104(f334(f334(f249(a1),f2(a1)),x71212))+P104(f334(f334(f249(a1),x71211),x71212))+~P104(f334(f334(f250(a1),f2(a1)),f334(f334(f40(a1),x71212),x71211))) % 169.19/169.65 [7150]P104(f334(f334(f249(a1),f2(a1)),x71501))+~P104(f334(f334(f250(a1),f2(a1)),x71502))+~P104(f334(f334(f249(a1),f2(a1)),f334(f334(f40(a1),x71501),x71502))) % 169.19/169.65 [7151]P104(f334(f334(f250(a1),f2(a1)),x71511))+~P104(f334(f334(f249(a1),f2(a1)),x71512))+~P104(f334(f334(f250(a1),f2(a1)),f334(f334(f40(a1),x71512),x71511))) % 169.19/169.65 [7598]~P104(f334(f63(x75982),f257(f886(x75982,a871))))+~P104(f334(f63(x75981),f257(f886(x75981,a871))))+P104(f334(f63(f884(x75981,x75982)),f257(f886(f884(x75981,x75982),a871)))) % 169.19/169.65 [7599]~P104(f334(f63(x75992),f257(f886(x75992,a871))))+~P104(f334(f63(x75991),f257(f886(x75991,a871))))+P104(f334(f63(f885(x75991,x75992)),f257(f886(f885(x75991,x75992),a871)))) % 169.19/169.65 [7668]~P104(f334(f334(f250(a877),f334(a115,f2(a877))),x76681))+~P104(f334(f334(f250(a877),f334(a115,f2(a877))),x76682))+P104(f334(f334(f250(a877),x76681),f334(f334(f82(a877),x76682),x76681))) % 169.19/169.65 [7669]~P104(f334(f334(f250(a877),f334(a115,f2(a877))),x76691))+~P104(f334(f334(f250(a877),f334(a115,f2(a877))),x76692))+P104(f334(f334(f250(a877),x76691),f334(f334(f82(a877),x76691),x76692))) % 169.19/169.65 [7703]E(f334(f39(x77031),f257(f886(x77031,a871))),f334(a115,f2(a877)))+P104(f334(f63(x77032),f257(f886(x77032,a871))))+~P104(f334(f63(f886(x77032,x77031)),f257(f886(f886(x77032,x77031),a871)))) % 169.19/169.65 [7831]~P104(f334(f334(f249(a877),f334(a115,f2(a877))),x78311))+~P104(f334(f334(f249(a877),f334(a115,f2(a877))),x78312))+P104(f334(f334(f249(a877),f334(a115,f2(a877))),f334(f334(f82(a877),x78311),x78312))) % 169.19/169.65 [7832]~P104(f334(f334(f250(a877),f334(a115,f2(a877))),x78322))+~P104(f334(f334(f250(a877),f334(a115,f2(a877))),x78321))+P104(f334(f334(f250(a877),f334(a115,f2(a877))),f334(f334(f82(a877),x78321),x78322))) % 169.19/169.65 [8503]E(x85031,f116(x85032))+~P104(f334(f137(x85032),x85031))+E(f178(x85032,f334(f334(f10(a871,a871,x85032),a329),f334(f334(f9(x85032,x85032,a871),a331),f144(x85032,x85031))),x85031),f117(x85032,x85031)) % 169.19/169.65 [8596]~P41(x85962)+~P41(x85961)+E(f334(f313(a877,a1,f103(a1)),f334(f334(f113(f886(a877,a871)),f334(f313(a1,a877,a107),x85961)),f334(f313(a1,a877,a107),x85962))),f334(f334(f113(f886(a1,a871)),x85961),x85962)) % 169.19/169.65 [8597]~P41(x85972)+~P41(x85971)+E(f334(f313(a877,a1,f103(a1)),f334(f334(f104(f886(a877,a871)),f334(f313(a1,a877,a107),x85971)),f334(f313(a1,a877,a107),x85972))),f334(f334(f104(f886(a1,a871)),x85971),x85972)) % 169.19/169.65 [9228]~P92(x92281)+~E(f334(f106(x92281),x92282),f79(x92281))+P32(x92281,f334(f106(x92281),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f80(a1),x92282)))) % 169.19/169.65 [9453]~P92(x94531)+E(f334(f106(x94531),x94532),f79(x94531))+~P32(x94531,f334(f106(x94531),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f80(a1),x94532)))) % 169.19/169.65 [10177]E(x101771,f2(a1))+E(x101772,f2(a1))+E(f334(f274(a1,a1,a1,a1,f35(a1),f334(f82(a1),f83(a1,x101772))),f334(f334(f334(f99(f885(a1,a1)),f334(f334(a331,f83(a1,x101771)),f83(a1,x101772))),f54(x101771,x101772)),f334(f334(f273(a1,a1,f885(a1,a1)),f334(f334(f20(a1,f886(a1,f885(a1,a1)),f886(a1,f885(a1,a1))),f334(f334(f10(f886(a1,f886(f885(a1,a1),f885(a1,a1))),f886(f886(a1,f885(a1,a1)),f886(a1,f885(a1,a1))),a1),f20(a1,f885(a1,a1),f885(a1,a1))),f334(f334(f10(f885(a1,a1),f886(a1,f886(f885(a1,a1),f885(a1,a1))),a1),f334(f9(a1,f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),f334(f334(f10(a871,f886(f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),a1),f99(f885(a1,a1))),f334(f334(f9(a1,a1,a871),a331),f2(a1))))),f334(f334(f9(a1,a1,f885(a1,a1)),f334(f334(f10(a1,f886(a1,f885(a1,a1)),a1),f269(a1,a1)),f80(a1))),f2(a1))))),f334(f334(f9(a1,f886(a1,a1),f886(a1,f885(a1,a1))),f334(f334(f10(f886(a1,f885(a1,a1)),f886(f886(a1,a1),f886(a1,f885(a1,a1))),a1),f10(a1,f885(a1,a1),a1)),f334(f334(f10(a1,f886(a1,f885(a1,a1)),a1),f269(a1,a1)),f334(f334(f9(a1,a1,a1),f334(f334(f10(a1,f886(a1,a1),a1),f3(a1)),f80(a1))),f79(a1))))),f334(f3(a1),f334(f76(a1),x101772))))),f54(x101771,x101772)))),f47(x101771,x101772)) % 169.19/169.65 [10178]E(x101781,f2(a1))+E(x101782,f2(a1))+E(f334(f274(a1,a1,a1,a1,f35(a1),f334(f82(a1),f83(a1,x101782))),f334(f334(f334(f99(f885(a1,a1)),f334(f334(a333,f334(f334(a332,f334(f334(f250(a1),f2(a1)),x101782)),f334(f334(f249(a1),f2(a1)),x101781))),f334(f334(a332,f334(f334(f250(a1),x101782),f2(a1))),f334(f334(f250(a1),x101781),f2(a1))))),f54(x101781,x101782)),f334(f334(f273(a1,a1,f885(a1,a1)),f334(f334(f20(a1,f886(a1,f885(a1,a1)),f886(a1,f885(a1,a1))),f334(f334(f10(f886(a1,f886(f885(a1,a1),f885(a1,a1))),f886(f886(a1,f885(a1,a1)),f886(a1,f885(a1,a1))),a1),f20(a1,f885(a1,a1),f885(a1,a1))),f334(f334(f10(f885(a1,a1),f886(a1,f886(f885(a1,a1),f885(a1,a1))),a1),f334(f9(a1,f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),f334(f334(f10(a871,f886(f885(a1,a1),f886(f885(a1,a1),f885(a1,a1))),a1),f99(f885(a1,a1))),f334(f334(f9(a1,a1,a871),a331),f2(a1))))),f334(f334(f9(a1,a1,f885(a1,a1)),f334(f334(f10(a1,f886(a1,f885(a1,a1)),a1),f269(a1,a1)),f80(a1))),f2(a1))))),f334(f334(f9(a1,f886(a1,a1),f886(a1,f885(a1,a1))),f334(f334(f10(f886(a1,f885(a1,a1)),f886(f886(a1,a1),f886(a1,f885(a1,a1))),a1),f10(a1,f885(a1,a1),a1)),f334(f334(f10(a1,f886(a1,f885(a1,a1)),a1),f269(a1,a1)),f334(f334(f9(a1,a1,a1),f334(f334(f10(a1,f886(a1,a1),a1),f3(a1)),f80(a1))),f79(a1))))),f334(f3(a1),f334(f76(a1),x101782))))),f54(x101781,x101782)))),f47(x101781,x101782)) % 169.19/169.65 [5751]~P120(x57511)+~P92(x57511)+E(f334(f76(x57511),f334(f334(f259(x57511),f334(f106(x57511),a100)),x57512)),f79(x57511)) % 169.19/169.65 [6240]~P137(x62401)+~P104(f334(f334(f250(a1),x62402),f2(a1)))+E(f334(f80(x62401),f334(f103(x62401),f334(a107,f334(f80(a1),x62402)))),f334(f105(x62401),x62402)) % 169.19/169.65 [6441]P104(f334(f334(f249(a102),x64411),f79(a102)))+E(f334(f334(f81(a102),f79(a102)),f282(x64411,f334(f334(f40(a102),x64412),x64411))),f282(x64411,x64412))+P104(f334(f334(f250(a102),x64412),x64411)) % 169.19/169.65 [7038]~P89(x70381)+~P104(f334(f334(f336(x70381),x70382),f112(x70381)))+~E(f334(f334(f81(x70381),f334(f334(f81(x70381),f79(x70381)),x70382)),x70382),f2(x70381)) % 169.19/169.65 [7152]~P104(f334(f334(f249(a1),x71522),f2(a1)))+~P104(f334(f334(f250(a1),x71521),f2(a1)))+E(f334(f268(a1,a1),f334(a52,f48(f334(f80(a1),x71521),f334(f80(a1),x71522)))),f334(f334(f40(a1),x71521),x71522)) % 169.19/169.65 [7169]~P104(f334(f334(f249(a1),x71692),f2(a1)))+~P104(f334(f334(f250(a1),x71691),f2(a1)))+E(f334(f272(a1,a1),f334(a52,f48(f334(f80(a1),x71691),f334(f80(a1),x71692)))),f46(a1,x71691,x71692)) % 169.19/169.65 [7175]~P104(f334(f334(f250(a1),x71752),f2(a1)))+E(f334(f268(a1,a1),f334(a52,f51(f334(f80(a1),x71751),f334(f80(a1),x71752)))),f334(f334(f40(a1),x71751),x71752))+~P104(f334(f334(f250(a1),f2(a1)),x71751)) % 169.19/169.65 [7193]~P104(f334(f334(f250(a1),x71932),f2(a1)))+E(f334(f272(a1,a1),f334(a52,f51(f334(f80(a1),x71931),f334(f80(a1),x71932)))),f46(a1,x71931,x71932))+~P104(f334(f334(f250(a1),f2(a1)),x71931)) % 169.19/169.65 [7246]E(f334(f334(f40(a1),f334(f334(f259(a1),x72461),x72462)),x72461),f334(f334(f259(a1),x72461),f334(f334(f3(a877),x72462),f334(a115,f2(a877)))))+~P104(f334(f334(f250(a877),f2(a877)),x72462))+~P104(f334(f334(f250(a1),f2(a1)),x72461)) % 169.19/169.65 [7342]~P104(f334(f334(f250(a877),f2(a877)),x73421))+~P104(f334(f334(f250(a877),f2(a877)),x73422))+P104(f334(f334(f250(a877),f334(f334(f3(a877),x73421),x73422)),x73421)) % 169.19/169.65 [7343]~P104(f334(f334(f250(a877),f2(a877)),x73431))+~P104(f334(f334(f250(a877),f79(a877)),x73432))+P104(f334(f334(f250(a877),f334(f334(f40(a877),x73431),x73432)),x73431)) % 169.19/169.65 [7344]~P104(f334(f334(f250(a1),f2(a1)),x73441))+~P104(f334(f334(f250(a1),f79(a1)),x73442))+P104(f334(f334(f250(a1),f334(f334(f40(a1),x73441),x73442)),x73441)) % 169.19/169.65 [7489]E(x74891,f2(a877))+~E(x74892,f2(a1))+~P104(f334(f334(f250(a1),f2(a1)),f334(f334(f259(a1),f334(f76(a1),x74892)),x74891))) % 169.19/169.65 [7908]~E(x79082,f116(f878(x79081)))+E(f334(f196(f878(f878(x79081))),f181(x79081,x79082)),f2(a877))+~P30(a877,f334(f169(a877),f334(f334(f154(f878(x79081),a877),f196(f878(x79081))),x79082))) % 169.19/169.65 [8153]P104(f334(x81531,x81532))+~P104(f334(x81531,f334(a110,f705(x81531,x81532))))+~P104(f334(f334(f336(f886(f885(a877,a877),a871)),x81532),a101)) % 169.19/169.65 [8171]E(x81711,f116(f878(x81712)))+E(f334(f196(f878(x81712)),f334(f334(f165(f878(x81712)),x81711),f2(a877))),f334(f196(f878(f878(x81712))),f181(x81712,x81711)))+~P30(a877,f334(f169(a877),f334(f334(f154(f878(x81712),a877),f196(f878(x81712))),x81711))) % 169.19/169.65 [8856]~P104(f334(f63(x88561),f334(f254(x88561),x88562)))+~P104(f334(f63(x88561),f257(f886(x88561,a871))))+P104(f334(f63(x88561),f334(f254(x88561),f334(f334(f10(a871,a871,x88561),a329),x88562)))) % 169.19/169.65 [8919]E(f334(f334(f269(a877,a877),f334(a115,f334(f334(f40(a877),f334(f334(f3(a877),x89191),x89192)),x89192))),f46(a877,f334(f334(f3(a877),x89191),x89192),x89192)),f86(f885(a877,a877),f49(x89191,x89192)))+~P104(f334(f334(f250(a877),f2(a877)),x89192))+~P104(f334(f334(f249(a877),x89192),x89191)) % 169.19/169.65 [9197]~P104(f334(f63(x91971),f334(f254(x91971),x91972)))+P104(f334(f63(x91971),f257(f886(x91971,a871))))+~P104(f334(f63(x91971),f334(f254(x91971),f334(f334(f10(a871,a871,x91971),a329),x91972)))) % 169.19/169.65 [9899]P22(x98991,x98992)+~P39(x98991,f334(f268(f886(f885(x98991,x98991),a871),f886(f885(x98991,x98991),a871)),x98992))+~P104(f334(f334(f249(f886(f885(x98991,x98991),a871)),f334(f334(f291(x98991,x98991,x98991),f334(f268(f886(f885(x98991,x98991),a871),f886(f885(x98991,x98991),a871)),x98992)),f334(f272(f886(f885(x98991,x98991),a871),f886(f885(x98991,x98991),a871)),x98992))),f334(f268(f886(f885(x98991,x98991),a871),f886(f885(x98991,x98991),a871)),x98992))) % 169.19/169.65 [7273]~P104(f334(f334(f250(a877),f2(a877)),x72732))+P104(f334(f334(f250(a877),x72731),x72732))+E(f334(a115,f334(f334(f40(a877),f334(f334(f3(a877),x72731),x72732)),x72732)),f334(f334(f40(a877),x72731),x72732)) % 169.19/169.65 [7410]~P104(f334(f334(f250(a877),f2(a877)),x74102))+~P104(f334(f334(f249(a877),x74102),x74101))+E(f334(a115,f334(f334(f40(a877),f334(f334(f3(a877),x74101),x74102)),x74102)),f334(f334(f40(a877),x74101),x74102)) % 169.19/169.65 [8378]~P92(x83781)+~P89(x83781)+~P32(x83781,f334(f106(x83781),f334(f334(f3(a1),f334(f334(f81(a1),x83782),x83782)),a100))) % 169.19/169.65 [9106]E(x91061,f2(a877))+E(f334(f334(f273(a877,a877,f885(a877,a877)),f334(f334(f10(a877,f886(a877,f885(a877,a877)),a877),f269(a877,a877)),a115)),f86(f885(a877,a877),f49(f334(f334(f3(a877),x91062),x91061),x91061))),f86(f885(a877,a877),f49(x91062,x91061)))+P104(f334(f334(f250(a877),x91062),x91061)) % 169.19/169.65 [9512]P104(f334(x95122,f791(x95122,x95121)))+P104(f334(x95121,f791(x95122,x95121)))+E(f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x95121)),f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x95122))) % 169.19/169.65 [9516]~P104(f334(x95162,f791(x95162,x95161)))+~P104(f334(x95161,f791(x95162,x95161)))+E(f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x95161)),f334(f254(a1),f334(f334(f20(a1,a871,a871),f334(f334(f10(a871,f886(a871,a871),a1),a332),f334(f249(a1),f2(a1)))),x95162))) % 169.19/169.65 [7626]~P60(x76261)+~P92(x76261)+E(f334(f334(f292(x76261),x76262),f334(f106(x76261),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))),x76262) % 169.19/169.65 [9227]~P92(x92271)+~E(f334(f106(x92271),x92272),f79(x92271))+P32(x92271,f334(f106(x92271),f334(f334(f81(a1),x92272),f334(f80(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [9397]~P136(x93971)+~E(x93972,f79(x93971))+E(f334(f334(f259(x93971),x93972),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f79(x93971)) % 169.19/169.65 [9398]~P136(x93981)+~E(x93982,f2(x93981))+E(f334(f334(f259(x93981),x93982),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f2(x93981)) % 169.19/169.65 [9411]~P136(x94111)+~E(x94112,f334(f80(x94111),f79(x94111)))+E(f334(f334(f259(x94111),x94112),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f79(x94111)) % 169.19/169.65 [9454]~P92(x94541)+E(f334(f106(x94541),x94542),f79(x94541))+~P32(x94541,f334(f106(x94541),f334(f334(f81(a1),x94542),f334(f80(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.19/169.65 [9835]~P120(x98352)+E(x98351,f2(x98352))+P104(f334(f334(f250(x98352),f2(x98352)),f334(f334(f259(x98352),x98351),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.65 [9898]~P120(x98982)+~E(x98981,f2(x98982))+~P104(f334(f334(f250(x98982),f2(x98982)),f334(f334(f259(x98982),x98981),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.19/169.65 [9924]P104(f334(f334(f249(a1),x99241),f2(a1)))+P104(f334(f334(f250(a1),x99242),x99241))+E(f334(f45(x99241),f48(x99242,f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99241))),f48(x99242,x99241)) % 169.19/169.65 [9925]~P104(f334(f334(f250(a1),f2(a1)),x99251))+P104(f334(f334(f250(a1),x99252),x99251))+E(f334(f45(x99251),f48(x99252,f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99251))),f48(x99252,x99251)) % 169.19/169.65 [9926]P104(f334(f334(f249(a1),x99261),f2(a1)))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),x99262),x99261)))+E(f334(f45(x99261),f51(x99262,f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99261))),f51(x99262,x99261)) % 169.19/169.65 [9927]~P104(f334(f334(f250(a1),f2(a1)),x99271))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),x99272),x99271)))+E(f334(f45(x99271),f51(x99272,f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99271))),f51(x99272,x99271)) % 169.19/169.65 [9928]~P142(x99281)+~P104(f334(f334(f249(a1),f2(a1)),x99282))+E(f334(f103(x99281),f334(a107,f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x99282))),f334(f334(f81(x99281),f334(f103(x99281),f334(a107,x99282))),f334(f103(x99281),f334(a107,x99282)))) % 169.19/169.65 [5082]~P145(x50821,x50823,x50822)+~E(x50823,f2(a1))+P104(f334(x50821,x50822)) % 169.19/169.65 [5204]~P107(x52041)+~P30(x52041,x52043)+P30(x52041,f171(x52041,x52042,x52043)) % 169.19/169.65 [5205]~P107(x52051)+~P30(x52051,x52053)+P30(x52051,f178(x52051,x52052,x52053)) % 169.19/169.65 [4783]~P67(x47832)+~E(x47833,f334(f80(x47832),x47831))+E(x47831,f334(f80(x47832),x47833)) % 169.19/169.65 [4785]~P67(x47851)+~E(f334(f80(x47851),x47853),x47852)+E(f334(f80(x47851),x47852),x47853) % 169.19/169.65 [4860]~P79(x48603)+E(x48601,x48602)+~E(f334(f80(x48603),x48601),f334(f80(x48603),x48602)) % 169.19/169.65 [4861]~P67(x48613)+E(x48611,x48612)+~E(f334(f80(x48613),x48611),f334(f80(x48613),x48612)) % 169.19/169.65 [4862]~P94(x48623)+E(x48621,x48622)+~E(f334(f103(x48623),x48621),f334(f103(x48623),x48622)) % 169.19/169.65 [4863]~P89(x48633)+E(x48631,x48632)+~E(f334(f105(x48633),x48631),f334(f105(x48633),x48632)) % 169.19/169.65 [4864]~P107(x48643)+E(x48641,x48642)+~E(f334(f303(x48643),x48641),f334(f303(x48643),x48642)) % 169.19/169.65 [4865]~P107(x48653)+E(x48651,x48652)+~E(f334(f255(x48653),x48651),f334(f255(x48653),x48652)) % 169.19/169.65 [4866]~P107(x48663)+E(x48661,x48662)+~E(f334(f306(x48663),x48661),f334(f306(x48663),x48662)) % 169.19/169.65 [4867]~P107(x48673)+E(x48671,x48672)+~E(f334(f256(x48673),x48671),f334(f256(x48673),x48672)) % 169.19/169.65 [4968]~P58(x49681)+~P104(f334(x49682,x49683))+P104(f334(f59(x49681),x49682)) % 169.19/169.65 [5001]~P58(x50013)+P104(f334(x50011,x50012))+~P104(f334(f60(x50013),x50011)) % 169.19/169.65 [5101]~P146(x51011,x51012,x51013)+~E(x51012,f2(a1))+P104(f334(x51011,f2(a1))) % 169.19/169.65 [5139]~E(x51391,f2(a877))+E(f730(x51391,x51392,x51393),f195(f886(x51393,a871)))+~E(f334(f39(x51393),x51392),f334(a115,x51391)) % 169.19/169.65 [5294]~E(x52942,f2(a877))+E(f334(f268(a877,a877),x52941),f2(a877))+~P104(f334(f49(x52943,x52942),x52941)) % 169.19/169.65 [5343]P104(f334(x53431,x53432))+~E(x53433,f334(f103(a1),x53432))+~P104(f334(x53431,f334(a107,x53433))) % 169.19/169.65 [5816]~E(x58163,f2(a877))+~P104(f334(x58161,x58162))+P104(f334(x58161,f46(a877,x58162,x58163))) % 169.19/169.65 [5947]~P104(f334(a25,x59473))+~P104(f334(a25,x59472))+P104(f334(a25,f31(x59471,x59472,x59473))) % 169.19/169.65 [5979]~P58(x59793)+~P7(x59793,x59791,x59792)+P104(f334(x59791,f654(x59792,x59791,x59793))) % 169.19/169.65 [6036]~P102(x60362)+~P102(x60361)+E(f131(x60361,x60362,f132(x60361,x60363),f132(x60362,x60363)),f132(f885(x60361,x60362),x60363)) % 169.19/169.65 [6222]~E(x62223,f2(a877))+P104(f334(x62221,x62222))+~P104(f334(x62221,f46(a877,x62222,x62223))) % 169.19/169.65 [6370]~P58(x63701)+P8(x63701,x63702,x63703)+~P104(f334(x63702,f655(x63703,x63702,x63701))) % 169.19/169.65 [6897]E(x68971,f2(a877))+~P104(f334(x68972,f352(x68971,x68973,x68972)))+P104(f334(x68972,f46(a877,x68973,x68971))) % 169.19/169.65 [7003]~P28(x70031)+~P104(f334(f334(f249(x70031),x70032),f440(x70033,x70032,x70031)))+P104(f334(f334(f249(x70031),x70032),f42(x70031,x70033))) % 169.19/169.65 [7005]~P104(f334(x70051,x70052))+~P104(f334(x70051,f352(x70053,x70052,x70051)))+P104(f334(x70051,f46(a877,x70052,x70053))) % 169.19/169.65 [7107]E(x71071,f116(x71072))+E(f334(f334(f151(x71072),f620(x71073,x71071,x71072)),f629(x71073,x71071,x71072)),x71071)+~P104(f334(f334(f336(f878(x71072)),x71071),f161(x71072,x71073))) % 169.19/169.65 [7138]~P137(x71381)+~P104(f334(f334(f336(x71381),x71382),f112(x71381)))+P104(f334(f334(f336(x71381),f334(f334(f259(x71381),x71382),x71383)),f112(x71381))) % 169.19/169.65 [7459]P39(x74591,x74592)+~P104(f334(f334(f336(x74591),x74593),f759(x74592,x74591)))+P104(f334(f334(f336(x74591),f788(x74592,x74591,x74593)),f759(x74592,x74591))) % 169.19/169.65 [7730]E(x77301,f116(x77302))+~P104(f334(f334(f336(f878(x77302)),x77301),f161(x77302,x77303)))+P104(f334(f334(f336(f878(x77302)),f629(x77303,x77301,x77302)),f161(x77302,x77303))) % 169.19/169.65 [7783]E(x77831,f2(a877))+E(f334(f334(f81(a877),f334(f334(f82(a877),x77831),f354(x77831,x77832,x77833))),f352(x77831,x77832,x77833)),x77832)+P104(f334(x77833,f46(a877,x77832,x77831))) % 169.19/169.65 [7826]~P104(f334(x78263,x78262))+E(f334(f334(f81(a877),f334(f334(f82(a877),x78261),f354(x78261,x78262,x78263))),f352(x78261,x78262,x78263)),x78262)+P104(f334(x78263,f46(a877,x78262,x78261))) % 169.19/169.65 [7963]P104(f334(f334(f250(a1),x79631),f346(x79632,x79633,x79631)))+P104(f334(f334(x79633,f334(f334(f40(a1),x79632),x79631)),f46(a1,x79632,x79631)))+~P104(f334(f334(f250(a1),x79631),f2(a1))) % 169.19/169.65 [8232]P104(f334(f334(x82322,f334(f334(f40(a1),x82321),x82323)),f46(a1,x82321,x82323)))+~P104(f334(f334(f250(a1),x82323),f2(a1)))+P104(f334(f334(f249(a1),f346(x82321,x82322,x82323)),f2(a1))) % 169.19/169.65 [8411]E(f334(f334(f81(a1),f334(f334(f82(a1),x84111),f349(x84112,x84113,x84111))),f346(x84112,x84113,x84111)),x84112)+P104(f334(f334(x84113,f334(f334(f40(a1),x84112),x84111)),f46(a1,x84112,x84111)))+~P104(f334(f334(f250(a1),x84111),f2(a1))) % 169.19/169.65 [8640]~P104(f334(f334(x86401,f349(x86402,x86401,x86403)),f346(x86402,x86401,x86403)))+P104(f334(f334(x86401,f334(f334(f40(a1),x86402),x86403)),f46(a1,x86402,x86403)))+~P104(f334(f334(f250(a1),x86403),f2(a1))) % 169.19/169.65 [8866]~P107(x88661)+~P30(x88661,x88663)+P30(x88661,f149(x88661,x88661,f7(x88661),x88662,x88663)) % 169.19/169.65 [9349]~P123(x93492)+E(x93491,f2(x93492))+~P104(f334(f334(f249(x93492),f334(f334(f81(x93492),f334(f334(f82(x93492),x93493),x93493)),f334(f334(f82(x93492),x93491),x93491))),f2(x93492))) % 169.19/169.65 [9350]~P123(x93502)+E(x93501,f2(x93502))+~P104(f334(f334(f249(x93502),f334(f334(f81(x93502),f334(f334(f82(x93502),x93501),x93501)),f334(f334(f82(x93502),x93503),x93503))),f2(x93502))) % 169.19/169.65 [10114]~P120(x101141)+~P104(f334(f334(f250(x101141),x101142),f2(x101141)))+P104(f334(f334(f250(x101141),f334(f334(f259(x101141),x101142),f334(a115,f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x101143)))),f2(x101141))) % 169.19/169.65 [10123]~P120(x101232)+E(x101231,f2(x101232))+~P104(f334(f334(f249(x101232),f334(f334(f81(x101232),f334(f334(f259(x101232),x101233),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x101232),x101231),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f2(x101232))) % 169.19/169.65 [10124]~P120(x101242)+E(x101241,f2(x101242))+~P104(f334(f334(f249(x101242),f334(f334(f81(x101242),f334(f334(f259(x101242),x101241),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x101242),x101243),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f2(x101242))) % 169.19/169.65 [4817]~E(x48172,x48173)+~P64(x48171)+E(f334(f334(f3(x48171),x48172),x48173),f2(x48171)) % 169.19/169.65 [4818]~E(x48182,x48183)+~P67(x48181)+E(f334(f334(f3(x48181),x48182),x48183),f2(x48181)) % 169.19/169.65 [4831]~P138(x48311)+~E(x48313,f2(x48311))+E(f334(f334(f81(x48311),x48312),x48313),x48312) % 169.19/169.65 [4846]~P140(x48461)+~E(x48463,f2(x48461))+E(f334(f334(f82(x48461),x48462),x48463),f2(x48461)) % 169.19/169.65 [4847]~P140(x48471)+~E(x48472,f2(x48471))+E(f334(f334(f82(x48471),x48472),x48473),f2(x48471)) % 169.19/169.65 [4869]~E(x48693,f116(x48691))+~E(x48692,f116(x48691))+E(f334(f334(f134(x48691),x48692),x48693),f116(x48691)) % 169.19/169.65 [4958]~P138(x49582)+E(x49581,f2(x49582))+~E(f334(f334(f81(x49582),x49583),x49581),x49583) % 169.19/169.65 [4959]~P67(x49591)+~E(x49592,f334(f80(x49591),x49593))+E(f334(f334(f81(x49591),x49592),x49593),f2(x49591)) % 169.19/169.65 [4966]E(x49661,f116(x49662))+E(x49663,f2(a877))+~E(f334(f334(f176(x49662),x49663),x49661),f116(x49662)) % 169.19/169.65 [4972]~P64(x49723)+E(x49721,x49722)+~E(f334(f334(f3(x49723),x49721),x49722),f2(x49723)) % 169.19/169.65 [4973]~P67(x49733)+E(x49731,x49732)+~E(f334(f334(f3(x49733),x49731),x49732),f2(x49733)) % 169.19/169.65 [4982]~P136(x49822)+E(x49821,f2(x49822))+~E(f334(f334(f259(x49822),x49821),x49823),f2(x49822)) % 169.19/169.65 [4983]~P97(x49832)+E(x49831,f195(x49832))+~E(f334(f334(f113(x49832),x49833),x49831),f195(x49832)) % 169.19/169.65 [4984]~P97(x49842)+E(x49841,f195(x49842))+~E(f334(f334(f113(x49842),x49841),x49843),f195(x49842)) % 169.19/169.65 [4985]~P96(x49852)+E(x49851,f257(x49852))+~E(f334(f334(f104(x49852),x49853),x49851),f257(x49852)) % 169.19/169.65 [4986]~P96(x49862)+E(x49861,f257(x49862))+~E(f334(f334(f104(x49862),x49861),x49863),f257(x49862)) % 169.19/169.65 [5052]~P67(x50522)+E(x50521,f334(f80(x50522),x50523))+~E(f334(f334(f81(x50522),x50521),x50523),f2(x50522)) % 169.19/169.65 [5053]~P67(x50531)+E(f334(f80(x50531),x50532),x50533)+~E(f334(f334(f81(x50531),x50532),x50533),f2(x50531)) % 169.19/169.65 [5055]~E(x50552,x50553)+~P105(x50551)+P104(f334(f334(f249(x50551),x50552),x50553)) % 169.19/169.65 [5057]~E(x50572,x50573)+~P108(x50571)+P104(f334(f334(f249(x50571),x50572),x50573)) % 169.19/169.65 [5058]~E(x50582,x50583)+~P91(x50581)+P104(f334(f334(f92(x50581),x50582),x50583)) % 169.19/169.65 [5155]~P110(x51551)+~E(x51552,f334(f80(x51551),x51553))+E(f334(f334(f82(x51551),x51552),x51552),f334(f334(f82(x51551),x51553),x51553)) % 169.19/169.65 [5163]~P107(x51631)+~P30(x51631,x51633)+P30(x51631,f334(f334(f176(x51631),x51632),x51633)) % 169.19/169.65 [5164]~P107(x51641)+~P30(x51641,x51643)+P30(x51641,f334(f334(f138(x51641),x51642),x51643)) % 169.19/169.65 [5202]E(x52021,x52022)+E(x52023,f2(a877))+~E(f334(f334(f82(a877),x52023),x52021),f334(f334(f82(a877),x52023),x52022)) % 169.19/169.65 [5203]E(x52031,x52032)+E(x52033,f2(a877))+~E(f334(f334(f82(a877),x52031),x52033),f334(f334(f82(a877),x52032),x52033)) % 169.19/169.65 [5285]~E(x52852,x52853)+~P108(x52851)+E(f305(x52851,x52852,x52853),f334(f334(f312(x52851),x52852),f195(f886(x52851,a871)))) % 169.19/169.65 [5330]E(x53301,x53302)+~P91(x53303)+~P104(f334(f334(f92(x53303),x53301),x53302)) % 169.19/169.65 [5341]~E(x53411,x53412)+~P107(x53413)+~P104(f334(f334(f250(x53413),x53411),x53412)) % 169.19/169.65 [5342]~E(x53421,x53422)+~P108(x53423)+~P104(f334(f334(f250(x53423),x53421),x53422)) % 169.19/169.65 [5352]~P108(x53521)+E(f334(f304(x53521,x53522),x53523),f195(f886(x53521,a871)))+P104(f334(f334(f250(x53521),x53522),x53523)) % 169.19/169.65 [5399]~P108(x53991)+E(f305(x53991,x53992,x53993),f195(f886(x53991,a871)))+P104(f334(f334(f249(x53991),x53992),x53993)) % 169.19/169.65 [5400]~P108(x54001)+E(f307(x54001,x54002,x54003),f195(f886(x54001,a871)))+P104(f334(f334(f250(x54001),x54002),x54003)) % 169.19/169.65 [5401]~P108(x54011)+E(f195(f886(x54011,a871)),f305(x54011,x54012,x54013))+P104(f334(f334(f249(x54011),x54012),x54013)) % 169.19/169.65 [5402]~P108(x54021)+E(f195(f886(x54021,a871)),f307(x54021,x54022,x54023))+P104(f334(f334(f250(x54021),x54022),x54023)) % 169.19/169.65 [5410]~P100(x54101)+~E(f334(f334(f113(x54101),x54102),x54103),x54103)+P104(f334(f334(f249(x54101),x54102),x54103)) % 169.19/169.65 [5411]~P101(x54111)+~E(f334(f334(f104(x54111),x54112),x54113),x54112)+P104(f334(f334(f249(x54111),x54112),x54113)) % 169.19/169.65 [5412]~P107(x54121)+~E(f334(f334(f247(x54121),x54122),x54123),x54122)+P104(f334(f334(f249(x54121),x54122),x54123)) % 169.19/169.65 [5413]~P107(x54131)+~E(f334(f334(f248(x54131),x54132),x54133),x54133)+P104(f334(f334(f249(x54131),x54132),x54133)) % 169.19/169.65 [5433]~P107(x54331)+P30(x54331,x54332)+~P30(x54331,f334(f334(f151(x54331),x54333),x54332)) % 169.19/169.65 [5434]~P107(x54341)+P30(x54341,x54342)+~P30(x54341,f334(f334(f134(x54341),x54343),x54342)) % 169.19/169.65 [5435]~P107(x54351)+P30(x54351,x54352)+~P30(x54351,f334(f334(f134(x54351),x54352),x54353)) % 169.19/169.65 [5500]~P107(x55001)+P104(f334(f334(f249(x55001),x55003),x55002))+P104(f334(f334(f249(x55001),x55002),x55003)) % 169.19/169.65 [5505]~P107(x55051)+P104(f334(f334(f250(x55051),x55053),x55052))+P104(f334(f334(f249(x55051),x55052),x55053)) % 169.19/169.65 [5543]~P100(x55431)+E(f334(f334(f113(x55431),x55432),x55433),x55432)+~P104(f334(f334(f249(x55431),x55433),x55432)) % 169.19/169.65 [5545]~P100(x55451)+E(f334(f334(f113(x55451),x55452),x55453),x55453)+~P104(f334(f334(f249(x55451),x55452),x55453)) % 169.19/169.65 [5546]~P101(x55461)+E(f334(f334(f104(x55461),x55462),x55463),x55463)+~P104(f334(f334(f249(x55461),x55463),x55462)) % 169.19/169.65 [5548]~P101(x55481)+E(f334(f334(f104(x55481),x55482),x55483),x55482)+~P104(f334(f334(f249(x55481),x55482),x55483)) % 169.19/169.65 [5549]~P107(x55491)+E(f334(f334(f247(x55491),x55492),x55493),x55493)+~P104(f334(f334(f249(x55491),x55493),x55492)) % 169.19/169.65 [5551]~P107(x55511)+E(f334(f334(f247(x55511),x55512),x55513),x55512)+~P104(f334(f334(f249(x55511),x55512),x55513)) % 169.19/169.65 [5552]~P107(x55521)+E(f334(f334(f248(x55521),x55522),x55523),x55522)+~P104(f334(f334(f249(x55521),x55523),x55522)) % 169.19/169.65 [5554]~P107(x55541)+E(f334(f334(f248(x55541),x55542),x55543),x55543)+~P104(f334(f334(f249(x55541),x55542),x55543)) % 169.19/169.65 [5561]~P117(x55612)+E(x55611,f2(x55612))+E(f334(f334(f292(x55612),f334(f80(x55612),x55613)),f334(f80(x55612),x55611)),f334(f334(f292(x55612),x55613),x55611)) % 169.19/169.65 [5608]~P108(x56081)+E(f334(f304(x56081,x56082),x56083),f195(f886(x56081,a871)))+~P104(f334(f334(f249(x56081),x56083),x56082)) % 169.19/169.65 [5640]~P108(x56401)+E(f308(x56401,x56402,x56403),f195(f886(x56401,a871)))+~P104(f334(f334(f249(x56401),x56403),x56402)) % 169.19/169.65 [5641]~P108(x56411)+E(f305(x56411,x56412,x56413),f195(f886(x56411,a871)))+~P104(f334(f334(f250(x56411),x56413),x56412)) % 169.19/169.65 [5642]~P108(x56421)+E(f307(x56421,x56422,x56423),f195(f886(x56421,a871)))+~P104(f334(f334(f249(x56421),x56423),x56422)) % 169.19/169.65 [5693]~E(f334(f334(f3(a877),x56931),x56933),x56932)+E(x56931,f334(f334(f81(a877),x56932),x56933))+~P104(f334(f334(f249(a877),x56933),x56931)) % 169.19/169.65 [5694]~E(x56941,f334(f334(f81(a877),x56943),x56942))+E(f334(f334(f3(a877),x56941),x56942),x56943)+~P104(f334(f334(f249(a877),x56942),x56941)) % 169.19/169.65 [5740]~P104(f334(x57401,x57403))+P104(f334(x57401,f365(x57401,x57402)))+~P104(f334(f334(f249(a877),x57403),x57402)) % 169.19/169.65 [5741]~P104(f334(x57411,x57413))+P104(f334(x57411,f408(x57411,x57412)))+~P104(f334(f334(f250(a877),x57413),x57412)) % 169.19/169.65 [5749]~P108(x57491)+~E(f334(f304(x57491,x57492),x57493),f195(f886(x57491,a871)))+~P104(f334(f334(f250(x57491),x57492),x57493)) % 169.19/169.65 [5754]~P105(x57541)+~P104(f334(f334(f250(x57541),x57542),x57543))+P104(f334(f334(f249(x57541),x57542),x57543)) % 169.19/169.65 [5756]~P108(x57561)+~P104(f334(f334(f250(x57561),x57562),x57563))+P104(f334(f334(f249(x57561),x57562),x57563)) % 169.19/169.65 [5864]~P108(x58641)+~E(f305(x58641,x58642,x58643),f195(f886(x58641,a871)))+~P104(f334(f334(f249(x58641),x58642),x58643)) % 169.19/169.65 [5865]~P108(x58651)+~E(f307(x58651,x58652,x58653),f195(f886(x58651,a871)))+~P104(f334(f334(f250(x58651),x58652),x58653)) % 169.19/169.65 [5866]~P108(x58661)+~E(f195(f886(x58661,a871)),f305(x58661,x58662,x58663))+~P104(f334(f334(f249(x58661),x58662),x58663)) % 169.19/169.65 [5867]~P108(x58671)+~E(f195(f886(x58671,a871)),f307(x58671,x58672,x58673))+~P104(f334(f334(f250(x58671),x58672),x58673)) % 169.19/169.65 [5875]P104(f334(x58751,x58752))+~P104(f334(x58751,f366(x58751,x58753)))+~P104(f334(f334(f249(a877),x58752),x58753)) % 169.19/169.65 [5876]P104(f334(x58761,x58762))+~P104(f334(x58761,f409(x58761,x58763)))+~P104(f334(f334(f250(a877),x58762),x58763)) % 169.19/169.65 [5884]~E(x58841,f334(a115,x58843))+P104(f334(f334(f250(a877),x58841),f334(a115,x58842)))+~P104(f334(f334(f250(a877),x58843),x58842)) % 169.19/169.65 [5900]E(x59001,x59002)+~E(f334(f334(f82(a877),x59003),x59001),f334(f334(f82(a877),x59003),x59002))+~P104(f334(f334(f250(a877),f2(a877)),x59003)) % 169.19/169.65 [5958]E(f334(x59581,f835(x59581,x59582,x59583)),f79(a877))+~E(f334(f334(f8(x59583,a877),x59581),x59582),f79(a877))+~P104(f334(f63(x59583),x59582)) % 169.19/169.65 [5970]~P28(x59701)+P104(f334(f334(f249(x59701),x59702),f41(x59701,x59703)))+~P104(f334(f334(f336(x59701),x59702),x59703)) % 169.19/169.65 [5996]~P105(x59961)+~P104(f334(f334(f250(x59961),x59963),x59962))+~P104(f334(f334(f249(x59961),x59962),x59963)) % 169.19/169.65 [6000]~P105(x60001)+~P104(f334(f334(f250(x60001),x60003),x60002))+~P104(f334(f334(f250(x60001),x60002),x60003)) % 169.19/169.65 [6003]~P107(x60031)+~P104(f334(f334(f250(x60031),x60033),x60032))+~P104(f334(f334(f249(x60031),x60032),x60033)) % 169.19/169.65 [6004]~P107(x60041)+~P104(f334(f334(f250(x60041),x60043),x60042))+~P104(f334(f334(f250(x60041),x60042),x60043)) % 169.19/169.65 [6005]~P108(x60051)+~P104(f334(f334(f250(x60051),x60053),x60052))+~P104(f334(f334(f250(x60051),x60052),x60053)) % 169.19/169.66 [6030]~E(f334(x60302,f836(x60302,x60303,x60301)),f2(a877))+E(f334(f334(f8(x60301,a877),x60302),x60303),f2(a877))+~P104(f334(f63(x60301),x60303)) % 169.19/169.66 [6031]~E(f334(x60312,f840(x60312,x60313,x60311)),f79(a877))+E(f334(f334(f11(x60311,a877),x60312),x60313),f79(a877))+~P104(f334(f63(x60311),x60313)) % 169.19/169.66 [6047]~P106(x60471)+~P104(f334(f334(f250(x60471),x60473),x60472))+P104(f334(f334(f336(x60471),x60472),f334(f306(x60471),x60473))) % 169.19/169.66 [6048]~P106(x60481)+~P104(f334(f334(f249(x60481),x60483),x60482))+P104(f334(f334(f336(x60481),x60482),f334(f256(x60481),x60483))) % 169.19/169.66 [6049]~P106(x60491)+~P104(f334(f334(f249(x60491),x60492),x60493))+P104(f334(f334(f336(x60491),x60492),f334(f303(x60491),x60493))) % 169.19/169.66 [6050]~P106(x60501)+~P104(f334(f334(f250(x60501),x60502),x60503))+P104(f334(f334(f336(x60501),x60502),f334(f255(x60501),x60503))) % 169.19/169.66 [6062]E(f334(x60621,f838(x60621,x60622,x60623)),f334(a115,f2(a877)))+~E(f334(f334(f8(x60623,a877),x60621),x60622),f334(a115,f2(a877)))+~P104(f334(f63(x60623),x60622)) % 169.19/169.66 [6145]~P28(x61451)+~P104(f334(f334(f336(x61451),x61453),x61452))+P104(f334(f334(f249(x61451),f42(x61451,x61452)),x61453)) % 169.19/169.66 [6162]~P104(f334(f334(f249(a877),x61621),x61623))+P104(f334(f334(f249(a877),x61621),x61622))+~P104(f334(f334(f249(a877),x61623),x61622)) % 169.19/169.66 [6163]~P104(f334(f334(f249(a1),x61631),x61633))+P104(f334(f334(f249(a1),x61631),x61632))+~P104(f334(f334(f249(a1),x61633),x61632)) % 169.19/169.66 [6180]~P106(x61801)+~P104(f334(f334(f336(x61801),x61803),f334(f256(x61801),x61802)))+P104(f334(f334(f249(x61801),x61802),x61803)) % 169.19/169.66 [6181]~P106(x61811)+~P104(f334(f334(f336(x61811),x61812),f334(f303(x61811),x61813)))+P104(f334(f334(f249(x61811),x61812),x61813)) % 169.19/169.66 [6182]~P106(x61821)+~P104(f334(f334(f336(x61821),x61823),f334(f306(x61821),x61822)))+P104(f334(f334(f250(x61821),x61822),x61823)) % 169.19/169.66 [6183]~P106(x61831)+~P104(f334(f334(f336(x61831),x61832),f334(f255(x61831),x61833)))+P104(f334(f334(f250(x61831),x61832),x61833)) % 169.19/169.66 [6406]~P61(x64061)+P104(f334(f334(f250(x64061),f2(x64061)),f854(x64063,x64062,x64061)))+P104(f334(f334(f249(x64061),x64062),x64063)) % 169.19/169.66 [6407]~P62(x64071)+P104(f334(f334(f250(x64071),f2(x64071)),f452(x64073,x64072,x64071)))+P104(f334(f334(f249(x64071),x64072),x64073)) % 169.19/169.66 [6474]~P75(x64741)+~P104(f334(f334(f249(x64741),x64743),f334(f80(x64741),x64742)))+P104(f334(f334(f249(x64741),x64742),f334(f80(x64741),x64743))) % 169.19/169.66 [6476]~P75(x64761)+~P104(f334(f334(f250(x64761),x64763),f334(f80(x64761),x64762)))+P104(f334(f334(f250(x64761),x64762),f334(f80(x64761),x64763))) % 169.19/169.66 [6488]~P104(f334(f334(f250(a877),x64881),x64883))+~P104(f334(f334(f250(a877),x64883),x64882))+P104(f334(f334(f250(a877),f334(a115,x64881)),x64882)) % 169.19/169.66 [6514]~P119(x65141)+P104(f334(f334(f249(x65141),f334(f103(x65141),x65142)),f334(f103(x65141),x65143)))+~P104(f334(f334(f249(a877),x65142),x65143)) % 169.19/169.66 [6515]~P120(x65151)+P104(f334(f334(f249(x65151),f334(f105(x65151),x65152)),f334(f105(x65151),x65153)))+~P104(f334(f334(f249(a1),x65152),x65153)) % 169.19/169.66 [6517]~P120(x65171)+P104(f334(f334(f250(x65171),f334(f105(x65171),x65172)),f334(f105(x65171),x65173)))+~P104(f334(f334(f250(a1),x65172),x65173)) % 169.19/169.66 [6518]~P119(x65181)+P104(f334(f334(f250(x65181),f334(f103(x65181),x65182)),f334(f103(x65181),x65183)))+~P104(f334(f334(f250(a877),x65182),x65183)) % 169.19/169.66 [6524]~P107(x65241)+E(f334(f334(f113(f886(x65241,a871)),f334(f255(x65241),x65242)),f334(f304(x65241,x65242),x65243)),f334(f255(x65241),x65243))+~P104(f334(f334(f249(x65241),x65242),x65243)) % 169.19/169.66 [6554]~P75(x65541)+~P104(f334(f334(f249(x65541),x65543),x65542))+P104(f334(f334(f249(x65541),f334(f80(x65541),x65542)),f334(f80(x65541),x65543))) % 169.19/169.66 [6556]~P79(x65561)+~P104(f334(f334(f249(x65561),x65563),x65562))+P104(f334(f334(f249(x65561),f334(f80(x65561),x65562)),f334(f80(x65561),x65563))) % 169.19/169.66 [6557]~P75(x65571)+~P104(f334(f334(f250(x65571),x65573),x65572))+P104(f334(f334(f250(x65571),f334(f80(x65571),x65572)),f334(f80(x65571),x65573))) % 169.19/169.66 [6589]~P107(x65891)+E(f334(f334(f113(f886(x65891,a871)),f334(f303(x65891),x65892)),f308(x65891,x65892,x65893)),f334(f255(x65891),x65893))+~P104(f334(f334(f250(x65891),x65892),x65893)) % 169.19/169.66 [6590]~P107(x65901)+E(f334(f334(f113(f886(x65901,a871)),f334(f303(x65901),x65902)),f307(x65901,x65902,x65903)),f334(f303(x65901),x65903))+~P104(f334(f334(f249(x65901),x65902),x65903)) % 169.19/169.66 [6591]~P107(x65911)+E(f334(f334(f113(f886(x65911,a871)),f334(f255(x65911),x65912)),f305(x65911,x65912,x65913)),f334(f303(x65911),x65913))+~P104(f334(f334(f249(x65911),x65912),x65913)) % 169.19/169.66 [6625]~P107(x66251)+E(f334(f334(f113(f886(x66251,a871)),f334(f304(x66251,x66252),x66253)),f334(f256(x66251),x66253)),f334(f256(x66251),x66252))+~P104(f334(f334(f249(x66251),x66252),x66253)) % 169.19/169.66 [6779]~P107(x67791)+E(f334(f334(f113(f886(x67791,a871)),f308(x67791,x67792,x67793)),f334(f256(x67791),x67793)),f334(f306(x67791),x67792))+~P104(f334(f334(f250(x67791),x67792),x67793)) % 169.19/169.66 [6780]~P107(x67801)+E(f334(f334(f113(f886(x67801,a871)),f305(x67801,x67802,x67803)),f334(f306(x67801),x67803)),f334(f256(x67801),x67802))+~P104(f334(f334(f249(x67801),x67802),x67803)) % 169.19/169.66 [6781]~P107(x67811)+E(f334(f334(f113(f886(x67811,a871)),f307(x67811,x67812,x67813)),f334(f306(x67811),x67813)),f334(f306(x67811),x67812))+~P104(f334(f334(f249(x67811),x67812),x67813)) % 169.19/169.66 [6799]P104(f334(x67991,x67992))+~P104(f334(f334(f249(a877),x67992),x67993))+P104(f334(f334(f336(a877),f366(x67991,x67993)),f305(a877,f2(a877),x67993))) % 169.19/169.66 [6833]E(x68331,x68332)+~E(f334(f334(f165(x68333),x68331),f577(x68333,x68332,x68331)),f334(f334(f165(x68333),x68332),f577(x68333,x68332,x68331)))+~E(f334(f196(f878(x68333)),x68331),f334(f196(f878(x68333)),x68332)) % 169.19/169.66 [6838]~E(x68383,f334(f334(f40(a877),x68381),x68382))+~P104(f334(f334(f250(a877),f2(a877)),x68382))+P104(f334(f334(f250(a877),x68381),f334(f334(f82(a877),x68382),f334(a115,x68383)))) % 169.19/169.66 [6855]~P104(f334(x68551,x68553))+~P104(f334(f334(f249(a877),x68553),x68552))+P104(f334(f334(f336(a877),f365(x68551,x68552)),f305(a877,f2(a877),x68552))) % 169.19/169.66 [6894]~P104(f334(x68941,x68943))+P104(f334(x68941,f392(x68941,x68942)))+~P104(f334(f334(f336(a877),x68943),f305(a877,f2(a877),x68942))) % 169.19/169.66 [6913]~P119(x69133)+~P104(f334(f334(f249(x69133),f334(f103(x69133),x69131)),f334(f103(x69133),x69132)))+P104(f334(f334(f249(a877),x69131),x69132)) % 169.19/169.66 [6914]~P120(x69143)+~P104(f334(f334(f249(x69143),f334(f105(x69143),x69141)),f334(f105(x69143),x69142)))+P104(f334(f334(f249(a1),x69141),x69142)) % 169.19/169.66 [6916]~P119(x69163)+~P104(f334(f334(f250(x69163),f334(f103(x69163),x69161)),f334(f103(x69163),x69162)))+P104(f334(f334(f250(a877),x69161),x69162)) % 169.19/169.66 [6917]~P120(x69173)+~P104(f334(f334(f250(x69173),f334(f105(x69173),x69171)),f334(f105(x69173),x69172)))+P104(f334(f334(f250(a1),x69171),x69172)) % 169.19/169.66 [6934]~P119(x69341)+~P104(f334(f334(f250(x69341),f79(x69341)),x69342))+P104(f334(f334(f250(x69341),f79(x69341)),f334(f334(f259(x69341),x69342),f334(a115,x69343)))) % 169.19/169.66 [6936]~P75(x69361)+~P104(f334(f334(f249(x69361),f334(f80(x69361),x69363)),f334(f80(x69361),x69362)))+P104(f334(f334(f249(x69361),x69362),x69363)) % 169.19/169.66 [6937]~P79(x69371)+~P104(f334(f334(f249(x69371),f334(f80(x69371),x69373)),f334(f80(x69371),x69372)))+P104(f334(f334(f249(x69371),x69372),x69373)) % 169.19/169.66 [6938]~P75(x69381)+~P104(f334(f334(f250(x69381),f334(f80(x69381),x69383)),f334(f80(x69381),x69382)))+P104(f334(f334(f250(x69381),x69382),x69383)) % 169.19/169.66 [6962]P104(f334(x69621,x69622))+~P104(f334(x69621,f367(x69621,x69623)))+~P104(f334(f334(f336(a877),x69622),f305(a877,f2(a877),x69623))) % 169.19/169.66 [6981]~P61(x69811)+P104(f334(f334(f250(x69811),f854(x69813,x69812,x69811)),f79(x69811)))+P104(f334(f334(f249(x69811),x69812),x69813)) % 169.19/169.66 [7000]~E(f46(a877,x70003,x70002),f46(a877,x70001,x70002))+E(f334(f334(f81(a877),x70001),f334(f334(f82(a877),x70002),f357(x70001,x70002,x70003))),x70003)+~P104(f334(f334(f249(a877),x70001),x70003)) % 169.19/169.66 [7019]E(f334(x70191,f424(x70191,x70192,x70193)),f198(x70192))+~P104(f334(f63(x70193),f185(x70193,x70192,x70191)))+P104(f334(f63(x70193),f257(f886(x70193,a871)))) % 169.19/169.66 [7058]E(f334(f334(f8(x70581,a877),x70582),x70583),f2(a877))+~P104(f334(f63(x70581),x70583))+P104(f334(f334(f336(x70581),f836(x70582,x70583,x70581)),x70583)) % 169.19/169.66 [7059]E(f334(f334(f11(x70591,a877),x70592),x70593),f79(a877))+~P104(f334(f63(x70591),x70593))+P104(f334(f334(f336(x70591),f840(x70592,x70593,x70591)),x70593)) % 169.19/169.66 [7081]~P108(x70811)+~P104(f334(f334(f249(x70811),x70812),x70813))+P104(f334(f334(f249(f886(x70811,a871)),f334(f303(x70811),x70812)),f334(f303(x70811),x70813))) % 169.19/169.66 [7082]~P107(x70821)+~P104(f334(f334(f249(x70821),x70822),x70823))+P104(f334(f334(f249(f886(x70821,a871)),f334(f255(x70821),x70822)),f334(f255(x70821),x70823))) % 169.19/169.66 [7083]~P107(x70831)+~P104(f334(f334(f249(x70831),x70833),x70832))+P104(f334(f334(f249(f886(x70831,a871)),f334(f306(x70831),x70832)),f334(f306(x70831),x70833))) % 169.19/169.66 [7084]~P108(x70841)+~P104(f334(f334(f249(x70841),x70843),x70842))+P104(f334(f334(f249(f886(x70841,a871)),f334(f256(x70841),x70842)),f334(f256(x70841),x70843))) % 169.19/169.66 [7085]~P107(x70851)+~P104(f334(f334(f250(x70851),x70852),x70853))+P104(f334(f334(f250(f886(x70851,a871)),f334(f255(x70851),x70852)),f334(f255(x70851),x70853))) % 169.19/169.66 [7093]~P28(x70931)+P104(f334(f334(f249(x70931),x70932),f42(x70931,x70933)))+P104(f334(f334(f336(x70931),f440(x70933,x70932,x70931)),x70933)) % 169.19/169.66 [7099]~P75(x70991)+P104(f334(f334(f249(x70991),f334(f334(f3(x70991),x70992),x70993)),f2(x70991)))+~P104(f334(f334(f249(x70991),x70992),x70993)) % 169.19/169.66 [7100]~P75(x71001)+P104(f334(f334(f250(x71001),f334(f334(f3(x71001),x71002),x71003)),f2(x71001)))+~P104(f334(f334(f250(x71001),x71002),x71003)) % 169.19/169.66 [7142]P104(f334(x71421,x71422))+P104(f334(f334(f249(a877),f367(x71421,x71423)),x71423))+~P104(f334(f334(f336(a877),x71422),f305(a877,f2(a877),x71423))) % 169.19/169.66 [7182]~E(f334(f334(f8(x71821,a877),x71822),x71823),f79(a877))+~P104(f334(f63(x71821),x71823))+P104(f334(f334(f336(x71821),f835(x71822,x71823,x71821)),x71823)) % 169.19/169.66 [7183]~P104(f334(x71831,x71833))+P104(f334(f334(f249(a877),f392(x71831,x71832)),x71832))+~P104(f334(f334(f336(a877),x71833),f305(a877,f2(a877),x71832))) % 169.19/169.66 [7223]~P28(x72231)+P104(f334(f334(f336(x72231),f416(x72233,x72232,x72231)),x72232))+P104(f334(f334(f249(x72231),f41(x72231,x72232)),x72233)) % 169.19/169.66 [7254]~E(f334(f334(f8(x72541,a877),x72542),x72543),f334(a115,f2(a877)))+~P104(f334(f63(x72541),x72543))+P104(f334(f334(f336(x72541),f838(x72542,x72543,x72541)),x72543)) % 169.19/169.66 [7265]E(x72651,f2(a877))+P104(f334(x72652,f46(a877,x72653,x72651)))+P104(f334(f334(f250(a877),f352(x72651,x72653,x72652)),x72651)) % 169.19/169.66 [7373]~P104(f334(x73731,x73732))+P104(f334(x73731,f46(a877,x73732,x73733)))+P104(f334(f334(f250(a877),f352(x73733,x73732,x73731)),x73733)) % 169.19/169.66 [7493]E(x74931,f116(x74932))+~P104(f334(f334(f336(f878(x74932)),x74931),f161(x74932,x74933)))+P104(f334(f334(f336(x74932),f620(x74933,x74931,x74932)),x74933)) % 169.19/169.66 [7515]~P107(x75151)+E(f334(f334(f113(f886(x75151,a871)),f334(f334(f312(x75151),x75152),f195(f886(x75151,a871)))),f308(x75151,x75152,x75153)),f334(f304(x75151,x75152),x75153))+~P104(f334(f334(f250(x75151),x75152),x75153)) % 169.19/169.66 [7541]~P107(x75411)+E(f334(f334(f113(f886(x75411,a871)),f334(f334(f312(x75411),x75412),f195(f886(x75411,a871)))),f307(x75411,x75412,x75413)),f305(x75411,x75412,x75413))+~P104(f334(f334(f249(x75411),x75412),x75413)) % 169.19/169.66 [7648]~P107(x76481)+P104(f334(f334(f249(x76481),x76482),x76483))+~P104(f334(f334(f249(f886(x76481,a871)),f334(f306(x76481),x76483)),f334(f306(x76481),x76482))) % 169.19/169.66 [7649]~P108(x76491)+P104(f334(f334(f249(x76491),x76492),x76493))+~P104(f334(f334(f249(f886(x76491,a871)),f334(f256(x76491),x76493)),f334(f256(x76491),x76492))) % 169.19/169.66 [7650]~P107(x76501)+P104(f334(f334(f249(x76501),x76502),x76503))+~P104(f334(f334(f249(f886(x76501,a871)),f334(f255(x76501),x76502)),f334(f255(x76501),x76503))) % 169.19/169.66 [7651]~P108(x76511)+P104(f334(f334(f249(x76511),x76512),x76513))+~P104(f334(f334(f249(f886(x76511,a871)),f334(f303(x76511),x76512)),f334(f303(x76511),x76513))) % 169.19/169.66 [7652]~P107(x76521)+P104(f334(f334(f250(x76521),x76522),x76523))+~P104(f334(f334(f250(f886(x76521,a871)),f334(f255(x76521),x76522)),f334(f255(x76521),x76523))) % 169.19/169.66 [7675]~P75(x76751)+~P104(f334(f334(f249(x76751),f334(f334(f3(x76751),x76752),x76753)),f2(x76751)))+P104(f334(f334(f249(x76751),x76752),x76753)) % 169.19/169.66 [7676]~P75(x76761)+~P104(f334(f334(f250(x76761),f334(f334(f3(x76761),x76762),x76763)),f2(x76761)))+P104(f334(f334(f250(x76761),x76762),x76763)) % 169.19/169.66 [7833]E(x78331,f2(a877))+~E(f334(f142(a877,a877,f81(a877),x78332),x78333),f2(a877))+~P104(f334(f334(f336(a877),x78331),f334(f173(a877),x78333))) % 169.19/169.66 [7837]~P28(x78371)+~P104(f334(f334(f249(x78371),f416(x78373,x78372,x78371)),x78373))+P104(f334(f334(f249(x78371),f41(x78371,x78372)),x78373)) % 169.19/169.66 [7990]P104(f334(f334(f249(a1),f2(a1)),f347(x79901,x79902,x79903)))+P104(f334(f334(x79902,f334(f334(f40(a1),x79901),x79903)),f46(a1,x79901,x79903)))+~P104(f334(f334(f250(a1),f2(a1)),x79903)) % 169.19/169.66 [8077]E(x80771,x80772)+~E(f334(f196(f878(x80773)),x80771),f334(f196(f878(x80773)),x80772))+~P104(f334(f334(f273(x80773,x80773,a871),a331),f593(x80773,x80771,x80772))) % 169.19/169.66 [8144]~P39(x81442,x81443)+E(x81441,f195(f886(x81442,a871)))+~P104(f334(f334(f249(f886(x81442,a871)),x81441),f334(f288(x81442,x81442,x81443),x81441))) % 169.19/169.66 [8173]~P62(x81731)+~P104(f334(f334(f249(x81731),x81732),f334(f334(f81(x81731),x81733),f452(x81733,x81732,x81731))))+P104(f334(f334(f249(x81731),x81732),x81733)) % 169.19/169.66 [8213]P49(x82131,x82132,x82133)+P104(f334(f334(f336(x82131),f606(x82133,x82132,x82131)),x82132))+P104(f334(f334(f336(f885(x82131,x82131)),f607(x82133,x82132,x82131)),x82133)) % 169.19/169.66 [8236]P104(f334(f334(x82362,f334(f334(f40(a1),x82361),x82363)),f46(a1,x82361,x82363)))+~P104(f334(f334(f250(a1),f2(a1)),x82363))+P104(f334(f334(f250(a1),f347(x82361,x82362,x82363)),x82363)) % 169.19/169.66 [8260]E(f334(f313(a877,a877,f334(f334(f9(a877,a877,a877),f3(a877)),x82601)),f334(f304(a877,x82602),x82603)),f195(f886(a877,a871)))+P104(f334(f334(f250(a877),x82601),x82603))+P104(f334(f334(f250(a877),x82602),x82603)) % 169.19/169.66 [8364]E(f334(f313(a877,a877,f334(f334(f9(a877,a877,a877),f3(a877)),x83641)),f334(f304(a877,x83642),x83643)),f334(f334(f312(a877),f2(a877)),f195(f886(a877,a871))))+P104(f334(f334(f250(a877),x83641),x83643))+~P104(f334(f334(f250(a877),x83642),x83643)) % 169.19/169.66 [8381]~P107(x83811)+E(f149(x83811,x83811,f7(x83811),x83812,x83813),x83813)+~P104(f334(f334(f336(x83811),x83812),f334(f173(x83811),x83813))) % 169.19/169.66 [8395]P21(x83951,x83951,x83952,x83953)+~P104(f334(f63(x83951),x83953))+~P104(f334(f334(f249(f886(x83951,a871)),x83953),f334(f313(x83951,x83951,x83952),x83953))) % 169.19/169.66 [8418]E(f334(f334(f81(a1),f334(f334(f82(a1),x84181),f348(x84182,x84183,x84181))),f347(x84182,x84183,x84181)),x84182)+P104(f334(f334(x84183,f334(f334(f40(a1),x84182),x84181)),f46(a1,x84182,x84181)))+~P104(f334(f334(f250(a1),f2(a1)),x84181)) % 169.19/169.66 [8646]~P104(f334(f334(x86461,f348(x86462,x86461,x86463)),f347(x86462,x86461,x86463)))+P104(f334(f334(x86461,f334(f334(f40(a1),x86462),x86463)),f46(a1,x86462,x86463)))+~P104(f334(f334(f250(a1),f2(a1)),x86463)) % 169.19/169.66 [9482]~P104(f334(f63(x94821),x94822))+~P104(f334(f334(f336(x94821),x94823),x94822))+P104(f334(f334(f250(a877),f334(f39(x94821),f334(f334(f3(f886(x94821,a871)),x94822),f334(f334(f312(x94821),x94823),f195(f886(x94821,a871)))))),f334(f39(x94821),x94822))) % 169.19/169.66 [10074]P49(x100741,x100742,x100743)+~P104(f334(f334(f273(x100741,x100741,a871),f334(f334(f9(x100741,f886(x100741,a871),f886(x100741,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x100741,a871),f886(x100741,a871)),x100741),f10(a871,a871,x100741)),f334(f334(f10(a871,f886(a871,a871),x100741),a332),f334(f334(f9(x100741,f886(x100741,a871),a871),f336(x100741)),x100742)))),f334(f334(f9(x100741,f886(x100741,a871),a871),f336(x100741)),x100742))),f607(x100743,x100742,x100741)))+P104(f334(f334(f336(x100741),f606(x100743,x100742,x100741)),x100742)) % 169.19/169.66 [5522]~P117(x55222)+E(x55221,f2(x55222))+E(f334(f334(f292(x55222),x55223),f334(f80(x55222),x55221)),f334(f80(x55222),f334(f334(f292(x55222),x55223),x55221))) % 169.19/169.66 [5656]~E(x56563,f195(f886(x56561,a871)))+~E(x56562,f195(f886(x56561,a871)))+E(f334(f334(f113(f886(x56561,a871)),x56562),x56563),f195(f886(x56561,a871))) % 169.19/169.66 [5714]~E(x57143,f2(a877))+~P104(f334(x57141,f2(a877)))+P104(f334(x57141,f334(f334(f40(a877),x57142),x57143))) % 169.19/169.66 [5856]~P62(x58562)+E(x58561,f2(x58562))+E(f334(f334(f292(x58562),f334(f76(x58562),x58563)),f334(f76(x58562),x58561)),f334(f76(x58562),f334(f334(f292(x58562),x58563),x58561))) % 169.19/169.66 [6020]~P104(f334(f63(x60201),x60203))+E(f334(f39(x60201),f334(f334(f312(x60201),x60202),x60203)),f334(a115,f334(f39(x60201),x60203)))+P104(f334(f334(f336(x60201),x60202),x60203)) % 169.19/169.66 [6094]~E(x60942,f2(a877))+P104(f334(x60941,f2(a877)))+~P104(f334(x60941,f334(f334(f40(a877),x60943),x60942))) % 169.19/169.66 [6113]~P104(f334(f63(x61131),x61133))+E(f334(f39(x61131),f334(f334(f312(x61131),x61132),x61133)),f334(f39(x61131),x61133))+~P104(f334(f334(f336(x61131),x61132),x61133)) % 169.19/169.66 [6147]~P104(f334(f63(x61471),x61473))+E(f334(f39(x61471),f334(f334(f312(x61471),x61472),x61473)),f334(f334(f81(a877),f79(a877)),f334(f39(x61471),x61473)))+P104(f334(f334(f336(x61471),x61472),x61473)) % 169.19/169.66 [6268]E(f334(f334(f81(a877),x62681),f804(x62681,x62682,x62683)),x62682)+~P104(f334(x62683,f2(a877)))+P104(f334(x62683,f334(f334(f3(a877),x62682),x62681))) % 169.19/169.66 [6269]E(f334(f334(f81(a877),x62691),f815(x62691,x62692,x62693)),x62692)+~P104(f334(x62693,f2(a877)))+P104(f334(x62693,f334(f334(f3(a877),x62692),x62691))) % 169.19/169.66 [6315]~P28(x63151)+~P104(f334(f63(x63151),x63153))+E(f334(f334(f66(x63151,x63151,f113(x63151)),x63152),x63153),f334(f334(f113(x63151),x63152),f41(x63151,x63153))) % 169.19/169.66 [6316]~P28(x63161)+~P104(f334(f63(x63161),x63163))+E(f334(f334(f66(x63161,x63161,f104(x63161)),x63162),x63163),f334(f334(f104(x63161),x63162),f42(x63161,x63163))) % 169.19/169.66 [6322]~P92(x63221)+~E(f334(f106(x63221),x63222),f334(f106(x63221),x63223))+P32(x63221,f334(f106(x63221),f334(f334(f81(a1),x63222),f334(f80(a1),x63223)))) % 169.19/169.66 [6329]~P137(x63291)+E(f334(f334(f3(x63291),f334(f103(x63291),x63292)),f334(f103(x63291),x63293)),f334(f103(x63291),f334(f334(f3(a877),x63292),x63293)))+~P104(f334(f334(f249(a877),x63293),x63292)) % 169.19/169.66 [6417]E(f334(f334(f81(a877),x64171),f804(x64171,x64172,x64173)),x64172)+P104(f334(f334(f250(a877),x64172),x64171))+P104(f334(x64173,f334(f334(f3(a877),x64172),x64171))) % 169.19/169.66 [6418]E(f334(f334(f81(a877),x64181),f815(x64181,x64182,x64183)),x64182)+P104(f334(f334(f250(a877),x64182),x64181))+P104(f334(x64183,f334(f334(f3(a877),x64182),x64181))) % 169.19/169.66 [6433]~P120(x64331)+E(f334(f334(f82(x64331),f334(f76(x64331),x64332)),x64333),f334(f76(x64331),f334(f334(f82(x64331),x64332),x64333)))+~P104(f334(f334(f249(x64331),f2(x64331)),x64333)) % 169.19/169.66 [6434]~P61(x64341)+E(f334(f334(f292(x64341),f334(f76(x64341),x64342)),x64343),f334(f76(x64341),f334(f334(f292(x64341),x64342),x64343)))+~P104(f334(f334(f250(x64341),f2(x64341)),x64343)) % 169.19/169.66 [6442]~P95(x64421)+~P104(f334(f63(x64421),x64423))+E(f334(f334(f66(x64421,x64421,f113(x64421)),x64422),x64423),f12(x64421,f334(f334(f312(x64421),x64422),x64423))) % 169.19/169.66 [6443]~P95(x64431)+~P104(f334(f63(x64431),x64433))+E(f334(f334(f66(x64431,x64431,f104(x64431)),x64432),x64433),f13(x64431,f334(f334(f312(x64431),x64432),x64433))) % 169.19/169.66 [6444]~P107(x64441)+~P104(f334(f63(x64441),x64443))+E(f334(f334(f66(x64441,x64441,f247(x64441)),x64442),x64443),f16(x64441,f334(f334(f312(x64441),x64442),x64443))) % 169.19/169.66 [6445]~P107(x64451)+~P104(f334(f63(x64451),x64453))+E(f334(f334(f66(x64451,x64451,f248(x64451)),x64452),x64453),f17(x64451,f334(f334(f312(x64451),x64452),x64453))) % 169.19/169.66 [6490]E(x64901,f116(x64902))+~E(f181(x64902,x64903),f116(f878(x64902)))+~P104(f334(f334(f336(f878(x64902)),x64901),f334(f173(f878(x64902)),x64903))) % 169.19/169.66 [6532]~P104(f334(f137(x65321),x65323))+P104(f334(f334(f336(x65321),x65322),f334(f173(x65321),x65323)))+P104(f334(f137(x65321),f334(f334(f151(x65321),x65322),x65323))) % 169.19/169.66 [6543]~P93(x65431)+~P104(f334(f63(x65431),x65433))+E(f334(f65(x65431,f82(x65431)),f334(f334(f312(x65431),x65432),x65433)),f334(f334(f66(x65431,x65431,f82(x65431)),x65432),x65433)) % 169.19/169.66 [6565]~P107(x65651)+~P104(f334(f63(x65651),x65653))+E(f14(x65651,f247(x65651),f334(f334(f312(x65651),x65652),x65653)),f334(f334(f66(x65651,x65651,f247(x65651)),x65652),x65653)) % 169.19/169.66 [6566]~P107(x65661)+~P104(f334(f63(x65661),x65663))+E(f15(x65661,f248(x65661),f334(f334(f312(x65661),x65662),x65663)),f334(f334(f66(x65661,x65661,f248(x65661)),x65662),x65663)) % 169.19/169.66 [6568]P104(f334(x65681,f2(a877)))+~P104(f334(f334(f250(a877),x65682),x65683))+~P104(f334(x65681,f334(f334(f3(a877),x65682),x65683))) % 169.19/169.66 [6587]~P83(x65871)+P104(f334(f334(f249(x65871),x65872),x65873))+~P104(f334(f334(f249(x65871),f334(f76(x65871),x65872)),x65873)) % 169.19/169.66 [6588]~P120(x65881)+P104(f334(f334(f250(x65881),x65882),x65883))+~P104(f334(f334(f250(x65881),f334(f76(x65881),x65882)),x65883)) % 169.19/169.66 [6605]E(x66051,f116(x66052))+E(f334(f141(x66052),f334(f334(f138(x66052),x66053),x66051)),f334(f334(f165(x66052),x66051),x66053))+~P104(f334(f334(f250(a877),x66053),f334(f196(f878(x66052)),x66051))) % 169.19/169.66 [6656]~P104(f334(x66561,x66563))+P104(f334(x66561,f413(x66561,x66562)))+~P104(f334(f334(f336(a877),x66563),f334(f304(a877,f2(a877)),x66562))) % 169.19/169.66 [6677]P104(f334(x66771,x66772))+~P104(f334(f334(f250(a877),x66772),x66773))+P104(f334(f334(f336(a877),f409(x66771,x66773)),f334(f304(a877,f2(a877)),x66773))) % 169.19/169.66 [6692]~P119(x66921)+~P104(f334(f334(f249(x66921),f79(x66921)),x66922))+P104(f334(f334(f249(x66921),f79(x66921)),f334(f334(f259(x66921),x66922),x66923))) % 169.19/169.66 [6694]~P119(x66941)+~P104(f334(f334(f249(x66941),f2(x66941)),x66942))+P104(f334(f334(f249(x66941),f2(x66941)),f334(f334(f259(x66941),x66942),x66943))) % 169.19/169.66 [6696]~P119(x66961)+~P104(f334(f334(f250(x66961),f2(x66961)),x66962))+P104(f334(f334(f250(x66961),f2(x66961)),f334(f334(f259(x66961),x66962),x66963))) % 169.19/169.66 [6720]~P104(f334(x67201,x67203))+~P104(f334(f334(f250(a877),x67203),x67202))+P104(f334(f334(f336(a877),f408(x67201,x67202)),f334(f304(a877,f2(a877)),x67202))) % 169.19/169.66 [6727]P104(f334(f63(x67271),x67272))+~P104(f334(f63(x67271),x67273))+~P104(f334(f334(f249(f886(x67271,a871)),x67272),x67273)) % 169.19/169.66 [6735]P104(f334(x67351,x67352))+~P104(f334(x67351,f410(x67351,x67353)))+~P104(f334(f334(f336(a877),x67352),f334(f304(a877,f2(a877)),x67353))) % 169.19/169.66 [6746]E(x67461,f2(a877))+P104(f334(x67462,f350(x67461,x67463,x67462)))+~P104(f334(x67462,f334(f334(f40(a877),x67463),x67461))) % 169.19/169.66 [6754]~P123(x67542)+E(x67541,f2(x67542))+~E(f334(f334(f81(x67542),f334(f334(f82(x67542),x67543),x67543)),f334(f334(f82(x67542),x67541),x67541)),f2(x67542)) % 169.19/169.66 [6755]~P123(x67552)+E(x67551,f2(x67552))+~E(f334(f334(f81(x67552),f334(f334(f82(x67552),x67551),x67551)),f334(f334(f82(x67552),x67553),x67553)),f2(x67552)) % 169.19/169.66 [6800]E(x68001,f2(a877))+~P104(f334(x68002,f351(x68001,x68003,x68002)))+P104(f334(x68002,f334(f334(f40(a877),x68003),x68001))) % 169.19/169.66 [6805]~P107(x68051)+~P30(x68051,x68053)+P30(x68051,f334(f334(f148(x68051,x68051,f7(x68051)),x68052),x68053)) % 169.19/169.66 [6848]P104(f334(x68481,f350(x68482,x68483,x68481)))+P104(f334(x68481,f2(a877)))+~P104(f334(x68481,f334(f334(f40(a877),x68483),x68482))) % 169.19/169.66 [6854]~P92(x68541)+E(f334(f106(x68541),x68542),f334(f106(x68541),x68543))+~P32(x68541,f334(f106(x68541),f334(f334(f81(a1),x68542),f334(f80(a1),x68543)))) % 169.19/169.66 [6920]E(x69201,f2(a1))+E(x69202,f2(a1))+~P104(f334(f50(x69202,x69202),f334(f334(f269(a1,a1),x69203),x69201))) % 169.19/169.66 [6921]E(x69211,f79(a1))+E(x69212,f2(a1))+~P104(f334(f50(x69212,x69212),f334(f334(f269(a1,a1),x69211),x69213))) % 169.19/169.66 [6935]P104(f334(x69351,x69352))+P104(f334(f334(f250(a877),f410(x69351,x69353)),x69353))+~P104(f334(f334(f336(a877),x69352),f334(f304(a877,f2(a877)),x69353))) % 169.19/169.66 [6957]~P104(f334(x69571,f804(x69573,x69572,x69571)))+~P104(f334(x69571,f2(a877)))+P104(f334(x69571,f334(f334(f3(a877),x69572),x69573))) % 169.19/169.66 [6958]~P104(f334(x69581,f815(x69583,x69582,x69581)))+~P104(f334(x69581,f2(a877)))+P104(f334(x69581,f334(f334(f3(a877),x69582),x69583))) % 169.19/169.66 [6959]~P104(f334(x69591,f351(x69593,x69592,x69591)))+~P104(f334(x69591,f2(a877)))+P104(f334(x69591,f334(f334(f40(a877),x69592),x69593))) % 169.19/169.66 [6977]~P104(f334(x69771,x69773))+P104(f334(f334(f250(a877),f413(x69771,x69772)),x69772))+~P104(f334(f334(f336(a877),x69773),f334(f304(a877,f2(a877)),x69772))) % 169.19/169.66 [6978]E(f334(f334(f3(a877),f334(f334(f3(a877),x69781),x69782)),f334(f334(f3(a877),x69783),x69782)),f334(f334(f3(a877),x69781),x69783))+~P104(f334(f334(f249(a877),x69782),x69781))+~P104(f334(f334(f249(a877),x69782),x69783)) % 169.19/169.66 [7013]~P75(x70131)+~P104(f334(f334(f249(x70131),f334(f80(x70131),x70133)),x70132))+P104(f334(f334(f249(x70131),f334(f80(x70131),x70132)),x70133)) % 169.19/169.66 [7015]~P83(x70151)+~P104(f334(f334(f249(x70151),f334(f76(x70151),x70152)),x70153))+P104(f334(f334(f249(x70151),f334(f80(x70151),x70152)),x70153)) % 169.19/169.66 [7017]~P75(x70171)+~P104(f334(f334(f250(x70171),f334(f80(x70171),x70173)),x70172))+P104(f334(f334(f250(x70171),f334(f80(x70171),x70172)),x70173)) % 169.19/169.66 [7018]~P120(x70181)+~P104(f334(f334(f250(x70181),f334(f76(x70181),x70182)),x70183))+P104(f334(f334(f250(x70181),f334(f80(x70181),x70182)),x70183)) % 169.19/169.66 [7052]~P104(f334(x70523,f804(x70522,x70521,x70523)))+P104(f334(f334(f250(a877),x70521),x70522))+P104(f334(x70523,f334(f334(f3(a877),x70521),x70522))) % 169.19/169.66 [7053]~P104(f334(x70533,f815(x70532,x70531,x70533)))+P104(f334(f334(f250(a877),x70531),x70532))+P104(f334(x70533,f334(f334(f3(a877),x70531),x70532))) % 169.19/169.66 [7103]~E(f430(x71033,x71032,x71031),f431(x71033,x71032,x71031))+E(f334(f334(f104(f886(x71031,a871)),x71032),f41(f886(x71031,a871),x71033)),f195(f886(x71031,a871)))+P104(f334(f334(f336(f886(x71031,a871)),x71032),x71033)) % 169.19/169.66 [7112]~P104(f334(f63(x71121),x71123))+P104(f334(f63(x71121),f42(f886(x71121,a871),x71122)))+~P104(f334(f334(f336(f886(x71121,a871)),x71123),x71122)) % 169.19/169.66 [7171]~P107(x71711)+E(f334(f334(f113(f886(x71711,a871)),f334(f304(x71711,x71712),x71713)),f334(f334(f312(x71711),x71713),f195(f886(x71711,a871)))),f305(x71711,x71712,x71713))+~P104(f334(f334(f249(x71711),x71712),x71713)) % 169.19/169.66 [7172]E(x71721,f2(a877))+P104(f334(f334(f250(a877),f353(x71721,x71723,x71722)),x71721))+P104(f334(x71722,f334(f334(f40(a877),x71723),x71721))) % 169.19/169.66 [7207]E(x72071,x72072)+~P104(f334(f334(f249(f886(x72073,a871)),x72071),x72072))+P104(f334(f334(f250(f886(x72073,a871)),x72071),x72072)) % 169.19/169.66 [7220]E(x72201,x72202)+~E(f334(f196(f878(x72203)),x72201),f334(f196(f878(x72203)),x72202))+P104(f334(f334(f250(a877),f577(x72203,x72201,x72202)),f334(f196(f878(x72203)),x72202))) % 169.19/169.66 [7266]P6(x72661,x72662,x72663)+~E(f334(f267(x72661,x72661),x72663),x72662)+~E(f334(f334(f291(x72661,x72661,x72661),f334(f289(x72661,x72661),x72663)),x72663),x72663) % 169.19/169.66 [7341]~P104(f334(x73411,f2(a877)))+P104(f334(f334(f250(a877),f353(x73413,x73412,x73411)),x73413))+P104(f334(x73411,f334(f334(f40(a877),x73412),x73413))) % 169.19/169.66 [7350]~P107(x73501)+E(f334(f334(f113(f886(x73501,a871)),f308(x73501,x73502,x73503)),f334(f334(f312(x73501),x73503),f195(f886(x73501,a871)))),f307(x73501,x73502,x73503))+~P104(f334(f334(f250(x73501),x73502),x73503)) % 169.19/169.66 [7448]~P104(f334(f63(x74481),x74483))+P104(f334(f334(f249(a877),f334(f39(x74481),x74482)),f334(f39(x74481),x74483)))+~P104(f334(f334(f249(f886(x74481,a871)),x74482),x74483)) % 169.19/169.66 [7449]~P104(f334(f63(x74491),x74493))+P104(f334(f334(f250(a877),f334(f39(x74491),x74492)),f334(f39(x74491),x74493)))+~P104(f334(f334(f250(f886(x74491,a871)),x74492),x74493)) % 169.19/169.66 [7586]E(x75861,x75862)+~P104(f334(f334(f249(f886(x75863,a871)),x75862),x75861))+~P104(f334(f334(f249(f886(x75863,a871)),x75861),x75862)) % 169.19/169.66 [7589]~P107(x75891)+P30(x75891,x75892)+~P30(x75891,f334(f334(f148(x75891,x75891,f7(x75891)),x75893),x75892)) % 169.19/169.66 [7657]~P104(f334(f334(f250(a877),x76573),x76572))+~P104(f334(f334(f250(a877),x76573),x76571))+P104(f334(f334(f250(a877),f334(f334(f3(a877),x76571),x76572)),f334(f334(f3(a877),x76571),x76573))) % 169.19/169.66 [7658]~P104(f334(f334(f249(a877),x76582),x76581))+~P104(f334(f334(f250(a877),x76581),x76583))+P104(f334(f334(f250(a877),f334(f334(f3(a877),x76581),x76582)),f334(f334(f3(a877),x76583),x76582))) % 169.19/169.66 [7673]~P104(f334(f334(f250(a1),x76732),f2(a1)))+~P104(f334(f334(f249(a1),x76733),x76731))+P104(f334(f334(f249(a1),f334(f334(f40(a1),x76731),x76732)),f334(f334(f40(a1),x76733),x76732))) % 169.19/169.66 [7691]~P104(f334(f334(f250(a877),f2(a877)),x76913))+~P104(f334(f334(f249(a877),x76913),x76912))+P104(f334(f334(f249(a877),f334(f334(f40(a877),x76911),x76912)),f334(f334(f40(a877),x76911),x76913))) % 169.19/169.66 [7692]~P104(f334(f334(f250(a1),f2(a1)),x76922))+~P104(f334(f334(f249(a1),x76921),x76923))+P104(f334(f334(f249(a1),f334(f334(f40(a1),x76921),x76922)),f334(f334(f40(a1),x76923),x76922))) % 169.19/169.66 [7696]~P104(f334(f334(f250(a877),f2(a877)),x76962))+~P104(f334(f334(f250(a877),x76961),x76963))+P104(f334(f334(f250(a877),f334(f334(f82(a877),x76961),x76962)),f334(f334(f82(a877),x76963),x76962))) % 169.19/169.66 [7697]~P104(f334(f334(f250(a877),f2(a877)),x76971))+~P104(f334(f334(f250(a877),x76972),x76973))+P104(f334(f334(f250(a877),f334(f334(f82(a877),x76971),x76972)),f334(f334(f82(a877),x76971),x76973))) % 169.19/169.66 [7698]~P104(f334(f334(f250(a1),f2(a1)),x76981))+~P104(f334(f334(f250(a1),x76982),x76983))+P104(f334(f334(f250(a1),f334(f334(f82(a1),x76981),x76982)),f334(f334(f82(a1),x76981),x76983))) % 169.19/169.66 [7748]E(x77481,f2(a877))+E(f334(f334(f81(a877),f334(f334(f82(a877),x77481),f351(x77481,x77482,x77483))),f353(x77481,x77482,x77483)),x77482)+P104(f334(x77483,f334(f334(f40(a877),x77482),x77481))) % 169.19/169.66 [7806]E(f334(f334(f81(a877),f334(f334(f82(a877),x78061),f351(x78061,x78062,x78063))),f353(x78061,x78062,x78063)),x78062)+~P104(f334(x78063,f2(a877)))+P104(f334(x78063,f334(f334(f40(a877),x78062),x78061))) % 169.19/169.66 [7824]~P104(f334(f63(x78241),x78243))+P104(f334(f334(f336(x78241),f849(x78242,x78243,x78241)),x78243))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f11(x78241,a877),x78242),x78243))) % 169.19/169.66 [7825]~P104(f334(f63(x78251),x78253))+P104(f334(f334(f336(x78251),f855(x78252,x78253,x78251)),x78253))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f11(x78251,a877),x78252),x78253))) % 169.19/169.66 [8110]E(x81101,f195(f886(x81102,a871)))+E(x81101,f334(f334(f312(x81102),x81103),f195(f886(x81102,a871))))+~P104(f334(f334(f249(f886(x81102,a871)),x81101),f334(f334(f312(x81102),x81103),f195(f886(x81102,a871))))) % 169.19/169.66 [8127]~P58(x81271)+P8(x81271,x81272,x81273)+P104(f334(f334(f336(f878(x81271)),f655(x81273,x81272,x81271)),f334(f173(f878(x81271)),f56(x81271,x81273,f57(x81271))))) % 169.19/169.66 [8146]~P104(f334(f334(f250(a877),f2(a877)),x81463))+P104(f334(f334(f249(a877),x81461),x81462))+~P104(f334(f334(f249(a877),f334(f334(f82(a877),x81463),x81461)),f334(f334(f82(a877),x81463),x81462))) % 169.19/169.66 [8147]~P104(f334(f334(f250(a877),f2(a877)),x81473))+P104(f334(f334(f249(a877),x81471),x81472))+~P104(f334(f334(f249(a877),f334(f334(f82(a877),x81471),x81473)),f334(f334(f82(a877),x81472),x81473))) % 169.19/169.66 [8149]~P104(f334(f334(f250(a877),f2(a877)),x81493))+P104(f334(f334(f250(a877),x81491),x81492))+~P104(f334(f334(f250(a877),f334(f334(f259(a877),x81493),x81491)),f334(f334(f259(a877),x81493),x81492))) % 169.19/169.66 [8175]~P58(x81751)+~P7(x81751,x81753,x81752)+P104(f334(f334(f336(f878(x81751)),f654(x81752,x81753,x81751)),f334(f173(f878(x81751)),f56(x81751,x81752,f57(x81751))))) % 169.19/169.66 [8191]~E(f334(f334(f104(f886(x81911,a871)),f431(x81913,x81912,x81911)),f430(x81913,x81912,x81911)),f195(f886(x81911,a871)))+E(f334(f334(f104(f886(x81911,a871)),x81912),f41(f886(x81911,a871),x81913)),f195(f886(x81911,a871)))+P104(f334(f334(f336(f886(x81911,a871)),x81912),x81913)) % 169.19/169.66 [8208]E(x82081,f116(x82082))+~E(f334(f142(f878(x82082),f878(x82082),f134(x82082),f116(x82082)),x82083),f116(x82082))+~P104(f334(f334(f336(f878(x82082)),x82081),f334(f173(f878(x82082)),x82083))) % 169.19/169.66 [8265]E(x82651,f195(f886(f886(x82652,a871),a871)))+P104(f334(f334(f336(f886(x82652,a871)),f455(x82653,x82651,x82652)),x82651))+P104(f334(f334(f249(f886(x82652,a871)),f42(f886(x82652,a871),x82651)),x82653)) % 169.19/169.66 [8272]~P68(x82721)+~P72(x82721)+E(f334(f334(f8(a1,x82721),f334(f334(f10(a877,x82721,a1),x82722),a107)),f334(f313(a877,a1,f103(a1)),x82723)),f334(f334(f8(a877,x82721),x82722),x82723)) % 169.19/169.66 [8273]~P68(x82731)+~P72(x82731)+E(f334(f334(f11(a1,x82731),f334(f334(f10(a877,x82731,a1),x82732),a107)),f334(f313(a877,a1,f103(a1)),x82733)),f334(f334(f11(a877,x82731),x82732),x82733)) % 169.19/169.66 [8312]~P104(f334(f63(x83121),x83123))+~P104(f334(f334(f250(a877),f2(a877)),f334(x83122,f849(x83122,x83123,x83121))))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f11(x83121,a877),x83122),x83123))) % 169.19/169.66 [8313]~P104(f334(f63(x83131),x83133))+~P104(f334(f334(f250(a877),f2(a877)),f334(x83132,f855(x83132,x83133,x83131))))+P104(f334(f334(f250(a877),f2(a877)),f334(f334(f11(x83131,a877),x83132),x83133))) % 169.19/169.66 [8346]~P60(x83462)+E(x83461,f79(x83462))+E(f334(f334(f292(x83462),f334(f334(f3(x83462),f334(f334(f259(x83462),x83461),x83463)),f79(x83462))),f334(f334(f3(x83462),x83461),f79(x83462))),f334(f334(f8(a877,x83462),f334(f259(x83462),x83461)),f334(f304(a877,f2(a877)),x83463))) % 169.19/169.66 [8404]E(x84041,f2(a877))+~P104(f334(x84043,f334(f334(f40(a877),x84042),x84041)))+P104(f334(f334(f250(a877),x84042),f334(f334(f82(a877),x84041),f334(a115,f350(x84041,x84042,x84043))))) % 169.19/169.66 [8421]P104(f334(x84211,f2(a877)))+~P104(f334(x84211,f334(f334(f40(a877),x84212),x84213)))+P104(f334(f334(f250(a877),x84212),f334(f334(f82(a877),x84213),f334(a115,f350(x84213,x84212,x84211))))) % 169.19/169.66 [8461]E(x84611,f2(a877))+~P104(f334(x84613,f334(f334(f40(a877),x84612),x84611)))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x84611),f350(x84611,x84612,x84613))),x84612)) % 169.19/169.66 [8494]P104(f334(x84941,f2(a877)))+~P104(f334(x84941,f334(f334(f40(a877),x84943),x84942)))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x84942),f350(x84942,x84943,x84941))),x84943)) % 169.19/169.66 [8497]~P107(x84971)+E(f334(f334(f148(x84971,x84971,f7(x84971)),x84972),x84973),f149(x84971,x84971,f7(x84971),x84972,x84973))+P104(f334(f334(f336(x84971),x84972),f334(f173(x84971),x84973))) % 169.19/169.66 [8532]~E(f334(x85323,f718(x85322,x85323,x85321)),f334(x85323,f720(x85322,x85323,x85321)))+~P57(x85321,f334(x85323,f719(x85322,x85323,x85321)))+P57(x85321,f334(f334(f44(x85322,f886(x85321,f886(x85321,a871))),f257(f886(x85322,a871))),x85323)) % 169.19/169.66 [8540]E(x85401,f195(f886(f886(x85402,a871),a871)))+~P104(f334(f334(f249(f886(x85402,a871)),f455(x85403,x85401,x85402)),x85403))+P104(f334(f334(f249(f886(x85402,a871)),f42(f886(x85402,a871),x85401)),x85403)) % 169.19/169.66 [8599]~P62(x85991)+~P104(f334(f334(f250(x85991),x85992),x85993))+P104(f334(f334(f250(x85991),x85992),f334(f334(f292(x85991),f334(f334(f81(x85991),x85992),x85993)),f334(f334(f81(x85991),f79(x85991)),f79(x85991))))) % 169.19/169.66 [8652]~P104(f334(f334(x86521,f503(x86521,x86523,x86522)),f504(x86521,x86523,x86522)))+P104(f334(f334(x86521,x86522),x86523))+~P104(f334(f322(f885(a1,a1),a53),f334(f334(f269(a1,a1),x86522),x86523))) % 169.19/169.66 [8653]~P104(f334(f334(x86531,f505(x86531,x86533,x86532)),f506(x86531,x86533,x86532)))+P104(f334(f334(x86531,x86532),x86533))+~P104(f334(f322(f885(a1,a1),a58),f334(f334(f269(a1,a1),x86532),x86533))) % 169.19/169.66 [8654]~P104(f334(f334(x86541,f507(x86541,x86543,x86542)),f508(x86541,x86543,x86542)))+P104(f334(f334(x86541,x86542),x86543))+~P104(f334(f322(f885(a1,a1),a230),f334(f334(f269(a1,a1),x86542),x86543))) % 169.19/169.66 [8655]~P104(f334(f334(x86551,f509(x86551,x86553,x86552)),f510(x86551,x86553,x86552)))+P104(f334(f334(x86551,x86552),x86553))+~P104(f334(f322(f885(a877,a877),a228),f334(f334(f269(a877,a877),x86552),x86553))) % 169.19/169.66 [8656]~P104(f334(f334(x86561,f596(x86561,x86563,x86562)),f597(x86561,x86563,x86562)))+P104(f334(f334(x86561,x86562),x86563))+~P104(f334(f322(f885(a1,a1),a184),f334(f334(f269(a1,a1),x86562),x86563))) % 169.19/169.66 [8657]~P104(f334(f334(x86571,f811(x86571,x86573,x86572)),f812(x86571,x86573,x86572)))+P104(f334(f334(x86571,x86572),x86573))+~P104(f334(f322(f885(a1,a1),a133),f334(f334(f269(a1,a1),x86572),x86573))) % 169.19/169.66 [8908]P104(f334(f334(x89081,x89082),x89083))+P104(f334(f322(f885(a877,a877),a228),f334(f334(f269(a877,a877),f509(x89081,x89083,x89082)),f510(x89081,x89083,x89082))))+~P104(f334(f322(f885(a877,a877),a228),f334(f334(f269(a877,a877),x89082),x89083))) % 169.19/169.66 [8909]P104(f334(f334(x89091,x89092),x89093))+P104(f334(f322(f885(a1,a1),a53),f334(f334(f269(a1,a1),f503(x89091,x89093,x89092)),f504(x89091,x89093,x89092))))+~P104(f334(f322(f885(a1,a1),a53),f334(f334(f269(a1,a1),x89092),x89093))) % 169.19/169.66 [8910]P104(f334(f334(x89101,x89102),x89103))+P104(f334(f322(f885(a1,a1),a58),f334(f334(f269(a1,a1),f505(x89101,x89103,x89102)),f506(x89101,x89103,x89102))))+~P104(f334(f322(f885(a1,a1),a58),f334(f334(f269(a1,a1),x89102),x89103))) % 169.19/169.66 [8911]P104(f334(f334(x89111,x89112),x89113))+P104(f334(f322(f885(a1,a1),a230),f334(f334(f269(a1,a1),f507(x89111,x89113,x89112)),f508(x89111,x89113,x89112))))+~P104(f334(f322(f885(a1,a1),a230),f334(f334(f269(a1,a1),x89112),x89113))) % 169.19/169.66 [8912]P104(f334(f334(x89121,x89122),x89123))+P104(f334(f322(f885(a1,a1),a184),f334(f334(f269(a1,a1),f596(x89121,x89123,x89122)),f597(x89121,x89123,x89122))))+~P104(f334(f322(f885(a1,a1),a184),f334(f334(f269(a1,a1),x89122),x89123))) % 169.19/169.66 [8913]P104(f334(f334(x89131,x89132),x89133))+P104(f334(f322(f885(a1,a1),a133),f334(f334(f269(a1,a1),f811(x89131,x89133,x89132)),f812(x89131,x89133,x89132))))+~P104(f334(f322(f885(a1,a1),a133),f334(f334(f269(a1,a1),x89132),x89133))) % 169.19/169.66 [9229]~P23(a872,f195(f886(f876(a872),a871)),f334(f334(f312(f876(a872)),f334(f334(f334(f93(a872),x92291),x92292),x92293)),f195(f886(f876(a872),a871))))+~P20(a872,f195(f886(f876(a872),a871)),f334(f334(f312(f876(a872)),f94(x92292)),f195(f886(f876(a872),a871))))+P20(a872,f195(f886(f876(a872),a871)),f334(f334(f312(f876(a872)),f334(f334(f334(f93(a872),x92291),x92292),x92293)),f195(f886(f876(a872),a871)))) % 169.19/169.66 [9239]~P104(f334(f63(x92391),x92393))+P104(f334(f334(f336(f885(f886(x92391,a871),f886(x92391,a871))),f334(f334(f269(f886(x92391,a871),f886(x92391,a871)),x92392),x92393)),f309(x92391)))+~P104(f334(f334(f250(f886(x92391,a871)),x92392),x92393)) % 169.19/169.66 [9305]~P57(x93051,f334(x93053,f719(x93052,x93053,x93051)))+P57(x93051,f334(f334(f44(x93052,f886(x93051,f886(x93051,a871))),f257(f886(x93052,a871))),x93053))+~E(f334(f334(f104(f886(x93051,a871)),f263(x93051,x93051,f334(x93053,f718(x93052,x93053,x93051)))),f264(x93051,x93051,f334(x93053,f720(x93052,x93053,x93051)))),f195(f886(x93051,a871))) % 169.19/169.66 [9494]P49(x94941,x94942,x94943)+P104(f334(f334(f336(f885(x94941,x94941)),f607(x94943,x94942,x94941)),x94943))+~P104(f334(f334(f336(f885(x94941,x94941)),f334(f334(f269(x94941,x94941),f606(x94943,x94942,x94941)),f606(x94943,x94942,x94941))),x94943)) % 169.19/169.66 [10075]P49(x100751,x100752,x100753)+~P104(f334(f334(f273(x100751,x100751,a871),f334(f334(f9(x100751,f886(x100751,a871),f886(x100751,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x100751,a871),f886(x100751,a871)),x100751),f10(a871,a871,x100751)),f334(f334(f10(a871,f886(a871,a871),x100751),a332),f334(f334(f9(x100751,f886(x100751,a871),a871),f336(x100751)),x100752)))),f334(f334(f9(x100751,f886(x100751,a871),a871),f336(x100751)),x100752))),f607(x100753,x100752,x100751)))+~P104(f334(f334(f336(f885(x100751,x100751)),f334(f334(f269(x100751,x100751),f606(x100753,x100752,x100751)),f606(x100753,x100752,x100751))),x100753)) % 169.19/169.66 [5695]~P26(x56952)+E(x56951,f2(x56952))+E(f334(f334(f40(x56952),f334(f334(f82(x56952),x56953),x56951)),x56951),x56953) % 169.19/169.66 [5696]~P26(x56962)+E(x56961,f2(x56962))+E(f334(f334(f40(x56962),f334(f334(f82(x56962),x56961),x56963)),x56961),x56963) % 169.19/169.66 [6489]~P72(x64891)+~E(f334(x64892,f2(a877)),f2(x64891))+E(f334(f334(f8(a877,x64891),x64892),f334(f304(a877,f334(a115,f2(a877))),x64893)),f334(f334(f8(a877,x64891),x64892),f334(f304(a877,f2(a877)),x64893))) % 169.19/169.66 [6617]~P26(x66172)+E(x66171,f2(x66172))+E(f334(f334(f40(x66172),f334(f334(f81(x66172),x66173),x66171)),x66171),f334(f334(f81(x66172),f334(f334(f40(x66172),x66173),x66171)),f79(x66172))) % 169.19/169.66 [6618]~P26(x66182)+E(x66181,f2(x66182))+E(f334(f334(f40(x66182),f334(f334(f81(x66182),x66181),x66183)),x66181),f334(f334(f81(x66182),f334(f334(f40(x66182),x66183),x66181)),f79(x66182))) % 169.19/169.66 [6836]~P104(f334(x68363,f2(a1)))+P104(f334(f334(f249(a877),x68361),x68362))+P104(f334(x68363,f334(f103(a1),f334(f334(f3(a877),x68362),x68361)))) % 169.19/169.66 [6941]P104(f334(f334(f250(a877),x69412),x69411))+P104(f334(f334(f249(a877),x69411),x69412))+P104(f334(x69413,f334(f103(a1),f334(f334(f3(a877),x69412),x69411)))) % 169.19/169.66 [7011]E(f334(f334(f81(a877),f334(f106(a877),x70111)),f334(f334(f81(a877),f334(f106(a877),x70112)),x70113)),f334(f334(f81(a877),f334(f106(a877),x70111)),x70113))+P104(f334(a201,f334(f106(a1),x70111)))+~P104(f334(a201,f334(f106(a1),x70112))) % 169.19/169.66 [7090]~E(x70902,f334(f334(f40(a877),x70903),x70901))+~P104(f334(f334(f250(a877),f2(a877)),x70901))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x70901),x70902)),x70903)) % 169.19/169.66 [7205]~P104(f334(f63(x72051),x72053))+~P104(f334(f63(x72051),x72052))+P104(f334(f63(x72051),f334(f334(f113(f886(x72051,a871)),x72052),x72053))) % 169.19/169.66 [7499]~P107(x74991)+~P104(f334(f63(x74991),x74992))+E(f139(x74991,f334(f334(f3(f886(x74991,a871)),x74992),f334(f334(f312(x74991),x74993),f195(f886(x74991,a871))))),f171(x74991,x74993,f139(x74991,x74992))) % 169.19/169.66 [7565]P104(f334(x75651,f2(a1)))+~P104(f334(f334(f250(a877),x75652),x75653))+~P104(f334(x75651,f334(f103(a1),f334(f334(f3(a877),x75652),x75653)))) % 169.19/169.66 [7583]~P104(f334(f63(x75831),x75832))+E(f334(f39(x75831),f334(f334(f3(f886(x75831,a871)),x75832),f334(f334(f312(x75831),x75833),f195(f886(x75831,a871))))),f334(f39(x75831),x75832))+P104(f334(f334(f336(x75831),x75833),x75832)) % 169.19/169.66 [7713]~P119(x77131)+~P104(f334(f334(f250(x77131),f79(x77131)),x77132))+P104(f334(f334(f250(x77131),f79(x77131)),f334(f334(f82(x77131),x77132),f334(f334(f259(x77131),x77132),x77133)))) % 169.19/169.66 [7758]~P104(f334(f63(x77581),x77583))+E(f334(f334(f3(a877),f334(f39(x77581),x77582)),f334(f39(x77581),x77583)),f334(f39(x77581),f334(f334(f3(f886(x77581,a871)),x77582),x77583)))+~P104(f334(f334(f249(f886(x77581,a871)),x77583),x77582)) % 169.19/169.66 [7815]~P104(f334(f334(f249(a877),x78152),x78153))+~P104(f334(f334(f249(a877),x78151),f334(f334(f3(a877),x78153),x78152)))+P104(f334(f334(f249(a877),f334(f334(f81(a877),x78151),x78152)),x78153)) % 169.19/169.66 [7866]P104(f334(f63(x78661),x78662))+~P104(f334(f63(x78661),x78663))+~P104(f334(f63(x78661),f334(f334(f3(f886(x78661,a871)),x78662),x78663))) % 169.19/169.66 [7872]~P104(f334(f63(x78721),x78722))+E(f334(f39(x78721),f334(f334(f3(f886(x78721,a871)),x78722),f334(f334(f312(x78721),x78723),f195(f886(x78721,a871))))),f334(f334(f3(a877),f334(f39(x78721),x78722)),f79(a877)))+~P104(f334(f334(f336(x78721),x78723),x78722)) % 169.19/169.66 [7947]P57(x79471,x79472)+~P57(x79471,x79473)+~P104(f334(f334(f249(f886(x79471,f886(x79471,a871))),x79472),x79473)) % 169.19/169.66 [7989]~P104(f334(f334(f249(a877),x79893),x79892))+P104(f334(f334(f249(a877),x79891),f334(f334(f3(a877),x79892),x79893)))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),x79891),x79893)),x79892)) % 169.19/169.66 [8007]P39(x80071,x80072)+~P39(x80071,x80073)+~P104(f334(f334(f249(f886(f885(x80071,x80071),a871)),x80072),x80073)) % 169.19/169.66 [8008]P55(x80081,x80082)+~P55(x80081,x80083)+~P104(f334(f334(f249(f886(f885(x80081,x80081),a871)),x80082),x80083)) % 169.19/169.66 [8243]~P119(x82431)+~P104(f334(f334(f250(x82431),f79(x82431)),x82432))+P104(f334(f334(f250(x82431),f334(f334(f259(x82431),x82432),x82433)),f334(f334(f82(x82431),x82432),f334(f334(f259(x82431),x82432),x82433)))) % 169.19/169.66 [8330]~P104(f334(x83301,f2(a1)))+~P104(f334(x83301,f334(f334(f3(a1),f334(f103(a1),x83302)),f334(f103(a1),x83303))))+P104(f334(x83301,f334(f103(a1),f334(f334(f3(a877),x83302),x83303)))) % 169.19/169.66 [8343]~P104(f334(f334(f249(a877),x83433),x83432))+P104(f334(x83431,f334(f334(f3(a1),f334(f103(a1),x83432)),f334(f103(a1),x83433))))+~P104(f334(x83431,f334(f103(a1),f334(f334(f3(a877),x83432),x83433)))) % 169.19/169.66 [8361]P104(f334(f334(f250(a877),x83611),x83612))+~P104(f334(x83613,f334(f334(f3(a1),f334(f103(a1),x83611)),f334(f103(a1),x83612))))+P104(f334(x83613,f334(f103(a1),f334(f334(f3(a877),x83611),x83612)))) % 169.19/169.66 [8415]~P123(x84152)+E(x84151,f2(x84152))+P104(f334(f334(f250(x84152),f2(x84152)),f334(f334(f81(x84152),f334(f334(f82(x84152),x84153),x84153)),f334(f334(f82(x84152),x84151),x84151)))) % 169.19/169.66 [8416]~P123(x84162)+E(x84161,f2(x84162))+P104(f334(f334(f250(x84162),f2(x84162)),f334(f334(f81(x84162),f334(f334(f82(x84162),x84161),x84161)),f334(f334(f82(x84162),x84163),x84163)))) % 169.19/169.66 [8515]~P104(f334(f334(f250(a877),f2(a877)),x85151))+~P104(f334(f334(f250(a1),x85152),x85153))+P104(f334(f334(f250(a1),f334(f334(f82(a1),f334(f103(a1),x85151)),x85152)),f334(f334(f82(a1),f334(f103(a1),x85151)),x85153))) % 169.19/169.66 [8568]E(f334(f334(f104(f886(x85681,a871)),x85682),f41(f886(x85681,a871),x85683)),f195(f886(x85681,a871)))+P104(f334(f334(f336(f886(x85681,a871)),x85682),x85683))+P104(f334(f334(f336(f886(x85681,a871)),f431(x85683,x85682,x85681)),f334(f334(f312(f886(x85681,a871)),x85682),x85683))) % 169.19/169.66 [8569]E(f334(f334(f104(f886(x85691,a871)),x85692),f41(f886(x85691,a871),x85693)),f195(f886(x85691,a871)))+P104(f334(f334(f336(f886(x85691,a871)),x85692),x85693))+P104(f334(f334(f336(f886(x85691,a871)),f430(x85693,x85692,x85691)),f334(f334(f312(f886(x85691,a871)),x85692),x85693))) % 169.19/169.66 [8598]E(x85981,x85982)+~E(f334(f196(f878(x85983)),x85981),f334(f196(f878(x85983)),x85982))+P104(f334(f334(f336(f885(x85983,x85983)),f593(x85983,x85981,x85982)),f334(f173(f885(x85983,x85983)),f334(f334(f183(x85983,x85983),x85982),x85981)))) % 169.19/169.66 [8827]E(f310(x88271,x88272),f310(x88271,x88273))+~P104(f334(f334(f249(f886(f885(x88271,x88271),a871)),x88273),f310(x88271,x88272)))+~P104(f334(f334(f249(f886(f885(x88271,x88271),a871)),x88272),x88273)) % 169.19/169.66 [8887]~P49(x88871,f257(f886(x88871,a871)),x88873)+P104(f334(f334(f249(f886(f885(f878(x88871),f878(x88871)),a871)),f157(x88871,x88872)),f158(x88871,x88873)))+~P104(f334(f334(f249(f886(f885(x88871,x88871),a871)),x88872),x88873)) % 169.19/169.66 [9082]P39(x90821,x90822)+~P104(f334(f334(f336(x90821),x90823),f759(x90822,x90821)))+P104(f334(f334(f336(f885(x90821,x90821)),f334(f334(f269(x90821,x90821),f788(x90822,x90821,x90823)),x90823)),x90822)) % 169.19/169.66 [9117]~P104(f334(f63(x91171),x91172))+P104(f334(f63(f886(x91171,a871)),f334(f334(f62(x91171),x91172),x91173)))+~P104(f334(f334(f249(f886(f885(x91171,x91171),a871)),x91173),f334(f334(f271(x91171,x91171),x91172),f334(f18(f886(x91171,a871),x91171),x91172)))) % 169.19/169.66 [9151]P49(x91511,x91512,x91513)+P104(f334(f334(f336(x91511),f693(x91513,x91512,x91511)),x91512))+~P104(f334(f334(f249(f886(f885(x91511,x91511),a871)),x91513),f334(f334(f271(x91511,x91511),x91512),f334(f18(f886(x91511,a871),x91511),x91512)))) % 169.19/169.66 [9152]P49(x91521,x91522,x91523)+P104(f334(f334(f336(x91521),f698(x91522,x91523,x91521)),x91522))+~P104(f334(f334(f249(f886(f885(x91521,x91521),a871)),x91523),f334(f334(f271(x91521,x91521),x91522),f334(f18(f886(x91521,a871),x91521),x91522)))) % 169.19/169.66 [9185]~P62(x91851)+~P104(f334(f334(f250(x91851),x91852),x91853))+P104(f334(f334(f250(x91851),f334(f334(f292(x91851),f334(f334(f81(x91851),x91852),x91853)),f334(f334(f81(x91851),f79(x91851)),f79(x91851)))),x91853)) % 169.19/169.66 [9214]~P61(x92141)+P104(f334(f334(f249(x92141),x92142),x92143))+~P104(f334(f334(f249(x92141),f334(f334(f82(x92141),f854(x92143,x92142,x92141)),x92142)),x92143)) % 169.19/169.66 [9340]E(f334(f196(f878(f878(x93401))),f334(f136(f878(x93401),f334(f334(f10(a877,a871,f878(x93401)),f334(f250(a877),x93402)),f196(f878(x93401)))),f181(x93401,x93403))),f334(f196(f878(x93401)),f334(f334(f165(f878(x93401)),x93403),x93402)))+~P30(a877,f334(f169(a877),f334(f334(f154(f878(x93401),a877),f196(f878(x93401))),x93403)))+~P104(f334(f334(f250(a877),x93402),f334(f196(f878(f878(x93401))),x93403))) % 169.19/169.66 [9444]~P39(x94441,x94442)+P22(x94441,f334(f334(f269(f886(f885(x94441,x94441),a871),f886(f885(x94441,x94441),a871)),x94442),x94443))+~P104(f334(f334(f249(f886(f885(x94441,x94441),a871)),f334(f334(f291(x94441,x94441,x94441),x94442),x94443)),x94442)) % 169.19/169.66 [9451]E(f334(f334(f154(f878(x94511),x94511),f334(f334(f9(f878(x94511),a877,x94511),f165(x94511)),x94512)),f334(f136(f878(x94511),f334(f334(f10(a877,a871,f878(x94511)),f334(f250(a877),x94512)),f196(f878(x94511)))),f181(x94511,x94513))),f334(f334(f165(f878(x94511)),x94513),x94512))+~P30(a877,f334(f169(a877),f334(f334(f154(f878(x94511),a877),f196(f878(x94511))),x94513)))+~P104(f334(f334(f250(a877),x94512),f334(f196(f878(f878(x94511))),x94513))) % 169.19/169.66 [9581]P49(x95811,x95812,x95813)+~P104(f334(f334(f336(f885(x95811,x95811)),f334(f334(f269(x95811,x95811),f693(x95813,x95812,x95811)),f693(x95813,x95812,x95811))),x95813))+~P104(f334(f334(f249(f886(f885(x95811,x95811),a871)),x95813),f334(f334(f271(x95811,x95811),x95812),f334(f18(f886(x95811,a871),x95811),x95812)))) % 169.19/169.66 [9582]P49(x95821,x95822,x95823)+~P104(f334(f334(f336(f885(x95821,x95821)),f334(f334(f269(x95821,x95821),f698(x95822,x95823,x95821)),f698(x95822,x95823,x95821))),x95823))+~P104(f334(f334(f249(f886(f885(x95821,x95821),a871)),x95823),f334(f334(f271(x95821,x95821),x95822),f334(f18(f886(x95821,a871),x95821),x95822)))) % 169.19/169.66 [9757]~P137(x97571)+~P122(x97571)+E(f334(f334(f292(x97571),f334(f105(x97571),f334(f334(f74(f885(a1,a1),a1,x97572,f268(a1,a1)),f221(x97572)),x97573))),f334(f105(x97571),f334(f334(f74(f885(a1,a1),a1,x97572,f272(a1,a1)),f221(x97572)),x97573))),f231(x97572,x97571,x97573)) % 169.19/169.66 [9956]~E(x99563,f2(a877))+~E(f334(f196(f878(x99561)),f334(f334(f165(f878(x99561)),x99562),f647(x99563,x99561,x99562))),x99563)+E(f334(f334(f154(a877,f878(x99561)),f334(f334(f9(a877,f878(a877),f878(x99561)),f334(f334(f10(f886(a877,x99561),f886(f878(a877),f878(x99561)),a877),f154(a877,x99561)),f334(f9(a877,a877,x99561),f334(f334(f10(f878(x99561),f886(a877,x99561),a877),f165(x99561)),f334(f165(f878(x99561)),x99562))))),f139(a877,f334(f304(a877,f2(a877)),f334(f196(f878(f878(x99561))),x99562))))),f139(a877,f334(f304(a877,f2(a877)),x99563))),f181(x99561,x99562)) % 169.19/169.66 [9957]E(x99571,f116(f878(x99572)))+~E(f334(f196(f878(x99572)),f334(f334(f165(f878(x99572)),x99571),f647(x99573,x99572,x99571))),x99573)+E(f334(f334(f154(a877,f878(x99572)),f334(f334(f9(a877,f878(a877),f878(x99572)),f334(f334(f10(f886(a877,x99572),f886(f878(a877),f878(x99572)),a877),f154(a877,x99572)),f334(f9(a877,a877,x99572),f334(f334(f10(f878(x99572),f886(a877,x99572),a877),f165(x99572)),f334(f165(f878(x99572)),x99571))))),f139(a877,f334(f304(a877,f2(a877)),f334(f196(f878(f878(x99572))),x99571))))),f139(a877,f334(f304(a877,f2(a877)),x99573))),f181(x99572,x99571)) % 169.19/169.66 [9958]~E(x99583,f2(a877))+E(f334(f334(f154(a877,f878(x99581)),f334(f334(f9(a877,f878(a877),f878(x99581)),f334(f334(f10(f886(a877,x99581),f886(f878(a877),f878(x99581)),a877),f154(a877,x99581)),f334(f9(a877,a877,x99581),f334(f334(f10(f878(x99581),f886(a877,x99581),a877),f165(x99581)),f334(f165(f878(x99581)),x99582))))),f139(a877,f334(f304(a877,f2(a877)),f334(f196(f878(f878(x99581))),x99582))))),f139(a877,f334(f304(a877,f2(a877)),x99583))),f181(x99581,x99582))+P104(f334(f334(f250(a877),f647(x99583,x99581,x99582)),f334(f196(f878(f878(x99581))),x99582))) % 169.19/169.66 [9959]E(x99591,f116(f878(x99592)))+E(f334(f334(f154(a877,f878(x99592)),f334(f334(f9(a877,f878(a877),f878(x99592)),f334(f334(f10(f886(a877,x99592),f886(f878(a877),f878(x99592)),a877),f154(a877,x99592)),f334(f9(a877,a877,x99592),f334(f334(f10(f878(x99592),f886(a877,x99592),a877),f165(x99592)),f334(f165(f878(x99592)),x99591))))),f139(a877,f334(f304(a877,f2(a877)),f334(f196(f878(f878(x99592))),x99591))))),f139(a877,f334(f304(a877,f2(a877)),x99593))),f181(x99592,x99591))+P104(f334(f334(f250(a877),f647(x99593,x99592,x99591)),f334(f196(f878(f878(x99592))),x99591))) % 169.19/169.66 [7755]E(f334(f334(f81(a877),f334(f106(a877),x77551)),f334(f334(f81(a877),f334(f106(a877),x77552)),x77553)),f334(f334(f81(a877),f334(f106(a877),f334(f334(f81(a1),x77551),x77552))),x77553))+P104(f334(a201,f334(f106(a1),x77551)))+P104(f334(a201,f334(f106(a1),x77552))) % 169.19/169.66 [8506]~P104(f334(f63(x85061),x85062))+~P104(f334(f334(f336(x85061),x85063),x85062))+E(f334(a115,f334(f39(x85061),f334(f334(f3(f886(x85061,a871)),x85062),f334(f334(f312(x85061),x85063),f195(f886(x85061,a871)))))),f334(f39(x85061),x85062)) % 169.19/169.66 [8522]~P104(f334(f63(x85221),x85222))+~P104(f334(f334(f336(x85221),x85223),x85222))+E(f334(f334(f81(a877),f79(a877)),f334(f39(x85221),f334(f334(f3(f886(x85221,a871)),x85222),f334(f334(f312(x85221),x85223),f195(f886(x85221,a871)))))),f334(f39(x85221),x85222)) % 169.19/169.66 [8607]~P107(x86071)+~P104(f334(f63(x86071),x86073))+E(f334(f334(f148(x86071,x86071,f7(x86071)),x86072),f139(x86071,f334(f334(f3(f886(x86071,a871)),x86073),f334(f334(f312(x86071),x86072),f195(f886(x86071,a871)))))),f139(x86071,f334(f334(f312(x86071),x86072),x86073))) % 169.19/169.66 [8757]~P104(f334(f63(x87571),x87573))+~P104(f334(f63(x87571),x87572))+E(f334(f334(f81(a877),f334(f39(x87571),f334(f334(f113(f886(x87571,a871)),x87572),x87573))),f334(f39(x87571),f334(f334(f104(f886(x87571,a871)),x87572),x87573))),f334(f334(f81(a877),f334(f39(x87571),x87572)),f334(f39(x87571),x87573))) % 169.19/169.66 [9904]~P21(x99041,f886(f886(x99041,a871),a871),f334(f334(f9(x99041,f886(f885(x99041,x99041),a871),f886(f886(x99041,a871),a871)),f334(f334(f10(f886(x99041,a871),f886(f886(f885(x99041,x99041),a871),f886(f886(x99041,a871),a871)),x99041),f62(x99041)),f334(f334(f9(x99041,f886(x99041,a871),f886(x99041,a871)),f312(x99041)),f195(f886(x99041,a871))))),x99043),x99042)+~P104(f334(f63(x99041),x99042))+E(f334(f39(f886(x99041,a871)),f334(f334(f62(x99041),x99042),x99043)),f334(f39(x99041),x99042)) % 169.19/169.66 [8021]~P92(x80211)+P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x80213)))+E(f334(f334(f259(x80211),x80212),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),x80213),x80213)),a100))),f79(x80211)) % 169.19/169.66 [9428]~P92(x94281)+~P104(f334(f334(f249(a1),f2(a1)),f334(f106(a1),x94283)))+E(f334(f334(f259(x94281),x94282),f334(f106(a877),f334(f334(f3(a1),f334(f334(f81(a1),x94283),x94283)),a100))),f334(f334(f87(x94281,x94281),f334(f334(f259(x94281),x94282),f334(f106(a877),x94283))),f334(f334(f20(x94281,x94281,x94281),f334(f334(f10(x94281,f886(x94281,x94281),x94281),f82(x94281)),f334(f82(x94281),x94282))),f7(x94281)))) % 169.19/169.66 [9817]~P104(f334(f137(x98171),x98173))+~P104(f334(f334(f336(x98171),x98172),f334(f173(x98171),x98173)))+E(f334(f334(f138(x98171),f334(f196(f878(x98171)),f178(x98171,f334(f334(f10(a871,a871,x98171),a329),f334(f334(f9(x98171,x98171,a871),a331),x98172)),f334(f169(x98171),x98173)))),f334(f169(x98171),x98173)),f334(f334(f151(x98171),x98172),f334(f169(x98171),f178(x98171,f334(f334(f10(a871,a871,x98171),a329),f334(f334(f9(x98171,x98171,a871),a331),x98172)),x98173)))) % 169.19/169.66 [9885]P104(f334(f334(f249(f886(f885(x98851,x98851),a871)),f310(x98851,x98852)),x98853))+~P104(f334(f334(f249(f886(f885(x98851,x98851),a871)),f310(x98851,f195(f886(f885(x98851,x98851),a871)))),x98853))+~P104(f334(f334(f249(f886(f885(x98851,x98851),a871)),f334(f334(f291(x98851,x98851,x98851),f334(f334(f104(f886(f885(x98851,x98851),a871)),f310(x98851,x98852)),x98853)),x98852)),x98853)) % 169.19/169.66 [9728]~P104(f334(f63(x97281),f334(f254(x97281),x97283)))+~P104(f334(f63(x97281),f334(f254(x97281),x97282)))+P104(f334(f63(x97281),f334(f254(x97281),f334(f334(f20(x97281,a871,a871),f334(f334(f10(a871,f886(a871,a871),x97281),a333),x97282)),x97283)))) % 169.19/169.66 [10019]P104(f334(f334(f249(f886(f885(x100191,x100191),a871)),f334(f334(f291(x100191,x100191,x100191),x100192),f310(x100191,x100192))),x100193))+~P104(f334(f334(f249(f886(f885(x100191,x100191),a871)),x100192),x100193))+~P104(f334(f334(f249(f886(f885(x100191,x100191),a871)),f334(f334(f291(x100191,x100191,x100191),f334(f334(f104(f886(f885(x100191,x100191),a871)),f334(f334(f291(x100191,x100191,x100191),x100192),f310(x100191,x100192))),x100193)),x100192)),x100193)) % 169.19/169.66 [9972]~P120(x99722)+E(x99721,f2(x99722))+~E(f334(f334(f81(x99722),f334(f334(f259(x99722),x99723),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x99722),x99721),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f2(x99722)) % 169.19/169.66 [9973]~P120(x99732)+E(x99731,f2(x99732))+~E(f334(f334(f81(x99732),f334(f334(f259(x99732),x99731),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x99732),x99733),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f2(x99732)) % 169.19/169.66 [9978]~P104(f334(f137(x99781),x99783))+~P104(f334(f334(f336(x99781),x99782),f334(f173(x99781),x99783)))+E(f334(f169(x99781),f334(f172(x99781),f334(f334(f138(x99781),f334(f196(f878(x99781)),f178(x99781,f334(f334(f10(a871,a871,x99781),a329),f334(f334(f9(x99781,x99781,a871),a331),x99782)),x99783))),x99783))),f178(x99781,f334(f334(f10(a871,a871,x99781),a329),f334(f334(f9(x99781,x99781,a871),a331),x99782)),f334(f169(x99781),x99783))) % 169.19/169.66 [10063]~P120(x100632)+E(x100631,f2(x100632))+P104(f334(f334(f250(x100632),f2(x100632)),f334(f334(f81(x100632),f334(f334(f259(x100632),x100633),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x100632),x100631),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))))) % 169.19/169.66 [10064]~P120(x100642)+E(x100641,f2(x100642))+P104(f334(f334(f250(x100642),f2(x100642)),f334(f334(f81(x100642),f334(f334(f259(x100642),x100641),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x100642),x100643),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))))) % 169.19/169.66 [10105]~P120(x101051)+P104(f334(f334(f249(x101051),f2(x101051)),x101052))+~P104(f334(f334(f249(x101051),f2(x101051)),f334(f334(f259(x101051),x101052),f334(a115,f334(f334(f82(a877),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),x101053))))) % 169.19/169.66 [5535]~P20(x55351,x55354,x55353)+P20(x55351,x55352,x55353)+~P20(x55351,x55352,x55354) % 169.19/169.66 [4992]~E(x49922,f91(x49923,x49921))+P104(f334(x49921,x49922))+~P104(f334(x49921,x49924)) % 169.19/169.66 [6747]~P39(x67472,x67474)+~P39(x67471,x67473)+P39(f885(x67471,x67472),f327(x67471,x67472,x67473,x67474)) % 169.19/169.66 [5174]~P5(x51744,x51741)+~E(f334(x51741,x51742),f334(x51741,x51743))+P104(f334(f334(x51741,x51742),x51743)) % 169.19/169.66 [5350]~P5(x53504,x53501)+E(f334(x53501,x53502),f334(x53501,x53503))+~P104(f334(f334(x53501,x53502),x53503)) % 169.19/169.66 [5442]~P14(x54423,x54424,x54421)+E(f334(x54421,x54422),f334(f65(x54423,x54424),x54422))+~P104(f334(f63(x54423),x54422)) % 169.19/169.66 [5443]~P3(x54433,x54434,x54431)+E(f334(x54431,x54432),f334(f65(x54433,x54434),x54432))+~P104(f334(f63(x54433),x54432)) % 169.19/169.66 [5568]~P5(x55684,x55681)+~P104(f334(f334(x55681,x55683),x55682))+P104(f334(f334(x55681,x55682),x55683)) % 169.19/169.66 [5638]E(x56381,x56382)+~E(f334(f268(x56383,x56384),x56381),f334(f268(x56383,x56384),x56382))+~E(f334(f272(x56383,x56384),x56381),f334(f272(x56383,x56384),x56382)) % 169.19/169.66 [5663]E(x56631,x56632)+~P104(f334(f49(x56633,x56634),x56632))+~P104(f334(f49(x56633,x56634),x56631)) % 169.19/169.66 [5855]~P72(x58552)+E(f239(x58551,x58552,x58553,x58554),f2(x58552))+P104(f334(f63(x58551),x58554)) % 169.19/169.66 [5991]~P104(f334(f322(x59911,x59912),x59914))+P104(f334(f322(x59911,x59912),x59913))+~P104(f334(f334(x59912,x59913),x59914)) % 169.19/169.66 [7861]E(x78611,f2(a877))+~P104(f334(x78612,x78613))+P104(f334(x78612,f808(x78612,x78613,x78611,x78614))) % 169.19/169.66 [7942]~P107(x79422)+~P104(f334(f137(x79421),x79424))+P104(f334(f137(x79421),f150(x79421,x79422,x79423,x79424))) % 169.19/169.66 [8162]~P104(f334(f63(x81622),x81624))+~P104(f334(f63(x81621),x81623))+P104(f334(f63(f884(x81621,x81622)),f321(x81621,x81622,x81623,x81624))) % 169.19/169.66 [8163]~P104(f334(f137(x81632),x81634))+~P104(f334(f137(x81631),x81633))+P104(f334(f137(f885(x81631,x81632)),f61(x81631,x81632,x81633,x81634))) % 169.19/169.66 [8167]P104(f334(f334(f336(f878(x81671)),f334(f334(f134(x81671),x81672),x81673)),f161(x81671,x81674)))+~P104(f334(f334(f336(f878(x81671)),x81673),f161(x81671,x81674)))+~P104(f334(f334(f336(f878(x81671)),x81672),f161(x81671,x81674))) % 169.19/169.66 [8446]E(x84461,f2(a877))+P104(f334(x84462,x84463))+~P104(f334(x84462,f810(x84462,x84463,x84461,x84464))) % 169.19/169.66 [8485]~P107(x84853)+~P104(f334(f137(x84851),f150(x84851,x84853,x84854,x84852)))+P104(f334(f137(x84851),x84852)) % 169.19/169.66 [8748]~P104(f334(f334(f336(f885(x87481,x87481)),f334(f334(f269(x87481,x87481),x87482),x87484)),f310(x87481,x87483)))+P104(f334(f334(f336(x87481),x87482),f323(x87481,x87483)))+~P104(f334(f334(f336(x87481),x87484),f323(x87481,x87483))) % 169.19/169.66 [5158]~P72(x51582)+E(f334(f334(f8(x51581,x51582),x51583),x51584),f2(x51582))+P104(f334(f63(x51581),x51584)) % 169.19/169.66 [5161]~P68(x51612)+E(f334(f334(f11(x51611,x51612),x51613),x51614),f79(x51612))+P104(f334(f63(x51611),x51614)) % 169.19/169.66 [5313]~P69(x53133)+E(x53131,x53132)+~E(f334(f334(f81(x53133),x53134),x53131),f334(f334(f81(x53133),x53134),x53132)) % 169.19/169.66 [5314]~P70(x53143)+E(x53141,x53142)+~E(f334(f334(f81(x53143),x53144),x53141),f334(f334(f81(x53143),x53144),x53142)) % 169.19/169.66 [5316]~P69(x53163)+E(x53161,x53162)+~E(f334(f334(f81(x53163),x53161),x53164),f334(f334(f81(x53163),x53162),x53164)) % 169.19/169.66 [5438]~P28(x54383)+E(x54381,f195(f886(x54382,a871)))+E(f334(f334(f43(x54382,x54383),x54381),f334(f18(x54383,x54382),x54384)),x54384) % 169.19/169.66 [5439]~P28(x54393)+E(x54391,f195(f886(x54392,a871)))+E(f334(f334(f44(x54392,x54393),x54391),f334(f18(x54393,x54392),x54394)),x54394) % 169.19/169.66 [5651]~P108(x56513)+E(x56511,x56512)+~E(f305(x56513,x56514,x56511),f334(f334(f312(x56513),x56512),f195(f886(x56513,a871)))) % 169.19/169.66 [5652]~P108(x56523)+E(x56521,x56522)+~E(f305(x56523,x56521,x56522),f334(f334(f312(x56523),x56524),f195(f886(x56523,a871)))) % 169.19/169.66 [5712]~P37(x57123,x57121,x57124)+P37(x57123,x57121,f334(f334(f151(x57123),x57122),x57124))+P104(f334(x57121,x57122)) % 169.19/169.66 [5815]~P33(x58151,x58152,x58154)+~P104(f334(x58152,x58153))+P33(x58151,x58152,f334(f334(f151(x58151),x58153),x58154)) % 169.19/169.66 [5948]P104(f334(x59481,x59482))+~P104(f334(f262(x59483,x59481),x59484))+~P104(f334(f334(f336(x59483),x59482),x59484)) % 169.19/169.66 [5957]~P33(x59571,x59572,x59574)+~P33(x59571,x59572,x59573)+P33(x59571,x59572,f334(f334(f134(x59571),x59573),x59574)) % 169.19/169.66 [5967]P35(x59671,x59672,x59673)+~P35(x59671,x59672,f334(f334(f151(x59671),x59674),x59673))+P104(f334(x59672,x59674)) % 169.19/169.66 [5968]P37(x59681,x59682,x59683)+~P37(x59681,x59682,f334(f334(f151(x59681),x59684),x59683))+P104(f334(x59682,x59684)) % 169.19/169.66 [6044]P35(x60441,x60442,x60443)+P35(x60441,x60442,x60444)+~P35(x60441,x60442,f334(f334(f134(x60441),x60444),x60443)) % 169.19/169.66 [6063]~P72(x60631)+E(f334(f334(f8(a877,x60631),x60632),f334(f304(a877,x60633),f334(a115,x60634))),f2(x60631))+~P104(f334(f334(f250(a877),x60634),x60633)) % 169.19/169.66 [6068]~P27(x60681)+~E(f46(x60681,x60682,x60683),f46(x60681,x60684,x60683))+E(f46(x60681,f334(f80(x60681),x60682),x60683),f46(x60681,f334(f80(x60681),x60684),x60683)) % 169.19/169.66 [6136]P104(f334(x61361,x61362))+~E(f334(f136(x61363,x61361),x61364),x61364)+~P104(f334(f334(f336(x61363),x61362),f334(f173(x61363),x61364))) % 169.19/169.66 [6155]~E(f334(f334(f81(a877),x61553),x61552),f334(f334(f81(a877),x61551),x61554))+~P104(f334(f334(f250(a877),x61553),x61554))+P104(f334(f334(f250(a877),x61551),x61552)) % 169.19/169.66 [6159]P35(x61591,x61592,x61593)+~P104(f334(x61592,x61594))+~P104(f334(f334(f336(x61591),x61594),f334(f173(x61591),x61593))) % 169.19/169.66 [6195]~P33(x61953,x61951,x61954)+P104(f334(x61951,x61952))+~P104(f334(f334(f336(x61953),x61952),f334(f173(x61953),x61954))) % 169.19/169.66 [6197]~E(f334(f136(x61971,x61972),x61973),f116(x61971))+~P104(f334(x61972,x61974))+~P104(f334(f334(f336(x61971),x61974),f334(f173(x61971),x61973))) % 169.19/169.66 [6198]~E(f178(x61983,x61981,x61984),x61984)+P104(f334(x61981,x61982))+~P104(f334(f334(f336(x61983),x61982),f334(f173(x61983),x61984))) % 169.19/169.66 [6233]~E(x62334,f195(f886(x62332,a871)))+~E(x62333,f195(f886(x62331,a871)))+E(f321(x62331,x62332,x62333,x62334),f195(f886(f884(x62331,x62332),a871))) % 169.19/169.66 [6377]P104(f334(x63771,x63772))+~P104(f334(f160(x63773,x63771),x63774))+~P104(f334(f334(f336(x63773),x63772),f334(f173(x63773),x63774))) % 169.19/169.66 [6646]~P72(x66461)+E(f334(f334(f8(a877,x66461),x66462),f305(a877,x66463,f334(a115,x66464))),f2(x66461))+~P104(f334(f334(f250(a877),f334(a115,x66464)),x66463)) % 169.19/169.66 [6786]~P107(x67861)+E(f334(f334(f3(f886(x67861,a871)),f334(f304(x67861,x67862),x67863)),f334(f304(x67861,x67862),x67864)),f334(f304(x67861,x67864),x67863))+~P104(f334(f334(f249(x67861),x67862),x67864)) % 169.19/169.66 [6858]~E(x68583,x68584)+E(x68581,f2(a877))+P104(f334(f334(f336(x68582),x68583),f334(f173(x68582),f170(x68582,x68581,x68584)))) % 169.19/169.66 [7136]~P104(f334(f334(f336(f878(x71361)),x71364),f161(x71361,x71363)))+P104(f334(f334(f336(x71361),x71362),x71363))+~P104(f334(f334(f336(x71361),x71362),f334(f173(x71361),x71364))) % 169.19/169.66 [7143]~P39(x71431,x71432)+P104(f334(f334(f336(x71431),f760(x71432,x71431,x71433)),x71433))+~P104(f334(f334(f336(x71431),x71434),x71433)) % 169.19/169.66 [7199]~P72(x71991)+E(f334(f334(f334(f67(x71991,x71992,f81(x71991)),x71993),f2(x71991)),x71994),f334(f334(f8(x71992,x71991),x71993),x71994))+~P104(f334(f63(x71992),x71994)) % 169.19/169.66 [7201]~P68(x72011)+E(f334(f334(f334(f67(x72011,x72012,f82(x72011)),x72013),f79(x72011)),x72014),f334(f334(f11(x72012,x72011),x72013),x72014))+~P104(f334(f63(x72012),x72014)) % 169.19/169.66 [7229]P21(x72291,x72292,x72293,x72294)+~E(f334(f39(x72292),f334(f313(x72291,x72292,x72293),x72294)),f334(f39(x72291),x72294))+~P104(f334(f63(x72291),x72294)) % 169.19/169.66 [7416]~P72(x74161)+E(f334(f334(f81(x74161),f334(x74162,x74163)),f334(f334(f8(a877,x74161),x74162),f307(a877,x74163,x74164))),f334(f334(f8(a877,x74161),x74162),f305(a877,x74163,x74164)))+~P104(f334(f334(f249(a877),x74163),x74164)) % 169.19/169.66 [7426]~P72(x74261)+~P21(x74262,x74261,x74263,x74264)+E(f334(f334(f8(x74261,x74261),f35(x74261)),f334(f313(x74262,x74261,x74263),x74264)),f334(f334(f8(x74262,x74261),x74263),x74264)) % 169.19/169.66 [7427]~P68(x74271)+~P21(x74272,x74271,x74273,x74274)+E(f334(f334(f11(x74271,x74271),f35(x74271)),f334(f313(x74272,x74271,x74273),x74274)),f334(f334(f11(x74272,x74271),x74273),x74274)) % 169.19/169.66 [7480]E(f334(f39(f884(x74801,x74802)),f321(x74801,x74802,x74803,x74804)),f334(f334(f81(a877),f334(f39(x74801),x74803)),f334(f39(x74802),x74804)))+~P104(f334(f63(x74802),x74804))+~P104(f334(f63(x74801),x74803)) % 169.19/169.66 [7566]E(x75661,x75662)+P104(f334(f334(f336(x75663),x75661),f334(f173(x75663),f171(x75663,x75662,x75664))))+~P104(f334(f334(f336(x75663),x75661),f334(f173(x75663),x75664))) % 169.19/169.66 [7792]~P72(x77921)+E(f334(f334(f81(x77921),f334(f334(f8(a877,x77921),x77922),f334(f304(a877,x77923),x77924))),f334(x77922,x77924)),f334(f334(f8(a877,x77921),x77922),f334(f304(a877,x77923),f334(a115,x77924))))+P104(f334(f334(f250(a877),x77924),x77923)) % 169.19/169.66 [7843]~P21(x78431,x78432,x78433,f257(f886(x78431,a871)))+~P104(f334(f63(x78432),x78434))+P104(f334(f63(x78431),f334(f314(x78431,x78432,x78433),x78434))) % 169.19/169.66 [7955]P104(f334(f334(f336(f878(x79551)),f334(f334(f151(x79551),x79552),x79553)),f161(x79551,x79554)))+~P104(f334(f334(f336(f878(x79551)),x79553),f161(x79551,x79554)))+~P104(f334(f334(f336(x79551),x79552),x79554)) % 169.19/169.66 [8045]~E(f334(f313(x80453,x80451,x80454),f257(f886(x80453,a871))),f257(f886(x80451,a871)))+P104(f334(f63(x80451),x80452))+~P104(f334(f63(x80453),f334(f314(x80453,x80451,x80454),x80452))) % 169.19/169.66 [8135]~P21(x81351,x81353,x81354,x81352)+P104(f334(f63(x81351),x81352))+~P104(f334(f63(x81353),f334(f313(x81351,x81353,x81354),x81352))) % 169.19/169.66 [8156]~E(x81562,x81563)+P104(f334(f334(f336(f885(x81561,x81561)),f334(f334(f269(x81561,x81561),x81562),x81563)),f266(x81561,x81564)))+~P104(f334(f334(f336(x81561),x81562),x81564)) % 169.19/169.66 [8193]~P72(x81931)+E(f334(f334(f81(x81931),f334(f334(f8(a877,x81931),x81932),f305(a877,x81933,x81934))),f334(x81932,f334(a115,x81934))),f334(f334(f8(a877,x81931),x81932),f305(a877,x81933,f334(a115,x81934))))+P104(f334(f334(f250(a877),f334(a115,x81934)),x81933)) % 169.19/169.66 [8257]P104(f334(x82571,x82572))+~P104(f334(x82571,f334(f334(f165(x82573),x82574),f579(x82571,x82574,x82573))))+~P104(f334(f334(f336(x82573),x82572),f334(f173(x82573),x82574))) % 169.19/169.66 [8394]~P104(f334(f334(f336(x83941),x83942),f323(x83941,x83944)))+P104(f334(f334(f336(f878(x83941)),f334(f334(f151(x83941),x83942),x83943)),f323(f878(x83941),f157(x83941,x83944))))+~P104(f334(f334(f336(f878(x83941)),x83943),f323(f878(x83941),f157(x83941,x83944)))) % 169.19/169.66 [8407]~P21(x84072,x84073,x84074,f456(x84074,x84073,x84072,x84071))+P21(x84072,x84073,x84074,f42(f886(x84072,a871),x84071))+E(x84071,f195(f886(f886(x84072,a871),a871))) % 169.19/169.66 [8667]E(x86671,x86672)+~P104(f334(f334(f336(f885(x86673,x86673)),f334(f334(f269(x86673,x86673),x86671),x86672)),f310(x86673,x86674)))+P104(f334(f334(f336(x86673),x86671),f334(f267(x86673,x86673),x86674))) % 169.19/169.66 [8930]E(x89301,f2(a877))+P104(f334(x89302,x89303))+P104(f334(f334(f336(x89304),f810(x89302,x89303,x89301,x89304)),f334(f173(x89304),f170(x89304,x89301,x89303)))) % 169.19/169.66 [8940]E(x89401,f2(a877))+~P104(f334(x89403,x89404))+P104(f334(f334(f336(x89402),f808(x89403,x89404,x89401,x89402)),f334(f173(x89402),f170(x89402,x89401,x89404)))) % 169.19/169.66 [8945]P21(x89452,x89453,x89454,f42(f886(x89452,a871),x89451))+E(x89451,f195(f886(f886(x89452,a871),a871)))+P104(f334(f334(f336(f886(x89452,a871)),f456(x89454,x89453,x89452,x89451)),x89451)) % 169.19/169.66 [9073]P104(f334(f63(x90731),x90732))+~P104(f334(f63(x90734),f334(f313(x90731,x90734,x90733),x90732)))+P104(f334(f334(f336(x90731),f710(x90733,x90734,x90732,x90731)),x90732)) % 169.19/169.66 [9163]~P28(x91632)+E(f334(f334(f66(x91631,x91632,f334(f334(f10(x91632,f886(x91632,x91632),x91631),f104(x91632)),x91633)),f257(x91632)),x91634),f334(f334(f43(x91631,x91632),x91634),x91633))+~P104(f334(f63(x91631),x91634)) % 169.19/169.66 [9164]~P28(x91642)+E(f334(f334(f66(x91641,x91642,f334(f334(f10(x91642,f886(x91642,x91642),x91641),f113(x91642)),x91643)),f195(x91642)),x91644),f334(f334(f44(x91641,x91642),x91644),x91643))+~P104(f334(f63(x91641),x91644)) % 169.19/169.66 [9242]P104(f334(x92421,x92422))+~P104(f334(x92421,f334(f334(f165(x92423),x92424),f668(x92422,x92421,x92424,x92423))))+~P104(f334(f334(f336(x92423),x92422),f334(f173(x92423),x92424))) % 169.19/169.66 [9262]E(x92621,x92622)+~P104(f334(f334(f336(f885(x92623,x92623)),f334(f334(f269(x92623,x92623),x92621),x92622)),f310(x92623,x92624)))+P104(f334(f334(f336(f885(x92623,x92623)),f334(f334(f269(x92623,x92623),x92621),x92622)),f334(f334(f291(x92623,x92623,x92623),x92624),f310(x92623,x92624)))) % 169.19/169.66 [9306]~E(f334(f196(f878(x93061)),x93062),f334(f196(f878(x93061)),x93063))+~P104(f334(f334(f336(f885(f878(x93061),f878(x93061))),f334(f334(f269(f878(x93061),f878(x93061)),x93062),x93063)),f147(x93061,x93064)))+P104(f334(f334(f336(f885(f878(x93061),f878(x93061))),f334(f334(f269(f878(x93061),f878(x93061)),x93062),x93063)),f145(x93061,x93064))) % 169.19/169.66 [9528]P33(x95281,f334(f334(f20(x95281,a871,a871),f334(f334(f10(a871,f886(a871,a871),x95281),a333),f334(f334(f10(a871,a871,x95281),a329),x95282))),f334(a331,x95283)),x95284)+~P104(f334(x95282,x95283))+~P37(x95281,x95282,f334(f334(f151(x95281),x95283),x95284)) % 169.19/169.66 [9690]~P33(x96901,f334(f334(f20(x96901,a871,a871),f334(f334(f10(a871,f886(a871,a871),x96901),a333),f334(f334(f10(a871,a871,x96901),a329),x96902))),f334(a331,x96903)),x96904)+~P104(f334(x96902,x96903))+P37(x96901,x96902,f334(f334(f151(x96901),x96903),x96904)) % 169.19/169.66 [9694]~P37(x96941,x96942,x96944)+~P33(x96941,f334(f334(f20(x96941,a871,a871),f334(f334(f10(a871,f886(a871,a871),x96941),a333),f334(f334(f10(a871,a871,x96941),a329),x96942))),f334(a331,x96943)),x96944)+P37(x96941,x96942,f334(f334(f151(x96941),x96943),x96944)) % 169.19/169.66 [9731]~P64(x97311)+E(f334(f334(f8(a877,x97311),f334(f334(f20(a877,x97311,x97311),f334(f334(f10(x97311,f886(x97311,x97311),a877),f3(x97311)),x97312)),f334(f334(f10(a877,x97311,a877),x97312),f334(f334(f9(a877,a877,a877),f81(a877)),f79(a877))))),f305(a877,x97313,x97314)),f2(x97311))+P104(f334(f334(f249(a877),x97313),x97314)) % 169.19/169.66 [9971]~P39(x99712,x99714)+~P21(x99712,x99711,x99713,f257(f886(x99712,a871)))+P39(x99711,f334(f313(f885(x99712,x99712),f885(x99711,x99711),f274(x99712,x99711,x99712,x99711,x99713,x99713)),x99714)) % 169.19/169.66 [10134]~E(f334(f196(f878(x101341)),x101343),f334(f196(f878(x101341)),x101342))+P104(f334(f334(f336(f885(f878(x101341),f878(x101341))),f334(f334(f269(f878(x101341),f878(x101341)),x101342),x101343)),f158(x101341,x101344)))+~P104(f334(f334(f273(x101341,x101341,a871),f334(f334(f9(x101341,f886(f885(x101341,x101341),a871),f886(x101341,a871)),f334(f334(f10(f886(x101341,f886(f886(f885(x101341,x101341),a871),a871)),f886(f886(f885(x101341,x101341),a871),f886(x101341,a871)),x101341),f9(x101341,f886(f885(x101341,x101341),a871),a871)),f334(f334(f10(f886(x101341,f885(x101341,x101341)),f886(x101341,f886(f886(f885(x101341,x101341),a871),a871)),x101341),f334(f10(f885(x101341,x101341),f886(f886(f885(x101341,x101341),a871),a871),x101341),f336(f885(x101341,x101341)))),f269(x101341,x101341)))),x101344)),f586(x101344,x101343,x101342,x101341))) % 169.19/169.66 [6120]~P26(x61201)+~E(x61202,f2(x61201))+E(f334(f334(f40(x61201),f334(f334(f82(x61201),x61202),x61203)),f334(f334(f82(x61201),x61202),x61204)),f2(x61201)) % 169.19/169.66 [6158]E(x61581,f116(x61582))+E(x61583,f334(f334(f3(a877),f334(f196(f878(x61582)),x61581)),f79(a877)))+E(f144(x61582,f334(f334(f159(x61582,x61581),x61583),x61584)),f144(x61582,x61581)) % 169.19/169.66 [6186]E(x61861,x61862)+P104(f334(x61863,x61862))+~P104(f334(f334(f334(f312(x61864),x61861),x61863),x61862)) % 169.19/169.66 [6202]~P72(x62021)+~P104(f334(f137(x62022),x62024))+E(f334(f166(x62021),f334(f334(f154(x62022,x62021),x62023),x62024)),f334(f334(f8(x62022,x62021),x62023),f334(f173(x62022),x62024))) % 169.19/169.66 [6226]~P68(x62262)+~P104(f334(f63(x62261),x62264))+E(f334(f334(f11(x62261,x62262),f334(f18(x62262,x62261),x62263)),x62264),f334(f334(f259(x62262),x62263),f334(f39(x62261),x62264))) % 169.19/169.66 [6281]~P59(x62812)+E(x62811,f2(x62812))+E(f334(f334(f292(x62812),f334(f334(f82(x62812),x62813),x62811)),f334(f334(f82(x62812),x62814),x62811)),f334(f334(f292(x62812),x62813),x62814)) % 169.19/169.66 [6282]~P59(x62822)+E(x62821,f2(x62822))+E(f334(f334(f292(x62822),f334(f334(f82(x62822),x62821),x62823)),f334(f334(f82(x62822),x62821),x62824)),f334(f334(f292(x62822),x62823),x62824)) % 169.19/169.66 [6283]~P26(x62832)+E(x62831,f2(x62832))+E(f334(f334(f40(x62832),f334(f334(f82(x62832),x62833),x62831)),f334(f334(f82(x62832),x62834),x62831)),f334(f334(f40(x62832),x62833),x62834)) % 169.19/169.66 [6285]~P26(x62852)+E(x62851,f2(x62852))+E(f334(f334(f40(x62852),f334(f334(f82(x62852),x62851),x62853)),f334(f334(f82(x62852),x62851),x62854)),f334(f334(f40(x62852),x62853),x62854)) % 169.19/169.66 [6347]P104(f334(x63471,x63472))+~E(x63473,f334(f334(f81(a877),x63474),x63472))+~P104(f334(x63471,f334(f334(f3(a877),x63473),x63474))) % 169.19/169.66 [6430]P23(x64301,x64302,x64303)+P31(x64301,f583(x64303,x64302,x64301),x64304)+~P104(f334(f334(f336(f876(x64301)),x64304),x64302)) % 169.19/169.66 [6432]~P104(f334(x64322,x64323))+~P104(f334(f160(x64321,x64322),x64324))+P104(f334(f160(x64321,x64322),f334(f334(f151(x64321),x64323),x64324))) % 169.19/169.66 [6472]E(x64721,f116(x64722))+~E(x64723,f334(f334(f3(a877),f334(f196(f878(x64722)),x64721)),f79(a877)))+E(f144(x64722,f334(f334(f159(x64722,x64721),x64723),x64724)),x64724) % 169.19/169.66 [6495]~P100(x64951)+~P104(f334(f334(f249(x64951),x64952),x64954))+P104(f334(f334(f249(x64951),x64952),f334(f334(f113(x64951),x64953),x64954))) % 169.19/169.66 [6496]~P100(x64961)+~P104(f334(f334(f249(x64961),x64962),x64963))+P104(f334(f334(f249(x64961),x64962),f334(f334(f113(x64961),x64963),x64964))) % 169.19/169.66 [6498]~P107(x64981)+~P104(f334(f334(f249(x64981),x64982),x64984))+P104(f334(f334(f249(x64981),x64982),f334(f334(f248(x64981),x64983),x64984))) % 169.19/169.66 [6500]~P107(x65001)+~P104(f334(f334(f249(x65001),x65002),x65003))+P104(f334(f334(f249(x65001),x65002),f334(f334(f248(x65001),x65003),x65004))) % 169.19/169.66 [6501]~P100(x65011)+~P104(f334(f334(f250(x65011),x65012),x65014))+P104(f334(f334(f250(x65011),x65012),f334(f334(f113(x65011),x65013),x65014))) % 169.19/169.66 [6502]~P100(x65021)+~P104(f334(f334(f250(x65021),x65022),x65023))+P104(f334(f334(f250(x65021),x65022),f334(f334(f113(x65021),x65023),x65024))) % 169.19/169.66 [6504]~P107(x65041)+~P104(f334(f334(f250(x65041),x65042),x65044))+P104(f334(f334(f250(x65041),x65042),f334(f334(f248(x65041),x65043),x65044))) % 169.19/169.66 [6506]~P107(x65061)+~P104(f334(f334(f250(x65061),x65062),x65063))+P104(f334(f334(f250(x65061),x65062),f334(f334(f248(x65061),x65063),x65064))) % 169.19/169.66 [6592]~E(f334(f334(f165(x65921),x65922),x65923),x65924)+E(f334(f334(f159(x65921,x65922),x65923),x65924),x65922)+~P104(f334(f334(f250(a877),x65923),f334(f196(f878(x65921)),x65922))) % 169.19/169.66 [6632]P104(f334(x66321,x66322))+~P104(f334(x66323,x66322))+~P104(f334(f334(f249(f886(x66324,a871)),x66323),x66321)) % 169.19/169.66 [6663]~E(f334(f334(f159(x66631,x66632),x66633),x66634),x66632)+E(f334(f334(f165(x66631),x66632),x66633),x66634)+~P104(f334(f334(f250(a877),x66633),f334(f196(f878(x66631)),x66632))) % 169.19/169.66 [6678]~P104(f334(f160(x66781,x66782),x66784))+~P104(f334(f160(x66781,x66782),x66783))+P104(f334(f160(x66781,x66782),f334(f334(f134(x66781),x66783),x66784))) % 169.19/169.66 [6774]P31(x67741,x67742,x67743)+~P31(x67741,f334(a115,x67742),f595(x67742,x67744,x67741))+~P104(f334(f334(f336(f876(x67741)),x67743),x67744)) % 169.19/169.66 [6783]E(x67831,f195(f886(x67832,a871)))+E(x67833,f195(f886(x67834,a871)))+~E(f334(f334(f271(x67834,x67832),x67833),f334(f18(f886(x67832,a871),x67834),x67831)),f195(f886(f885(x67834,x67832),a871))) % 169.19/169.66 [6802]E(x68021,x68022)+P104(f334(f334(f336(x68023),x68021),x68024))+~P104(f334(f334(f336(x68023),x68021),f334(f334(f312(x68023),x68022),x68024))) % 169.19/169.66 [6819]~P107(x68191)+P104(f334(f334(f249(x68191),x68192),x68193))+~P104(f334(f334(f249(x68191),x68192),f334(f334(f247(x68191),x68194),x68193))) % 169.19/169.66 [6821]~P107(x68211)+P104(f334(f334(f249(x68211),x68212),x68213))+~P104(f334(f334(f249(x68211),x68212),f334(f334(f247(x68211),x68213),x68214))) % 169.19/169.66 [6823]~P101(x68231)+P104(f334(f334(f249(x68231),x68232),x68233))+~P104(f334(f334(f249(x68231),x68232),f334(f334(f104(x68231),x68234),x68233))) % 169.19/169.66 [6825]~P101(x68251)+P104(f334(f334(f249(x68251),x68252),x68253))+~P104(f334(f334(f249(x68251),x68252),f334(f334(f104(x68251),x68253),x68254))) % 169.19/169.66 [6826]~P107(x68261)+P104(f334(f334(f250(x68261),x68262),x68263))+~P104(f334(f334(f250(x68261),x68262),f334(f334(f247(x68261),x68264),x68263))) % 169.19/169.66 [6827]~P107(x68271)+P104(f334(f334(f250(x68271),x68272),x68273))+~P104(f334(f334(f250(x68271),x68272),f334(f334(f247(x68271),x68273),x68274))) % 169.19/169.66 [6849]~E(f334(f334(f165(x68491),x68493),x68494),x68492)+P104(f334(f334(f336(x68491),x68492),f334(f173(x68491),x68493)))+~P104(f334(f334(f250(a877),x68494),f334(f196(f878(x68491)),x68493))) % 169.39/169.66 [6861]~P107(x68611)+~P30(x68611,f334(f334(f151(x68611),x68612),f334(f334(f151(x68611),x68613),x68614)))+P104(f334(f334(f249(x68611),x68612),x68613)) % 169.39/169.66 [7001]~P33(x70012,x70011,x70013)+P104(f334(x70011,f334(f334(f165(x70012),x70013),x70014)))+~P104(f334(f334(f250(a877),x70014),f334(f196(f878(x70012)),x70013))) % 169.39/169.66 [7020]E(x70201,f2(a1))+E(f334(f334(f40(a1),x70202),x70201),x70203)+~P104(f334(f50(x70202,x70201),f334(f334(f269(a1,a1),x70203),x70204))) % 169.39/169.66 [7041]E(f46(a1,x70412,x70411),x70413)+E(x70411,f2(a1))+~P104(f334(f50(x70412,x70411),f334(f334(f269(a1,a1),x70414),x70413))) % 169.39/169.66 [7160]P104(f334(f334(f336(x71601),x71602),x71603))+~P104(f334(f334(f336(x71601),x71602),x71604))+~P104(f334(f334(f250(f886(x71601,a871)),x71604),x71603)) % 169.39/169.66 [7161]P104(f334(f334(f336(x71611),x71612),x71613))+~P104(f334(f334(f336(x71611),x71612),x71614))+~P104(f334(f334(f249(f886(x71611,a871)),x71614),x71613)) % 169.39/169.66 [7269]P35(x72691,x72692,x72693)+~P104(f334(x72692,f334(f334(f165(x72691),x72693),x72694)))+~P104(f334(f334(f250(a877),x72694),f334(f196(f878(x72691)),x72693))) % 169.39/169.66 [7381]~P106(x73812)+~P104(f334(f334(f250(f886(x73811,x73812)),x73813),x73814))+P104(f334(f334(f249(f886(x73811,x73812)),x73813),x73814)) % 169.39/169.66 [7468]~P20(x74681,x74682,x74684)+P20(x74681,x74682,f334(f334(f312(f876(x74681)),x74683),x74684))+~P20(x74681,x74682,f334(f334(f312(f876(x74681)),x74683),f195(f886(f876(x74681),a871)))) % 169.39/169.66 [7512]~P104(f334(f334(f336(x75121),x75122),x75124))+P104(f334(f334(f336(x75121),x75122),f41(f886(x75121,a871),x75123)))+~P104(f334(f334(f336(f886(x75121,a871)),x75124),x75123)) % 169.39/169.66 [7524]P31(x75241,x75242,x75243)+P104(f334(f334(f336(f876(x75241)),f595(x75242,x75244,x75241)),x75244))+~P104(f334(f334(f336(f876(x75241)),x75243),x75244)) % 169.39/169.66 [7544]~P81(x75441)+~P104(f334(f334(f249(x75441),x75443),x75444))+P104(f334(f334(f249(x75441),f334(f334(f81(x75441),x75442),x75443)),f334(f334(f81(x75441),x75442),x75444))) % 169.39/169.66 [7545]~P82(x75451)+~P104(f334(f334(f249(x75451),x75453),x75454))+P104(f334(f334(f249(x75451),f334(f334(f81(x75451),x75452),x75453)),f334(f334(f81(x75451),x75452),x75454))) % 169.39/169.66 [7546]~P81(x75461)+~P104(f334(f334(f249(x75461),x75462),x75464))+P104(f334(f334(f249(x75461),f334(f334(f81(x75461),x75462),x75463)),f334(f334(f81(x75461),x75464),x75463))) % 169.39/169.66 [7547]~P82(x75471)+~P104(f334(f334(f249(x75471),x75472),x75474))+P104(f334(f334(f249(x75471),f334(f334(f81(x75471),x75472),x75473)),f334(f334(f81(x75471),x75474),x75473))) % 169.39/169.66 [7548]~P81(x75481)+~P104(f334(f334(f250(x75481),x75483),x75484))+P104(f334(f334(f250(x75481),f334(f334(f81(x75481),x75482),x75483)),f334(f334(f81(x75481),x75482),x75484))) % 169.39/169.66 [7549]~P84(x75491)+~P104(f334(f334(f250(x75491),x75493),x75494))+P104(f334(f334(f250(x75491),f334(f334(f81(x75491),x75492),x75493)),f334(f334(f81(x75491),x75492),x75494))) % 169.39/169.66 [7550]~P81(x75501)+~P104(f334(f334(f250(x75501),x75502),x75504))+P104(f334(f334(f250(x75501),f334(f334(f81(x75501),x75502),x75503)),f334(f334(f81(x75501),x75504),x75503))) % 169.39/169.66 [7551]~P84(x75511)+~P104(f334(f334(f250(x75511),x75512),x75514))+P104(f334(f334(f250(x75511),f334(f334(f81(x75511),x75512),x75513)),f334(f334(f81(x75511),x75514),x75513))) % 169.39/169.66 [7560]~P109(x75601)+~P90(x75601)+E(f334(f334(f3(x75601),f334(f334(f82(x75601),x75602),f334(f106(x75601),x75603))),f334(f334(f82(x75601),x75604),f334(f106(x75601),x75603))),f334(f334(f82(x75601),f334(f334(f3(x75601),x75602),x75604)),f334(f106(x75601),x75603))) % 169.39/169.66 [7561]~P139(x75611)+~P90(x75611)+E(f334(f334(f81(x75611),f334(f334(f82(x75611),x75612),f334(f106(x75611),x75613))),f334(f334(f82(x75611),x75614),f334(f106(x75611),x75613))),f334(f334(f82(x75611),f334(f334(f81(x75611),x75612),x75614)),f334(f106(x75611),x75613))) % 169.39/169.66 [7597]~P72(x75971)+E(f334(f334(f81(x75971),f334(x75972,x75973)),f334(f334(f8(a877,x75971),x75972),f305(a877,f334(a115,x75973),x75974))),f334(f334(f8(a877,x75971),x75972),f305(a877,x75973,x75974)))+~P104(f334(f334(f249(a877),x75973),x75974)) % 169.39/169.66 [7608]~P21(x76082,x76081,x76083,f334(f173(x76082),x76084))+~P104(f334(f137(x76082),x76084))+P104(f334(f137(x76081),f334(f334(f154(x76082,x76081),x76083),x76084))) % 169.39/169.66 [7655]~P104(f334(f334(f249(a877),x76552),x76554))+~P104(f334(f334(f249(a877),x76551),x76553))+P104(f334(f334(f249(a877),f334(f334(f82(a877),x76551),x76552)),f334(f334(f82(a877),x76553),x76554))) % 169.39/169.66 [7656]~P104(f334(f334(f249(a877),x76562),x76564))+~P104(f334(f334(f249(a877),x76561),x76563))+P104(f334(f334(f249(a877),f334(f334(f81(a877),x76561),x76562)),f334(f334(f81(a877),x76563),x76564))) % 169.39/169.66 [7659]~P104(f334(f334(f250(a877),x76592),x76594))+~P104(f334(f334(f250(a877),x76591),x76593))+P104(f334(f334(f250(a877),f334(f334(f81(a877),x76591),x76592)),f334(f334(f81(a877),x76593),x76594))) % 169.39/169.66 [7660]~P104(f334(f334(f249(a1),x76602),x76604))+~P104(f334(f334(f250(a1),x76601),x76603))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x76601),x76602)),f334(f334(f81(a1),x76603),x76604))) % 169.39/169.66 [7708]P104(f334(f334(f336(x77081),x77082),x77083))+~P104(f334(f334(f336(x77081),x77082),f42(f886(x77081,a871),x77084)))+~P104(f334(f334(f336(f886(x77081,a871)),x77083),x77084)) % 169.39/169.66 [7724]~P104(f334(x77241,f578(x77241,x77243,x77242)))+P104(f334(x77241,f334(f334(f165(x77242),x77243),x77244)))+~P104(f334(f334(f250(a877),x77244),f334(f196(f878(x77242)),x77243))) % 169.39/169.66 [7729]P104(f334(x77291,x77292))+~P104(f334(f334(f336(x77294),x77292),f334(f173(x77294),x77293)))+P104(f334(f334(f250(a877),f579(x77291,x77293,x77294)),f334(f196(f878(x77294)),x77293))) % 169.39/169.66 [7777]~P106(x77771)+~P104(f334(f334(f250(f886(x77772,x77771)),x77774),x77773))+~P104(f334(f334(f249(f886(x77772,x77771)),x77773),x77774)) % 169.39/169.66 [7822]~P104(f334(x78224,x78222))+~P104(f334(f334(f336(x78221),x78222),x78223))+P104(f334(f334(f336(x78221),x78222),f334(f334(f104(f886(x78221,a871)),x78223),f334(f254(x78221),x78224)))) % 169.39/169.66 [7964]~P104(f334(f334(f336(x79641),x79643),x79644))+~P104(f334(f334(f250(f886(x79641,a871)),x79642),x79644))+P104(f334(f334(f250(f886(x79641,a871)),x79642),f334(f334(f312(x79641),x79643),x79644))) % 169.39/169.66 [7966]E(f334(f334(f104(f886(x79661,a871)),x79662),x79663),f195(f886(x79661,a871)))+~E(f334(f334(f104(f886(x79661,a871)),f41(f886(x79661,a871),x79664)),x79663),f195(f886(x79661,a871)))+~P104(f334(f334(f336(f886(x79661,a871)),x79662),x79664)) % 169.39/169.66 [8041]P104(f334(f334(f336(x80411),x80412),x80413))+~P104(f334(f334(f249(f886(x80411,a871)),x80413),f334(f334(f312(x80411),x80412),x80414)))+P104(f334(f334(f249(f886(x80411,a871)),x80413),x80414)) % 169.39/169.66 [8058]P104(f334(f334(f336(x80582),f578(x80581,x80583,x80582)),f334(f173(x80582),x80583)))+P104(f334(x80581,f334(f334(f165(x80582),x80583),x80584)))+~P104(f334(f334(f250(a877),x80584),f334(f196(f878(x80582)),x80583))) % 169.39/169.66 [8066]~P104(f334(f334(f249(f886(x80661,a871)),x80662),x80664))+P104(f334(f334(f249(f886(x80661,a871)),x80662),x80663))+~P104(f334(f334(f249(f886(x80661,a871)),x80664),x80663)) % 169.39/169.66 [8067]~P104(f334(f334(f250(f886(x80671,a871)),x80672),x80674))+~P104(f334(f334(f249(f886(x80671,a871)),x80674),x80673))+P104(f334(f334(f250(f886(x80671,a871)),x80672),x80673)) % 169.39/169.66 [8068]~P104(f334(f334(f249(f886(x80681,a871)),x80682),x80684))+~P104(f334(f334(f250(f886(x80681,a871)),x80684),x80683))+P104(f334(f334(f250(f886(x80681,a871)),x80682),x80683)) % 169.39/169.66 [8069]~P104(f334(f334(f250(f886(x80691,a871)),x80692),x80694))+P104(f334(f334(f250(f886(x80691,a871)),x80692),x80693))+~P104(f334(f334(f250(f886(x80691,a871)),x80694),x80693)) % 169.39/169.66 [8109]~P104(f334(f334(f336(x81091),x81094),x81093))+~P104(f334(f334(f250(f886(x81091,a871)),x81092),f334(f334(f312(x81091),x81094),x81093)))+P104(f334(f334(f250(f886(x81091,a871)),x81092),x81093)) % 169.39/169.66 [8120]~P81(x81201)+P104(f334(f334(f249(x81201),x81202),x81203))+~P104(f334(f334(f249(x81201),f334(f334(f81(x81201),x81204),x81202)),f334(f334(f81(x81201),x81204),x81203))) % 169.39/169.66 [8122]~P81(x81221)+P104(f334(f334(f249(x81221),x81222),x81223))+~P104(f334(f334(f249(x81221),f334(f334(f81(x81221),x81222),x81224)),f334(f334(f81(x81221),x81223),x81224))) % 169.39/169.66 [8124]~P81(x81241)+P104(f334(f334(f250(x81241),x81242),x81243))+~P104(f334(f334(f250(x81241),f334(f334(f81(x81241),x81244),x81242)),f334(f334(f81(x81241),x81244),x81243))) % 169.39/169.66 [8126]~P81(x81261)+P104(f334(f334(f250(x81261),x81262),x81263))+~P104(f334(f334(f250(x81261),f334(f334(f81(x81261),x81262),x81264)),f334(f334(f81(x81261),x81263),x81264))) % 169.39/169.66 [8174]P104(f334(x81741,x81742))+~E(f334(f334(f138(x81743),f334(f196(f878(x81743)),f178(x81743,x81741,x81744))),x81744),f116(x81743))+~P104(f334(f334(f336(x81743),x81742),f334(f173(x81743),x81744))) % 169.39/169.66 [8299]P104(f334(x82991,x82992))+~P104(f334(f334(f336(x82993),x82992),f334(f173(x82993),x82994)))+P104(f334(f334(f250(a877),f334(f196(f878(x82993)),f334(f136(x82993,x82991),x82994))),f334(f196(f878(x82993)),x82994))) % 169.39/169.66 [8759]~P104(f334(x87591,f747(x87591,x87593,x87592,x87594)))+P104(f334(x87591,f334(f334(f165(x87592),x87593),x87594)))+~P104(f334(f334(f250(a877),x87594),f334(f196(f878(x87592)),x87593))) % 169.39/169.66 [8782]~P21(x87824,x87823,x87821,f257(f886(x87824,a871)))+E(f334(x87821,f418(x87822,x87821,x87823,x87824)),x87822)+~P104(f334(f334(f336(x87823),x87822),f334(f313(x87824,x87823,x87821),f257(f886(x87824,a871))))) % 169.39/169.66 [8847]E(f178(x88471,x88472,x88473),f334(f334(f176(x88471),x88474),x88473))+P104(f334(f334(f250(a877),f661(x88472,x88473,x88471,x88474)),x88474))+P104(f334(f334(f250(a877),x88474),f334(f196(f878(x88471)),x88473))) % 169.39/169.66 [8850]E(f178(x88501,x88502,x88503),f334(f334(f176(x88501),x88504),x88503))+P104(f334(f334(f250(a877),f661(x88502,x88503,x88501,x88504)),x88504))+P104(f334(x88502,f334(f334(f165(x88501),x88503),x88504))) % 169.39/169.66 [8879]P104(f334(x88791,x88792))+~P104(f334(f334(f336(x88794),x88792),f334(f173(x88794),x88793)))+P104(f334(f334(f250(a877),f668(x88792,x88791,x88793,x88794)),f334(f196(f878(x88794)),x88793))) % 169.39/169.66 [8882]E(f178(x88821,x88822,x88823),f334(f334(f176(x88821),x88824),x88823))+P104(f334(f334(f250(a877),x88824),f334(f196(f878(x88821)),x88823)))+P104(f334(f334(f250(a877),f661(x88822,x88823,x88821,x88824)),f334(f196(f878(x88821)),x88823))) % 169.39/169.66 [8889]E(f178(x88891,x88892,x88893),f334(f334(f176(x88891),x88894),x88893))+P104(f334(x88892,f334(f334(f165(x88891),x88893),x88894)))+P104(f334(f334(f250(a877),f661(x88892,x88893,x88891,x88894)),f334(f196(f878(x88891)),x88893))) % 169.39/169.66 [8916]~P119(x89164)+P104(f334(f334(f336(x89161),f459(x89162,x89163,x89161,x89164)),x89163))+P104(f334(f334(f250(x89164),f2(x89164)),f334(f334(f11(x89161,x89164),x89162),x89163))) % 169.39/169.66 [8917]~P119(x89174)+P104(f334(f334(f336(x89171),f460(x89172,x89173,x89171,x89174)),x89173))+P104(f334(f334(f249(x89174),f2(x89174)),f334(f334(f11(x89171,x89174),x89172),x89173))) % 169.39/169.66 [8947]~P104(f334(f63(x89471),x89474))+P104(f334(f334(f336(x89471),f697(x89472,x89473,x89474,x89471)),x89474))+P104(f334(f63(f885(x89471,x89473)),f334(f334(f271(x89471,x89473),x89474),x89472))) % 169.39/169.66 [8975]P104(f334(f334(f336(x89752),f747(x89751,x89753,x89752,x89754)),f334(f173(x89752),x89753)))+P104(f334(x89751,f334(f334(f165(x89752),x89753),x89754)))+~P104(f334(f334(f250(a877),x89754),f334(f196(f878(x89752)),x89753))) % 169.39/169.66 [9102]P104(f334(f334(f249(a877),x91024),f334(f196(f878(x91022)),f178(x91022,x91023,x91021))))+P104(f334(f334(f250(a877),f662(x91021,x91022,x91023,x91024)),x91024))+~P104(f334(f334(f249(a877),x91024),f334(f196(f878(x91022)),x91021))) % 169.39/169.66 [9204]~E(f334(f334(f179(x92041,x92042),x92043),f711(x92044,x92043,x92042,x92041)),f334(f334(f179(x92041,x92042),x92044),f711(x92044,x92043,x92042,x92041)))+E(f334(f179(x92041,x92042),x92043),f334(f179(x92041,x92042),x92044))+~E(f334(f173(x92041),f334(f334(f154(f885(x92041,x92042),x92041),f268(x92041,x92042)),x92043)),f334(f173(x92041),f334(f334(f154(f885(x92041,x92042),x92041),f268(x92041,x92042)),x92044))) % 169.39/169.66 [9245]E(f178(x92451,x92452,x92453),f334(f334(f176(x92451),x92454),x92453))+~P104(f334(x92452,f334(f334(f165(x92451),x92453),f661(x92452,x92453,x92451,x92454))))+P104(f334(f334(f250(a877),x92454),f334(f196(f878(x92451)),x92453))) % 169.39/169.66 [9249]E(f178(x92491,x92492,x92493),f334(f334(f176(x92491),x92494),x92493))+~P104(f334(x92492,f334(f334(f165(x92491),x92493),f661(x92492,x92493,x92491,x92494))))+P104(f334(x92492,f334(f334(f165(x92491),x92493),x92494))) % 169.39/169.66 [9256]~P104(f334(f63(x92561),x92563))+~P104(f334(f63(x92562),f334(x92564,f697(x92564,x92562,x92563,x92561))))+P104(f334(f63(f885(x92561,x92562)),f334(f334(f271(x92561,x92562),x92563),x92564))) % 169.39/169.66 [9264]~P119(x92641)+~P104(f334(f334(f249(x92641),f2(x92641)),f334(x92643,f460(x92643,x92644,x92642,x92641))))+P104(f334(f334(f249(x92641),f2(x92641)),f334(f334(f11(x92642,x92641),x92643),x92644))) % 169.39/169.66 [9265]~P119(x92651)+~P104(f334(f334(f250(x92651),f2(x92651)),f334(x92653,f459(x92653,x92654,x92652,x92651))))+P104(f334(f334(f250(x92651),f2(x92651)),f334(f334(f11(x92652,x92651),x92653),x92654))) % 169.39/169.66 [9271]~E(f334(f196(f878(x92714)),x92712),f334(f196(f878(x92714)),x92713))+P104(f334(f334(f336(f885(f878(x92714),f878(x92714))),f334(f334(f269(f878(x92714),f878(x92714)),x92713),x92712)),f158(x92714,x92711)))+P104(f334(f334(f250(a877),f585(x92711,x92712,x92713,x92714)),f334(f196(f878(x92714)),x92713))) % 169.39/169.66 [9320]~P104(f334(x93203,f334(f334(f165(x93202),x93204),f662(x93204,x93202,x93203,x93201))))+P104(f334(f334(f249(a877),x93201),f334(f196(f878(x93202)),f178(x93202,x93203,x93204))))+~P104(f334(f334(f249(a877),x93201),f334(f196(f878(x93202)),x93204))) % 169.39/169.66 [9394]E(f334(f334(f176(x93941),f610(x93942,x93943,x93944,x93941)),x93943),f334(f334(f176(x93941),f610(x93942,x93943,x93944,x93941)),x93944))+~P104(f334(f334(f336(f885(f878(x93941),f878(x93941))),f334(f334(f269(f878(x93941),f878(x93941)),x93944),x93943)),f147(x93941,x93942)))+P104(f334(f334(f250(a877),f334(f196(f878(x93941)),x93944)),f334(f196(f878(x93941)),x93943))) % 169.39/169.66 [9447]~P104(f334(f334(f250(a877),f2(a877)),x94473))+~P104(f334(f334(f250(a877),x94474),x94471))+P104(f334(f334(f250(a877),f334(f334(f81(a877),f334(f334(f82(a877),x94471),f46(a877,x94472,x94473))),x94474)),f334(f334(f82(a877),x94471),x94473))) % 169.39/169.66 [9634]~P106(x96342)+~P104(f334(f334(f249(x96342),f334(x96343,f391(x96344,x96343,x96341,x96342))),f334(x96344,f391(x96344,x96343,x96341,x96342))))+P104(f334(f334(f249(f886(x96341,x96342)),x96343),x96344)) % 169.39/169.66 [9738]~P64(x97381)+E(f334(f334(f8(a877,x97381),f334(f334(f20(a877,x97381,x97381),f334(f334(f10(x97381,f886(x97381,x97381),a877),f3(x97381)),x97382)),f334(f334(f10(a877,x97381,a877),x97382),f334(f334(f9(a877,a877,a877),f81(a877)),f79(a877))))),f305(a877,x97383,x97384)),f334(f334(f3(x97381),f334(x97382,x97383)),f334(x97382,f334(f334(f81(a877),x97384),f79(a877)))))+~P104(f334(f334(f249(a877),x97383),x97384)) % 169.39/169.66 [6853]E(f334(f334(f134(x68531),x68532),x68533),x68534)+~E(x68533,f334(f334(f138(x68531),f334(f196(f878(x68531)),x68532)),x68534))+~E(f334(f334(f176(x68531),f334(f196(f878(x68531)),x68532)),x68534),x68532) % 169.39/169.66 [6909]~P60(x69092)+E(x69091,f2(x69092))+E(f334(f334(f292(x69092),f334(f334(f259(x69092),x69093),x69094)),f334(f334(f259(x69092),x69091),x69094)),f334(f334(f259(x69092),f334(f334(f292(x69092),x69093),x69091)),x69094)) % 169.39/169.66 [7043]~E(f334(f196(f878(x70431)),x70433),f334(f196(f878(x70432)),x70434))+~P104(f334(f137(x70431),x70433))+E(f185(x70431,x70432,f334(f179(x70431,x70432),f334(f334(f183(x70431,x70432),x70433),x70434))),f334(f173(x70431),x70433)) % 169.39/169.66 [7060]~P101(x70601)+~P104(f334(f334(f249(x70601),x70603),x70604))+P104(f334(f334(f249(x70601),f334(f334(f104(x70601),x70602),x70603)),x70604)) % 169.39/169.66 [7061]~P101(x70611)+~P104(f334(f334(f249(x70611),x70612),x70614))+P104(f334(f334(f249(x70611),f334(f334(f104(x70611),x70612),x70613)),x70614)) % 169.39/169.66 [7063]~P107(x70631)+~P104(f334(f334(f249(x70631),x70633),x70634))+P104(f334(f334(f249(x70631),f334(f334(f247(x70631),x70632),x70633)),x70634)) % 169.39/169.66 [7065]~P107(x70651)+~P104(f334(f334(f249(x70651),x70652),x70654))+P104(f334(f334(f249(x70651),f334(f334(f247(x70651),x70652),x70653)),x70654)) % 169.39/169.66 [7066]~P101(x70661)+~P104(f334(f334(f250(x70661),x70663),x70664))+P104(f334(f334(f250(x70661),f334(f334(f104(x70661),x70662),x70663)),x70664)) % 169.39/169.66 [7067]~P101(x70671)+~P104(f334(f334(f250(x70671),x70672),x70674))+P104(f334(f334(f250(x70671),f334(f334(f104(x70671),x70672),x70673)),x70674)) % 169.39/169.66 [7069]~P107(x70691)+~P104(f334(f334(f250(x70691),x70693),x70694))+P104(f334(f334(f250(x70691),f334(f334(f247(x70691),x70692),x70693)),x70694)) % 169.39/169.66 [7071]~P107(x70711)+~P104(f334(f334(f250(x70711),x70712),x70714))+P104(f334(f334(f250(x70711),f334(f334(f247(x70711),x70712),x70713)),x70714)) % 169.39/169.66 [7091]~P104(f334(x70913,x70914))+~P104(f334(x70912,x70914))+P104(f334(f334(f334(f104(f886(x70911,a871)),x70912),x70913),x70914)) % 169.39/169.66 [7215]P20(x72151,x72152,x72153)+~P20(x72151,x72154,x72153)+~P104(f334(f334(f249(f886(f876(x72151),a871)),x72154),x72152)) % 169.39/169.66 [7216]P20(x72161,x72162,x72163)+~P20(x72161,x72162,x72164)+~P104(f334(f334(f249(f886(f876(x72161),a871)),x72163),x72164)) % 169.39/169.66 [7587]~P72(x75871)+E(f334(f334(f81(x75871),f334(x75872,x75873)),f334(f334(f8(a877,x75871),x75872),f334(f304(a877,f334(a115,x75873)),x75874))),f334(f334(f8(a877,x75871),x75872),f334(f304(a877,x75873),x75874)))+~P104(f334(f334(f250(a877),x75873),x75874)) % 169.39/169.66 [7616]~P107(x76161)+P104(f334(f334(f249(x76161),x76162),x76163))+~P104(f334(f334(f249(x76161),f334(f334(f248(x76161),x76164),x76162)),x76163)) % 169.39/169.66 [7618]~P107(x76181)+P104(f334(f334(f249(x76181),x76182),x76183))+~P104(f334(f334(f249(x76181),f334(f334(f248(x76181),x76182),x76184)),x76183)) % 169.39/169.66 [7620]~P100(x76201)+P104(f334(f334(f249(x76201),x76202),x76203))+~P104(f334(f334(f249(x76201),f334(f334(f113(x76201),x76204),x76202)),x76203)) % 169.39/169.66 [7622]~P100(x76221)+P104(f334(f334(f249(x76221),x76222),x76223))+~P104(f334(f334(f249(x76221),f334(f334(f113(x76221),x76222),x76224)),x76223)) % 169.39/169.66 [7623]~P107(x76231)+P104(f334(f334(f250(x76231),x76232),x76233))+~P104(f334(f334(f250(x76231),f334(f334(f248(x76231),x76234),x76232)),x76233)) % 169.39/169.66 [7624]~P107(x76241)+P104(f334(f334(f250(x76241),x76242),x76243))+~P104(f334(f334(f250(x76241),f334(f334(f248(x76241),x76242),x76244)),x76243)) % 169.39/169.66 [7700]~P104(f334(f334(f336(x77001),x77002),x77004))+P104(f334(f334(f336(x77001),x77002),x77003))+P104(f334(f334(f336(x77001),x77002),f334(f334(f3(f886(x77001,a871)),x77004),x77003))) % 169.39/169.66 [7784]P104(f334(x77841,x77842))+P104(f334(x77843,x77842))+~P104(f334(f334(f334(f113(f886(x77844,a871)),x77843),x77841),x77842)) % 169.39/169.66 [7795]~P104(f334(f334(f336(x77951),x77952),x77954))+~P104(f334(f334(f336(x77951),x77952),x77953))+P104(f334(f334(f336(x77951),x77952),f334(f334(f104(f886(x77951,a871)),x77953),x77954))) % 169.39/169.66 [7844]~P100(x78441)+~P104(f334(f63(x78441),x78444))+E(f334(f334(f66(x78441,x78441,f113(x78441)),x78442),f334(f334(f312(x78441),x78443),x78444)),f334(f334(f113(x78441),x78443),f334(f334(f66(x78441,x78441,f113(x78441)),x78442),x78444))) % 169.39/169.66 [7845]~P101(x78451)+~P104(f334(f63(x78451),x78454))+E(f334(f334(f66(x78451,x78451,f104(x78451)),x78452),f334(f334(f312(x78451),x78453),x78454)),f334(f334(f104(x78451),x78453),f334(f334(f66(x78451,x78451,f104(x78451)),x78452),x78454))) % 169.39/169.66 [7846]~P107(x78461)+~P104(f334(f63(x78461),x78464))+E(f334(f334(f66(x78461,x78461,f247(x78461)),x78462),f334(f334(f312(x78461),x78463),x78464)),f334(f334(f247(x78461),x78463),f334(f334(f66(x78461,x78461,f247(x78461)),x78462),x78464))) % 169.39/169.66 [7847]~P107(x78471)+~P104(f334(f63(x78471),x78474))+E(f334(f334(f66(x78471,x78471,f248(x78471)),x78472),f334(f334(f312(x78471),x78473),x78474)),f334(f334(f248(x78471),x78473),f334(f334(f66(x78471,x78471,f248(x78471)),x78472),x78474))) % 169.39/169.66 [7848]~P109(x78481)+~P90(x78481)+E(f334(f334(f3(x78481),f334(f334(f82(x78481),f334(f106(x78481),x78482)),x78483)),f334(f334(f82(x78481),f334(f106(x78481),x78482)),x78484)),f334(f334(f82(x78481),f334(f106(x78481),x78482)),f334(f334(f3(x78481),x78483),x78484))) % 169.39/169.66 [7849]~P139(x78491)+~P90(x78491)+E(f334(f334(f81(x78491),f334(f334(f82(x78491),f334(f106(x78491),x78492)),x78493)),f334(f334(f82(x78491),f334(f106(x78491),x78492)),x78494)),f334(f334(f82(x78491),f334(f106(x78491),x78492)),f334(f334(f81(x78491),x78493),x78494))) % 169.39/169.66 [7962]E(x79621,x79622)+P104(f334(f334(f336(x79623),x79621),f334(f173(x79623),x79624)))+~P104(f334(f334(f336(x79623),x79621),f334(f173(x79623),f334(f334(f151(x79623),x79622),x79624)))) % 169.39/169.66 [7988]~P58(x79881)+~E(f334(f196(f878(x79882)),x79883),f334(f196(f878(x79881)),f57(x79881)))+E(f334(f334(f179(x79881,x79882),f334(f334(f183(x79881,x79882),f57(x79881)),x79883)),x79884),f334(f241(x79882),f659(x79884,x79883,x79882,x79881))) % 169.39/169.66 [8133]P52(x81331,x81332,x81333)+~P52(x81331,x81332,x81334)+~P104(f334(f334(f249(f886(f885(x81331,x81332),a871)),x81333),x81334)) % 169.39/169.66 [8177]P104(f334(f334(f336(x81771),x81772),x81773))+P104(f334(f334(f336(x81771),x81772),x81774))+~P104(f334(f334(f336(x81771),x81772),f334(f334(f113(f886(x81771,a871)),x81774),x81773))) % 169.39/169.66 [8187]~P49(x81871,x81874,x81873)+~P104(f334(f334(f336(x81871),x81872),x81874))+P104(f334(f334(f336(f885(x81871,x81871)),f334(f334(f269(x81871,x81871),x81872),x81872)),x81873)) % 169.39/169.66 [8202]~P104(f334(f63(x82022),x82024))+~P104(f334(f63(x82021),x82023))+P104(f334(f63(f885(x82021,x82022)),f334(f334(f271(x82021,x82022),x82023),f334(f18(f886(x82022,a871),x82021),x82024)))) % 169.39/169.66 [8203]~P104(f334(f334(f336(x82031),x82032),x82034))+~P104(f334(f334(f249(f886(x82031,a871)),x82033),x82034))+P104(f334(f334(f249(f886(x82031,a871)),f334(f334(f312(x82031),x82032),x82033)),x82034)) % 169.39/169.66 [8211]~P68(x82112)+~P142(x82112)+E(f334(f334(f11(x82111,x82112),f334(f334(f10(a877,x82112,x82111),f103(x82112)),x82113)),x82114),f334(f103(x82112),f334(f334(f11(x82111,a877),x82113),x82114))) % 169.39/169.66 [8212]~P68(x82122)+~P137(x82122)+E(f334(f334(f11(x82121,x82122),f334(f334(f10(a1,x82122,x82121),f105(x82122)),x82123)),x82124),f334(f105(x82122),f334(f334(f11(x82121,a1),x82123),x82124))) % 169.39/169.66 [8238]E(f334(f334(f3(f886(x82381,a871)),x82382),f334(f334(f3(f886(x82381,a871)),x82383),x82384)),x82384)+~P104(f334(f334(f249(f886(x82381,a871)),x82382),x82383))+~P104(f334(f334(f249(f886(x82381,a871)),x82384),x82382)) % 169.39/169.66 [8331]~P104(f334(f63(x83311),x83314))+E(f334(f334(f3(a877),f334(f334(f8(x83311,a877),x83312),x83313)),f334(f334(f8(x83311,a877),x83312),x83314)),f334(f334(f8(x83311,a877),x83312),f334(f334(f3(f886(x83311,a871)),x83313),x83314)))+~P104(f334(f334(f249(f886(x83311,a871)),x83314),x83313)) % 169.39/169.66 [8481]~P6(x84811,x84814,x84813)+~P104(f334(f334(f336(x84811),x84812),x84814))+P104(f334(f334(f336(x84811),x84812),f334(f288(x84811,x84811,x84813),f334(f334(f312(x84811),x84812),f195(f886(x84811,a871)))))) % 169.39/169.66 [8538]~P104(f334(f334(f249(f886(x85381,a871)),x85382),x85383))+~P104(f334(f334(f249(f886(x85381,a871)),x85382),x85384))+P104(f334(f334(f249(f886(x85381,a871)),x85382),f334(f334(f104(f886(x85381,a871)),x85383),x85384))) % 169.39/169.66 [8636]E(x86361,f195(f886(x86362,a871)))+P104(f334(f63(x86363),x86364))+~P104(f334(f63(f885(x86363,x86362)),f334(f334(f271(x86363,x86362),x86364),f334(f18(f886(x86362,a871),x86363),x86361)))) % 169.39/169.66 [8637]E(x86371,f195(f886(x86372,a871)))+P104(f334(f63(x86373),x86374))+~P104(f334(f63(f885(x86372,x86373)),f334(f334(f271(x86372,x86373),x86371),f334(f18(f886(x86373,a871),x86372),x86374)))) % 169.39/169.66 [8702]P104(f334(f334(f336(x87021),x87022),f323(x87021,x87023)))+~P104(f334(f334(f336(x87021),x87024),f323(x87021,x87023)))+~P104(f334(f334(f336(f885(x87021,x87021)),f334(f334(f269(x87021,x87021),x87022),x87024)),x87023)) % 169.39/169.66 [8754]~P39(x87541,x87544)+P104(f334(f334(f336(f885(x87541,x87541)),f334(f334(f269(x87541,x87541),x87543),x87542)),f310(x87541,x87544)))+P39(x87541,f334(f334(f312(f885(x87541,x87541)),f334(f334(f269(x87541,x87541),x87542),x87543)),x87544)) % 169.39/169.66 [8755]~P55(x87551,x87554)+P104(f334(f334(f336(f885(x87551,x87551)),f334(f334(f269(x87551,x87551),x87553),x87552)),f310(x87551,x87554)))+P55(x87551,f334(f334(f312(f885(x87551,x87551)),f334(f334(f269(x87551,x87551),x87552),x87553)),x87554)) % 169.39/169.66 [8832]~E(x88322,x88323)+~P104(f334(f334(f336(x88321),x88322),f334(f173(x88321),x88324)))+P104(f334(f334(f336(f885(x88321,x88321)),f334(f334(f269(x88321,x88321),x88322),x88323)),f334(f173(f885(x88321,x88321)),f334(f334(f183(x88321,x88321),x88324),x88324)))) % 169.39/169.66 [8914]~E(x89143,x89144)+P104(f334(f334(f273(x89141,x89141,a871),a331),x89142))+~P104(f334(f334(f336(f885(x89141,x89141)),x89142),f334(f173(f885(x89141,x89141)),f334(f334(f183(x89141,x89141),x89143),x89144)))) % 169.39/169.66 [8962]P104(f334(f334(f336(f885(f878(x89621),f878(x89621))),f334(f334(f269(f878(x89621),f878(x89621)),x89622),x89623)),f147(x89621,x89624)))+~E(f334(f334(f176(x89621),f334(f196(f878(x89621)),x89622)),x89623),x89622)+~P104(f334(f334(f250(a877),f334(f196(f878(x89621)),x89622)),f334(f196(f878(x89621)),x89623))) % 169.39/169.66 [9054]~P104(f334(f63(x90541),x90544))+P104(f334(f334(f336(x90541),f526(x90542,x90543,x90544,x90541)),x90544))+P104(f334(f63(x90543),f334(f334(f44(x90541,f886(x90543,a871)),x90544),x90542))) % 169.39/169.66 [9055]~P104(f334(f63(x90551),x90554))+P104(f334(f334(f336(x90551),f717(x90552,x90553,x90554,x90551)),x90554))+P104(f334(f63(x90553),f334(f334(f44(x90551,f886(x90553,a871)),x90554),x90552))) % 169.39/169.66 [9137]P104(f334(f334(f336(f885(x91371,x91371)),x91372),f334(f334(f291(x91371,x91371,x91371),x91373),f310(x91371,x91373))))+~P104(f334(f334(f250(a877),f2(a877)),x91374))+~P104(f334(f334(f336(f885(x91371,x91371)),x91372),f334(f334(f190(f885(x91371,x91371),a871),x91374),x91373))) % 169.39/169.66 [9145]~P39(x91451,x91452)+~P104(f334(f334(f336(f885(x91451,x91451)),f334(f334(f269(x91451,x91451),x91454),x91453)),x91452))+~P104(f334(f334(f336(f885(x91451,x91451)),f334(f334(f269(x91451,x91451),x91453),x91454)),x91452)) % 169.39/169.66 [9263]~P104(f334(f63(x92631),x92634))+E(f334(f334(f8(x92631,a877),f334(f334(f10(f886(x92632,a871),a877,x92631),f39(x92632)),x92633)),x92634),f334(f39(f885(x92631,x92632)),f334(f334(f271(x92631,x92632),x92634),x92633)))+P104(f334(f334(f336(x92631),f700(x92633,x92632,x92634,x92631)),x92634)) % 169.39/169.66 [9267]~P104(f334(f137(x92671),x92672))+P104(f334(f137(x92671),f334(f334(f159(x92671,x92672),x92673),x92674)))+P104(f334(f334(f336(x92671),x92674),f334(f334(f3(f886(x92671,a871)),f334(f173(x92671),x92672)),f334(f334(f312(x92671),f334(f334(f165(x92671),x92672),x92673)),f195(f886(x92671,a871)))))) % 169.39/169.66 [9280]~P104(f334(f63(x92802),x92803))+~P104(f334(f63(x92801),f334(x92804,f526(x92804,x92801,x92803,x92802))))+P104(f334(f63(x92801),f334(f334(f44(x92802,f886(x92801,a871)),x92803),x92804))) % 169.39/169.66 [9281]~P104(f334(f63(x92812),x92813))+~P104(f334(f63(x92811),f334(x92814,f717(x92814,x92811,x92813,x92812))))+P104(f334(f63(x92811),f334(f334(f44(x92812,f886(x92811,a871)),x92813),x92814))) % 169.39/169.66 [9357]~P104(f334(f334(f336(f885(x93571,x93571)),x93572),f334(f334(f291(x93571,x93571,x93571),x93574),f310(x93571,x93574))))+P104(f334(f334(f336(f885(x93571,x93571)),x93572),f334(f334(f291(x93571,x93571,x93571),x93573),f310(x93571,x93573))))+~P104(f334(f334(f249(f886(f885(x93571,x93571),a871)),x93574),x93573)) % 169.39/169.66 [9364]E(f334(f334(f176(x93641),f610(x93644,x93643,x93642,x93641)),x93643),f334(f334(f176(x93641),f610(x93644,x93643,x93642,x93641)),x93642))+~P104(f334(f334(f336(f885(f878(x93641),f878(x93641))),f334(f334(f269(f878(x93641),f878(x93641)),x93642),x93643)),f147(x93641,x93644)))+E(f334(f334(f176(x93641),f334(f196(f878(x93641)),x93642)),x93643),x93642) % 169.39/169.66 [9380]~P104(f334(f63(x93801),x93804))+E(f334(f334(f8(x93801,a877),f334(f334(f10(f886(x93802,a871),a877,x93801),f39(x93802)),x93803)),x93804),f334(f39(f885(x93801,x93802)),f334(f334(f271(x93801,x93802),x93804),x93803)))+~P104(f334(f63(x93802),f334(x93803,f700(x93803,x93802,x93804,x93801)))) % 169.39/169.66 [9383]~E(f334(f196(f878(x93831)),x93833),f334(f196(f878(x93831)),x93832))+P104(f334(f334(f336(f885(f878(x93831),f878(x93831))),f334(f334(f269(f878(x93831),f878(x93831)),x93832),x93833)),f158(x93831,x93834)))+P104(f334(f334(f336(f885(x93831,x93831)),f586(x93834,x93833,x93832,x93831)),f334(f173(f885(x93831,x93831)),f334(f334(f183(x93831,x93831),x93832),x93833)))) % 169.39/169.66 [9459]~P104(f334(f334(f336(f885(f878(x94591),f878(x94591))),f334(f334(f269(f878(x94591),f878(x94591)),x94592),x94593)),f147(x94591,x94594)))+E(f334(f334(f176(x94591),f334(f196(f878(x94591)),x94592)),x94593),x94592)+P104(f334(f334(f250(a877),f610(x94594,x94593,x94592,x94591)),f334(f334(f247(a877),f334(f196(f878(x94591)),x94592)),f334(f196(f878(x94591)),x94593)))) % 169.39/169.66 [9460]E(f334(f179(x94601,x94602),x94603),f334(f179(x94601,x94602),x94604))+~E(f334(f173(x94601),f334(f334(f154(f885(x94601,x94602),x94601),f268(x94601,x94602)),x94603)),f334(f173(x94601),f334(f334(f154(f885(x94601,x94602),x94601),f268(x94601,x94602)),x94604)))+P104(f334(f334(f336(x94601),f711(x94603,x94604,x94602,x94601)),f334(f173(x94601),f334(f334(f154(f885(x94601,x94602),x94601),f268(x94601,x94602)),x94604)))) % 169.39/169.66 [9480]~P104(f334(f334(f336(f885(f878(x94801),f878(x94801))),f334(f334(f269(f878(x94801),f878(x94801)),x94802),x94803)),f147(x94801,x94804)))+P104(f334(f334(f250(a877),f334(f196(f878(x94801)),x94802)),f334(f196(f878(x94801)),x94803)))+P104(f334(f334(f250(a877),f610(x94804,x94803,x94802,x94801)),f334(f334(f247(a877),f334(f196(f878(x94801)),x94802)),f334(f196(f878(x94801)),x94803)))) % 169.39/169.66 [9775]~P104(f334(f334(f334(x97751,f513(x97751,x97754,x97753,x97752)),f514(x97751,x97754,x97753,x97752)),f515(x97751,x97754,x97753,x97752)))+P104(f334(f334(f334(x97751,x97752),x97753),x97754))+~P104(f334(f322(f885(f886(a1,f881(f878(a330))),f885(a1,a1)),a320),f334(f334(f269(f886(a1,f881(f878(a330))),f885(a1,a1)),x97752),f334(f334(f269(a1,a1),x97753),x97754)))) % 169.39/169.66 [9852]P104(f334(f334(f334(x98521,x98522),x98523),x98524))+P104(f334(f322(f885(f886(a1,f881(f878(a330))),f885(a1,a1)),a320),f334(f334(f269(f886(a1,f881(f878(a330))),f885(a1,a1)),f513(x98521,x98524,x98523,x98522)),f334(f334(f269(a1,a1),f514(x98521,x98524,x98523,x98522)),f515(x98521,x98524,x98523,x98522)))))+~P104(f334(f322(f885(f886(a1,f881(f878(a330))),f885(a1,a1)),a320),f334(f334(f269(f886(a1,f881(f878(a330))),f885(a1,a1)),x98522),f334(f334(f269(a1,a1),x98523),x98524)))) % 169.39/169.66 [9891]~P104(f334(f334(f336(f885(f878(x98911),f878(x98911))),f334(f334(f269(f878(x98911),f878(x98911)),x98912),x98913)),f147(x98911,x98914)))+E(f334(f334(f176(x98911),f334(f196(f878(x98911)),x98912)),x98913),x98912)+P104(f334(f334(f336(f885(x98911,x98911)),f334(f334(f269(x98911,x98911),f334(f334(f165(x98911),x98912),f610(x98914,x98913,x98912,x98911))),f334(f334(f165(x98911),x98913),f610(x98914,x98913,x98912,x98911)))),x98914)) % 169.39/169.66 [9892]~P104(f334(f334(f336(f885(f878(x98921),f878(x98921))),f334(f334(f269(f878(x98921),f878(x98921)),x98922),x98923)),f147(x98921,x98924)))+P104(f334(f334(f250(a877),f334(f196(f878(x98921)),x98922)),f334(f196(f878(x98921)),x98923)))+P104(f334(f334(f336(f885(x98921,x98921)),f334(f334(f269(x98921,x98921),f334(f334(f165(x98921),x98922),f610(x98924,x98923,x98922,x98921))),f334(f334(f165(x98921),x98923),f610(x98924,x98923,x98922,x98921)))),x98924)) % 169.39/169.66 [9949]~E(f334(f196(f878(x99491)),x99492),f334(f196(f878(x99491)),x99493))+P104(f334(f334(f336(f885(f878(x99491),f878(x99491))),f334(f334(f269(f878(x99491),f878(x99491)),x99492),x99493)),f158(x99491,x99494)))+~P104(f334(f334(f336(f885(x99491,x99491)),f334(f334(f269(x99491,x99491),f334(f334(f165(x99491),x99492),f585(x99494,x99493,x99492,x99491))),f334(f334(f165(x99491),x99493),f585(x99494,x99493,x99492,x99491)))),x99494)) % 169.39/169.66 [10083]~P72(x100831)+~P104(f334(f63(x100832),x100834))+E(f334(f166(x100831),f334(f334(f154(x100832,x100831),x100833),f91(f878(x100832),f334(f334(f20(f878(x100832),a871,a871),f334(f334(f10(a871,f886(a871,a871),f878(x100832)),a332),f334(f334(f9(f878(x100832),f886(x100832,a871),a871),f334(f334(f10(f886(x100832,a871),f886(f886(x100832,a871),a871),f878(x100832)),a331),f173(x100832))),x100834))),f137(x100832))))),f239(x100832,x100831,x100833,x100834)) % 169.39/169.66 [7428]~P59(x74282)+E(x74281,f2(x74282))+E(f334(f334(f292(x74282),f334(f334(f81(x74282),x74283),f334(f334(f82(x74282),x74284),x74281))),x74281),f334(f334(f81(x74282),x74284),f334(f334(f292(x74282),x74283),x74281))) % 169.39/169.66 [7429]~P26(x74292)+E(x74291,f2(x74292))+E(f334(f334(f40(x74292),f334(f334(f81(x74292),x74293),f334(f334(f82(x74292),x74294),x74291))),x74291),f334(f334(f81(x74292),x74294),f334(f334(f40(x74292),x74293),x74291))) % 169.39/169.66 [7430]~P26(x74302)+E(x74301,f2(x74302))+E(f334(f334(f40(x74302),f334(f334(f81(x74302),x74303),f334(f334(f82(x74302),x74301),x74304))),x74301),f334(f334(f81(x74302),x74304),f334(f334(f40(x74302),x74303),x74301))) % 169.39/169.66 [7663]~P60(x76632)+E(x76631,f2(x76632))+E(f334(f334(f292(x76632),f334(f334(f3(x76632),x76633),f334(f334(f82(x76632),x76631),x76634))),x76631),f334(f334(f3(x76632),f334(f334(f292(x76632),x76633),x76631)),x76634)) % 169.39/169.66 [7664]~P59(x76642)+E(x76641,f2(x76642))+E(f334(f334(f292(x76642),f334(f334(f81(x76642),x76643),f334(f334(f82(x76642),x76644),x76641))),x76641),f334(f334(f81(x76642),f334(f334(f292(x76642),x76643),x76641)),x76644)) % 169.39/169.66 [7665]~P60(x76652)+E(x76651,f2(x76652))+E(f334(f334(f292(x76652),f334(f334(f81(x76652),x76653),f334(f334(f82(x76652),x76651),x76654))),x76651),f334(f334(f81(x76652),f334(f334(f292(x76652),x76653),x76651)),x76654)) % 169.39/169.66 [8359]~P104(f334(f160(x83591,x83593),x83594))+~P104(f334(f160(x83591,x83592),x83594))+P104(f334(f160(x83591,f334(f334(f104(f886(x83591,a871)),x83592),x83593)),x83594)) % 169.39/169.66 [8716]~E(f334(f334(f291(x87161,x87161,x87161),x87162),x87164),f195(f886(f885(x87161,x87161),a871)))+~E(f334(f334(f291(x87161,x87161,x87161),x87162),x87163),f195(f886(f885(x87161,x87161),a871)))+E(f334(f334(f291(x87161,x87161,x87161),x87162),f334(f334(f113(f886(f885(x87161,x87161),a871)),x87163),x87164)),f195(f886(f885(x87161,x87161),a871))) % 169.39/169.66 [8833]~P104(f334(f334(f249(f886(x88331,a871)),x88333),x88334))+~P104(f334(f334(f249(f886(x88331,a871)),x88332),x88334))+P104(f334(f334(f249(f886(x88331,a871)),f334(f334(f113(f886(x88331,a871)),x88332),x88333)),x88334)) % 169.39/169.66 [9198]~P104(f334(f63(x91981),x91984))+~P104(f334(f63(x91981),x91983))+E(f334(f334(f3(a877),f334(f334(f81(a877),f334(f334(f8(x91981,a877),x91982),x91983)),f334(f334(f8(x91981,a877),x91982),x91984))),f334(f334(f8(x91981,a877),x91982),f334(f334(f104(f886(x91981,a871)),x91983),x91984))),f334(f334(f8(x91981,a877),x91982),f334(f334(f113(f886(x91981,a871)),x91983),x91984))) % 169.39/169.66 [9277]~P104(f334(f334(f336(x92771),x92773),x92772))+~P104(f334(f334(f249(f886(x92771,a871)),x92772),f334(f334(f312(x92771),x92773),x92774)))+P104(f334(f334(f249(f886(x92771,a871)),f334(f334(f3(f886(x92771,a871)),x92772),f334(f334(f312(x92771),x92773),f195(f886(x92771,a871))))),x92774)) % 169.39/169.66 [9432]~P104(f334(f334(f336(x94321),x94323),x94322))+P104(f334(f334(f249(f886(x94321,a871)),x94322),f334(f334(f312(x94321),x94323),x94324)))+~P104(f334(f334(f249(f886(x94321,a871)),f334(f334(f3(f886(x94321,a871)),x94322),f334(f334(f312(x94321),x94323),f195(f886(x94321,a871))))),x94324)) % 169.39/169.66 [9517]~P104(f334(f334(f249(a877),x95171),x95173))+~P104(f334(f334(f250(a877),x95172),x95174))+P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),f334(f334(f269(a877,a877),x95171),x95172)),f334(f334(f269(a877,a877),x95173),x95174))),a36)) % 169.39/169.66 [9518]~P104(f334(f334(f249(a877),x95182),x95184))+~P104(f334(f334(f249(a877),x95181),x95183))+P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),f334(f334(f269(a877,a877),x95181),x95182)),f334(f334(f269(a877,a877),x95183),x95184))),a71)) % 169.39/169.66 [9815]~P104(f334(f334(f336(f878(x98151)),x98154),f161(x98151,x98153)))+~P104(f334(f334(f336(f878(x98151)),x98154),f161(x98151,x98152)))+P104(f334(f160(x98151,f334(f334(f104(f886(x98151,a871)),f334(f334(f9(x98151,f886(x98151,a871),a871),f336(x98151)),x98152)),f334(f334(f9(x98151,f886(x98151,a871),a871),f336(x98151)),x98153))),x98154)) % 169.39/169.66 [9914]~P21(x99141,f886(f886(x99141,a871),a871),f334(f334(f9(x99141,f886(f885(x99141,x99141),a871),f886(f886(x99141,a871),a871)),f334(f334(f10(f886(x99141,a871),f886(f886(f885(x99141,x99141),a871),f886(f886(x99141,a871),a871)),x99141),f62(x99141)),f334(f334(f9(x99141,f886(x99141,a871),f886(x99141,a871)),f312(x99141)),f195(f886(x99141,a871))))),x99143),x99142)+~P104(f334(f334(f336(x99141),x99144),x99142))+E(f334(f334(f3(f886(f886(x99141,a871),a871)),f334(f334(f62(x99141),x99142),x99143)),f334(f334(f62(x99141),f334(f334(f312(x99141),x99144),f195(f886(x99141,a871)))),x99143)),f334(f334(f62(x99141),f334(f334(f3(f886(x99141,a871)),x99142),f334(f334(f312(x99141),x99144),f195(f886(x99141,a871))))),x99143)) % 169.39/169.66 [10048]~P49(x100481,x100482,x100484)+~P104(f334(f334(f336(f885(x100481,x100481)),x100483),x100484))+P104(f334(f334(f273(x100481,x100481,a871),f334(f334(f9(x100481,f886(x100481,a871),f886(x100481,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x100481,a871),f886(x100481,a871)),x100481),f10(a871,a871,x100481)),f334(f334(f10(a871,f886(a871,a871),x100481),a332),f334(f334(f9(x100481,f886(x100481,a871),a871),f336(x100481)),x100482)))),f334(f334(f9(x100481,f886(x100481,a871),a871),f336(x100481)),x100482))),x100483)) % 169.39/169.66 [10060]P104(f334(f63(x100601),x100602))+~P104(f334(f63(x100603),f334(f313(x100601,x100603,x100604),x100602)))+~P104(f334(f63(x100601),f334(f254(x100601),f334(f334(f20(x100601,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100601),a332),f334(f334(f9(x100601,f886(x100601,a871),a871),f336(x100601)),x100602))),f334(f334(f9(x100601,x100603,a871),f334(f334(f10(x100603,f886(x100603,a871),x100601),a331),x100604)),f334(x100604,f710(x100604,x100603,x100602,x100601))))))) % 169.39/169.66 [8115]~P60(x81152)+E(x81151,f2(x81152))+E(f334(f334(f292(x81152),f334(f334(f3(x81152),f334(f334(f82(x81152),x81151),x81153)),x81154)),x81151),f334(f334(f3(x81152),x81153),f334(f334(f292(x81152),x81154),x81151))) % 169.39/169.66 [8116]~P60(x81162)+E(x81161,f2(x81162))+E(f334(f334(f292(x81162),f334(f334(f81(x81162),f334(f334(f82(x81162),x81161),x81163)),x81164)),x81161),f334(f334(f81(x81162),x81163),f334(f334(f292(x81162),x81164),x81161))) % 169.39/169.66 [8989]~E(f334(f334(f291(x89891,x89891,x89891),x89893),x89894),f195(f886(f885(x89891,x89891),a871)))+~E(f334(f334(f291(x89891,x89891,x89891),x89892),x89894),f195(f886(f885(x89891,x89891),a871)))+E(f334(f334(f291(x89891,x89891,x89891),f334(f334(f113(f886(f885(x89891,x89891),a871)),x89892),x89893)),x89894),f195(f886(f885(x89891,x89891),a871))) % 169.39/169.66 [9991]~P144(x99911)+~P144(x99912)+E(f334(f334(f319(x99911),f334(f334(f9(x99911,a102,f881(f878(a330))),f334(f334(f10(f886(x99912,f881(f878(a330))),f886(a102,f881(f878(a330))),x99911),f319(x99912)),f334(f334(f10(f886(x99912,f885(x99911,x99912)),f886(x99912,f881(f878(a330))),x99911),f334(f10(f885(x99911,x99912),f881(f878(a330)),x99912),x99913)),f269(x99911,x99912)))),x99914)),x99914),f334(f334(f319(f885(x99911,x99912)),x99913),x99914)) % 169.39/169.66 [9723]~P104(f334(f160(x97231,x97233),x97234))+~P104(f334(f160(x97231,x97232),x97234))+P104(f334(f160(x97231,f334(f334(f20(x97231,a871,a871),f334(f334(f10(a871,f886(a871,a871),x97231),a332),x97232)),x97233)),x97234)) % 169.39/169.66 [9983]P104(f334(x99831,f568(x99832,x99833,x99831,x99834)))+~P104(f334(f63(x99834),f334(f254(x99834),x99831)))+P104(f334(f63(x99833),f334(f254(x99833),f334(f334(f10(f886(x99834,a871),a871,x99833),f88(x99834)),f334(f334(f10(f886(x99834,a871),f886(x99834,a871),x99833),f334(f20(x99834,a871,a871),f334(f334(f10(a871,f886(a871,a871),x99834),a332),x99831))),x99832))))) % 169.39/169.66 [10004]~P104(f334(f63(x100042),f334(f254(x100042),x100043)))+~P104(f334(f63(x100041),f334(f254(x100041),f334(f334(f9(x100041,x100042,a871),x100044),f568(x100044,x100041,x100043,x100042)))))+P104(f334(f63(x100041),f334(f254(x100041),f334(f334(f10(f886(x100042,a871),a871,x100041),f88(x100042)),f334(f334(f10(f886(x100042,a871),f886(x100042,a871),x100041),f334(f20(x100042,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100042),a332),x100043))),x100044))))) % 169.39/169.66 [5067]~E(x50672,x50674)+E(f170(x50671,x50672,x50673),f170(x50671,x50674,x50675))+~E(x50672,f2(a877)) % 169.39/169.66 [5333]E(x53331,x53332)+~E(f170(x53334,x53333,x53331),f170(x53334,x53335,x53332))+E(x53333,f2(a877)) % 169.39/169.66 [6573]E(x65731,x65732)+~E(f334(x65733,x65731),f334(x65733,x65732))+~P21(x65734,x65735,x65733,f257(f886(x65734,a871))) % 169.39/169.66 [6731]~E(f334(x67313,x67315),f198(x67312))+~E(f334(x67314,x67315),f198(x67312))+E(f334(f186(x67311,x67312,x67313,x67314),x67315),f198(x67312)) % 169.39/169.66 [7463]E(x74631,x74632)+~P21(x74633,x74634,x74635,f257(f886(x74633,a871)))+~E(f334(f313(x74633,x74634,x74635),x74631),f334(f313(x74633,x74634,x74635),x74632)) % 169.39/169.66 [7717]P21(x77172,x77173,f822(x77174,x77173,x77172,x77171),x77171)+~E(f334(f313(x77173,x77172,x77175),x77174),x77171)+E(x77171,f195(f886(x77172,a871))) % 169.39/169.66 [8249]~P104(f334(f334(x82493,x82492),x82495))+~P104(f334(f334(x82493,x82494),x82492))+P104(f334(f334(f336(x82491),x82492),f298(x82491,x82493,x82494,x82495))) % 169.39/169.66 [8250]~P104(f334(f334(x82503,x82502),x82505))+~P104(f334(f334(x82503,x82504),x82502))+P104(f334(f334(f336(x82501),x82502),f301(x82501,x82503,x82504,x82505))) % 169.39/169.66 [8791]~P21(x87911,x87913,x87915,f257(f886(x87911,a871)))+~P21(x87913,x87912,x87914,f257(f886(x87913,a871)))+P21(x87911,x87912,f334(f74(x87913,x87912,x87911,x87914),x87915),f257(f886(x87911,a871))) % 169.39/169.66 [9334]P104(f334(f334(f336(f885(x93341,x93341)),f334(f334(f269(x93341,x93341),x93342),x93343)),f310(x93341,x93344)))+~P104(f334(f334(f336(f885(x93341,x93341)),f334(f334(f269(x93341,x93341),x93342),x93345)),f310(x93341,x93344)))+~P104(f334(f334(f336(f885(x93341,x93341)),f334(f334(f269(x93341,x93341),x93345),x93343)),f310(x93341,x93344))) % 169.39/169.66 [9371]~P107(x93712)+~P104(f334(f137(x93711),x93715))+P104(f334(f137(x93711),f149(x93711,x93712,x93713,x93714,x93715))) % 169.39/169.66 [5404]~E(x54042,f116(x54041))+E(f334(f334(f134(x54041),x54042),x54043),f334(f334(f151(x54041),x54044),x54045))+~E(x54043,f334(f334(f151(x54041),x54044),x54045)) % 169.39/169.66 [5405]~E(x54052,f116(x54051))+E(f334(f334(f134(x54051),x54052),x54053),f334(f334(f151(x54051),x54054),x54055))+~E(f334(f334(f151(x54051),x54054),x54055),x54053) % 169.39/169.66 [6530]~E(f334(f196(f878(x65301)),x65305),f334(f196(f878(x65302)),x65304))+E(f334(f334(f154(f885(x65301,x65302),x65302),f272(x65301,x65302)),x65303),x65304)+~E(f334(f334(f183(x65301,x65302),x65305),x65304),x65303) % 169.39/169.66 [6531]~E(f334(f196(f878(x65311)),x65314),f334(f196(f878(x65312)),x65315))+E(f334(f334(f154(f885(x65311,x65312),x65311),f268(x65311,x65312)),x65313),x65314)+~E(f334(f334(f183(x65311,x65312),x65314),x65315),x65313) % 169.39/169.66 [7002]~P107(x70021)+~P30(x70021,f334(f334(f154(x70022,x70021),x70023),x70025))+P30(x70021,f334(f334(f154(x70022,x70021),x70023),f334(f136(x70022,x70024),x70025))) % 169.39/169.66 [7047]~P104(f334(x70473,x70475))+~P104(f334(f334(x70472,x70474),x70475))+P104(f334(f334(f95(x70471,x70472,x70473),x70474),x70475)) % 169.39/169.66 [7144]~P107(x71441)+P30(x71441,f334(f334(f154(x71442,x71441),x71443),f171(x71442,x71444,x71445)))+~P30(x71441,f334(f334(f154(x71442,x71441),x71443),x71445)) % 169.39/169.66 [7167]~P52(x71673,x71672,x71675)+~P52(x71671,x71673,x71674)+P52(x71671,x71672,f334(f334(f291(x71671,x71673,x71672),x71674),x71675)) % 169.39/169.66 [7259]E(x72591,x72592)+~P21(x72593,x72594,x72595,f257(f886(x72593,a871)))+~E(f334(f334(f154(x72593,x72594),x72595),x72591),f334(f334(f154(x72593,x72594),x72595),x72592)) % 169.39/169.66 [7414]~P104(f334(f334(f249(a877),x74141),f334(x74143,x74145)))+P104(f334(f334(f249(a877),x74141),f155(x74142,x74143,x74144)))+~P104(f334(f334(f336(x74142),x74145),f334(f173(x74142),x74144))) % 169.39/169.66 [7415]~P104(f334(f334(f250(a877),x74151),f334(x74153,x74155)))+P104(f334(f334(f250(a877),x74151),f155(x74152,x74153,x74154)))+~P104(f334(f334(f336(x74152),x74155),f334(f173(x74152),x74154))) % 169.39/169.66 [7816]P104(f334(x78161,x78162))+~P104(f334(x78161,x78163))+~P104(f334(f334(f336(x78164),x78162),f334(f173(x78164),f170(x78164,x78165,x78163)))) % 169.39/169.66 [7817]P104(f334(x78171,x78172))+~P104(f334(x78171,x78173))+~P104(f334(f334(f336(x78174),x78173),f334(f173(x78174),f170(x78174,x78175,x78172)))) % 169.39/169.66 [7821]~P108(x78211)+P104(f334(f334(f249(f886(x78211,a871)),f305(x78211,x78212,x78213)),f305(x78211,x78214,x78215)))+P104(f334(f334(f249(x78211),x78212),x78213)) % 169.39/169.66 [7842]~P28(x78421)+P104(f334(f334(f249(x78421),f334(f334(f43(x78422,x78421),x78423),x78424)),f334(x78424,x78425)))+~P104(f334(f334(f336(x78422),x78425),x78423)) % 169.39/169.66 [7909]~P21(x79091,x79092,x79094,x79093)+E(f334(f78(x79091,x79092,x79093,x79094),f334(x79094,x79095)),x79095)+~P104(f334(f334(f336(x79091),x79095),x79093)) % 169.39/169.66 [8104]~P104(f334(x81041,x81045))+P104(f334(x81041,f411(x81041,x81042,x81043,x81044)))+~P104(f334(f334(f336(x81044),x81045),x81043)) % 169.39/169.66 [8105]~P104(f334(x81051,x81055))+P104(f334(x81051,f411(x81051,x81052,x81053,x81054)))+~P104(f334(f334(f336(x81054),x81055),x81052)) % 169.39/169.66 [8200]P104(f334(f63(x82001),x82002))+~P104(f334(f63(x82003),x82004))+~P104(f334(f334(f249(f886(x82001,a871)),x82002),f334(f313(x82003,x82001,x82005),x82004))) % 169.39/169.66 [8363]E(x83631,x83632)+~P21(x83633,x83634,x83635,f334(f334(f113(f886(x83633,a871)),f334(f173(x83633),x83631)),f334(f173(x83633),x83632)))+~E(f334(f334(f154(x83633,x83634),x83635),x83631),f334(f334(f154(x83633,x83634),x83635),x83632)) % 169.39/169.66 [8417]~P108(x84171)+~P104(f334(f334(f250(f886(x84171,a871)),f305(x84171,x84174,x84175)),f305(x84171,x84172,x84173)))+P104(f334(f334(f249(x84171),x84172),x84173)) % 169.39/169.66 [8480]~P21(x84801,x84804,x84805,f257(f886(x84801,a871)))+~P104(f334(f334(f336(x84804),f334(x84805,x84802)),f334(f313(x84801,x84804,x84805),x84803)))+P104(f334(f334(f336(x84801),x84802),x84803)) % 169.39/169.66 [8551]P104(f334(x85511,x85512))+~P104(f334(x85511,f398(x85511,x85513,x85514,x85515)))+~P104(f334(f334(f336(x85515),x85512),x85514)) % 169.39/169.66 [8552]P104(f334(x85521,x85522))+~P104(f334(x85521,f398(x85521,x85523,x85524,x85525)))+~P104(f334(f334(f336(x85525),x85522),x85523)) % 169.39/169.66 [8830]~P21(x88302,x88303,x88301,x88304)+E(f334(x88301,f334(f78(x88302,x88303,x88304,x88301),x88305)),x88305)+~P104(f334(f334(f336(x88303),x88305),f334(f313(x88302,x88303,x88301),x88304))) % 169.39/169.66 [8935]E(x89351,f116(x89352))+E(f334(f334(f151(x89352),x89353),f600(x89354,x89353,x89355,x89351,x89352)),x89351)+~E(f334(f334(f134(x89352),x89351),x89355),f334(f334(f151(x89352),x89353),x89354)) % 169.39/169.66 [8936]E(x89361,f116(x89362))+E(f334(f334(f151(x89362),x89363),f603(x89364,x89361,x89365,x89363,x89362)),x89361)+~E(f334(f334(f134(x89362),x89361),x89364),f334(f334(f151(x89362),x89363),x89365)) % 169.39/169.66 [8951]E(f334(f334(f151(x89512),x89513),f600(x89514,x89513,x89511,x89515,x89512)),x89515)+~E(f334(f334(f134(x89512),x89515),x89511),f334(f334(f151(x89512),x89513),x89514))+E(x89511,f334(f334(f151(x89512),x89513),x89514)) % 169.39/169.66 [8952]E(f334(f334(f151(x89521),x89522),f603(x89524,x89525,x89523,x89522,x89521)),x89525)+~E(f334(f334(f134(x89521),x89525),x89524),f334(f334(f151(x89521),x89522),x89523))+E(f334(f334(f151(x89521),x89522),x89523),x89524) % 169.39/169.66 [9025]~E(f334(f313(x90253,x90252,x90254),f257(f886(x90253,a871))),f257(f886(x90252,a871)))+~E(f334(f313(x90251,x90253,x90255),f257(f886(x90251,a871))),f257(f886(x90253,a871)))+E(f334(f313(x90251,x90252,f334(f74(x90253,x90252,x90251,x90254),x90255)),f257(f886(x90251,a871))),f257(f886(x90252,a871))) % 169.39/169.66 [9377]E(x93771,f116(x93772))+~E(f334(f334(f134(x93772),x93771),x93773),f334(f334(f151(x93772),x93775),x93774))+E(f334(f334(f134(x93772),f603(x93773,x93771,x93774,x93775,x93772)),x93773),x93774) % 169.39/169.66 [9378]E(x93781,f116(x93782))+~E(f334(f334(f134(x93782),x93781),x93785),f334(f334(f151(x93782),x93784),x93783))+E(f334(f334(f134(x93782),f600(x93783,x93784,x93785,x93781,x93782)),x93785),x93783) % 169.39/169.66 [9384]E(f334(f334(f134(x93842),f600(x93844,x93843,x93841,x93845,x93842)),x93841),x93844)+~E(f334(f334(f134(x93842),x93845),x93841),f334(f334(f151(x93842),x93843),x93844))+E(x93841,f334(f334(f151(x93842),x93843),x93844)) % 169.39/169.66 [9385]~E(f334(f334(f134(x93851),x93855),x93854),f334(f334(f151(x93851),x93852),x93853))+E(f334(f334(f134(x93851),f603(x93854,x93855,x93853,x93852,x93851)),x93854),x93853)+E(f334(f334(f151(x93851),x93852),x93853),x93854) % 169.39/169.66 [9386]E(f334(f334(f134(x93861),x93865),f602(x93863,x93862,x93864,x93865,x93861)),x93862)+E(f334(f334(f134(x93861),x93862),f601(x93863,x93862,x93864,x93865,x93861)),x93865)+~E(f334(f334(f134(x93861),x93865),x93864),f334(f334(f134(x93861),x93862),x93863)) % 169.39/169.66 [9418]~P107(x94181)+P30(x94181,f334(f334(f154(x94182,x94181),x94183),f149(x94182,x94181,x94183,x94184,x94185)))+~P30(x94181,f334(f334(f154(x94182,x94181),x94183),x94185)) % 169.39/169.66 [9429]~P56(x94295,x94291,x94294,x94293)+P104(f334(f334(x94291,x94292),f686(x94293,x94294,x94291,x94295,x94292)))+~P104(f334(f334(f336(x94295),x94292),x94294)) % 169.39/169.66 [9529]~P104(f334(f334(f336(f885(x95291,x95291)),f334(f334(f269(x95291,x95291),x95295),x95293)),f310(x95291,x95294)))+P104(f334(f334(f336(f885(x95291,x95291)),f334(f334(f269(x95291,x95291),x95292),x95293)),f334(f334(f291(x95291,x95291,x95291),x95294),f310(x95291,x95294))))+~P104(f334(f334(f336(f885(x95291,x95291)),f334(f334(f269(x95291,x95291),x95292),x95295)),f334(f334(f291(x95291,x95291,x95291),x95294),f310(x95291,x95294)))) % 169.39/169.66 [9530]~P104(f334(f334(f336(f885(x95301,x95301)),f334(f334(f269(x95301,x95301),x95302),x95305)),f310(x95301,x95304)))+P104(f334(f334(f336(f885(x95301,x95301)),f334(f334(f269(x95301,x95301),x95302),x95303)),f334(f334(f291(x95301,x95301,x95301),x95304),f310(x95301,x95304))))+~P104(f334(f334(f336(f885(x95301,x95301)),f334(f334(f269(x95301,x95301),x95305),x95303)),f334(f334(f291(x95301,x95301,x95301),x95304),f310(x95301,x95304)))) % 169.39/169.66 [9533]P104(f334(f334(f336(f885(f878(x95331),f878(x95331))),f334(f334(f269(f878(x95331),f878(x95331)),x95332),x95333)),f158(x95331,f310(x95331,x95334))))+~P104(f334(f334(f336(f885(f878(x95331),f878(x95331))),f334(f334(f269(f878(x95331),f878(x95331)),x95332),x95335)),f158(x95331,f310(x95331,x95334))))+~P104(f334(f334(f336(f885(f878(x95331),f878(x95331))),f334(f334(f269(f878(x95331),f878(x95331)),x95335),x95333)),f158(x95331,f310(x95331,x95334)))) % 169.39/169.66 [9537]E(f334(f334(f134(x95371),x95372),f601(x95373,x95372,x95374,x95375,x95371)),x95375)+E(f334(f334(f134(x95371),f602(x95373,x95372,x95374,x95375,x95371)),x95373),x95374)+~E(f334(f334(f134(x95371),x95372),x95373),f334(f334(f134(x95371),x95375),x95374)) % 169.39/169.66 [9538]E(f334(f334(f134(x95381),x95382),f602(x95383,x95384,x95385,x95382,x95381)),x95384)+E(f334(f334(f134(x95381),f601(x95383,x95384,x95385,x95382,x95381)),x95385),x95383)+~E(f334(f334(f134(x95381),x95382),x95385),f334(f334(f134(x95381),x95384),x95383)) % 169.39/169.66 [9592]P104(f334(f334(f336(f885(x95921,x95921)),f334(f334(f269(x95921,x95921),x95922),x95923)),f334(f334(f291(x95921,x95921,x95921),x95924),f310(x95921,x95924))))+~P104(f334(f334(f336(f885(x95921,x95921)),f334(f334(f269(x95921,x95921),x95922),x95925)),f334(f334(f291(x95921,x95921,x95921),x95924),f310(x95921,x95924))))+~P104(f334(f334(f336(f885(x95921,x95921)),f334(f334(f269(x95921,x95921),x95925),x95923)),f334(f334(f291(x95921,x95921,x95921),x95924),f310(x95921,x95924)))) % 169.39/169.66 [9619]P36(x96191,x96192,x96193,x96194,x96195)+~E(f334(f196(f878(x96191)),x96194),f334(f196(f878(x96192)),x96195))+~P104(f334(f334(f273(x96191,x96192,a871),x96193),f664(x96195,x96194,x96193,x96192,x96191))) % 169.39/169.66 [9620]P36(x96201,x96202,x96203,x96204,x96205)+~E(f334(f196(f878(x96201)),x96204),f334(f196(f878(x96202)),x96205))+~P104(f334(f334(f273(x96201,x96202,a871),x96203),f669(x96203,x96205,x96204,x96202,x96201))) % 169.39/169.66 [9625]E(f334(f334(f134(x96251),f601(x96252,x96253,x96254,x96255,x96251)),x96254),x96252)+~E(f334(f334(f134(x96251),x96253),x96252),f334(f334(f134(x96251),x96255),x96254))+E(f334(f334(f134(x96251),f602(x96252,x96253,x96254,x96255,x96251)),x96252),x96254) % 169.39/169.66 [9640]~P107(x96402)+E(f334(f334(f148(x96401,x96402,x96403),x96404),x96405),f334(f334(f151(x96401),x96404),x96405))+P104(f334(f334(f336(x96401),f729(x96404,x96403,x96405,x96401,x96402)),f334(f173(x96401),x96405))) % 169.39/169.66 [9645]~P56(x96451,x96454,x96453,x96452)+~P104(f334(f334(f336(x96451),x96455),x96453))+P104(f334(f334(f336(x96451),f686(x96452,x96453,x96454,x96451,x96455)),x96452)) % 169.39/169.66 [9766]~P104(f334(f334(f336(f885(f886(x97661,a871),f886(x97661,a871))),f334(f334(f269(f886(x97661,a871),f886(x97661,a871)),x97664),x97663)),f326(x97661,x97662)))+~P104(f334(f334(f336(x97661),x97665),x97664))+P104(f334(f334(f336(x97661),f749(x97662,x97663,x97664,x97661,x97665)),x97663)) % 169.39/169.66 [9778]~P107(x97782)+E(f334(f334(f148(x97781,x97782,x97783),x97784),x97785),f334(f334(f151(x97781),x97784),x97785))+~P104(f334(f334(f249(x97782),f334(x97783,x97784)),f334(x97783,f729(x97784,x97783,x97785,x97781,x97782)))) % 169.39/169.66 [9966]P36(x99661,x99662,x99663,x99664,x99665)+~E(f334(f196(f878(x99661)),x99664),f334(f196(f878(x99662)),x99665))+~P104(f334(f334(x99663,f334(f334(f165(x99661),x99664),f670(x99665,x99664,x99663,x99662,x99661))),f334(f334(f165(x99662),x99665),f670(x99665,x99664,x99663,x99662,x99661)))) % 169.39/169.66 [9967]P36(x99671,x99672,x99673,x99674,x99675)+~E(f334(f196(f878(x99671)),x99674),f334(f196(f878(x99672)),x99675))+~P104(f334(f334(x99673,f334(f334(f165(x99671),x99674),f723(x99673,x99675,x99672,x99674,x99671))),f334(f334(f165(x99672),x99675),f723(x99673,x99675,x99672,x99674,x99671)))) % 169.39/169.66 [6601]~P13(x66012,x66015,x66011)+~P104(f334(f63(x66012),x66014))+E(f334(x66011,f334(f334(f312(x66012),x66013),x66014)),f334(f334(f66(x66012,x66012,x66015),x66013),x66014)) % 169.39/169.66 [6602]~E(x66023,x66024)+~E(x66022,x66025)+E(f334(f334(f312(x66021),x66022),f334(f334(f312(x66021),x66023),f195(f886(x66021,a871)))),f334(f334(f312(x66021),x66024),f334(f334(f312(x66021),x66025),f195(f886(x66021,a871))))) % 169.39/169.66 [6612]P104(f334(x66122,x66125))+E(f178(x66121,x66122,f334(f334(f134(x66121),x66123),x66124)),f178(x66121,x66122,x66123))+~P104(f334(f334(f336(x66121),x66125),f334(f173(x66121),x66123))) % 169.39/169.66 [6649]E(f334(x66491,x66492),f195(f886(x66493,a871)))+~E(f334(f334(f44(x66494,f886(x66493,a871)),x66495),x66491),f195(f886(x66493,a871)))+~P104(f334(f334(f336(x66494),x66492),x66495)) % 169.39/169.66 [6650]E(f334(x66501,x66502),f257(f886(x66503,a871)))+~E(f334(f334(f43(x66504,f886(x66503,a871)),x66505),x66501),f257(f886(x66503,a871)))+~P104(f334(f334(f336(x66504),x66502),x66505)) % 169.39/169.66 [7154]~E(x71542,x71544)+~P138(x71541)+E(f334(f334(f81(x71541),f334(f334(f82(x71541),x71542),x71543)),f334(f334(f82(x71541),x71544),x71545)),f334(f334(f81(x71541),f334(f334(f82(x71541),x71542),x71545)),f334(f334(f82(x71541),x71544),x71543))) % 169.39/169.66 [7214]~P28(x72141)+~P104(f334(f334(f336(x72144),x72143),x72145))+P104(f334(f334(f249(x72141),f334(x72142,x72143)),f334(f334(f44(x72144,x72141),x72145),x72142))) % 169.39/169.66 [7264]~P106(x72641)+P104(f334(f334(f249(x72641),f334(x72642,x72643)),f334(x72644,x72643)))+~P104(f334(f334(f249(f886(x72645,x72641)),x72642),x72644)) % 169.39/169.66 [7382]E(x73821,x73822)+E(x73823,x73821)+~E(f334(f334(f312(x73824),x73821),f334(f334(f312(x73824),x73825),f195(f886(x73824,a871)))),f334(f334(f312(x73824),x73822),f334(f334(f312(x73824),x73823),f195(f886(x73824,a871))))) % 169.39/169.66 [7383]E(x73831,x73832)+E(x73833,x73831)+~E(f334(f334(f312(x73834),x73833),f334(f334(f312(x73834),x73832),f195(f886(x73834,a871)))),f334(f334(f312(x73834),x73835),f334(f334(f312(x73834),x73831),f195(f886(x73834,a871))))) % 169.39/169.66 [7384]E(x73841,x73842)+E(x73841,x73843)+~E(f334(f334(f312(x73844),x73843),f334(f334(f312(x73844),x73842),f195(f886(x73844,a871)))),f334(f334(f312(x73844),x73845),f334(f334(f312(x73844),x73841),f195(f886(x73844,a871))))) % 169.39/169.66 [7385]E(x73851,x73852)+E(x73851,x73853)+~E(f334(f334(f312(x73854),x73851),f334(f334(f312(x73854),x73855),f195(f886(x73854,a871)))),f334(f334(f312(x73854),x73852),f334(f334(f312(x73854),x73853),f195(f886(x73854,a871))))) % 169.39/169.66 [7919]P21(x79191,x79192,x79193,x79194)+~P21(x79191,x79192,x79193,x79195)+~P104(f334(f334(f249(f886(x79191,a871)),x79194),x79195)) % 169.39/169.66 [8094]E(x80941,x80942)+~E(f334(f313(x80943,x80944,x80945),x80941),f334(f313(x80943,x80944,x80945),x80942))+~P21(x80943,x80944,x80945,f334(f334(f113(f886(x80943,a871)),x80941),x80942)) % 169.39/169.66 [8166]P104(f334(x81662,x81664))+E(f334(f334(f138(x81661),f334(f196(f878(x81661)),f178(x81661,x81662,x81663))),x81663),f334(f334(f151(x81661),x81664),x81665))+~E(f334(f334(f134(x81661),f178(x81661,x81662,x81663)),f334(f334(f151(x81661),x81664),x81665)),x81663) % 169.39/169.66 [8197]~P21(x81971,x81972,x81973,x81975)+~P21(x81971,x81972,x81973,x81974)+P21(x81971,x81972,x81973,f334(f334(f104(f886(x81971,a871)),x81974),x81975)) % 169.39/169.66 [8306]~P72(x83061)+E(f334(f334(f81(x83061),f334(x83062,x83063)),f334(f166(x83061),f334(f334(f154(x83064,x83061),x83062),f171(x83064,x83063,x83065)))),f334(f166(x83061),f334(f334(f154(x83064,x83061),x83062),x83065)))+~P104(f334(f334(f336(x83064),x83063),f334(f173(x83064),x83065))) % 169.39/169.66 [8393]~P107(x83931)+~P30(x83931,f334(f334(f154(x83932,x83931),x83933),x83935))+P30(x83931,f334(f334(f154(x83932,x83931),x83933),f334(f334(f148(x83932,x83931,x83933),x83934),x83935))) % 169.39/169.66 [8476]~P28(x84761)+P104(f334(f334(f249(x84761),f334(f334(f43(x84762,x84761),x84763),x84764)),f334(f334(f43(x84762,x84761),x84765),x84764)))+~P104(f334(f334(f249(f886(x84762,a871)),x84765),x84763)) % 169.39/169.66 [8477]~P28(x84771)+P104(f334(f334(f249(x84771),f334(f334(f44(x84772,x84771),x84773),x84774)),f334(f334(f44(x84772,x84771),x84775),x84774)))+~P104(f334(f334(f249(f886(x84772,a871)),x84773),x84775)) % 169.39/169.66 [8508]~P107(x85083)+P104(f334(f137(x85081),x85082))+~P104(f334(f137(x85081),f334(f334(f148(x85081,x85083,x85084),x85085),x85082))) % 169.39/169.66 [8645]~P107(x86451)+~P104(f334(f334(f336(x86452),x86453),f334(f173(x86452),x86454)))+~P104(f334(f137(x86452),f334(f334(f148(x86452,x86451,x86455),x86453),x86454))) % 169.39/169.66 [8726]~P107(x87261)+P30(x87261,f334(f334(f154(x87262,x87261),x87263),x87264))+~P30(x87261,f334(f334(f154(x87262,x87261),x87263),f334(f334(f148(x87262,x87261,x87263),x87265),x87264))) % 169.39/169.66 [8818]~P107(x88182)+E(f334(f334(f148(x88181,x88182,x88183),x88184),x88185),f149(x88181,x88182,x88183,x88184,x88185))+P104(f334(f334(f336(x88182),f334(x88183,x88184)),f334(f313(x88181,x88182,x88183),f334(f173(x88181),x88185)))) % 169.39/169.66 [8892]~P107(x88922)+E(f149(x88921,x88922,x88923,x88924,x88925),x88925)+~P104(f334(f334(f336(x88922),f334(x88923,x88924)),f334(f313(x88921,x88922,x88923),f334(f173(x88921),x88925)))) % 169.39/169.66 [8907]~P21(x89072,x89071,x89073,x89075)+P104(f334(f334(f250(f886(x89071,a871)),f334(f313(x89072,x89071,x89073),x89074)),f334(f313(x89072,x89071,x89073),x89075)))+~P104(f334(f334(f250(f886(x89072,a871)),x89074),x89075)) % 169.39/169.66 [9066]~P21(x90661,x90662,x90663,f257(f886(x90661,a871)))+~P104(f334(f334(f249(f886(x90662,a871)),x90664),f334(f313(x90661,x90662,x90663),x90665)))+P104(f334(f334(f249(f886(x90661,a871)),f334(f314(x90661,x90662,x90663),x90664)),x90665)) % 169.39/169.66 [9086]~E(f334(f313(x90863,x90861,x90864),f257(f886(x90863,a871))),f257(f886(x90861,a871)))+P104(f334(f334(f249(f886(x90861,a871)),x90862),f334(f313(x90863,x90861,x90864),x90865)))+~P104(f334(f334(f249(f886(x90863,a871)),f334(f314(x90863,x90861,x90864),x90862)),x90865)) % 169.39/169.66 [9111]~E(f334(f241(x91112),x91114),f334(f334(f179(x91111,x91112),x91115),x91113))+~P104(f334(f137(x91111),f334(f334(f154(f885(x91111,x91112),x91111),f268(x91111,x91112)),x91115)))+P104(f334(f334(f336(f885(x91111,x91112)),f334(f334(f269(x91111,x91112),x91113),x91114)),f334(f173(f885(x91111,x91112)),x91115))) % 169.39/169.66 [9190]~P21(x91901,x91904,x91905,f257(f886(x91901,a871)))+~P104(f334(f334(f249(f886(x91904,a871)),f334(f313(x91901,x91904,x91905),x91902)),f334(f313(x91901,x91904,x91905),x91903)))+P104(f334(f334(f249(f886(x91901,a871)),x91902),x91903)) % 169.39/169.66 [9250]E(f334(f241(x92501),x92502),f334(f334(f179(x92503,x92501),x92504),x92505))+~P104(f334(f137(x92503),f334(f334(f154(f885(x92503,x92501),x92503),f268(x92503,x92501)),x92504)))+~P104(f334(f334(f336(f885(x92503,x92501)),f334(f334(f269(x92503,x92501),x92505),x92502)),f334(f173(f885(x92503,x92501)),x92504))) % 169.39/169.66 [9252]E(f334(f334(f179(x92521,x92522),x92523),x92524),f334(f241(x92522),x92525))+~P104(f334(f137(x92521),f334(f334(f154(f885(x92521,x92522),x92521),f268(x92521,x92522)),x92523)))+~P104(f334(f334(f336(f885(x92521,x92522)),f334(f334(f269(x92521,x92522),x92524),x92525)),f334(f173(f885(x92521,x92522)),x92523))) % 169.39/169.66 [9302]~P78(x93021)+~E(f334(x93023,f651(x93023,x93024,x93025,x93022,x93021)),f2(x93021))+E(f334(f166(x93021),f334(f334(f154(x93022,x93021),x93023),f334(f136(x93022,x93024),x93025))),f334(f166(x93021),f334(f334(f154(x93022,x93021),x93023),x93025))) % 169.39/169.66 [9475]~P12(x94751,x94752,x94753)+~P104(f334(f63(x94751),x94755))+P104(f334(f68(x94751,x94752,x94753,x94754,x94755),f334(f334(f66(x94751,x94752,x94753),x94754),x94755))) % 169.39/169.66 [9550]P104(f334(x95501,f792(x95502,x95501,x95503,x95504,x95505)))+~P104(f334(f334(f249(f886(x95505,a871)),x95504),x95503))+P104(f334(f334(f249(f886(x95505,a871)),f334(f334(f104(f886(x95505,a871)),x95504),f334(f254(x95505),x95501))),f334(f334(f104(f886(x95505,a871)),x95503),f334(f254(x95505),x95502)))) % 169.39/169.66 [9564]~P78(x95641)+~P104(f334(x95644,f651(x95643,x95644,x95645,x95642,x95641)))+E(f334(f166(x95641),f334(f334(f154(x95642,x95641),x95643),f334(f136(x95642,x95644),x95645))),f334(f166(x95641),f334(f334(f154(x95642,x95641),x95643),x95645))) % 169.39/169.66 [9643]~P28(x96435)+P104(f334(f334(f336(x96431),f516(x96432,x96433,x96431,x96434,x96435)),x96433))+P104(f334(f334(f249(x96435),x96434),f334(f334(f43(x96431,x96435),x96433),x96432))) % 169.39/169.66 [9646]~P78(x96461)+E(f334(f166(x96461),f334(f334(f154(x96462,x96461),x96463),f334(f136(x96462,x96464),x96465))),f334(f166(x96461),f334(f334(f154(x96462,x96461),x96463),x96465)))+P104(f334(f334(f336(x96462),f651(x96463,x96464,x96465,x96462,x96461)),f334(f173(x96462),x96465))) % 169.39/169.66 [9656]~P104(f334(x96565,f792(x96565,x96563,x96564,x96562,x96561)))+~P104(f334(f334(f249(f886(x96561,a871)),x96562),x96564))+P104(f334(f334(f249(f886(x96561,a871)),f334(f334(f104(f886(x96561,a871)),x96562),f334(f254(x96561),x96563))),f334(f334(f104(f886(x96561,a871)),x96564),f334(f254(x96561),x96565)))) % 169.39/169.66 [9691]P36(x96911,x96912,x96913,x96914,x96915)+~E(f334(f196(f878(x96912)),x96915),f334(f196(f878(x96911)),x96914))+P104(f334(f334(f250(a877),f670(x96915,x96914,x96913,x96912,x96911)),f334(f196(f878(x96911)),x96914))) % 169.39/169.66 [9692]P36(x96921,x96922,x96923,x96924,x96925)+~E(f334(f196(f878(x96922)),x96925),f334(f196(f878(x96921)),x96924))+P104(f334(f334(f250(a877),f723(x96923,x96925,x96922,x96924,x96921)),f334(f196(f878(x96921)),x96924))) % 169.39/169.66 [9725]P104(f334(f334(f336(x97251),f792(x97252,x97253,x97254,x97255,x97251)),x97255))+~P104(f334(f334(f249(f886(x97251,a871)),x97255),x97254))+P104(f334(f334(f249(f886(x97251,a871)),f334(f334(f104(f886(x97251,a871)),x97255),f334(f254(x97251),x97253))),f334(f334(f104(f886(x97251,a871)),x97254),f334(f254(x97251),x97252)))) % 169.39/169.66 [9779]~P28(x97791)+~P104(f334(f334(f249(x97791),x97792),f334(x97795,f516(x97795,x97794,x97793,x97792,x97791))))+P104(f334(f334(f249(x97791),x97792),f334(f334(f43(x97793,x97791),x97794),x97795))) % 169.39/169.66 [9813]~P68(x98131)+~P104(f334(f63(x98132),x98135))+E(f334(f334(f334(f67(x98131,x98132,f82(x98131)),f334(f334(f20(x98132,x98131,x98131),f334(f334(f10(x98131,f886(x98131,x98131),x98132),f82(x98131)),x98133)),x98134)),f79(x98131)),x98135),f334(f334(f82(x98131),f334(f334(f334(f67(x98131,x98132,f82(x98131)),x98133),f79(x98131)),x98135)),f334(f334(f334(f67(x98131,x98132,f82(x98131)),x98134),f79(x98131)),x98135))) % 169.39/169.66 [9873]~P104(f334(f334(f336(f885(f886(x98731,a871),f886(x98731,a871))),f334(f334(f269(f886(x98731,a871),f886(x98731,a871)),x98735),x98734)),f326(x98731,x98733)))+~P104(f334(f334(f336(x98731),x98732),x98735))+P104(f334(f334(f336(f885(x98731,x98731)),f334(f334(f269(x98731,x98731),x98732),f749(x98733,x98734,x98735,x98731,x98732))),x98733)) % 169.39/169.66 [10001]~P104(f334(f334(f336(f885(f878(x100011),f878(x100011))),f334(f334(f269(f878(x100011),f878(x100011)),f334(f334(f134(x100011),x100015),x100012)),f334(f334(f134(x100011),x100015),x100013))),f147(x100011,x100014)))+P104(f334(f334(f336(f885(f878(x100011),f878(x100011))),f334(f334(f269(f878(x100011),f878(x100011)),x100012),x100013)),f147(x100011,x100014)))+P104(f334(f334(f336(f885(x100011,x100011)),f334(f334(f269(x100011,x100011),f616(x100014,x100013,x100012,x100015,x100011)),f616(x100014,x100013,x100012,x100015,x100011))),x100014)) % 169.39/169.66 [7194]~E(f334(f196(f878(x71941)),x71943),f334(f196(f878(x71942)),x71944))+E(f334(f334(f179(x71941,x71942),f334(f334(f183(x71941,x71942),x71943),x71944)),x71945),f198(x71942))+P104(f334(f334(f336(x71941),x71945),f334(f173(x71941),x71943))) % 169.39/169.66 [7267]~E(x72673,x72675)+E(f334(f334(f165(x72671),f334(f334(f159(x72671,x72672),x72673),x72674)),x72675),x72674)+~P104(f334(f334(f250(a877),x72673),f334(f196(f878(x72671)),x72672))) % 169.39/169.66 [7379]~E(f334(f334(f134(x73791),x73792),x73794),f334(f334(f134(x73791),x73793),x73795))+E(f334(f334(f176(x73791),f334(f196(f878(x73791)),x73792)),x73793),x73792)+P104(f334(f334(f249(a877),f334(f196(f878(x73791)),x73793)),f334(f196(f878(x73791)),x73792))) % 169.39/169.66 [7880]~E(f334(f334(f134(x78801),x78802),x78804),f334(f334(f134(x78801),x78803),x78805))+E(f334(f334(f176(x78801),f334(f196(f878(x78801)),x78802)),x78803),x78802)+~P104(f334(f334(f249(a877),f334(f196(f878(x78801)),x78802)),f334(f196(f878(x78801)),x78803))) % 169.39/169.66 [7904]~P104(f334(f63(x79041),f334(x79044,x79045)))+~P104(f334(f334(f336(x79042),x79045),x79043))+P104(f334(f63(x79041),f334(f334(f43(x79042,f886(x79041,a871)),x79043),x79044))) % 169.39/169.66 [7956]~E(f334(f196(f878(x79561)),x79562),f334(f196(f878(x79563)),x79564))+~E(f334(f334(f179(x79561,x79563),f334(f334(f183(x79561,x79563),x79562),x79564)),x79565),f198(x79563))+~P104(f334(f334(f336(x79561),x79565),f334(f173(x79561),x79562))) % 169.39/169.66 [8079]~P49(x80791,x80793,x80795)+~P49(x80791,x80792,x80794)+P49(x80791,f334(f334(f113(f886(x80791,a871)),x80792),x80793),f334(f334(f113(f886(f885(x80791,x80791),a871)),x80794),x80795)) % 169.39/169.66 [8080]~P49(x80801,x80803,x80805)+~P49(x80801,x80802,x80804)+P49(x80801,f334(f334(f104(f886(x80801,a871)),x80802),x80803),f334(f334(f104(f886(f885(x80801,x80801),a871)),x80804),x80805)) % 169.39/169.66 [8429]E(f334(f334(f269(x84291,x84292),f334(f334(f165(x84291),x84293),x84294)),f334(f334(f165(x84292),x84295),x84294)),f334(f334(f165(f885(x84291,x84292)),f334(f334(f183(x84291,x84292),x84293),x84295)),x84294))+~P104(f334(f334(f250(a877),x84294),f334(f196(f878(x84291)),x84293)))+~P104(f334(f334(f250(a877),x84294),f334(f196(f878(x84292)),x84295))) % 169.39/169.66 [8579]~P49(x85791,x85793,x85794)+P104(f334(f334(f336(x85791),x85792),x85793))+~P104(f334(f334(f336(f885(x85791,x85791)),f334(f334(f269(x85791,x85791),x85795),x85792)),x85794)) % 169.39/169.66 [8580]~P49(x85801,x85803,x85804)+P104(f334(f334(f336(x85801),x85802),x85803))+~P104(f334(f334(f336(f885(x85801,x85801)),f334(f334(f269(x85801,x85801),x85802),x85805)),x85804)) % 169.39/169.66 [8581]~P6(x85811,x85813,x85814)+P104(f334(f334(f336(x85811),x85812),x85813))+~P104(f334(f334(f336(f885(x85811,x85811)),f334(f334(f269(x85811,x85811),x85815),x85812)),x85814)) % 169.39/169.66 [8582]~P6(x85821,x85823,x85824)+P104(f334(f334(f336(x85821),x85822),x85823))+~P104(f334(f334(f336(f885(x85821,x85821)),f334(f334(f269(x85821,x85821),x85822),x85825)),x85824)) % 169.39/169.66 [8840]~P6(x88401,x88405,x88402)+E(f334(f288(x88401,x88401,x88402),f334(f334(f312(x88401),x88403),f195(f886(x88401,a871)))),f334(f288(x88401,x88401,x88402),f334(f334(f312(x88401),x88404),f195(f886(x88401,a871)))))+~P104(f334(f334(f336(f885(x88401,x88401)),f334(f334(f269(x88401,x88401),x88403),x88404)),x88402)) % 169.39/169.66 [9022]P104(f334(x90221,x90222))+~P104(f334(f334(f336(x90223),x90222),x90225))+P104(f334(f334(f336(x90223),f398(x90221,x90224,x90225,x90223)),f334(f334(f113(f886(x90223,a871)),x90225),x90224))) % 169.39/169.66 [9023]P104(f334(x90231,x90232))+~P104(f334(f334(f336(x90233),x90232),x90234))+P104(f334(f334(f336(x90233),f398(x90231,x90234,x90235,x90233)),f334(f334(f113(f886(x90233,a871)),x90235),x90234))) % 169.39/169.66 [9031]~P104(f334(x90312,x90315))+~P104(f334(f334(f336(x90311),x90315),x90314))+P104(f334(f334(f336(x90311),f411(x90312,x90313,x90314,x90311)),f334(f334(f113(f886(x90311,a871)),x90314),x90313))) % 169.39/169.66 [9032]~P104(f334(x90322,x90325))+~P104(f334(f334(f336(x90321),x90325),x90323))+P104(f334(f334(f336(x90321),f411(x90322,x90323,x90324,x90321)),f334(f334(f113(f886(x90321,a871)),x90324),x90323))) % 169.39/169.66 [9047]~P104(f334(f334(f249(f886(x90471,a871)),x90475),x90473))+~P104(f334(f334(f249(f886(x90471,a871)),x90472),x90474))+P104(f334(f334(f249(f886(x90471,a871)),f334(f334(f3(f886(x90471,a871)),x90472),x90473)),f334(f334(f3(f886(x90471,a871)),x90474),x90475))) % 169.39/169.66 [9048]~P104(f334(f334(f249(f886(x90481,a871)),x90483),x90485))+~P104(f334(f334(f249(f886(x90481,a871)),x90482),x90484))+P104(f334(f334(f249(f886(x90481,a871)),f334(f334(f113(f886(x90481,a871)),x90482),x90483)),f334(f334(f113(f886(x90481,a871)),x90484),x90485))) % 169.39/169.66 [9049]~P104(f334(f334(f249(f886(x90491,a871)),x90493),x90495))+~P104(f334(f334(f249(f886(x90491,a871)),x90492),x90494))+P104(f334(f334(f249(f886(x90491,a871)),f334(f334(f104(f886(x90491,a871)),x90492),x90493)),f334(f334(f104(f886(x90491,a871)),x90494),x90495))) % 169.39/169.66 [9136]~E(f334(f196(f878(x91361)),x91363),f334(f196(f878(x91362)),x91364))+E(f334(f334(f179(x91361,x91362),f334(f334(f183(x91361,x91362),x91363),x91364)),x91365),f334(f241(x91362),f575(x91365,x91364,x91362,x91363,x91361)))+~P104(f334(f334(f336(x91361),x91365),f334(f173(x91361),x91363))) % 169.39/169.66 [9140]P104(f334(f334(f336(f885(x91401,x91401)),f334(f334(f269(x91401,x91401),x91402),x91403)),f328(x91401,x91404,x91405)))+~P104(f334(f334(f249(a877),f334(x91404,x91402)),f334(x91404,x91403)))+~P104(f334(f334(f336(f885(x91401,x91401)),f334(f334(f269(x91401,x91401),x91402),x91403)),x91405)) % 169.39/169.66 [9312]P104(f334(f334(f336(f885(x93121,x93121)),f334(f334(f269(x93121,x93121),x93122),x93123)),f310(x93121,x93124)))+~P104(f334(f334(f336(f885(x93121,x93121)),f334(f334(f269(x93121,x93121),x93122),x93125)),f310(x93121,x93124)))+~P104(f334(f334(f336(f885(x93121,x93121)),f334(f334(f269(x93121,x93121),x93125),x93123)),x93124)) % 169.39/169.66 [9313]P104(f334(f334(f336(f885(x93131,x93131)),f334(f334(f269(x93131,x93131),x93132),x93133)),f310(x93131,x93134)))+~P104(f334(f334(f336(f885(x93131,x93131)),f334(f334(f269(x93131,x93131),x93135),x93133)),f310(x93131,x93134)))+~P104(f334(f334(f336(f885(x93131,x93131)),f334(f334(f269(x93131,x93131),x93132),x93135)),x93134)) % 169.39/169.66 [9407]E(x94071,x94072)+E(f334(a115,f767(x94073,x94074,x94071,x94072,x94075)),x94074)+~P104(f334(f334(f336(f885(x94075,x94075)),f334(f334(f269(x94075,x94075),x94072),x94071)),f334(f334(f190(f885(x94075,x94075),a871),x94074),x94073))) % 169.39/169.66 [9408]E(x94081,x94082)+E(f334(a115,f769(x94083,x94084,x94081,x94082,x94085)),x94084)+~P104(f334(f334(f336(f885(x94085,x94085)),f334(f334(f269(x94085,x94085),x94082),x94081)),f334(f334(f190(f885(x94085,x94085),a871),x94084),x94083))) % 169.39/169.66 [9409]E(x94091,f2(a877))+E(f334(a115,f767(x94092,x94091,x94093,x94094,x94095)),x94091)+~P104(f334(f334(f336(f885(x94095,x94095)),f334(f334(f269(x94095,x94095),x94094),x94093)),f334(f334(f190(f885(x94095,x94095),a871),x94091),x94092))) % 169.39/169.66 [9410]E(x94101,f2(a877))+E(f334(a115,f769(x94102,x94101,x94103,x94104,x94105)),x94101)+~P104(f334(f334(f336(f885(x94105,x94105)),f334(f334(f269(x94105,x94105),x94104),x94103)),f334(f334(f190(f885(x94105,x94105),a871),x94101),x94102))) % 169.39/169.66 [9426]P104(f334(f334(f336(f885(x94261,x94261)),f334(f334(f269(x94261,x94261),x94262),x94263)),f334(f334(f291(x94261,x94261,x94261),x94264),f310(x94261,x94264))))+~P104(f334(f334(f336(f885(x94261,x94261)),f334(f334(f269(x94261,x94261),x94262),x94265)),x94264))+~P104(f334(f334(f336(f885(x94261,x94261)),f334(f334(f269(x94261,x94261),x94265),x94263)),x94264)) % 169.39/169.66 [9433]~P104(f334(f334(f336(f885(x94331,x94331)),f334(f334(f269(x94331,x94331),x94332),x94335)),f310(x94331,x94334)))+P104(f334(f334(f336(f885(x94331,x94331)),f334(f334(f269(x94331,x94331),x94332),x94333)),f334(f334(f291(x94331,x94331,x94331),x94334),f310(x94331,x94334))))+~P104(f334(f334(f336(f885(x94331,x94331)),f334(f334(f269(x94331,x94331),x94335),x94333)),x94334)) % 169.39/169.66 [9471]~P6(x94711,x94715,x94712)+~P104(f334(f334(f336(f885(x94711,x94711)),f334(f334(f269(x94711,x94711),x94713),x94714)),x94712))+P104(f334(f334(f249(f886(x94711,a871)),f334(f288(x94711,x94711,x94712),f334(f334(f312(x94711),x94713),f195(f886(x94711,a871))))),f334(f288(x94711,x94711,x94712),f334(f334(f312(x94711),x94714),f195(f886(x94711,a871)))))) % 169.39/169.66 [9522]P104(f334(f334(f336(f885(x95221,x95221)),f334(f334(f269(x95221,x95221),x95222),x95223)),f334(f334(f291(x95221,x95221,x95221),x95224),f310(x95221,x95224))))+~P104(f334(f334(f336(f885(x95221,x95221)),f334(f334(f269(x95221,x95221),x95222),x95225)),f334(f334(f291(x95221,x95221,x95221),x95224),f310(x95221,x95224))))+~P104(f334(f334(f336(f885(x95221,x95221)),f334(f334(f269(x95221,x95221),x95225),x95223)),x95224)) % 169.39/169.66 [9523]P104(f334(f334(f336(f885(x95231,x95231)),f334(f334(f269(x95231,x95231),x95232),x95233)),f334(f334(f291(x95231,x95231,x95231),x95234),f310(x95231,x95234))))+~P104(f334(f334(f336(f885(x95231,x95231)),f334(f334(f269(x95231,x95231),x95235),x95233)),f334(f334(f291(x95231,x95231,x95231),x95234),f310(x95231,x95234))))+~P104(f334(f334(f336(f885(x95231,x95231)),f334(f334(f269(x95231,x95231),x95232),x95235)),x95234)) % 169.39/169.66 [9573]~P104(f334(f68(x95731,x95731,x95734,x95732,x95733),x95735))+P104(f334(f334(f336(x95731),x95732),x95733))+P104(f334(f64(x95731,x95734,f334(f334(f312(x95731),x95732),x95733)),x95735)) % 169.39/169.66 [9612]~E(f334(f313(x96123,x96122,x96125),x96124),x96121)+E(x96121,f195(f886(x96122,a871)))+P104(f334(f334(f249(f886(x96123,a871)),f334(f313(x96122,x96123,f822(x96124,x96123,x96122,x96121)),x96121)),x96124)) % 169.39/169.66 [9659]~P28(x96595)+P104(f334(f334(f336(x96591),f528(x96592,x96593,x96594,x96591,x96595)),x96594))+P104(f334(f334(f249(x96595),f334(f334(f44(x96591,x96595),x96594),x96593)),x96592)) % 169.39/169.66 [9711]P36(x97111,x97112,x97113,x97114,x97115)+~E(f334(f196(f878(x97111)),x97114),f334(f196(f878(x97112)),x97115))+P104(f334(f334(f336(f885(x97111,x97112)),f664(x97115,x97114,x97113,x97112,x97111)),f334(f173(f885(x97111,x97112)),f334(f334(f183(x97111,x97112),x97114),x97115)))) % 169.39/169.66 [9712]P36(x97121,x97122,x97123,x97124,x97125)+~E(f334(f196(f878(x97121)),x97124),f334(f196(f878(x97122)),x97125))+P104(f334(f334(f336(f885(x97121,x97122)),f669(x97123,x97125,x97124,x97122,x97121)),f334(f173(f885(x97121,x97122)),f334(f334(f183(x97121,x97122),x97124),x97125)))) % 169.39/169.66 [9850]E(x98501,x98502)+P104(f334(f334(f336(f885(x98503,x98503)),f334(f334(f269(x98503,x98503),x98501),f768(x98504,x98505,x98502,x98501,x98503))),x98504))+~P104(f334(f334(f336(f885(x98503,x98503)),f334(f334(f269(x98503,x98503),x98501),x98502)),f334(f334(f190(f885(x98503,x98503),a871),x98505),x98504))) % 169.39/169.66 [9851]E(x98511,f2(a877))+P104(f334(f334(f336(f885(x98512,x98512)),f334(f334(f269(x98512,x98512),x98513),f768(x98514,x98511,x98515,x98513,x98512))),x98514))+~P104(f334(f334(f336(f885(x98512,x98512)),f334(f334(f269(x98512,x98512),x98513),x98515)),f334(f334(f190(f885(x98512,x98512),a871),x98511),x98514))) % 169.39/169.66 [9894]~P28(x98941)+~P104(f334(f334(f249(x98941),f334(x98944,f528(x98945,x98944,x98943,x98942,x98941))),x98945))+P104(f334(f334(f249(x98941),f334(f334(f44(x98942,x98941),x98943),x98944)),x98945)) % 169.39/169.66 [9936]E(x99361,x99362)+P104(f334(f334(f336(f885(x99363,x99363)),f334(f334(f269(x99363,x99363),f770(x99364,x99365,x99361,x99362,x99363)),x99361)),x99364))+~P104(f334(f334(f336(f885(x99363,x99363)),f334(f334(f269(x99363,x99363),x99362),x99361)),f334(f334(f190(f885(x99363,x99363),a871),x99365),x99364))) % 169.39/169.66 [9937]E(x99371,f2(a877))+P104(f334(f334(f336(f885(x99372,x99372)),f334(f334(f269(x99372,x99372),f770(x99373,x99371,x99374,x99375,x99372)),x99374)),x99373))+~P104(f334(f334(f336(f885(x99372,x99372)),f334(f334(f269(x99372,x99372),x99375),x99374)),f334(f334(f190(f885(x99372,x99372),a871),x99371),x99373))) % 169.39/169.66 [9941]E(x99411,x99412)+P104(f334(f334(f336(f885(x99413,x99413)),f334(f334(f269(x99413,x99413),x99411),f770(x99414,x99415,x99412,x99411,x99413))),f334(f334(f190(f885(x99413,x99413),a871),f769(x99414,x99415,x99412,x99411,x99413)),x99414)))+~P104(f334(f334(f336(f885(x99413,x99413)),f334(f334(f269(x99413,x99413),x99411),x99412)),f334(f334(f190(f885(x99413,x99413),a871),x99415),x99414))) % 169.39/169.66 [9942]E(x99421,f2(a877))+P104(f334(f334(f336(f885(x99422,x99422)),f334(f334(f269(x99422,x99422),x99423),f770(x99424,x99421,x99425,x99423,x99422))),f334(f334(f190(f885(x99422,x99422),a871),f769(x99424,x99421,x99425,x99423,x99422)),x99424)))+~P104(f334(f334(f336(f885(x99422,x99422)),f334(f334(f269(x99422,x99422),x99423),x99425)),f334(f334(f190(f885(x99422,x99422),a871),x99421),x99424))) % 169.39/169.66 [9992]E(x99921,x99922)+P104(f334(f334(f336(f885(x99923,x99923)),f334(f334(f269(x99923,x99923),f768(x99924,x99925,x99921,x99922,x99923)),x99921)),f334(f334(f190(f885(x99923,x99923),a871),f767(x99924,x99925,x99921,x99922,x99923)),x99924)))+~P104(f334(f334(f336(f885(x99923,x99923)),f334(f334(f269(x99923,x99923),x99922),x99921)),f334(f334(f190(f885(x99923,x99923),a871),x99925),x99924))) % 169.39/169.66 [9993]E(x99931,f2(a877))+P104(f334(f334(f336(f885(x99932,x99932)),f334(f334(f269(x99932,x99932),f768(x99933,x99931,x99934,x99935,x99932)),x99934)),f334(f334(f190(f885(x99932,x99932),a871),f767(x99933,x99931,x99934,x99935,x99932)),x99933)))+~P104(f334(f334(f336(f885(x99932,x99932)),f334(f334(f269(x99932,x99932),x99935),x99934)),f334(f334(f190(f885(x99932,x99932),a871),x99931),x99933))) % 169.39/169.66 [10027]~P72(x100272)+~P104(f334(f63(x100271),x100275))+E(f334(f334(f8(x100271,x100272),f334(f334(f9(x100271,x100272,x100272),f334(f334(f20(x100271,x100272,f886(x100272,x100272)),f334(f334(f10(a871,f886(x100272,f886(x100272,x100272)),x100271),f99(x100272)),f334(f334(f9(x100271,f886(x100271,a871),a871),f336(x100271)),x100273))),x100274)),f2(x100272))),x100275),f334(f334(f8(x100271,x100272),x100274),f334(f334(f104(f886(x100271,a871)),x100275),x100273))) % 169.39/169.66 [8642]~P72(x86421)+~P104(f334(f63(x86424),x86425))+E(f334(f334(f81(x86421),f334(x86422,x86423)),f334(f334(f8(x86424,x86421),x86422),f334(f334(f3(f886(x86424,a871)),x86425),f334(f334(f312(x86424),x86423),f195(f886(x86424,a871)))))),f334(f334(f8(x86424,x86421),x86422),f334(f334(f312(x86424),x86423),x86425))) % 169.39/169.66 [8643]~P68(x86431)+~P104(f334(f63(x86434),x86435))+E(f334(f334(f82(x86431),f334(x86432,x86433)),f334(f334(f11(x86434,x86431),x86432),f334(f334(f3(f886(x86434,a871)),x86435),f334(f334(f312(x86434),x86433),f195(f886(x86434,a871)))))),f334(f334(f11(x86434,x86431),x86432),f334(f334(f312(x86434),x86433),x86435))) % 169.39/169.66 [8957]~P107(x89572)+~P30(x89572,f334(f169(x89572),f334(f334(f154(x89571,x89572),x89574),x89575)))+E(f334(f136(x89571,f334(f334(f10(x89572,a871,x89571),f334(f250(x89572),x89573)),x89574)),x89575),f178(x89571,f334(f334(f10(x89572,a871,x89571),f334(f250(x89572),x89573)),x89574),x89575)) % 169.39/169.66 [8979]~P72(x89791)+E(f334(f334(f81(x89791),f334(f334(f8(a877,x89791),x89792),f305(a877,x89793,x89794))),f334(f334(f8(a877,x89791),x89792),f305(a877,f334(f334(f81(a877),x89794),f79(a877)),f334(f334(f81(a877),x89794),x89795)))),f334(f334(f8(a877,x89791),x89792),f305(a877,x89793,f334(f334(f81(a877),x89794),x89795))))+~P104(f334(f334(f249(a877),x89793),f334(f334(f81(a877),x89794),f79(a877)))) % 169.39/169.66 [8980]~P104(f334(f334(f336(x89801),x89804),x89805))+~P104(f334(f334(f249(f886(x89801,a871)),f334(f173(x89801),x89802)),x89805))+P104(f334(f334(f249(f886(x89801,a871)),f334(f173(x89801),f334(f334(f159(x89801,x89802),x89803),x89804))),x89805)) % 169.39/169.66 [9200]~P28(x92002)+~P104(f334(f63(x92001),x92005))+E(f334(f334(f66(x92001,x92002,f334(f334(f10(x92002,f886(x92002,x92002),x92001),f113(x92002)),x92003)),x92004),x92005),f334(f334(f113(x92002),x92004),f334(f334(f44(x92001,x92002),x92005),x92003))) % 169.39/169.66 [9201]~P28(x92012)+~P104(f334(f63(x92011),x92015))+E(f334(f334(f66(x92011,x92012,f334(f334(f10(x92012,f886(x92012,x92012),x92011),f104(x92012)),x92013)),x92014),x92015),f334(f334(f104(x92012),x92014),f334(f334(f43(x92011,x92012),x92015),x92013))) % 169.39/169.66 [9243]E(f334(x92431,x92432),f334(x92431,x92433))+P104(f334(f334(f250(a877),f334(x92431,x92432)),f334(x92431,x92433)))+~P104(f334(f334(f336(f885(x92434,x92434)),f334(f334(f269(x92434,x92434),x92432),x92433)),f153(x92434,f334(f334(f151(f886(x92434,a877)),x92431),x92435)))) % 169.39/169.66 [9274]~E(f334(x92744,x92742),f334(x92744,x92743))+~P104(f334(f334(f336(f885(x92741,x92741)),f334(f334(f269(x92741,x92741),x92742),x92743)),f153(x92741,x92745)))+P104(f334(f334(f336(f885(x92741,x92741)),f334(f334(f269(x92741,x92741),x92742),x92743)),f153(x92741,f334(f334(f151(f886(x92741,a877)),x92744),x92745)))) % 169.39/169.66 [9292]~P21(x92921,x92922,x92923,x92925)+P21(x92921,x92922,x92923,f334(f334(f312(x92921),x92924),x92925))+P104(f334(f334(f336(x92922),f334(x92923,x92924)),f334(f313(x92921,x92922,x92923),f334(f334(f3(f886(x92921,a871)),x92925),f334(f334(f312(x92921),x92924),f195(f886(x92921,a871))))))) % 169.39/169.66 [9295]P104(f334(x92952,x92955))+~P104(f334(f334(f336(x92951),x92955),f334(f173(x92951),x92953)))+E(f334(f334(f138(x92951),f334(f196(f878(x92951)),f178(x92951,x92952,f334(f334(f134(x92951),x92953),x92954)))),f334(f334(f134(x92951),x92953),x92954)),f334(f334(f134(x92951),f334(f334(f138(x92951),f334(f196(f878(x92951)),f178(x92951,x92952,x92953))),x92953)),x92954)) % 169.39/169.66 [9298]~P104(f334(f334(f336(f885(x92981,x92981)),f334(f334(f269(x92981,x92981),x92982),x92983)),f153(x92981,x92985)))+~P104(f334(f334(f249(a877),f334(x92984,x92982)),f334(x92984,x92983)))+P104(f334(f334(f336(f885(x92981,x92981)),f334(f334(f269(x92981,x92981),x92982),x92983)),f153(x92981,f334(f334(f151(f886(x92981,a877)),x92984),x92985)))) % 169.39/169.66 [9362]P104(f334(f334(f336(f885(x93624,x93624)),f334(f334(f269(x93624,x93624),x93622),x93623)),f153(x93624,x93625)))+P104(f334(f334(f250(a877),f334(x93621,x93622)),f334(x93621,x93623)))+~P104(f334(f334(f336(f885(x93624,x93624)),f334(f334(f269(x93624,x93624),x93622),x93623)),f153(x93624,f334(f334(f151(f886(x93624,a877)),x93621),x93625)))) % 169.39/169.66 [9496]~P104(f334(f334(f336(f885(f878(x94961),f878(x94961))),f334(f334(f269(f878(x94961),f878(x94961)),x94962),x94964)),f158(x94961,x94965)))+~P104(f334(f334(f250(a877),x94963),f334(f196(f878(x94961)),x94962)))+P104(f334(f334(f336(f885(x94961,x94961)),f334(f334(f269(x94961,x94961),f334(f334(f165(x94961),x94962),x94963)),f334(f334(f165(x94961),x94964),x94963))),x94965)) % 169.39/169.66 [9739]E(x97391,f2(a1))+~P104(f334(f50(x97393,x97391),f334(f334(f269(a1,a1),x97394),x97395)))+P104(f334(f50(f334(f334(f82(a1),x97392),x97393),x97391),f334(f334(f269(a1,a1),f334(f334(f81(a1),f334(f334(f82(a1),x97392),x97394)),f334(f334(f40(a1),f334(f334(f82(a1),x97392),x97395)),x97391))),f46(a1,f334(f334(f82(a1),x97392),x97395),x97391)))) % 169.39/169.66 [9741]~P104(f334(f334(f250(a877),f2(a877)),x97413))+~P104(f334(f49(x97412,x97413),f334(f334(f269(a877,a877),x97414),x97415)))+P104(f334(f49(f334(f334(f82(a877),x97411),x97412),x97413),f334(f334(f269(a877,a877),f334(f334(f81(a877),f334(f334(f82(a877),x97411),x97414)),f334(f334(f40(a877),f334(f334(f82(a877),x97411),x97415)),x97413))),f46(a877,f334(f334(f82(a877),x97411),x97415),x97413)))) % 169.39/169.66 [10049]~P72(x100492)+~P104(f334(f63(x100491),x100494))+E(f334(f334(f8(x100491,x100492),x100493),f334(f254(x100491),f334(f334(f20(x100491,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100491),a332),f334(f334(f9(x100491,f886(x100491,a871),a871),f336(x100491)),x100494))),f334(f334(f9(x100491,f886(x100491,a871),a871),f336(x100491)),x100495)))),f334(f334(f8(x100491,x100492),f334(f334(f9(x100491,x100492,x100492),f334(f334(f20(x100491,x100492,f886(x100492,x100492)),f334(f334(f10(a871,f886(x100492,f886(x100492,x100492)),x100491),f99(x100492)),f334(f334(f9(x100491,f886(x100491,a871),a871),f336(x100491)),x100495))),x100493)),f2(x100492))),x100494)) % 169.39/169.66 [8288]~E(f334(f334(f134(x82881),x82882),x82885),f334(f334(f134(x82881),x82883),x82884))+E(f334(f334(f134(x82881),f334(f334(f138(x82881),f334(f196(f878(x82881)),x82882)),x82883)),x82884),x82885)+P104(f334(f334(f249(a877),f334(f196(f878(x82881)),x82883)),f334(f196(f878(x82881)),x82882))) % 169.39/169.66 [8479]~E(f334(f334(f134(x84792),x84793),x84791),f334(f334(f134(x84792),x84794),x84795))+E(x84791,f334(f334(f134(x84792),f334(f334(f138(x84792),f334(f196(f878(x84792)),x84793)),x84794)),x84795))+~P104(f334(f334(f249(a877),f334(f196(f878(x84792)),x84793)),f334(f196(f878(x84792)),x84794))) % 169.39/169.66 [8562]~E(f334(f334(f81(a877),f334(f334(f82(a877),x85623),x85624)),x85621),f334(f334(f81(a877),f334(f334(f82(a877),x85622),x85624)),x85625))+~P104(f334(f334(f249(a877),x85623),x85622))+E(x85621,f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x85622),x85623)),x85624)),x85625)) % 169.39/169.66 [8563]~E(f334(f334(f81(a877),f334(f334(f82(a877),x85631),x85633)),x85634),f334(f334(f81(a877),f334(f334(f82(a877),x85632),x85633)),x85635))+~P104(f334(f334(f249(a877),x85632),x85631))+E(f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x85631),x85632)),x85633)),x85634),x85635) % 169.39/169.66 [8719]E(f334(f334(f81(a877),f334(f334(f82(a877),x87191),x87192)),x87193),f334(f334(f81(a877),f334(f334(f82(a877),x87194),x87192)),x87195))+~P104(f334(f334(f249(a877),x87194),x87191))+~E(x87195,f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x87191),x87194)),x87192)),x87193)) % 169.39/169.66 [8720]E(f334(f334(f81(a877),f334(f334(f82(a877),x87201),x87202)),x87203),f334(f334(f81(a877),f334(f334(f82(a877),x87204),x87202)),x87205))+~P104(f334(f334(f249(a877),x87204),x87201))+~E(f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x87201),x87204)),x87202)),x87203),x87205) % 169.39/169.66 [9549]~P59(x95492)+~P104(f334(f63(x95491),x95495))+E(f334(f334(f11(x95491,x95492),f334(f334(f20(x95491,x95492,x95492),f334(f334(f10(x95492,f886(x95492,x95492),x95491),f292(x95492)),x95493)),x95494)),x95495),f334(f334(f292(x95492),f334(f334(f11(x95491,x95492),x95493),x95495)),f334(f334(f11(x95491,x95492),x95494),x95495))) % 169.39/169.66 [9675]~E(f771(x96755,x96754,x96753,x96752,x96751),f772(x96755,x96754,x96753,x96752,x96751))+P104(f334(f334(f336(f885(x96751,x96751)),f334(f334(f269(x96751,x96751),x96752),x96753)),f310(x96751,x96754)))+~P104(f334(f334(f336(f885(x96751,x96751)),f334(f334(f269(x96751,x96751),x96752),x96753)),f310(x96751,f334(f334(f113(f886(f885(x96751,x96751),a871)),x96754),x96755)))) % 169.39/169.66 [9676]~E(f773(x96765,x96764,x96763,x96762,x96761),f774(x96765,x96764,x96763,x96762,x96761))+P104(f334(f334(f336(f885(x96761,x96761)),f334(f334(f269(x96761,x96761),x96762),x96763)),f310(x96761,x96764)))+~P104(f334(f334(f336(f885(x96761,x96761)),f334(f334(f269(x96761,x96761),x96762),x96763)),f310(x96761,f334(f334(f113(f886(f885(x96761,x96761),a871)),x96764),x96765)))) % 169.39/169.66 [9884]P104(f334(f334(f336(f885(x98841,x98841)),f334(f334(f269(x98841,x98841),x98842),f774(x98845,x98844,x98843,x98842,x98841))),f310(x98841,x98844)))+P104(f334(f334(f336(f885(x98841,x98841)),f334(f334(f269(x98841,x98841),x98842),x98843)),f310(x98841,x98844)))+~P104(f334(f334(f336(f885(x98841,x98841)),f334(f334(f269(x98841,x98841),x98842),x98843)),f310(x98841,f334(f334(f113(f886(f885(x98841,x98841),a871)),x98844),x98845)))) % 169.39/169.66 [9963]P104(f334(f334(f336(f885(x99631,x99631)),f334(f334(f269(x99631,x99631),f772(x99635,x99634,x99633,x99632,x99631)),x99633)),f310(x99631,x99634)))+P104(f334(f334(f336(f885(x99631,x99631)),f334(f334(f269(x99631,x99631),x99632),x99633)),f310(x99631,x99634)))+~P104(f334(f334(f336(f885(x99631,x99631)),f334(f334(f269(x99631,x99631),x99632),x99633)),f310(x99631,f334(f334(f113(f886(f885(x99631,x99631),a871)),x99634),x99635)))) % 169.39/169.66 [9999]P104(f334(f334(f336(f885(x99991,x99991)),f334(f334(f269(x99991,x99991),x99992),x99993)),f310(x99991,x99994)))+P104(f334(f334(f336(f885(x99991,x99991)),f334(f334(f269(x99991,x99991),f771(x99995,x99994,x99993,x99992,x99991)),f772(x99995,x99994,x99993,x99992,x99991))),x99995))+~P104(f334(f334(f336(f885(x99991,x99991)),f334(f334(f269(x99991,x99991),x99992),x99993)),f310(x99991,f334(f334(f113(f886(f885(x99991,x99991),a871)),x99994),x99995)))) % 169.39/169.66 [10000]P104(f334(f334(f336(f885(x100001,x100001)),f334(f334(f269(x100001,x100001),x100002),x100003)),f310(x100001,x100004)))+P104(f334(f334(f336(f885(x100001,x100001)),f334(f334(f269(x100001,x100001),f774(x100005,x100004,x100003,x100002,x100001)),f773(x100005,x100004,x100003,x100002,x100001))),x100005))+~P104(f334(f334(f336(f885(x100001,x100001)),f334(f334(f269(x100001,x100001),x100002),x100003)),f310(x100001,f334(f334(f113(f886(f885(x100001,x100001),a871)),x100004),x100005)))) % 169.39/169.66 [10121]~P104(f334(f334(f336(f885(f878(x101211),f878(x101211))),f334(f334(f269(f878(x101211),f878(x101211)),x101214),x101215)),f158(x101211,x101212)))+~P104(f334(f334(f336(f885(x101211,x101211)),x101213),f334(f173(f885(x101211,x101211)),f334(f334(f183(x101211,x101211),x101214),x101215))))+P104(f334(f334(f273(x101211,x101211,a871),f334(f334(f9(x101211,f886(f885(x101211,x101211),a871),f886(x101211,a871)),f334(f334(f10(f886(x101211,f886(f886(f885(x101211,x101211),a871),a871)),f886(f886(f885(x101211,x101211),a871),f886(x101211,a871)),x101211),f9(x101211,f886(f885(x101211,x101211),a871),a871)),f334(f334(f10(f886(x101211,f885(x101211,x101211)),f886(x101211,f886(f886(f885(x101211,x101211),a871),a871)),x101211),f334(f10(f885(x101211,x101211),f886(f886(f885(x101211,x101211),a871),a871),x101211),f336(f885(x101211,x101211)))),f269(x101211,x101211)))),x101212)),x101213)) % 169.39/169.66 [9577]~P104(f334(f334(f249(a877),x95773),x95772))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),f334(f334(f82(a877),x95773),x95774)),x95771)),f334(f334(f81(a877),f334(f334(f82(a877),x95772),x95774)),x95775)))+P104(f334(f334(f249(a877),x95771),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x95772),x95773)),x95774)),x95775))) % 169.39/169.66 [9578]~P104(f334(f334(f249(a877),x95783),x95782))+~P104(f334(f334(f250(a877),f334(f334(f81(a877),f334(f334(f82(a877),x95783),x95784)),x95781)),f334(f334(f81(a877),f334(f334(f82(a877),x95782),x95784)),x95785)))+P104(f334(f334(f250(a877),x95781),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x95782),x95783)),x95784)),x95785))) % 169.39/169.66 [9596]~P104(f334(f334(f249(a877),x95961),x95964))+P104(f334(f334(f249(a877),f334(f334(f81(a877),f334(f334(f82(a877),x95961),x95962)),x95963)),f334(f334(f81(a877),f334(f334(f82(a877),x95964),x95962)),x95965)))+~P104(f334(f334(f249(a877),x95963),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x95964),x95961)),x95962)),x95965))) % 169.39/169.66 [9597]~P104(f334(f334(f249(a877),x95971),x95974))+P104(f334(f334(f250(a877),f334(f334(f81(a877),f334(f334(f82(a877),x95971),x95972)),x95973)),f334(f334(f81(a877),f334(f334(f82(a877),x95974),x95972)),x95975)))+~P104(f334(f334(f250(a877),x95973),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x95974),x95971)),x95972)),x95975))) % 169.39/169.66 [9709]~P104(f334(f334(f249(a877),x97092),x97091))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),f334(f334(f82(a877),x97091),x97093)),x97094)),f334(f334(f81(a877),f334(f334(f82(a877),x97092),x97093)),x97095)))+P104(f334(f334(f249(a877),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x97091),x97092)),x97093)),x97094)),x97095)) % 169.39/169.66 [9710]~P104(f334(f334(f249(a877),x97102),x97101))+~P104(f334(f334(f250(a877),f334(f334(f81(a877),f334(f334(f82(a877),x97101),x97103)),x97104)),f334(f334(f81(a877),f334(f334(f82(a877),x97102),x97103)),x97105)))+P104(f334(f334(f250(a877),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x97101),x97102)),x97103)),x97104)),x97105)) % 169.39/169.66 [9763]~P104(f334(f334(f249(a877),x97634),x97631))+P104(f334(f334(f249(a877),f334(f334(f81(a877),f334(f334(f82(a877),x97631),x97632)),x97633)),f334(f334(f81(a877),f334(f334(f82(a877),x97634),x97632)),x97635)))+~P104(f334(f334(f249(a877),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x97631),x97634)),x97632)),x97633)),x97635)) % 169.39/169.66 [9764]~P104(f334(f334(f249(a877),x97644),x97641))+P104(f334(f334(f250(a877),f334(f334(f81(a877),f334(f334(f82(a877),x97641),x97642)),x97643)),f334(f334(f81(a877),f334(f334(f82(a877),x97644),x97642)),x97645)))+~P104(f334(f334(f250(a877),f334(f334(f81(a877),f334(f334(f82(a877),f334(f334(f3(a877),x97641),x97644)),x97642)),x97643)),x97645)) % 169.39/169.66 [9984]~P9(x99841,x99842,x99845,x99843)+~P104(f334(f334(f336(f885(x99841,x99841)),x99844),x99845))+P104(f334(f334(f273(x99841,x99841,a871),f334(f334(f9(x99841,f886(x99841,x99842),f886(x99841,a871)),f334(f334(f10(f886(x99842,a871),f886(f886(x99841,x99842),f886(x99841,a871)),x99841),f10(x99842,a871,x99841)),f334(f334(f10(x99842,f886(x99842,a871),x99841),a331),x99843))),x99843)),x99844)) % 169.39/169.66 [6841]~E(f334(x68414,x68415),f198(x68412))+E(f334(f186(x68411,x68412,x68413,x68414),x68415),f334(f241(x68412),x68416))+~E(f334(x68413,x68415),f334(f241(x68412),x68416)) % 169.39/169.66 [6942]~E(f334(x69423,x69426),f198(x69421))+E(f334(f243(f881(x69421),x69422,f198(x69421),x69423),f334(x69424,x69425)),f198(x69421))+~E(f334(x69424,x69425),f334(f241(x69422),x69426)) % 169.39/169.66 [7523]E(f334(x75231,x75232),f198(x75233))+~E(f334(f186(x75235,x75233,x75236,x75231),x75232),f334(f241(x75233),x75234))+E(f334(x75231,x75232),f334(f241(x75233),x75234)) % 169.39/169.66 [7559]~E(f334(f186(x75596,x75593,x75595,x75591),x75592),f334(f241(x75593),x75594))+E(f334(x75591,x75592),f334(f241(x75593),x75594))+E(f334(x75595,x75592),f334(f241(x75593),x75594)) % 169.39/169.66 [8442]~P15(x84426,x84421,x84422,x84424)+E(f334(f74(x84421,x84421,x84421,f334(x84422,x84423)),f334(x84424,x84425)),f334(f74(x84421,x84421,x84421,f334(x84424,x84425)),f334(x84422,x84423)))+~P104(f334(f63(x84426),x84425)) % 169.39/169.66 [8852]~P21(x88521,x88523,x88525,x88526)+~P21(x88523,x88522,x88524,f334(f313(x88521,x88523,x88525),x88526))+P21(x88521,x88522,f334(f74(x88523,x88522,x88521,x88524),x88525),x88526) % 169.39/169.66 [9392]~P104(f334(f334(x93924,x93922),x93926))+~P104(f334(f334(x93923,x93925),x93922))+P104(f334(f334(f336(x93921),x93922),f299(x93921,x93923,x93924,x93925,x93926))) % 169.39/169.66 [9393]~P104(f334(f334(x93933,x93932),x93936))+~P104(f334(f334(x93934,x93935),x93932))+P104(f334(f334(f336(x93931),x93932),f302(x93931,x93933,x93934,x93935,x93936))) % 169.39/169.66 [9497]E(x94971,x94972)+E(x94973,x94974)+~P104(f334(f334(f336(f885(f878(x94975),f878(x94975))),f334(f334(f269(f878(x94975),f878(x94975)),f334(f334(f151(x94975),x94973),x94971)),f334(f334(f151(x94975),x94974),x94972))),f157(x94975,x94976))) % 169.39/169.66 [9506]~E(x95062,x95064)+P104(f334(f334(f336(f885(f878(x95061),f878(x95061))),f334(f334(f269(f878(x95061),f878(x95061)),f334(f334(f151(x95061),x95062),x95063)),f334(f334(f151(x95061),x95064),x95065))),f145(x95061,x95066)))+~P104(f334(f334(f336(f885(f878(x95061),f878(x95061))),f334(f334(f269(f878(x95061),f878(x95061)),x95063),x95065)),f145(x95061,x95066))) % 169.39/169.66 [9507]~E(x95072,x95074)+P104(f334(f334(f336(f885(f878(x95071),f878(x95071))),f334(f334(f269(f878(x95071),f878(x95071)),f334(f334(f151(x95071),x95072),x95073)),f334(f334(f151(x95071),x95074),x95075))),f147(x95071,x95076)))+~P104(f334(f334(f336(f885(f878(x95071),f878(x95071))),f334(f334(f269(f878(x95071),f878(x95071)),x95073),x95075)),f147(x95071,x95076))) % 169.39/169.66 [9508]~E(x95082,x95084)+P104(f334(f334(f336(f885(f878(x95081),f878(x95081))),f334(f334(f269(f878(x95081),f878(x95081)),f334(f334(f151(x95081),x95082),x95083)),f334(f334(f151(x95081),x95084),x95085))),f157(x95081,x95086)))+~P104(f334(f334(f336(f885(f878(x95081),f878(x95081))),f334(f334(f269(f878(x95081),f878(x95081)),x95083),x95085)),f157(x95081,x95086))) % 169.39/169.66 [9509]~E(x95092,x95094)+P104(f334(f334(f336(f885(f878(x95091),f878(x95091))),f334(f334(f269(f878(x95091),f878(x95091)),f334(f334(f134(x95091),x95092),x95093)),f334(f334(f134(x95091),x95094),x95095))),f157(x95091,x95096)))+~P104(f334(f334(f336(f885(f878(x95091),f878(x95091))),f334(f334(f269(f878(x95091),f878(x95091)),x95093),x95095)),f157(x95091,x95096))) % 169.39/169.66 [9510]~E(x95103,x95105)+P104(f334(f334(f336(f885(f878(x95101),f878(x95101))),f334(f334(f269(f878(x95101),f878(x95101)),f334(f334(f134(x95101),x95102),x95103)),f334(f334(f134(x95101),x95104),x95105))),f157(x95101,x95106)))+~P104(f334(f334(f336(f885(f878(x95101),f878(x95101))),f334(f334(f269(f878(x95101),f878(x95101)),x95102),x95104)),f157(x95101,x95106))) % 169.39/169.66 [9565]E(x95651,x95652)+P104(f334(f334(f336(f885(f878(x95653),f878(x95653))),f334(f334(f269(f878(x95653),f878(x95653)),x95651),x95652)),f157(x95653,x95654)))+~P104(f334(f334(f336(f885(f878(x95653),f878(x95653))),f334(f334(f269(f878(x95653),f878(x95653)),f334(f334(f151(x95653),x95655),x95651)),f334(f334(f151(x95653),x95656),x95652))),f157(x95653,x95654))) % 169.39/169.66 [9713]~E(x97133,x97135)+P104(f334(f334(f336(f885(f878(x97131),f878(x97131))),f334(f334(f269(f878(x97131),f878(x97131)),f334(f334(f134(x97131),x97132),f334(f334(f151(x97131),x97133),f116(x97131)))),f334(f334(f134(x97131),x97134),f334(f334(f151(x97131),x97135),f116(x97131))))),f157(x97131,x97136)))+~P104(f334(f334(f336(f885(f878(x97131),f878(x97131))),f334(f334(f269(f878(x97131),f878(x97131)),x97132),x97134)),f157(x97131,x97136))) % 169.39/169.66 [9729]E(f334(x97291,x97292),f198(x97293))+~E(f334(f243(f881(x97296),x97293,f198(x97296),x97294),f334(x97291,x97292)),f198(x97296))+E(f334(x97294,f590(x97292,x97291,x97294,x97295,x97296,x97293)),f198(x97296)) % 169.39/169.66 [9730]E(f334(x97301,x97302),f198(x97303))+~E(f334(f243(f881(x97306),x97303,f198(x97306),x97304),f334(x97301,x97302)),f198(x97306))+E(f334(f241(x97303),f590(x97302,x97301,x97304,x97305,x97306,x97303)),f334(x97301,x97302)) % 169.39/169.66 [9767]E(x97671,x97672)+E(x97673,x97674)+~P104(f334(f334(f336(f885(f878(x97675),f878(x97675))),f334(f334(f269(f878(x97675),f878(x97675)),f334(f334(f134(x97675),x97673),f334(f334(f151(x97675),x97671),f116(x97675)))),f334(f334(f134(x97675),x97674),f334(f334(f151(x97675),x97672),f116(x97675))))),f157(x97675,x97676))) % 169.39/169.66 [9793]E(x97931,x97932)+~P104(f334(f334(f336(f885(f878(x97933),f878(x97933))),f334(f334(f269(f878(x97933),f878(x97933)),f334(f334(f134(x97933),x97931),f334(f334(f151(x97933),x97935),f116(x97933)))),f334(f334(f134(x97933),x97932),f334(f334(f151(x97933),x97936),f116(x97933))))),f157(x97933,x97934)))+P104(f334(f334(f336(f885(f878(x97933),f878(x97933))),f334(f334(f269(f878(x97933),f878(x97933)),x97931),x97932)),f157(x97933,x97934))) % 169.39/169.66 [9829]~P104(f334(f334(f336(f885(f886(x98291,a871),f886(x98291,a871))),f334(f334(f269(f886(x98291,a871),f886(x98291,a871)),x98292),x98294)),f326(x98291,x98296)))+~P104(f334(f334(f336(f885(f886(x98291,a871),f886(x98291,a871))),f334(f334(f269(f886(x98291,a871),f886(x98291,a871)),x98293),x98295)),f326(x98291,x98296)))+P104(f334(f334(f336(f885(f886(x98291,a871),f886(x98291,a871))),f334(f334(f269(f886(x98291,a871),f886(x98291,a871)),f334(f334(f113(f886(x98291,a871)),x98292),x98293)),f334(f334(f113(f886(x98291,a871)),x98294),x98295))),f326(x98291,x98296))) % 169.39/169.66 [5286]~E(f334(x52863,x52866),x52865)+~E(x52864,f334(f241(x52861),x52866))+E(f334(f334(f207(x52861,x52862),x52863),x52864),f334(f241(x52862),x52865)) % 169.39/169.66 [5704]~E(f334(f334(f134(x57041),x57046),x57043),x57045)+E(f334(f334(f134(x57041),x57042),x57043),f334(f334(f151(x57041),x57044),x57045))+~E(x57042,f334(f334(f151(x57041),x57044),x57046)) % 169.39/169.66 [5705]~E(f334(f334(f134(x57051),x57056),x57053),x57055)+E(f334(f334(f134(x57051),x57052),x57053),f334(f334(f134(x57051),x57054),x57055))+~E(x57052,f334(f334(f134(x57051),x57054),x57056)) % 169.39/169.66 [5707]E(f334(f334(f134(x57071),x57072),x57073),f334(f334(f151(x57071),x57074),x57075))+~E(f334(f334(f151(x57071),x57074),x57076),x57072)+~E(x57075,f334(f334(f134(x57071),x57076),x57073)) % 169.39/169.66 [5709]~E(f334(f334(f134(x57091),x57092),x57096),x57094)+E(f334(f334(f134(x57091),x57092),x57093),f334(f334(f134(x57091),x57094),x57095))+~E(x57093,f334(f334(f134(x57091),x57096),x57095)) % 169.39/169.66 [6835]E(f334(x68351,x68352),f334(x68353,x68352))+~E(f334(f334(f154(x68354,x68355),x68351),x68356),f334(f334(f154(x68354,x68355),x68353),x68356))+~P104(f334(f334(f336(x68354),x68352),f334(f173(x68354),x68356))) % 169.39/169.66 [7217]~P15(x72174,x72175,x72176,x72171)+E(f334(f334(x72171,x72172),x72173),f334(f334(f66(x72174,x72175,x72176),x72173),x72172))+~P104(f334(f63(x72174),x72172)) % 169.39/169.66 [7284]~E(x72842,f334(x72844,x72846))+~P104(f334(f334(f336(x72843),x72846),x72845))+P104(f334(f334(f336(x72841),x72842),f334(f313(x72843,x72841,x72844),x72845))) % 169.39/169.66 [7285]~E(f334(x72854,x72852),x72856)+~P104(f334(f334(f336(x72853),x72856),x72855))+P104(f334(f334(f336(x72851),x72852),f334(f314(x72851,x72853,x72854),x72855))) % 169.39/169.66 [7739]~P34(x77391,x77392,x77394,x77396)+P34(x77391,x77392,f334(f334(f151(x77391),x77393),x77394),f334(f334(f151(x77391),x77395),x77396))+~P104(f334(f334(x77392,x77393),x77395)) % 169.39/169.66 [8727]~P54(x87274,x87275,x87271,x87272,x87276)+E(f334(x87271,f334(x87272,x87273)),x87273)+~P104(f334(f334(f336(x87275),x87273),x87276)) % 169.39/169.66 [9499]E(x94991,x94992)+E(f334(f196(f878(x94993)),x94994),f334(f196(f878(x94993)),x94995))+~P104(f334(f334(f336(f885(f878(x94993),f878(x94993))),f334(f334(f269(f878(x94993),f878(x94993)),f334(f334(f151(x94993),x94991),x94994)),f334(f334(f151(x94993),x94992),x94995))),f145(x94993,x94996))) % 169.39/169.66 [9561]~P12(x95611,x95612,x95613)+E(f334(f334(f66(x95611,x95612,x95613),x95614),x95615),x95616)+~P104(f334(f68(x95611,x95612,x95613,x95614,x95615),x95616)) % 169.39/169.66 [9568]E(f334(f196(f878(x95681)),x95682),f334(f196(f878(x95681)),x95683))+P104(f334(f334(f336(f885(f878(x95681),f878(x95681))),f334(f334(f269(f878(x95681),f878(x95681)),x95682),x95683)),f145(x95681,x95684)))+~P104(f334(f334(f336(f885(f878(x95681),f878(x95681))),f334(f334(f269(f878(x95681),f878(x95681)),f334(f334(f151(x95681),x95685),x95682)),f334(f334(f151(x95681),x95686),x95683))),f145(x95681,x95684))) % 169.39/169.66 [9590]~P104(f334(f334(f336(f885(x95901,x95901)),f334(f334(f269(x95901,x95901),x95902),x95904)),f310(x95901,x95906)))+P104(f334(f334(f336(f885(f878(x95901),f878(x95901))),f334(f334(f269(f878(x95901),f878(x95901)),f334(f334(f151(x95901),x95902),x95903)),f334(f334(f151(x95901),x95904),x95905))),f310(f878(x95901),f157(x95901,x95906))))+~P104(f334(f334(f336(f885(f878(x95901),f878(x95901))),f334(f334(f269(f878(x95901),f878(x95901)),x95903),x95905)),f310(f878(x95901),f157(x95901,x95906)))) % 169.39/169.66 [9773]~P104(f334(x97732,x97736))+~E(f334(f136(x97731,x97732),x97733),f334(f334(f151(x97731),x97734),x97735))+~P104(f334(f334(f336(x97731),x97736),f334(f173(x97731),f741(x97735,x97734,x97733,x97732,x97731)))) % 169.39/169.66 [9774]~P104(f334(x97744,x97746))+~E(f334(f334(f151(x97741),x97742),x97743),f334(f136(x97741,x97744),x97745))+~P104(f334(f334(f336(x97741),x97746),f334(f173(x97741),f740(x97745,x97744,x97743,x97742,x97741)))) % 169.39/169.66 [10076]~P72(x100762)+E(f334(f334(f8(x100761,x100762),f334(f334(f10(f886(x100763,a871),x100762,x100761),f334(f8(x100763,x100762),x100764)),f334(f334(f10(f886(x100763,a871),f886(x100763,a871),x100761),f254(x100763)),f334(f334(f10(f886(x100763,a871),f886(x100763,a871),x100761),f334(f20(x100763,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100763),a332),f334(f334(f9(x100763,f886(x100763,a871),a871),f336(x100763)),x100765)))),f334(f9(x100763,x100761,a871),f334(f334(f10(x100761,f886(x100761,a871),x100763),a331),x100766)))))),f334(f313(x100763,x100761,x100766),x100765)),f334(f334(f8(x100763,x100762),x100764),x100765))+~P104(f334(f63(x100763),x100765)) % 169.39/169.66 [6893]~P107(x68933)+P104(f334(x68932,x68935))+E(f334(f136(x68931,x68932),f334(f334(f148(x68931,x68933,x68934),x68935),x68936)),f334(f136(x68931,x68932),x68936)) % 169.39/169.66 [6895]P104(f334(x68951,x68952))+~E(f167(x68953,x68951,x68954),f334(f334(f269(f878(x68953),f878(x68953)),x68955),x68956))+~P104(f334(f334(f336(x68953),x68952),f334(f173(x68953),x68955))) % 169.39/169.66 [6939]~P104(f334(x69392,x69396))+~E(f167(x69391,x69392,x69393),f334(f334(f269(f878(x69391),f878(x69391)),x69394),x69395))+~P104(f334(f334(f336(x69391),x69396),f334(f173(x69391),x69395))) % 169.39/169.66 [7604]~P11(x76041,x76042,x76043)+~P104(f334(f63(x76041),x76046))+E(f334(f334(f66(x76041,x76042,x76043),x76044),f334(f334(f312(x76041),x76045),x76046)),f334(f334(f66(x76041,x76042,x76043),f334(f334(x76043,x76045),x76044)),x76046)) % 169.39/169.66 [7654]~P107(x76542)+~P104(f334(f334(f249(x76542),f334(x76543,x76544)),f334(x76543,x76545)))+E(f334(f334(f148(x76541,x76542,x76543),x76544),f334(f334(f151(x76541),x76545),x76546)),f334(f334(f151(x76541),x76544),f334(f334(f151(x76541),x76545),x76546))) % 169.39/169.66 [7769]E(x77691,x77692)+~E(f334(f334(f271(x77693,x77694),x77691),f334(f18(f886(x77694,a871),x77693),x77695)),f334(f334(f271(x77693,x77694),x77692),f334(f18(f886(x77694,a871),x77693),x77695)))+~P104(f334(f334(f336(x77694),x77696),x77695)) % 169.39/169.66 [7834]~P11(x78341,x78342,x78343)+~P104(f334(f63(x78341),x78346))+E(f334(f334(f66(x78341,x78342,x78343),x78344),f334(f334(f312(x78341),x78345),x78346)),f334(f334(x78343,x78345),f334(f334(f66(x78341,x78342,x78343),x78344),x78346))) % 169.39/169.66 [7948]~P12(x79481,x79482,x79483)+~P104(f334(f63(x79481),x79486))+E(f334(f334(f66(x79481,x79482,x79483),f334(f334(x79483,x79484),x79485)),x79486),f334(f334(x79483,x79484),f334(f334(f66(x79481,x79482,x79483),x79485),x79486))) % 169.39/169.66 [8019]~P16(x80192,x80195,x80196,x80191)+~P104(f334(f63(x80192),x80194))+E(f334(x80191,f334(f334(f312(x80192),x80193),x80194)),f334(f74(x80195,x80195,x80195,f334(x80191,x80194)),f334(x80196,x80193))) % 169.39/169.66 [8051]~P107(x80512)+P104(f334(f334(f249(x80512),f334(x80513,x80514)),f334(x80513,x80515)))+E(f334(f334(f148(x80511,x80512,x80513),x80514),f334(f334(f151(x80511),x80515),x80516)),f334(f334(f151(x80511),x80515),f334(f334(f148(x80511,x80512,x80513),x80514),x80516))) % 169.39/169.66 [8189]~E(f334(f196(f878(x81891)),x81895),f334(f196(f878(x81892)),x81896))+~E(f334(f196(f878(x81891)),x81893),f334(f196(f878(x81892)),x81894))+E(f334(f334(f134(f885(x81891,x81892)),f334(f334(f183(x81891,x81892),x81893),x81894)),f334(f334(f183(x81891,x81892),x81895),x81896)),f334(f334(f183(x81891,x81892),f334(f334(f134(x81891),x81893),x81895)),f334(f334(f134(x81892),x81894),x81896))) % 169.39/169.66 [8303]~E(x83032,f334(f313(x83033,x83031,x83034),x83036))+P104(f334(f334(f249(f886(x83031,a871)),x83032),f334(f313(x83033,x83031,x83034),x83035)))+~P104(f334(f334(f249(f886(x83033,a871)),x83036),x83035)) % 169.39/169.66 [8402]~P107(x84025)+E(f334(x84021,x84022),f334(x84021,x84023))+E(f334(f334(f148(x84024,x84025,x84021),x84022),f334(f334(f148(x84024,x84025,x84021),x84023),x84026)),f334(f334(f148(x84024,x84025,x84021),x84023),f334(f334(f148(x84024,x84025,x84021),x84022),x84026))) % 169.39/169.66 [8435]~P21(x84353,x84351,x84354,x84355)+P21(x84353,x84351,f334(f334(f334(f73(x84353,x84351),x84354),x84356),x84352),x84355)+P104(f334(f334(f336(x84351),x84352),f334(f313(x84353,x84351,x84354),x84355))) % 169.39/169.66 [8571]~P104(f334(f334(f336(x85712),x85714),f334(x85716,x85713)))+~P104(f334(f334(f336(x85711),x85713),x85715))+P104(f334(f334(f336(f885(x85711,x85712)),f334(f334(f269(x85711,x85712),x85713),x85714)),f334(f334(f271(x85711,x85712),x85715),x85716))) % 169.39/169.66 [9020]~P72(x90202)+~P21(x90204,x90201,x90205,x90206)+E(f334(f334(f8(x90201,x90202),x90203),f334(f313(x90204,x90201,x90205),x90206)),f334(f334(f8(x90204,x90202),f334(f74(x90201,x90202,x90204,x90203),x90205)),x90206)) % 169.39/169.66 [9021]~P68(x90212)+~P21(x90214,x90211,x90215,x90216)+E(f334(f334(f11(x90211,x90212),x90213),f334(f313(x90214,x90211,x90215),x90216)),f334(f334(f11(x90214,x90212),f334(f74(x90211,x90212,x90214,x90213),x90215)),x90216)) % 169.39/169.66 [9068]~P36(x90682,x90685,x90681,x90683,x90686)+P104(f334(f334(x90681,f334(f334(f165(x90682),x90683),x90684)),f334(f334(f165(x90685),x90686),x90684)))+~P104(f334(f334(f250(a877),x90684),f334(f196(f878(x90685)),x90686))) % 169.39/169.66 [9069]~P36(x90692,x90695,x90691,x90693,x90696)+P104(f334(f334(x90691,f334(f334(f165(x90692),x90693),x90694)),f334(f334(f165(x90695),x90696),x90694)))+~P104(f334(f334(f250(a877),x90694),f334(f196(f878(x90692)),x90693))) % 169.39/169.66 [9270]~P15(x92703,x92701,x92706,x92702)+~P104(f334(f63(x92703),x92704))+E(f334(f74(x92701,x92701,x92701,f334(x92702,f334(f334(f3(f886(x92703,a871)),x92704),f334(f334(f312(x92703),x92705),f195(f886(x92703,a871)))))),f334(x92706,x92705)),f334(x92702,f334(f334(f312(x92703),x92705),x92704))) % 169.39/169.66 [9864]~E(f334(f313(x98642,x98644,x98646),f257(f886(x98642,a871))),f257(f886(x98644,a871)))+~E(f334(f313(x98641,x98643,x98645),f257(f886(x98641,a871))),f257(f886(x98643,a871)))+E(f334(f313(f885(x98641,x98642),f885(x98643,x98644),f274(x98641,x98643,x98642,x98644,x98645,x98646)),f257(f886(f885(x98641,x98642),a871))),f257(f886(f885(x98643,x98644),a871))) % 169.39/169.66 [9912]~P21(x99123,x99124,x99125,f334(x99126,f712(x99126,x99125,x99124,x99123,x99122,x99121)))+P21(x99123,x99124,x99125,f334(f334(f43(x99122,f886(x99123,a871)),x99121),x99126))+E(x99121,f195(f886(x99122,a871))) % 169.39/169.66 [9970]P21(x99706,x99705,x99704,f334(f334(f43(x99702,f886(x99706,a871)),x99701),x99703))+E(x99701,f195(f886(x99702,a871)))+P104(f334(f334(f336(x99702),f712(x99703,x99704,x99705,x99706,x99702,x99701)),x99701)) % 169.39/169.66 [9975]P104(f334(f334(f336(x99751),f744(x99752,x99753,x99754,x99755,x99756,x99751)),x99756))+P104(f334(f334(f249(f886(f885(x99751,x99754),a871)),f334(f334(f271(x99751,x99754),x99756),x99753)),f334(f334(f271(x99751,x99754),x99755),x99752)))+~P104(f334(f334(f249(f886(x99751,a871)),x99756),x99755)) % 169.39/169.66 [10013]P20(x100136,x100135,f334(f334(f312(f876(x100136)),f334(f334(f334(f93(x100136),x100131),x100133),x100132)),f195(f886(f876(x100136),a871))))+~P20(x100136,x100135,f334(f334(f312(f876(x100136)),f334(f334(f334(f93(x100136),x100134),x100133),x100132)),f195(f886(f876(x100136),a871))))+P104(f334(f334(x100131,f787(x100131,x100132,x100133,x100134,x100135,x100136)),f829(x100131,x100132,x100133,x100134,x100135,x100136))) % 169.39/169.66 [10014]P20(x100146,x100145,f334(f334(f312(f876(x100146)),f334(f334(f334(f93(x100146),x100144),x100143),x100142)),f195(f886(f876(x100146),a871))))+~P20(x100146,x100145,f334(f334(f312(f876(x100146)),f334(f334(f334(f93(x100146),x100144),x100143),x100141)),f195(f886(f876(x100146),a871))))+P104(f334(f334(x100141,f842(x100142,x100141,x100143,x100144,x100145,x100146)),f853(x100142,x100141,x100143,x100144,x100145,x100146))) % 169.39/169.66 [10052]~P20(x100521,x100522,f334(f334(f312(f876(x100521)),f334(f334(f334(f93(x100521),x100523),x100524),x100526)),f195(f886(f876(x100521),a871))))+P20(x100521,x100522,f334(f334(f312(f876(x100521)),f334(f334(f334(f93(x100521),x100523),x100524),x100525)),f195(f886(f876(x100521),a871))))+~P104(f334(f334(x100525,f842(x100525,x100526,x100524,x100523,x100522,x100521)),f853(x100525,x100526,x100524,x100523,x100522,x100521))) % 169.39/169.66 [10053]~P20(x100531,x100532,f334(f334(f312(f876(x100531)),f334(f334(f334(f93(x100531),x100536),x100534),x100535)),f195(f886(f876(x100531),a871))))+P20(x100531,x100532,f334(f334(f312(f876(x100531)),f334(f334(f334(f93(x100531),x100533),x100534),x100535)),f195(f886(f876(x100531),a871))))+~P104(f334(f334(x100536,f787(x100533,x100535,x100534,x100536,x100532,x100531)),f829(x100533,x100535,x100534,x100536,x100532,x100531))) % 169.39/169.66 [10087]~P104(f334(f334(f249(f886(x100872,a871)),f334(x100874,f744(x100876,x100874,x100872,x100875,x100873,x100871))),f334(x100876,f744(x100876,x100874,x100872,x100875,x100873,x100871))))+~P104(f334(f334(f249(f886(x100871,a871)),x100873),x100875))+P104(f334(f334(f249(f886(f885(x100871,x100872),a871)),f334(f334(f271(x100871,x100872),x100873),x100874)),f334(f334(f271(x100871,x100872),x100875),x100876))) % 169.39/169.66 [7789]~P104(f334(x77891,x77895))+~P104(f334(x77896,x77894))+P104(f334(x77891,f334(f272(x77892,x77893),f334(f334(f269(x77892,x77893),x77894),x77895)))) % 169.39/169.66 [7790]~P104(f334(x77901,x77904))+~P104(f334(x77906,x77905))+P104(f334(x77901,f334(f268(x77902,x77903),f334(f334(f269(x77902,x77903),x77904),x77905)))) % 169.39/169.66 [7811]~E(f334(f196(f878(x78111)),x78113),f334(f196(f878(x78114)),x78115))+~E(f334(f334(f179(x78111,x78114),f334(f334(f183(x78111,x78114),x78113),x78115)),x78112),f334(f241(x78114),x78116))+P104(f334(f334(f336(x78111),x78112),f334(f173(x78111),x78113))) % 169.39/169.66 [7839]~P104(f334(f334(x78394,x78396),x78395))+~P104(f334(f334(f336(x78391),x78396),x78393))+P104(f334(f334(f334(f44(x78391,f886(x78392,a871)),x78393),x78394),x78395)) % 169.39/169.66 [8139]~P104(f334(f334(f336(x81391),x81392),f334(x81395,x81396)))+~P104(f334(f334(f336(x81393),x81396),x81394))+P104(f334(f334(f336(x81391),x81392),f334(f334(f44(x81393,f886(x81391,a871)),x81394),x81395))) % 169.39/169.66 [8182]P104(f334(f334(x81821,x81822),x81823))+~P104(f334(f334(x81824,x81822),x81823))+~P104(f334(f334(f249(f886(x81825,f886(x81826,a871))),x81824),x81821)) % 169.39/169.66 [8325]P104(f334(f334(x83251,x83252),x83253))+~P104(f334(f334(f336(x83254),x83252),x83255))+~P104(f334(f334(f334(f43(x83254,f886(x83256,a871)),x83255),x83251),x83253)) % 169.39/169.66 [8458]P104(f334(f334(f336(x84581),x84582),f334(x84583,x84584)))+~P104(f334(f334(f336(x84585),x84584),x84586))+~P104(f334(f334(f336(x84581),x84582),f334(f334(f43(x84585,f886(x84581,a871)),x84586),x84583))) % 169.39/169.66 [8709]~P9(x87094,x87095,x87096,x87091)+E(f334(x87091,x87092),f334(x87091,x87093))+~P104(f334(f334(f336(f885(x87094,x87094)),f334(f334(f269(x87094,x87094),x87092),x87093)),x87096)) % 169.39/169.66 [8740]P104(f334(f334(f249(f886(x87401,a871)),x87402),f334(x87403,x87404)))+~P104(f334(f334(f336(x87405),x87404),x87406))+~P104(f334(f334(f249(f886(x87401,a871)),x87402),f334(f334(f43(x87405,f886(x87401,a871)),x87406),x87403))) % 169.39/169.66 [8768]~P52(x87683,x87684,f334(f289(x87684,x87683),x87685))+E(x87681,f195(f886(x87682,a871)))+E(f334(f334(f43(x87682,f886(x87683,a871)),x87681),f334(f334(f10(f886(x87684,a871),f886(x87683,a871),x87682),f288(x87684,x87683,x87685)),x87686)),f334(f288(x87684,x87683,x87685),f334(f334(f43(x87682,f886(x87684,a871)),x87681),x87686))) % 169.39/169.66 [8843]P104(f334(f334(f336(x88431),x88432),f334(f288(x88433,x88431,x88434),x88435)))+~P104(f334(f334(f336(x88433),x88436),x88435))+~P104(f334(f334(f336(f885(x88433,x88431)),f334(f334(f269(x88433,x88431),x88436),x88432)),x88434)) % 169.39/169.66 [9142]P104(f334(f334(f249(f886(x91421,a871)),f334(f288(x91422,x91421,x91423),x91424)),f334(f288(x91422,x91421,x91425),x91426)))+~P104(f334(f334(f249(f886(x91422,a871)),x91424),x91426))+~P104(f334(f334(f249(f886(f885(x91422,x91421),a871)),x91423),x91425)) % 169.39/169.66 [9314]~P104(f334(f334(f336(x93142),x93146),x93144))+~P104(f334(f334(f249(f886(x93141,a871)),x93143),x93145))+P104(f334(f334(f249(f886(f885(x93141,x93142),a871)),f334(f334(f271(x93141,x93142),x93143),f334(f18(f886(x93142,a871),x93141),x93144))),f334(f334(f271(x93141,x93142),x93145),f334(f18(f886(x93142,a871),x93141),x93144)))) % 169.39/169.66 [9327]~P36(x93271,x93272,x93273,x93275,x93276)+P104(f334(f334(f273(x93271,x93272,a871),x93273),x93274))+~P104(f334(f334(f336(f885(x93271,x93272)),x93274),f334(f173(f885(x93271,x93272)),f334(f334(f183(x93271,x93272),x93275),x93276)))) % 169.39/169.66 [9457]~E(x94573,x94575)+P104(f334(f334(f336(f885(f878(x94571),f878(x94571))),f334(f334(f269(f878(x94571),f878(x94571)),f334(f334(f151(x94571),x94572),x94573)),f334(f334(f151(x94571),x94574),x94575))),f157(x94571,x94576)))+~P104(f334(f334(f336(f885(x94571,x94571)),f334(f334(f269(x94571,x94571),x94572),x94574)),x94576)) % 169.39/169.66 [9463]~E(f334(f196(f878(x94631)),x94635),f334(f196(f878(x94632)),x94636))+E(f188(x94631,x94632,f189(x94631,x94632,x94633,f334(f334(f3(f886(x94631,a871)),x94634),f334(f173(x94631),x94635))),x94635,x94636),f189(x94631,x94632,f188(x94631,x94632,x94633,x94635,x94636),x94634))+~P104(f334(f334(f249(f886(x94631,a871)),f334(f173(x94631),x94635)),x94634)) % 169.39/169.66 [9464]~E(f334(f196(f878(x94641)),x94643),f334(f196(f878(x94641)),x94645))+P104(f334(f334(f336(f885(f878(x94641),f878(x94641))),f334(f334(f269(f878(x94641),f878(x94641)),f334(f334(f151(x94641),x94642),x94643)),f334(f334(f151(x94641),x94644),x94645))),f145(x94641,x94646)))+~P104(f334(f334(f336(f885(x94641,x94641)),f334(f334(f269(x94641,x94641),x94642),x94644)),x94646)) % 169.39/169.66 [9491]P104(f334(f334(f336(f885(x94911,x94911)),f334(f334(f269(x94911,x94911),x94912),x94913)),f334(f334(f190(f885(x94911,x94911),a871),f334(a115,x94914)),x94915)))+~P104(f334(f334(f336(f885(x94911,x94911)),f334(f334(f269(x94911,x94911),x94916),x94913)),x94915))+~P104(f334(f334(f336(f885(x94911,x94911)),f334(f334(f269(x94911,x94911),x94912),x94916)),f334(f334(f190(f885(x94911,x94911),a871),x94914),x94915))) % 169.39/169.66 [9492]P104(f334(f334(f336(f885(x94921,x94921)),f334(f334(f269(x94921,x94921),x94922),x94923)),f334(f334(f190(f885(x94921,x94921),a871),f334(a115,x94924)),x94925)))+~P104(f334(f334(f336(f885(x94921,x94921)),f334(f334(f269(x94921,x94921),x94922),x94926)),x94925))+~P104(f334(f334(f336(f885(x94921,x94921)),f334(f334(f269(x94921,x94921),x94926),x94923)),f334(f334(f190(f885(x94921,x94921),a871),x94924),x94925))) % 169.39/169.66 [9495]~P104(f334(f334(f336(x94954),x94955),x94956))+P104(f334(f334(f249(f886(x94951,a871)),x94952),x94953))+~P104(f334(f334(f249(f886(f885(x94951,x94954),a871)),f334(f334(f271(x94951,x94954),x94952),f334(f18(f886(x94954,a871),x94951),x94956))),f334(f334(f271(x94951,x94954),x94953),f334(f18(f886(x94954,a871),x94951),x94956)))) % 169.39/169.66 [9539]E(x95391,x95392)+~P104(f334(f334(f336(f885(f878(x95393),f878(x95393))),f334(f334(f269(f878(x95393),f878(x95393)),f334(f334(f151(x95393),x95391),x95395)),f334(f334(f151(x95393),x95392),x95396))),f145(x95393,x95394)))+P104(f334(f334(f336(f885(x95393,x95393)),f334(f334(f269(x95393,x95393),x95391),x95392)),x95394)) % 169.39/169.66 [9540]E(x95401,x95402)+~P104(f334(f334(f336(f885(f878(x95403),f878(x95403))),f334(f334(f269(f878(x95403),f878(x95403)),f334(f334(f151(x95403),x95401),x95405)),f334(f334(f151(x95403),x95402),x95406))),f147(x95403,x95404)))+P104(f334(f334(f336(f885(x95403,x95403)),f334(f334(f269(x95403,x95403),x95401),x95402)),x95404)) % 169.39/169.66 [9541]E(x95411,x95412)+~P104(f334(f334(f336(f885(f878(x95413),f878(x95413))),f334(f334(f269(f878(x95413),f878(x95413)),f334(f334(f151(x95413),x95411),x95415)),f334(f334(f151(x95413),x95412),x95416))),f157(x95413,x95414)))+P104(f334(f334(f336(f885(x95413,x95413)),f334(f334(f269(x95413,x95413),x95411),x95412)),x95414)) % 169.39/169.66 [9576]P104(f334(f334(f336(f885(f878(x95761),f878(x95761))),f334(f334(f269(f878(x95761),f878(x95761)),f334(f334(f151(x95761),x95762),x95763)),f334(f334(f151(x95761),x95764),x95765))),f158(x95761,x95766)))+~P104(f334(f334(f336(f885(f878(x95761),f878(x95761))),f334(f334(f269(f878(x95761),f878(x95761)),x95763),x95765)),f158(x95761,x95766)))+~P104(f334(f334(f336(f885(x95761,x95761)),f334(f334(f269(x95761,x95761),x95762),x95764)),x95766)) % 169.39/169.66 [9594]P104(f334(x95941,x95942))+~P104(f334(x95941,f535(x95941,x95943,x95944,x95945,x95946)))+~P104(f334(f334(f336(x95946),x95942),f334(f334(f44(x95945,f886(x95946,a871)),x95944),x95943))) % 169.39/169.66 [9599]~P104(f334(f334(f336(f885(f878(x95991),f878(x95991))),f334(f334(f269(f878(x95991),f878(x95991)),f334(f334(f151(x95991),x95992),x95995)),f334(f334(f151(x95991),x95993),x95996))),f145(x95991,x95994)))+P104(f334(f334(f336(f885(f878(x95991),f878(x95991))),f334(f334(f269(f878(x95991),f878(x95991)),x95995),x95996)),f145(x95991,x95994)))+P104(f334(f334(f336(f885(x95991,x95991)),f334(f334(f269(x95991,x95991),x95992),x95993)),x95994)) % 169.39/169.66 [9600]~P104(f334(f334(f336(f885(f878(x96001),f878(x96001))),f334(f334(f269(f878(x96001),f878(x96001)),f334(f334(f151(x96001),x96002),x96005)),f334(f334(f151(x96001),x96003),x96006))),f147(x96001,x96004)))+P104(f334(f334(f336(f885(f878(x96001),f878(x96001))),f334(f334(f269(f878(x96001),f878(x96001)),x96005),x96006)),f147(x96001,x96004)))+P104(f334(f334(f336(f885(x96001,x96001)),f334(f334(f269(x96001,x96001),x96002),x96003)),x96004)) % 169.39/169.66 [9601]~P104(f334(f334(f336(f885(f878(x96011),f878(x96011))),f334(f334(f269(f878(x96011),f878(x96011)),f334(f334(f151(x96011),x96012),x96015)),f334(f334(f151(x96011),x96013),x96016))),f157(x96011,x96014)))+P104(f334(f334(f336(f885(f878(x96011),f878(x96011))),f334(f334(f269(f878(x96011),f878(x96011)),x96015),x96016)),f157(x96011,x96014)))+P104(f334(f334(f336(f885(x96011,x96011)),f334(f334(f269(x96011,x96011),x96012),x96013)),x96014)) % 169.39/169.66 [9685]P104(f334(x96851,x96852))+P104(f334(f334(f336(x96853),f536(x96851,x96854,x96855,x96853,x96856)),x96855))+~P104(f334(f334(f336(x96856),x96852),f334(f334(f44(x96853,f886(x96856,a871)),x96855),x96854))) % 169.39/169.66 [9696]~E(x96962,x96964)+P104(f334(f334(f336(f885(f878(x96961),f878(x96961))),f334(f334(f269(f878(x96961),f878(x96961)),f334(f334(f134(x96961),x96962),f334(f334(f151(x96961),x96963),f116(x96961)))),f334(f334(f134(x96961),x96964),f334(f334(f151(x96961),x96965),f116(x96961))))),f157(x96961,x96966)))+~P104(f334(f334(f336(f885(x96961,x96961)),f334(f334(f269(x96961,x96961),x96963),x96965)),x96966)) % 169.39/169.66 [9783]E(x97831,x97832)+~P104(f334(f334(f336(f885(f878(x97833),f878(x97833))),f334(f334(f269(f878(x97833),f878(x97833)),f334(f334(f134(x97833),x97835),f334(f334(f151(x97833),x97831),f116(x97833)))),f334(f334(f134(x97833),x97836),f334(f334(f151(x97833),x97832),f116(x97833))))),f157(x97833,x97834)))+P104(f334(f334(f336(f885(x97833,x97833)),f334(f334(f269(x97833,x97833),x97831),x97832)),x97834)) % 169.39/169.66 [9812]~P104(f334(f334(f336(f885(f878(x98121),f878(x98121))),f334(f334(f269(f878(x98121),f878(x98121)),f334(f334(f134(x98121),x98125),f334(f334(f151(x98121),x98122),f116(x98121)))),f334(f334(f134(x98121),x98126),f334(f334(f151(x98121),x98123),f116(x98121))))),f157(x98121,x98124)))+P104(f334(f334(f336(f885(f878(x98121),f878(x98121))),f334(f334(f269(f878(x98121),f878(x98121)),x98125),x98126)),f157(x98121,x98124)))+P104(f334(f334(f336(f885(x98121,x98121)),f334(f334(f269(x98121,x98121),x98122),x98123)),x98124)) % 169.39/169.66 [9830]P104(f334(x98301,x98302))+P104(f334(f334(f336(x98303),f535(x98301,x98304,x98305,x98306,x98303)),f334(x98304,f536(x98301,x98304,x98305,x98306,x98303))))+~P104(f334(f334(f336(x98303),x98302),f334(f334(f44(x98306,f886(x98303,a871)),x98305),x98304))) % 169.39/169.66 [8858]~P12(x88583,x88584,x88581)+~P104(f334(f63(x88583),x88586))+E(f334(f334(x88581,x88582),f334(f334(f66(x88583,x88584,x88581),x88585),f334(f334(f3(f886(x88583,a871)),x88586),f334(f334(f312(x88583),x88582),f195(f886(x88583,a871)))))),f334(f334(f66(x88583,x88584,x88581),x88585),f334(f334(f312(x88583),x88582),x88586))) % 169.39/169.66 [8942]~E(f334(f334(f179(x89421,x89422),x89424),x89425),f334(f241(x89422),x89426))+~P104(f334(f334(x89423,x89425),x89426))+E(f334(f334(f179(x89421,x89422),f334(f136(f885(x89421,x89422),f334(f273(x89421,x89422,a871),x89423)),x89424)),x89425),f334(f241(x89422),x89426)) % 169.39/169.66 [9149]~P104(f334(f334(f336(x91495),x91493),x91496))+P104(f334(f334(f249(f886(x91491,a871)),f334(x91492,x91493)),x91494))+~P104(f334(f334(f249(f886(x91491,a871)),f334(f334(f44(x91495,f886(x91491,a871)),x91496),x91492)),x91494)) % 169.39/169.66 [9756]~P6(x97561,x97565,x97564)+P104(f334(f334(f336(f885(x97561,x97561)),f334(f334(f269(x97561,x97561),x97562),x97563)),x97564))+~P104(f334(f334(f336(x97561),x97566),f334(f334(f104(f886(x97561,a871)),f334(f288(x97561,x97561,x97564),f334(f334(f312(x97561),x97562),f195(f886(x97561,a871))))),f334(f288(x97561,x97561,x97564),f334(f334(f312(x97561),x97563),f195(f886(x97561,a871))))))) % 169.39/169.66 [8608]~P109(x86082)+~E(f334(f334(f81(x86082),f334(f334(f82(x86082),x86084),x86085)),x86081),f334(f334(f81(x86082),f334(f334(f82(x86082),x86083),x86085)),x86086))+E(x86081,f334(f334(f81(x86082),f334(f334(f82(x86082),f334(f334(f3(x86082),x86083),x86084)),x86085)),x86086)) % 169.39/169.66 [8609]~P109(x86091)+~E(f334(f334(f81(x86091),f334(f334(f82(x86091),x86092),x86094)),x86095),f334(f334(f81(x86091),f334(f334(f82(x86091),x86093),x86094)),x86096))+E(f334(f334(f81(x86091),f334(f334(f82(x86091),f334(f334(f3(x86091),x86092),x86093)),x86094)),x86095),x86096) % 169.39/169.66 [8771]~P109(x87711)+E(f334(f334(f81(x87711),f334(f334(f82(x87711),x87712),x87713)),x87714),f334(f334(f81(x87711),f334(f334(f82(x87711),x87715),x87713)),x87716))+~E(x87716,f334(f334(f81(x87711),f334(f334(f82(x87711),f334(f334(f3(x87711),x87712),x87715)),x87713)),x87714)) % 169.39/169.66 [8772]~P109(x87721)+E(f334(f334(f81(x87721),f334(f334(f82(x87721),x87722),x87723)),x87724),f334(f334(f81(x87721),f334(f334(f82(x87721),x87725),x87723)),x87726))+~E(f334(f334(f81(x87721),f334(f334(f82(x87721),f334(f334(f3(x87721),x87722),x87725)),x87723)),x87724),x87726) % 169.39/169.66 [9088]~P104(f334(f334(x90884,x90885),x90886))+~P104(f334(f334(x90883,x90885),x90886))+P104(f334(f334(f334(f334(f104(f886(x90881,f886(x90882,a871))),x90883),x90884),x90885),x90886)) % 169.39/169.66 [9335]P104(f334(f334(x93351,x93352),x93353))+P104(f334(f334(x93354,x93352),x93353))+~P104(f334(f334(f334(f334(f113(f886(x93355,f886(x93356,a871))),x93354),x93351),x93352),x93353)) % 169.39/169.66 [9614]~P125(x96141)+~P104(f334(f334(f249(x96141),f334(f334(f81(x96141),f334(f334(f82(x96141),x96144),x96145)),x96142)),f334(f334(f81(x96141),f334(f334(f82(x96141),x96143),x96145)),x96146)))+P104(f334(f334(f249(x96141),x96142),f334(f334(f81(x96141),f334(f334(f82(x96141),f334(f334(f3(x96141),x96143),x96144)),x96145)),x96146))) % 169.39/169.66 [9615]~P125(x96151)+~P104(f334(f334(f250(x96151),f334(f334(f81(x96151),f334(f334(f82(x96151),x96154),x96155)),x96152)),f334(f334(f81(x96151),f334(f334(f82(x96151),x96153),x96155)),x96156)))+P104(f334(f334(f250(x96151),x96152),f334(f334(f81(x96151),f334(f334(f82(x96151),f334(f334(f3(x96151),x96153),x96154)),x96155)),x96156))) % 169.39/169.66 [9638]~P125(x96381)+P104(f334(f334(f249(x96381),f334(f334(f81(x96381),f334(f334(f82(x96381),x96382),x96383)),x96384)),f334(f334(f81(x96381),f334(f334(f82(x96381),x96385),x96383)),x96386)))+~P104(f334(f334(f249(x96381),x96384),f334(f334(f81(x96381),f334(f334(f82(x96381),f334(f334(f3(x96381),x96385),x96382)),x96383)),x96386))) % 169.39/169.66 [9639]~P125(x96391)+P104(f334(f334(f250(x96391),f334(f334(f81(x96391),f334(f334(f82(x96391),x96392),x96393)),x96394)),f334(f334(f81(x96391),f334(f334(f82(x96391),x96395),x96393)),x96396)))+~P104(f334(f334(f250(x96391),x96394),f334(f334(f81(x96391),f334(f334(f82(x96391),f334(f334(f3(x96391),x96395),x96392)),x96393)),x96396))) % 169.39/169.66 [9744]~P125(x97441)+~P104(f334(f334(f249(x97441),f334(f334(f81(x97441),f334(f334(f82(x97441),x97442),x97444)),x97445)),f334(f334(f81(x97441),f334(f334(f82(x97441),x97443),x97444)),x97446)))+P104(f334(f334(f249(x97441),f334(f334(f81(x97441),f334(f334(f82(x97441),f334(f334(f3(x97441),x97442),x97443)),x97444)),x97445)),x97446)) % 169.39/169.66 [9745]~P125(x97451)+~P104(f334(f334(f250(x97451),f334(f334(f81(x97451),f334(f334(f82(x97451),x97452),x97454)),x97455)),f334(f334(f81(x97451),f334(f334(f82(x97451),x97453),x97454)),x97456)))+P104(f334(f334(f250(x97451),f334(f334(f81(x97451),f334(f334(f82(x97451),f334(f334(f3(x97451),x97452),x97453)),x97454)),x97455)),x97456)) % 169.39/169.66 [9795]~P125(x97951)+P104(f334(f334(f249(x97951),f334(f334(f81(x97951),f334(f334(f82(x97951),x97952),x97953)),x97954)),f334(f334(f81(x97951),f334(f334(f82(x97951),x97955),x97953)),x97956)))+~P104(f334(f334(f249(x97951),f334(f334(f81(x97951),f334(f334(f82(x97951),f334(f334(f3(x97951),x97952),x97955)),x97953)),x97954)),x97956)) % 169.39/169.66 [9796]~P125(x97961)+P104(f334(f334(f250(x97961),f334(f334(f81(x97961),f334(f334(f82(x97961),x97962),x97963)),x97964)),f334(f334(f81(x97961),f334(f334(f82(x97961),x97965),x97963)),x97966)))+~P104(f334(f334(f250(x97961),f334(f334(f81(x97961),f334(f334(f82(x97961),f334(f334(f3(x97961),x97962),x97965)),x97963)),x97964)),x97966)) % 169.39/169.66 [9964]~P72(x99642)+~P104(f334(f63(x99641),x99646))+E(f334(f334(f8(x99641,x99642),f334(f334(f20(x99641,x99642,x99642),f334(f334(f20(x99641,x99642,f886(x99642,x99642)),f334(f334(f10(a871,f886(x99642,f886(x99642,x99642)),x99641),f99(x99642)),x99643)),x99644)),x99645)),x99646),f334(f334(f81(x99642),f334(f334(f8(x99641,x99642),x99644),f334(f334(f104(f886(x99641,a871)),x99646),f334(f254(x99641),x99643)))),f334(f334(f8(x99641,x99642),x99645),f334(f334(f104(f886(x99641,a871)),x99646),f334(f80(f886(x99641,a871)),f334(f254(x99641),x99643)))))) % 169.39/169.66 [10023]P104(f334(f334(f336(x100232),x100234),x100236))+P104(f334(f334(f336(x100232),x100235),x100236))+E(f334(f314(x100231,x100232,f334(f334(f9(x100231,x100232,x100232),f334(f334(f9(x100231,x100232,f886(x100232,x100232)),f334(f334(f10(a871,f886(x100232,f886(x100232,x100232)),x100231),f99(x100232)),f334(f334(f9(x100231,f886(x100231,a871),a871),f336(x100231)),x100233))),x100234)),x100235)),x100236),f195(f886(x100231,a871))) % 169.39/169.66 [10024]P104(f334(f334(f336(x100242),x100245),x100246))+~P104(f334(f334(f336(x100242),x100244),x100246))+E(f334(f314(x100241,x100242,f334(f334(f9(x100241,x100242,x100242),f334(f334(f9(x100241,x100242,f886(x100242,x100242)),f334(f334(f10(a871,f886(x100242,f886(x100242,x100242)),x100241),f99(x100242)),f334(f334(f9(x100241,f886(x100241,a871),a871),f336(x100241)),x100243))),x100244)),x100245)),x100246),x100243) % 169.39/169.66 [10025]P104(f334(f334(f336(x100252),x100254),x100256))+~P104(f334(f334(f336(x100252),x100255),x100256))+E(f334(f314(x100251,x100252,f334(f334(f9(x100251,x100252,x100252),f334(f334(f9(x100251,x100252,f886(x100252,x100252)),f334(f334(f10(a871,f886(x100252,f886(x100252,x100252)),x100251),f99(x100252)),f334(f334(f9(x100251,f886(x100251,a871),a871),f336(x100251)),x100253))),x100254)),x100255)),x100256),f334(f80(f886(x100251,a871)),x100253)) % 169.39/169.66 [10026]~P104(f334(f334(f336(x100262),x100264),x100266))+~P104(f334(f334(f336(x100262),x100265),x100266))+E(f334(f314(x100261,x100262,f334(f334(f9(x100261,x100262,x100262),f334(f334(f9(x100261,x100262,f886(x100262,x100262)),f334(f334(f10(a871,f886(x100262,f886(x100262,x100262)),x100261),f99(x100262)),f334(f334(f9(x100261,f886(x100261,a871),a871),f336(x100261)),x100263))),x100264)),x100265)),x100266),f257(f886(x100261,a871))) % 169.39/169.66 [10156]P20(x101561,x101562,f334(f334(f312(f876(x101561)),f334(f334(f334(f93(x101561),f334(x101563,x101564)),f334(a26,x101564)),f334(x101565,x101564))),f195(f886(f876(x101561),a871))))+~P104(f334(f334(f336(a874),x101564),x101566))+~P20(x101561,f334(f334(f113(f886(f876(x101561),a871)),x101562),f334(f313(a874,f876(x101561),f334(f334(f20(a874,f886(x101561,f886(a872,a871)),f876(x101561)),f334(f334(f20(a874,a873,f886(f886(x101561,f886(a872,a871)),f876(x101561))),f334(f334(f10(f886(x101561,f886(a872,a871)),f886(a873,f886(f886(x101561,f886(a872,a871)),f876(x101561))),a874),f93(x101561)),x101563)),a26)),x101565)),x101566)),f334(f313(a874,f876(x101561),f334(f334(f20(a874,f886(x101561,f886(a872,a871)),f876(x101561)),f334(f334(f20(a874,a873,f886(f886(x101561,f886(a872,a871)),f876(x101561))),f334(f334(f10(f886(x101561,f886(a872,a871)),f886(a873,f886(f886(x101561,f886(a872,a871)),f876(x101561))),a874),f93(x101561)),x101563)),f334(f334(f10(f881(a873),a873,a874),f245(a873)),a28))),x101565)),x101566)) % 169.39/169.66 [8638]E(x86381,x86382)+~P54(x86384,x86385,x86383,x86386,x86387)+~E(f334(x86383,x86381),f334(x86383,x86382)) % 169.39/169.66 [7045]E(f334(f243(f881(x70451),x70452,f198(x70451),x70453),f334(x70454,x70455)),f334(f241(x70451),x70456))+~E(f334(x70454,x70455),f334(f241(x70452),x70457))+~E(f334(x70453,x70457),f334(f241(x70451),x70456)) % 169.39/169.66 [8665]~P4(x86656,x86655,x86657,x86654,x86651)+E(f334(f334(x86651,x86652),x86653),x86654)+P104(f334(f63(x86655),x86653)) % 169.39/169.66 [9483]P43(x94831,x94832,x94833,x94834,x94835,f334(f334(x94833,x94836),x94837))+~E(f334(f334(x94833,x94836),x94837),x94834)+~E(x94835,f195(f886(x94831,a871))) % 169.39/169.66 [9660]~P104(f334(x96606,x96603))+~P104(f334(f334(f336(f885(x96602,x96602)),f334(f334(f269(x96602,x96602),x96604),x96605)),f334(x96607,x96603)))+P104(f334(f334(f336(f885(f885(x96601,x96602),f885(x96601,x96602))),f334(f334(f269(f885(x96601,x96602),f885(x96601,x96602)),f334(f334(f269(x96601,x96602),x96603),x96604)),f334(f334(f269(x96601,x96602),x96603),x96605))),f286(x96601,x96602,x96606,x96607))) % 169.39/169.66 [10078]~P43(x100782,x100787,x100783,x100786,x100781,f334(f334(x100783,x100785),x100784))+E(f334(f334(x100783,f560(x100784,x100785,x100781,x100786,x100783,x100787,x100782)),f576(x100784,x100785,x100781,x100786,x100783,x100787,x100782)),f334(f334(x100783,x100785),x100784))+E(x100781,f195(f886(x100782,a871))) % 169.39/169.66 [10079]~P43(x100797,x100796,x100791,x100794,x100795,f334(f334(x100791,x100792),x100793))+E(f334(f334(x100791,f560(x100793,x100792,x100795,x100794,x100791,x100796,x100797)),f576(x100793,x100792,x100795,x100794,x100791,x100796,x100797)),f334(f334(x100791,x100792),x100793))+E(f334(f334(x100791,x100792),x100793),x100794) % 169.39/169.66 [9184]~P36(x91841,x91842,x91843,x91845,x91847)+P36(x91841,x91842,x91843,f334(f334(f151(x91841),x91844),x91845),f334(f334(f151(x91842),x91846),x91847))+~P104(f334(f334(x91843,x91844),x91846)) % 169.39/169.66 [9202]P36(x92021,x92022,x92023,x92024,x92025)+~P36(x92021,x92022,x92023,f334(f334(f134(x92021),x92026),x92024),f334(f334(f134(x92022),x92027),x92025))+~E(f334(f196(f878(x92021)),x92026),f334(f196(f878(x92022)),x92027)) % 169.39/169.66 [9203]P36(x92031,x92032,x92033,x92034,x92035)+~P36(x92031,x92032,x92033,f334(f334(f134(x92031),x92034),x92036),f334(f334(f134(x92032),x92035),x92037))+~E(f334(f196(f878(x92031)),x92034),f334(f196(f878(x92032)),x92035)) % 169.39/169.66 [9395]~P36(x93951,x93952,x93953,x93955,x93957)+~P36(x93951,x93952,x93953,x93954,x93956)+P36(x93951,x93952,x93953,f334(f334(f134(x93951),x93954),x93955),f334(f334(f134(x93952),x93956),x93957)) % 169.39/169.66 [9733]~P104(f334(f68(x97331,x97334,x97335,x97336,x97333),x97337))+P104(f334(f68(x97331,x97334,x97335,x97336,f334(f334(f312(x97331),x97332),x97333)),f334(f334(x97335,x97332),x97337)))+P104(f334(f334(f336(x97331),x97332),x97333)) % 169.39/169.66 [9862]~P21(x98623,x98621,x98624,f257(f886(x98623,a871)))+E(f334(f334(f179(x98621,x98622),f334(f334(f154(f885(x98623,x98622),f885(x98621,x98622)),f334(f273(x98623,x98622,f885(x98621,x98622)),f334(f334(f10(x98621,f886(x98622,f885(x98621,x98622)),x98623),f269(x98621,x98622)),x98624))),x98625)),f334(x98624,x98626)),f334(f241(x98622),x98627))+~E(f334(f334(f179(x98623,x98622),x98625),x98626),f334(f241(x98622),x98627)) % 169.39/169.66 [10099]~P43(x100992,x100997,x100996,x100995,x100991,f334(f334(x100996,x100994),x100993))+E(x100991,f195(f886(x100992,a871)))+P104(f334(f334(f336(x100992),f560(x100993,x100994,x100991,x100995,x100996,x100997,x100992)),x100991)) % 169.39/169.66 [10100]~P43(x101005,x101007,x101001,x101004,x101006,f334(f334(x101001,x101002),x101003))+E(f334(f334(x101001,x101002),x101003),x101004)+P104(f334(f334(f336(x101005),f560(x101003,x101002,x101006,x101004,x101001,x101007,x101005)),x101006)) % 169.39/169.66 [6834]~E(x68345,x68347)+~E(x68346,x68344)+E(f334(f334(f334(f334(f73(x68341,f881(x68342)),x68343),x68344),f334(f241(x68342),x68345)),x68346),f334(f241(x68342),x68347)) % 169.39/169.66 [6961]E(x69611,x69612)+~E(f334(x69615,x69611),f334(f241(x69614),x69617))+E(f334(f334(f334(f334(f73(x69613,f881(x69614)),x69615),x69612),f334(f241(x69614),x69616)),x69611),f334(f241(x69614),x69617)) % 169.39/169.66 [7679]E(x76791,x76792)+~E(x76793,x76794)+~E(f334(f334(f334(f334(f73(x76795,f881(x76796)),x76797),x76794),f334(f241(x76796),x76791)),x76793),f334(f241(x76796),x76792)) % 169.39/169.66 [7745]E(x77451,x77452)+E(f334(x77453,x77454),f334(f241(x77455),x77451))+~E(f334(f334(f334(f334(f73(x77456,f881(x77455)),x77453),x77457),f334(f241(x77455),x77452)),x77454),f334(f241(x77455),x77451)) % 169.39/169.66 [7746]E(x77461,x77462)+E(f334(x77463,x77461),f334(f241(x77464),x77465))+~E(f334(f334(f334(f334(f73(x77466,f881(x77464)),x77463),x77462),f334(f241(x77464),x77467)),x77461),f334(f241(x77464),x77465)) % 169.39/169.66 [8883]~P17(x88834,x88835,x88836,x88837,x88831)+~P104(f334(f63(x88835),x88833))+E(f334(f334(x88831,x88832),x88833),f334(f334(f334(f67(x88834,x88835,x88836),x88832),x88837),x88833)) % 169.39/169.66 [8884]~P4(x88844,x88845,x88846,x88847,x88841)+~P104(f334(f63(x88845),x88843))+E(f334(f334(x88841,x88842),x88843),f334(f334(f334(f67(x88844,x88845,x88846),x88842),x88847),x88843)) % 169.39/169.66 [9450]~P20(x94501,x94502,f334(f334(f312(f876(x94501)),f334(f334(f334(f93(x94501),x94503),x94504),x94507)),f195(f886(f876(x94501),a871))))+P20(x94501,x94502,f334(f334(f312(f876(x94501)),f334(f334(f334(f93(x94501),x94503),f34(x94504,x94505)),x94506)),f195(f886(f876(x94501),a871))))+~P20(x94501,x94502,f334(f334(f312(f876(x94501)),f334(f334(f334(f93(x94501),x94507),x94505),x94506)),f195(f886(f876(x94501),a871)))) % 169.39/169.66 [9633]~P19(x96333,x96334,x96335,x96337,x96336,x96331)+~P104(f334(f63(x96334),x96332))+E(f334(x96331,x96332),f334(f334(f334(f67(x96333,x96334,x96335),x96336),x96337),x96332)) % 169.39/169.66 [9790]P43(x97901,x97902,x97903,x97904,x97905,f334(f334(x97903,x97906),x97907))+~P43(x97901,x97902,x97903,x97904,f334(f334(f3(f886(x97901,a871)),x97905),f334(f334(f312(x97901),x97906),f195(f886(x97901,a871)))),x97907)+~P104(f334(f334(f336(x97901),x97906),x97905)) % 169.39/169.66 [10054]~P20(x100541,x100542,f334(f334(f312(f876(x100541)),f334(f334(f334(f93(x100541),f95(x100541,x100543,x100544)),x100545),x100547)),f195(f886(f876(x100541),a871))))+P20(x100541,x100542,f334(f334(f312(f876(x100541)),f334(f334(f334(f93(x100541),x100543),f31(x100544,x100545,x100546)),x100547)),f195(f886(f876(x100541),a871))))+~P20(x100541,x100542,f334(f334(f312(f876(x100541)),f334(f334(f334(f93(x100541),f95(x100541,x100543,f334(f74(a871,a871,a872,a329),x100544))),x100546),x100547)),f195(f886(f876(x100541),a871)))) % 169.39/169.66 [10117]P20(x101177,x101176,f334(f334(f312(f876(x101177)),f334(f334(f334(f93(x101177),x101171),x101174),x101172)),f195(f886(f876(x101177),a871))))+~P20(x101177,x101176,f334(f334(f312(f876(x101177)),f334(f334(f334(f93(x101177),x101175),x101174),x101173)),f195(f886(f876(x101177),a871))))+P104(f334(f334(x101171,f863(x101172,x101171,x101173,x101174,x101175,x101176,x101177)),f870(x101172,x101171,x101173,x101174,x101175,x101176,x101177))) % 169.39/169.66 [10126]~P43(x101262,x101263,x101264,x101265,x101261,f334(f334(x101264,x101267),x101266))+P43(x101262,x101263,x101264,x101265,f334(f334(f3(f886(x101262,a871)),x101261),f334(f334(f312(x101262),f560(x101266,x101267,x101261,x101265,x101264,x101263,x101262)),f195(f886(x101262,a871)))),f576(x101266,x101267,x101261,x101265,x101264,x101263,x101262))+E(x101261,f195(f886(x101262,a871))) % 169.39/169.66 [10127]~P43(x101275,x101276,x101271,x101274,x101277,f334(f334(x101271,x101272),x101273))+P43(x101275,x101276,x101271,x101274,f334(f334(f3(f886(x101275,a871)),x101277),f334(f334(f312(x101275),f560(x101273,x101272,x101277,x101274,x101271,x101276,x101275)),f195(f886(x101275,a871)))),f576(x101273,x101272,x101277,x101274,x101271,x101276,x101275))+E(f334(f334(x101271,x101272),x101273),x101274) % 169.39/169.66 [10128]~P20(x101281,x101282,f334(f334(f312(f876(x101281)),f334(f334(f334(f93(x101281),x101287),x101284),x101286)),f195(f886(f876(x101281),a871))))+P20(x101281,x101282,f334(f334(f312(f876(x101281)),f334(f334(f334(f93(x101281),x101283),x101284),x101285)),f195(f886(f876(x101281),a871))))+~P104(f334(f334(x101285,f863(x101285,x101283,x101286,x101284,x101287,x101282,x101281)),f355(x101285,x101283,x101286,x101284,x101287,x101282,x101281))) % 169.39/169.66 [9191]E(f188(x91911,x91912,x91913,x91914,f334(f334(f159(x91912,x91915),x91916),x91917)),f188(x91911,x91912,x91913,x91914,x91915))+~P104(f334(f334(f250(a877),x91916),f334(f196(f878(x91912)),x91915)))+~P104(f334(f334(f249(a877),f334(f196(f878(x91911)),x91914)),x91916)) % 169.39/169.66 [9472]P104(f334(f334(f249(f886(f885(x94721,x94722),a871)),f334(f334(f291(x94721,x94723,x94722),x94724),x94725)),f334(f334(f291(x94721,x94723,x94722),x94726),x94727)))+~P104(f334(f334(f249(f886(f885(x94723,x94722),a871)),x94725),x94727))+~P104(f334(f334(f249(f886(f885(x94721,x94723),a871)),x94724),x94726)) % 169.39/169.66 [9801]~P104(f334(f334(f336(x98011),x98016),x98015))+P104(f334(f68(x98011,x98012,x98013,x98014,x98015),f334(f334(x98013,x98016),x98017)))+~P104(f334(f68(x98011,x98012,x98013,x98014,f334(f334(f3(f886(x98011,a871)),x98015),f334(f334(f312(x98011),x98016),f195(f886(x98011,a871))))),x98017)) % 169.39/169.66 [10184]~P143(x101841)+~P21(f885(x101842,x101843),x101841,f334(f273(x101842,x101843,x101841),f334(f334(f9(x101842,f886(x101843,x101841),f886(x101843,x101841)),f334(f334(f10(f886(x101841,x101841),f886(f886(x101843,x101841),f886(x101843,x101841)),x101842),f10(x101841,x101841,x101843)),f334(f334(f10(x101841,f886(x101841,x101841),x101842),f82(x101841)),x101844))),x101845)),f334(f334(f271(x101842,x101843),x101846),f334(f18(f886(x101843,a871),x101842),x101847)))+E(f334(f334(f8(x101841,x101841),f35(x101841)),f334(f254(x101841),f334(f334(f10(f886(x101842,a871),a871,x101841),f88(x101842)),f334(f334(f10(f886(x101842,f886(x101843,a871)),f886(x101842,a871),x101841),f334(f10(f886(x101843,a871),a871,x101842),f88(x101843))),f334(f334(f9(x101841,f886(x101842,f886(x101843,a871)),f886(x101842,f886(x101843,a871))),f334(f334(f10(f886(x101842,f886(f886(x101843,a871),f886(x101843,a871))),f886(f886(x101842,f886(x101843,a871)),f886(x101842,f886(x101843,a871))),x101841),f20(x101842,f886(x101843,a871),f886(x101843,a871))),f334(f334(f10(f886(x101842,f886(x101843,f886(a871,a871))),f886(x101842,f886(f886(x101843,a871),f886(x101843,a871))),x101841),f334(f10(f886(x101843,f886(a871,a871)),f886(f886(x101843,a871),f886(x101843,a871)),x101842),f20(x101843,a871,a871))),f334(f334(f10(f886(x101842,f886(x101843,a871)),f886(x101842,f886(x101843,f886(a871,a871))),x101841),f334(f10(f886(x101843,a871),f886(x101843,f886(a871,a871)),x101842),f334(f10(a871,f886(a871,a871),x101843),a332))),f334(f334(f9(x101841,f886(x101842,f886(x101843,x101841)),f886(x101842,f886(x101843,a871))),f334(f334(f10(f886(f886(x101843,x101841),f886(x101843,a871)),f886(f886(x101842,f886(x101843,x101841)),f886(x101842,f886(x101843,a871))),x101841),f10(f886(x101843,x101841),f886(x101843,a871),x101842)),f334(f334(f10(f886(x101841,a871),f886(f886(x101843,x101841),f886(x101843,a871)),x101841),f10(x101841,a871,x101843)),a331))),f334(f334(f9(x101842,f886(x101843,x101841),f886(x101843,x101841)),f334(f334(f10(f886(x101841,x101841),f886(f886(x101843,x101841),f886(x101843,x101841)),x101842),f10(x101841,x101841,x101843)),f334(f334(f10(x101841,f886(x101841,x101841),x101842),f82(x101841)),x101844))),x101845)))))),f334(f334(f9(x101842,f886(x101843,a871),f886(x101843,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x101843,a871),f886(x101843,a871)),x101842),f10(a871,a871,x101843)),f334(f334(f10(a871,f886(a871,a871),x101842),a332),f334(f334(f9(x101842,f886(x101842,a871),a871),f336(x101842)),x101846)))),f334(f334(f9(x101843,f886(x101843,a871),a871),f336(x101843)),x101847))))))),f334(f334(f82(x101841),f334(f334(f8(x101842,x101841),x101844),x101846)),f334(f334(f8(x101843,x101841),x101845),x101847))) % 169.39/169.66 [9631]~P104(f334(f334(x96314,x96316),x96318))+~P104(f334(f334(x96315,x96318),x96317))+P104(f334(f334(f270(x96311,x96312,x96313,x96314,x96315),x96316),x96317)) % 169.39/169.66 [9247]~P15(x92478,x92471,x92473,x92475)+~P104(f334(f63(x92478),x92476))+E(f334(f74(x92471,x92471,x92472,f334(x92473,x92474)),f334(f74(x92471,x92471,x92472,f334(x92475,x92476)),x92477)),f334(f74(x92471,x92471,x92472,f334(x92475,x92476)),f334(f74(x92471,x92471,x92472,f334(x92473,x92474)),x92477))) % 169.39/169.66 [9621]~P18(x96217,x96212,x96215,x96218,x96216,x96211)+~P104(f334(f63(x96212),x96214))+E(f334(x96211,f334(f334(f312(x96212),x96213),x96214)),f334(f334(x96215,f334(x96216,x96213)),f334(x96211,x96214))) % 169.39/169.66 [9742]~P21(x97422,x97424,x97426,x97428)+~P21(x97421,x97423,x97425,x97427)+P21(f885(x97421,x97422),f885(x97423,x97424),f274(x97421,x97423,x97422,x97424,x97425,x97426),f334(f334(f271(x97421,x97422),x97427),f334(f18(f886(x97422,a871),x97421),x97428))) % 169.39/169.66 [9419]P104(f334(f334(f336(f885(x94191,x94192)),f334(f334(f269(x94191,x94192),x94193),x94194)),f334(f334(f291(x94191,x94195,x94192),x94196),x94197)))+~P104(f334(f334(f336(f885(x94191,x94195)),f334(f334(f269(x94191,x94195),x94193),x94198)),x94196))+~P104(f334(f334(f336(f885(x94195,x94192)),f334(f334(f269(x94195,x94192),x94198),x94194)),x94197)) % 169.39/169.66 [9602]~P104(f334(f334(f249(f886(f885(x96023,x96022),a871)),x96025),f334(f334(f271(x96023,x96022),x96028),f334(f18(f886(x96022,a871),x96023),x96027))))+~P104(f334(f334(f249(f886(f885(x96021,x96023),a871)),x96024),f334(f334(f271(x96021,x96023),x96026),f334(f18(f886(x96023,a871),x96021),x96028))))+P104(f334(f334(f249(f886(f885(x96021,x96022),a871)),f334(f334(f291(x96021,x96023,x96022),x96024),x96025)),f334(f334(f271(x96021,x96022),x96026),f334(f18(f886(x96022,a871),x96021),x96027)))) % 169.39/169.66 [9655]~E(x96553,x96555)+P104(f334(f334(f336(f885(f885(x96551,x96552),f885(x96551,x96552))),f334(f334(f269(f885(x96551,x96552),f885(x96551,x96552)),f334(f334(f269(x96551,x96552),x96553),x96554)),f334(f334(f269(x96551,x96552),x96555),x96556))),f327(x96551,x96552,x96557,x96558)))+~P104(f334(f334(f336(f885(x96552,x96552)),f334(f334(f269(x96552,x96552),x96554),x96556)),x96558)) % 169.39/169.66 [9765]E(x97651,x97652)+~P104(f334(f334(f336(f885(f885(x97653,x97655),f885(x97653,x97655))),f334(f334(f269(f885(x97653,x97655),f885(x97653,x97655)),f334(f334(f269(x97653,x97655),x97651),x97656)),f334(f334(f269(x97653,x97655),x97652),x97657))),f327(x97653,x97655,x97654,x97658)))+P104(f334(f334(f336(f885(x97653,x97653)),f334(f334(f269(x97653,x97653),x97651),x97652)),x97654)) % 169.39/169.66 [9782]~P104(f334(f334(f336(f885(f885(x97821,x97825),f885(x97821,x97825))),f334(f334(f269(f885(x97821,x97825),f885(x97821,x97825)),f334(f334(f269(x97821,x97825),x97822),x97826)),f334(f334(f269(x97821,x97825),x97823),x97827))),f327(x97821,x97825,x97824,x97828)))+P104(f334(f334(f336(f885(x97821,x97821)),f334(f334(f269(x97821,x97821),x97822),x97823)),x97824))+P104(f334(f334(f336(f885(x97825,x97825)),f334(f334(f269(x97825,x97825),x97826),x97827)),x97828)) % 169.39/169.66 [9686]~P19(x96867,x96865,x96861,x96868,x96862,x96864)+~P104(f334(f63(x96865),x96866))+E(f334(f334(x96861,f334(x96862,x96863)),f334(x96864,f334(f334(f3(f886(x96865,a871)),x96866),f334(f334(f312(x96865),x96863),f195(f886(x96865,a871)))))),f334(x96864,f334(f334(f312(x96865),x96863),x96866))) % 169.39/169.66 [9210]~P104(f334(f334(f334(x92105,x92108),x92106),x92107))+~P104(f334(f334(f336(x92101),x92108),x92104))+P104(f334(f334(f334(f334(f44(x92101,f886(x92102,f886(x92103,a871))),x92104),x92105),x92106),x92107)) % 169.39/169.66 [9406]P104(f334(f334(f334(x94061,x94062),x94063),x94064))+~P104(f334(f334(f336(x94065),x94062),x94066))+~P104(f334(f334(f334(f334(f43(x94065,f886(x94067,f886(x94068,a871))),x94066),x94061),x94063),x94064)) % 169.39/169.66 [9595]~P17(x95953,x95952,x95954,x95958,x95951)+~P104(f334(f63(x95952),x95957))+E(f334(f334(x95951,f334(f334(f20(x95952,x95953,x95953),f334(f334(f10(x95953,f886(x95953,x95953),x95952),x95954),x95955)),x95956)),x95957),f334(f334(x95954,f334(f334(x95951,x95955),x95957)),f334(f334(x95951,x95956),x95957))) % 169.39/169.66 [9870]~E(f334(f313(x98702,x98704,x98706),x98708),x987010)+~E(f334(f313(x98701,x98703,x98705),x98707),x98709)+E(f334(f313(f885(x98701,x98702),f885(x98703,x98704),f274(x98701,x98703,x98702,x98704,x98705,x98706)),f334(f334(f271(x98701,x98702),x98707),f334(f18(f886(x98702,a871),x98701),x98708))),f334(f334(f271(x98703,x98704),x98709),f334(f18(f886(x98704,a871),x98703),x987010))) % 169.39/169.66 [4876]~P107(x48762)+~P30(x48762,x48761)+P30(x48762,f117(x48762,x48761))+E(x48761,f116(x48762)) % 169.39/169.66 [4877]~P107(x48772)+~P30(x48772,x48771)+P30(x48772,f633(x48771,x48772))+E(x48771,f116(x48772)) % 169.39/169.66 [5112]~P28(x51122)+E(f12(x51122,x51121),f41(x51122,x51121))+E(x51121,f195(f886(x51122,a871)))+~P104(f334(f63(x51122),x51121)) % 169.39/169.66 [5113]~P28(x51132)+E(f13(x51132,x51131),f42(x51132,x51131))+E(x51131,f195(f886(x51132,a871)))+~P104(f334(f63(x51132),x51131)) % 169.39/169.66 [5274]~P107(x52742)+~P30(x52742,x52741)+E(x52741,f116(x52742))+E(f334(f334(f151(x52742),f665(x52741,x52742)),f633(x52741,x52742)),x52741) % 169.39/169.66 [6072]~P95(x60722)+E(x60721,f195(f886(x60722,a871)))+P104(f334(f334(f249(x60722),f13(x60722,x60721)),f12(x60722,x60721)))+~P104(f334(f63(x60722),x60721)) % 169.39/169.66 [6084]~P41(x60842)+~P41(x60841)+E(x60841,x60842)+~E(f334(f313(a1,a877,a107),x60841),f334(f313(a1,a877,a107),x60842)) % 169.39/169.66 [9070]~P120(x90701)+~P104(f334(f334(f336(x90701),x90702),f112(x90701)))+P104(f334(f334(f250(x90701),f334(f334(f81(x90701),f334(f334(f81(x90701),f79(x90701)),x90702)),x90702)),f2(x90701)))+~P104(f334(f334(f250(x90701),x90702),f2(x90701))) % 169.39/169.66 [9297]~P120(x92971)+~P104(f334(f334(f336(x92971),x92972),f112(x92971)))+~P104(f334(f334(f250(x92971),f334(f334(f81(x92971),f334(f334(f81(x92971),f79(x92971)),x92972)),x92972)),f2(x92971)))+P104(f334(f334(f250(x92971),x92972),f2(x92971))) % 169.39/169.66 [4932]~P112(x49322)+~P143(x49322)+E(x49321,f2(a877))+E(f334(f334(f259(x49322),f2(x49322)),x49321),f2(x49322)) % 169.39/169.66 [4936]~P112(x49361)+~P143(x49361)+~E(x49362,f2(a877))+E(f334(f334(f259(x49361),f2(x49361)),x49362),f79(x49361)) % 169.39/169.66 [5099]~P136(x50992)+E(x50991,f79(x50992))+E(x50991,f334(f80(x50992),f79(x50992)))+~E(f334(f334(f82(x50992),x50991),x50991),f79(x50992)) % 169.39/169.66 [5360]~P86(x53602)+E(x53601,f2(x53602))+E(f83(x53602,x53601),f334(f80(x53602),f79(x53602)))+P104(f334(f334(f250(x53602),f2(x53602)),x53601)) % 169.39/169.66 [5595]~P86(x55952)+E(f83(x55952,x55951),f79(x55952))+E(x55951,f2(x55952))+~P104(f334(f334(f250(x55952),f2(x55952)),x55951)) % 169.39/169.66 [5604]E(x56041,x56042)+~E(f334(f106(a877),x56041),f334(f106(a877),x56042))+P104(f334(a201,f334(f106(a1),x56042)))+P104(f334(a201,f334(f106(a1),x56041))) % 169.39/169.66 [5654]~P89(x56541)+~E(x56542,f2(x56541))+E(f334(f334(f81(x56541),x56542),x56542),f2(x56541))+~P104(f334(f334(f336(x56541),x56542),f112(x56541))) % 169.39/169.66 [5692]E(x56921,f2(a1))+~E(f334(f334(f40(a1),x56922),x56921),f2(a1))+P104(f334(f334(f250(a1),x56921),x56922))+P104(f334(f334(f250(a1),x56922),x56921)) % 169.39/169.66 [5723]E(x57231,f2(a1))+~E(f334(f334(f40(a1),x57232),x57231),f2(a1))+P104(f334(f334(f249(a1),x57232),f2(a1)))+P104(f334(f334(f250(a1),x57232),x57231)) % 169.39/169.66 [5757]E(x57571,f2(a1))+~E(f334(f334(f40(a1),x57572),x57571),f2(a1))+P104(f334(f334(f249(a1),f2(a1)),x57572))+P104(f334(f334(f250(a1),x57571),x57572)) % 169.39/169.66 [5793]~P89(x57932)+E(x57931,f2(x57932))+~E(f334(f334(f81(x57932),x57931),x57931),f2(x57932))+~P104(f334(f334(f336(x57932),x57931),f112(x57932))) % 169.39/169.66 [5853]E(f334(f106(a877),x58531),f334(f106(a877),x58532))+~E(f334(f106(a1),x58532),f2(a1))+P104(f334(a201,f334(f106(a1),x58532)))+~P104(f334(a201,f334(f106(a1),x58531))) % 169.39/169.66 [5880]~E(f334(f106(a877),x58802),f334(f106(a877),x58801))+E(f334(f106(a1),x58801),f2(a1))+P104(f334(a201,f334(f106(a1),x58801)))+~P104(f334(a201,f334(f106(a1),x58802))) % 169.39/169.66 [5889]~P107(x58892)+E(x58891,f195(f886(x58892,a871)))+~P104(f334(f63(x58892),x58891))+P104(f334(f334(f336(x58892),f16(x58892,x58891)),x58891)) % 169.39/169.66 [5890]~P107(x58902)+E(x58901,f195(f886(x58902,a871)))+~P104(f334(f63(x58902),x58901))+P104(f334(f334(f336(x58902),f17(x58902,x58901)),x58901)) % 169.39/169.66 [6052]~P120(x60521)+~P92(x60521)+P104(f334(f334(f249(x60521),f2(x60521)),f334(f106(x60521),x60522)))+~P104(f334(f334(f249(a1),a84),x60522)) % 169.39/169.66 [6053]~P120(x60531)+~P92(x60531)+P104(f334(f334(f250(x60531),f2(x60531)),f334(f106(x60531),x60532)))+~P104(f334(f334(f250(a1),a84),x60532)) % 169.39/169.66 [6071]~P120(x60711)+~P92(x60711)+E(f334(f76(x60711),f334(f106(x60711),x60712)),f334(f106(x60711),x60712))+P104(f334(f334(f250(x60711),f334(f106(x60711),x60712)),f2(x60711))) % 169.39/169.66 [6111]E(x61111,x61112)+~E(f334(a107,x61111),f334(a107,x61112))+~P104(f334(f334(f249(a1),f2(a1)),x61112))+~P104(f334(f334(f249(a1),f2(a1)),x61111)) % 169.39/169.66 [6307]~P92(x63072)+~P120(x63072)+~P104(f334(f334(f249(x63072),f2(x63072)),f334(f106(x63072),x63071)))+P104(f334(f334(f249(a1),a84),x63071)) % 169.39/169.66 [6308]~P92(x63082)+~P120(x63082)+~P104(f334(f334(f250(x63082),f2(x63082)),f334(f106(x63082),x63081)))+P104(f334(f334(f250(a1),a84),x63081)) % 169.39/169.66 [6313]~P120(x63131)+~P92(x63131)+P104(f334(f334(f249(x63131),f334(f106(x63131),x63132)),f2(x63131)))+~P104(f334(f334(f249(a1),x63132),a84)) % 169.39/169.66 [6314]~P120(x63141)+~P92(x63141)+P104(f334(f334(f250(x63141),f334(f106(x63141),x63142)),f2(x63141)))+~P104(f334(f334(f250(a1),x63142),a84)) % 169.39/169.66 [6623]~P92(x66232)+~P120(x66232)+~P104(f334(f334(f249(x66232),f334(f106(x66232),x66231)),f2(x66232)))+P104(f334(f334(f249(a1),x66231),a84)) % 169.39/169.66 [6624]~P92(x66242)+~P120(x66242)+~P104(f334(f334(f250(x66242),f334(f106(x66242),x66241)),f2(x66242)))+P104(f334(f334(f250(a1),x66241),a84)) % 169.39/169.66 [6714]~P120(x67141)+~P92(x67141)+E(f334(f76(x67141),f334(f106(x67141),x67142)),f334(f80(x67141),f334(f106(x67141),x67142)))+~P104(f334(f334(f250(x67141),f334(f106(x67141),x67142)),f2(x67141))) % 169.39/169.66 [6732]E(f334(f106(a877),x67321),f334(f106(a877),x67322))+~E(f334(f106(a1),x67322),f2(a1))+~P104(f334(f334(f249(a1),f334(f106(a1),x67321)),f2(a1)))+~P104(f334(a201,f334(f106(a1),x67321))) % 169.39/169.66 [7610]~P107(x76102)+E(x76101,f195(f886(x76102,a871)))+~P104(f334(f63(x76102),x76101))+P104(f334(f334(f249(x76102),f14(x76102,f247(x76102),x76101)),f15(x76102,f248(x76102),x76101))) % 169.39/169.66 [7925]~P41(x79252)+~P29(x79251)+P104(f334(f334(f336(a1),x79251),x79252))+~P104(f334(f334(f336(a877),f334(a107,x79251)),f334(f313(a1,a877,a107),x79252))) % 169.39/169.66 [8192]~P58(x81922)+P104(f334(x81921,f198(x81922)))+~P104(f334(f59(f881(x81922)),x81921))+P104(f334(f59(x81922),f334(f334(f10(f881(x81922),a871,x81922),x81921),f241(x81922)))) % 169.39/169.66 [8644]~P58(x86441)+~P104(f334(x86442,f198(x86441)))+P104(f334(f60(f881(x86441)),x86442))+~P104(f334(f60(x86441),f334(f334(f10(f881(x86441),a871,x86441),x86442),f241(x86441)))) % 169.39/169.66 [5886]~P137(x58862)+E(x58861,f2(a1))+E(f334(f80(x58862),f334(f105(x58862),f334(f80(a1),x58861))),f334(f105(x58862),x58861))+~P104(f334(f334(f250(a1),x58861),f2(a1))) % 169.39/169.66 [5959]~P89(x59591)+~P92(x59591)+~P32(x59591,f334(f106(x59591),x59592))+P32(x59591,f334(f106(x59591),f334(f334(f81(a1),x59592),x59592))) % 169.39/169.66 [6296]~P73(x62962)+E(x62961,f195(f886(x62962,a871)))+E(f17(x62962,f334(f313(x62962,x62962,f80(x62962)),x62961)),f334(f80(x62962),f16(x62962,x62961)))+~P104(f334(f63(x62962),x62961)) % 169.39/169.66 [6297]~P73(x62972)+E(x62971,f195(f886(x62972,a871)))+E(f16(x62972,f334(f313(x62972,x62972,f80(x62972)),x62971)),f334(f80(x62972),f17(x62972,x62971)))+~P104(f334(f63(x62972),x62971)) % 169.39/169.66 [6328]~P89(x63281)+~P92(x63281)+P32(x63281,f334(f106(x63281),x63282))+~P32(x63281,f334(f106(x63281),f334(f334(f81(a1),x63282),x63282))) % 169.39/169.66 [6419]E(x64191,f2(a1))+E(f334(a52,f51(f334(f80(a1),x64191),f334(f80(a1),x64192))),f47(x64191,x64192))+P104(f334(f334(f249(a1),f2(a1)),x64192))+~P104(f334(f334(f249(a1),f2(a1)),x64191)) % 169.39/169.66 [7270]~P1(a5000)+~P104(f334(a25,x72701))+P20(a872,x72702,f334(f334(f312(f876(a872)),f94(x72701)),f195(f886(f876(a872),a871))))+P104(f334(f334(f336(a874),f368(x72701,x72702)),f185(a874,a873,a28))) % 169.39/169.66 [8585]~P1(a5000)+~P104(f334(a25,x85852))+P20(a872,x85851,f334(f334(f312(f876(a872)),f94(x85852)),f195(f886(f876(a872),a871))))+~P20(a872,x85851,f334(f334(f312(f876(a872)),f94(f334(a26,f368(x85852,x85851)))),f195(f886(f876(a872),a871)))) % 169.39/169.66 [8689]~P41(x86892)+~P41(x86891)+P104(f334(f334(f250(f886(a877,a871)),f334(f313(a1,a877,a107),x86891)),f334(f313(a1,a877,a107),x86892)))+~P104(f334(f334(f250(f886(a1,a871)),x86891),x86892)) % 169.39/169.66 [8902]~E(f675(x89022,x89021),f676(x89022,x89021))+~P104(f334(f137(x89021),f677(x89022,x89021)))+~P104(f334(f137(f878(x89021)),x89022))+P104(f334(f137(x89021),f334(f142(f878(x89021),f878(x89021),f134(x89021),f116(x89021)),x89022))) % 169.39/169.66 [8990]~P41(x89902)+~P41(x89901)+~P104(f334(f334(f249(f886(a877,a871)),f334(f313(a1,a877,a107),x89901)),f334(f313(a1,a877,a107),x89902)))+P104(f334(f334(f249(f886(a1,a871)),x89901),x89902)) % 169.39/169.66 [8991]~P41(x89912)+~P41(x89911)+~P104(f334(f334(f250(f886(a877,a871)),f334(f313(a1,a877,a107),x89911)),f334(f313(a1,a877,a107),x89912)))+P104(f334(f334(f250(f886(a1,a871)),x89911),x89912)) % 169.39/169.66 [8997]~E(f675(x89972,x89971),f676(x89972,x89971))+~P104(f334(f137(f878(x89971)),x89972))+P104(f334(f137(x89971),f334(f142(f878(x89971),f878(x89971),f134(x89971),f116(x89971)),x89972)))+P104(f334(f334(f336(f878(x89971)),f677(x89972,x89971)),f334(f173(f878(x89971)),x89972))) % 169.39/169.66 [9038]~P104(f334(f137(x90381),f677(x90382,x90381)))+~P104(f334(f137(f878(x90381)),x90382))+P104(f334(f137(x90381),f334(f142(f878(x90381),f878(x90381),f134(x90381),f116(x90381)),x90382)))+P104(f334(f334(f336(f878(x90381)),f676(x90382,x90381)),f334(f173(f878(x90381)),x90382))) % 169.39/169.66 [9039]~P104(f334(f137(x90391),f677(x90392,x90391)))+~P104(f334(f137(f878(x90391)),x90392))+P104(f334(f137(x90391),f334(f142(f878(x90391),f878(x90391),f134(x90391),f116(x90391)),x90392)))+P104(f334(f334(f336(f878(x90391)),f675(x90392,x90391)),f334(f173(f878(x90391)),x90392))) % 169.39/169.66 [9114]~P104(f334(f137(f878(x91141)),x91142))+P104(f334(f137(x91141),f334(f142(f878(x91141),f878(x91141),f134(x91141),f116(x91141)),x91142)))+P104(f334(f334(f336(f878(x91141)),f676(x91142,x91141)),f334(f173(f878(x91141)),x91142)))+P104(f334(f334(f336(f878(x91141)),f677(x91142,x91141)),f334(f173(f878(x91141)),x91142))) % 169.39/169.66 [9115]~P104(f334(f137(f878(x91151)),x91152))+P104(f334(f137(x91151),f334(f142(f878(x91151),f878(x91151),f134(x91151),f116(x91151)),x91152)))+P104(f334(f334(f336(f878(x91151)),f675(x91152,x91151)),f334(f173(f878(x91151)),x91152)))+P104(f334(f334(f336(f878(x91151)),f677(x91152,x91151)),f334(f173(f878(x91151)),x91152))) % 169.39/169.66 [9128]~E(f334(f334(f104(f886(x91281,a871)),f334(f173(x91281),f676(x91282,x91281))),f334(f173(x91281),f675(x91282,x91281))),f195(f886(x91281,a871)))+~P104(f334(f137(x91281),f677(x91282,x91281)))+~P104(f334(f137(f878(x91281)),x91282))+P104(f334(f137(x91281),f334(f142(f878(x91281),f878(x91281),f134(x91281),f116(x91281)),x91282))) % 169.39/169.66 [9187]~E(f334(f334(f104(f886(x91871,a871)),f334(f173(x91871),f676(x91872,x91871))),f334(f173(x91871),f675(x91872,x91871))),f195(f886(x91871,a871)))+~P104(f334(f137(f878(x91871)),x91872))+P104(f334(f137(x91871),f334(f142(f878(x91871),f878(x91871),f134(x91871),f116(x91871)),x91872)))+P104(f334(f334(f336(f878(x91871)),f677(x91872,x91871)),f334(f173(f878(x91871)),x91872))) % 169.39/169.66 [9442]E(x94421,f2(a1))+E(x94422,f2(a1))+E(f334(f334(f87(a1,f885(a1,a1)),f334(f334(a226,x94422),x94421)),f334(f334(f20(a1,a1,f885(a1,a1)),f334(f334(f10(a1,f886(a1,f885(a1,a1)),a1),f269(a1,a1)),f334(f40(a1),x94422))),f334(f40(a1),x94421))),f224(x94422,x94421))+P104(f334(f334(f250(a1),x94421),f2(a1))) % 169.39/169.66 [8253]~P92(x82532)+~P120(x82532)+~P104(f334(f334(f249(x82532),f334(f106(x82532),x82531)),f79(x82532)))+P104(f334(f334(f249(a1),x82531),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))) % 169.39/169.66 [8254]~P92(x82542)+~P120(x82542)+~P104(f334(f334(f250(x82542),f334(f106(x82542),x82541)),f79(x82542)))+P104(f334(f334(f250(a1),x82541),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))) % 169.39/169.66 [8517]~P120(x85171)+~P92(x85171)+P104(f334(f334(f249(x85171),f334(f106(x85171),x85172)),f79(x85171)))+~P104(f334(f334(f249(a1),x85172),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))) % 169.39/169.66 [8518]~P120(x85181)+~P92(x85181)+P104(f334(f334(f250(x85181),f334(f106(x85181),x85182)),f79(x85181)))+~P104(f334(f334(f250(a1),x85182),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))) % 169.39/169.66 [8714]~P92(x87142)+~P120(x87142)+~P104(f334(f334(f249(x87142),f79(x87142)),f334(f106(x87142),x87141)))+P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),x87141)) % 169.39/169.66 [8715]~P92(x87152)+~P120(x87152)+~P104(f334(f334(f250(x87152),f79(x87152)),f334(f106(x87152),x87151)))+P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),x87151)) % 169.39/169.66 [9076]~P120(x90761)+~P92(x90761)+P104(f334(f334(f249(x90761),f79(x90761)),f334(f106(x90761),x90762)))+~P104(f334(f334(f249(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),x90762)) % 169.39/169.66 [9077]~P120(x90771)+~P92(x90771)+P104(f334(f334(f250(x90771),f79(x90771)),f334(f106(x90771),x90772)))+~P104(f334(f334(f250(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),x90772)) % 169.39/169.66 [9567]~P136(x95672)+E(x95671,f79(x95672))+E(x95671,f334(f80(x95672),f79(x95672)))+~E(f334(f334(f259(x95672),x95671),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f79(x95672)) % 169.39/169.66 [9840]~P92(x98401)+~P61(x98401)+~P104(f334(f334(f250(x98401),f2(x98401)),x98402))+P104(f334(f334(f250(x98401),f2(x98401)),f334(f334(f292(x98401),x98402),f334(f106(x98401),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.39/169.66 [9900]~P92(x99001)+~P61(x99001)+P104(f334(f334(f250(x99001),f2(x99001)),x99002))+~P104(f334(f334(f250(x99001),f2(x99001)),f334(f334(f292(x99001),x99002),f334(f106(x99001),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.39/169.66 [10155]~P137(x101552)+E(x101551,f2(a1))+P104(f334(f334(f250(a1),x101551),f2(a1)))+E(f334(f334(f273(a1,a1,x101552),f334(f334(f9(a1,f886(a1,f886(x101552,x101552)),f886(a1,x101552)),f334(f334(f10(f886(f886(x101552,x101552),x101552),f886(f886(a1,f886(x101552,x101552)),f886(a1,x101552)),a1),f10(f886(x101552,x101552),x101552,a1)),f334(f334(f10(x101552,f886(f886(x101552,x101552),x101552),a1),f87(x101552,x101552)),f105(x101552)))),f334(f334(f9(a1,f886(x101552,x101552),f886(x101552,x101552)),f334(f334(f10(f886(x101552,f886(x101552,x101552)),f886(f886(x101552,x101552),f886(x101552,x101552)),a1),f20(x101552,x101552,x101552)),f334(f334(f9(a1,f886(x101552,x101552),f886(x101552,f886(x101552,x101552))),f334(f334(f10(f886(x101552,f886(x101552,x101552)),f886(f886(x101552,x101552),f886(x101552,f886(x101552,x101552))),a1),f10(x101552,f886(x101552,x101552),x101552)),f334(f334(f10(a871,f886(x101552,f886(x101552,x101552)),a1),f99(x101552)),f334(f334(f9(a1,a1,a871),a331),f2(a1))))),f334(f334(f20(x101552,x101552,x101552),f81(x101552)),f7(x101552))))),f334(f334(f9(x101552,x101552,x101552),f334(f334(f10(x101552,f886(x101552,x101552),x101552),f81(x101552)),f334(f334(f20(x101552,x101552,x101552),f81(x101552)),f7(x101552)))),f79(x101552))))),f47(x101551,f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f105(x101552),x101551)) % 169.39/169.66 [5269]~P58(x52693)+~P37(x52693,x52692,f57(x52693))+E(x52691,f731(x52692,x52693))+~P104(f334(x52692,x52691)) % 169.39/169.66 [5430]~P58(x54301)+P37(x54301,x54302,f57(x54301))+~E(f794(x54302,x54301,x54303),x54303)+~P104(f334(x54302,x54303)) % 169.39/169.66 [4903]~P89(x49033)+~P92(x49033)+E(x49031,x49032)+~E(f334(f106(x49033),x49031),f334(f106(x49033),x49032)) % 169.39/169.66 [6051]~P58(x60511)+P37(x60511,x60512,f57(x60511))+~P104(f334(x60512,x60513))+P104(f334(x60512,f794(x60512,x60511,x60513))) % 169.39/169.66 [6061]~P104(f334(x60611,x60612))+~P104(f334(x60611,x60613))+~P104(f334(f334(f249(a877),x60613),f832(x60612,x60611)))+P104(f334(x60611,f2(a877))) % 169.39/169.66 [6482]P146(x64822,x64821,x64823)+E(x64821,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f805(x64823,x64821,x64822)))+P104(f334(f334(f250(a1),x64821),f2(a1))) % 169.39/169.66 [6483]P145(x64832,x64831,x64833)+E(x64831,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f818(x64833,x64831,x64832)))+P104(f334(f334(f250(a1),x64831),f2(a1))) % 169.39/169.66 [6603]P145(x66031,x66032,x66033)+~P104(f334(x66031,x66033))+P104(f334(f334(f249(a1),f2(a1)),f818(x66033,x66032,x66031)))+P104(f334(f334(f250(a1),x66032),f2(a1))) % 169.39/169.66 [6629]P146(x66291,x66292,x66293)+P104(f334(f334(f249(a1),f2(a1)),f805(x66293,x66292,x66291)))+~P104(f334(x66291,f2(a1)))+P104(f334(f334(f250(a1),x66292),f2(a1))) % 169.39/169.66 [6657]P146(x66572,x66571,x66573)+E(x66571,f2(a1))+~P104(f334(x66572,f806(x66573,x66571,x66572)))+P104(f334(f334(f250(a1),x66571),f2(a1))) % 169.39/169.66 [6658]P145(x66582,x66581,x66583)+E(x66581,f2(a1))+~P104(f334(x66582,f818(x66583,x66581,x66582)))+P104(f334(f334(f250(a1),x66581),f2(a1))) % 169.39/169.66 [6757]~P107(x67571)+~P28(x67571)+~P104(f334(f334(f250(x67571),x67572),f41(x67571,x67573)))+P104(f334(f334(f250(x67571),x67572),f415(x67573,x67572,x67571))) % 169.39/169.66 [6766]P145(x67661,x67662,x67663)+~P104(f334(x67661,x67663))+~P104(f334(x67661,f818(x67663,x67662,x67661)))+P104(f334(f334(f250(a1),x67662),f2(a1))) % 169.39/169.66 [6798]P146(x67981,x67982,x67983)+~P104(f334(x67981,f806(x67983,x67982,x67981)))+~P104(f334(x67981,f2(a1)))+P104(f334(f334(f250(a1),x67982),f2(a1))) % 169.39/169.66 [7048]P146(x70482,x70481,x70483)+E(x70481,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f805(x70483,x70481,x70482)))+P104(f334(f334(f250(a1),x70481),f816(x70483,x70481,x70482))) % 169.39/169.66 [7049]P145(x70492,x70491,x70493)+E(x70491,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f818(x70493,x70491,x70492)))+P104(f334(f334(f250(a1),x70491),f817(x70493,x70491,x70492))) % 169.39/169.66 [7166]P145(x71661,x71662,x71663)+~P104(f334(x71661,x71663))+P104(f334(f334(f249(a1),f2(a1)),f818(x71663,x71662,x71661)))+P104(f334(f334(f250(a1),x71662),f817(x71663,x71662,x71661))) % 169.39/169.66 [7185]P146(x71851,x71852,x71853)+P104(f334(f334(f249(a1),f2(a1)),f805(x71853,x71852,x71851)))+P104(f334(f334(f250(a1),x71852),f816(x71853,x71852,x71851)))+~P104(f334(x71851,f2(a1))) % 169.39/169.66 [7218]P146(x72182,x72181,x72183)+E(x72181,f2(a1))+~P104(f334(x72182,f806(x72183,x72181,x72182)))+P104(f334(f334(f250(a1),x72181),f816(x72183,x72181,x72182))) % 169.39/169.66 [7219]P145(x72192,x72191,x72193)+E(x72191,f2(a1))+~P104(f334(x72192,f818(x72193,x72191,x72192)))+P104(f334(f334(f250(a1),x72191),f817(x72193,x72191,x72192))) % 169.39/169.66 [7260]P146(x72602,x72601,x72603)+E(x72601,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f805(x72603,x72601,x72602)))+~P104(f334(x72602,f814(x72603,x72601,x72602))) % 169.39/169.66 [7261]P145(x72612,x72611,x72613)+E(x72611,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f818(x72613,x72611,x72612)))+~P104(f334(x72612,f817(x72613,x72611,x72612))) % 169.39/169.66 [7352]P145(x73521,x73522,x73523)+~P104(f334(x73521,x73523))+~P104(f334(x73521,f818(x73523,x73522,x73521)))+P104(f334(f334(f250(a1),x73522),f817(x73523,x73522,x73521))) % 169.39/169.66 [7368]P146(x73681,x73682,x73683)+~P104(f334(x73681,f806(x73683,x73682,x73681)))+P104(f334(f334(f250(a1),x73682),f816(x73683,x73682,x73681)))+~P104(f334(x73681,f2(a1))) % 169.39/169.66 [7372]P145(x73721,x73722,x73723)+~P104(f334(x73721,x73723))+P104(f334(f334(f249(a1),f2(a1)),f818(x73723,x73722,x73721)))+~P104(f334(x73721,f817(x73723,x73722,x73721))) % 169.39/169.66 [7388]P146(x73881,x73882,x73883)+P104(f334(f334(f249(a1),f2(a1)),f805(x73883,x73882,x73881)))+~P104(f334(x73881,f814(x73883,x73882,x73881)))+~P104(f334(x73881,f2(a1))) % 169.39/169.66 [7412]P146(x74122,x74121,x74123)+E(x74121,f2(a1))+~P104(f334(x74122,f806(x74123,x74121,x74122)))+~P104(f334(x74122,f814(x74123,x74121,x74122))) % 169.39/169.66 [7413]P145(x74132,x74131,x74133)+E(x74131,f2(a1))+~P104(f334(x74132,f818(x74133,x74131,x74132)))+~P104(f334(x74132,f817(x74133,x74131,x74132))) % 169.39/169.66 [7504]P145(x75041,x75042,x75043)+~P104(f334(x75041,x75043))+~P104(f334(x75041,f818(x75043,x75042,x75041)))+~P104(f334(x75041,f817(x75043,x75042,x75041))) % 169.39/169.66 [7521]P146(x75211,x75212,x75213)+~P104(f334(x75211,f806(x75213,x75212,x75211)))+~P104(f334(x75211,f814(x75213,x75212,x75211)))+~P104(f334(x75211,f2(a1))) % 169.39/169.66 [7570]P146(x75702,x75701,x75703)+E(x75701,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f805(x75703,x75701,x75702)))+P104(f334(f334(f249(a1),f816(x75703,x75701,x75702)),f2(a1))) % 169.39/169.66 [7571]P145(x75712,x75711,x75713)+E(x75711,f2(a1))+P104(f334(f334(f249(a1),f2(a1)),f818(x75713,x75711,x75712)))+P104(f334(f334(f249(a1),f817(x75713,x75711,x75712)),f2(a1))) % 169.39/169.66 [7572]~P137(x75721)+~P104(f334(f334(f336(x75721),x75723),f112(x75721)))+~P104(f334(f334(f336(x75721),x75722),f112(x75721)))+P104(f334(f334(f336(x75721),f334(f334(f3(x75721),x75722),x75723)),f112(x75721))) % 169.39/169.66 [7573]~P137(x75731)+~P104(f334(f334(f336(x75731),x75733),f112(x75731)))+~P104(f334(f334(f336(x75731),x75732),f112(x75731)))+P104(f334(f334(f336(x75731),f334(f334(f82(x75731),x75732),x75733)),f112(x75731))) % 169.39/169.66 [7574]~P142(x75741)+~P104(f334(f334(f336(x75741),x75743),f193(x75741)))+~P104(f334(f334(f336(x75741),x75742),f193(x75741)))+P104(f334(f334(f336(x75741),f334(f334(f82(x75741),x75742),x75743)),f193(x75741))) % 169.39/169.66 [7575]~P137(x75751)+~P104(f334(f334(f336(x75751),x75753),f112(x75751)))+~P104(f334(f334(f336(x75751),x75752),f112(x75751)))+P104(f334(f334(f336(x75751),f334(f334(f81(x75751),x75752),x75753)),f112(x75751))) % 169.39/169.66 [7576]~P142(x75761)+~P104(f334(f334(f336(x75761),x75763),f193(x75761)))+~P104(f334(f334(f336(x75761),x75762),f193(x75761)))+P104(f334(f334(f336(x75761),f334(f334(f81(x75761),x75762),x75763)),f193(x75761))) % 169.39/169.66 [7577]~P85(x75771)+~P104(f334(f334(f249(x75771),x75773),f2(x75771)))+~P104(f334(f334(f249(x75771),x75772),f2(x75771)))+P104(f334(f334(f249(x75771),f334(f334(f81(x75771),x75772),x75773)),f2(x75771))) % 169.39/169.66 [7578]~P85(x75781)+~P104(f334(f334(f249(x75781),x75783),f2(x75781)))+~P104(f334(f334(f250(x75781),x75782),f2(x75781)))+P104(f334(f334(f250(x75781),f334(f334(f81(x75781),x75782),x75783)),f2(x75781))) % 169.39/169.66 [7579]~P85(x75791)+~P104(f334(f334(f249(x75791),x75792),f2(x75791)))+~P104(f334(f334(f250(x75791),x75793),f2(x75791)))+P104(f334(f334(f250(x75791),f334(f334(f81(x75791),x75792),x75793)),f2(x75791))) % 169.39/169.66 [7580]~P85(x75801)+~P104(f334(f334(f250(x75801),x75803),f2(x75801)))+~P104(f334(f334(f250(x75801),x75802),f2(x75801)))+P104(f334(f334(f250(x75801),f334(f334(f81(x75801),x75802),x75803)),f2(x75801))) % 169.39/169.66 [7606]P146(x76063,x76061,x76062)+E(x76061,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x76061),f806(x76062,x76061,x76063))),f805(x76062,x76061,x76063)),x76062)+P104(f334(f334(f250(a1),x76061),f2(a1))) % 169.39/169.66 [7607]P145(x76073,x76071,x76072)+E(x76071,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x76071),f819(x76072,x76071,x76073))),f818(x76072,x76071,x76073)),x76072)+P104(f334(f334(f250(a1),x76071),f2(a1))) % 169.39/169.66 [7689]P145(x76891,x76892,x76893)+~P104(f334(x76891,x76893))+P104(f334(f334(f249(a1),f2(a1)),f818(x76893,x76892,x76891)))+P104(f334(f334(f249(a1),f817(x76893,x76892,x76891)),f2(a1))) % 169.39/169.66 [7718]P146(x77181,x77182,x77183)+P104(f334(f334(f249(a1),f2(a1)),f805(x77183,x77182,x77181)))+~P104(f334(x77181,f2(a1)))+P104(f334(f334(f249(a1),f816(x77183,x77182,x77181)),f2(a1))) % 169.39/169.66 [7727]P145(x77273,x77271,x77272)+~P104(f334(x77273,x77272))+E(f334(f334(f81(a1),f334(f334(f82(a1),x77271),f819(x77272,x77271,x77273))),f818(x77272,x77271,x77273)),x77272)+P104(f334(f334(f250(a1),x77271),f2(a1))) % 169.39/169.66 [7734]P146(x77342,x77341,x77343)+E(x77341,f2(a1))+~P104(f334(x77342,f806(x77343,x77341,x77342)))+P104(f334(f334(f249(a1),f816(x77343,x77341,x77342)),f2(a1))) % 169.39/169.66 [7735]P145(x77352,x77351,x77353)+E(x77351,f2(a1))+~P104(f334(x77352,f818(x77353,x77351,x77352)))+P104(f334(f334(f249(a1),f817(x77353,x77351,x77352)),f2(a1))) % 169.39/169.66 [7740]P146(x77403,x77401,x77402)+E(f334(f334(f81(a1),f334(f334(f82(a1),x77401),f806(x77402,x77401,x77403))),f805(x77402,x77401,x77403)),x77402)+~P104(f334(x77403,f2(a1)))+P104(f334(f334(f250(a1),x77401),f2(a1))) % 169.39/169.66 [7796]P145(x77961,x77962,x77963)+~P104(f334(x77961,x77963))+~P104(f334(x77961,f818(x77963,x77962,x77961)))+P104(f334(f334(f249(a1),f817(x77963,x77962,x77961)),f2(a1))) % 169.39/169.66 [7800]P146(x78001,x78002,x78003)+~P104(f334(x78001,f806(x78003,x78002,x78001)))+~P104(f334(x78001,f2(a1)))+P104(f334(f334(f249(a1),f816(x78003,x78002,x78001)),f2(a1))) % 169.39/169.66 [7867]~P123(x78671)+~P104(f334(f334(f249(x78671),f334(f334(f82(x78671),x78673),x78672)),f2(x78671)))+P104(f334(f334(f249(x78671),x78672),f2(x78671)))+P104(f334(f334(f249(x78671),x78673),f2(x78671))) % 169.39/169.66 [7868]~P61(x78681)+~P104(f334(f334(f249(x78681),f334(f334(f292(x78681),x78683),x78682)),f2(x78681)))+P104(f334(f334(f249(x78681),x78682),f2(x78681)))+P104(f334(f334(f249(x78681),x78683),f2(x78681))) % 169.39/169.66 [7869]~P61(x78691)+~P104(f334(f334(f250(x78691),f334(f334(f292(x78691),x78693),x78692)),f2(x78691)))+P104(f334(f334(f250(x78691),x78692),f2(x78691)))+P104(f334(f334(f250(x78691),x78693),f2(x78691))) % 169.39/169.66 [7982]P146(x79823,x79821,x79822)+E(x79821,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x79821),f806(x79822,x79821,x79823))),f805(x79822,x79821,x79823)),x79822)+P104(f334(f334(f250(a1),x79821),f816(x79822,x79821,x79823))) % 169.39/169.66 [7983]P145(x79833,x79831,x79832)+E(x79831,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x79831),f819(x79832,x79831,x79833))),f818(x79832,x79831,x79833)),x79832)+P104(f334(f334(f250(a1),x79831),f817(x79832,x79831,x79833))) % 169.39/169.66 [7996]P146(x79963,x79961,x79962)+E(x79961,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x79961),f814(x79962,x79961,x79963))),f816(x79962,x79961,x79963)),x79962)+P104(f334(f334(f249(a1),f2(a1)),f805(x79962,x79961,x79963))) % 169.39/169.66 [7997]P145(x79973,x79971,x79972)+E(x79971,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x79971),f820(x79972,x79971,x79973))),f817(x79972,x79971,x79973)),x79972)+P104(f334(f334(f249(a1),f2(a1)),f818(x79972,x79971,x79973))) % 169.39/169.66 [8039]P145(x80393,x80391,x80392)+~P104(f334(x80393,x80392))+E(f334(f334(f81(a1),f334(f334(f82(a1),x80391),f819(x80392,x80391,x80393))),f818(x80392,x80391,x80393)),x80392)+P104(f334(f334(f250(a1),x80391),f817(x80392,x80391,x80393))) % 169.39/169.66 [8048]P146(x80483,x80481,x80482)+E(f334(f334(f81(a1),f334(f334(f82(a1),x80481),f806(x80482,x80481,x80483))),f805(x80482,x80481,x80483)),x80482)+P104(f334(f334(f250(a1),x80481),f816(x80482,x80481,x80483)))+~P104(f334(x80483,f2(a1))) % 169.39/169.66 [8054]P145(x80543,x80541,x80542)+~P104(f334(x80543,x80542))+E(f334(f334(f81(a1),f334(f334(f82(a1),x80541),f820(x80542,x80541,x80543))),f817(x80542,x80541,x80543)),x80542)+P104(f334(f334(f249(a1),f2(a1)),f818(x80542,x80541,x80543))) % 169.39/169.66 [8060]P146(x80603,x80601,x80602)+E(f334(f334(f81(a1),f334(f334(f82(a1),x80601),f814(x80602,x80601,x80603))),f816(x80602,x80601,x80603)),x80602)+P104(f334(f334(f249(a1),f2(a1)),f805(x80602,x80601,x80603)))+~P104(f334(x80603,f2(a1))) % 169.39/169.66 [8071]P146(x80713,x80711,x80712)+E(x80711,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x80711),f806(x80712,x80711,x80713))),f805(x80712,x80711,x80713)),x80712)+~P104(f334(x80713,f814(x80712,x80711,x80713))) % 169.39/169.66 [8072]P145(x80723,x80721,x80722)+E(x80721,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x80721),f819(x80722,x80721,x80723))),f818(x80722,x80721,x80723)),x80722)+~P104(f334(x80723,f817(x80722,x80721,x80723))) % 169.39/169.66 [8073]P146(x80733,x80731,x80732)+E(x80731,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x80731),f814(x80732,x80731,x80733))),f816(x80732,x80731,x80733)),x80732)+~P104(f334(x80733,f806(x80732,x80731,x80733))) % 169.39/169.66 [8074]P145(x80743,x80741,x80742)+E(x80741,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x80741),f820(x80742,x80741,x80743))),f817(x80742,x80741,x80743)),x80742)+~P104(f334(x80743,f818(x80742,x80741,x80743))) % 169.39/169.66 [8131]P145(x81313,x81311,x81312)+~P104(f334(x81313,x81312))+E(f334(f334(f81(a1),f334(f334(f82(a1),x81311),f819(x81312,x81311,x81313))),f818(x81312,x81311,x81313)),x81312)+~P104(f334(x81313,f817(x81312,x81311,x81313))) % 169.39/169.66 [8132]P145(x81323,x81321,x81322)+~P104(f334(x81323,x81322))+E(f334(f334(f81(a1),f334(f334(f82(a1),x81321),f820(x81322,x81321,x81323))),f817(x81322,x81321,x81323)),x81322)+~P104(f334(x81323,f818(x81322,x81321,x81323))) % 169.39/169.66 [8142]P146(x81423,x81421,x81422)+E(f334(f334(f81(a1),f334(f334(f82(a1),x81421),f806(x81422,x81421,x81423))),f805(x81422,x81421,x81423)),x81422)+~P104(f334(x81423,f814(x81422,x81421,x81423)))+~P104(f334(x81423,f2(a1))) % 169.39/169.66 [8143]P146(x81433,x81431,x81432)+E(f334(f334(f81(a1),f334(f334(f82(a1),x81431),f814(x81432,x81431,x81433))),f816(x81432,x81431,x81433)),x81432)+~P104(f334(x81433,f806(x81432,x81431,x81433)))+~P104(f334(x81433,f2(a1))) % 169.39/169.66 [8246]P146(x82463,x82461,x82462)+E(x82461,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x82461),f806(x82462,x82461,x82463))),f805(x82462,x82461,x82463)),x82462)+P104(f334(f334(f249(a1),f816(x82462,x82461,x82463)),f2(a1))) % 169.39/169.66 [8247]P145(x82473,x82471,x82472)+E(x82471,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x82471),f819(x82472,x82471,x82473))),f818(x82472,x82471,x82473)),x82472)+P104(f334(f334(f249(a1),f817(x82472,x82471,x82473)),f2(a1))) % 169.39/169.66 [8287]P145(x82873,x82871,x82872)+~P104(f334(x82873,x82872))+E(f334(f334(f81(a1),f334(f334(f82(a1),x82871),f819(x82872,x82871,x82873))),f818(x82872,x82871,x82873)),x82872)+P104(f334(f334(f249(a1),f817(x82872,x82871,x82873)),f2(a1))) % 169.39/169.66 [8292]P146(x82923,x82921,x82922)+E(f334(f334(f81(a1),f334(f334(f82(a1),x82921),f806(x82922,x82921,x82923))),f805(x82922,x82921,x82923)),x82922)+~P104(f334(x82923,f2(a1)))+P104(f334(f334(f249(a1),f816(x82922,x82921,x82923)),f2(a1))) % 169.39/169.66 [8419]P146(x84193,x84191,x84192)+E(x84191,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x84191),f814(x84192,x84191,x84193))),f816(x84192,x84191,x84193)),x84192)+E(f334(f334(f81(a1),f334(f334(f82(a1),x84191),f806(x84192,x84191,x84193))),f805(x84192,x84191,x84193)),x84192) % 169.39/169.66 [8420]P145(x84203,x84201,x84202)+E(x84201,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x84201),f820(x84202,x84201,x84203))),f817(x84202,x84201,x84203)),x84202)+E(f334(f334(f81(a1),f334(f334(f82(a1),x84201),f819(x84202,x84201,x84203))),f818(x84202,x84201,x84203)),x84202) % 169.39/169.66 [8441]P145(x84413,x84411,x84412)+~P104(f334(x84413,x84412))+E(f334(f334(f81(a1),f334(f334(f82(a1),x84411),f820(x84412,x84411,x84413))),f817(x84412,x84411,x84413)),x84412)+E(f334(f334(f81(a1),f334(f334(f82(a1),x84411),f819(x84412,x84411,x84413))),f818(x84412,x84411,x84413)),x84412) % 169.39/169.66 [8453]P146(x84533,x84531,x84532)+E(f334(f334(f81(a1),f334(f334(f82(a1),x84531),f814(x84532,x84531,x84533))),f816(x84532,x84531,x84533)),x84532)+E(f334(f334(f81(a1),f334(f334(f82(a1),x84531),f806(x84532,x84531,x84533))),f805(x84532,x84531,x84533)),x84532)+~P104(f334(x84533,f2(a1))) % 169.39/169.66 [9081]~P123(x90811)+~E(x90813,f2(x90811))+~E(x90812,f2(x90811))+P104(f334(f334(f249(x90811),f334(f334(f81(x90811),f334(f334(f82(x90811),x90812),x90812)),f334(f334(f82(x90811),x90813),x90813))),f2(x90811))) % 169.39/169.66 [10102]~P120(x101021)+~E(x101023,f2(x101021))+~E(x101022,f2(x101021))+P104(f334(f334(f249(x101021),f334(f334(f81(x101021),f334(f334(f259(x101021),x101022),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x101021),x101023),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))),f2(x101021))) % 169.39/169.66 [4851]~E(x48513,x48511)+~P117(x48512)+E(x48511,f2(x48512))+E(f334(f334(f292(x48512),x48513),x48511),f79(x48512)) % 169.39/169.66 [4904]~P97(x49041)+~E(x49043,f195(x49041))+~E(x49042,f195(x49041))+E(f334(f334(f113(x49041),x49042),x49043),f195(x49041)) % 169.39/169.66 [4905]~P96(x49051)+~E(x49053,f257(x49051))+~E(x49052,f257(x49051))+E(f334(f334(f104(x49051),x49052),x49053),f257(x49051)) % 169.39/169.66 [4993]~P117(x49933)+E(x49931,x49932)+E(x49932,f2(x49933))+~E(f334(f334(f292(x49933),x49931),x49932),f79(x49933)) % 169.39/169.66 [5012]~P129(x50122)+E(x50121,f2(x50122))+E(x50123,f2(x50122))+~E(f334(f334(f82(x50122),x50123),x50121),f2(x50122)) % 169.39/169.66 [5013]~P140(x50132)+E(x50131,f2(x50132))+E(x50133,f2(x50132))+~E(f334(f334(f82(x50132),x50133),x50131),f2(x50132)) % 169.39/169.66 [5397]~P110(x53973)+E(x53971,x53972)+E(x53971,f334(f80(x53973),x53972))+~E(f334(f334(f82(x53973),x53971),x53971),f334(f334(f82(x53973),x53972),x53972)) % 169.39/169.66 [5437]~P79(x54371)+E(f334(f80(x54371),x54372),x54373)+~E(f334(f334(f113(x54371),x54372),x54373),f257(x54371))+~E(f334(f334(f104(x54371),x54372),x54373),f195(x54371)) % 169.39/169.66 [5516]~P120(x55163)+E(x55161,x55162)+P104(f334(f334(f250(x55163),x55162),x55161))+P104(f334(f334(f250(x55163),x55161),x55162)) % 169.39/169.66 [5517]~P107(x55173)+E(x55171,x55172)+P104(f334(f334(f250(x55173),x55172),x55171))+P104(f334(f334(f250(x55173),x55171),x55172)) % 169.39/169.66 [5518]~E(x55182,x55183)+~P107(x55181)+P104(f334(f334(f250(x55181),x55182),x55183))+P104(f334(f334(f249(x55181),x55182),x55183)) % 169.39/169.66 [5773]~P108(x57733)+E(x57731,x57732)+~P104(f334(f334(f249(x57733),x57732),x57731))+P104(f334(f334(f250(x57733),x57732),x57731)) % 169.39/169.66 [5775]~P107(x57753)+E(x57751,x57752)+~P104(f334(f334(f249(x57753),x57751),x57752))+P104(f334(f334(f250(x57753),x57751),x57752)) % 169.39/169.66 [5781]~P108(x57813)+E(x57811,x57812)+~P104(f334(f334(f249(x57813),x57811),x57812))+P104(f334(f334(f250(x57813),x57811),x57812)) % 169.39/169.66 [5883]P145(x58831,x58832,x58833)+~P104(f334(x58831,x58833))+P104(f334(f334(f250(a1),x58832),f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x58832)) % 169.39/169.66 [5930]P146(x59301,x59302,x59303)+~P104(f334(x59301,f2(a1)))+P104(f334(f334(f250(a1),x59302),f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x59302)) % 169.39/169.66 [5934]~P95(x59341)+E(f334(f334(f113(x59341),x59342),f13(x59341,x59343)),x59342)+~P104(f334(f63(x59341),x59343))+~P104(f334(f334(f336(x59341),x59342),x59343)) % 169.39/169.66 [5935]~P95(x59351)+E(f334(f334(f104(x59351),x59352),f12(x59351,x59353)),x59352)+~P104(f334(f63(x59351),x59353))+~P104(f334(f334(f336(x59351),x59352),x59353)) % 169.39/169.66 [5971]~P95(x59711)+E(f334(f334(f113(x59711),x59712),f12(x59711,x59713)),f12(x59711,x59713))+~P104(f334(f63(x59711),x59713))+~P104(f334(f334(f336(x59711),x59712),x59713)) % 169.39/169.66 [5972]~P95(x59721)+E(f334(f334(f104(x59721),x59722),f13(x59721,x59723)),f13(x59721,x59723))+~P104(f334(f63(x59721),x59723))+~P104(f334(f334(f336(x59721),x59722),x59723)) % 169.39/169.66 [5973]~P107(x59731)+E(f334(f334(f247(x59731),x59732),f16(x59731,x59733)),f16(x59731,x59733))+~P104(f334(f63(x59731),x59733))+~P104(f334(f334(f336(x59731),x59732),x59733)) % 169.39/169.66 [5974]~P107(x59741)+E(f334(f334(f248(x59741),x59742),f17(x59741,x59743)),f17(x59741,x59743))+~P104(f334(f63(x59741),x59743))+~P104(f334(f334(f336(x59741),x59742),x59743)) % 169.39/169.66 [6015]E(x60151,x60152)+~P108(x60153)+~P104(f334(f334(f249(x60153),x60152),x60151))+~P104(f334(f334(f249(x60153),x60151),x60152)) % 169.39/169.66 [6156]~P105(x61561)+P104(f334(f334(f250(x61561),x61563),x61562))+~P104(f334(f334(f249(x61561),x61563),x61562))+P104(f334(f334(f249(x61561),x61562),x61563)) % 169.39/169.66 [6177]~P107(x61771)+~P104(f334(f63(x61771),x61773))+P104(f334(f334(f249(x61771),x61772),f17(x61771,x61773)))+~P104(f334(f334(f336(x61771),x61772),x61773)) % 169.39/169.66 [6231]~P107(x62311)+E(f334(f334(f247(x62311),x62312),f15(x62311,f248(x62311),x62313)),x62312)+~P104(f334(f63(x62311),x62313))+~P104(f334(f334(f336(x62311),x62312),x62313)) % 169.39/169.66 [6232]~P107(x62321)+E(f334(f334(f248(x62321),x62322),f14(x62321,f247(x62321),x62323)),x62322)+~P104(f334(f63(x62321),x62323))+~P104(f334(f334(f336(x62321),x62322),x62323)) % 169.39/169.66 [6369]E(x63691,x63692)+~E(f334(f334(f3(a877),x63691),x63693),f334(f334(f3(a877),x63692),x63693))+~P104(f334(f334(f249(a877),x63693),x63691))+~P104(f334(f334(f249(a877),x63693),x63692)) % 169.39/169.66 [6398]~P107(x63981)+~P104(f334(f63(x63981),x63982))+~P104(f334(f334(f336(x63981),x63983),x63982))+P104(f334(f334(f249(x63981),f16(x63981,x63982)),x63983)) % 169.39/169.66 [6461]P146(x64612,x64611,x64613)+E(x64611,f2(a1))+P104(f334(f334(f250(a1),x64611),f816(x64613,x64611,x64612)))+P104(f334(f334(f250(a1),f2(a1)),x64611)) % 169.39/169.66 [6462]P145(x64622,x64621,x64623)+E(x64621,f2(a1))+P104(f334(f334(f250(a1),x64621),f817(x64623,x64621,x64622)))+P104(f334(f334(f250(a1),f2(a1)),x64621)) % 169.39/169.66 [6463]~P107(x64631)+E(f334(f334(f247(x64631),x64632),f14(x64631,f247(x64631),x64633)),f14(x64631,f247(x64631),x64633))+~P104(f334(f63(x64631),x64633))+~P104(f334(f334(f336(x64631),x64632),x64633)) % 169.39/169.66 [6464]~P107(x64641)+E(f334(f334(f248(x64641),x64642),f15(x64641,f248(x64641),x64643)),f15(x64641,f248(x64641),x64643))+~P104(f334(f63(x64641),x64643))+~P104(f334(f334(f336(x64641),x64642),x64643)) % 169.39/169.66 [6470]~P104(f334(x64701,x64702))+P104(f334(x64701,f356(x64702,x64701,x64703)))+P104(f334(x64701,f2(a877)))+~P104(f334(f334(f250(a877),x64702),x64703)) % 169.39/169.66 [6525]~P104(f334(x65251,x65252))+~P104(f334(f63(x65253),x65252))+P104(f334(x65251,f462(x65251,x65252,x65253)))+P104(f334(x65251,f195(f886(x65253,a871)))) % 169.39/169.66 [6538]~P120(x65381)+~P92(x65381)+P104(f334(f334(f249(x65381),f334(f106(x65381),x65382)),f334(f106(x65381),x65383)))+~P104(f334(f334(f249(a1),x65382),x65383)) % 169.39/169.66 [6539]~P120(x65391)+~P92(x65391)+P104(f334(f334(f250(x65391),f334(f106(x65391),x65392)),f334(f106(x65391),x65393)))+~P104(f334(f334(f250(a1),x65392),x65393)) % 169.39/169.66 [6542]~P104(f334(x65421,x65423))+~P104(f334(f63(x65422),x65423))+P104(f334(f63(x65422),f462(x65421,x65423,x65422)))+P104(f334(x65421,f195(f886(x65422,a871)))) % 169.39/169.66 [6575]P145(x65751,x65752,x65753)+~P104(f334(x65751,x65753))+P104(f334(f334(f250(a1),x65752),f817(x65753,x65752,x65751)))+P104(f334(f334(f250(a1),f2(a1)),x65752)) % 169.39/169.66 [6609]P146(x66091,x66092,x66093)+P104(f334(f334(f250(a1),x66092),f816(x66093,x66092,x66091)))+~P104(f334(x66091,f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x66092)) % 169.39/169.66 [6640]~P106(x66401)+~P90(x66401)+E(f334(f334(f247(x66401),f334(f106(x66401),x66402)),f334(f106(x66401),x66403)),f334(f106(x66401),x66403))+P104(f334(f334(f249(x66401),f334(f106(x66401),x66402)),f334(f106(x66401),x66403))) % 169.39/169.66 [6641]~P106(x66411)+~P90(x66411)+E(f334(f334(f248(x66411),f334(f106(x66411),x66412)),f334(f106(x66411),x66413)),f334(f106(x66411),x66412))+P104(f334(f334(f249(x66411),f334(f106(x66411),x66412)),f334(f106(x66411),x66413))) % 169.39/169.66 [6698]P146(x66982,x66981,x66983)+E(x66981,f2(a1))+~P104(f334(x66982,f814(x66983,x66981,x66982)))+P104(f334(f334(f250(a1),f2(a1)),x66981)) % 169.39/169.66 [6699]P145(x66992,x66991,x66993)+E(x66991,f2(a1))+~P104(f334(x66992,f817(x66993,x66991,x66992)))+P104(f334(f334(f250(a1),f2(a1)),x66991)) % 169.39/169.66 [6703]P104(f334(x67031,x67032))+~P104(f334(f63(x67033),x67032))+P104(f334(x67031,f548(x67031,x67032,x67033)))+~P104(f334(x67031,f195(f886(x67033,a871)))) % 169.39/169.66 [6722]P104(f334(x67221,x67222))+P104(f334(f63(x67223),f548(x67221,x67222,x67223)))+~P104(f334(f63(x67223),x67222))+~P104(f334(x67221,f195(f886(x67223,a871)))) % 169.39/169.66 [6787]P145(x67871,x67872,x67873)+~P104(f334(x67871,x67873))+~P104(f334(x67871,f817(x67873,x67872,x67871)))+P104(f334(f334(f250(a1),f2(a1)),x67872)) % 169.39/169.66 [6817]P146(x68171,x68172,x68173)+~P104(f334(x68171,f814(x68173,x68172,x68171)))+~P104(f334(x68171,f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x68172)) % 169.39/169.66 [6925]~P92(x69253)+~P120(x69253)+~P104(f334(f334(f249(x69253),f334(f106(x69253),x69251)),f334(f106(x69253),x69252)))+P104(f334(f334(f249(a1),x69251),x69252)) % 169.39/169.66 [6926]~P92(x69263)+~P120(x69263)+~P104(f334(f334(f250(x69263),f334(f106(x69263),x69261)),f334(f106(x69263),x69262)))+P104(f334(f334(f250(a1),x69261),x69262)) % 169.39/169.66 [6953]~P107(x69531)+~P30(x69531,x69533)+P30(x69531,f334(f334(f151(x69531),x69532),x69533))+~P104(f334(f334(f249(x69531),x69532),f638(x69533,x69532,x69531))) % 169.39/169.66 [6954]~P107(x69541)+~P30(x69541,x69543)+P30(x69541,f334(f334(f151(x69541),x69542),x69543))+~P104(f334(f334(f249(x69541),x69542),f639(x69543,x69542,x69541))) % 169.39/169.66 [6955]~P107(x69551)+~P30(x69551,x69553)+P30(x69551,f334(f334(f151(x69551),x69552),x69553))+~P104(f334(f334(f249(x69551),x69552),f736(x69552,x69553,x69551))) % 169.39/169.66 [7039]P146(x70392,x70391,x70393)+E(x70391,f2(a1))+P104(f334(f334(f250(a1),x70391),f2(a1)))+P104(f334(f334(f250(a1),f805(x70393,x70391,x70392)),x70391)) % 169.39/169.66 [7040]P145(x70402,x70401,x70403)+E(x70401,f2(a1))+P104(f334(f334(f250(a1),x70401),f2(a1)))+P104(f334(f334(f250(a1),f818(x70403,x70401,x70402)),x70401)) % 169.39/169.66 [7079]P146(x70792,x70791,x70793)+E(x70791,f2(a1))+P104(f334(f334(f249(a1),f816(x70793,x70791,x70792)),f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x70791)) % 169.39/169.66 [7080]P145(x70802,x70801,x70803)+E(x70801,f2(a1))+P104(f334(f334(f249(a1),f817(x70803,x70801,x70802)),f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x70801)) % 169.39/169.66 [7102]~P107(x71021)+~P30(x71021,x71023)+E(f334(f334(f148(x71021,x71021,f7(x71021)),x71022),f171(x71021,x71022,x71023)),x71023)+~P104(f334(f334(f336(x71021),x71022),f334(f173(x71021),x71023))) % 169.39/169.66 [7149]P145(x71491,x71492,x71493)+~P104(f334(x71491,x71493))+P104(f334(f334(f250(a1),x71492),f2(a1)))+P104(f334(f334(f250(a1),f818(x71493,x71492,x71491)),x71492)) % 169.39/169.66 [7155]~P106(x71551)+~P90(x71551)+E(f334(f334(f247(x71551),f334(f106(x71551),x71552)),f334(f106(x71551),x71553)),f334(f106(x71551),x71552))+~P104(f334(f334(f249(x71551),f334(f106(x71551),x71552)),f334(f106(x71551),x71553))) % 169.39/169.66 [7156]~P106(x71561)+~P90(x71561)+E(f334(f334(f248(x71561),f334(f106(x71561),x71562)),f334(f106(x71561),x71563)),f334(f106(x71561),x71563))+~P104(f334(f334(f249(x71561),f334(f106(x71561),x71562)),f334(f106(x71561),x71563))) % 169.39/169.66 [7170]P146(x71701,x71702,x71703)+~P104(f334(x71701,f2(a1)))+P104(f334(f334(f250(a1),x71702),f2(a1)))+P104(f334(f334(f250(a1),f805(x71703,x71702,x71701)),x71702)) % 169.39/169.66 [7178]P145(x71781,x71782,x71783)+~P104(f334(x71781,x71783))+P104(f334(f334(f249(a1),f817(x71783,x71782,x71781)),f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x71782)) % 169.39/169.66 [7202]P146(x72021,x72022,x72023)+~P104(f334(x72021,f2(a1)))+P104(f334(f334(f249(a1),f816(x72023,x72022,x72021)),f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x72022)) % 169.39/169.66 [7230]~P104(f334(x72301,x72302))+P104(f334(x72301,f2(a877)))+~P104(f334(f334(f250(a877),x72302),x72303))+P104(f334(f334(f250(a877),f356(x72302,x72301,x72303)),x72303)) % 169.39/169.66 [7247]~P107(x72471)+~P30(x72471,x72473)+P30(x72471,f334(f334(f151(x72471),x72472),x72473))+P104(f334(f334(f336(x72471),f638(x72473,x72472,x72471)),f334(f173(x72471),x72473))) % 169.39/169.66 [7248]~P107(x72481)+~P30(x72481,x72483)+P30(x72481,f334(f334(f151(x72481),x72482),x72483))+P104(f334(f334(f336(x72481),f639(x72483,x72482,x72481)),f334(f173(x72481),x72483))) % 169.39/169.66 [7249]~P107(x72491)+~P30(x72491,x72493)+P30(x72491,f334(f334(f151(x72491),x72492),x72493))+P104(f334(f334(f336(x72491),f736(x72492,x72493,x72491)),f334(f173(x72491),x72493))) % 169.39/169.66 [7356]~P107(x73561)+~P28(x73561)+~P104(f334(f334(f250(x73561),x73563),f41(x73561,x73562)))+P104(f334(f334(f336(x73561),f415(x73562,x73563,x73561)),x73562)) % 169.39/169.66 [7519]~P107(x75191)+~P28(x75191)+~P104(f334(f334(f250(x75191),f42(x75191,x75193)),x75192))+P104(f334(f334(f336(x75191),f447(x75192,x75193,x75191)),x75193)) % 169.39/169.66 [7520]~P107(x75201)+~P28(x75201)+~P104(f334(f334(f250(x75201),f42(x75201,x75203)),x75202))+P104(f334(f334(f250(x75201),f447(x75202,x75203,x75201)),x75202)) % 169.39/169.66 [7535]P146(x75352,x75351,x75353)+E(x75351,f2(a1))+P104(f334(f334(f250(a1),x75351),f816(x75353,x75351,x75352)))+P104(f334(f334(f250(a1),f805(x75353,x75351,x75352)),x75351)) % 169.39/169.66 [7536]P145(x75362,x75361,x75363)+E(x75361,f2(a1))+P104(f334(f334(f250(a1),x75361),f817(x75363,x75361,x75362)))+P104(f334(f334(f250(a1),f818(x75363,x75361,x75362)),x75361)) % 169.39/169.66 [7627]P146(x76273,x76271,x76272)+E(x76271,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x76271),f814(x76272,x76271,x76273))),f816(x76272,x76271,x76273)),x76272)+P104(f334(f334(f250(a1),f2(a1)),x76271)) % 169.39/169.66 [7628]P145(x76283,x76281,x76282)+E(x76281,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x76281),f820(x76282,x76281,x76283))),f817(x76282,x76281,x76283)),x76282)+P104(f334(f334(f250(a1),f2(a1)),x76281)) % 169.39/169.66 [7631]~P132(x76311)+~P104(f334(f334(f249(x76311),x76313),f2(x76311)))+P104(f334(f334(f249(x76311),f334(f334(f82(x76311),x76312),x76313)),f2(x76311)))+~P104(f334(f334(f249(x76311),f2(x76311)),x76312)) % 169.39/169.66 [7633]~P132(x76331)+~P104(f334(f334(f249(x76331),x76332),f2(x76331)))+P104(f334(f334(f249(x76331),f334(f334(f82(x76331),x76332),x76333)),f2(x76331)))+~P104(f334(f334(f249(x76331),f2(x76331)),x76333)) % 169.39/169.66 [7634]~P123(x76341)+~P104(f334(f334(f249(x76341),x76343),f2(x76341)))+P104(f334(f334(f249(x76341),f334(f334(f82(x76341),x76342),x76343)),f2(x76341)))+~P104(f334(f334(f249(x76341),f2(x76341)),x76342)) % 169.39/169.66 [7635]~P123(x76351)+~P104(f334(f334(f249(x76351),x76352),f2(x76351)))+P104(f334(f334(f249(x76351),f334(f334(f82(x76351),x76352),x76353)),f2(x76351)))+~P104(f334(f334(f249(x76351),f2(x76351)),x76353)) % 169.39/169.66 [7636]~P61(x76361)+~P104(f334(f334(f249(x76361),x76363),f2(x76361)))+P104(f334(f334(f249(x76361),f334(f334(f292(x76361),x76362),x76363)),f2(x76361)))+~P104(f334(f334(f249(x76361),f2(x76361)),x76362)) % 169.39/169.66 [7637]~P61(x76371)+~P104(f334(f334(f249(x76371),x76372),f2(x76371)))+P104(f334(f334(f249(x76371),f334(f334(f292(x76371),x76372),x76373)),f2(x76371)))+~P104(f334(f334(f249(x76371),f2(x76371)),x76373)) % 169.39/169.66 [7638]~P62(x76381)+~P104(f334(f334(f249(x76381),x76382),f2(x76381)))+P104(f334(f334(f249(x76381),f334(f334(f292(x76381),x76382),x76383)),f2(x76381)))+~P104(f334(f334(f250(x76381),f2(x76381)),x76383)) % 169.39/169.66 [7639]~P62(x76391)+~P104(f334(f334(f250(x76391),x76393),f2(x76391)))+P104(f334(f334(f249(x76391),f334(f334(f292(x76391),x76392),x76393)),f2(x76391)))+~P104(f334(f334(f249(x76391),f2(x76391)),x76392)) % 169.39/169.66 [7641]~P131(x76411)+~P104(f334(f334(f250(x76411),x76413),f2(x76411)))+P104(f334(f334(f250(x76411),f334(f334(f82(x76411),x76412),x76413)),f2(x76411)))+~P104(f334(f334(f250(x76411),f2(x76411)),x76412)) % 169.39/169.66 [7642]~P131(x76421)+~P104(f334(f334(f250(x76421),x76422),f2(x76421)))+P104(f334(f334(f250(x76421),f334(f334(f82(x76421),x76422),x76423)),f2(x76421)))+~P104(f334(f334(f250(x76421),f2(x76421)),x76423)) % 169.39/169.66 [7643]~P61(x76431)+~P104(f334(f334(f250(x76431),x76433),f2(x76431)))+P104(f334(f334(f250(x76431),f334(f334(f292(x76431),x76432),x76433)),f2(x76431)))+~P104(f334(f334(f250(x76431),f2(x76431)),x76432)) % 169.39/169.66 [7644]~P61(x76441)+~P104(f334(f334(f250(x76441),x76442),f2(x76441)))+P104(f334(f334(f250(x76441),f334(f334(f292(x76441),x76442),x76443)),f2(x76441)))+~P104(f334(f334(f250(x76441),f2(x76441)),x76443)) % 169.39/169.66 [7645]~P62(x76451)+~P104(f334(f334(f250(x76451),x76453),f2(x76451)))+P104(f334(f334(f250(x76451),f334(f334(f292(x76451),x76452),x76453)),f2(x76451)))+~P104(f334(f334(f250(x76451),f2(x76451)),x76452)) % 169.39/169.66 [7646]~P62(x76461)+~P104(f334(f334(f250(x76461),x76462),f2(x76461)))+P104(f334(f334(f250(x76461),f334(f334(f292(x76461),x76462),x76463)),f2(x76461)))+~P104(f334(f334(f250(x76461),f2(x76461)),x76463)) % 169.39/169.66 [7661]P145(x76611,x76612,x76613)+~P104(f334(x76611,x76613))+P104(f334(f334(f250(a1),x76612),f817(x76613,x76612,x76611)))+P104(f334(f334(f250(a1),f818(x76613,x76612,x76611)),x76612)) % 169.39/169.66 [7674]P146(x76741,x76742,x76743)+P104(f334(f334(f250(a1),x76742),f816(x76743,x76742,x76741)))+~P104(f334(x76741,f2(a1)))+P104(f334(f334(f250(a1),f805(x76743,x76742,x76741)),x76742)) % 169.39/169.66 [7725]P146(x77252,x77251,x77253)+E(x77251,f2(a1))+~P104(f334(x77252,f814(x77253,x77251,x77252)))+P104(f334(f334(f250(a1),f805(x77253,x77251,x77252)),x77251)) % 169.39/169.66 [7726]P145(x77262,x77261,x77263)+E(x77261,f2(a1))+~P104(f334(x77262,f817(x77263,x77261,x77262)))+P104(f334(f334(f250(a1),f818(x77263,x77261,x77262)),x77261)) % 169.39/169.66 [7737]P145(x77373,x77371,x77372)+~P104(f334(x77373,x77372))+E(f334(f334(f81(a1),f334(f334(f82(a1),x77371),f820(x77372,x77371,x77373))),f817(x77372,x77371,x77373)),x77372)+P104(f334(f334(f250(a1),f2(a1)),x77371)) % 169.39/169.66 [7754]P146(x77543,x77541,x77542)+E(f334(f334(f81(a1),f334(f334(f82(a1),x77541),f814(x77542,x77541,x77543))),f816(x77542,x77541,x77543)),x77542)+~P104(f334(x77543,f2(a1)))+P104(f334(f334(f250(a1),f2(a1)),x77541)) % 169.39/169.66 [7780]~P104(f334(x77801,x77803))+~P104(f334(f63(x77802),x77803))+P104(f334(f334(f336(x77802),f466(x77801,x77803,x77802)),f462(x77801,x77803,x77802)))+P104(f334(x77801,f195(f886(x77802,a871)))) % 169.39/169.66 [7791]P145(x77911,x77912,x77913)+~P104(f334(x77911,x77913))+~P104(f334(x77911,f817(x77913,x77912,x77911)))+P104(f334(f334(f250(a1),f818(x77913,x77912,x77911)),x77912)) % 169.39/169.66 [7797]P146(x77971,x77972,x77973)+~P104(f334(x77971,f814(x77973,x77972,x77971)))+~P104(f334(x77971,f2(a1)))+P104(f334(f334(f250(a1),f805(x77973,x77972,x77971)),x77972)) % 169.39/169.66 [7898]~P123(x78981)+~P104(f334(f334(f249(x78981),f334(f334(f82(x78981),x78983),x78982)),f2(x78981)))+P104(f334(f334(f249(x78981),x78982),f2(x78981)))+P104(f334(f334(f249(x78981),f2(x78981)),x78982)) % 169.39/169.66 [7899]~P123(x78991)+~P104(f334(f334(f249(x78991),f334(f334(f82(x78991),x78992),x78993)),f2(x78991)))+P104(f334(f334(f249(x78991),x78992),f2(x78991)))+P104(f334(f334(f249(x78991),f2(x78991)),x78992)) % 169.39/169.66 [7900]~P61(x79001)+~P104(f334(f334(f249(x79001),f334(f334(f292(x79001),x79003),x79002)),f2(x79001)))+P104(f334(f334(f249(x79001),x79002),f2(x79001)))+P104(f334(f334(f249(x79001),f2(x79001)),x79002)) % 169.39/169.66 [7901]~P61(x79011)+~P104(f334(f334(f249(x79011),f334(f334(f292(x79011),x79012),x79013)),f2(x79011)))+P104(f334(f334(f249(x79011),x79012),f2(x79011)))+P104(f334(f334(f249(x79011),f2(x79011)),x79012)) % 169.39/169.66 [7902]~P61(x79021)+~P104(f334(f334(f250(x79021),f334(f334(f292(x79021),x79023),x79022)),f2(x79021)))+P104(f334(f334(f250(x79021),x79022),f2(x79021)))+P104(f334(f334(f250(x79021),f2(x79021)),x79022)) % 169.39/169.66 [7903]~P61(x79031)+~P104(f334(f334(f250(x79031),f334(f334(f292(x79031),x79032),x79033)),f2(x79031)))+P104(f334(f334(f250(x79031),x79032),f2(x79031)))+P104(f334(f334(f250(x79031),f2(x79031)),x79032)) % 169.39/169.66 [7926]~P123(x79261)+~P104(f334(f334(f249(x79261),f334(f334(f82(x79261),x79262),x79263)),f2(x79261)))+P104(f334(f334(f249(x79261),f2(x79261)),x79262))+P104(f334(f334(f249(x79261),f2(x79261)),x79263)) % 169.39/169.66 [7927]~P61(x79271)+~P104(f334(f334(f249(x79271),f334(f334(f292(x79271),x79272),x79273)),f2(x79271)))+P104(f334(f334(f249(x79271),f2(x79271)),x79272))+P104(f334(f334(f249(x79271),f2(x79271)),x79273)) % 169.39/169.66 [7928]~P61(x79281)+~P104(f334(f334(f250(x79281),f334(f334(f292(x79281),x79282),x79283)),f2(x79281)))+P104(f334(f334(f250(x79281),f2(x79281)),x79282))+P104(f334(f334(f250(x79281),f2(x79281)),x79283)) % 169.39/169.66 [7949]P146(x79492,x79491,x79493)+E(x79491,f2(a1))+P104(f334(f334(f249(a1),f816(x79493,x79491,x79492)),f2(a1)))+P104(f334(f334(f250(a1),f805(x79493,x79491,x79492)),x79491)) % 169.39/169.66 [7950]P145(x79502,x79501,x79503)+E(x79501,f2(a1))+P104(f334(f334(f249(a1),f817(x79503,x79501,x79502)),f2(a1)))+P104(f334(f334(f250(a1),f818(x79503,x79501,x79502)),x79501)) % 169.39/169.66 [7957]~P119(x79571)+~P104(f334(f334(f250(x79571),x79572),f79(x79571)))+P104(f334(f334(f250(x79571),f334(f334(f259(x79571),x79572),f334(a115,x79573))),f79(x79571)))+~P104(f334(f334(f250(x79571),f2(x79571)),x79572)) % 169.39/169.66 [8013]~P107(x80131)+~E(x80133,f116(x80131))+~P30(x80131,f334(f169(x80131),x80133))+E(f334(f142(x80131,x80131,f334(f9(x80131,x80131,x80131),f248(x80131)),x80132),f334(f169(x80131),x80133)),x80132) % 169.39/169.66 [8016]P145(x80161,x80162,x80163)+~P104(f334(x80161,x80163))+P104(f334(f334(f249(a1),f817(x80163,x80162,x80161)),f2(a1)))+P104(f334(f334(f250(a1),f818(x80163,x80162,x80161)),x80162)) % 169.39/169.66 [8023]P146(x80231,x80232,x80233)+~P104(f334(x80231,f2(a1)))+P104(f334(f334(f249(a1),f816(x80233,x80232,x80231)),f2(a1)))+P104(f334(f334(f250(a1),f805(x80233,x80232,x80231)),x80232)) % 169.39/169.66 [8241]P146(x82413,x82411,x82412)+E(x82411,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x82411),f814(x82412,x82411,x82413))),f816(x82412,x82411,x82413)),x82412)+P104(f334(f334(f250(a1),f805(x82412,x82411,x82413)),x82411)) % 169.39/169.66 [8242]P145(x82423,x82421,x82422)+E(x82421,f2(a1))+E(f334(f334(f81(a1),f334(f334(f82(a1),x82421),f820(x82422,x82421,x82423))),f817(x82422,x82421,x82423)),x82422)+P104(f334(f334(f250(a1),f818(x82422,x82421,x82423)),x82421)) % 169.39/169.66 [8278]P145(x82783,x82781,x82782)+~P104(f334(x82783,x82782))+E(f334(f334(f81(a1),f334(f334(f82(a1),x82781),f820(x82782,x82781,x82783))),f817(x82782,x82781,x82783)),x82782)+P104(f334(f334(f250(a1),f818(x82782,x82781,x82783)),x82781)) % 169.39/169.66 [8279]~P68(x82791)+~P72(x82791)+~P41(x82793)+E(f334(f334(f8(a877,x82791),f334(f334(f10(a1,x82791,a877),x82792),f103(a1))),f334(f313(a1,a877,a107),x82793)),f334(f334(f8(a1,x82791),x82792),x82793)) % 169.39/169.66 [8280]~P68(x82801)+~P72(x82801)+~P41(x82803)+E(f334(f334(f11(a877,x82801),f334(f334(f10(a1,x82801,a877),x82802),f103(a1))),f334(f313(a1,a877,a107),x82803)),f334(f334(f11(a1,x82801),x82802),x82803)) % 169.39/169.66 [8289]P146(x82893,x82891,x82892)+E(f334(f334(f81(a1),f334(f334(f82(a1),x82891),f814(x82892,x82891,x82893))),f816(x82892,x82891,x82893)),x82892)+~P104(f334(x82893,f2(a1)))+P104(f334(f334(f250(a1),f805(x82892,x82891,x82893)),x82891)) % 169.39/169.66 [8308]~E(x83082,f2(a877))+~E(f334(f268(a877,a877),x83083),f2(a877))+~E(x83081,f334(f334(f81(a877),f334(f334(f82(a877),f334(f268(a877,a877),x83083)),x83082)),f334(f272(a877,a877),x83083)))+P104(f334(f49(x83081,x83082),x83083)) % 169.39/169.66 [8360]P104(f334(x83601,x83602))+~P104(f334(f334(f336(x83603),f524(x83601,x83602,x83603)),f548(x83601,x83602,x83603)))+~P104(f334(f63(x83603),x83602))+~P104(f334(x83601,f195(f886(x83603,a871)))) % 169.39/169.66 [8958]P104(f334(x89581,x89582))+~P104(f334(f63(x89583),x89582))+~P104(f334(x89581,f334(f334(f312(x89583),f524(x89581,x89582,x89583)),f548(x89581,x89582,x89583))))+~P104(f334(x89581,f195(f886(x89583,a871)))) % 169.39/169.66 [9183]P104(f334(f334(f249(a1),x91831),f2(a1)))+~P104(f334(f334(f250(a1),f334(f334(f81(a1),f334(f334(f82(a1),x91833),x91831)),x91832)),f2(a1)))+~P104(f334(f334(f249(a1),f2(a1)),x91832))+~P104(f334(f334(f250(a1),f2(a1)),x91833)) % 169.39/169.66 [5844]~P95(x58442)+E(x58441,f195(f886(x58442,a871)))+~P104(f334(f63(x58442),x58441))+E(f12(x58442,f334(f334(f312(x58442),x58443),x58441)),f334(f334(f113(x58442),x58443),f12(x58442,x58441))) % 169.39/169.66 [5845]~P95(x58452)+E(x58451,f195(f886(x58452,a871)))+~P104(f334(f63(x58452),x58451))+E(f13(x58452,f334(f334(f312(x58452),x58453),x58451)),f334(f334(f104(x58452),x58453),f13(x58452,x58451))) % 169.39/169.66 [5846]~P107(x58462)+E(x58461,f195(f886(x58462,a871)))+~P104(f334(f63(x58462),x58461))+E(f16(x58462,f334(f334(f312(x58462),x58463),x58461)),f334(f334(f247(x58462),x58463),f16(x58462,x58461))) % 169.39/169.66 [5847]~P107(x58472)+E(x58471,f195(f886(x58472,a871)))+~P104(f334(f63(x58472),x58471))+E(f17(x58472,f334(f334(f312(x58472),x58473),x58471)),f334(f334(f248(x58472),x58473),f17(x58472,x58471))) % 169.39/169.66 [6153]~P123(x61531)+~E(x61533,f2(x61531))+~E(x61532,f2(x61531))+E(f334(f334(f81(x61531),f334(f334(f82(x61531),x61532),x61532)),f334(f334(f82(x61531),x61533),x61533)),f2(x61531)) % 169.39/169.66 [6224]~P93(x62242)+E(x62241,f195(f886(x62242,a871)))+~P104(f334(f63(x62242),x62241))+E(f334(f65(x62242,f82(x62242)),f334(f334(f312(x62242),x62243),x62241)),f334(f334(f82(x62242),x62243),f334(f65(x62242,f82(x62242)),x62241))) % 169.39/169.66 [6348]~P107(x63482)+E(x63481,f195(f886(x63482,a871)))+~P104(f334(f63(x63482),x63481))+E(f14(x63482,f247(x63482),f334(f334(f312(x63482),x63483),x63481)),f334(f334(f247(x63482),x63483),f14(x63482,f247(x63482),x63481))) % 169.39/169.66 [6349]~P107(x63492)+E(x63491,f195(f886(x63492,a871)))+~P104(f334(f63(x63492),x63491))+E(f15(x63492,f248(x63492),f334(f334(f312(x63492),x63493),x63491)),f334(f334(f248(x63492),x63493),f15(x63492,f248(x63492),x63491))) % 169.39/169.66 [6852]~P65(x68521)+~P104(f334(f63(x68521),x68523))+E(f334(f65(x68521,f82(x68521)),f334(f334(f312(x68521),x68522),x68523)),f334(f334(f66(x68521,x68521,f82(x68521)),x68522),x68523))+P104(f334(f334(f336(x68521),x68522),x68523)) % 169.39/169.66 [6933]~E(f334(f334(f81(a1),x69332),f334(f334(f82(a1),x69333),x69331)),x69333)+~P104(f334(f334(f250(a1),f2(a1)),x69333))+P104(f334(f334(f249(a1),f79(a1)),x69331))+~P104(f334(f334(f250(a1),x69332),x69333)) % 169.39/169.66 [6960]~E(f334(f334(f81(a1),x69602),f334(f334(f82(a1),x69603),x69601)),x69603)+P104(f334(f334(f249(a1),x69601),f79(a1)))+~P104(f334(f334(f249(a1),f2(a1)),x69602))+~P104(f334(f334(f250(a1),f2(a1)),x69603)) % 169.39/169.66 [6976]E(x69761,f2(a877))+~P104(f334(f49(x69763,x69761),x69762))+~P104(f334(f334(f250(a877),f2(a877)),x69761))+P104(f334(f334(f250(a877),f334(f272(a877,a877),x69762)),x69761)) % 169.39/169.66 [7006]~P135(x70061)+~P104(f334(f334(f249(x70061),x70062),f2(x70061)))+~P104(f334(f334(f249(x70061),x70063),f2(x70061)))+E(f334(f334(f82(x70061),f334(f76(x70061),x70062)),f334(f76(x70061),x70063)),f334(f76(x70061),f334(f334(f82(x70061),x70062),x70063))) % 169.39/169.66 [7056]~P135(x70561)+~P104(f334(f334(f249(x70561),x70562),f2(x70561)))+E(f334(f334(f82(x70561),f334(f76(x70561),x70562)),f334(f76(x70561),x70563)),f334(f76(x70561),f334(f334(f82(x70561),x70562),x70563)))+~P104(f334(f334(f249(x70561),f2(x70561)),x70563)) % 169.39/169.66 [7057]~P135(x70571)+~P104(f334(f334(f249(x70571),x70573),f2(x70571)))+E(f334(f334(f82(x70571),f334(f76(x70571),x70572)),f334(f76(x70571),x70573)),f334(f76(x70571),f334(f334(f82(x70571),x70572),x70573)))+~P104(f334(f334(f249(x70571),f2(x70571)),x70572)) % 169.39/169.66 [7111]~P135(x71111)+E(f334(f334(f82(x71111),f334(f76(x71111),x71112)),f334(f76(x71111),x71113)),f334(f76(x71111),f334(f334(f82(x71111),x71112),x71113)))+~P104(f334(f334(f249(x71111),f2(x71111)),x71112))+~P104(f334(f334(f249(x71111),f2(x71111)),x71113)) % 169.39/169.66 [7128]~P125(x71281)+~P104(f334(f334(f249(x71281),x71283),f2(x71281)))+~P104(f334(f334(f249(x71281),x71282),f2(x71281)))+P104(f334(f334(f249(x71281),f2(x71281)),f334(f334(f82(x71281),x71282),x71283))) % 169.39/169.66 [7129]~P123(x71291)+~P104(f334(f334(f249(x71291),x71293),f2(x71291)))+~P104(f334(f334(f249(x71291),x71292),f2(x71291)))+P104(f334(f334(f249(x71291),f2(x71291)),f334(f334(f82(x71291),x71292),x71293))) % 169.39/169.66 [7130]~P61(x71301)+~P104(f334(f334(f249(x71301),x71303),f2(x71301)))+~P104(f334(f334(f249(x71301),x71302),f2(x71301)))+P104(f334(f334(f249(x71301),f2(x71301)),f334(f334(f292(x71301),x71302),x71303))) % 169.39/169.66 [7131]~P62(x71311)+~P104(f334(f334(f250(x71311),x71313),f2(x71311)))+~P104(f334(f334(f249(x71311),x71312),f2(x71311)))+P104(f334(f334(f249(x71311),f2(x71311)),f334(f334(f292(x71311),x71312),x71313))) % 169.39/169.66 [7132]~P123(x71321)+~P104(f334(f334(f250(x71321),x71323),f2(x71321)))+~P104(f334(f334(f250(x71321),x71322),f2(x71321)))+P104(f334(f334(f250(x71321),f2(x71321)),f334(f334(f82(x71321),x71322),x71323))) % 169.39/169.66 [7133]~P61(x71331)+~P104(f334(f334(f250(x71331),x71333),f2(x71331)))+~P104(f334(f334(f250(x71331),x71332),f2(x71331)))+P104(f334(f334(f250(x71331),f2(x71331)),f334(f334(f292(x71331),x71332),x71333))) % 169.39/169.66 [7134]~P62(x71341)+~P104(f334(f334(f250(x71341),x71343),f2(x71341)))+~P104(f334(f334(f250(x71341),x71342),f2(x71341)))+P104(f334(f334(f250(x71341),f2(x71341)),f334(f334(f292(x71341),x71342),x71343))) % 169.39/169.66 [7135]~P119(x71351)+~P104(f334(f334(f250(a877),f2(a877)),x71353))+~P104(f334(f334(f250(x71351),f79(x71351)),x71352))+P104(f334(f334(f250(x71351),f79(x71351)),f334(f334(f259(x71351),x71352),x71353))) % 169.39/169.66 [7231]~P125(x72311)+~P104(f334(f334(f249(x72311),f2(x72311)),x72313))+~P104(f334(f334(f249(x72311),f2(x72311)),x72312))+P104(f334(f334(f249(x72311),f2(x72311)),f334(f334(f82(x72311),x72312),x72313))) % 169.39/169.66 [7232]~P132(x72321)+~P104(f334(f334(f249(x72321),f2(x72321)),x72323))+~P104(f334(f334(f249(x72321),f2(x72321)),x72322))+P104(f334(f334(f249(x72321),f2(x72321)),f334(f334(f82(x72321),x72322),x72323))) % 169.39/169.66 [7233]~P123(x72331)+~P104(f334(f334(f249(x72331),f2(x72331)),x72333))+~P104(f334(f334(f249(x72331),f2(x72331)),x72332))+P104(f334(f334(f249(x72331),f2(x72331)),f334(f334(f82(x72331),x72332),x72333))) % 169.39/169.66 [7235]~P61(x72351)+~P104(f334(f334(f249(x72351),f2(x72351)),x72353))+~P104(f334(f334(f249(x72351),f2(x72351)),x72352))+P104(f334(f334(f249(x72351),f2(x72351)),f334(f334(f292(x72351),x72352),x72353))) % 169.39/169.66 [7236]~P62(x72361)+~P104(f334(f334(f250(x72361),f2(x72361)),x72363))+~P104(f334(f334(f249(x72361),f2(x72361)),x72362))+P104(f334(f334(f249(x72361),f2(x72361)),f334(f334(f292(x72361),x72362),x72363))) % 169.39/169.66 [7237]~P119(x72371)+~P104(f334(f334(f250(x72371),f79(x72371)),x72373))+~P104(f334(f334(f250(x72371),f79(x72371)),x72372))+P104(f334(f334(f250(x72371),f79(x72371)),f334(f334(f82(x72371),x72372),x72373))) % 169.39/169.66 [7238]~P131(x72381)+~P104(f334(f334(f250(x72381),f2(x72381)),x72383))+~P104(f334(f334(f250(x72381),f2(x72381)),x72382))+P104(f334(f334(f250(x72381),f2(x72381)),f334(f334(f82(x72381),x72382),x72383))) % 169.39/169.66 [7241]~P85(x72411)+~P104(f334(f334(f250(x72411),f2(x72411)),x72413))+~P104(f334(f334(f250(x72411),f2(x72411)),x72412))+P104(f334(f334(f250(x72411),f2(x72411)),f334(f334(f81(x72411),x72412),x72413))) % 169.39/169.66 [7242]~P61(x72421)+~P104(f334(f334(f250(x72421),f2(x72421)),x72423))+~P104(f334(f334(f250(x72421),f2(x72421)),x72422))+P104(f334(f334(f250(x72421),f2(x72421)),f334(f334(f292(x72421),x72422),x72423))) % 169.39/169.66 [7243]~P62(x72431)+~P104(f334(f334(f250(x72431),f2(x72431)),x72433))+~P104(f334(f334(f250(x72431),f2(x72431)),x72432))+P104(f334(f334(f250(x72431),f2(x72431)),f334(f334(f292(x72431),x72432),x72433))) % 169.39/169.66 [7317]~P95(x73171)+~P104(f334(f63(x73171),x73173))+E(f12(x73171,f334(f334(f312(x73171),x73172),x73173)),x73172)+~E(f334(f334(f3(f886(x73171,a871)),x73173),f334(f334(f312(x73171),x73172),f195(f886(x73171,a871)))),f195(f886(x73171,a871))) % 169.39/169.66 [7318]~P95(x73181)+~P104(f334(f63(x73181),x73183))+E(f13(x73181,f334(f334(f312(x73181),x73182),x73183)),x73182)+~E(f334(f334(f3(f886(x73181,a871)),x73183),f334(f334(f312(x73181),x73182),f195(f886(x73181,a871)))),f195(f886(x73181,a871))) % 169.39/169.66 [7319]~P107(x73191)+~P104(f334(f63(x73191),x73193))+E(f16(x73191,f334(f334(f312(x73191),x73192),x73193)),x73192)+~E(f334(f334(f3(f886(x73191,a871)),x73193),f334(f334(f312(x73191),x73192),f195(f886(x73191,a871)))),f195(f886(x73191,a871))) % 169.39/169.66 [7320]~P107(x73201)+~P104(f334(f63(x73201),x73203))+E(f17(x73201,f334(f334(f312(x73201),x73202),x73203)),x73202)+~E(f334(f334(f3(f886(x73201,a871)),x73203),f334(f334(f312(x73201),x73202),f195(f886(x73201,a871)))),f195(f886(x73201,a871))) % 169.39/169.66 [7321]~P123(x73211)+P104(f334(f334(f249(x73211),x73212),f2(x73211)))+P104(f334(f334(f249(x73211),f2(x73211)),x73213))+~P104(f334(f334(f249(x73211),f2(x73211)),f334(f334(f82(x73211),x73213),x73212))) % 169.39/169.66 [7322]~P123(x73221)+P104(f334(f334(f249(x73221),x73222),f2(x73221)))+P104(f334(f334(f249(x73221),f2(x73221)),x73223))+~P104(f334(f334(f249(x73221),f2(x73221)),f334(f334(f82(x73221),x73222),x73223))) % 169.39/169.66 [7323]~P61(x73231)+P104(f334(f334(f249(x73231),x73232),f2(x73231)))+P104(f334(f334(f249(x73231),f2(x73231)),x73233))+~P104(f334(f334(f249(x73231),f2(x73231)),f334(f334(f292(x73231),x73233),x73232))) % 169.39/169.66 [7324]~P61(x73241)+P104(f334(f334(f249(x73241),x73242),f2(x73241)))+P104(f334(f334(f249(x73241),f2(x73241)),x73243))+~P104(f334(f334(f249(x73241),f2(x73241)),f334(f334(f292(x73241),x73242),x73243))) % 169.39/169.66 [7325]~P123(x73251)+P104(f334(f334(f249(x73251),x73252),f2(x73251)))+P104(f334(f334(f249(x73251),f2(x73251)),x73252))+~P104(f334(f334(f249(x73251),f2(x73251)),f334(f334(f82(x73251),x73253),x73252))) % 169.39/169.66 [7326]~P123(x73261)+P104(f334(f334(f249(x73261),x73262),f2(x73261)))+P104(f334(f334(f249(x73261),f2(x73261)),x73262))+~P104(f334(f334(f249(x73261),f2(x73261)),f334(f334(f82(x73261),x73262),x73263))) % 169.39/169.66 [7327]~P61(x73271)+P104(f334(f334(f249(x73271),x73272),f2(x73271)))+P104(f334(f334(f249(x73271),f2(x73271)),x73272))+~P104(f334(f334(f249(x73271),f2(x73271)),f334(f334(f292(x73271),x73273),x73272))) % 169.39/169.66 [7328]~P61(x73281)+P104(f334(f334(f249(x73281),x73282),f2(x73281)))+P104(f334(f334(f249(x73281),f2(x73281)),x73282))+~P104(f334(f334(f249(x73281),f2(x73281)),f334(f334(f292(x73281),x73282),x73283))) % 169.39/169.66 [7329]~P61(x73291)+P104(f334(f334(f250(x73291),x73292),f2(x73291)))+P104(f334(f334(f250(x73291),f2(x73291)),x73293))+~P104(f334(f334(f250(x73291),f2(x73291)),f334(f334(f292(x73291),x73293),x73292))) % 169.39/169.66 [7330]~P61(x73301)+P104(f334(f334(f250(x73301),x73302),f2(x73301)))+P104(f334(f334(f250(x73301),f2(x73301)),x73303))+~P104(f334(f334(f250(x73301),f2(x73301)),f334(f334(f292(x73301),x73302),x73303))) % 169.39/169.66 [7331]~P61(x73311)+P104(f334(f334(f250(x73311),x73312),f2(x73311)))+P104(f334(f334(f250(x73311),f2(x73311)),x73312))+~P104(f334(f334(f250(x73311),f2(x73311)),f334(f334(f292(x73311),x73313),x73312))) % 169.39/169.66 [7332]~P61(x73321)+P104(f334(f334(f250(x73321),x73322),f2(x73321)))+P104(f334(f334(f250(x73321),f2(x73321)),x73322))+~P104(f334(f334(f250(x73321),f2(x73321)),f334(f334(f292(x73321),x73322),x73323))) % 169.39/169.66 [7420]~E(f334(f334(f104(f886(x74201,a871)),f334(f173(x74201),x74202)),f334(f173(x74201),x74203)),f195(f886(x74201,a871)))+~P104(f334(f137(x74201),x74203))+~P104(f334(f137(x74201),x74202))+P104(f334(f137(x74201),f334(f334(f134(x74201),x74202),x74203))) % 169.39/169.66 [7421]~P107(x74211)+~P104(f334(f63(x74211),x74213))+E(f14(x74211,f247(x74211),f334(f334(f312(x74211),x74212),x74213)),x74212)+~E(f334(f334(f3(f886(x74211,a871)),x74213),f334(f334(f312(x74211),x74212),f195(f886(x74211,a871)))),f195(f886(x74211,a871))) % 169.39/169.66 [7422]~P107(x74221)+~P104(f334(f63(x74221),x74223))+E(f15(x74221,f248(x74221),f334(f334(f312(x74221),x74222),x74223)),x74222)+~E(f334(f334(f3(f886(x74221,a871)),x74223),f334(f334(f312(x74221),x74222),f195(f886(x74221,a871)))),f195(f886(x74221,a871))) % 169.39/169.66 [7438]~P83(x74381)+~P104(f334(f334(f249(x74381),x74382),x74383))+~P104(f334(f334(f249(x74381),f334(f80(x74381),x74382)),x74383))+P104(f334(f334(f249(x74381),f334(f76(x74381),x74382)),x74383)) % 169.39/169.66 [7439]~P120(x74391)+~P104(f334(f334(f250(x74391),x74392),x74393))+~P104(f334(f334(f250(x74391),f334(f80(x74391),x74392)),x74393))+P104(f334(f334(f250(x74391),f334(f76(x74391),x74392)),x74393)) % 169.39/169.66 [7509]~P131(x75091)+P104(f334(f334(f250(x75091),f2(x75091)),x75092))+~P104(f334(f334(f250(x75091),f2(x75091)),x75093))+~P104(f334(f334(f250(x75091),f2(x75091)),f334(f334(f82(x75091),x75093),x75092))) % 169.39/169.66 [7510]~P131(x75101)+P104(f334(f334(f250(x75101),f2(x75101)),x75102))+~P104(f334(f334(f250(x75101),f2(x75101)),x75103))+~P104(f334(f334(f250(x75101),f2(x75101)),f334(f334(f82(x75101),x75102),x75103))) % 169.39/169.66 [7813]E(x78131,x78132)+~P104(f334(f63(x78133),x78131))+~P104(f334(f334(f249(a877),f334(f39(x78133),x78131)),f334(f39(x78133),x78132)))+~P104(f334(f334(f249(f886(x78133,a871)),x78132),x78131)) % 169.39/169.66 [7953]~P104(f334(f334(f250(a1),x79531),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x79532))+~P104(f334(f334(f249(a1),x79532),x79533))+P104(f334(f334(f249(a1),f334(f334(f40(a1),x79531),x79532)),f334(f334(f40(a1),x79531),x79533))) % 169.39/169.66 [7965]~P104(f334(f334(f249(a1),f2(a1)),x79651))+~P104(f334(f334(f250(a1),f2(a1)),x79653))+~P104(f334(f334(f249(a1),x79653),x79652))+P104(f334(f334(f249(a1),f334(f334(f40(a1),x79651),x79652)),f334(f334(f40(a1),x79651),x79653))) % 169.39/169.66 [8099]E(f334(x80991,f358(x80992,x80991,x80993)),x80992)+~P104(f334(f334(f249(a1),x80992),f334(x80991,x80993)))+P104(f334(f334(f250(a877),f359(x80992,x80991,x80993)),x80993))+~P104(f334(f334(f249(a1),f334(x80991,f2(a877))),x80992)) % 169.39/169.66 [8100]E(f334(x81001,f360(x81002,x81001,x81003)),x81002)+~P104(f334(f334(f249(a1),x81002),f334(x81001,x81003)))+P104(f334(f334(f250(a877),f361(x81002,x81001,x81003)),x81003))+~P104(f334(f334(f249(a1),f334(x81001,f2(a877))),x81002)) % 169.39/169.66 [8201]~P104(f334(f63(x82011),x82013))+~P104(f334(f334(f250(a877),f334(f39(x82011),x82012)),f334(f39(x82011),x82013)))+~P104(f334(f334(f249(f886(x82011,a871)),x82012),x82013))+P104(f334(f334(f250(f886(x82011,a871)),x82012),x82013)) % 169.39/169.66 [8230]E(f334(f334(f81(a1),f369(x82303,x82301,x82302)),f370(x82303,x82301,x82302)),x82301)+E(f334(f334(f3(a1),x82301),x82302),x82301)+~P104(f334(f334(f250(a1),f2(a1)),x82302))+~P104(f334(f334(f336(a1),f334(f334(f3(a1),x82301),f79(a1))),x82303)) % 169.39/169.66 [8231]E(f334(f334(f3(a1),f377(x82313,x82311,x82312)),f378(x82313,x82311,x82312)),x82311)+E(f334(f334(f81(a1),x82311),x82312),x82311)+~P104(f334(f334(f250(a1),f2(a1)),x82312))+~P104(f334(f334(f336(a1),f334(f334(f81(a1),x82311),f79(a1))),x82313)) % 169.39/169.66 [8284]~P104(f334(f334(f249(a877),x82843),x82841))+P104(f334(f334(f249(a877),x82841),x82842))+~P104(f334(f334(f249(a877),x82843),x82842))+~P104(f334(f334(f249(a877),f334(f334(f3(a877),x82841),x82843)),f334(f334(f3(a877),x82842),x82843))) % 169.39/169.66 [8285]~P104(f334(f334(f249(a877),x82853),x82851))+P104(f334(f334(f250(a877),x82851),x82852))+~P104(f334(f334(f249(a877),x82853),x82852))+~P104(f334(f334(f250(a877),f334(f334(f3(a877),x82851),x82853)),f334(f334(f3(a877),x82852),x82853))) % 169.39/169.66 [8301]~P107(x83012)+E(x83011,f116(x83012))+~P30(x83012,f334(f169(x83012),x83011))+E(f334(f142(x83012,x83012,f334(f9(x83012,x83012,x83012),f248(x83012)),x83013),f334(f169(x83012),x83011)),f334(f334(f248(x83012),f334(f334(f165(x83012),x83011),f2(a877))),x83013)) % 169.39/169.66 [8365]E(f334(f334(f3(a1),x83651),x83652),x83651)+~P104(f334(f334(f250(a1),f2(a1)),x83652))+P104(f334(f334(f336(a1),f369(x83653,x83651,x83652)),x83653))+~P104(f334(f334(f336(a1),f334(f334(f3(a1),x83651),f79(a1))),x83653)) % 169.39/169.66 [8366]E(f334(f334(f81(a1),x83661),x83662),x83661)+~P104(f334(f334(f250(a1),f2(a1)),x83662))+P104(f334(f334(f336(a1),f377(x83663,x83661,x83662)),x83663))+~P104(f334(f334(f336(a1),f334(f334(f81(a1),x83661),f79(a1))),x83663)) % 169.39/169.66 [8439]~P104(f334(f334(f249(a1),x84391),f334(x84392,x84393)))+P104(f334(f334(f250(a877),f359(x84391,x84392,x84393)),x84393))+P104(f334(f334(f249(a877),f358(x84391,x84392,x84393)),x84393))+~P104(f334(f334(f249(a1),f334(x84392,f2(a877))),x84391)) % 169.39/169.66 [8440]~P104(f334(f334(f249(a1),x84401),f334(x84402,x84403)))+P104(f334(f334(f250(a877),f361(x84401,x84402,x84403)),x84403))+P104(f334(f334(f249(a877),f360(x84401,x84402,x84403)),x84403))+~P104(f334(f334(f249(a1),f334(x84402,f2(a877))),x84401)) % 169.39/169.66 [8511]E(f334(f334(f3(a1),x85111),x85112),x85111)+~P104(f334(f334(f250(a1),f2(a1)),x85112))+P104(f334(f334(f336(a1),f370(x85113,x85111,x85112)),f305(a1,f79(a1),x85112)))+~P104(f334(f334(f336(a1),f334(f334(f3(a1),x85111),f79(a1))),x85113)) % 169.39/169.66 [8512]E(f334(f334(f81(a1),x85121),x85122),x85121)+~P104(f334(f334(f250(a1),f2(a1)),x85122))+P104(f334(f334(f336(a1),f378(x85123,x85121,x85122)),f305(a1,f79(a1),x85122)))+~P104(f334(f334(f336(a1),f334(f334(f81(a1),x85121),f79(a1))),x85123)) % 169.39/169.66 [8639]~P119(x86391)+~P104(f334(f334(f250(x86391),x86392),f79(x86391)))+~P104(f334(f334(f250(x86391),f2(x86391)),x86392))+P104(f334(f334(f250(x86391),f334(f334(f82(x86391),x86392),f334(f334(f259(x86391),x86392),x86393))),f334(f334(f259(x86391),x86392),x86393))) % 169.39/169.66 [8721]~P104(f334(x87211,x87212))+P104(f334(x87211,f2(a877)))+~P104(f334(f334(f250(a877),x87212),x87213))+~P104(f334(x87211,f46(a877,f334(a115,f356(x87212,x87211,x87213)),x87213))) % 169.39/169.66 [8859]E(f510(x88591,x88592,x88593),f2(a877))+P104(f334(f334(x88591,x88593),x88592))+P104(f334(f334(x88591,f510(x88591,x88592,x88593)),f46(a877,f509(x88591,x88592,x88593),f510(x88591,x88592,x88593))))+~P104(f334(f322(f885(a877,a877),a228),f334(f334(f269(a877,a877),x88593),x88592))) % 169.39/169.66 [8897]~P21(x88971,x88971,x88972,x88973)+E(f334(f313(x88971,x88971,x88972),x88973),x88973)+~P104(f334(f63(x88971),x88973))+~P104(f334(f334(f249(f886(x88971,a871)),f334(f313(x88971,x88971,x88972),x88973)),x88973)) % 169.39/169.66 [9110]P104(f334(f334(x91101,x91102),x91103))+P104(f334(f334(f250(a1),f811(x91101,x91103,x91102)),f812(x91101,x91103,x91102)))+P104(f334(f334(x91101,f811(x91101,x91103,x91102)),f334(f334(f81(a1),f812(x91101,x91103,x91102)),f79(a1))))+~P104(f334(f322(f885(a1,a1),a133),f334(f334(f269(a1,a1),x91102),x91103))) % 169.39/169.66 [9127]P104(f334(f334(x91271,x91272),x91273))+~P104(f334(f334(f250(a1),f508(x91271,x91273,x91272)),f2(a1)))+P104(f334(f334(x91271,f334(f80(a1),f507(x91271,x91273,x91272))),f334(f80(a1),f508(x91271,x91273,x91272))))+~P104(f334(f322(f885(a1,a1),a230),f334(f334(f269(a1,a1),x91272),x91273))) % 169.39/169.66 [9301]P104(f334(f334(x93011,x93012),x93013))+P104(f334(f334(x93011,f334(f334(f81(a1),f596(x93011,x93013,x93012)),f79(a1))),f597(x93011,x93013,x93012)))+~P104(f334(f334(f249(a1),f596(x93011,x93013,x93012)),f597(x93011,x93013,x93012)))+~P104(f334(f322(f885(a1,a1),a184),f334(f334(f269(a1,a1),x93012),x93013))) % 169.39/169.66 [9718]~P58(x97182)+~P58(x97181)+~P104(f334(f60(f885(x97181,x97182)),x97183))+P104(f334(f60(x97181),f334(f334(f10(f886(x97182,a871),a871,x97181),f60(x97182)),f334(f334(f10(f886(x97182,f885(x97181,x97182)),f886(x97182,a871),x97181),f334(f10(f885(x97181,x97182),a871,x97182),x97183)),f269(x97181,x97182))))) % 169.39/169.66 [9719]~P58(x97192)+~P58(x97191)+~P104(f334(f59(f885(x97191,x97192)),x97193))+P104(f334(f59(x97191),f334(f334(f10(f886(x97192,a871),a871,x97191),f59(x97192)),f334(f334(f10(f886(x97192,f885(x97191,x97192)),f886(x97192,a871),x97191),f334(f10(f885(x97191,x97192),a871,x97192),x97193)),f269(x97191,x97192))))) % 169.39/169.66 [9822]~P58(x98222)+~P58(x98221)+P104(f334(f60(f885(x98221,x98222)),x98223))+~P104(f334(f60(x98221),f334(f334(f10(f886(x98222,a871),a871,x98221),f60(x98222)),f334(f334(f10(f886(x98222,f885(x98221,x98222)),f886(x98222,a871),x98221),f334(f10(f885(x98221,x98222),a871,x98222),x98223)),f269(x98221,x98222))))) % 169.39/169.66 [9823]~P58(x98232)+~P58(x98231)+P104(f334(f59(f885(x98231,x98232)),x98233))+~P104(f334(f59(x98231),f334(f334(f10(f886(x98232,a871),a871,x98231),f59(x98232)),f334(f334(f10(f886(x98232,f885(x98231,x98232)),f886(x98232,a871),x98231),f334(f10(f885(x98231,x98232),a871,x98232),x98233)),f269(x98231,x98232))))) % 169.39/169.66 [9989]E(f334(x99891,f358(x99892,x99891,x99893)),x99892)+~P104(f334(f334(f249(a1),x99892),f334(x99891,x99893)))+~P104(f334(f334(f249(a1),f334(f76(a1),f334(f334(f3(a1),f334(x99891,f334(f334(f81(a877),f359(x99892,x99891,x99893)),f79(a877)))),f334(x99891,f359(x99892,x99891,x99893))))),f79(a1)))+~P104(f334(f334(f249(a1),f334(x99891,f2(a877))),x99892)) % 169.39/169.66 [9990]E(f334(x99901,f360(x99902,x99901,x99903)),x99902)+~P104(f334(f334(f249(a1),x99902),f334(x99901,x99903)))+~P104(f334(f334(f249(a1),f334(f76(a1),f334(f334(f3(a1),f334(x99901,f334(f334(f81(a877),f361(x99902,x99901,x99903)),f79(a877)))),f334(x99901,f361(x99902,x99901,x99903))))),f79(a1)))+~P104(f334(f334(f249(a1),f334(x99901,f2(a877))),x99902)) % 169.39/169.66 [9994]~P104(f334(f334(f249(a1),x99941),f334(x99942,x99943)))+~P104(f334(f334(f249(a1),f334(f76(a1),f334(f334(f3(a1),f334(x99942,f334(f334(f81(a877),f359(x99941,x99942,x99943)),f79(a877)))),f334(x99942,f359(x99941,x99942,x99943))))),f79(a1)))+P104(f334(f334(f249(a877),f358(x99941,x99942,x99943)),x99943))+~P104(f334(f334(f249(a1),f334(x99942,f2(a877))),x99941)) % 169.39/169.66 [9995]~P104(f334(f334(f249(a1),x99951),f334(x99952,x99953)))+~P104(f334(f334(f249(a1),f334(f76(a1),f334(f334(f3(a1),f334(x99952,f334(f334(f81(a877),f361(x99951,x99952,x99953)),f79(a877)))),f334(x99952,f361(x99951,x99952,x99953))))),f79(a1)))+P104(f334(f334(f249(a877),f360(x99951,x99952,x99953)),x99953))+~P104(f334(f334(f249(a1),f334(x99952,f2(a877))),x99951)) % 169.39/169.66 [10050]E(x100501,x100502)+~E(f334(f142(f878(x100503),f878(x100503),f134(x100503),f116(x100503)),x100501),f334(f142(f878(x100503),f878(x100503),f134(x100503),f116(x100503)),x100502))+~E(f334(f196(f878(f878(x100503))),x100501),f334(f196(f878(f878(x100503))),x100502))+~P104(f334(f334(f273(f878(x100503),f878(x100503),a871),f334(f334(f9(f878(x100503),f886(f878(x100503),a877),f886(f878(x100503),a871)),f334(f334(f10(f886(a877,a871),f886(f886(f878(x100503),a877),f886(f878(x100503),a871)),f878(x100503)),f10(a877,a871,f878(x100503))),f334(f334(f10(a877,f886(a877,a871),f878(x100503)),a331),f196(f878(x100503))))),f196(f878(x100503)))),f648(x100501,x100502,x100503))) % 169.39/169.66 [10051]E(x100511,x100512)+~E(f334(f142(f878(x100513),f878(x100513),f134(x100513),f116(x100513)),x100511),f334(f142(f878(x100513),f878(x100513),f134(x100513),f116(x100513)),x100512))+~E(f334(f196(f878(f878(x100513))),x100511),f334(f196(f878(f878(x100513))),x100512))+~P104(f334(f334(f273(f878(x100513),f878(x100513),a871),f334(f334(f9(f878(x100513),f886(f878(x100513),a877),f886(f878(x100513),a871)),f334(f334(f10(f886(a877,a871),f886(f886(f878(x100513),a877),f886(f878(x100513),a871)),f878(x100513)),f10(a877,a871,f878(x100513))),f334(f334(f10(a877,f886(a877,a871),f878(x100513)),a331),f196(f878(x100513))))),f196(f878(x100513)))),f649(x100512,x100511,x100513))) % 169.39/169.66 [6839]~E(f79(a877),f2(a877))+~P104(f334(f63(x68391),x68393))+~P104(f334(f63(x68391),x68392))+E(f334(f334(f81(a877),f334(f39(x68391),x68392)),f334(f39(x68391),x68393)),f334(f39(x68391),f334(f334(f113(f886(x68391,a871)),x68392),x68393))) % 169.39/169.66 [7250]~P101(x72501)+~P104(f334(f63(x72501),x72502))+~P104(f334(f334(f336(x72501),x72503),x72502))+P104(f334(f334(f249(x72501),f334(f65(x72501,f104(x72501)),x72502)),x72503)) % 169.39/169.66 [7251]~P107(x72511)+~P104(f334(f63(x72511),x72512))+~P104(f334(f334(f336(x72511),x72513),x72512))+P104(f334(f334(f249(x72511),f334(f65(x72511,f247(x72511)),x72512)),x72513)) % 169.39/169.66 [7503]~P104(f334(f63(x75031),x75033))+~P104(f334(f63(x75031),x75032))+~E(f334(f334(f104(f886(x75031,a871)),x75032),x75033),f195(f886(x75031,a871)))+E(f334(f334(f81(a877),f334(f39(x75031),x75032)),f334(f39(x75031),x75033)),f334(f39(x75031),f334(f334(f113(f886(x75031,a871)),x75032),x75033))) % 169.39/169.66 [8290]~P39(x82901,x82903)+~P39(x82901,x82902)+~E(f334(f334(f104(f886(x82901,a871)),f334(f267(x82901,x82901),x82902)),f334(f265(x82901,x82901),x82903)),f195(f886(x82901,a871)))+P39(x82901,f334(f334(f113(f886(f885(x82901,x82901),a871)),x82902),x82903)) % 169.39/169.66 [8380]E(x83801,f334(f334(f40(a877),x83802),x83803))+~P104(f334(f334(f250(a877),f2(a877)),x83803))+~P104(f334(f334(f250(a877),x83802),f334(f334(f82(a877),x83803),f334(a115,x83801))))+~P104(f334(f334(f249(a877),f334(f334(f82(a877),x83803),x83801)),x83802)) % 169.39/169.66 [8509]~P104(f334(f63(x85091),x85092))+~P104(f334(f63(x85091),x85093))+E(f334(f334(f81(a877),f334(f39(x85091),x85092)),f334(f39(x85091),x85093)),f334(f39(x85091),f334(f334(f113(f886(x85091,a871)),x85092),x85093)))+P104(f334(f334(f336(x85091),f428(x85093,x85092,x85091)),f334(f334(f104(f886(x85091,a871)),x85092),x85093))) % 169.39/169.66 [8871]~P123(x88712)+~E(x88711,f2(x88712))+~E(x88713,f2(x88712))+~P104(f334(f334(f250(x88712),f2(x88712)),f334(f334(f81(x88712),f334(f334(f82(x88712),x88713),x88713)),f334(f334(f82(x88712),x88711),x88711)))) % 169.39/169.66 [9379]~P39(x93791,x93793)+~P39(x93791,x93792)+P39(x93791,f334(f334(f113(f886(f885(x93791,x93791),a871)),x93792),x93793))+~P104(f334(f334(f249(f886(f885(x93791,x93791),a871)),f334(f334(f291(x93791,x93791,x93791),x93792),x93793)),x93792)) % 169.39/169.66 [9498]~P104(f334(x94981,x94983))+~P104(f334(f63(x94982),x94983))+P104(f334(x94981,f195(f886(x94982,a871))))+~P104(f334(x94981,f334(f334(f3(f886(x94982,a871)),f462(x94981,x94983,x94982)),f334(f334(f312(x94982),f466(x94981,x94983,x94982)),f195(f886(x94982,a871)))))) % 169.39/169.66 [9748]~P58(x97481)+~P58(x97482)+P7(x97481,f334(f334(f10(f886(x97482,x97481),a871,f878(x97481)),x97483),f334(f334(f10(f886(x97482,f881(x97481)),f886(x97482,x97481),f878(x97481)),f74(f881(x97481),x97481,x97482,f245(x97481))),f334(f334(f10(f878(f885(x97482,x97481)),f886(x97482,f881(x97481)),f878(x97481)),f179(x97482,x97481)),f334(f183(x97482,x97481),f57(x97482))))),f334(f196(f878(x97482)),f57(x97482)))+~P104(f334(f59(f886(x97482,x97481)),x97483)) % 169.39/169.66 [9749]~P58(x97491)+~P58(x97492)+P8(x97491,f334(f334(f10(f886(x97492,x97491),a871,f878(x97491)),x97493),f334(f334(f10(f886(x97492,f881(x97491)),f886(x97492,x97491),f878(x97491)),f74(f881(x97491),x97491,x97492,f245(x97491))),f334(f334(f10(f878(f885(x97492,x97491)),f886(x97492,f881(x97491)),f878(x97491)),f179(x97492,x97491)),f334(f183(x97492,x97491),f57(x97492))))),f334(f196(f878(x97492)),f57(x97492)))+~P104(f334(f60(f886(x97492,x97491)),x97493)) % 169.39/169.66 [9843]~P58(x98431)+~P58(x98432)+~P8(x98432,f334(f334(f10(f886(x98431,x98432),a871,f878(x98432)),x98433),f334(f334(f10(f886(x98431,f881(x98432)),f886(x98431,x98432),f878(x98432)),f74(f881(x98432),x98432,x98431,f245(x98432))),f334(f334(f10(f878(f885(x98431,x98432)),f886(x98431,f881(x98432)),f878(x98432)),f179(x98431,x98432)),f334(f183(x98431,x98432),f57(x98431))))),f334(f196(f878(x98431)),f57(x98431)))+P104(f334(f60(f886(x98431,x98432)),x98433)) % 169.39/169.66 [9844]~P58(x98441)+~P58(x98442)+~P7(x98442,f334(f334(f10(f886(x98441,x98442),a871,f878(x98442)),x98443),f334(f334(f10(f886(x98441,f881(x98442)),f886(x98441,x98442),f878(x98442)),f74(f881(x98442),x98442,x98441,f245(x98442))),f334(f334(f10(f878(f885(x98441,x98442)),f886(x98441,f881(x98442)),f878(x98442)),f179(x98441,x98442)),f334(f183(x98441,x98442),f57(x98441))))),f334(f196(f878(x98441)),f57(x98441)))+P104(f334(f59(f886(x98441,x98442)),x98443)) % 169.39/169.66 [8673]~P104(f334(f334(f250(a1),f2(a1)),x86733))+P104(f334(f334(f249(a1),f2(a1)),x86731))+~P104(f334(f334(f250(a1),x86732),x86733))+~P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),f334(f334(f82(a1),x86733),x86731)),x86732))) % 169.39/169.66 [8695]~P95(x86951)+~P104(f334(f63(x86951),x86952))+E(f334(f334(f3(f886(x86951,a871)),x86952),f334(f334(f312(x86951),x86953),f195(f886(x86951,a871)))),f195(f886(x86951,a871)))+E(f334(f334(f113(x86951),x86953),f12(x86951,f334(f334(f3(f886(x86951,a871)),x86952),f334(f334(f312(x86951),x86953),f195(f886(x86951,a871)))))),f12(x86951,f334(f334(f312(x86951),x86953),x86952))) % 169.39/169.66 [8696]~P95(x86961)+~P104(f334(f63(x86961),x86962))+E(f334(f334(f3(f886(x86961,a871)),x86962),f334(f334(f312(x86961),x86963),f195(f886(x86961,a871)))),f195(f886(x86961,a871)))+E(f334(f334(f104(x86961),x86963),f13(x86961,f334(f334(f3(f886(x86961,a871)),x86962),f334(f334(f312(x86961),x86963),f195(f886(x86961,a871)))))),f13(x86961,f334(f334(f312(x86961),x86963),x86962))) % 169.39/169.66 [8697]~P107(x86971)+~P104(f334(f63(x86971),x86972))+E(f334(f334(f3(f886(x86971,a871)),x86972),f334(f334(f312(x86971),x86973),f195(f886(x86971,a871)))),f195(f886(x86971,a871)))+E(f334(f334(f247(x86971),x86973),f16(x86971,f334(f334(f3(f886(x86971,a871)),x86972),f334(f334(f312(x86971),x86973),f195(f886(x86971,a871)))))),f16(x86971,f334(f334(f312(x86971),x86973),x86972))) % 169.39/169.66 [8698]~P107(x86981)+~P104(f334(f63(x86981),x86982))+E(f334(f334(f3(f886(x86981,a871)),x86982),f334(f334(f312(x86981),x86983),f195(f886(x86981,a871)))),f195(f886(x86981,a871)))+E(f334(f334(f248(x86981),x86983),f17(x86981,f334(f334(f3(f886(x86981,a871)),x86982),f334(f334(f312(x86981),x86983),f195(f886(x86981,a871)))))),f17(x86981,f334(f334(f312(x86981),x86983),x86982))) % 169.39/169.66 [8762]~P107(x87621)+~P104(f334(f63(x87621),x87622))+E(f334(f334(f3(f886(x87621,a871)),x87622),f334(f334(f312(x87621),x87623),f195(f886(x87621,a871)))),f195(f886(x87621,a871)))+E(f334(f334(f247(x87621),x87623),f14(x87621,f247(x87621),f334(f334(f3(f886(x87621,a871)),x87622),f334(f334(f312(x87621),x87623),f195(f886(x87621,a871)))))),f14(x87621,f247(x87621),f334(f334(f312(x87621),x87623),x87622))) % 169.39/169.66 [8763]~P107(x87631)+~P104(f334(f63(x87631),x87632))+E(f334(f334(f3(f886(x87631,a871)),x87632),f334(f334(f312(x87631),x87633),f195(f886(x87631,a871)))),f195(f886(x87631,a871)))+E(f334(f334(f248(x87631),x87633),f15(x87631,f248(x87631),f334(f334(f3(f886(x87631,a871)),x87632),f334(f334(f312(x87631),x87633),f195(f886(x87631,a871)))))),f15(x87631,f248(x87631),f334(f334(f312(x87631),x87633),x87632))) % 169.39/169.66 [9321]E(x93211,x93212)+~E(f334(f142(f878(x93213),f878(x93213),f134(x93213),f116(x93213)),x93211),f334(f142(f878(x93213),f878(x93213),f134(x93213),f116(x93213)),x93212))+~E(f334(f196(f878(f878(x93213))),x93211),f334(f196(f878(f878(x93213))),x93212))+P104(f334(f334(f336(f885(f878(x93213),f878(x93213))),f648(x93211,x93212,x93213)),f334(f173(f885(f878(x93213),f878(x93213))),f334(f334(f183(f878(x93213),f878(x93213)),x93212),x93211)))) % 169.39/169.66 [9322]E(x93221,x93222)+~E(f334(f142(f878(x93223),f878(x93223),f134(x93223),f116(x93223)),x93221),f334(f142(f878(x93223),f878(x93223),f134(x93223),f116(x93223)),x93222))+~E(f334(f196(f878(f878(x93223))),x93221),f334(f196(f878(f878(x93223))),x93222))+P104(f334(f334(f336(f885(f878(x93223),f878(x93223))),f649(x93222,x93221,x93223)),f334(f173(f885(f878(x93223),f878(x93223))),f334(f334(f183(f878(x93223),f878(x93223)),x93221),x93222)))) % 169.39/169.66 [10137]~P74(x101372)+E(x101371,f195(f886(x101372,a871)))+~P104(f334(f63(x101372),x101371))+E(f16(x101372,f334(f254(x101372),f334(f334(f10(f886(x101372,a871),a871,x101372),f88(x101372)),f334(f334(f9(x101372,f886(x101372,a871),f886(x101372,a871)),f334(f334(f10(f886(x101372,f886(a871,a871)),f886(f886(x101372,a871),f886(x101372,a871)),x101372),f20(x101372,a871,a871)),f334(f334(f10(f886(x101372,a871),f886(x101372,f886(a871,a871)),x101372),f334(f10(a871,f886(a871,a871),x101372),a332)),f334(f334(f9(x101372,f886(x101372,x101372),f886(x101372,a871)),f334(f334(f10(f886(x101372,a871),f886(f886(x101372,x101372),f886(x101372,a871)),x101372),f10(x101372,a871,x101372)),a331)),f334(f81(x101372),x101373))))),f334(f334(f9(x101372,f886(x101372,a871),a871),f336(x101372)),x101371))))),f334(f334(f81(x101372),x101373),f16(x101372,x101371))) % 169.39/169.66 [10138]~P74(x101382)+E(x101381,f195(f886(x101382,a871)))+~P104(f334(f63(x101382),x101381))+E(f17(x101382,f334(f254(x101382),f334(f334(f10(f886(x101382,a871),a871,x101382),f88(x101382)),f334(f334(f9(x101382,f886(x101382,a871),f886(x101382,a871)),f334(f334(f10(f886(x101382,f886(a871,a871)),f886(f886(x101382,a871),f886(x101382,a871)),x101382),f20(x101382,a871,a871)),f334(f334(f10(f886(x101382,a871),f886(x101382,f886(a871,a871)),x101382),f334(f10(a871,f886(a871,a871),x101382),a332)),f334(f334(f9(x101382,f886(x101382,x101382),f886(x101382,a871)),f334(f334(f10(f886(x101382,a871),f886(f886(x101382,x101382),f886(x101382,a871)),x101382),f10(x101382,a871,x101382)),a331)),f334(f81(x101382),x101383))))),f334(f334(f9(x101382,f886(x101382,a871),a871),f336(x101382)),x101381))))),f334(f334(f81(x101382),x101383),f17(x101382,x101381))) % 169.39/169.66 [10139]~P99(x101392)+E(x101391,f195(f886(x101392,a871)))+~P104(f334(f63(x101392),x101391))+E(f13(x101392,f334(f254(x101392),f334(f334(f10(f886(x101392,a871),a871,x101392),f88(x101392)),f334(f334(f9(x101392,f886(x101392,a871),f886(x101392,a871)),f334(f334(f10(f886(x101392,f886(a871,a871)),f886(f886(x101392,a871),f886(x101392,a871)),x101392),f20(x101392,a871,a871)),f334(f334(f10(f886(x101392,a871),f886(x101392,f886(a871,a871)),x101392),f334(f10(a871,f886(a871,a871),x101392),a332)),f334(f334(f9(x101392,f886(x101392,x101392),f886(x101392,a871)),f334(f334(f10(f886(x101392,a871),f886(f886(x101392,x101392),f886(x101392,a871)),x101392),f10(x101392,a871,x101392)),a331)),f334(f113(x101392),x101393))))),f334(f334(f9(x101392,f886(x101392,a871),a871),f336(x101392)),x101391))))),f334(f334(f113(x101392),x101393),f13(x101392,x101391))) % 169.39/169.66 [10140]~P99(x101402)+E(x101401,f195(f886(x101402,a871)))+~P104(f334(f63(x101402),x101401))+E(f12(x101402,f334(f254(x101402),f334(f334(f10(f886(x101402,a871),a871,x101402),f88(x101402)),f334(f334(f9(x101402,f886(x101402,a871),f886(x101402,a871)),f334(f334(f10(f886(x101402,f886(a871,a871)),f886(f886(x101402,a871),f886(x101402,a871)),x101402),f20(x101402,a871,a871)),f334(f334(f10(f886(x101402,a871),f886(x101402,f886(a871,a871)),x101402),f334(f10(a871,f886(a871,a871),x101402),a332)),f334(f334(f9(x101402,f886(x101402,x101402),f886(x101402,a871)),f334(f334(f10(f886(x101402,a871),f886(f886(x101402,x101402),f886(x101402,a871)),x101402),f10(x101402,a871,x101402)),a331)),f334(f104(x101402),x101403))))),f334(f334(f9(x101402,f886(x101402,a871),a871),f336(x101402)),x101401))))),f334(f334(f104(x101402),x101403),f12(x101402,x101401))) % 169.39/169.66 [10141]~P107(x101412)+E(x101411,f195(f886(x101412,a871)))+~P104(f334(f63(x101412),x101411))+E(f15(x101412,f248(x101412),f334(f254(x101412),f334(f334(f10(f886(x101412,a871),a871,x101412),f88(x101412)),f334(f334(f9(x101412,f886(x101412,a871),f886(x101412,a871)),f334(f334(f10(f886(x101412,f886(a871,a871)),f886(f886(x101412,a871),f886(x101412,a871)),x101412),f20(x101412,a871,a871)),f334(f334(f10(f886(x101412,a871),f886(x101412,f886(a871,a871)),x101412),f334(f10(a871,f886(a871,a871),x101412),a332)),f334(f334(f9(x101412,f886(x101412,x101412),f886(x101412,a871)),f334(f334(f10(f886(x101412,a871),f886(f886(x101412,x101412),f886(x101412,a871)),x101412),f10(x101412,a871,x101412)),a331)),f334(f247(x101412),x101413))))),f334(f334(f9(x101412,f886(x101412,a871),a871),f336(x101412)),x101411))))),f334(f334(f247(x101412),x101413),f15(x101412,f248(x101412),x101411))) % 169.39/169.66 [10142]~P107(x101422)+E(x101421,f195(f886(x101422,a871)))+~P104(f334(f63(x101422),x101421))+E(f14(x101422,f247(x101422),f334(f254(x101422),f334(f334(f10(f886(x101422,a871),a871,x101422),f88(x101422)),f334(f334(f9(x101422,f886(x101422,a871),f886(x101422,a871)),f334(f334(f10(f886(x101422,f886(a871,a871)),f886(f886(x101422,a871),f886(x101422,a871)),x101422),f20(x101422,a871,a871)),f334(f334(f10(f886(x101422,a871),f886(x101422,f886(a871,a871)),x101422),f334(f10(a871,f886(a871,a871),x101422),a332)),f334(f334(f9(x101422,f886(x101422,x101422),f886(x101422,a871)),f334(f334(f10(f886(x101422,a871),f886(f886(x101422,x101422),f886(x101422,a871)),x101422),f10(x101422,a871,x101422)),a331)),f334(f248(x101422),x101423))))),f334(f334(f9(x101422,f886(x101422,a871),a871),f336(x101422)),x101421))))),f334(f334(f248(x101422),x101423),f14(x101422,f247(x101422),x101421))) % 169.39/169.66 [9893]~P120(x98931)+~E(x98933,f2(x98931))+~E(x98932,f2(x98931))+E(f334(f334(f81(x98931),f334(f334(f259(x98931),x98932),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x98931),x98933),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f2(x98931)) % 169.39/169.66 [10034]~P119(x100341)+~P104(f334(f334(f249(x100341),f2(x100341)),x100343))+P104(f334(f334(f249(x100341),x100342),x100343))+~P104(f334(f334(f249(x100341),f334(f334(f259(x100341),x100342),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x100341),x100343),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))))) % 169.39/169.66 [10080]~P120(x100802)+~E(x100801,f2(x100802))+~E(x100803,f2(x100802))+~P104(f334(f334(f250(x100802),f2(x100802)),f334(f334(f81(x100802),f334(f334(f259(x100802),x100803),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))),f334(f334(f259(x100802),x100801),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))))) % 169.39/169.66 [9285]E(x92851,x92852)+~E(f625(x92851,x92852,x92854,x92853),f628(x92851,x92852,x92854,x92853))+P104(f334(f334(f336(f885(f878(x92853),f878(x92853))),f334(f334(f269(f878(x92853),f878(x92853)),x92852),x92851)),f147(x92853,x92854)))+P104(f334(f334(f336(f885(f878(x92853),f878(x92853))),f334(f334(f269(f878(x92853),f878(x92853)),x92851),x92852)),f147(x92853,x92854))) % 169.39/169.66 [4890]~P59(x48902)+~E(x48904,f2(x48902))+~E(x48901,f2(x48902))+E(x48901,f334(f334(f292(x48902),x48903),x48904)) % 169.39/169.66 [4891]~P59(x48911)+~E(x48913,f2(x48911))+~E(x48914,f2(x48911))+E(f334(f334(f292(x48911),x48912),x48913),x48914) % 169.39/169.66 [5002]~P59(x50022)+E(x50021,f2(x50022))+~E(x50023,f2(x50022))+~E(x50021,f334(f334(f292(x50022),x50024),x50023)) % 169.39/169.66 [5003]~P59(x50032)+E(x50031,f2(x50032))+~E(x50033,f2(x50032))+~E(f334(f334(f292(x50032),x50034),x50033),x50031) % 169.39/169.66 [5181]~P117(x51812)+E(x51811,f2(x51812))+~E(f334(f334(f292(x51812),x51813),x51811),x51814)+E(x51813,f334(f334(f82(x51812),x51814),x51811)) % 169.39/169.66 [5183]~P117(x51832)+E(x51831,f2(x51832))+~E(f334(f334(f82(x51832),x51833),x51831),x51834)+E(x51833,f334(f334(f292(x51832),x51834),x51831)) % 169.39/169.66 [5184]~P59(x51842)+E(x51841,f2(x51842))+~E(f334(f334(f292(x51842),x51843),x51841),x51844)+E(x51843,f334(f334(f82(x51842),x51844),x51841)) % 169.39/169.66 [5185]~P59(x51852)+E(x51851,f2(x51852))+~E(f334(f334(f82(x51852),x51853),x51851),x51854)+E(x51853,f334(f334(f292(x51852),x51854),x51851)) % 169.39/169.66 [5186]~P117(x51862)+E(x51861,f2(x51862))+~E(x51863,f334(f334(f292(x51862),x51864),x51861))+E(f334(f334(f82(x51862),x51863),x51861),x51864) % 169.39/169.66 [5188]~P117(x51882)+E(x51881,f2(x51882))+~E(x51883,f334(f334(f82(x51882),x51884),x51881))+E(f334(f334(f292(x51882),x51883),x51881),x51884) % 169.39/169.66 [5189]~P59(x51892)+E(x51891,f2(x51892))+~E(x51893,f334(f334(f292(x51892),x51894),x51891))+E(f334(f334(f82(x51892),x51893),x51891),x51894) % 169.39/169.66 [5190]~P59(x51902)+E(x51901,f2(x51902))+~E(x51903,f334(f334(f82(x51902),x51904),x51901))+E(f334(f334(f292(x51902),x51903),x51901),x51904) % 169.39/169.66 [5222]~P59(x52222)+~E(x52221,f2(x52222))+~E(f334(f334(f82(x52222),x52221),x52224),x52223)+E(x52221,f334(f334(f292(x52222),x52223),x52224)) % 169.39/169.66 [5223]~P59(x52231)+~E(x52234,f2(x52231))+~E(x52232,f334(f334(f82(x52231),x52234),x52233))+E(f334(f334(f292(x52231),x52232),x52233),x52234) % 169.39/169.66 [5297]~E(x52973,x52974)+~E(x52972,x52973)+~P108(x52971)+E(f305(x52971,x52972,x52973),f334(f334(f312(x52971),x52974),f195(f886(x52971,a871)))) % 169.39/169.66 [5506]~E(f144(x55062,x55061),x55064)+~E(f117(x55062,x55061),x55063)+E(x55061,f116(x55062))+E(f334(f334(f134(x55062),x55063),f334(f334(f151(x55062),x55064),f116(x55062))),x55061) % 169.39/169.66 [6121]~P119(x61213)+E(x61211,x61212)+~E(f334(f334(f259(x61213),x61214),x61211),f334(f334(f259(x61213),x61214),x61212))+~P104(f334(f334(f250(x61213),f79(x61213)),x61214)) % 169.39/169.66 [6122]E(x61221,x61222)+~E(f334(f334(f312(x61223),x61224),x61221),f334(f334(f312(x61223),x61224),x61222))+P104(f334(f334(f336(x61223),x61224),x61222))+P104(f334(f334(f336(x61223),x61224),x61221)) % 169.39/169.66 [6160]E(f334(x61601,x61602),f79(a877))+~E(f334(f334(f11(x61603,a877),x61601),x61604),f79(a877))+~P104(f334(f63(x61603),x61604))+~P104(f334(f334(f336(x61603),x61602),x61604)) % 169.39/169.66 [6161]E(f334(x61611,x61612),f2(a877))+~E(f334(f334(f8(x61613,a877),x61611),x61614),f2(a877))+~P104(f334(f63(x61613),x61614))+~P104(f334(f334(f336(x61613),x61612),x61614)) % 169.39/169.66 [6381]~P108(x63811)+~P104(f334(f334(f249(x63811),x63814),x63813))+P104(f334(f334(f249(x63811),x63812),x63813))+~P104(f334(f334(f249(x63811),x63812),x63814)) % 169.39/169.66 [6382]~P105(x63821)+~P104(f334(f334(f249(x63821),x63822),x63824))+P104(f334(f334(f249(x63821),x63822),x63823))+~P104(f334(f334(f249(x63821),x63824),x63823)) % 169.39/169.66 [6383]~P108(x63831)+~P104(f334(f334(f250(x63831),x63834),x63833))+P104(f334(f334(f250(x63831),x63832),x63833))+~P104(f334(f334(f249(x63831),x63832),x63834)) % 169.39/169.66 [6384]~P108(x63841)+~P104(f334(f334(f250(x63841),x63842),x63844))+P104(f334(f334(f250(x63841),x63842),x63843))+~P104(f334(f334(f249(x63841),x63844),x63843)) % 169.39/169.66 [6385]~P108(x63851)+~P104(f334(f334(f250(x63851),x63854),x63853))+P104(f334(f334(f250(x63851),x63852),x63853))+~P104(f334(f334(f250(x63851),x63852),x63854)) % 169.39/169.66 [6386]~P105(x63861)+~P104(f334(f334(f250(x63861),x63862),x63864))+P104(f334(f334(f250(x63861),x63862),x63863))+~P104(f334(f334(f249(x63861),x63864),x63863)) % 169.39/169.66 [6387]~P105(x63871)+~P104(f334(f334(f250(x63871),x63874),x63873))+P104(f334(f334(f250(x63871),x63872),x63873))+~P104(f334(f334(f249(x63871),x63872),x63874)) % 169.39/169.66 [6388]~P105(x63881)+~P104(f334(f334(f250(x63881),x63882),x63884))+P104(f334(f334(f250(x63881),x63882),x63883))+~P104(f334(f334(f250(x63881),x63884),x63883)) % 169.39/169.66 [6471]~P37(x64714,x64713,x64712)+E(x64711,f803(x64712,x64713,x64714))+~P104(f334(x64713,x64711))+~P104(f334(f334(f336(x64714),x64711),f334(f173(x64714),x64712))) % 169.39/169.66 [6615]~P28(x66151)+~P104(f334(f334(f249(x66151),x66152),f42(x66151,x66154)))+P104(f334(f334(f249(x66151),x66152),x66153))+~P104(f334(f334(f336(x66151),x66153),x66154)) % 169.39/169.66 [6760]~P107(x67601)+~P30(x67601,f334(f334(f151(x67601),x67602),x67604))+~P104(f334(f334(f336(x67601),x67603),f334(f173(x67601),x67604)))+P104(f334(f334(f249(x67601),x67602),x67603)) % 169.39/169.66 [6850]~P28(x68501)+~P104(f334(f334(f249(x68501),f41(x68501,x68504)),x68503))+P104(f334(f334(f249(x68501),x68502),x68503))+~P104(f334(f334(f336(x68501),x68502),x68504)) % 169.39/169.66 [7253]~P107(x72531)+E(f334(f334(f113(f886(x72531,a871)),f334(f304(x72531,x72532),x72533)),f334(f304(x72531,x72533),x72534)),f334(f304(x72531,x72532),x72534))+~P104(f334(f334(f249(x72531),x72533),x72534))+~P104(f334(f334(f249(x72531),x72532),x72533)) % 169.39/169.66 [7293]P37(x72931,x72932,x72933)+~E(f807(x72933,x72932,x72931,x72934),x72934)+~P104(f334(x72932,x72934))+~P104(f334(f334(f336(x72931),x72934),f334(f173(x72931),x72933))) % 169.39/169.66 [7367]~P107(x73671)+E(f334(f334(f113(f886(x73671,a871)),f334(f304(x73671,x73672),x73673)),f305(x73671,x73673,x73674)),f305(x73671,x73672,x73674))+~P104(f334(f334(f249(x73671),x73673),x73674))+~P104(f334(f334(f249(x73671),x73672),x73673)) % 169.39/169.66 [7431]~P107(x74311)+E(f334(f334(f113(f886(x74311,a871)),f308(x74311,x74312,x74313)),f334(f304(x74311,x74313),x74314)),f308(x74311,x74312,x74314))+~P104(f334(f334(f249(x74311),x74313),x74314))+~P104(f334(f334(f250(x74311),x74312),x74313)) % 169.39/169.66 [7451]~P107(x74511)+E(f334(f334(f113(f886(x74511,a871)),f305(x74511,x74512,x74513)),f308(x74511,x74513,x74514)),f334(f304(x74511,x74512),x74514))+~P104(f334(f334(f249(x74511),x74512),x74513))+~P104(f334(f334(f250(x74511),x74513),x74514)) % 169.39/169.66 [7483]~P107(x74831)+E(f334(f334(f113(f886(x74831,a871)),f308(x74831,x74832,x74833)),f305(x74831,x74833,x74834)),f307(x74831,x74832,x74834))+~P104(f334(f334(f249(x74831),x74833),x74834))+~P104(f334(f334(f250(x74831),x74832),x74833)) % 169.39/169.66 [7484]~P107(x74841)+E(f334(f334(f113(f886(x74841,a871)),f305(x74841,x74842,x74843)),f307(x74841,x74843,x74844)),f305(x74841,x74842,x74844))+~P104(f334(f334(f249(x74841),x74843),x74844))+~P104(f334(f334(f249(x74841),x74842),x74843)) % 169.39/169.66 [7485]~P107(x74851)+E(f334(f334(f113(f886(x74851,a871)),f307(x74851,x74852,x74853)),f308(x74851,x74853,x74854)),f308(x74851,x74852,x74854))+~P104(f334(f334(f249(x74851),x74852),x74853))+~P104(f334(f334(f250(x74851),x74853),x74854)) % 169.39/169.66 [7486]~P107(x74861)+E(f334(f334(f113(f886(x74861,a871)),f307(x74861,x74862,x74863)),f307(x74861,x74863,x74864)),f307(x74861,x74862,x74864))+~P104(f334(f334(f249(x74861),x74863),x74864))+~P104(f334(f334(f249(x74861),x74862),x74863)) % 169.39/169.66 [8274]P21(x82741,x82742,f823(x82743,x82742,x82744,x82741),x82744)+~P104(f334(f63(x82742),x82743))+~P104(f334(f63(x82741),x82744))+~P104(f334(f334(f249(a877),f334(f39(x82741),x82744)),f334(f39(x82742),x82743))) % 169.39/169.66 [8295]P37(x82951,x82952,x82953)+~P104(f334(x82952,x82954))+P104(f334(x82952,f807(x82953,x82952,x82951,x82954)))+~P104(f334(f334(f336(x82951),x82954),f334(f173(x82951),x82953))) % 169.39/169.66 [8344]~P68(x83441)+~E(f334(x83443,f448(x83443,x83444,x83442,x83441)),f79(x83441))+E(f334(f334(f334(f67(x83441,x83442,f82(x83441)),x83443),f79(x83441)),x83444),f79(x83441))+~P104(f334(f63(x83442),x83444)) % 169.39/169.66 [8606]~P119(x86061)+~P104(f334(f334(f249(x86061),f2(x86061)),x86063))+P104(f334(f334(f249(x86061),x86062),x86063))+~P104(f334(f334(f249(x86061),f334(f334(f259(x86061),x86062),f334(a115,x86064))),f334(f334(f259(x86061),x86063),f334(a115,x86064)))) % 169.39/169.66 [8899]P37(x88991,x88992,x88993)+~P104(f334(x88992,x88994))+~P104(f334(f334(f336(x88991),x88994),f334(f173(x88991),x88993)))+P104(f334(f334(f336(x88991),f807(x88993,x88992,x88991,x88994)),f334(f173(x88991),x88993))) % 169.39/169.66 [8976]~P68(x89761)+E(f334(f334(f334(f67(x89761,x89762,f82(x89761)),x89763),f79(x89761)),x89764),f79(x89761))+~P104(f334(f63(x89762),x89764))+P104(f334(f334(f336(x89762),f448(x89763,x89764,x89762,x89761)),x89764)) % 169.39/169.66 [9443]~P104(f334(f334(f249(a1),x94434),f2(a1)))+P104(f334(f334(f249(a1),f334(f334(f81(a1),f334(f334(f82(a1),x94431),f46(a1,x94432,x94433))),x94434)),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x94433))+~P104(f334(f334(f250(a1),x94431),x94434)) % 169.39/169.66 [9886]~P104(f334(f63(x98861),x98862))+~P104(f334(f334(f336(x98861),x98864),x98862))+~P104(f334(f334(f336(x98861),x98863),x98862))+P104(f334(f334(f250(a877),f334(f39(x98861),f334(f334(f3(f886(x98861,a871)),f334(f334(f3(f886(x98861,a871)),x98862),f334(f334(f312(x98861),x98863),f195(f886(x98861,a871))))),f334(f334(f312(x98861),x98864),f195(f886(x98861,a871)))))),f334(f39(x98861),x98862))) % 169.39/169.66 [6965]~P101(x69651)+~P104(f334(f334(f249(x69651),x69652),x69654))+~P104(f334(f334(f249(x69651),x69652),x69653))+P104(f334(f334(f249(x69651),x69652),f334(f334(f104(x69651),x69653),x69654))) % 169.39/169.66 [6968]~P107(x69681)+~P104(f334(f334(f249(x69681),x69682),x69684))+~P104(f334(f334(f249(x69681),x69682),x69683))+P104(f334(f334(f249(x69681),x69682),f334(f334(f247(x69681),x69683),x69684))) % 169.39/169.66 [6969]~P107(x69691)+~P104(f334(f334(f250(x69691),x69692),x69694))+~P104(f334(f334(f250(x69691),x69692),x69693))+P104(f334(f334(f250(x69691),x69692),f334(f334(f247(x69691),x69693),x69694))) % 169.39/169.66 [6988]~P60(x69882)+E(x69881,f2(x69882))+E(f334(f334(f292(x69882),f334(f334(f259(x69882),x69881),x69883)),f334(f334(f259(x69882),x69881),x69884)),f334(f334(f259(x69882),x69881),f334(f334(f3(a877),x69883),x69884)))+~P104(f334(f334(f249(a877),x69884),x69883)) % 169.39/169.66 [7033]~P107(x70331)+~P30(x70331,f334(f334(f151(x70331),x70333),x70334))+P30(x70331,f334(f334(f151(x70331),x70332),f334(f334(f151(x70331),x70333),x70334)))+~P104(f334(f334(f249(x70331),x70332),x70333)) % 169.39/169.66 [7072]~P85(x70721)+~P104(f334(f334(f249(x70721),f2(x70721)),x70724))+~P104(f334(f334(f249(x70721),x70722),x70723))+P104(f334(f334(f249(x70721),x70722),f334(f334(f81(x70721),x70723),x70724))) % 169.39/169.66 [7073]~P85(x70731)+~P104(f334(f334(f249(x70731),f2(x70731)),x70733))+~P104(f334(f334(f249(x70731),x70732),x70734))+P104(f334(f334(f249(x70731),x70732),f334(f334(f81(x70731),x70733),x70734))) % 169.39/169.66 [7074]~P119(x70741)+~P104(f334(f334(f250(x70741),f2(x70741)),x70743))+~P104(f334(f334(f250(x70741),x70742),x70744))+P104(f334(f334(f250(x70741),x70742),f334(f334(f81(x70741),x70743),x70744))) % 169.39/169.66 [7075]~P85(x70751)+~P104(f334(f334(f249(x70751),x70752),x70754))+~P104(f334(f334(f250(x70751),f2(x70751)),x70753))+P104(f334(f334(f250(x70751),x70752),f334(f334(f81(x70751),x70753),x70754))) % 169.39/169.66 [7076]~P85(x70761)+~P104(f334(f334(f249(x70761),f2(x70761)),x70763))+~P104(f334(f334(f250(x70761),x70762),x70764))+P104(f334(f334(f250(x70761),x70762),f334(f334(f81(x70761),x70763),x70764))) % 169.39/169.66 [7115]~P107(x71151)+P104(f334(f334(f249(x71151),x71152),x71153))+P104(f334(f334(f249(x71151),x71152),x71154))+~P104(f334(f334(f249(x71151),x71152),f334(f334(f248(x71151),x71154),x71153))) % 169.39/169.66 [7116]~P107(x71161)+P104(f334(f334(f250(x71161),x71162),x71163))+P104(f334(f334(f250(x71161),x71162),x71164))+~P104(f334(f334(f250(x71161),x71162),f334(f334(f248(x71161),x71164),x71163))) % 169.39/169.66 [7403]~P108(x74032)+~P58(x74031)+~P104(f334(f334(f250(f886(x74031,x74032)),x74033),x74034))+P104(f334(f334(f249(f886(x74031,x74032)),x74033),x74034)) % 169.39/169.66 [7773]~P62(x77731)+~P104(f334(f334(f250(x77731),x77734),f2(x77731)))+~P104(f334(f334(f249(x77731),x77733),f334(f334(f292(x77731),x77732),x77734)))+P104(f334(f334(f249(x77731),x77732),f334(f334(f82(x77731),x77733),x77734))) % 169.39/169.66 [7774]~P62(x77741)+~P104(f334(f334(f250(x77741),x77744),f2(x77741)))+~P104(f334(f334(f249(x77741),x77743),f334(f334(f82(x77741),x77742),x77744)))+P104(f334(f334(f249(x77741),x77742),f334(f334(f292(x77741),x77743),x77744))) % 169.39/169.66 [7775]~P62(x77751)+~P104(f334(f334(f250(x77751),x77754),f2(x77751)))+~P104(f334(f334(f250(x77751),x77753),f334(f334(f292(x77751),x77752),x77754)))+P104(f334(f334(f250(x77751),x77752),f334(f334(f82(x77751),x77753),x77754))) % 169.39/169.66 [7776]~P62(x77761)+~P104(f334(f334(f250(x77761),x77764),f2(x77761)))+~P104(f334(f334(f250(x77761),x77763),f334(f334(f82(x77761),x77762),x77764)))+P104(f334(f334(f250(x77761),x77762),f334(f334(f292(x77761),x77763),x77764))) % 169.39/169.66 [7881]~P125(x78811)+~P104(f334(f334(f249(x78811),x78812),f2(x78811)))+~P104(f334(f334(f249(x78811),x78814),x78813))+P104(f334(f334(f249(x78811),f334(f334(f82(x78811),x78812),x78813)),f334(f334(f82(x78811),x78812),x78814))) % 169.39/169.66 [7882]~P123(x78821)+~P104(f334(f334(f250(x78821),x78822),f2(x78821)))+~P104(f334(f334(f249(x78821),x78824),x78823))+P104(f334(f334(f249(x78821),f334(f334(f82(x78821),x78822),x78823)),f334(f334(f82(x78821),x78822),x78824))) % 169.39/169.66 [7883]~P125(x78831)+~P104(f334(f334(f249(x78831),x78833),f2(x78831)))+~P104(f334(f334(f249(x78831),x78834),x78832))+P104(f334(f334(f249(x78831),f334(f334(f82(x78831),x78832),x78833)),f334(f334(f82(x78831),x78834),x78833))) % 169.39/169.66 [7884]~P61(x78841)+~P104(f334(f334(f249(x78841),x78843),f2(x78841)))+~P104(f334(f334(f249(x78841),x78844),x78842))+P104(f334(f334(f249(x78841),f334(f334(f292(x78841),x78842),x78843)),f334(f334(f292(x78841),x78844),x78843))) % 169.39/169.66 [7888]~P123(x78881)+~P104(f334(f334(f250(x78881),x78883),f2(x78881)))+~P104(f334(f334(f250(x78881),x78884),x78882))+P104(f334(f334(f250(x78881),f334(f334(f82(x78881),x78882),x78883)),f334(f334(f82(x78881),x78884),x78883))) % 169.39/169.66 [7889]~P123(x78891)+~P104(f334(f334(f250(x78891),x78892),f2(x78891)))+~P104(f334(f334(f250(x78891),x78894),x78893))+P104(f334(f334(f250(x78891),f334(f334(f82(x78891),x78892),x78893)),f334(f334(f82(x78891),x78892),x78894))) % 169.39/169.66 [7890]~P62(x78901)+~P104(f334(f334(f250(x78901),x78903),f2(x78901)))+~P104(f334(f334(f250(x78901),x78904),x78902))+P104(f334(f334(f250(x78901),f334(f334(f292(x78901),x78902),x78903)),f334(f334(f292(x78901),x78904),x78903))) % 169.39/169.66 [7891]~P119(x78911)+~P104(f334(f334(f250(x78911),f79(x78911)),x78912))+~P104(f334(f334(f249(a877),x78913),x78914))+P104(f334(f334(f249(x78911),f334(f334(f259(x78911),x78912),x78913)),f334(f334(f259(x78911),x78912),x78914))) % 169.39/169.66 [7892]~P119(x78921)+~P104(f334(f334(f249(x78921),f79(x78921)),x78922))+~P104(f334(f334(f249(a877),x78923),x78924))+P104(f334(f334(f249(x78921),f334(f334(f259(x78921),x78922),x78923)),f334(f334(f259(x78921),x78922),x78924))) % 169.39/169.66 [7894]~P119(x78941)+~P104(f334(f334(f250(x78941),f79(x78941)),x78942))+~P104(f334(f334(f250(a877),x78943),x78944))+P104(f334(f334(f250(x78941),f334(f334(f259(x78941),x78942),x78943)),f334(f334(f259(x78941),x78942),x78944))) % 169.39/169.66 [7921]P104(f334(f334(f250(a877),f2(a877)),f334(x79211,x79212)))+~P104(f334(f63(x79213),x79214))+~P104(f334(f334(f336(x79213),x79212),x79214))+~P104(f334(f334(f250(a877),f2(a877)),f334(f334(f11(x79213,a877),x79211),x79214))) % 169.39/169.66 [7929]~P134(x79291)+~P104(f334(f334(f249(x79291),x79293),x79294))+~P104(f334(f334(f249(x79291),f2(x79291)),x79292))+P104(f334(f334(f249(x79291),f334(f334(f82(x79291),x79292),x79293)),f334(f334(f82(x79291),x79292),x79294))) % 169.39/169.66 [7930]~P133(x79301)+~P104(f334(f334(f249(x79301),x79303),x79304))+~P104(f334(f334(f249(x79301),f2(x79301)),x79302))+P104(f334(f334(f249(x79301),f334(f334(f82(x79301),x79302),x79303)),f334(f334(f82(x79301),x79302),x79304))) % 169.39/169.66 [7931]~P123(x79311)+~P104(f334(f334(f250(x79311),f2(x79311)),x79312))+~P104(f334(f334(f249(x79311),x79313),x79314))+P104(f334(f334(f249(x79311),f334(f334(f82(x79311),x79312),x79313)),f334(f334(f82(x79311),x79312),x79314))) % 169.39/169.66 [7932]~P134(x79321)+~P104(f334(f334(f249(x79321),x79322),x79324))+~P104(f334(f334(f249(x79321),f2(x79321)),x79323))+P104(f334(f334(f249(x79321),f334(f334(f82(x79321),x79322),x79323)),f334(f334(f82(x79321),x79324),x79323))) % 169.39/169.66 [7933]~P61(x79331)+~P104(f334(f334(f249(x79331),x79332),x79334))+~P104(f334(f334(f249(x79331),f2(x79331)),x79333))+P104(f334(f334(f249(x79331),f334(f334(f292(x79331),x79332),x79333)),f334(f334(f292(x79331),x79334),x79333))) % 169.39/169.66 [7934]~P119(x79341)+~P104(f334(f334(f249(x79341),x79342),x79344))+~P104(f334(f334(f249(x79341),f2(x79341)),x79342))+P104(f334(f334(f249(x79341),f334(f334(f259(x79341),x79342),x79343)),f334(f334(f259(x79341),x79344),x79343))) % 169.39/169.66 [7936]~P121(x79361)+~P104(f334(f334(f250(x79361),x79363),x79364))+~P104(f334(f334(f250(x79361),f2(x79361)),x79362))+P104(f334(f334(f250(x79361),f334(f334(f82(x79361),x79362),x79363)),f334(f334(f82(x79361),x79362),x79364))) % 169.39/169.66 [7937]~P131(x79371)+~P104(f334(f334(f250(x79371),x79373),x79374))+~P104(f334(f334(f250(x79371),f2(x79371)),x79372))+P104(f334(f334(f250(x79371),f334(f334(f82(x79371),x79372),x79373)),f334(f334(f82(x79371),x79372),x79374))) % 169.39/169.66 [7938]~P123(x79381)+~P104(f334(f334(f250(x79381),x79382),x79384))+~P104(f334(f334(f250(x79381),f2(x79381)),x79383))+P104(f334(f334(f250(x79381),f334(f334(f82(x79381),x79382),x79383)),f334(f334(f82(x79381),x79384),x79383))) % 169.39/169.66 [7939]~P131(x79391)+~P104(f334(f334(f250(x79391),x79392),x79394))+~P104(f334(f334(f250(x79391),f2(x79391)),x79393))+P104(f334(f334(f250(x79391),f334(f334(f82(x79391),x79392),x79393)),f334(f334(f82(x79391),x79394),x79393))) % 169.39/169.66 [7940]~P123(x79401)+~P104(f334(f334(f250(x79401),x79403),x79404))+~P104(f334(f334(f250(x79401),f2(x79401)),x79402))+P104(f334(f334(f250(x79401),f334(f334(f82(x79401),x79402),x79403)),f334(f334(f82(x79401),x79402),x79404))) % 169.39/169.66 [7941]~P62(x79411)+~P104(f334(f334(f250(x79411),x79412),x79414))+~P104(f334(f334(f250(x79411),f2(x79411)),x79413))+P104(f334(f334(f250(x79411),f334(f334(f292(x79411),x79412),x79413)),f334(f334(f292(x79411),x79414),x79413))) % 169.39/169.66 [7985]~P106(x79852)+P104(f334(f334(f250(f886(x79851,x79852)),x79854),x79853))+~P104(f334(f334(f249(f886(x79851,x79852)),x79854),x79853))+P104(f334(f334(f249(f886(x79851,x79852)),x79853),x79854)) % 169.39/169.66 [8025]P104(f334(f334(f336(x80251),x80252),x80253))+P104(f334(f334(f336(x80251),x80252),x80254))+~P104(f334(f334(f249(f886(x80251,a871)),x80254),x80253))+P104(f334(f334(f250(f886(x80251,a871)),x80254),f334(f334(f312(x80251),x80252),x80253))) % 169.39/169.66 [8180]P104(f334(f334(f336(x81801),x81802),x81803))+P104(f334(f334(f336(x81801),x81802),x81804))+~P104(f334(f334(f250(f886(x81801,a871)),x81804),f334(f334(f312(x81801),x81802),x81803)))+P104(f334(f334(f249(f886(x81801,a871)),x81804),x81803)) % 169.39/169.66 [8188]~P58(x81881)+P7(x81881,x81882,x81883)+~P104(f334(x81882,x81884))+~P104(f334(f334(f336(f878(x81881)),x81884),f334(f173(f878(x81881)),f56(x81881,x81883,f57(x81881))))) % 169.39/169.66 [8198]~P8(x81983,x81981,x81984)+~P58(x81983)+P104(f334(x81981,x81982))+~P104(f334(f334(f336(f878(x81983)),x81982),f334(f173(f878(x81983)),f56(x81983,x81984,f57(x81983))))) % 169.39/169.66 [8251]~P123(x82511)+P104(f334(f334(f250(x82511),x82513),x82512))+P104(f334(f334(f250(x82511),x82512),x82513))+~P104(f334(f334(f250(x82511),f334(f334(f82(x82511),x82514),x82512)),f334(f334(f82(x82511),x82514),x82513))) % 169.39/169.66 [8252]~P123(x82521)+P104(f334(f334(f250(x82521),x82523),x82522))+P104(f334(f334(f250(x82521),x82522),x82523))+~P104(f334(f334(f250(x82521),f334(f334(f82(x82521),x82522),x82524)),f334(f334(f82(x82521),x82523),x82524))) % 169.39/169.66 [8263]~P123(x82631)+P104(f334(f334(f250(x82631),x82634),f2(x82631)))+P104(f334(f334(f250(x82631),x82632),x82633))+~P104(f334(f334(f250(x82631),f334(f334(f82(x82631),x82632),x82634)),f334(f334(f82(x82631),x82633),x82634))) % 169.39/169.66 [8264]~P123(x82641)+P104(f334(f334(f250(x82641),x82644),f2(x82641)))+P104(f334(f334(f250(x82641),x82642),x82643))+~P104(f334(f334(f250(x82641),f334(f334(f82(x82641),x82644),x82642)),f334(f334(f82(x82641),x82644),x82643))) % 169.39/169.66 [8268]~P123(x82681)+P104(f334(f334(f250(x82681),x82682),x82683))+P104(f334(f334(f250(x82681),f2(x82681)),x82684))+~P104(f334(f334(f250(x82681),f334(f334(f82(x82681),x82684),x82683)),f334(f334(f82(x82681),x82684),x82682))) % 169.39/169.66 [8269]~P123(x82691)+P104(f334(f334(f250(x82691),x82692),x82693))+P104(f334(f334(f250(x82691),f2(x82691)),x82694))+~P104(f334(f334(f250(x82691),f334(f334(f82(x82691),x82693),x82694)),f334(f334(f82(x82691),x82692),x82694))) % 169.39/169.66 [8282]~P123(x82821)+P104(f334(f334(f250(x82821),x82822),f2(x82821)))+P104(f334(f334(f250(x82821),f2(x82821)),x82822))+~P104(f334(f334(f250(x82821),f334(f334(f82(x82821),x82823),x82822)),f334(f334(f82(x82821),x82824),x82822))) % 169.39/169.66 [8283]~P123(x82831)+P104(f334(f334(f250(x82831),x82832),f2(x82831)))+P104(f334(f334(f250(x82831),f2(x82831)),x82832))+~P104(f334(f334(f250(x82831),f334(f334(f82(x82831),x82832),x82833)),f334(f334(f82(x82831),x82832),x82834))) % 169.39/169.66 [8309]~P123(x83091)+~P104(f334(f334(f250(x83091),x83094),f2(x83091)))+P104(f334(f334(f249(x83091),x83092),x83093))+~P104(f334(f334(f249(x83091),f334(f334(f82(x83091),x83094),x83093)),f334(f334(f82(x83091),x83094),x83092))) % 169.39/169.66 [8310]~P123(x83101)+~P104(f334(f334(f250(x83101),x83104),f2(x83101)))+P104(f334(f334(f250(x83101),x83102),x83103))+~P104(f334(f334(f250(x83101),f334(f334(f82(x83101),x83104),x83103)),f334(f334(f82(x83101),x83104),x83102))) % 169.39/169.66 [8320]~P119(x83203)+~P104(f334(f334(f250(x83203),f79(x83203)),x83204))+P104(f334(f334(f249(a877),x83201),x83202))+~P104(f334(f334(f249(x83203),f334(f334(f259(x83203),x83204),x83201)),f334(f334(f259(x83203),x83204),x83202))) % 169.39/169.66 [8322]~P119(x83223)+~P104(f334(f334(f250(x83223),f79(x83223)),x83224))+P104(f334(f334(f250(a877),x83221),x83222))+~P104(f334(f334(f250(x83223),f334(f334(f259(x83223),x83224),x83221)),f334(f334(f259(x83223),x83224),x83222))) % 169.39/169.66 [8332]~P123(x83321)+P104(f334(f334(f249(x83321),x83322),x83323))+~P104(f334(f334(f250(x83321),f2(x83321)),x83324))+~P104(f334(f334(f249(x83321),f334(f334(f82(x83321),x83324),x83322)),f334(f334(f82(x83321),x83324),x83323))) % 169.39/169.66 [8333]~P131(x83331)+P104(f334(f334(f249(x83331),x83332),x83333))+~P104(f334(f334(f250(x83331),f2(x83331)),x83334))+~P104(f334(f334(f249(x83331),f334(f334(f82(x83331),x83334),x83332)),f334(f334(f82(x83331),x83334),x83333))) % 169.39/169.66 [8334]~P131(x83341)+P104(f334(f334(f249(x83341),x83342),x83343))+~P104(f334(f334(f250(x83341),f2(x83341)),x83344))+~P104(f334(f334(f249(x83341),f334(f334(f82(x83341),x83342),x83344)),f334(f334(f82(x83341),x83343),x83344))) % 169.39/169.66 [8335]~P123(x83351)+P104(f334(f334(f250(x83351),x83352),x83353))+~P104(f334(f334(f250(x83351),f2(x83351)),x83354))+~P104(f334(f334(f250(x83351),f334(f334(f82(x83351),x83354),x83352)),f334(f334(f82(x83351),x83354),x83353))) % 169.39/169.66 [8336]~P131(x83361)+P104(f334(f334(f250(x83361),x83362),x83363))+~P104(f334(f334(f249(x83361),f2(x83361)),x83364))+~P104(f334(f334(f250(x83361),f334(f334(f82(x83361),x83364),x83362)),f334(f334(f82(x83361),x83364),x83363))) % 169.39/169.66 [8337]~P127(x83371)+P104(f334(f334(f250(x83371),x83372),x83373))+~P104(f334(f334(f249(x83371),f2(x83371)),x83374))+~P104(f334(f334(f250(x83371),f334(f334(f82(x83371),x83374),x83372)),f334(f334(f82(x83371),x83374),x83373))) % 169.39/169.66 [8338]~P119(x83381)+~P104(f334(f334(f249(x83381),f2(x83381)),x83383))+P104(f334(f334(f250(x83381),x83382),x83383))+~P104(f334(f334(f250(x83381),f334(f334(f259(x83381),x83382),x83384)),f334(f334(f259(x83381),x83383),x83384))) % 169.39/169.66 [8339]~P131(x83391)+P104(f334(f334(f250(x83391),x83392),x83393))+~P104(f334(f334(f249(x83391),f2(x83391)),x83394))+~P104(f334(f334(f250(x83391),f334(f334(f82(x83391),x83392),x83394)),f334(f334(f82(x83391),x83393),x83394))) % 169.39/169.66 [8340]~P127(x83401)+P104(f334(f334(f250(x83401),x83402),x83403))+~P104(f334(f334(f249(x83401),f2(x83401)),x83404))+~P104(f334(f334(f250(x83401),f334(f334(f82(x83401),x83402),x83404)),f334(f334(f82(x83401),x83403),x83404))) % 169.39/169.66 [8383]P104(f334(f334(f336(x83831),x83832),x83833))+~P104(f334(f334(f249(f886(x83831,a871)),x83833),x83834))+~P104(f334(f334(f250(f886(x83831,a871)),x83833),x83834))+P104(f334(f334(f250(f886(x83831,a871)),x83833),f334(f334(f312(x83831),x83832),x83834))) % 169.39/169.66 [8629]~P58(x86291)+~P91(x86292)+~E(f334(x86293,f809(x86294,x86293,x86291,x86292)),f334(x86294,f809(x86294,x86293,x86291,x86292)))+P104(f334(f334(f92(f886(x86291,x86292)),x86293),x86294)) % 169.39/169.66 [8742]E(f334(f334(f3(a1),f385(x87421,x87422,x87423,x87424)),f386(x87421,x87422,x87423,x87424)),x87424)+~P104(f334(f334(f250(a1),f2(a1)),x87423))+~P104(f334(f334(f249(a1),x87421),x87424))+P104(f334(f334(f249(a1),x87421),f334(f334(f81(a1),x87424),x87423))) % 169.39/169.66 [8743]E(f334(f334(f3(a1),f399(x87431,x87432,x87433,x87434)),f400(x87431,x87432,x87433,x87434)),x87434)+~P104(f334(f334(f250(a1),f2(a1)),x87433))+~P104(f334(f334(f250(a1),x87431),x87434))+P104(f334(f334(f250(a1),x87431),f334(f334(f81(a1),x87434),x87433))) % 169.39/169.66 [8878]~E(f334(f334(f165(x88781),x88783),f631(x88784,x88783,x88781,x88782)),f334(f334(f165(x88781),x88784),f631(x88784,x88783,x88781,x88782)))+E(f334(f334(f176(x88781),x88782),x88783),f334(f334(f176(x88781),x88782),x88784))+~P104(f334(f334(f249(a877),x88782),f334(f196(f878(x88781)),x88783)))+~P104(f334(f334(f249(a877),x88782),f334(f196(f878(x88781)),x88784))) % 169.39/169.66 [8948]~P104(f334(f334(f250(a1),f2(a1)),x89483))+~P104(f334(f334(f249(a1),x89481),x89484))+P104(f334(f334(f336(a1),f385(x89481,x89482,x89483,x89484)),x89482))+P104(f334(f334(f249(a1),x89481),f334(f334(f81(a1),x89484),x89483))) % 169.39/169.66 [8949]~P104(f334(f334(f250(a1),f2(a1)),x89493))+~P104(f334(f334(f250(a1),x89491),x89494))+P104(f334(f334(f336(a1),f399(x89491,x89492,x89493,x89494)),x89492))+P104(f334(f334(f250(a1),x89491),f334(f334(f81(a1),x89494),x89493))) % 169.39/169.66 [8985]~P101(x89851)+~P104(f334(f63(x89851),x89853))+~P104(f334(f334(f336(x89851),x89854),x89853))+P104(f334(f334(f249(x89851),f334(f334(f66(x89851,x89851,f104(x89851)),x89852),x89853)),f334(f334(f104(x89851),x89854),x89852))) % 169.39/169.66 [8986]~P107(x89861)+~P104(f334(f63(x89861),x89863))+~P104(f334(f334(f336(x89861),x89864),x89863))+P104(f334(f334(f249(x89861),f334(f334(f66(x89861,x89861,f247(x89861)),x89862),x89863)),f334(f334(f247(x89861),x89864),x89862))) % 169.39/169.66 [9030]E(f334(f334(f176(x90301),x90302),x90303),f334(f334(f176(x90301),x90302),x90304))+P104(f334(f334(f250(a877),f631(x90303,x90304,x90301,x90302)),x90302))+~P104(f334(f334(f249(a877),x90302),f334(f196(f878(x90301)),x90303)))+~P104(f334(f334(f249(a877),x90302),f334(f196(f878(x90301)),x90304))) % 169.39/169.66 [9035]~P104(f334(f334(f250(a1),f2(a1)),x90353))+~P104(f334(f334(f249(a1),x90351),x90352))+P104(f334(f334(f336(a1),f386(x90351,x90354,x90353,x90352)),f305(a1,f79(a1),x90353)))+P104(f334(f334(f249(a1),x90351),f334(f334(f81(a1),x90352),x90353))) % 169.39/169.66 [9036]~P104(f334(f334(f250(a1),f2(a1)),x90363))+~P104(f334(f334(f250(a1),x90361),x90362))+P104(f334(f334(f336(a1),f400(x90361,x90364,x90363,x90362)),f305(a1,f79(a1),x90363)))+P104(f334(f334(f250(a1),x90361),f334(f334(f81(a1),x90362),x90363))) % 169.39/169.66 [9196]~E(f334(f179(x91961,x91962),x91963),f334(f179(x91961,x91962),x91964))+E(f334(f173(f885(x91961,x91962)),x91963),f334(f173(f885(x91961,x91962)),x91964))+~P104(f334(f137(x91961),f334(f334(f154(f885(x91961,x91962),x91961),f268(x91961,x91962)),x91964)))+~P104(f334(f137(x91961),f334(f334(f154(f885(x91961,x91962),x91961),f268(x91961,x91962)),x91963))) % 169.39/169.66 [9208]E(f334(f179(x92081,x92082),x92083),f334(f179(x92081,x92082),x92084))+~E(f334(f173(f885(x92081,x92082)),x92083),f334(f173(f885(x92081,x92082)),x92084))+~P104(f334(f137(x92081),f334(f334(f154(f885(x92081,x92082),x92081),f268(x92081,x92082)),x92084)))+~P104(f334(f137(x92081),f334(f334(f154(f885(x92081,x92082),x92081),f268(x92081,x92082)),x92083))) % 169.39/169.66 [9341]~P100(x93411)+~P104(f334(f63(x93411),x93414))+P104(f334(f334(f336(x93411),f458(x93412,x93413,x93414,x93411)),x93414))+P104(f334(f334(f249(x93411),f334(f334(f66(x93411,x93411,f113(x93411)),x93412),x93414)),f334(f334(f113(x93411),x93413),x93412))) % 169.39/169.66 [9342]~P107(x93421)+~P104(f334(f63(x93421),x93424))+P104(f334(f334(f336(x93421),f489(x93422,x93423,x93424,x93421)),x93424))+P104(f334(f334(f249(x93421),f334(f334(f66(x93421,x93421,f248(x93421)),x93422),x93424)),f334(f334(f248(x93421),x93423),x93422))) % 169.39/169.66 [9461]~P100(x94611)+~P104(f334(f63(x94611),x94613))+~P104(f334(f334(f249(x94611),f458(x94612,x94614,x94613,x94611)),x94614))+P104(f334(f334(f249(x94611),f334(f334(f66(x94611,x94611,f113(x94611)),x94612),x94613)),f334(f334(f113(x94611),x94614),x94612))) % 169.39/169.66 [9462]~P107(x94621)+~P104(f334(f63(x94621),x94623))+~P104(f334(f334(f249(x94621),f489(x94622,x94624,x94623,x94621)),x94624))+P104(f334(f334(f249(x94621),f334(f334(f66(x94621,x94621,f248(x94621)),x94622),x94623)),f334(f334(f248(x94621),x94624),x94622))) % 169.39/169.66 [9465]~P104(f334(f334(f249(a1),f2(a1)),x94654))+~P104(f334(f334(f250(a1),f2(a1)),x94653))+~P104(f334(f334(f250(a1),x94654),x94651))+P104(f334(f334(f250(a1),f334(f334(f81(a1),f334(f334(f82(a1),x94651),f46(a1,x94652,x94653))),x94654)),f334(f334(f82(a1),x94651),x94653))) % 169.39/169.66 [9855]E(x98551,x98552)+P104(f334(f334(f336(f885(f878(x98553),f878(x98553))),f334(f334(f269(f878(x98553),f878(x98553)),x98552),x98551)),f147(x98553,x98554)))+P104(f334(f334(f336(f885(f878(x98553),f878(x98553))),f334(f334(f269(f878(x98553),f878(x98553)),x98551),x98552)),f147(x98553,x98554)))+~P104(f334(f334(f336(f885(x98553,x98553)),f334(f334(f269(x98553,x98553),f625(x98551,x98552,x98554,x98553)),f628(x98551,x98552,x98554,x98553))),x98554)) % 169.39/169.66 [9856]E(x98561,x98562)+P104(f334(f334(f336(f885(f878(x98563),f878(x98563))),f334(f334(f269(f878(x98563),f878(x98563)),x98562),x98561)),f147(x98563,x98564)))+P104(f334(f334(f336(f885(f878(x98563),f878(x98563))),f334(f334(f269(f878(x98563),f878(x98563)),x98561),x98562)),f147(x98563,x98564)))+~P104(f334(f334(f336(f885(x98563,x98563)),f334(f334(f269(x98563,x98563),f628(x98561,x98562,x98564,x98563)),f625(x98561,x98562,x98564,x98563))),x98564)) % 169.39/169.66 [7473]~P100(x74731)+~P104(f334(f334(f249(x74731),x74733),x74734))+~P104(f334(f334(f249(x74731),x74732),x74734))+P104(f334(f334(f249(x74731),f334(f334(f113(x74731),x74732),x74733)),x74734)) % 169.39/169.66 [7476]~P107(x74761)+~P104(f334(f334(f249(x74761),x74763),x74764))+~P104(f334(f334(f249(x74761),x74762),x74764))+P104(f334(f334(f249(x74761),f334(f334(f248(x74761),x74762),x74763)),x74764)) % 169.39/169.66 [7477]~P107(x74771)+~P104(f334(f334(f250(x74771),x74773),x74774))+~P104(f334(f334(f250(x74771),x74772),x74774))+P104(f334(f334(f250(x74771),f334(f334(f248(x74771),x74772),x74773)),x74774)) % 169.39/169.66 [7798]~E(x77981,x77983)+E(f139(a877,f334(f304(a877,x77981),x77982)),f334(f334(f151(a877),x77983),x77984))+~E(f139(a877,f334(f304(a877,f334(f334(f81(a877),x77981),f79(a877))),x77982)),x77984)+~P104(f334(f334(f250(a877),x77981),x77982)) % 169.39/169.66 [7807]~P107(x78071)+P104(f334(f334(f249(x78071),x78072),x78073))+P104(f334(f334(f249(x78071),x78074),x78073))+~P104(f334(f334(f249(x78071),f334(f334(f247(x78071),x78074),x78072)),x78073)) % 169.39/169.66 [7808]~P107(x78081)+P104(f334(f334(f250(x78081),x78082),x78083))+P104(f334(f334(f250(x78081),x78084),x78083))+~P104(f334(f334(f250(x78081),f334(f334(f247(x78081),x78084),x78082)),x78083)) % 169.39/169.66 [8081]~P61(x80811)+~P104(f334(f334(f250(x80811),f2(x80811)),x80813))+~P104(f334(f334(f249(x80811),x80812),f334(f334(f292(x80811),x80814),x80813)))+P104(f334(f334(f249(x80811),f334(f334(f82(x80811),x80812),x80813)),x80814)) % 169.39/169.66 [8082]~P62(x80821)+~P104(f334(f334(f250(x80821),f2(x80821)),x80823))+~P104(f334(f334(f249(x80821),x80822),f334(f334(f292(x80821),x80824),x80823)))+P104(f334(f334(f249(x80821),f334(f334(f82(x80821),x80822),x80823)),x80824)) % 169.39/169.66 [8083]~P61(x80831)+~P104(f334(f334(f250(x80831),f2(x80831)),x80833))+~P104(f334(f334(f249(x80831),x80832),f334(f334(f82(x80831),x80834),x80833)))+P104(f334(f334(f249(x80831),f334(f334(f292(x80831),x80832),x80833)),x80834)) % 169.39/169.66 [8085]~P62(x80851)+~P104(f334(f334(f250(x80851),f2(x80851)),x80853))+~P104(f334(f334(f249(x80851),x80852),f334(f334(f82(x80851),x80854),x80853)))+P104(f334(f334(f249(x80851),f334(f334(f292(x80851),x80852),x80853)),x80854)) % 169.39/169.66 [8086]~P61(x80861)+~P104(f334(f334(f250(x80861),f2(x80861)),x80863))+~P104(f334(f334(f250(x80861),x80862),f334(f334(f292(x80861),x80864),x80863)))+P104(f334(f334(f250(x80861),f334(f334(f82(x80861),x80862),x80863)),x80864)) % 169.39/169.66 [8087]~P62(x80871)+~P104(f334(f334(f250(x80871),f2(x80871)),x80873))+~P104(f334(f334(f250(x80871),x80872),f334(f334(f292(x80871),x80874),x80873)))+P104(f334(f334(f250(x80871),f334(f334(f82(x80871),x80872),x80873)),x80874)) % 169.39/169.66 [8088]~P61(x80881)+~P104(f334(f334(f250(x80881),f2(x80881)),x80883))+~P104(f334(f334(f250(x80881),x80882),f334(f334(f82(x80881),x80884),x80883)))+P104(f334(f334(f250(x80881),f334(f334(f292(x80881),x80882),x80883)),x80884)) % 169.39/169.66 [8090]~P62(x80901)+~P104(f334(f334(f250(x80901),f2(x80901)),x80903))+~P104(f334(f334(f250(x80901),x80902),f334(f334(f82(x80901),x80904),x80903)))+P104(f334(f334(f250(x80901),f334(f334(f292(x80901),x80902),x80903)),x80904)) % 169.39/169.66 [8220]~P61(x82201)+~P104(f334(f334(f250(x82201),f2(x82201)),x82204))+P104(f334(f334(f249(x82201),x82202),f334(f334(f82(x82201),x82203),x82204)))+~P104(f334(f334(f249(x82201),f334(f334(f292(x82201),x82202),x82204)),x82203)) % 169.39/169.66 [8221]~P61(x82211)+~P104(f334(f334(f250(x82211),f2(x82211)),x82214))+P104(f334(f334(f249(x82211),x82212),f334(f334(f292(x82211),x82213),x82214)))+~P104(f334(f334(f249(x82211),f334(f334(f82(x82211),x82212),x82214)),x82213)) % 169.39/169.66 [8223]~P62(x82231)+~P104(f334(f334(f250(x82231),f2(x82231)),x82234))+P104(f334(f334(f249(x82231),x82232),f334(f334(f82(x82231),x82233),x82234)))+~P104(f334(f334(f249(x82231),f334(f334(f292(x82231),x82232),x82234)),x82233)) % 169.39/169.66 [8224]~P62(x82241)+~P104(f334(f334(f250(x82241),f2(x82241)),x82244))+P104(f334(f334(f249(x82241),x82242),f334(f334(f292(x82241),x82243),x82244)))+~P104(f334(f334(f249(x82241),f334(f334(f82(x82241),x82242),x82244)),x82243)) % 169.39/169.66 [8225]~P61(x82251)+~P104(f334(f334(f250(x82251),f2(x82251)),x82254))+P104(f334(f334(f250(x82251),x82252),f334(f334(f82(x82251),x82253),x82254)))+~P104(f334(f334(f250(x82251),f334(f334(f292(x82251),x82252),x82254)),x82253)) % 169.39/169.66 [8226]~P61(x82261)+~P104(f334(f334(f250(x82261),f2(x82261)),x82264))+P104(f334(f334(f250(x82261),x82262),f334(f334(f292(x82261),x82263),x82264)))+~P104(f334(f334(f250(x82261),f334(f334(f82(x82261),x82262),x82264)),x82263)) % 169.39/169.66 [8228]~P62(x82281)+~P104(f334(f334(f250(x82281),f2(x82281)),x82284))+P104(f334(f334(f250(x82281),x82282),f334(f334(f82(x82281),x82283),x82284)))+~P104(f334(f334(f250(x82281),f334(f334(f292(x82281),x82282),x82284)),x82283)) % 169.39/169.66 [8229]~P62(x82291)+~P104(f334(f334(f250(x82291),f2(x82291)),x82294))+P104(f334(f334(f250(x82291),x82292),f334(f334(f292(x82291),x82293),x82294)))+~P104(f334(f334(f250(x82291),f334(f334(f82(x82291),x82292),x82294)),x82293)) % 169.39/169.66 [8387]~P62(x83871)+~P104(f334(f334(f250(x83871),x83873),f2(x83871)))+~P104(f334(f334(f249(x83871),f334(f334(f292(x83871),x83874),x83873)),x83872))+P104(f334(f334(f249(x83871),f334(f334(f82(x83871),x83872),x83873)),x83874)) % 169.39/169.66 [8388]~P62(x83881)+~P104(f334(f334(f250(x83881),x83883),f2(x83881)))+~P104(f334(f334(f249(x83881),f334(f334(f82(x83881),x83884),x83883)),x83882))+P104(f334(f334(f249(x83881),f334(f334(f292(x83881),x83882),x83883)),x83884)) % 169.39/169.66 [8389]~P62(x83891)+~P104(f334(f334(f250(x83891),x83893),f2(x83891)))+~P104(f334(f334(f250(x83891),f334(f334(f292(x83891),x83894),x83893)),x83892))+P104(f334(f334(f250(x83891),f334(f334(f82(x83891),x83892),x83893)),x83894)) % 169.39/169.66 [8390]~P62(x83901)+~P104(f334(f334(f250(x83901),x83903),f2(x83901)))+~P104(f334(f334(f250(x83901),f334(f334(f82(x83901),x83904),x83903)),x83902))+P104(f334(f334(f250(x83901),f334(f334(f292(x83901),x83902),x83903)),x83904)) % 169.39/169.66 [8400]~P104(f334(x84001,x84004))+~P104(f334(f334(f250(a877),x84002),f334(f334(f82(a877),x84003),f334(a115,x84004))))+P104(f334(x84001,f334(f334(f40(a877),x84002),x84003)))+~P104(f334(f334(f249(a877),f334(f334(f82(a877),x84003),x84004)),x84002)) % 169.39/169.66 [8603]~P100(x86031)+~P104(f334(f63(x86031),x86034))+~P104(f334(f334(f336(x86031),x86032),x86034))+P104(f334(f334(f249(x86031),f334(f334(f113(x86031),x86032),x86033)),f334(f334(f66(x86031,x86031,f113(x86031)),x86033),x86034))) % 169.39/169.66 [8604]~P107(x86041)+~P104(f334(f63(x86041),x86044))+~P104(f334(f334(f336(x86041),x86042),x86044))+P104(f334(f334(f249(x86041),f334(f334(f248(x86041),x86042),x86043)),f334(f334(f66(x86041,x86041,f248(x86041)),x86043),x86044))) % 169.39/169.66 [8744]~P104(f334(f63(x87441),x87442))+E(f334(f39(x87441),f334(f334(f3(f886(x87441,a871)),x87442),f334(f334(f312(x87441),x87443),x87444))),f334(f334(f3(a877),f334(f39(x87441),f334(f334(f3(f886(x87441,a871)),x87442),x87444))),f79(a877)))+P104(f334(f334(f336(x87441),x87443),x87444))+~P104(f334(f334(f336(x87441),x87443),x87442)) % 169.39/169.66 [8814]E(f334(f334(f81(a1),f389(x88141,x88142,x88143,x88144)),f390(x88141,x88142,x88143,x88144)),x88144)+~P104(f334(f334(f250(a1),f2(a1)),x88143))+~P104(f334(f334(f249(a1),x88144),x88141))+P104(f334(f334(f249(a1),f334(f334(f3(a1),x88144),x88143)),x88141)) % 169.39/169.66 [8815]E(f334(f334(f81(a1),f401(x88151,x88152,x88153,x88154)),f402(x88151,x88152,x88153,x88154)),x88154)+~P104(f334(f334(f250(a1),f2(a1)),x88153))+~P104(f334(f334(f250(a1),x88154),x88151))+P104(f334(f334(f250(a1),f334(f334(f3(a1),x88154),x88153)),x88151)) % 169.39/169.66 [9015]~P104(f334(f334(f250(a1),f2(a1)),x90153))+~P104(f334(f334(f249(a1),x90154),x90151))+P104(f334(f334(f336(a1),f389(x90151,x90152,x90153,x90154)),x90152))+P104(f334(f334(f249(a1),f334(f334(f3(a1),x90154),x90153)),x90151)) % 169.39/169.66 [9016]~P104(f334(f334(f250(a1),f2(a1)),x90163))+~P104(f334(f334(f250(a1),x90164),x90161))+P104(f334(f334(f336(a1),f401(x90161,x90162,x90163,x90164)),x90162))+P104(f334(f334(f250(a1),f334(f334(f3(a1),x90164),x90163)),x90161)) % 169.39/169.66 [9100]~P104(f334(f334(f250(a1),f2(a1)),x91002))+~P104(f334(f334(f249(a1),x91001),x91003))+P104(f334(f334(f336(a1),f390(x91003,x91004,x91002,x91001)),f305(a1,f79(a1),x91002)))+P104(f334(f334(f249(a1),f334(f334(f3(a1),x91001),x91002)),x91003)) % 169.39/169.66 [9101]~P104(f334(f334(f250(a1),f2(a1)),x91012))+~P104(f334(f334(f250(a1),x91011),x91013))+P104(f334(f334(f336(a1),f402(x91013,x91014,x91012,x91011)),f305(a1,f79(a1),x91012)))+P104(f334(f334(f250(a1),f334(f334(f3(a1),x91011),x91012)),x91013)) % 169.39/169.66 [9118]~P104(f334(f334(f249(a1),f2(a1)),x91184))+~P104(f334(f334(f250(a1),f2(a1)),x91183))+~P104(f334(f334(f250(a1),x91184),x91181))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),f334(f334(f82(a1),x91181),f46(a1,x91182,x91183))),x91184))) % 169.39/169.66 [9179]~P101(x91791)+~P104(f334(f63(x91791),x91794))+~P104(f334(f334(f249(x91791),x91792),f457(x91793,x91792,x91794,x91791)))+P104(f334(f334(f249(x91791),f334(f334(f104(x91791),x91792),x91793)),f334(f334(f66(x91791,x91791,f104(x91791)),x91793),x91794))) % 169.39/169.66 [9180]~P107(x91801)+~P104(f334(f63(x91801),x91804))+~P104(f334(f334(f249(x91801),x91802),f476(x91803,x91802,x91804,x91801)))+P104(f334(f334(f249(x91801),f334(f334(f247(x91801),x91802),x91803)),f334(f334(f66(x91801,x91801,f247(x91801)),x91803),x91804))) % 169.39/169.66 [9195]~P104(f334(f334(f249(a1),x91954),f2(a1)))+~P104(f334(f334(f250(a1),f2(a1)),x91952))+~P104(f334(f334(f250(a1),x91951),x91954))+P104(f334(f334(f250(a1),f334(f334(f82(a1),x91951),x91952)),f334(f334(f81(a1),f334(f334(f82(a1),x91951),f46(a1,x91953,x91952))),x91954))) % 169.39/169.66 [9217]P104(f334(f63(x92171),x92172))+~P104(f334(f63(x92171),x92173))+~P104(f334(f334(f336(f886(x92171,a871)),x92172),f334(f334(f62(x92171),x92173),x92174)))+~P104(f334(f334(f249(f886(f885(x92171,x92171),a871)),x92174),f334(f334(f271(x92171,x92171),x92173),f334(f18(f886(x92171,a871),x92171),x92173)))) % 169.39/169.66 [9240]~P101(x92401)+~P104(f334(f63(x92401),x92404))+P104(f334(f334(f336(x92401),f457(x92402,x92403,x92404,x92401)),x92404))+P104(f334(f334(f249(x92401),f334(f334(f104(x92401),x92403),x92402)),f334(f334(f66(x92401,x92401,f104(x92401)),x92402),x92404))) % 169.39/169.66 [9241]~P107(x92411)+~P104(f334(f63(x92411),x92414))+P104(f334(f334(f336(x92411),f476(x92412,x92413,x92414,x92411)),x92414))+P104(f334(f334(f249(x92411),f334(f334(f247(x92411),x92413),x92412)),f334(f334(f66(x92411,x92411,f247(x92411)),x92412),x92414))) % 169.39/169.66 [9623]~P104(f334(f63(x96232),x96234))+~P104(f334(f63(x96231),x96233))+~P104(f334(f334(f249(a877),f334(f39(x96232),x96234)),f334(f39(x96231),x96233)))+P104(f334(f334(f249(f886(x96231,a871)),f334(f313(x96232,x96231,f823(x96233,x96231,x96234,x96232)),x96234)),x96233)) % 169.39/169.66 [9284]~P104(f334(f334(f336(x92841),x92842),x92844))+P104(f334(f334(f336(x92841),x92842),x92843))+~P104(f334(f334(f250(f886(x92841,a871)),x92844),f334(f334(f312(x92841),x92842),x92843)))+P104(f334(f334(f250(f886(x92841,a871)),f334(f334(f3(f886(x92841,a871)),x92844),f334(f334(f312(x92841),x92842),f195(f886(x92841,a871))))),x92843)) % 169.39/169.66 [9439]~P104(f334(f334(f336(x94391),x94392),x94394))+P104(f334(f334(f336(x94391),x94392),x94393))+P104(f334(f334(f250(f886(x94391,a871)),x94394),f334(f334(f312(x94391),x94392),x94393)))+~P104(f334(f334(f250(f886(x94391,a871)),f334(f334(f3(f886(x94391,a871)),x94394),f334(f334(f312(x94391),x94392),f195(f886(x94391,a871))))),x94393)) % 169.39/169.66 [9468]P104(f334(f334(f336(x94681),x94682),x94683))+~P104(f334(f334(f249(f886(x94681,a871)),x94684),x94683))+P104(f334(f334(f250(f886(x94681,a871)),x94684),f334(f334(f312(x94681),x94682),x94683)))+~P104(f334(f334(f250(f886(x94681,a871)),f334(f334(f3(f886(x94681,a871)),x94684),f334(f334(f312(x94681),x94682),f195(f886(x94681,a871))))),x94683)) % 169.39/169.66 [9473]~P104(f334(f334(f336(x94731),x94733),x94732))+~P104(f334(f334(f250(f886(x94731,a871)),x94732),x94734))+P104(f334(f334(f250(f886(x94731,a871)),x94732),f334(f334(f312(x94731),x94733),x94734)))+~P104(f334(f334(f250(f886(x94731,a871)),f334(f334(f3(f886(x94731,a871)),x94732),f334(f334(f312(x94731),x94733),f195(f886(x94731,a871))))),x94734)) % 169.39/169.66 [9485]~P104(f334(f334(f249(f886(x94851,a871)),x94852),x94854))+~P104(f334(f334(f250(f886(x94851,a871)),x94852),x94854))+P104(f334(f334(f250(f886(x94851,a871)),x94852),f334(f334(f312(x94851),x94853),x94854)))+~P104(f334(f334(f250(f886(x94851,a871)),f334(f334(f3(f886(x94851,a871)),x94852),f334(f334(f312(x94851),x94853),f195(f886(x94851,a871))))),x94854)) % 169.39/169.66 [9526]~P108(x95262)+~P58(x95261)+~P104(f334(f334(f249(f886(x95261,x95262)),x95263),x95264))+P104(f334(f60(x95261),f334(f334(f20(x95261,x95262,a871),f334(f334(f10(x95262,f886(x95262,a871),x95261),f249(x95262)),x95263)),x95264))) % 169.39/169.66 [9670]~P108(x96702)+~P58(x96701)+P104(f334(f334(f249(f886(x96701,x96702)),x96703),x96704))+~P104(f334(f60(x96701),f334(f334(f20(x96701,x96702,a871),f334(f334(f10(x96702,f886(x96702,a871),x96701),f249(x96702)),x96703)),x96704))) % 169.39/169.66 [9841]E(f334(f334(f165(x98411),f334(f334(f165(f878(x98411)),f181(x98411,x98412)),x98413)),x98414),f334(f334(f165(x98411),f334(f334(f165(f878(x98411)),x98412),x98414)),x98413))+~P104(f334(f334(f250(a877),x98413),f334(f196(f878(f878(x98411))),f181(x98411,x98412))))+~P30(a877,f334(f169(a877),f334(f334(f154(f878(x98411),a877),f196(f878(x98411))),x98412)))+~P104(f334(f334(f250(a877),x98414),f334(f196(f878(f878(x98411))),f334(f136(f878(x98411),f334(f334(f10(a877,a871,f878(x98411)),f334(f250(a877),x98413)),f196(f878(x98411)))),x98412)))) % 169.39/169.66 [9868]~P104(f334(f334(f336(f885(a877,a877)),x98684),x98681))+~P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),x98684),x98682)),a36))+~P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x98681),x98683)),a37))+P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x98681),f334(f334(f312(f885(a877,a877)),x98682),x98683))),a37)) % 169.39/169.66 [9869]~P104(f334(f334(f336(f885(a877,a877)),x98694),x98691))+~P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),x98694),x98692)),a71))+~P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x98691),x98693)),a72))+P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x98691),f334(f334(f312(f885(a877,a877)),x98692),x98693))),a72)) % 169.39/169.66 [9755]~P108(x97552)+~P58(x97551)+~P104(f334(f334(f250(f886(x97551,x97552)),x97553),x97554))+P104(f334(f59(x97551),f334(f334(f10(a871,a871,x97551),a329),f334(f334(f20(x97551,x97552,a871),f334(f334(f10(x97552,f886(x97552,a871),x97551),a331),x97553)),x97554)))) % 169.39/169.66 [9882]~P104(f334(f334(f336(f885(a877,a877)),x98824),x98823))+~P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),x98821),x98824)),a71))+~P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x98822),x98823)),a70))+P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),f334(f334(f312(f885(a877,a877)),x98821),x98822)),x98823)),a70)) % 169.39/169.66 [9883]~P104(f334(f334(f336(f885(a877,a877)),x98834),x98833))+~P104(f334(f334(f336(f885(f885(a877,a877),f885(a877,a877))),f334(f334(f269(f885(a877,a877),f885(a877,a877)),x98831),x98834)),a36))+~P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),x98832),x98833)),a38))+P104(f334(f334(f336(f885(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871))),f334(f334(f269(f886(f885(a877,a877),a871),f886(f885(a877,a877),a871)),f334(f334(f312(f885(a877,a877)),x98831),x98832)),x98833)),a38)) % 169.39/169.66 [6070]~P5(x60704,x60701)+~P104(f334(f334(x60701,x60702),x60705))+P104(f334(f334(x60701,x60702),x60703))+~P104(f334(f334(x60701,x60705),x60703)) % 169.39/169.66 [5332]~P64(x53325)+E(x53321,x53322)+~E(x53323,x53324)+~E(f334(f334(f3(x53325),x53323),x53324),f334(f334(f3(x53325),x53321),x53322)) % 169.39/169.66 [6178]~P13(x61785,x61781,x61783)+E(f334(f334(x61781,x61782),f334(x61783,x61784)),f334(x61783,x61784))+~P104(f334(f63(x61785),x61784))+~P104(f334(f334(f336(x61785),x61782),x61784)) % 169.39/169.66 [6372]~P75(x63721)+~E(f334(f334(f3(x63721),x63724),x63725),f334(f334(f3(x63721),x63722),x63723))+~P104(f334(f334(f249(x63721),x63724),x63725))+P104(f334(f334(f249(x63721),x63722),x63723)) % 169.39/169.66 [6374]~P75(x63741)+~E(f334(f334(f3(x63741),x63744),x63745),f334(f334(f3(x63741),x63742),x63743))+~P104(f334(f334(f250(x63741),x63744),x63745))+P104(f334(f334(f250(x63741),x63742),x63743)) % 169.39/169.66 [7334]~E(x73342,f334(f334(f151(x73341),x73344),x73345))+P104(f334(f334(f336(f878(x73341)),x73342),f161(x73341,x73343)))+~P104(f334(f334(f336(f878(x73341)),x73345),f161(x73341,x73343)))+~P104(f334(f334(f336(x73341),x73344),x73343)) % 169.39/169.66 [7749]~E(f334(f196(f878(x77491)),x77493),f334(f196(f878(x77492)),x77494))+~E(f334(f334(f154(f885(x77491,x77492),x77492),f272(x77491,x77492)),x77495),x77494)+~E(f334(f334(f154(f885(x77491,x77492),x77491),f268(x77491,x77492)),x77495),x77493)+E(f334(f334(f183(x77491,x77492),x77493),x77494),x77495) % 169.39/169.66 [8078]~P108(x80781)+P104(f334(f334(f250(f886(x80781,a871)),f305(x80781,x80782,x80783)),f305(x80781,x80784,x80785)))+~P104(f334(f334(f249(x80781),x80784),x80785))+P104(f334(f334(f249(x80781),x80782),x80783)) % 169.39/169.66 [8172]~P108(x81721)+P104(f334(f334(f249(f886(x81721,a871)),f305(x81721,x81722,x81723)),f305(x81721,x81724,x81725)))+~P104(f334(f334(f249(x81721),x81723),x81725))+~P104(f334(f334(f249(x81721),x81724),x81722)) % 169.39/169.66 [8297]~P107(x82971)+P104(f334(f334(f249(x82971),x82972),x82973))+P104(f334(f334(f249(x82971),x82974),x82973))+~P104(f334(f334(f249(f886(x82971,a871)),f334(f304(x82971,x82973),x82972)),f334(f304(x82971,x82974),x82975))) % 169.39/169.66 [8298]~P107(x82981)+P104(f334(f334(f249(x82981),x82982),x82983))+P104(f334(f334(f249(x82981),x82982),x82984))+~P104(f334(f334(f249(f886(x82981,a871)),f334(f304(x82981,x82983),x82982)),f334(f304(x82981,x82985),x82984))) % 169.39/169.66 [8523]~P108(x85231)+~P104(f334(f334(f249(f886(x85231,a871)),f305(x85231,x85234,x85232)),f305(x85231,x85235,x85233)))+P104(f334(f334(f249(x85231),x85232),x85233))+~P104(f334(f334(f249(x85231),x85234),x85232)) % 169.39/169.66 [8524]~P108(x85241)+~P104(f334(f334(f250(f886(x85241,a871)),f305(x85241,x85244,x85242)),f305(x85241,x85245,x85243)))+P104(f334(f334(f249(x85241),x85242),x85243))+~P104(f334(f334(f249(x85241),x85244),x85242)) % 169.39/169.66 [8525]~P108(x85251)+~P104(f334(f334(f249(f886(x85251,a871)),f305(x85251,x85253,x85254)),f305(x85251,x85252,x85255)))+P104(f334(f334(f249(x85251),x85252),x85253))+~P104(f334(f334(f249(x85251),x85253),x85254)) % 169.39/169.66 [8526]~P108(x85261)+~P104(f334(f334(f250(f886(x85261,a871)),f305(x85261,x85263,x85264)),f305(x85261,x85262,x85265)))+P104(f334(f334(f249(x85261),x85262),x85263))+~P104(f334(f334(f249(x85261),x85263),x85264)) % 169.39/169.66 [6069]~P13(x60692,x60695,x60693)+E(x60691,f195(f886(x60692,a871)))+~P104(f334(f63(x60692),x60691))+E(f334(x60693,f334(f334(f312(x60692),x60694),x60691)),f334(f334(x60695,x60694),f334(x60693,x60691))) % 169.39/169.66 [6837]~E(x68371,x68372)+~E(f334(f334(f104(f886(x68373,a871)),x68374),x68375),f195(f886(x68373,a871)))+~P104(f334(f334(f336(x68373),x68372),x68375))+~P104(f334(f334(f336(x68373),x68371),x68374)) % 169.39/169.66 [6919]~P14(x69192,x69195,x69191)+~P104(f334(f63(x69192),x69194))+E(f334(x69191,f334(f334(f312(x69192),x69193),x69194)),f334(f334(f66(x69192,x69192,x69195),x69193),x69194))+P104(f334(f334(f336(x69192),x69193),x69194)) % 169.39/169.66 [6984]~P72(x69842)+~P104(f334(f63(x69841),x69845))+E(f334(f334(f8(x69841,x69842),x69843),f334(f334(f312(x69841),x69844),x69845)),f334(f334(f81(x69842),f334(x69843,x69844)),f334(f334(f8(x69841,x69842),x69843),x69845)))+P104(f334(f334(f336(x69841),x69844),x69845)) % 169.39/169.66 [6986]~P68(x69862)+~P104(f334(f63(x69861),x69865))+E(f334(f334(f11(x69861,x69862),x69863),f334(f334(f312(x69861),x69864),x69865)),f334(f334(f82(x69862),f334(x69863,x69864)),f334(f334(f11(x69861,x69862),x69863),x69865)))+P104(f334(f334(f336(x69861),x69864),x69865)) % 169.39/169.66 [7488]~P14(x74882,x74885,x74881)+~P104(f334(f63(x74882),x74884))+E(f334(x74881,f334(f334(f312(x74882),x74883),x74884)),x74883)+~E(f334(f334(f3(f886(x74882,a871)),x74884),f334(f334(f312(x74882),x74883),f195(f886(x74882,a871)))),f195(f886(x74882,a871))) % 169.39/169.66 [7851]~P82(x78511)+~P104(f334(f334(f249(x78511),x78513),x78515))+~P104(f334(f334(f249(x78511),x78512),x78514))+P104(f334(f334(f249(x78511),f334(f334(f81(x78511),x78512),x78513)),f334(f334(f81(x78511),x78514),x78515))) % 169.39/169.66 [7852]~P100(x78521)+~P104(f334(f334(f249(x78521),x78523),x78525))+~P104(f334(f334(f249(x78521),x78522),x78524))+P104(f334(f334(f249(x78521),f334(f334(f113(x78521),x78522),x78523)),f334(f334(f113(x78521),x78524),x78525))) % 169.39/169.66 [7853]~P101(x78531)+~P104(f334(f334(f249(x78531),x78533),x78535))+~P104(f334(f334(f249(x78531),x78532),x78534))+P104(f334(f334(f249(x78531),f334(f334(f104(x78531),x78532),x78533)),f334(f334(f104(x78531),x78534),x78535))) % 169.39/169.66 [7854]~P107(x78541)+~P104(f334(f334(f249(x78541),x78543),x78545))+~P104(f334(f334(f249(x78541),x78542),x78544))+P104(f334(f334(f249(x78541),f334(f334(f247(x78541),x78542),x78543)),f334(f334(f247(x78541),x78544),x78545))) % 169.39/169.66 [7855]~P107(x78551)+~P104(f334(f334(f249(x78551),x78553),x78555))+~P104(f334(f334(f249(x78551),x78552),x78554))+P104(f334(f334(f249(x78551),f334(f334(f248(x78551),x78552),x78553)),f334(f334(f248(x78551),x78554),x78555))) % 169.39/169.66 [7856]~P84(x78561)+~P104(f334(f334(f249(x78561),x78563),x78565))+~P104(f334(f334(f250(x78561),x78562),x78564))+P104(f334(f334(f250(x78561),f334(f334(f81(x78561),x78562),x78563)),f334(f334(f81(x78561),x78564),x78565))) % 169.39/169.66 [7857]~P84(x78571)+~P104(f334(f334(f249(x78571),x78572),x78574))+~P104(f334(f334(f250(x78571),x78573),x78575))+P104(f334(f334(f250(x78571),f334(f334(f81(x78571),x78572),x78573)),f334(f334(f81(x78571),x78574),x78575))) % 169.39/169.66 [7858]~P84(x78581)+~P104(f334(f334(f250(x78581),x78583),x78585))+~P104(f334(f334(f250(x78581),x78582),x78584))+P104(f334(f334(f250(x78581),f334(f334(f81(x78581),x78582),x78583)),f334(f334(f81(x78581),x78584),x78585))) % 169.39/169.66 [7995]~P138(x79955)+E(x79951,x79952)+E(x79953,x79954)+~E(f334(f334(f81(x79955),f334(f334(f82(x79955),x79953),x79951)),f334(f334(f82(x79955),x79954),x79952)),f334(f334(f81(x79955),f334(f334(f82(x79955),x79953),x79952)),f334(f334(f82(x79955),x79954),x79951))) % 169.39/169.66 [8128]P31(x81281,x81282,x81283)+~P23(x81281,x81284,x81285)+~P31(x81281,x81282,f599(x81285,x81284,x81281,x81282))+~P104(f334(f334(f336(f876(x81281)),x81283),x81285)) % 169.39/169.66 [8195]~P107(x81954)+~P104(f334(f137(x81951),x81953))+P104(f334(f334(f336(x81951),x81952),f334(f173(x81951),x81953)))+P104(f334(f137(x81951),f334(f334(f148(x81951,x81954,x81955),x81952),x81953))) % 169.39/169.66 [8341]~P64(x83411)+E(f334(f334(f3(x83411),f334(f334(f8(a877,x83411),x83412),f334(f304(a877,x83413),x83414))),f334(f334(f8(a877,x83411),x83412),f334(f304(a877,x83413),x83415))),f334(f334(f8(a877,x83411),x83412),f334(f304(a877,x83415),x83414)))+~P104(f334(f334(f249(a877),x83415),x83414))+~P104(f334(f334(f249(a877),x83413),x83415)) % 169.39/169.66 [8342]~P72(x83421)+E(f334(f334(f81(x83421),f334(f334(f8(a877,x83421),x83422),f334(f304(a877,x83423),x83424))),f334(f334(f8(a877,x83421),x83422),f334(f304(a877,x83424),x83425))),f334(f334(f8(a877,x83421),x83422),f334(f304(a877,x83423),x83425)))+~P104(f334(f334(f249(a877),x83424),x83425))+~P104(f334(f334(f249(a877),x83423),x83424)) % 169.39/169.66 [8659]~P60(x86592)+E(x86591,f2(x86592))+E(x86593,f2(x86592))+E(f334(f334(f292(x86592),f334(f334(f3(x86592),f334(f334(f82(x86592),x86594),x86591)),f334(f334(f82(x86592),x86595),x86593))),f334(f334(f82(x86592),x86593),x86591)),f334(f334(f3(x86592),f334(f334(f292(x86592),x86594),x86593)),f334(f334(f292(x86592),x86595),x86591))) % 169.39/169.66 [8660]~P60(x86602)+E(x86601,f2(x86602))+E(x86603,f2(x86602))+E(f334(f334(f292(x86602),f334(f334(f81(x86602),f334(f334(f82(x86602),x86604),x86601)),f334(f334(f82(x86602),x86605),x86603))),f334(f334(f82(x86602),x86603),x86601)),f334(f334(f81(x86602),f334(f334(f292(x86602),x86604),x86603)),f334(f334(f292(x86602),x86605),x86601))) % 169.39/169.66 [8669]~E(x86692,f334(x86693,x86691))+E(x86691,f418(x86692,x86693,x86694,x86695))+~P21(x86695,x86694,x86693,f257(f886(x86695,a871)))+~P104(f334(f334(f336(x86694),x86692),f334(f313(x86695,x86694,x86693),f257(f886(x86695,a871))))) % 169.39/169.66 [8863]~P120(x88631)+~P104(f334(f334(f250(x88631),f334(f76(x88631),x88632)),x88634))+P104(f334(f334(f250(x88631),f334(f334(f82(x88631),f334(f76(x88631),x88632)),f334(f76(x88631),x88633))),f334(f334(f82(x88631),x88634),x88635)))+~P104(f334(f334(f250(x88631),f334(f76(x88631),x88633)),x88635)) % 169.39/169.66 [8880]~P23(x88801,x88805,x88804)+P31(x88801,x88802,x88803)+P104(f334(f334(f336(f876(x88801)),f599(x88804,x88805,x88801,x88802)),x88805))+~P104(f334(f334(f336(f876(x88801)),x88803),x88804)) % 169.39/169.66 [8977]~P21(x89771,x89773,x89775,x89772)+~P104(f334(f63(x89773),x89774))+P104(f334(f334(f249(a877),f334(f39(x89771),x89772)),f334(f39(x89773),x89774)))+~P104(f334(f334(f249(f886(x89773,a871)),f334(f313(x89771,x89773,x89775),x89772)),x89774)) % 169.39/169.66 [9044]~P72(x90442)+~P21(x90441,x90441,x90444,x90445)+~P104(f334(f63(x90441),x90445))+E(f334(f334(f8(x90441,x90442),f334(f74(x90441,x90442,x90441,x90443),x90444)),x90445),f334(f334(f8(x90441,x90442),x90443),f334(f313(x90441,x90441,x90444),x90445))) % 169.39/169.66 [9045]~P68(x90452)+~P21(x90451,x90451,x90454,x90455)+~P104(f334(f63(x90451),x90455))+E(f334(f334(f11(x90451,x90452),f334(f74(x90451,x90452,x90451,x90453),x90454)),x90455),f334(f334(f11(x90451,x90452),x90453),f334(f313(x90451,x90451,x90454),x90455))) % 169.39/169.66 [9158]~P39(x91581,x91582)+~P104(f334(f334(f336(x91581),x91583),x91584))+~P104(f334(f334(f336(x91581),x91585),x91584))+~P104(f334(f334(f336(f885(x91581,x91581)),f334(f334(f269(x91581,x91581),x91585),f760(x91582,x91581,x91584))),x91582)) % 169.39/169.66 [9194]~P21(x91942,x91943,x91945,x91941)+E(x91941,f195(f886(x91942,a871)))+E(f334(f313(x91943,x91942,f824(x91944,x91943,x91942,x91941)),x91944),x91941)+~P104(f334(f334(f249(f886(x91943,a871)),f334(f313(x91942,x91943,x91945),x91941)),x91944)) % 169.39/169.66 [9652]~P107(x96525)+~P28(x96525)+P104(f334(f334(f336(x96521),f527(x96522,x96523,x96521,x96524,x96525)),x96523))+~P104(f334(f334(f250(x96525),x96524),f334(f334(f44(x96521,x96525),x96523),x96522))) % 169.39/169.66 [9657]~P107(x96571)+~P28(x96571)+P104(f334(f334(f250(x96571),x96572),f334(x96573,f527(x96573,x96574,x96575,x96572,x96571))))+~P104(f334(f334(f250(x96571),x96572),f334(f334(f44(x96575,x96571),x96574),x96573))) % 169.39/169.66 [9735]~P65(x97351)+~P104(f334(f68(x97351,x97351,f82(x97351),x97352,x97353),x97355))+P104(f334(f334(f336(x97351),x97352),x97353))+P104(f334(f68(x97351,x97351,f82(x97351),x97354,f334(f334(f312(x97351),x97352),x97353)),f334(f334(f82(x97351),x97354),x97355))) % 169.39/169.66 [9950]~P72(x99502)+~P104(f334(f63(x99501),x99505))+E(f334(f334(f8(x99501,x99502),f334(f334(f9(x99501,x99502,x99502),f334(f334(f20(x99501,x99502,f886(x99502,x99502)),f334(f334(f10(a871,f886(x99502,f886(x99502,x99502)),x99501),f99(x99502)),f334(a331,x99503))),x99504)),f2(x99502))),x99505),f2(x99502))+P104(f334(f334(f336(x99501),x99503),x99505)) % 169.39/169.66 [9951]~P68(x99512)+~P104(f334(f63(x99511),x99515))+E(f334(f334(f11(x99511,x99512),f334(f334(f9(x99511,x99512,x99512),f334(f334(f20(x99511,x99512,f886(x99512,x99512)),f334(f334(f10(a871,f886(x99512,f886(x99512,x99512)),x99511),f99(x99512)),f334(a331,x99513))),x99514)),f79(x99512))),x99515),f79(x99512))+P104(f334(f334(f336(x99511),x99513),x99515)) % 169.39/169.66 [9952]~P72(x99522)+~P104(f334(f63(x99521),x99525))+E(f334(f334(f8(x99521,x99522),f334(f334(f9(x99521,x99522,x99522),f334(f334(f20(x99521,x99522,f886(x99522,x99522)),f334(f334(f10(a871,f886(x99522,f886(x99522,x99522)),x99521),f99(x99522)),f334(a331,x99523))),x99524)),f2(x99522))),x99525),f334(x99524,x99523))+~P104(f334(f334(f336(x99521),x99523),x99525)) % 169.39/169.66 [9953]~P68(x99532)+~P104(f334(f63(x99531),x99535))+E(f334(f334(f11(x99531,x99532),f334(f334(f9(x99531,x99532,x99532),f334(f334(f20(x99531,x99532,f886(x99532,x99532)),f334(f334(f10(a871,f886(x99532,f886(x99532,x99532)),x99531),f99(x99532)),f334(a331,x99533))),x99534)),f79(x99532))),x99535),f334(x99534,x99533))+~P104(f334(f334(f336(x99531),x99533),x99535)) % 169.39/169.66 [10008]~P72(x100082)+~P104(f334(f63(x100081),x100085))+E(f334(f334(f8(x100081,x100082),f334(f334(f9(x100081,x100082,x100082),f334(f334(f20(x100081,x100082,f886(x100082,x100082)),f334(f334(f10(a871,f886(x100082,f886(x100082,x100082)),x100081),f99(x100082)),f334(f334(f9(x100081,x100081,a871),a331),x100083))),x100084)),f2(x100082))),x100085),f2(x100082))+P104(f334(f334(f336(x100081),x100083),x100085)) % 169.39/169.66 [10009]~P68(x100092)+~P104(f334(f63(x100091),x100095))+E(f334(f334(f11(x100091,x100092),f334(f334(f9(x100091,x100092,x100092),f334(f334(f20(x100091,x100092,f886(x100092,x100092)),f334(f334(f10(a871,f886(x100092,f886(x100092,x100092)),x100091),f99(x100092)),f334(f334(f9(x100091,x100091,a871),a331),x100093))),x100094)),f79(x100092))),x100095),f79(x100092))+P104(f334(f334(f336(x100091),x100093),x100095)) % 169.39/169.66 [10011]~P72(x100112)+~P104(f334(f63(x100111),x100115))+E(f334(f334(f8(x100111,x100112),f334(f334(f9(x100111,x100112,x100112),f334(f334(f20(x100111,x100112,f886(x100112,x100112)),f334(f334(f10(a871,f886(x100112,f886(x100112,x100112)),x100111),f99(x100112)),f334(f334(f9(x100111,x100111,a871),a331),x100113))),x100114)),f2(x100112))),x100115),f334(x100114,x100113))+~P104(f334(f334(f336(x100111),x100113),x100115)) % 169.39/169.66 [10012]~P68(x100122)+~P104(f334(f63(x100121),x100125))+E(f334(f334(f11(x100121,x100122),f334(f334(f9(x100121,x100122,x100122),f334(f334(f20(x100121,x100122,f886(x100122,x100122)),f334(f334(f10(a871,f886(x100122,f886(x100122,x100122)),x100121),f99(x100122)),f334(f334(f9(x100121,x100121,a871),a331),x100123))),x100124)),f79(x100122))),x100125),f334(x100124,x100123))+~P104(f334(f334(f336(x100121),x100123),x100125)) % 169.39/169.66 [7850]~P64(x78502)+~P104(f334(f63(x78501),x78504))+E(f334(f334(f8(x78501,x78502),x78503),f334(f334(f3(f886(x78501,a871)),x78504),f334(f334(f312(x78501),x78505),f195(f886(x78501,a871))))),f334(f334(f8(x78501,x78502),x78503),x78504))+P104(f334(f334(f336(x78501),x78505),x78504)) % 169.39/169.66 [8347]~P109(x83472)+~P104(f334(f63(x83471),x83474))+E(f334(f334(f8(x83471,x83472),x83473),f334(f334(f3(f886(x83471,a871)),x83474),f334(f334(f312(x83471),x83475),f195(f886(x83471,a871))))),f334(f334(f3(x83472),f334(f334(f8(x83471,x83472),x83473),x83474)),f334(x83473,x83475)))+~P104(f334(f334(f336(x83471),x83475),x83474)) % 169.39/169.66 [8348]~P64(x83482)+~P104(f334(f63(x83481),x83484))+E(f334(f334(f8(x83481,x83482),x83483),f334(f334(f3(f886(x83481,a871)),x83484),f334(f334(f312(x83481),x83485),f195(f886(x83481,a871))))),f334(f334(f3(x83482),f334(f334(f8(x83481,x83482),x83483),x83484)),f334(x83483,x83485)))+~P104(f334(f334(f336(x83481),x83485),x83484)) % 169.39/169.66 [8379]~P64(x83791)+~P104(f334(f63(x83792),x83794))+E(f334(f334(f3(x83791),f334(f334(f8(x83792,x83791),x83793),x83794)),f334(f334(f8(x83792,x83791),x83793),x83795)),f334(f334(f8(x83792,x83791),x83793),f334(f334(f3(f886(x83792,a871)),x83794),x83795)))+~P104(f334(f334(f249(f886(x83792,a871)),x83795),x83794)) % 169.39/169.66 [8399]P104(f334(f63(x83991),f334(x83992,x83993)))+~P104(f334(f63(x83994),x83995))+~P104(f334(f334(f336(x83994),x83993),x83995))+~P104(f334(f63(x83991),f334(f334(f44(x83994,f886(x83991,a871)),x83995),x83992))) % 169.39/169.66 [8826]~P6(x88261,x88265,x88264)+~E(f334(f288(x88261,x88261,x88264),f334(f334(f312(x88261),x88262),f195(f886(x88261,a871)))),f334(f288(x88261,x88261,x88264),f334(f334(f312(x88261),x88263),f195(f886(x88261,a871)))))+~P104(f334(f334(f336(x88261),x88263),x88265))+P104(f334(f334(f336(f885(x88261,x88261)),f334(f334(f269(x88261,x88261),x88262),x88263)),x88264)) % 169.39/169.66 [9116]~P104(f334(x91161,x91165))+P104(f334(x91161,f407(x91161,x91162,x91163,x91164)))+P104(f334(x91161,f404(x91161,x91162,x91163,x91164)))+~P104(f334(f334(f336(x91164),x91165),f334(f334(f113(f886(x91164,a871)),x91163),x91162))) % 169.39/169.66 [9289]~P104(f334(x92891,x92895))+P104(f334(x92891,f404(x92891,x92892,x92893,x92894)))+P104(f334(f334(f336(x92894),f407(x92891,x92892,x92893,x92894)),x92892))+~P104(f334(f334(f336(x92894),x92895),f334(f334(f113(f886(x92894,a871)),x92893),x92892))) % 169.39/169.66 [9290]~P104(f334(x92901,x92905))+P104(f334(x92901,f407(x92901,x92902,x92903,x92904)))+P104(f334(f334(f336(x92904),f404(x92901,x92902,x92903,x92904)),x92903))+~P104(f334(f334(f336(x92904),x92905),f334(f334(f113(f886(x92904,a871)),x92903),x92902))) % 169.39/169.66 [9294]P104(f334(x92941,x92942))+~P104(f334(x92941,f406(x92941,x92943,x92944,x92945)))+~P104(f334(x92941,f405(x92941,x92943,x92944,x92945)))+~P104(f334(f334(f336(x92945),x92942),f334(f334(f113(f886(x92945,a871)),x92944),x92943))) % 169.39/169.66 [9336]E(x93361,x93362)+~P104(f334(f334(f336(f885(x93363,x93363)),f334(f334(f269(x93363,x93363),x93361),x93362)),f310(x93363,x93365)))+P104(f334(f334(f336(x93363),x93361),x93364))+~P104(f334(f334(f249(f886(f885(x93363,x93363),a871)),x93365),f334(f334(f271(x93363,x93363),x93364),f334(f18(f886(x93363,a871),x93363),x93364)))) % 169.39/169.66 [9354]P104(f334(x93541,x93542))+~P104(f334(x93541,f405(x93541,x93544,x93545,x93543)))+P104(f334(f334(f336(x93543),f406(x93541,x93544,x93545,x93543)),x93544))+~P104(f334(f334(f336(x93543),x93542),f334(f334(f113(f886(x93543,a871)),x93545),x93544))) % 169.39/169.66 [9355]P104(f334(x93551,x93552))+~P104(f334(x93551,f406(x93551,x93554,x93555,x93553)))+P104(f334(f334(f336(x93553),f405(x93551,x93554,x93555,x93553)),x93555))+~P104(f334(f334(f336(x93553),x93552),f334(f334(f113(f886(x93553,a871)),x93555),x93554))) % 169.39/169.66 [9414]P104(f334(x94141,x94142))+P104(f334(f334(f336(x94143),f406(x94141,x94144,x94145,x94143)),x94144))+P104(f334(f334(f336(x94143),f405(x94141,x94144,x94145,x94143)),x94145))+~P104(f334(f334(f336(x94143),x94142),f334(f334(f113(f886(x94143,a871)),x94145),x94144))) % 169.39/169.66 [9416]~P104(f334(x94162,x94165))+P104(f334(f334(f336(x94161),f407(x94162,x94163,x94164,x94161)),x94163))+P104(f334(f334(f336(x94161),f404(x94162,x94163,x94164,x94161)),x94164))+~P104(f334(f334(f336(x94161),x94165),f334(f334(f113(f886(x94161,a871)),x94164),x94163))) % 169.39/169.66 [9559]~P6(x95591,x95595,x95594)+~P104(f334(f334(f336(x95591),x95593),x95595))+P104(f334(f334(f336(f885(x95591,x95591)),f334(f334(f269(x95591,x95591),x95592),x95593)),x95594))+~P104(f334(f334(f249(f886(x95591,a871)),f334(f288(x95591,x95591,x95594),f334(f334(f312(x95591),x95593),f195(f886(x95591,a871))))),f334(f288(x95591,x95591,x95594),f334(f334(f312(x95591),x95592),f195(f886(x95591,a871)))))) % 169.39/169.66 [9683]~P107(x96835)+~P28(x96835)+P104(f334(f334(f336(x96831),f521(x96832,x96833,x96834,x96831,x96835)),x96834))+~P104(f334(f334(f250(x96835),f334(f334(f43(x96831,x96835),x96834),x96833)),x96832)) % 169.39/169.66 [9715]~P82(x97155)+~P78(x97155)+P104(f334(f334(f336(x97151),f627(x97152,x97153,x97154,x97151,x97155)),f334(f173(x97151),x97154)))+P104(f334(f334(f249(x97155),f334(f166(x97155),f334(f334(f154(x97151,x97155),x97153),x97154))),f334(f166(x97155),f334(f334(f154(x97151,x97155),x97152),x97154)))) % 169.39/169.66 [9831]~P107(x98311)+~P28(x98311)+P104(f334(f334(f250(x98311),f334(x98312,f521(x98313,x98312,x98314,x98315,x98311))),x98313))+~P104(f334(f334(f250(x98311),f334(f334(f43(x98315,x98311),x98314),x98312)),x98313)) % 169.39/169.66 [9968]~P82(x99681)+~P78(x99681)+~P104(f334(f334(f249(x99681),f334(x99683,f627(x99685,x99683,x99684,x99682,x99681))),f334(x99685,f627(x99685,x99683,x99684,x99682,x99681))))+P104(f334(f334(f249(x99681),f334(f166(x99681),f334(f334(f154(x99682,x99681),x99683),x99684))),f334(f166(x99681),f334(f334(f154(x99682,x99681),x99685),x99684)))) % 169.39/169.66 [8677]~P72(x86771)+~P104(f334(f63(x86774),x86775))+~P104(f334(f334(f336(x86774),x86773),x86775))+E(f334(f334(f81(x86771),f334(x86772,x86773)),f334(f334(f8(x86774,x86771),x86772),f334(f334(f3(f886(x86774,a871)),x86775),f334(f334(f312(x86774),x86773),f195(f886(x86774,a871)))))),f334(f334(f8(x86774,x86771),x86772),x86775)) % 169.39/169.66 [8678]~P68(x86781)+~P104(f334(f63(x86784),x86785))+~P104(f334(f334(f336(x86784),x86783),x86785))+E(f334(f334(f82(x86781),f334(x86782,x86783)),f334(f334(f11(x86784,x86781),x86782),f334(f334(f3(f886(x86784,a871)),x86785),f334(f334(f312(x86784),x86783),f195(f886(x86784,a871)))))),f334(f334(f11(x86784,x86781),x86782),x86785)) % 169.39/169.66 [8733]~P14(x87331,x87334,x87335)+~P104(f334(f63(x87331),x87332))+E(f334(f334(f3(f886(x87331,a871)),x87332),f334(f334(f312(x87331),x87333),f195(f886(x87331,a871)))),f195(f886(x87331,a871)))+E(f334(f334(x87334,x87333),f334(x87335,f334(f334(f3(f886(x87331,a871)),x87332),f334(f334(f312(x87331),x87333),f195(f886(x87331,a871)))))),f334(x87335,f334(f334(f312(x87331),x87333),x87332))) % 169.39/169.66 [9096]~P68(x90961)+~P104(f334(f63(x90962),x90965))+~P104(f334(f63(x90962),x90964))+E(f334(f334(f82(x90961),f334(f334(f11(x90962,x90961),x90963),f334(f334(f113(f886(x90962,a871)),x90964),x90965))),f334(f334(f11(x90962,x90961),x90963),f334(f334(f104(f886(x90962,a871)),x90964),x90965))),f334(f334(f82(x90961),f334(f334(f11(x90962,x90961),x90963),x90964)),f334(f334(f11(x90962,x90961),x90963),x90965))) % 169.39/169.66 [9097]~P72(x90971)+~P104(f334(f63(x90972),x90975))+~P104(f334(f63(x90972),x90974))+E(f334(f334(f81(x90971),f334(f334(f8(x90972,x90971),x90973),f334(f334(f113(f886(x90972,a871)),x90974),x90975))),f334(f334(f8(x90972,x90971),x90973),f334(f334(f104(f886(x90972,a871)),x90974),x90975))),f334(f334(f81(x90971),f334(f334(f8(x90972,x90971),x90973),x90974)),f334(f334(f8(x90972,x90971),x90973),x90975))) % 169.39/169.66 [9231]~P64(x92311)+~P104(f334(f63(x92312),x92315))+~P104(f334(f63(x92312),x92314))+E(f334(f334(f3(x92311),f334(f334(f81(x92311),f334(f334(f8(x92312,x92311),x92313),x92314)),f334(f334(f8(x92312,x92311),x92313),x92315))),f334(f334(f8(x92312,x92311),x92313),f334(f334(f104(f886(x92312,a871)),x92314),x92315))),f334(f334(f8(x92312,x92311),x92313),f334(f334(f113(f886(x92312,a871)),x92314),x92315))) % 169.39/169.66 [9425]~P21(x94251,x94252,x94253,x94255)+~P21(x94251,x94252,x94253,x94254)+P21(x94251,x94252,x94253,f334(f334(f113(f886(x94251,a871)),x94254),x94255))+~E(f334(f334(f104(f886(x94252,a871)),f334(f313(x94251,x94252,x94253),f334(f334(f3(f886(x94251,a871)),x94254),x94255))),f334(f313(x94251,x94252,x94253),f334(f334(f3(f886(x94251,a871)),x94255),x94254))),f195(f886(x94252,a871))) % 169.39/169.66 [9534]E(x95341,f2(a1))+~P104(f334(f334(f250(a1),f2(a1)),x95343))+~P104(f334(f50(x95342,x95341),f334(f334(f269(a1,a1),x95344),x95345)))+P104(f334(f50(x95342,f334(f334(f82(a1),x95341),x95343)),f334(f334(f269(a1,a1),f334(f334(f40(a1),x95344),x95343)),f334(f334(f81(a1),f334(f334(f82(a1),x95341),f46(a1,x95344,x95343))),x95345)))) % 169.39/169.66 [9542]~P104(f334(f334(f250(a877),f2(a877)),x95423))+~P104(f334(f334(f250(a877),f2(a877)),x95422))+~P104(f334(f49(x95421,x95422),f334(f334(f269(a877,a877),x95424),x95425)))+P104(f334(f49(x95421,f334(f334(f82(a877),x95422),x95423)),f334(f334(f269(a877,a877),f334(f334(f40(a877),x95424),x95423)),f334(f334(f81(a877),f334(f334(f82(a877),x95422),f46(a877,x95424,x95423))),x95425)))) % 169.39/169.66 [9591]~P68(x95911)+~P104(f334(f63(x95912),x95915))+~P104(f334(f63(x95912),x95914))+E(f334(f334(f82(x95911),f334(f334(f334(f67(x95911,x95912,f82(x95911)),x95913),f79(x95911)),f334(f334(f113(f886(x95912,a871)),x95914),x95915))),f334(f334(f334(f67(x95911,x95912,f82(x95911)),x95913),f79(x95911)),f334(f334(f104(f886(x95912,a871)),x95914),x95915))),f334(f334(f82(x95911),f334(f334(f334(f67(x95911,x95912,f82(x95911)),x95913),f79(x95911)),x95914)),f334(f334(f334(f67(x95911,x95912,f82(x95911)),x95913),f79(x95911)),x95915))) % 169.39/169.66 [9593]~E(f334(f334(f176(x95931),x95935),x95932),f334(f334(f176(x95931),x95935),x95933))+P104(f334(f334(f336(f885(f878(x95931),f878(x95931))),f334(f334(f269(f878(x95931),f878(x95931)),x95932),x95933)),f147(x95931,x95934)))+~P104(f334(f334(f250(a877),x95935),f334(f334(f247(a877),f334(f196(f878(x95931)),x95932)),f334(f196(f878(x95931)),x95933))))+~P104(f334(f334(f336(f885(x95931,x95931)),f334(f334(f269(x95931,x95931),f334(f334(f165(x95931),x95932),x95935)),f334(f334(f165(x95931),x95933),x95935))),x95934)) % 169.39/169.66 [9703]~P82(x97035)+~P142(x97035)+P104(f334(f334(f336(x97031),f865(x97032,x97033,x97034,x97031,x97035)),x97034))+P104(f334(f334(f249(x97035),f334(f334(f8(x97031,x97035),x97033),x97034)),f334(f334(f82(x97035),f334(f103(x97035),f334(f39(x97031),x97034))),x97032))) % 169.39/169.66 [9896]~P82(x98961)+~P142(x98961)+~P104(f334(f334(f249(x98961),f334(x98963,f865(x98965,x98963,x98964,x98962,x98961))),x98965))+P104(f334(f334(f249(x98961),f334(f334(f8(x98962,x98961),x98963),x98964)),f334(f334(f82(x98961),f334(f103(x98961),f334(f39(x98962),x98964))),x98965))) % 169.39/169.66 [8705]E(f334(f334(f134(x87051),x87052),x87053),f334(f334(f134(x87051),x87054),x87055))+~E(f334(f334(f176(x87051),f334(f196(f878(x87051)),x87052)),x87054),x87052)+~E(f334(f334(f134(x87051),f334(f334(f138(x87051),f334(f196(f878(x87051)),x87052)),x87054)),x87055),x87053)+P104(f334(f334(f249(a877),f334(f196(f878(x87051)),x87054)),f334(f196(f878(x87051)),x87052))) % 169.39/169.66 [8825]E(f334(f334(f134(x88251),x88252),x88253),f334(f334(f134(x88251),x88254),x88255))+~E(f334(f334(f176(x88251),f334(f196(f878(x88251)),x88252)),x88254),x88252)+~E(x88253,f334(f334(f134(x88251),f334(f334(f138(x88251),f334(f196(f878(x88251)),x88252)),x88254)),x88255))+~P104(f334(f334(f249(a877),f334(f196(f878(x88251)),x88252)),f334(f196(f878(x88251)),x88254))) % 169.39/169.66 [10030]~P104(f334(x100305,x100304))+~P104(f334(f63(x100302),f334(f254(x100302),x100305)))+P104(f334(f63(x100301),f334(f254(x100301),f334(f334(f9(x100301,x100302,a871),x100303),x100304))))+~P104(f334(f63(x100301),f334(f254(x100301),f334(f334(f10(f886(x100302,a871),a871,x100301),f88(x100302)),f334(f334(f10(f886(x100302,a871),f886(x100302,a871),x100301),f334(f20(x100302,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100302),a332),x100305))),x100303))))) % 169.39/169.66 [8504]~P15(x85045,x85041,x85046,x85042)+E(f334(f74(x85041,x85041,x85041,f334(x85042,x85043)),f334(x85042,x85044)),f334(f74(x85041,x85041,x85041,f334(x85042,x85044)),f334(x85042,x85043)))+~P104(f334(f63(x85045),x85044))+~P104(f334(f63(x85045),x85043)) % 169.39/169.66 [7906]~P21(x79061,x79062,x79064,x79063)+~E(f334(x79064,x79066),x79065)+E(f334(f78(x79061,x79062,x79063,x79064),x79065),x79066)+~P104(f334(f334(f336(x79061),x79066),x79063)) % 169.39/169.66 [8098]~P16(x80986,x80981,x80984,x80982)+E(f334(f74(x80981,x80981,x80981,f334(x80982,x80983)),f334(x80984,x80985)),f334(x80982,x80983))+~P104(f334(f63(x80986),x80983))+~P104(f334(f334(f336(x80986),x80985),x80983)) % 169.39/169.66 [9275]~P15(x92753,x92751,x92756,x92752)+E(f334(f74(x92751,x92751,x92751,f334(x92752,f334(f334(f3(f886(x92753,a871)),x92754),f334(f334(f312(x92753),x92755),f195(f886(x92753,a871)))))),f334(x92756,x92755)),f334(x92752,x92754))+~P104(f334(f63(x92753),x92754))+~P104(f334(f334(f336(x92753),x92755),x92754)) % 169.39/169.66 [6989]~P27(x69891)+~E(f46(x69891,x69893,x69894),f46(x69891,x69896,x69894))+~E(f46(x69891,x69892,x69894),f46(x69891,x69895,x69894))+E(f46(x69891,f334(f334(f3(x69891),x69892),x69893),x69894),f46(x69891,f334(f334(f3(x69891),x69895),x69896),x69894)) % 169.39/169.66 [6990]~P26(x69901)+~E(f46(x69901,x69903,x69904),f46(x69901,x69906,x69904))+~E(f46(x69901,x69902,x69904),f46(x69901,x69905,x69904))+E(f46(x69901,f334(f334(f82(x69901),x69902),x69903),x69904),f46(x69901,f334(f334(f82(x69901),x69905),x69906),x69904)) % 169.39/169.66 [6991]~P26(x69911)+~E(f46(x69911,x69913,x69914),f46(x69911,x69916,x69914))+~E(f46(x69911,x69912,x69914),f46(x69911,x69915,x69914))+E(f46(x69911,f334(f334(f81(x69911),x69912),x69913),x69914),f46(x69911,f334(f334(f81(x69911),x69915),x69916),x69914)) % 169.39/169.66 [7802]~P12(x78021,x78022,x78023)+~P104(f334(f63(x78021),x78026))+E(f334(f334(f66(x78021,x78022,x78023),x78024),f334(f334(f312(x78021),x78025),x78026)),f334(f334(f66(x78021,x78022,x78023),f334(f334(x78023,x78025),x78024)),x78026))+P104(f334(f334(f336(x78021),x78025),x78026)) % 169.39/169.66 [7864]~P28(x78641)+P104(f334(f334(f249(x78641),x78642),f334(x78643,x78644)))+~P104(f334(f334(f336(x78645),x78644),x78646))+~P104(f334(f334(f249(x78641),x78642),f334(f334(f43(x78645,x78641),x78646),x78643))) % 169.39/169.66 [8022]~P12(x80221,x80222,x80223)+~P104(f334(f63(x80221),x80226))+E(f334(f334(f66(x80221,x80222,x80223),x80224),f334(f334(f312(x80221),x80225),x80226)),f334(f334(x80223,x80225),f334(f334(f66(x80221,x80222,x80223),x80224),x80226)))+P104(f334(f334(f336(x80221),x80225),x80226)) % 169.39/169.66 [8114]~P107(x81143)+~P104(f334(x81142,x81145))+~P30(x81143,f334(f334(f154(x81141,x81143),x81144),x81146))+E(f334(f136(x81141,x81142),f334(f334(f148(x81141,x81143,x81144),x81145),x81146)),f334(f334(f148(x81141,x81143,x81144),x81145),f334(f136(x81141,x81142),x81146))) % 169.39/169.66 [8136]E(x81361,x81362)+E(x81363,f2(a1))+~P104(f334(f50(x81364,x81363),f334(f334(f269(a1,a1),x81365),x81362)))+~P104(f334(f50(x81364,x81363),f334(f334(f269(a1,a1),x81366),x81361))) % 169.39/169.66 [8137]E(x81371,x81372)+E(x81373,f2(a1))+~P104(f334(f50(x81374,x81373),f334(f334(f269(a1,a1),x81372),x81375)))+~P104(f334(f50(x81374,x81373),f334(f334(f269(a1,a1),x81371),x81376))) % 169.39/169.66 [8157]~P15(x81572,x81575,x81576,x81571)+~P104(f334(f63(x81572),x81574))+E(f334(x81571,f334(f334(f312(x81572),x81573),x81574)),f334(f74(x81575,x81575,x81575,f334(x81571,x81574)),f334(x81576,x81573)))+P104(f334(f334(f336(x81572),x81573),x81574)) % 169.39/169.66 [8382]~P16(x83825,x83821,x83826,x83822)+E(f334(f74(x83821,x83821,x83821,f334(x83822,x83823)),f334(x83822,x83824)),f334(x83822,x83823))+~P104(f334(f63(x83825),x83823))+~P104(f334(f334(f249(f886(x83825,a871)),x83824),x83823)) % 169.39/169.66 [9470]~P21(x94701,x94702,x94704,x94703)+~P104(f334(f334(f336(x94702),x94705),f334(f313(x94701,x94702,x94704),x94703)))+P104(f334(f334(f336(x94701),f334(f78(x94701,x94702,x94703,x94704),x94705)),x94706))+~P104(f334(f334(f249(f886(x94701,a871)),x94703),x94706)) % 169.39/169.66 [9842]~P72(x98422)+~E(f566(x98421,x98423,x98425,x98426,x98424,x98422),f567(x98421,x98423,x98425,x98426,x98424,x98422))+~P104(f334(f63(x98424),x98426))+E(f334(f334(f8(x98421,x98422),x98423),f334(f313(x98424,x98421,x98425),x98426)),f334(f334(f8(x98424,x98422),f334(f74(x98421,x98422,x98424,x98423),x98425)),x98426)) % 169.39/169.66 [9878]~P72(x98786)+E(f334(x98781,f566(x98782,x98783,x98781,x98784,x98785,x98786)),f334(x98781,f567(x98782,x98783,x98781,x98784,x98785,x98786)))+E(f334(f334(f8(x98782,x98786),x98783),f334(f313(x98785,x98782,x98781),x98784)),f334(f334(f8(x98785,x98786),f334(f74(x98782,x98786,x98785,x98783),x98781)),x98784))+~P104(f334(f63(x98785),x98784)) % 169.39/169.66 [9918]~P72(x99182)+~E(f334(x99183,f334(x99185,f567(x99181,x99183,x99185,x99186,x99184,x99182))),f2(x99182))+~P104(f334(f63(x99184),x99186))+E(f334(f334(f8(x99181,x99182),x99183),f334(f313(x99184,x99181,x99185),x99186)),f334(f334(f8(x99184,x99182),f334(f74(x99181,x99182,x99184,x99183),x99185)),x99186)) % 169.39/169.66 [9976]~P72(x99762)+~P104(f334(f63(x99764),x99766))+E(f334(f334(f8(x99761,x99762),x99763),f334(f313(x99764,x99761,x99765),x99766)),f334(f334(f8(x99764,x99762),f334(f74(x99761,x99762,x99764,x99763),x99765)),x99766))+P104(f334(f334(f336(x99764),f567(x99761,x99763,x99765,x99766,x99764,x99762)),x99766)) % 169.39/169.66 [9977]~P72(x99772)+~P104(f334(f63(x99774),x99776))+E(f334(f334(f8(x99771,x99772),x99773),f334(f313(x99774,x99771,x99775),x99776)),f334(f334(f8(x99774,x99772),f334(f74(x99771,x99772,x99774,x99773),x99775)),x99776))+P104(f334(f334(f336(x99774),f566(x99771,x99773,x99775,x99776,x99774,x99772)),x99776)) % 169.39/169.66 [10088]~P68(x100881)+~P104(f334(f63(x100882),x100886))+E(f334(f334(f334(f67(x100881,x100882,f82(x100881)),f334(f334(f20(x100882,f886(x100883,a871),x100881),f334(f334(f9(x100882,x100881,f886(f886(x100883,a871),x100881)),f334(f334(f10(f886(x100883,x100881),f886(x100881,f886(f886(x100883,a871),x100881)),x100882),f67(x100881,x100883,f82(x100881))),x100884)),f79(x100881))),x100885)),f79(x100881)),x100886),f334(f334(f334(f67(x100881,f885(x100882,x100883),f82(x100881)),f334(f273(x100882,x100883,x100881),x100884)),f79(x100881)),f334(f334(f271(x100882,x100883),x100886),x100885)))+P104(f334(f334(f336(x100882),f702(x100884,x100885,x100883,x100886,x100882,x100881)),x100886)) % 169.39/169.66 [10106]~P68(x101061)+~P104(f334(f63(x101062),x101066))+E(f334(f334(f334(f67(x101061,x101062,f82(x101061)),f334(f334(f20(x101062,f886(x101063,a871),x101061),f334(f334(f9(x101062,x101061,f886(f886(x101063,a871),x101061)),f334(f334(f10(f886(x101063,x101061),f886(x101061,f886(f886(x101063,a871),x101061)),x101062),f67(x101061,x101063,f82(x101061))),x101064)),f79(x101061))),x101065)),f79(x101061)),x101066),f334(f334(f334(f67(x101061,f885(x101062,x101063),f82(x101061)),f334(f273(x101062,x101063,x101061),x101064)),f79(x101061)),f334(f334(f271(x101062,x101063),x101066),x101065)))+~P104(f334(f63(x101063),f334(x101065,f702(x101064,x101065,x101063,x101066,x101062,x101061)))) % 169.39/169.66 [8296]~P16(x82962,x82965,x82966,x82961)+~P104(f334(f63(x82962),x82964))+~P104(f334(f63(x82962),x82963))+E(f334(x82961,f334(f334(f113(f886(x82962,a871)),x82963),x82964)),f334(f74(x82965,x82965,x82965,f334(x82961,x82963)),f334(x82961,x82964))) % 169.39/169.66 [8505]~P28(x85051)+P104(f334(f334(f249(x85051),f334(x85052,x85053)),x85054))+~P104(f334(f334(f336(x85055),x85053),x85056))+~P104(f334(f334(f249(x85051),f334(f334(f44(x85055,x85051),x85056),x85052)),x85054)) % 169.39/169.66 [8905]~P21(x89052,x89051,x89053,x89056)+E(f334(f334(f3(f886(x89051,a871)),f334(f313(x89052,x89051,x89053),x89054)),f334(f313(x89052,x89051,x89053),x89055)),f334(f313(x89052,x89051,x89053),f334(f334(f3(f886(x89052,a871)),x89054),x89055)))+~P104(f334(f334(f249(f886(x89052,a871)),x89055),x89056))+~P104(f334(f334(f249(f886(x89052,a871)),x89054),x89056)) % 169.39/169.66 [8906]~P21(x89062,x89061,x89063,x89066)+E(f334(f334(f104(f886(x89061,a871)),f334(f313(x89062,x89061,x89063),x89064)),f334(f313(x89062,x89061,x89063),x89065)),f334(f313(x89062,x89061,x89063),f334(f334(f104(f886(x89062,a871)),x89064),x89065)))+~P104(f334(f334(f249(f886(x89062,a871)),x89065),x89066))+~P104(f334(f334(f249(f886(x89062,a871)),x89064),x89066)) % 169.39/169.66 [9160]E(x91601,x91602)+~P52(x91603,x91604,x91605)+~P104(f334(f334(f336(f885(x91603,x91604)),f334(f334(f269(x91603,x91604),x91606),x91602)),x91605))+~P104(f334(f334(f336(f885(x91603,x91604)),f334(f334(f269(x91603,x91604),x91606),x91601)),x91605)) % 169.39/169.66 [9913]~P65(x99131)+~E(f334(x99133,f449(x99134,x99136,x99133,x99135,x99132,x99131)),f334(x99136,f449(x99134,x99136,x99133,x99135,x99132,x99131)))+~P104(f334(f63(x99132),x99135))+E(f334(f334(f334(f67(x99131,x99132,f82(x99131)),x99133),x99134),x99135),f334(f334(f334(f67(x99131,x99132,f82(x99131)),x99136),x99134),x99135)) % 169.39/169.66 [9974]~P65(x99741)+~P104(f334(f63(x99742),x99745))+E(f334(f334(f334(f67(x99741,x99742,f82(x99741)),x99743),x99744),x99745),f334(f334(f334(f67(x99741,x99742,f82(x99741)),x99746),x99744),x99745))+P104(f334(f334(f336(x99742),f449(x99744,x99743,x99746,x99745,x99742,x99741)),x99745)) % 169.39/169.66 [8718]~P65(x87181)+~P104(f334(f63(x87182),x87186))+P104(f334(f334(f336(x87182),x87185),x87186))+E(f334(f334(f334(f67(x87181,x87182,f82(x87181)),x87183),x87184),f334(f334(f312(x87182),x87185),x87186)),f334(f334(f82(x87181),f334(x87183,x87185)),f334(f334(f334(f67(x87181,x87182,f82(x87181)),x87183),x87184),x87186))) % 169.39/169.66 [8764]~P6(x87641,x87646,x87643)+~P9(x87641,f886(x87642,a871),x87643,x87645)+~P104(f334(f334(f336(x87641),x87644),x87646))+E(f334(f334(f44(x87641,f886(x87642,a871)),f334(f288(x87641,x87641,x87643),f334(f334(f312(x87641),x87644),f195(f886(x87641,a871))))),x87645),f334(x87645,x87644)) % 169.39/169.66 [8881]~P12(x88813,x88814,x88811)+~P104(f334(f63(x88813),x88816))+~P104(f334(f334(f336(x88813),x88812),x88816))+E(f334(f334(x88811,x88812),f334(f334(f66(x88813,x88814,x88811),x88815),f334(f334(f3(f886(x88813,a871)),x88816),f334(f334(f312(x88813),x88812),f195(f886(x88813,a871)))))),f334(f334(f66(x88813,x88814,x88811),x88815),x88816)) % 169.39/169.66 [9171]~P15(x91713,x91711,x91716,x91712)+~P104(f334(f63(x91713),x91715))+~P104(f334(f63(x91713),x91714))+E(f334(f74(x91711,x91711,x91711,f334(x91712,f334(f334(f113(f886(x91713,a871)),x91714),x91715))),f334(x91712,f334(f334(f104(f886(x91713,a871)),x91714),x91715))),f334(f74(x91711,x91711,x91711,f334(x91712,x91714)),f334(x91712,x91715))) % 169.39/169.66 [9489]~E(x94893,f334(f334(f159(x94891,x94892),x94895),x94896))+P104(f334(f334(f336(f885(f878(x94891),f878(x94891))),f334(f334(f269(f878(x94891),f878(x94891)),x94892),x94893)),f157(x94891,x94894)))+~P104(f334(f334(f250(a877),x94895),f334(f196(f878(x94891)),x94892)))+~P104(f334(f334(f336(f885(x94891,x94891)),f334(f334(f269(x94891,x94891),f334(f334(f165(x94891),x94892),x94895)),x94896)),x94894)) % 169.39/169.66 [9987]~P72(x99872)+~P104(f334(f63(x99871),x99876))+P104(f334(f334(f336(x99871),f701(x99874,x99875,x99873,x99876,x99871,x99872)),x99876))+E(f334(f334(f8(x99871,x99872),f334(f334(f20(x99871,f886(x99873,a871),x99872),f334(f334(f10(f886(x99873,x99872),f886(f886(x99873,a871),x99872),x99871),f8(x99873,x99872)),x99874)),x99875)),x99876),f334(f334(f8(f885(x99871,x99873),x99872),f334(f273(x99871,x99873,x99872),x99874)),f334(f334(f271(x99871,x99873),x99876),x99875))) % 169.39/169.66 [9988]~P68(x99882)+~P104(f334(f63(x99881),x99886))+P104(f334(f334(f336(x99881),f699(x99884,x99885,x99883,x99886,x99881,x99882)),x99886))+E(f334(f334(f11(x99881,x99882),f334(f334(f20(x99881,f886(x99883,a871),x99882),f334(f334(f10(f886(x99883,x99882),f886(f886(x99883,a871),x99882),x99881),f11(x99883,x99882)),x99884)),x99885)),x99886),f334(f334(f11(f885(x99881,x99883),x99882),f334(f273(x99881,x99883,x99882),x99884)),f334(f334(f271(x99881,x99883),x99886),x99885))) % 169.39/169.66 [10028]~P72(x100282)+~P104(f334(f63(x100281),x100286))+~P104(f334(f63(x100283),f334(x100285,f701(x100284,x100285,x100283,x100286,x100281,x100282))))+E(f334(f334(f8(x100281,x100282),f334(f334(f20(x100281,f886(x100283,a871),x100282),f334(f334(f10(f886(x100283,x100282),f886(f886(x100283,a871),x100282),x100281),f8(x100283,x100282)),x100284)),x100285)),x100286),f334(f334(f8(f885(x100281,x100283),x100282),f334(f273(x100281,x100283,x100282),x100284)),f334(f334(f271(x100281,x100283),x100286),x100285))) % 169.39/169.66 [10029]~P68(x100292)+~P104(f334(f63(x100291),x100296))+~P104(f334(f63(x100293),f334(x100295,f699(x100294,x100295,x100293,x100296,x100291,x100292))))+E(f334(f334(f11(x100291,x100292),f334(f334(f20(x100291,f886(x100293,a871),x100292),f334(f334(f10(f886(x100293,x100292),f886(f886(x100293,a871),x100292),x100291),f11(x100293,x100292)),x100294)),x100295)),x100296),f334(f334(f11(f885(x100291,x100293),x100292),f334(f273(x100291,x100293,x100292),x100294)),f334(f334(f271(x100291,x100293),x100296),x100295))) % 169.39/169.66 [10010]~P68(x100102)+~P104(f334(f63(x100101),x100106))+P104(f334(f334(f336(x100101),x100103),x100106))+E(f334(f334(f11(x100101,x100102),f334(f334(f9(x100101,x100102,x100102),f334(f334(f20(x100101,x100102,f886(x100102,x100102)),f334(f334(f10(a871,f886(x100102,f886(x100102,x100102)),x100101),f99(x100102)),f334(f334(f9(x100101,x100101,a871),a331),x100103))),x100104)),x100105)),x100106),f334(f334(f259(x100102),x100105),f334(f39(x100101),x100106))) % 169.39/169.66 [10015]~P68(x100152)+~P104(f334(f63(x100151),x100156))+~P104(f334(f334(f336(x100151),x100153),x100156))+E(f334(f334(f11(x100151,x100152),f334(f334(f9(x100151,x100152,x100152),f334(f334(f20(x100151,x100152,f886(x100152,x100152)),f334(f334(f10(a871,f886(x100152,f886(x100152,x100152)),x100151),f99(x100152)),f334(f334(f9(x100151,x100151,a871),a331),x100153))),x100154)),x100155)),x100156),f334(f334(f82(x100152),f334(x100154,x100153)),f334(f334(f259(x100152),x100155),f334(f334(f3(a877),f334(f39(x100151),x100156)),f79(a877))))) % 169.39/169.66 [10081]~P104(f334(f63(x100811),x100815))+~P104(f334(f63(x100812),x100813))+P104(f334(f334(f336(x100812),f569(x100816,x100814,x100813,x100812,x100815,x100811)),x100813))+E(f334(f334(f8(x100811,a877),f334(f334(f10(f886(x100812,a871),a877,x100811),f39(x100812)),f334(f334(f10(f886(x100812,a871),f886(x100812,a871),x100811),f254(x100812)),f334(f334(f10(f886(x100812,a871),f886(x100812,a871),x100811),f334(f20(x100812,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100812),a332),f334(f334(f9(x100812,f886(x100812,a871),a871),f336(x100812)),x100813)))),x100814)))),x100815),f334(f334(f82(a877),x100816),f334(f39(x100812),x100813))) % 169.39/169.66 [10082]~P104(f334(f63(x100821),x100825))+~P104(f334(f63(x100822),x100823))+P104(f334(f334(f336(x100822),f570(x100826,x100824,x100823,x100822,x100825,x100821)),x100823))+E(f334(f334(f8(x100821,a877),f334(f334(f10(f886(x100822,a871),a877,x100821),f39(x100822)),f334(f334(f10(f886(x100822,a871),f886(x100822,a871),x100821),f254(x100822)),f334(f334(f10(f886(x100822,a871),f886(x100822,a871),x100821),f334(f20(x100822,a871,a871),f334(f334(f10(a871,f886(a871,a871),x100822),a332),f334(f334(f9(x100822,f886(x100822,a871),a871),f336(x100822)),x100823)))),x100824)))),x100825),f334(f334(f8(x100822,a877),x100826),x100823)) % 169.39/169.66 [10113]~P104(f334(f63(x101132),x101133))+~P104(f334(f63(x101131),x101135))+~E(f334(f39(x101131),f334(f254(x101131),f334(f334(f20(x101131,a871,a871),f334(f334(f10(a871,f886(a871,a871),x101131),a332),f334(f334(f9(x101131,f886(x101131,a871),a871),f336(x101131)),x101135))),f334(f334(f9(x101131,x101132,a871),x101134),f569(x101136,x101134,x101133,x101132,x101135,x101131))))),x101136)+E(f334(f334(f8(x101131,a877),f334(f334(f10(f886(x101132,a871),a877,x101131),f39(x101132)),f334(f334(f10(f886(x101132,a871),f886(x101132,a871),x101131),f254(x101132)),f334(f334(f10(f886(x101132,a871),f886(x101132,a871),x101131),f334(f20(x101132,a871,a871),f334(f334(f10(a871,f886(a871,a871),x101132),a332),f334(f334(f9(x101132,f886(x101132,a871),a871),f336(x101132)),x101133)))),x101134)))),x101135),f334(f334(f82(a877),x101136),f334(f39(x101132),x101133))) % 169.39/169.66 [10115]~P104(f334(f63(x101152),x101153))+~P104(f334(f63(x101151),x101155))+~E(f334(f39(x101151),f334(f254(x101151),f334(f334(f20(x101151,a871,a871),f334(f334(f10(a871,f886(a871,a871),x101151),a332),f334(f334(f9(x101151,f886(x101151,a871),a871),f336(x101151)),x101155))),f334(f334(f9(x101151,x101152,a871),x101154),f570(x101156,x101154,x101153,x101152,x101155,x101151))))),f334(x101156,f570(x101156,x101154,x101153,x101152,x101155,x101151)))+E(f334(f334(f8(x101151,a877),f334(f334(f10(f886(x101152,a871),a877,x101151),f39(x101152)),f334(f334(f10(f886(x101152,a871),f886(x101152,a871),x101151),f254(x101152)),f334(f334(f10(f886(x101152,a871),f886(x101152,a871),x101151),f334(f20(x101152,a871,a871),f334(f334(f10(a871,f886(a871,a871),x101152),a332),f334(f334(f9(x101152,f886(x101152,a871),a871),f336(x101152)),x101153)))),x101154)))),x101155),f334(f334(f8(x101152,a877),x101156),x101153)) % 169.39/169.66 [9770]E(x97701,x97702)+~P12(x97703,x97704,x97705)+~P104(f334(f68(x97703,x97704,x97705,x97706,x97707),x97702))+~P104(f334(f68(x97703,x97704,x97705,x97706,x97707),x97701)) % 169.39/169.66 [9562]P104(f334(x95621,x95622))+~P104(f334(f334(f336(x95627),x95622),f334(x95626,x95624)))+~P104(f334(x95621,f532(x95621,x95626,x95625,x95623,x95627)))+~P104(f334(f334(f336(x95623),x95624),x95625)) % 169.39/169.66 [10002]~P12(x100027,x100026,x100021)+E(f334(f334(x100021,x100022),f833(x100022,x100023,x100024,x100025,x100021,x100026,x100027)),x100023)+~P104(f334(f68(x100027,x100026,x100021,x100025,x100024),x100023))+~P104(f334(f334(f336(x100027),x100022),x100024)) % 169.39/169.66 [10067]~P12(x100671,x100672,x100673)+~P104(f334(f68(x100671,x100672,x100673,x100674,x100675),x100677))+P104(f334(f68(x100671,x100672,x100673,x100674,f334(f334(f3(f886(x100671,a871)),x100675),f334(f334(f312(x100671),x100676),f195(f886(x100671,a871))))),f833(x100676,x100677,x100675,x100674,x100673,x100672,x100671)))+~P104(f334(f334(f336(x100671),x100676),x100675)) % 169.39/169.66 [9466]~P65(x94661)+~P21(x94665,x94662,x94666,x94667)+~P104(f334(f63(x94665),x94667))+E(f334(f334(f334(f67(x94661,x94662,f82(x94661)),x94663),x94664),f334(f313(x94665,x94662,x94666),x94667)),f334(f334(f334(f67(x94661,x94665,f82(x94661)),f334(f74(x94662,x94661,x94665,x94663),x94666)),x94664),x94667)) % 169.39/169.66 [9586]~E(f334(f334(f312(x95861),x95865),x95866),f334(f334(f312(x95861),x95862),x95863))+~P104(f334(f68(x95861,x95861,x95864,x95862,x95863),x95867))+P104(f334(f334(f336(x95861),x95862),x95863))+P104(f334(f64(x95861,x95864,f334(f334(f312(x95861),x95865),x95866)),x95867)) % 169.39/169.66 [9669]P104(f334(x96691,x96692))+~P104(f334(f334(f336(x96693),x96692),f334(x96694,x96697)))+~P104(f334(f334(f336(x96696),x96697),x96695))+P104(f334(f334(f336(x96693),f532(x96691,x96694,x96695,x96696,x96693)),f334(f334(f44(x96696,f886(x96693,a871)),x96695),x96694))) % 169.39/169.66 [9684]~P21(x96842,x96841,x96845,x96844)+~P21(x96841,x96843,x96846,f334(f313(x96842,x96841,x96845),x96844))+E(f334(f334(f74(x96841,x96842,x96843,f78(x96842,x96841,x96844,x96845)),f78(x96841,x96843,f334(f313(x96842,x96841,x96845),x96844),x96846)),x96847),f334(f78(x96842,x96843,x96844,f334(f74(x96841,x96843,x96842,x96846),x96845)),x96847))+~P104(f334(f334(f336(x96843),x96847),f334(f313(x96841,x96843,x96846),f334(f313(x96842,x96841,x96845),x96844)))) % 169.39/169.66 [10003]~P12(x100037,x100036,x100031)+E(f334(f334(x100031,x100032),f837(x100033,x100034,x100032,x100035,x100031,x100036,x100037)),x100033)+P104(f334(f334(f336(x100037),x100032),x100034))+~P104(f334(f68(x100037,x100036,x100031,x100035,f334(f334(f312(x100037),x100032),x100034)),x100033)) % 169.39/169.66 [10066]~P12(x100661,x100664,x100665)+P104(f334(f68(x100661,x100664,x100665,x100666,x100663),f837(x100667,x100663,x100662,x100666,x100665,x100664,x100661)))+P104(f334(f334(f336(x100661),x100662),x100663))+~P104(f334(f68(x100661,x100664,x100665,x100666,f334(f334(f312(x100661),x100662),x100663)),x100667)) % 169.39/169.66 [9752]E(x97521,f2(a1))+~P104(f334(f50(x97523,x97521),f334(f334(f269(a1,a1),x97525),x97527)))+~P104(f334(f50(x97522,x97521),f334(f334(f269(a1,a1),x97524),x97526)))+P104(f334(f50(f334(f334(f81(a1),x97522),x97523),x97521),f334(f334(f269(a1,a1),f334(f334(f81(a1),f334(f334(f81(a1),x97524),x97525)),f334(f334(f40(a1),f334(f334(f81(a1),x97526),x97527)),x97521))),f46(a1,f334(f334(f81(a1),x97526),x97527),x97521)))) % 169.39/169.66 [9754]~P104(f334(f334(f250(a877),f2(a877)),x97543))+~P104(f334(f49(x97542,x97543),f334(f334(f269(a877,a877),x97545),x97547)))+~P104(f334(f49(x97541,x97543),f334(f334(f269(a877,a877),x97544),x97546)))+P104(f334(f49(f334(f334(f81(a877),x97541),x97542),x97543),f334(f334(f269(a877,a877),f334(f334(f81(a877),f334(f334(f81(a877),x97544),x97545)),f334(f334(f40(a877),f334(f334(f81(a877),x97546),x97547)),x97543))),f46(a877,f334(f334(f81(a877),x97546),x97547),x97543)))) % 169.39/169.66 [10112]~P72(x101122)+~P104(f334(f63(x101123),x101125))+~P104(f334(f63(x101121),x101127))+E(f334(f334(f8(x101121,x101122),f334(f334(f20(x101121,f886(x101123,a871),x101122),f334(f334(f10(f886(x101123,x101122),f886(f886(x101123,a871),x101122),x101121),f8(x101123,x101122)),x101124)),f334(f334(f10(f886(x101123,a871),f886(x101123,a871),x101121),f254(x101123)),f334(f334(f10(f886(x101123,a871),f886(x101123,a871),x101121),f334(f20(x101123,a871,a871),f334(f334(f10(a871,f886(a871,a871),x101123),a332),f334(f334(f9(x101123,f886(x101123,a871),a871),f336(x101123)),x101125)))),x101126)))),x101127),f334(f334(f8(x101123,x101122),f334(f334(f20(x101123,f886(x101121,a871),x101122),f334(f334(f10(f886(x101121,x101122),f886(f886(x101121,a871),x101122),x101123),f8(x101121,x101122)),f334(f9(x101121,x101123,x101122),x101124))),f334(f334(f10(f886(x101121,a871),f886(x101121,a871),x101123),f254(x101121)),f334(f334(f10(f886(x101121,a871),f886(x101121,a871),x101123),f334(f20(x101121,a871,a871),f334(f334(f10(a871,f886(a871,a871),x101121),a332),f334(f334(f9(x101121,f886(x101121,a871),a871),f336(x101121)),x101127)))),f334(f9(x101121,x101123,a871),x101126))))),x101125)) % 169.39/169.66 [9622]~P18(x96227,x96226,x96221,x96228,x96222,x96224)+E(f334(f334(x96221,f334(x96222,x96223)),f334(x96224,x96225)),f334(x96224,x96225))+~P104(f334(f63(x96226),x96225))+~P104(f334(f334(f336(x96226),x96223),x96225)) % 169.39/169.66 [9626]~P10(x96266,x96261,x96262,x96268,x96263,x96264)+~P6(x96266,x96267,x96268)+P9(x96261,x96262,x96263,f334(x96264,x96265))+~P104(f334(f334(f336(x96266),x96265),x96267)) % 169.39/169.66 [9260]~P15(x92607,x92601,x92608,x92603)+~P104(f334(f63(x92607),x92605))+~P104(f334(f63(x92607),x92604))+E(f334(f74(x92601,x92601,x92602,f334(x92603,x92604)),f334(f74(x92601,x92601,x92602,f334(x92603,x92605)),x92606)),f334(f74(x92601,x92601,x92602,f334(x92603,x92605)),f334(f74(x92601,x92601,x92602,f334(x92603,x92604)),x92606))) % 169.39/169.66 [9268]~P36(x92681,x92682,x92683,x92684,x92687)+P36(x92681,x92682,x92683,f334(f334(f159(x92681,x92684),x92685),x92686),f334(f334(f159(x92682,x92687),x92685),x92688))+~P104(f334(f334(x92683,x92686),x92688))+~P104(f334(f334(f250(a877),x92685),f334(f196(f878(x92681)),x92684))) % 169.39/169.66 [9269]~P36(x92691,x92692,x92693,x92694,x92697)+P36(x92691,x92692,x92693,f334(f334(f159(x92691,x92694),x92695),x92696),f334(f334(f159(x92692,x92697),x92695),x92698))+~P104(f334(f334(x92693,x92696),x92698))+~P104(f334(f334(f250(a877),x92695),f334(f196(f878(x92692)),x92697))) % 169.39/169.66 [9343]~P21(x93432,x93432,x93435,x93436)+~P17(x93433,x93432,x93437,x93438,x93431)+~P104(f334(f63(x93432),x93436))+E(f334(f334(x93431,f334(f74(x93432,x93433,x93432,x93434),x93435)),x93436),f334(f334(x93431,x93434),f334(f313(x93432,x93432,x93435),x93436))) % 169.39/169.66 [9624]~P19(x96247,x96242,x96245,x96248,x96246,x96241)+~P104(f334(f63(x96242),x96244))+E(f334(x96241,f334(f334(f312(x96242),x96243),x96244)),f334(f334(x96245,f334(x96246,x96243)),f334(x96241,x96244)))+P104(f334(f334(f336(x96242),x96243),x96244)) % 169.39/169.66 [9635]~P18(x96356,x96355,x96351,x96357,x96358,x96352)+E(f334(f334(x96351,f334(x96352,x96353)),f334(x96352,x96354)),f334(x96352,x96354))+~P104(f334(f63(x96355),x96354))+~P104(f334(f334(f249(f886(x96355,a871)),x96353),x96354)) % 169.39/169.66 [10110]P20(x101108,x101107,f334(f334(f312(f876(x101108)),f334(f334(f334(f93(x101108),x101104),x101105),x101103)),f195(f886(f876(x101108),a871))))+~P20(x101108,x101107,f334(f334(f312(f876(x101108)),f334(f334(f334(f93(x101108),x101106),x101105),x101101)),f195(f886(f876(x101108),a871))))+~P104(f334(f334(x101106,x101102),f870(x101103,x101104,x101101,x101105,x101106,x101107,x101108)))+P104(f334(f334(x101101,x101102),f355(x101103,x101104,x101101,x101105,x101106,x101107,x101108))) % 169.39/169.66 [9246]P104(f334(f334(f336(f885(f878(x92461),f878(x92461))),f334(f334(f269(f878(x92461),f878(x92461)),x92462),x92463)),f157(x92461,x92464)))+~E(x92463,f334(f334(f134(x92461),x92465),f334(f334(f151(x92461),x92466),x92467)))+~E(x92462,f334(f334(f134(x92461),x92465),f334(f334(f151(x92461),x92468),x92467)))+~P104(f334(f334(f336(f885(x92461,x92461)),f334(f334(f269(x92461,x92461),x92468),x92466)),x92464)) % 169.39/169.66 [9629]~P18(x96296,x96292,x96295,x96297,x96298,x96291)+~P104(f334(f63(x96292),x96294))+~P104(f334(f63(x96292),x96293))+E(f334(x96291,f334(f334(f113(f886(x96292,a871)),x96293),x96294)),f334(f334(x96295,f334(x96291,x96293)),f334(x96291,x96294))) % 169.39/169.66 [10152]~P21(x101524,x101522,x101525,x101528)+E(f334(f334(f43(x101521,f886(x101522,a871)),x101523),f334(f334(f10(f886(x101524,a871),f886(x101522,a871),x101521),f313(x101524,x101522,x101525)),x101526)),f334(f313(x101524,x101522,x101525),f334(f334(f43(x101521,f886(x101524,a871)),x101523),x101526)))+~P104(f334(f334(f336(x101521),x101527),x101523))+P104(f334(f334(f336(x101521),f541(x101527,x101526,x101523,x101521,x101528,x101525,x101522,x101524)),x101523)) % 169.39/169.66 [10176]~P21(x101764,x101762,x101765,x101767)+E(f334(f334(f43(x101761,f886(x101762,a871)),x101763),f334(f334(f10(f886(x101764,a871),f886(x101762,a871),x101761),f313(x101764,x101762,x101765)),x101766)),f334(f313(x101764,x101762,x101765),f334(f334(f43(x101761,f886(x101764,a871)),x101763),x101766)))+~P104(f334(f334(f336(x101761),x101768),x101763))+~P104(f334(f334(f249(f886(x101764,a871)),f334(x101766,f541(x101768,x101766,x101763,x101761,x101767,x101765,x101762,x101764))),x101767)) % 169.39/169.66 [9693]~P19(x96937,x96935,x96931,x96938,x96932,x96934)+~P104(f334(f63(x96935),x96936))+~P104(f334(f334(f336(x96935),x96933),x96936))+E(f334(f334(x96931,f334(x96932,x96933)),f334(x96934,f334(f334(f3(f886(x96935,a871)),x96936),f334(f334(f312(x96935),x96933),f195(f886(x96935,a871)))))),f334(x96934,x96936)) % 169.39/169.66 [9701]~P19(x97016,x97013,x97011,x97017,x97018,x97012)+~P104(f334(f63(x97013),x97015))+~P104(f334(f63(x97013),x97014))+E(f334(f334(x97011,f334(x97012,f334(f334(f113(f886(x97013,a871)),x97014),x97015))),f334(x97012,f334(f334(f104(f886(x97013,a871)),x97014),x97015))),f334(f334(x97011,f334(x97012,x97014)),f334(x97012,x97015))) % 169.39/169.66 [9794]P43(x97941,x97942,x97943,x97944,x97945,f334(f334(x97943,x97946),x97947))+~P43(x97941,x97942,x97943,x97944,f334(f334(f3(f886(x97941,a871)),x97945),f334(f334(f312(x97941),x97948),f195(f886(x97941,a871)))),x97949)+~E(f334(f334(x97943,x97946),x97947),f334(f334(x97943,x97948),x97949))+~P104(f334(f334(f336(x97941),x97948),x97945)) % 169.39/169.66 [10187]P20(x101871,x101872,f334(f334(f312(f876(x101871)),f334(f334(f334(f93(x101871),f334(x101873,f493(x101874,x101875,x101876,x101877,x101873,x101872,x101871,x101878,x101879))),f334(x101877,f493(x101874,x101875,x101876,x101877,x101873,x101872,x101871,x101878,x101879))),f334(x101876,f493(x101874,x101875,x101876,x101877,x101873,x101872,x101871,x101878,x101879)))),f195(f886(f876(x101871),a871))))+~P104(f334(f63(x101879),x101878))+~P20(x101871,x101872,f334(f313(x101879,f876(x101871),f334(f334(f20(x101879,f886(x101871,f886(a872,a871)),f876(x101871)),f334(f334(f20(x101879,a873,f886(f886(x101871,f886(a872,a871)),f876(x101871))),f334(f334(f10(f886(x101871,f886(a872,a871)),f886(a873,f886(f886(x101871,f886(a872,a871)),f876(x101871))),x101879),f93(x101871)),x101873)),x101877)),x101876)),x101878))+P20(x101871,x101872,f334(f313(x101879,f876(x101871),f334(f334(f20(x101879,f886(x101871,f886(a872,a871)),f876(x101871)),f334(f334(f20(x101879,a873,f886(f886(x101871,f886(a872,a871)),f876(x101871))),f334(f334(f10(f886(x101871,f886(a872,a871)),f886(a873,f886(f886(x101871,f886(a872,a871)),f876(x101871))),x101879),f93(x101871)),x101875)),x101877)),x101874)),x101878)) % 169.39/169.66 [10188]~P20(x101881,x101882,f334(f334(f312(f876(x101881)),f334(f334(f334(f93(x101881),f334(x101884,f493(x101886,x101884,x101888,x101885,x101889,x101882,x101881,x101887,x101883))),f334(x101885,f493(x101886,x101884,x101888,x101885,x101889,x101882,x101881,x101887,x101883))),f334(x101886,f493(x101886,x101884,x101888,x101885,x101889,x101882,x101881,x101887,x101883)))),f195(f886(f876(x101881),a871))))+~P104(f334(f63(x101883),x101887))+~P20(x101881,x101882,f334(f313(x101883,f876(x101881),f334(f334(f20(x101883,f886(x101881,f886(a872,a871)),f876(x101881)),f334(f334(f20(x101883,a873,f886(f886(x101881,f886(a872,a871)),f876(x101881))),f334(f334(f10(f886(x101881,f886(a872,a871)),f886(a873,f886(f886(x101881,f886(a872,a871)),f876(x101881))),x101883),f93(x101881)),x101889)),x101885)),x101888)),x101887))+P20(x101881,x101882,f334(f313(x101883,f876(x101881),f334(f334(f20(x101883,f886(x101881,f886(a872,a871)),f876(x101881)),f334(f334(f20(x101883,a873,f886(f886(x101881,f886(a872,a871)),f876(x101881))),f334(f334(f10(f886(x101881,f886(a872,a871)),f886(a873,f886(f886(x101881,f886(a872,a871)),f876(x101881))),x101883),f93(x101881)),x101884)),x101885)),x101886)),x101887)) % 169.39/169.66 [9727]~P10(x97276,x97277,x97278,x97279,x972710,x97271)+E(f334(f334(x97271,x97272),x97273),f334(f334(x97271,x97274),x97275))+~P104(f334(f334(f336(f885(x97277,x97277)),f334(f334(f269(x97277,x97277),x97273),x97275)),x972710))+~P104(f334(f334(f336(f885(x97276,x97276)),f334(f334(f269(x97276,x97276),x97272),x97274)),x97279)) % 169.39/169.66 [9345]~P95(x93452)+E(x93451,f195(f886(x93452,a871)))+~P104(f334(f63(x93452),x93451))+P104(f334(f334(f336(x93452),f12(x93452,x93451)),x93451))+~P104(f334(f334(f336(x93452),f334(f334(f113(x93452),f421(x93451,x93452)),f422(x93451,x93452))),f334(f334(f312(x93452),f421(x93451,x93452)),f334(f334(f312(x93452),f422(x93451,x93452)),f195(f886(x93452,a871)))))) % 169.39/169.66 [9346]~P95(x93462)+E(x93461,f195(f886(x93462,a871)))+~P104(f334(f63(x93462),x93461))+P104(f334(f334(f336(x93462),f13(x93462,x93461)),x93461))+~P104(f334(f334(f336(x93462),f334(f334(f104(x93462),f438(x93461,x93462)),f439(x93461,x93462))),f334(f334(f312(x93462),f438(x93461,x93462)),f334(f334(f312(x93462),f439(x93461,x93462)),f195(f886(x93462,a871)))))) % 169.39/169.66 [9376]~P65(x93762)+E(x93761,f195(f886(x93762,a871)))+~P104(f334(f63(x93762),x93761))+P104(f334(f334(f336(x93762),f334(f65(x93762,f82(x93762)),x93761)),x93761))+~P104(f334(f334(f336(x93762),f334(f334(f82(x93762),f722(x93761,x93762)),f743(x93761,x93762))),f334(f334(f312(x93762),f722(x93761,x93762)),f334(f334(f312(x93762),f743(x93761,x93762)),f195(f886(x93762,a871)))))) % 169.39/169.66 [9381]~P107(x93812)+E(x93811,f195(f886(x93812,a871)))+~P104(f334(f63(x93812),x93811))+P104(f334(f334(f336(x93812),f14(x93812,f247(x93812),x93811)),x93811))+~P104(f334(f334(f336(x93812),f334(f334(f247(x93812),f471(x93811,x93812)),f472(x93811,x93812))),f334(f334(f312(x93812),f471(x93811,x93812)),f334(f334(f312(x93812),f472(x93811,x93812)),f195(f886(x93812,a871)))))) % 169.39/169.66 [9382]~P107(x93822)+E(x93821,f195(f886(x93822,a871)))+~P104(f334(f63(x93822),x93821))+P104(f334(f334(f336(x93822),f15(x93822,f248(x93822),x93821)),x93821))+~P104(f334(f334(f336(x93822),f334(f334(f248(x93822),f481(x93821,x93822)),f482(x93821,x93822))),f334(f334(f312(x93822),f481(x93821,x93822)),f334(f334(f312(x93822),f482(x93821,x93822)),f195(f886(x93822,a871)))))) % 169.39/169.66 [6561]~P85(x65612)+E(x65611,f2(x65612))+~E(f334(f334(f81(x65612),x65613),x65611),f2(x65612))+~P104(f334(f334(f249(x65612),f2(x65612)),x65613))+~P104(f334(f334(f249(x65612),f2(x65612)),x65611)) % 169.39/169.66 [6562]~P85(x65622)+E(x65621,f2(x65622))+~E(f334(f334(f81(x65622),x65621),x65623),f2(x65622))+~P104(f334(f334(f249(x65622),f2(x65622)),x65623))+~P104(f334(f334(f249(x65622),f2(x65622)),x65621)) % 169.39/169.66 [7089]~P107(x70892)+~P30(x70892,x70891)+E(x70891,f116(x70892))+~P104(f334(f334(f336(x70892),x70893),f334(f173(x70892),f633(x70891,x70892))))+P104(f334(f334(f249(x70892),f665(x70891,x70892)),x70893)) % 169.39/169.66 [7255]~P107(x72551)+E(f16(x72551,x72552),x72553)+~P104(f334(f63(x72551),x72552))+~P104(f334(f334(f249(x72551),x72553),f463(x72553,x72552,x72551)))+~P104(f334(f334(f336(x72551),x72553),x72552)) % 169.39/169.66 [7287]~P107(x72871)+~P30(x72871,x72872)+~P30(x72871,x72873)+P30(x72871,f334(f334(f134(x72871),x72872),x72873))+P104(f334(f334(f336(x72871),f640(x72873,x72872,x72871)),f334(f173(x72871),x72872))) % 169.39/169.66 [7288]~P107(x72881)+~P30(x72881,x72882)+~P30(x72881,x72883)+P30(x72881,f334(f334(f134(x72881),x72882),x72883))+P104(f334(f334(f336(x72881),f641(x72883,x72882,x72881)),f334(f173(x72881),x72883))) % 169.39/169.66 [7346]~P107(x73461)+E(f16(x73461,x73462),x73463)+~P104(f334(f63(x73461),x73462))+P104(f334(f334(f336(x73461),f463(x73463,x73462,x73461)),x73462))+~P104(f334(f334(f336(x73461),x73463),x73462)) % 169.39/169.66 [7347]~P107(x73471)+E(f17(x73471,x73472),x73473)+~P104(f334(f63(x73471),x73472))+P104(f334(f334(f336(x73471),f477(x73473,x73472,x73471)),x73472))+~P104(f334(f334(f336(x73471),x73473),x73472)) % 169.39/169.66 [7924]~P107(x79241)+E(f17(x79241,x79242),x79243)+~P104(f334(f63(x79241),x79242))+~P104(f334(f334(f336(x79241),x79243),x79242))+~P104(f334(f334(f249(x79241),f477(x79243,x79242,x79241)),x79243)) % 169.39/169.66 [8244]~P107(x82441)+~P30(x82441,x82442)+~P30(x82441,x82443)+P30(x82441,f334(f334(f134(x82441),x82442),x82443))+~P104(f334(f334(f249(x82441),f640(x82443,x82442,x82441)),f641(x82443,x82442,x82441))) % 169.39/169.66 [9000]~P95(x90002)+E(x90001,f195(f886(x90002,a871)))+~E(f334(f334(f113(x90002),f334(x90003,f419(x90001,x90003,x90002))),f334(x90003,f423(x90001,x90003,x90002))),f334(x90003,f334(f334(f113(x90002),f419(x90001,x90003,x90002)),f423(x90001,x90003,x90002))))+E(f12(x90002,f334(f313(x90002,x90002,x90003),x90001)),f334(x90003,f12(x90002,x90001)))+~P104(f334(f63(x90002),x90001)) % 169.39/169.66 [9001]~P95(x90012)+E(x90011,f195(f886(x90012,a871)))+~E(f334(f334(f104(x90012),f334(x90013,f437(x90011,x90013,x90012))),f334(x90013,f444(x90011,x90013,x90012))),f334(x90013,f334(f334(f104(x90012),f437(x90011,x90013,x90012)),f444(x90011,x90013,x90012))))+E(f13(x90012,f334(f313(x90012,x90012,x90013),x90011)),f334(x90013,f13(x90012,x90011)))+~P104(f334(f63(x90012),x90011)) % 169.39/169.66 [9002]~P107(x90022)+E(x90021,f195(f886(x90022,a871)))+~E(f334(f334(f247(x90022),f334(x90023,f468(x90021,x90023,x90022))),f334(x90023,f475(x90021,x90023,x90022))),f334(x90023,f334(f334(f247(x90022),f468(x90021,x90023,x90022)),f475(x90021,x90023,x90022))))+E(f16(x90022,f334(f313(x90022,x90022,x90023),x90021)),f334(x90023,f16(x90022,x90021)))+~P104(f334(f63(x90022),x90021)) % 169.39/169.66 [9003]~P107(x90032)+E(x90031,f195(f886(x90032,a871)))+~E(f334(f334(f248(x90032),f334(x90033,f487(x90031,x90033,x90032))),f334(x90033,f488(x90031,x90033,x90032))),f334(x90033,f334(f334(f248(x90032),f487(x90031,x90033,x90032)),f488(x90031,x90033,x90032))))+E(f17(x90032,f334(f313(x90032,x90032,x90033),x90031)),f334(x90033,f17(x90032,x90031)))+~P104(f334(f63(x90032),x90031)) % 169.39/169.66 [9071]~P107(x90712)+E(x90711,f195(f886(x90712,a871)))+~E(f334(f334(f247(x90712),f334(x90713,f469(x90711,x90713,x90712))),f334(x90713,f474(x90711,x90713,x90712))),f334(x90713,f334(f334(f247(x90712),f469(x90711,x90713,x90712)),f474(x90711,x90713,x90712))))+E(f14(x90712,f247(x90712),f334(f313(x90712,x90712,x90713),x90711)),f334(x90713,f14(x90712,f247(x90712),x90711)))+~P104(f334(f63(x90712),x90711)) % 169.39/169.66 [9072]~P107(x90722)+E(x90721,f195(f886(x90722,a871)))+~E(f334(f334(f248(x90722),f334(x90723,f478(x90721,x90723,x90722))),f334(x90723,f483(x90721,x90723,x90722))),f334(x90723,f334(f334(f248(x90722),f478(x90721,x90723,x90722)),f483(x90721,x90723,x90722))))+E(f15(x90722,f248(x90722),f334(f313(x90722,x90722,x90723),x90721)),f334(x90723,f15(x90722,f248(x90722),x90721)))+~P104(f334(f63(x90722),x90721)) % 169.39/169.66 [6577]~P65(x65772)+E(x65771,f195(f886(x65772,a871)))+~P104(f334(f63(x65772),x65771))+E(f334(f65(x65772,f82(x65772)),f334(f334(f312(x65772),x65773),x65771)),f334(f334(f82(x65772),x65773),f334(f65(x65772,f82(x65772)),x65771)))+P104(f334(f334(f336(x65772),x65773),x65771)) % 169.39/169.66 [7095]~P95(x70952)+E(f334(f334(f113(x70952),f12(x70952,x70951)),f12(x70952,x70953)),f12(x70952,x70953))+E(x70951,f195(f886(x70952,a871)))+~P104(f334(f63(x70952),x70953))+~P104(f334(f334(f249(f886(x70952,a871)),x70951),x70953)) % 169.39/169.66 [7096]~P95(x70962)+E(f334(f334(f104(x70962),f13(x70962,x70961)),f13(x70962,x70963)),f13(x70962,x70963))+E(x70961,f195(f886(x70962,a871)))+~P104(f334(f63(x70962),x70963))+~P104(f334(f334(f249(f886(x70962,a871)),x70961),x70963)) % 169.39/169.66 [7097]~P107(x70972)+E(f334(f334(f247(x70972),f16(x70972,x70971)),f16(x70972,x70973)),f16(x70972,x70973))+E(x70971,f195(f886(x70972,a871)))+~P104(f334(f63(x70972),x70973))+~P104(f334(f334(f249(f886(x70972,a871)),x70971),x70973)) % 169.39/169.66 [7098]~P107(x70982)+E(f334(f334(f248(x70982),f17(x70982,x70981)),f17(x70982,x70983)),f17(x70982,x70983))+E(x70981,f195(f886(x70982,a871)))+~P104(f334(f63(x70982),x70983))+~P104(f334(f334(f249(f886(x70982,a871)),x70981),x70983)) % 169.39/169.66 [7395]~P107(x73952)+E(x73951,f195(f886(x73952,a871)))+~P104(f334(f63(x73952),x73953))+P104(f334(f334(f249(x73952),f16(x73952,x73953)),f16(x73952,x73951)))+~P104(f334(f334(f249(f886(x73952,a871)),x73951),x73953)) % 169.39/169.66 [7396]~P107(x73962)+E(x73961,f195(f886(x73962,a871)))+~P104(f334(f63(x73962),x73963))+P104(f334(f334(f249(x73962),f17(x73962,x73961)),f17(x73962,x73963)))+~P104(f334(f334(f249(f886(x73962,a871)),x73961),x73963)) % 169.39/169.66 [7455]~P95(x74551)+E(f12(x74551,x74552),x74553)+~P104(f334(f63(x74551),x74552))+~E(f334(f334(f3(f886(x74551,a871)),x74552),f334(f334(f312(x74551),x74553),f195(f886(x74551,a871)))),f195(f886(x74551,a871)))+~P104(f334(f334(f336(x74551),x74553),x74552)) % 169.39/169.66 [7456]~P95(x74561)+E(f13(x74561,x74562),x74563)+~P104(f334(f63(x74561),x74562))+~E(f334(f334(f3(f886(x74561,a871)),x74562),f334(f334(f312(x74561),x74563),f195(f886(x74561,a871)))),f195(f886(x74561,a871)))+~P104(f334(f334(f336(x74561),x74563),x74562)) % 169.39/169.66 [7457]~P107(x74571)+E(f16(x74571,x74572),x74573)+~P104(f334(f63(x74571),x74572))+~E(f334(f334(f3(f886(x74571,a871)),x74572),f334(f334(f312(x74571),x74573),f195(f886(x74571,a871)))),f195(f886(x74571,a871)))+~P104(f334(f334(f336(x74571),x74573),x74572)) % 169.39/169.66 [7458]~P107(x74581)+E(f17(x74581,x74582),x74583)+~P104(f334(f63(x74581),x74582))+~E(f334(f334(f3(f886(x74581,a871)),x74582),f334(f334(f312(x74581),x74583),f195(f886(x74581,a871)))),f195(f886(x74581,a871)))+~P104(f334(f334(f336(x74581),x74583),x74582)) % 169.39/169.66 [7556]~P107(x75561)+E(f14(x75561,f247(x75561),x75562),x75563)+~P104(f334(f63(x75561),x75562))+~E(f334(f334(f3(f886(x75561,a871)),x75562),f334(f334(f312(x75561),x75563),f195(f886(x75561,a871)))),f195(f886(x75561,a871)))+~P104(f334(f334(f336(x75561),x75563),x75562)) % 169.39/169.66 [7557]~P107(x75571)+E(f15(x75571,f248(x75571),x75572),x75573)+~P104(f334(f63(x75571),x75572))+~E(f334(f334(f3(f886(x75571,a871)),x75572),f334(f334(f312(x75571),x75573),f195(f886(x75571,a871)))),f195(f886(x75571,a871)))+~P104(f334(f334(f336(x75571),x75573),x75572)) % 169.39/169.66 [7594]~P101(x75942)+E(x75941,f195(f886(x75942,a871)))+~P104(f334(f63(x75942),x75941))+~P104(f334(f334(f249(x75942),x75943),f426(x75943,x75941,x75942)))+P104(f334(f334(f249(x75942),x75943),f334(f65(x75942,f104(x75942)),x75941))) % 169.39/169.66 [7595]~P107(x75952)+E(x75951,f195(f886(x75952,a871)))+~P104(f334(f63(x75952),x75951))+~P104(f334(f334(f249(x75952),x75953),f464(x75953,x75951,x75952)))+P104(f334(f334(f249(x75952),x75953),f334(f65(x75952,f247(x75952)),x75951))) % 169.39/169.66 [7596]~P107(x75962)+E(x75961,f195(f886(x75962,a871)))+~P104(f334(f63(x75962),x75961))+~P104(f334(f334(f250(x75962),x75963),f465(x75963,x75961,x75962)))+P104(f334(f334(f250(x75962),x75963),f334(f65(x75962,f247(x75962)),x75961))) % 169.39/169.66 [7681]~P101(x76812)+E(x76811,f195(f886(x76812,a871)))+~P104(f334(f63(x76812),x76811))+P104(f334(f334(f336(x76812),f426(x76813,x76811,x76812)),x76811))+P104(f334(f334(f249(x76812),x76813),f334(f65(x76812,f104(x76812)),x76811))) % 169.39/169.66 [7682]~P107(x76822)+E(x76821,f195(f886(x76822,a871)))+~P104(f334(f63(x76822),x76821))+P104(f334(f334(f336(x76822),f464(x76823,x76821,x76822)),x76821))+P104(f334(f334(f249(x76822),x76823),f334(f65(x76822,f247(x76822)),x76821))) % 169.39/169.66 [7683]~P107(x76832)+E(x76831,f195(f886(x76832,a871)))+~P104(f334(f63(x76832),x76831))+P104(f334(f334(f336(x76832),f465(x76833,x76831,x76832)),x76831))+P104(f334(f334(f250(x76832),x76833),f334(f65(x76832,f247(x76832)),x76831))) % 169.39/169.66 [7804]~P107(x78042)+E(x78041,f195(f886(x78042,a871)))+E(f334(f334(f247(x78042),f14(x78042,f247(x78042),x78041)),f14(x78042,f247(x78042),x78043)),f14(x78042,f247(x78042),x78043))+~P104(f334(f63(x78042),x78043))+~P104(f334(f334(f249(f886(x78042,a871)),x78041),x78043)) % 169.39/169.66 [7805]~P107(x78052)+E(x78051,f195(f886(x78052,a871)))+E(f334(f334(f248(x78052),f15(x78052,f248(x78052),x78051)),f15(x78052,f248(x78052),x78053)),f15(x78052,f248(x78052),x78053))+~P104(f334(f63(x78052),x78053))+~P104(f334(f334(f249(f886(x78052,a871)),x78051),x78053)) % 169.39/169.66 [8003]~E(f441(x80031,x80033,x80032),f442(x80031,x80033,x80032))+~E(f334(f39(x80032),f443(x80031,x80033,x80032)),x80031)+E(f334(f334(f82(a877),x80031),f334(f39(f886(x80032,a871)),x80033)),f334(f39(x80032),f41(f886(x80032,a871),x80033)))+~P104(f334(f63(x80032),f41(f886(x80032,a871),x80033)))+~P104(f334(f63(f886(x80032,a871)),x80033)) % 169.39/169.66 [8178]~P107(x81782)+E(x81781,f195(f886(x81782,a871)))+~P104(f334(f63(x81782),x81783))+P104(f334(f334(f249(x81782),f334(f65(x81782,f247(x81782)),x81783)),f334(f65(x81782,f247(x81782)),x81781)))+~P104(f334(f334(f249(f886(x81782,a871)),x81781),x81783)) % 169.39/169.66 [8478]~E(f441(x84781,x84783,x84782),f442(x84781,x84783,x84782))+E(f334(f334(f82(a877),x84781),f334(f39(f886(x84782,a871)),x84783)),f334(f39(x84782),f41(f886(x84782,a871),x84783)))+P104(f334(f334(f336(f886(x84782,a871)),f443(x84781,x84783,x84782)),x84783))+~P104(f334(f63(x84782),f41(f886(x84782,a871),x84783)))+~P104(f334(f63(f886(x84782,a871)),x84783)) % 169.39/169.66 [8501]~E(f334(f39(x85012),f443(x85011,x85013,x85012)),x85011)+E(f334(f334(f82(a877),x85011),f334(f39(f886(x85012,a871)),x85013)),f334(f39(x85012),f41(f886(x85012,a871),x85013)))+P104(f334(f334(f336(f886(x85012,a871)),f442(x85011,x85013,x85012)),x85013))+~P104(f334(f63(x85012),f41(f886(x85012,a871),x85013)))+~P104(f334(f63(f886(x85012,a871)),x85013)) % 169.39/169.66 [8502]~E(f334(f39(x85022),f443(x85021,x85023,x85022)),x85021)+E(f334(f334(f82(a877),x85021),f334(f39(f886(x85022,a871)),x85023)),f334(f39(x85022),f41(f886(x85022,a871),x85023)))+P104(f334(f334(f336(f886(x85022,a871)),f441(x85021,x85023,x85022)),x85023))+~P104(f334(f63(x85022),f41(f886(x85022,a871),x85023)))+~P104(f334(f63(f886(x85022,a871)),x85023)) % 169.39/169.66 [8527]~E(f334(f39(x85272),f443(x85271,x85273,x85272)),x85271)+~E(f334(f334(f104(f886(x85272,a871)),f442(x85271,x85273,x85272)),f441(x85271,x85273,x85272)),f195(f886(x85272,a871)))+E(f334(f334(f82(a877),x85271),f334(f39(f886(x85272,a871)),x85273)),f334(f39(x85272),f41(f886(x85272,a871),x85273)))+~P104(f334(f63(f886(x85272,a871)),x85273))+~P104(f334(f63(x85272),f41(f886(x85272,a871),x85273))) % 169.39/169.66 [8769]E(f334(f334(f82(a877),x87691),f334(f39(f886(x87692,a871)),x87693)),f334(f39(x87692),f41(f886(x87692,a871),x87693)))+P104(f334(f334(f336(f886(x87692,a871)),f443(x87691,x87693,x87692)),x87693))+P104(f334(f334(f336(f886(x87692,a871)),f442(x87691,x87693,x87692)),x87693))+~P104(f334(f63(f886(x87692,a871)),x87693))+~P104(f334(f63(x87692),f41(f886(x87692,a871),x87693))) % 169.39/169.66 [8770]E(f334(f334(f82(a877),x87701),f334(f39(f886(x87702,a871)),x87703)),f334(f39(x87702),f41(f886(x87702,a871),x87703)))+P104(f334(f334(f336(f886(x87702,a871)),f443(x87701,x87703,x87702)),x87703))+P104(f334(f334(f336(f886(x87702,a871)),f441(x87701,x87703,x87702)),x87703))+~P104(f334(f63(f886(x87702,a871)),x87703))+~P104(f334(f63(x87702),f41(f886(x87702,a871),x87703))) % 169.39/169.66 [8795]~E(f334(f334(f104(f886(x87952,a871)),f442(x87951,x87953,x87952)),f441(x87951,x87953,x87952)),f195(f886(x87952,a871)))+E(f334(f334(f82(a877),x87951),f334(f39(f886(x87952,a871)),x87953)),f334(f39(x87952),f41(f886(x87952,a871),x87953)))+~P104(f334(f63(f886(x87952,a871)),x87953))+P104(f334(f334(f336(f886(x87952,a871)),f443(x87951,x87953,x87952)),x87953))+~P104(f334(f63(x87952),f41(f886(x87952,a871),x87953))) % 169.39/169.66 [9046]~P93(x90462)+E(x90461,f195(f886(x90462,a871)))+~E(f334(f334(f82(x90462),f334(x90463,f752(x90461,x90463,x90462))),f334(x90463,f766(x90461,x90463,x90462))),f334(x90463,f334(f334(f82(x90462),f752(x90461,x90463,x90462)),f766(x90461,x90463,x90462))))+~P104(f334(f63(x90462),x90461))+E(f334(f65(x90462,f82(x90462)),f334(f313(x90462,x90462,x90463),x90461)),f334(x90463,f334(f65(x90462,f82(x90462)),x90461))) % 169.39/169.66 [9948]P104(f334(f334(x99481,x99482),x99483))+P104(f334(f334(f250(a1),f505(x99481,x99483,x99482)),f506(x99481,x99483,x99482)))+P104(f334(f334(f249(a1),f506(x99481,x99483,x99482)),f2(a1)))+P104(f334(f334(x99481,f505(x99481,x99483,x99482)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f506(x99481,x99483,x99482))))+~P104(f334(f322(f885(a1,a1),a58),f334(f334(f269(a1,a1),x99482),x99483))) % 169.39/169.66 [9954]P104(f334(f334(x99541,x99542),x99543))+P104(f334(f334(f249(a1),f504(x99541,x99543,x99542)),f2(a1)))+P104(f334(f334(x99541,f503(x99541,x99543,x99542)),f334(f334(f82(a1),f334(f106(a1),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f504(x99541,x99543,x99542))))+P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),f503(x99541,x99543,x99542)),f504(x99541,x99543,x99542))))+~P104(f334(f322(f885(a1,a1),a53),f334(f334(f269(a1,a1),x99542),x99543))) % 169.39/169.66 [7973]~P120(x79731)+~P104(f334(f334(f249(x79731),x79732),f79(x79731)))+~P104(f334(f334(f249(x79731),f2(x79731)),x79732))+~P104(f334(f334(f249(x79731),f2(x79731)),x79733))+P104(f334(f334(f249(x79731),f334(f334(f82(x79731),x79732),x79733)),x79733)) % 169.39/169.66 [7974]~P120(x79741)+~P104(f334(f334(f249(x79741),x79743),f79(x79741)))+~P104(f334(f334(f249(x79741),f2(x79741)),x79743))+~P104(f334(f334(f249(x79741),f2(x79741)),x79742))+P104(f334(f334(f249(x79741),f334(f334(f82(x79741),x79742),x79743)),x79742)) % 169.39/169.66 [8326]~P107(x83262)+E(x83261,f195(f886(x83262,a871)))+~P104(f334(f63(x83262),x83261))+P104(f334(f334(f336(x83262),f461(x83263,x83261,x83262)),x83261))+~P104(f334(f334(f249(x83262),f334(f65(x83262,f247(x83262)),x83261)),x83263)) % 169.39/169.66 [8327]~P107(x83272)+E(x83271,f195(f886(x83272,a871)))+~P104(f334(f63(x83272),x83271))+P104(f334(f334(f336(x83272),f467(x83273,x83271,x83272)),x83271))+~P104(f334(f334(f250(x83272),f334(f65(x83272,f247(x83272)),x83271)),x83273)) % 169.39/169.66 [8328]~P107(x83282)+E(x83281,f195(f886(x83282,a871)))+~P104(f334(f63(x83282),x83281))+P104(f334(f334(f249(x83282),f461(x83283,x83281,x83282)),x83283))+~P104(f334(f334(f249(x83282),f334(f65(x83282,f247(x83282)),x83281)),x83283)) % 169.39/169.66 [8329]~P107(x83292)+E(x83291,f195(f886(x83292,a871)))+~P104(f334(f63(x83292),x83291))+P104(f334(f334(f250(x83292),f467(x83293,x83291,x83292)),x83293))+~P104(f334(f334(f250(x83292),f334(f65(x83292,f247(x83292)),x83291)),x83293)) % 169.39/169.66 [8413]~P104(f334(x84131,x84133))+P104(f334(x84131,f394(x84131,x84132)))+P104(f334(x84131,f393(x84131,x84132)))+~P104(f334(f334(f250(a1),f2(a1)),x84132))+P104(f334(x84131,f334(f334(f3(a1),f393(x84131,x84132)),f334(f334(f82(a1),f395(x84131,x84132)),x84132)))) % 169.39/169.66 [8623]~P104(f334(x86231,x86233))+P104(f334(x86231,f393(x86231,x86232)))+~P104(f334(f334(f250(a1),f2(a1)),x86232))+P104(f334(f334(f336(a1),f394(x86231,x86232)),f305(a1,f79(a1),x86232)))+P104(f334(x86231,f334(f334(f3(a1),f393(x86231,x86232)),f334(f334(f82(a1),f395(x86231,x86232)),x86232)))) % 169.39/169.66 [8817]~P104(f334(x88171,x88173))+~P104(f334(x88171,f393(x88171,x88172)))+P104(f334(x88171,f394(x88171,x88172)))+~P104(f334(f334(f250(a1),f2(a1)),x88172))+~P104(f334(x88171,f334(f334(f3(a1),f393(x88171,x88172)),f334(f334(f82(a1),f395(x88171,x88172)),x88172)))) % 169.39/169.66 [8941]~P104(f334(x89411,x89413))+~P104(f334(x89411,f393(x89411,x89412)))+~P104(f334(f334(f250(a1),f2(a1)),x89412))+P104(f334(f334(f336(a1),f394(x89411,x89412)),f305(a1,f79(a1),x89412)))+~P104(f334(x89411,f334(f334(f3(a1),f393(x89411,x89412)),f334(f334(f82(a1),f395(x89411,x89412)),x89412)))) % 169.39/169.66 [8729]~P95(x87291)+~P104(f334(f63(x87291),x87292))+E(f334(f334(f3(f886(x87291,a871)),x87292),f334(f334(f312(x87291),x87293),f195(f886(x87291,a871)))),f195(f886(x87291,a871)))+~P104(f334(f334(f336(x87291),x87293),x87292))+E(f334(f334(f113(x87291),x87293),f12(x87291,f334(f334(f3(f886(x87291,a871)),x87292),f334(f334(f312(x87291),x87293),f195(f886(x87291,a871)))))),f12(x87291,x87292)) % 169.39/169.66 [8730]~P95(x87301)+~P104(f334(f63(x87301),x87302))+E(f334(f334(f3(f886(x87301,a871)),x87302),f334(f334(f312(x87301),x87303),f195(f886(x87301,a871)))),f195(f886(x87301,a871)))+~P104(f334(f334(f336(x87301),x87303),x87302))+E(f334(f334(f104(x87301),x87303),f13(x87301,f334(f334(f3(f886(x87301,a871)),x87302),f334(f334(f312(x87301),x87303),f195(f886(x87301,a871)))))),f13(x87301,x87302)) % 169.39/169.66 [8731]~P107(x87311)+~P104(f334(f63(x87311),x87312))+E(f334(f334(f3(f886(x87311,a871)),x87312),f334(f334(f312(x87311),x87313),f195(f886(x87311,a871)))),f195(f886(x87311,a871)))+~P104(f334(f334(f336(x87311),x87313),x87312))+E(f334(f334(f247(x87311),x87313),f16(x87311,f334(f334(f3(f886(x87311,a871)),x87312),f334(f334(f312(x87311),x87313),f195(f886(x87311,a871)))))),f16(x87311,x87312)) % 169.39/169.66 [8732]~P107(x87321)+~P104(f334(f63(x87321),x87322))+E(f334(f334(f3(f886(x87321,a871)),x87322),f334(f334(f312(x87321),x87323),f195(f886(x87321,a871)))),f195(f886(x87321,a871)))+~P104(f334(f334(f336(x87321),x87323),x87322))+E(f334(f334(f248(x87321),x87323),f17(x87321,f334(f334(f3(f886(x87321,a871)),x87322),f334(f334(f312(x87321),x87323),f195(f886(x87321,a871)))))),f17(x87321,x87322)) % 169.39/169.66 [8789]~P107(x87891)+~P104(f334(f63(x87891),x87892))+E(f334(f334(f3(f886(x87891,a871)),x87892),f334(f334(f312(x87891),x87893),f195(f886(x87891,a871)))),f195(f886(x87891,a871)))+~P104(f334(f334(f336(x87891),x87893),x87892))+E(f334(f334(f247(x87891),x87893),f14(x87891,f247(x87891),f334(f334(f3(f886(x87891,a871)),x87892),f334(f334(f312(x87891),x87893),f195(f886(x87891,a871)))))),f14(x87891,f247(x87891),x87892)) % 169.39/169.66 [8790]~P107(x87901)+~P104(f334(f63(x87901),x87902))+E(f334(f334(f3(f886(x87901,a871)),x87902),f334(f334(f312(x87901),x87903),f195(f886(x87901,a871)))),f195(f886(x87901,a871)))+~P104(f334(f334(f336(x87901),x87903),x87902))+E(f334(f334(f248(x87901),x87903),f15(x87901,f248(x87901),f334(f334(f3(f886(x87901,a871)),x87902),f334(f334(f312(x87901),x87903),f195(f886(x87901,a871)))))),f15(x87901,f248(x87901),x87902)) % 169.39/169.66 [8804]~P95(x88041)+~P104(f334(f63(x88041),x88043))+~P104(f334(f63(x88041),x88042))+E(f334(f334(f104(f886(x88041,a871)),x88042),x88043),f195(f886(x88041,a871)))+E(f334(f334(f113(x88041),f12(x88041,f334(f334(f113(f886(x88041,a871)),x88042),x88043))),f12(x88041,f334(f334(f104(f886(x88041,a871)),x88042),x88043))),f334(f334(f113(x88041),f12(x88041,x88042)),f12(x88041,x88043))) % 169.39/169.66 [8805]~P95(x88051)+~P104(f334(f63(x88051),x88053))+~P104(f334(f63(x88051),x88052))+E(f334(f334(f104(f886(x88051,a871)),x88052),x88053),f195(f886(x88051,a871)))+E(f334(f334(f104(x88051),f13(x88051,f334(f334(f113(f886(x88051,a871)),x88052),x88053))),f13(x88051,f334(f334(f104(f886(x88051,a871)),x88052),x88053))),f334(f334(f104(x88051),f13(x88051,x88052)),f13(x88051,x88053))) % 169.39/169.66 [8806]~P107(x88061)+~P104(f334(f63(x88061),x88063))+~P104(f334(f63(x88061),x88062))+E(f334(f334(f104(f886(x88061,a871)),x88062),x88063),f195(f886(x88061,a871)))+E(f334(f334(f247(x88061),f16(x88061,f334(f334(f113(f886(x88061,a871)),x88062),x88063))),f16(x88061,f334(f334(f104(f886(x88061,a871)),x88062),x88063))),f334(f334(f247(x88061),f16(x88061,x88062)),f16(x88061,x88063))) % 169.39/169.66 [8807]~P107(x88071)+~P104(f334(f63(x88071),x88073))+~P104(f334(f63(x88071),x88072))+E(f334(f334(f104(f886(x88071,a871)),x88072),x88073),f195(f886(x88071,a871)))+E(f334(f334(f248(x88071),f17(x88071,f334(f334(f113(f886(x88071,a871)),x88072),x88073))),f17(x88071,f334(f334(f104(f886(x88071,a871)),x88072),x88073))),f334(f334(f248(x88071),f17(x88071,x88072)),f17(x88071,x88073))) % 169.39/169.66 [9018]~P107(x90181)+~P104(f334(f63(x90181),x90183))+~P104(f334(f63(x90181),x90182))+E(f334(f334(f104(f886(x90181,a871)),x90182),x90183),f195(f886(x90181,a871)))+E(f334(f334(f247(x90181),f14(x90181,f247(x90181),f334(f334(f113(f886(x90181,a871)),x90182),x90183))),f14(x90181,f247(x90181),f334(f334(f104(f886(x90181,a871)),x90182),x90183))),f334(f334(f247(x90181),f14(x90181,f247(x90181),x90182)),f14(x90181,f247(x90181),x90183))) % 169.39/169.66 [9019]~P107(x90191)+~P104(f334(f63(x90191),x90193))+~P104(f334(f63(x90191),x90192))+E(f334(f334(f104(f886(x90191,a871)),x90192),x90193),f195(f886(x90191,a871)))+E(f334(f334(f248(x90191),f15(x90191,f248(x90191),f334(f334(f113(f886(x90191,a871)),x90192),x90193))),f15(x90191,f248(x90191),f334(f334(f104(f886(x90191,a871)),x90192),x90193))),f334(f334(f248(x90191),f15(x90191,f248(x90191),x90192)),f15(x90191,f248(x90191),x90193))) % 169.39/169.66 [9791]~P119(x97913)+E(x97911,x97912)+~P104(f334(f334(f249(x97913),f2(x97913)),x97912))+~P104(f334(f334(f249(x97913),f2(x97913)),x97911))+~E(f334(f334(f259(x97913),x97911),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)))),f334(f334(f259(x97913),x97912),f334(f106(a877),f334(f334(f81(a1),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100)),f334(f334(f3(a1),f334(f334(f81(a1),a84),a84)),a100))))) % 169.39/169.66 [6376]E(f835(x63761,x63762,x63763),x63764)+E(f334(x63761,x63764),f2(a877))+~E(f334(f334(f8(x63763,a877),x63761),x63762),f79(a877))+~P104(f334(f63(x63763),x63762))+~P104(f334(f334(f336(x63763),x63764),x63762)) % 169.39/169.66 [6440]E(f838(x64401,x64402,x64403),x64404)+E(f334(x64401,x64404),f2(a877))+~E(f334(f334(f8(x64403,a877),x64401),x64402),f334(a115,f2(a877)))+~P104(f334(f63(x64403),x64402))+~P104(f334(f334(f336(x64403),x64404),x64402)) % 169.39/169.66 [6546]~P107(x65461)+~P28(x65461)+P104(f334(f334(f250(x65461),x65462),f41(x65461,x65463)))+~P104(f334(f334(f250(x65461),x65462),x65464))+~P104(f334(f334(f336(x65461),x65464),x65463)) % 169.39/169.66 [6717]~P107(x67171)+~P28(x67171)+~P104(f334(f334(f250(x67171),x67174),x67173))+P104(f334(f334(f250(x67171),f42(x67171,x67172)),x67173))+~P104(f334(f334(f336(x67171),x67174),x67172)) % 169.39/169.66 [6975]~P119(x69753)+E(x69751,x69752)+~E(f334(f334(f259(x69753),x69751),f334(a115,x69754)),f334(f334(f259(x69753),x69752),f334(a115,x69754)))+~P104(f334(f334(f249(x69753),f2(x69753)),x69752))+~P104(f334(f334(f249(x69753),f2(x69753)),x69751)) % 169.39/169.66 [7184]~E(f841(x71842,x71843,x71841,x71844),x71844)+~E(f334(x71842,x71844),f79(a877))+E(f334(f334(f8(x71841,a877),x71842),x71843),f79(a877))+~P104(f334(f63(x71841),x71843))+~P104(f334(f334(f336(x71841),x71844),x71843)) % 169.39/169.66 [7191]~P115(x71914)+~P129(x71914)+E(f334(x71911,f843(x71911,x71912,x71913,x71914)),f2(x71914))+~E(f334(f334(f11(x71913,x71914),x71911),x71912),f2(x71914))+~P104(f334(f63(x71913),x71912)) % 169.39/169.66 [7278]~E(f839(x72782,x72783,x72781,x72784),x72784)+~E(f334(x72782,x72784),f334(a115,f2(a877)))+E(f334(f334(f8(x72781,a877),x72782),x72783),f334(a115,f2(a877)))+~P104(f334(f63(x72781),x72783))+~P104(f334(f334(f336(x72781),x72784),x72783)) % 169.39/169.66 [8015]~E(f334(x80152,x80154),f79(a877))+~E(f334(x80152,f841(x80152,x80153,x80151,x80154)),f2(a877))+E(f334(f334(f8(x80151,a877),x80152),x80153),f79(a877))+~P104(f334(f63(x80151),x80153))+~P104(f334(f334(f336(x80151),x80154),x80153)) % 169.39/169.66 [8053]~E(f334(x80532,x80534),f334(a115,f2(a877)))+~E(f334(x80532,f839(x80532,x80533,x80531,x80534)),f2(a877))+E(f334(f334(f8(x80531,a877),x80532),x80533),f334(a115,f2(a877)))+~P104(f334(f63(x80531),x80533))+~P104(f334(f334(f336(x80531),x80534),x80533)) % 169.39/169.66 [8593]~P107(x85931)+~P30(x85931,x85934)+P30(x85931,x85932)+~E(x85932,f334(f334(f151(x85931),x85933),x85934))+~P104(f334(f334(f249(x85931),x85933),f667(x85932,x85931,x85934,x85933))) % 169.39/169.66 [8627]E(x86271,x86272)+E(f334(f334(f3(a1),f379(x86273,x86272,x86274,x86271)),f380(x86273,x86272,x86274,x86271)),x86271)+~E(f334(f334(f81(a1),x86271),x86274),x86272)+~P104(f334(f334(f250(a1),f2(a1)),x86274))+~P104(f334(f334(f336(a1),x86272),x86273)) % 169.39/169.66 [8628]E(x86281,x86282)+E(f334(f334(f81(a1),f383(x86283,x86282,x86284,x86281)),f384(x86283,x86282,x86284,x86281)),x86281)+~E(f334(f334(f3(a1),x86281),x86284),x86282)+~P104(f334(f334(f250(a1),f2(a1)),x86284))+~P104(f334(f334(f336(a1),x86282),x86283)) % 169.39/169.66 [8802]E(f334(x88021,f371(x88022,x88021,x88023,x88024)),x88022)+P104(f334(f334(f249(a877),x88024),f372(x88022,x88021,x88023,x88024)))+~P104(f334(f334(f249(a1),x88022),f334(x88021,x88023)))+~P104(f334(f334(f250(a877),x88024),x88023))+~P104(f334(f334(f249(a1),f334(x88021,x88024)),x88022)) % 169.39/169.66 [8803]~P107(x88031)+~P30(x88031,x88033)+P30(x88031,x88032)+~E(x88032,f334(f334(f151(x88031),x88034),x88033))+P104(f334(f334(f336(x88031),f667(x88032,x88031,x88033,x88034)),f334(f173(x88031),x88033))) % 169.39/169.66 [8821]~P115(x88214)+~P129(x88214)+~E(f334(f334(f11(x88211,x88214),x88212),x88213),f2(x88214))+~P104(f334(f63(x88211),x88213))+P104(f334(f334(f336(x88211),f843(x88212,x88213,x88211,x88214)),x88213)) % 169.39/169.66 [8855]~E(f334(x88552,x88554),f79(a877))+E(f334(f334(f8(x88551,a877),x88552),x88553),f79(a877))+~P104(f334(f63(x88551),x88553))+~P104(f334(f334(f336(x88551),x88554),x88553))+P104(f334(f334(f336(x88551),f841(x88552,x88553,x88551,x88554)),x88553)) % 169.39/169.66 [8864]E(x88641,x88642)+~E(f334(f334(f81(a1),x88642),x88644),x88641)+~P104(f334(f334(f250(a1),f2(a1)),x88644))+~P104(f334(f334(f336(a1),x88641),x88643))+P104(f334(f334(f336(a1),f379(x88643,x88641,x88644,x88642)),x88643)) % 169.39/169.66 [8865]E(x88651,x88652)+~E(f334(f334(f3(a1),x88652),x88654),x88651)+~P104(f334(f334(f250(a1),f2(a1)),x88654))+~P104(f334(f334(f336(a1),x88651),x88653))+P104(f334(f334(f336(a1),f383(x88653,x88651,x88654,x88652)),x88653)) % 169.39/169.66 [8867]~E(f334(x88672,x88674),f334(a115,f2(a877)))+E(f334(f334(f8(x88671,a877),x88672),x88673),f334(a115,f2(a877)))+~P104(f334(f63(x88671),x88673))+~P104(f334(f334(f336(x88671),x88674),x88673))+P104(f334(f334(f336(x88671),f839(x88672,x88673,x88671,x88674)),x88673)) % 169.39/169.66 [8872]P56(x88722,x88723,x88724,x88721)+E(x88721,f195(f886(x88722,a871)))+~P104(f334(f63(x88722),x88724))+~P104(f334(f63(x88722),x88721))+P104(f334(f334(f336(x88722),f682(x88721,x88724,x88723,x88722)),x88724)) % 169.39/169.66 [8953]E(x89531,x89532)+~E(f334(f334(f81(a1),x89532),x89534),x89531)+~P104(f334(f334(f250(a1),f2(a1)),x89534))+~P104(f334(f334(f336(a1),x89531),x89533))+P104(f334(f334(f336(a1),f380(x89533,x89531,x89534,x89532)),f305(a1,f79(a1),x89534))) % 169.39/169.66 [8954]E(x89541,x89542)+~E(f334(f334(f3(a1),x89542),x89544),x89541)+~P104(f334(f334(f250(a1),f2(a1)),x89544))+~P104(f334(f334(f336(a1),x89541),x89543))+P104(f334(f334(f336(a1),f384(x89543,x89541,x89544,x89542)),f305(a1,f79(a1),x89544))) % 169.39/169.66 [9024]P104(f334(f334(f249(a877),x90241),f371(x90242,x90243,x90244,x90241)))+~P104(f334(f334(f249(a1),x90242),f334(x90243,x90244)))+P104(f334(f334(f249(a877),x90241),f372(x90242,x90243,x90244,x90241)))+~P104(f334(f334(f250(a877),x90241),x90244))+~P104(f334(f334(f249(a1),f334(x90243,x90241)),x90242)) % 169.39/169.66 [9134]E(f334(x91341,f371(x91342,x91341,x91343,x91344)),x91342)+~P104(f334(f334(f249(a1),x91342),f334(x91341,x91343)))+P104(f334(f334(f250(a877),f372(x91342,x91341,x91343,x91344)),x91343))+~P104(f334(f334(f250(a877),x91344),x91343))+~P104(f334(f334(f249(a1),f334(x91341,x91344)),x91342)) % 169.39/169.66 [9257]~P104(f334(f334(f249(a1),x92572),f334(x92573,x92574)))+P104(f334(f334(f249(a877),x92571),f372(x92572,x92573,x92574,x92571)))+P104(f334(f334(f249(a877),f371(x92572,x92573,x92574,x92571)),x92574))+~P104(f334(f334(f250(a877),x92571),x92574))+~P104(f334(f334(f249(a1),f334(x92573,x92571)),x92572)) % 169.39/169.66 [9258]~P104(f334(f334(f249(a1),x92582),f334(x92583,x92584)))+P104(f334(f334(f249(a877),x92581),f371(x92582,x92583,x92584,x92581)))+P104(f334(f334(f250(a877),f372(x92582,x92583,x92584,x92581)),x92584))+~P104(f334(f334(f250(a877),x92581),x92584))+~P104(f334(f334(f249(a1),f334(x92583,x92581)),x92582)) % 169.39/169.66 [9359]~P104(f334(f334(f249(a1),x93591),f334(x93592,x93593)))+P104(f334(f334(f250(a877),f372(x93591,x93592,x93593,x93594)),x93593))+~P104(f334(f334(f250(a877),x93594),x93593))+~P104(f334(f334(f249(a1),f334(x93592,x93594)),x93591))+P104(f334(f334(f249(a877),f371(x93591,x93592,x93593,x93594)),x93593)) % 169.39/169.66 [9435]E(x94351,f195(f886(x94352,a871)))+~P104(f334(f63(x94352),x94354))+~P104(f334(f63(x94352),x94351))+P104(f334(f334(f336(f885(f886(x94352,a871),f886(x94352,a871))),f334(f334(f269(f886(x94352,a871),f886(x94352,a871)),x94354),x94351)),f326(x94352,x94353)))+P104(f334(f334(f336(x94352),f689(x94353,x94351,x94354,x94352)),x94354)) % 169.39/169.66 [9436]E(x94361,f195(f886(x94362,a871)))+~P104(f334(f63(x94362),x94364))+~P104(f334(f63(x94362),x94361))+P104(f334(f334(f336(f885(f886(x94362,a871),f886(x94362,a871))),f334(f334(f269(f886(x94362,a871),f886(x94362,a871)),x94364),x94361)),f326(x94362,x94363)))+P104(f334(f334(f336(x94362),f748(x94363,x94361,x94364,x94362)),x94364)) % 169.39/169.66 [10089]E(f334(x100891,f371(x100892,x100891,x100893,x100894)),x100892)+~P104(f334(f334(f249(a1),x100892),f334(x100891,x100893)))+~P104(f334(f334(f249(a1),f334(f76(a1),f334(f334(f3(a1),f334(x100891,f334(f334(f81(a877),f372(x100892,x100891,x100893,x100894)),f79(a877)))),f334(x100891,f372(x100892,x100891,x100893,x100894))))),f79(a1)))+~P104(f334(f334(f250(a877),x100894),x100893))+~P104(f334(f334(f249(a1),f334(x100891,x100894)),x100892)) % 169.39/169.66 [10090]~P104(f334(f334(f249(a1),x100902),f334(x100903,x100904)))+P104(f334(f334(f249(a877),x100901),f371(x100902,x100903,x100904,x100901)))+~P104(f334(f334(f249(a1),f334(f76(a1),f334(f334(f3(a1),f334(x100903,f334(f334(f81(a877),f372(x100902,x100903,x100904,x100901)),f79(a877)))),f334(x100903,f372(x100902,x100903,x100904,x100901))))),f79(a1)))+~P104(f334(f334(f250(a877),x100901),x100904))+~P104(f334(f334(f249(a1),f334(x100903,x100901)),x100902)) % 169.39/169.66 [10091]~P104(f334(f334(f249(a1),x100911),f334(x100912,x100913)))+~P104(f334(f334(f249(a1),f334(f76(a1),f334(f334(f3(a1),f334(x100912,f334(f334(f81(a877),f372(x100911,x100912,x100913,x100914)),f79(a877)))),f334(x100912,f372(x100911,x100912,x100913,x100914))))),f79(a1)))+~P104(f334(f334(f250(a877),x100914),x100913))+~P104(f334(f334(f249(a1),f334(x100912,x100914)),x100911))+P104(f334(f334(f249(a877),f371(x100911,x100912,x100913,x100914)),x100913)) % 169.39/169.66 [7244]~P61(x72441)+P104(f334(f334(f250(x72441),x72442),f2(x72441)))+~P104(f334(f334(f249(x72441),x72443),f2(x72441)))+P104(f334(f334(f250(x72441),f2(x72441)),x72442))+P104(f334(f334(f249(x72441),x72443),f334(f334(f292(x72441),x72444),x72442))) % 169.39/169.66 [7245]~P61(x72451)+P104(f334(f334(f250(x72451),x72452),f2(x72451)))+~P104(f334(f334(f250(x72451),x72453),f2(x72451)))+P104(f334(f334(f250(x72451),f2(x72451)),x72452))+P104(f334(f334(f250(x72451),x72453),f334(f334(f292(x72451),x72454),x72452))) % 169.39/169.66 [7494]~P61(x74941)+P104(f334(f334(f249(x74941),x74942),f2(x74941)))+P104(f334(f334(f250(x74941),x74943),f2(x74941)))+P104(f334(f334(f250(x74941),f2(x74941)),x74943))+~P104(f334(f334(f249(x74941),x74942),f334(f334(f292(x74941),x74944),x74943))) % 169.39/169.66 [7495]~P61(x74951)+P104(f334(f334(f250(x74951),x74952),f2(x74951)))+P104(f334(f334(f250(x74951),x74953),f2(x74951)))+P104(f334(f334(f250(x74951),f2(x74951)),x74953))+~P104(f334(f334(f250(x74951),x74952),f334(f334(f292(x74951),x74954),x74953))) % 169.39/169.66 [7614]E(x76141,x76142)+~E(f334(f334(f165(x76143),x76144),x76141),f334(f334(f165(x76143),x76144),x76142))+~P104(f334(f137(x76143),x76144))+~P104(f334(f334(f250(a877),x76142),f334(f196(f878(x76143)),x76144)))+~P104(f334(f334(f250(a877),x76141),f334(f196(f878(x76143)),x76144))) % 169.39/169.66 [7975]~P61(x79751)+~P104(f334(f334(f249(x79751),x79753),f2(x79751)))+P104(f334(f334(f250(x79751),f2(x79751)),x79752))+~P104(f334(f334(f249(x79751),x79754),f334(f334(f82(x79751),x79753),x79752)))+P104(f334(f334(f249(x79751),x79753),f334(f334(f292(x79751),x79754),x79752))) % 169.39/169.66 [7976]~P61(x79761)+~P104(f334(f334(f250(x79761),x79763),f2(x79761)))+P104(f334(f334(f250(x79761),f2(x79761)),x79762))+~P104(f334(f334(f250(x79761),x79764),f334(f334(f82(x79761),x79763),x79762)))+P104(f334(f334(f250(x79761),x79763),f334(f334(f292(x79761),x79764),x79762))) % 169.39/169.66 [7977]~P61(x79771)+~P104(f334(f334(f250(x79771),x79772),f2(x79771)))+P104(f334(f334(f250(x79771),f2(x79771)),x79772))+~P104(f334(f334(f249(x79771),x79774),f334(f334(f82(x79771),x79773),x79772)))+P104(f334(f334(f249(x79771),x79773),f334(f334(f292(x79771),x79774),x79772))) % 169.39/169.66 [7978]~P61(x79781)+~P104(f334(f334(f250(x79781),x79782),f2(x79781)))+P104(f334(f334(f250(x79781),f2(x79781)),x79782))+~P104(f334(f334(f249(x79781),x79784),f334(f334(f292(x79781),x79783),x79782)))+P104(f334(f334(f249(x79781),x79783),f334(f334(f82(x79781),x79784),x79782))) % 169.39/169.66 [7979]~P61(x79791)+~P104(f334(f334(f250(x79791),x79792),f2(x79791)))+P104(f334(f334(f250(x79791),f2(x79791)),x79792))+~P104(f334(f334(f250(x79791),x79794),f334(f334(f82(x79791),x79793),x79792)))+P104(f334(f334(f250(x79791),x79793),f334(f334(f292(x79791),x79794),x79792))) % 169.39/169.66 [7980]~P61(x79801)+~P104(f334(f334(f250(x79801),x79802),f2(x79801)))+P104(f334(f334(f250(x79801),f2(x79801)),x79802))+~P104(f334(f334(f250(x79801),x79804),f334(f334(f292(x79801),x79803),x79802)))+P104(f334(f334(f250(x79801),x79803),f334(f334(f82(x79801),x79804),x79802))) % 169.39/169.66 [8118]~P107(x81181)+~P30(x81181,x81182)+~P104(f334(f334(f249(a877),x81183),x81184))+P104(f334(f334(f249(x81181),f334(f334(f165(x81181),x81182),x81183)),f334(f334(f165(x81181),x81182),x81184)))+~P104(f334(f334(f250(a877),x81184),f334(f196(f878(x81181)),x81182))) % 169.39/169.66 [8168]~P119(x81681)+~P104(f334(f334(f249(x81681),x81682),f79(x81681)))+~P104(f334(f334(f249(x81681),f2(x81681)),x81682))+~P104(f334(f334(f249(a877),x81684),x81683))+P104(f334(f334(f249(x81681),f334(f334(f259(x81681),x81682),x81683)),f334(f334(f259(x81681),x81682),x81684))) % 169.39/169.66 [8169]~P119(x81691)+~P104(f334(f334(f250(x81691),x81692),f79(x81691)))+~P104(f334(f334(f250(x81691),f2(x81691)),x81692))+~P104(f334(f334(f250(a877),x81694),x81693))+P104(f334(f334(f250(x81691),f334(f334(f259(x81691),x81692),x81693)),f334(f334(f259(x81691),x81692),x81694))) % 169.39/169.66 [8170]~P119(x81701)+~P104(f334(f334(f249(x81701),f2(x81701)),x81702))+~P104(f334(f334(f250(a877),f2(a877)),x81703))+~P104(f334(f334(f250(x81701),x81702),x81704))+P104(f334(f334(f250(x81701),f334(f334(f259(x81701),x81702),x81703)),f334(f334(f259(x81701),x81704),x81703))) % 169.39/169.66 [8190]~P107(x81901)+~P30(x81901,f334(f169(x81901),x81902))+~P104(f334(f334(f249(a877),x81904),x81903))+P104(f334(f334(f249(x81901),f334(f334(f165(x81901),x81902),x81903)),f334(f334(f165(x81901),x81902),x81904)))+~P104(f334(f334(f250(a877),x81903),f334(f196(f878(x81901)),x81902))) % 169.39/169.66 [8433]~P61(x84331)+~P104(f334(f334(f249(x84331),x84332),f2(x84331)))+~P104(f334(f334(f249(x84331),x84333),x84334))+~P104(f334(f334(f250(x84331),f2(x84331)),f334(f334(f82(x84331),x84333),x84334)))+P104(f334(f334(f249(x84331),f334(f334(f292(x84331),x84332),x84333)),f334(f334(f292(x84331),x84332),x84334))) % 169.39/169.66 [8434]~P62(x84341)+~P104(f334(f334(f250(x84341),x84342),f2(x84341)))+~P104(f334(f334(f250(x84341),x84343),x84344))+~P104(f334(f334(f250(x84341),f2(x84341)),f334(f334(f82(x84341),x84343),x84344)))+P104(f334(f334(f250(x84341),f334(f334(f292(x84341),x84342),x84343)),f334(f334(f292(x84341),x84342),x84344))) % 169.39/169.66 [8444]~P62(x84441)+~P104(f334(f334(f249(x84441),x84444),x84443))+~P104(f334(f334(f249(x84441),f2(x84441)),x84442))+~P104(f334(f334(f250(x84441),f2(x84441)),f334(f334(f82(x84441),x84443),x84444)))+P104(f334(f334(f249(x84441),f334(f334(f292(x84441),x84442),x84443)),f334(f334(f292(x84441),x84442),x84444))) % 169.39/169.66 [8445]~P62(x84451)+~P104(f334(f334(f250(x84451),x84454),x84453))+~P104(f334(f334(f250(x84451),f2(x84451)),x84452))+~P104(f334(f334(f250(x84451),f2(x84451)),f334(f334(f82(x84451),x84453),x84454)))+P104(f334(f334(f250(x84451),f334(f334(f292(x84451),x84452),x84453)),f334(f334(f292(x84451),x84452),x84454))) % 169.39/169.66 [8542]P104(f334(x85421,x85422))+~P104(f334(f63(x85424),x85422))+P104(f334(x85421,f502(x85421,x85423,x85422,x85424)))+~P104(f334(x85421,f195(f886(x85424,a871))))+~P104(f334(f334(f249(f886(x85424,a871)),x85422),x85423)) % 169.39/169.66 [8550]P104(f334(x85501,x85502))+P104(f334(f63(x85503),f502(x85501,x85504,x85502,x85503)))+~P104(f334(f63(x85503),x85502))+~P104(f334(x85501,f195(f886(x85503,a871))))+~P104(f334(f334(f249(f886(x85503,a871)),x85502),x85504)) % 169.39/169.66 [8797]E(f334(f334(f81(a1),f387(x87971,x87972,x87973,x87974)),f388(x87971,x87972,x87973,x87974)),x87974)+~P104(f334(f334(f250(a1),f2(a1)),x87973))+~P104(f334(f334(f250(a1),x87972),x87974))+~P104(f334(f334(f336(a1),x87972),x87971))+P104(f334(f334(f250(a1),x87972),f334(f334(f3(a1),x87974),x87973))) % 169.39/169.66 [9006]~P104(f334(f334(f250(a1),f2(a1)),x90063))+~P104(f334(f334(f250(a1),x90062),x90064))+~P104(f334(f334(f336(a1),x90062),x90061))+P104(f334(f334(f336(a1),f387(x90061,x90062,x90063,x90064)),x90061))+P104(f334(f334(f250(a1),x90062),f334(f334(f3(a1),x90064),x90063))) % 169.39/169.66 [9017]P104(f334(x90171,x90172))+~P104(f334(f63(x90173),x90172))+P104(f334(f334(f336(x90173),f497(x90171,x90174,x90172,x90173)),x90174))+~P104(f334(x90171,f195(f886(x90173,a871))))+~P104(f334(f334(f249(f886(x90173,a871)),x90172),x90174)) % 169.39/169.66 [9034]E(f334(f334(f81(a1),f373(x90341,x90342,x90343,x90344)),f374(x90341,x90342,x90343,x90344)),x90344)+~P104(f334(f334(f250(a1),f2(a1)),x90343))+~P104(f334(f334(f249(a1),x90342),x90344))+P104(f334(f334(f249(a1),x90342),f334(f334(f3(a1),x90344),x90343)))+~P104(f334(f334(f336(a1),f334(f334(f3(a1),x90342),f79(a1))),x90341)) % 169.39/169.66 [9085]~P104(f334(f334(f250(a1),f2(a1)),x90853))+~P104(f334(f334(f250(a1),x90851),x90852))+~P104(f334(f334(f336(a1),x90851),x90854))+P104(f334(f334(f336(a1),f388(x90854,x90851,x90853,x90852)),f305(a1,f79(a1),x90853)))+P104(f334(f334(f250(a1),x90851),f334(f334(f3(a1),x90852),x90853))) % 169.39/169.66 [9178]~P104(f334(f334(f250(a1),f2(a1)),x91783))+~P104(f334(f334(f249(a1),x91782),x91784))+P104(f334(f334(f336(a1),f373(x91781,x91782,x91783,x91784)),x91781))+P104(f334(f334(f249(a1),x91782),f334(f334(f3(a1),x91784),x91783)))+~P104(f334(f334(f336(a1),f334(f334(f3(a1),x91782),f79(a1))),x91781)) % 169.39/169.66 [9218]~P104(f334(f334(f250(a1),f2(a1)),x92183))+~P104(f334(f334(f249(a1),x92181),x92182))+P104(f334(f334(f336(a1),f374(x92184,x92181,x92183,x92182)),f305(a1,f79(a1),x92183)))+P104(f334(f334(f249(a1),x92181),f334(f334(f3(a1),x92182),x92183)))+~P104(f334(f334(f336(a1),f334(f334(f3(a1),x92181),f79(a1))),x92184)) % 169.39/169.66 [9438]P104(f334(x94381,x94382))+~P104(f334(f334(f336(x94383),f497(x94381,x94384,x94382,x94383)),f502(x94381,x94384,x94382,x94383)))+~P104(f334(f63(x94383),x94382))+~P104(f334(x94381,f195(f886(x94383,a871))))+~P104(f334(f334(f249(f886(x94383,a871)),x94382),x94384)) % 169.39/169.66 [9649]P104(f334(x96491,x96492))+~P104(f334(f63(x96493),x96492))+~P104(f334(x96491,f334(f334(f312(x96493),f497(x96491,x96494,x96492,x96493)),f502(x96491,x96494,x96492,x96493))))+~P104(f334(x96491,f195(f886(x96493,a871))))+~P104(f334(f334(f249(f886(x96493,a871)),x96492),x96494)) % 169.39/169.66 [7750]~P61(x77501)+P104(f334(f334(f250(x77501),x77502),f2(x77501)))+~P104(f334(f334(f249(x77501),f2(x77501)),x77504))+P104(f334(f334(f250(x77501),f2(x77501)),x77502))+P104(f334(f334(f249(x77501),f334(f334(f292(x77501),x77503),x77502)),x77504)) % 169.39/169.66 [7751]~P61(x77511)+P104(f334(f334(f250(x77511),x77512),f2(x77511)))+P104(f334(f334(f250(x77511),f2(x77511)),x77512))+~P104(f334(f334(f250(x77511),f2(x77511)),x77514))+P104(f334(f334(f250(x77511),f334(f334(f292(x77511),x77513),x77512)),x77514)) % 169.39/169.66 [8028]~P104(f334(f334(f249(a1),x80284),f2(a1)))+~E(x80282,f334(f334(f81(a1),f334(f334(f82(a1),x80281),x80283)),x80284))+P104(f334(f334(f250(a1),f2(a1)),x80281))+~P104(f334(f334(f250(a1),x80281),x80284))+P104(f334(f50(x80282,x80281),f334(f334(f269(a1,a1),x80283),x80284))) % 169.39/169.66 [8062]~P104(f334(x80621,x80624))+P104(f334(x80621,f864(x80622,x80621,x80623)))+~P104(f334(f334(f249(a1),f2(a1)),x80622))+~P104(f334(f334(f250(a1),f2(a1)),x80623))+P104(f334(x80621,f334(f334(f3(a1),x80624),f334(f334(f82(a1),x80622),x80623)))) % 169.39/169.66 [8063]~P104(f334(x80631,x80634))+P104(f334(x80631,f866(x80632,x80631,x80633)))+~P104(f334(f334(f249(a1),f2(a1)),x80632))+~P104(f334(f334(f250(a1),f2(a1)),x80633))+P104(f334(x80631,f334(f334(f81(a1),x80634),f334(f334(f82(a1),x80632),x80633)))) % 169.39/169.66 [8064]~P61(x80641)+P104(f334(f334(f250(x80641),x80642),f2(x80641)))+P104(f334(f334(f250(x80641),f2(x80641)),x80642))+P104(f334(f334(f249(x80641),f2(x80641)),x80643))+~P104(f334(f334(f249(x80641),f334(f334(f292(x80641),x80644),x80642)),x80643)) % 169.39/169.66 [8065]~P61(x80651)+P104(f334(f334(f250(x80651),x80652),f2(x80651)))+P104(f334(f334(f250(x80651),f2(x80651)),x80652))+P104(f334(f334(f250(x80651),f2(x80651)),x80653))+~P104(f334(f334(f250(x80651),f334(f334(f292(x80651),x80654),x80652)),x80653)) % 169.39/169.66 [8113]~E(x81131,f334(f334(f81(a1),f334(f334(f82(a1),x81132),x81133)),x81134))+~P104(f334(f334(f249(a1),f2(a1)),x81134))+~P104(f334(f334(f250(a1),f2(a1)),x81132))+~P104(f334(f334(f250(a1),x81134),x81132))+P104(f334(f50(x81131,x81132),f334(f334(f269(a1,a1),x81133),x81134))) % 169.39/169.66 [8234]~P61(x82341)+P104(f334(f334(f250(x82341),x82342),f2(x82341)))+~P104(f334(f334(f249(x82341),f2(x82341)),x82344))+~P104(f334(f334(f249(x82341),x82343),f334(f334(f82(x82341),x82344),x82342)))+P104(f334(f334(f249(x82341),f334(f334(f292(x82341),x82343),x82342)),x82344)) % 169.39/169.66 [8235]~P61(x82351)+P104(f334(f334(f250(x82351),x82352),f2(x82351)))+~P104(f334(f334(f250(x82351),f2(x82351)),x82354))+~P104(f334(f334(f250(x82351),x82353),f334(f334(f82(x82351),x82354),x82352)))+P104(f334(f334(f250(x82351),f334(f334(f292(x82351),x82353),x82352)),x82354)) % 169.39/169.66 [8316]~P61(x83161)+P104(f334(f334(f250(x83161),x83162),f2(x83161)))+~P104(f334(f334(f249(x83161),x83163),f2(x83161)))+P104(f334(f334(f249(x83161),x83163),f334(f334(f292(x83161),x83164),x83162)))+~P104(f334(f334(f249(x83161),f334(f334(f82(x83161),x83163),x83162)),x83164)) % 169.39/169.66 [8317]~P61(x83171)+P104(f334(f334(f250(x83171),x83172),f2(x83171)))+~P104(f334(f334(f250(x83171),x83173),f2(x83171)))+P104(f334(f334(f250(x83171),x83173),f334(f334(f292(x83171),x83174),x83172)))+~P104(f334(f334(f250(x83171),f334(f334(f82(x83171),x83173),x83172)),x83174)) % 169.39/169.66 [8467]~P61(x84671)+~P104(f334(f334(f250(x84671),x84672),f2(x84671)))+P104(f334(f334(f250(x84671),f2(x84671)),x84672))+~P104(f334(f334(f249(x84671),f334(f334(f292(x84671),x84674),x84672)),x84673))+P104(f334(f334(f249(x84671),f334(f334(f82(x84671),x84673),x84672)),x84674)) % 169.39/169.66 [8468]~P61(x84681)+~P104(f334(f334(f250(x84681),x84682),f2(x84681)))+P104(f334(f334(f250(x84681),f2(x84681)),x84682))+~P104(f334(f334(f249(x84681),f334(f334(f82(x84681),x84684),x84682)),x84683))+P104(f334(f334(f249(x84681),f334(f334(f292(x84681),x84683),x84682)),x84684)) % 169.39/169.66 [8469]~P61(x84691)+~P104(f334(f334(f250(x84691),x84692),f2(x84691)))+P104(f334(f334(f250(x84691),f2(x84691)),x84692))+~P104(f334(f334(f250(x84691),f334(f334(f292(x84691),x84694),x84692)),x84693))+P104(f334(f334(f250(x84691),f334(f334(f82(x84691),x84693),x84692)),x84694)) % 169.39/169.66 [8470]~P61(x84701)+~P104(f334(f334(f250(x84701),x84702),f2(x84701)))+P104(f334(f334(f250(x84701),f2(x84701)),x84702))+~P104(f334(f334(f250(x84701),f334(f334(f82(x84701),x84704),x84702)),x84703))+P104(f334(f334(f250(x84701),f334(f334(f292(x84701),x84703),x84702)),x84704)) % 169.39/169.66 [8488]~P61(x84881)+~P104(f334(f334(f249(x84881),f2(x84881)),x84884))+P104(f334(f334(f250(x84881),f2(x84881)),x84882))+~P104(f334(f334(f249(x84881),f334(f334(f82(x84881),x84884),x84882)),x84883))+P104(f334(f334(f249(x84881),f334(f334(f292(x84881),x84883),x84882)),x84884)) % 169.39/169.66 [8489]~P61(x84891)+~P104(f334(f334(f250(x84891),f2(x84891)),x84894))+P104(f334(f334(f250(x84891),f2(x84891)),x84892))+~P104(f334(f334(f250(x84891),f334(f334(f82(x84891),x84894),x84892)),x84893))+P104(f334(f334(f250(x84891),f334(f334(f292(x84891),x84893),x84892)),x84894)) % 169.39/169.66 [8558]~P61(x85581)+~P104(f334(f334(f250(x85581),x85584),f2(x85581)))+~P104(f334(f334(f249(x85581),x85583),f334(f334(f82(x85581),x85582),x85584)))+P104(f334(f334(f249(x85581),x85582),f334(f334(f292(x85581),x85583),x85584)))+~P104(f334(f334(f249(x85581),f334(f334(f82(x85581),x85582),x85584)),x85583)) % 169.39/169.66 [8559]~P61(x85591)+~P104(f334(f334(f249(x85591),x85592),f2(x85591)))+~P104(f334(f334(f249(x85591),x85593),f334(f334(f82(x85591),x85592),x85594)))+P104(f334(f334(f249(x85591),x85592),f334(f334(f292(x85591),x85593),x85594)))+~P104(f334(f334(f249(x85591),f334(f334(f82(x85591),x85592),x85594)),x85593)) % 169.39/169.66 [8560]~P61(x85601)+~P104(f334(f334(f250(x85601),x85604),f2(x85601)))+~P104(f334(f334(f250(x85601),x85603),f334(f334(f82(x85601),x85602),x85604)))+P104(f334(f334(f250(x85601),x85602),f334(f334(f292(x85601),x85603),x85604)))+~P104(f334(f334(f250(x85601),f334(f334(f82(x85601),x85602),x85604)),x85603)) % 169.39/169.66 [8561]~P61(x85611)+~P104(f334(f334(f250(x85611),x85612),f2(x85611)))+~P104(f334(f334(f250(x85611),x85613),f334(f334(f82(x85611),x85612),x85614)))+P104(f334(f334(f250(x85611),x85612),f334(f334(f292(x85611),x85613),x85614)))+~P104(f334(f334(f250(x85611),f334(f334(f82(x85611),x85612),x85614)),x85613)) % 169.39/169.66 [8674]~P61(x86741)+~P104(f334(f334(f250(x86741),x86743),f2(x86741)))+~P104(f334(f334(f249(x86741),x86742),f334(f334(f82(x86741),x86744),x86743)))+~P104(f334(f334(f249(x86741),f334(f334(f82(x86741),x86744),x86743)),x86742))+P104(f334(f334(f249(x86741),f334(f334(f292(x86741),x86742),x86743)),x86744)) % 169.39/169.66 [8675]~P61(x86751)+~P104(f334(f334(f250(x86751),x86753),f2(x86751)))+~P104(f334(f334(f250(x86751),x86752),f334(f334(f82(x86751),x86754),x86753)))+~P104(f334(f334(f250(x86751),f334(f334(f82(x86751),x86754),x86753)),x86752))+P104(f334(f334(f250(x86751),f334(f334(f292(x86751),x86752),x86753)),x86754)) % 169.39/169.66 [8690]~P61(x86901)+~P104(f334(f334(f249(x86901),f2(x86901)),x86904))+~P104(f334(f334(f249(x86901),x86902),f334(f334(f82(x86901),x86904),x86903)))+~P104(f334(f334(f249(x86901),f334(f334(f82(x86901),x86904),x86903)),x86902))+P104(f334(f334(f249(x86901),f334(f334(f292(x86901),x86902),x86903)),x86904)) % 169.39/169.66 [8691]~P61(x86911)+~P104(f334(f334(f250(x86911),f2(x86911)),x86914))+~P104(f334(f334(f250(x86911),x86912),f334(f334(f82(x86911),x86914),x86913)))+~P104(f334(f334(f250(x86911),f334(f334(f82(x86911),x86914),x86913)),x86912))+P104(f334(f334(f250(x86911),f334(f334(f292(x86911),x86912),x86913)),x86914)) % 169.39/169.66 [8857]E(f334(f334(f3(a1),f381(x88571,x88572,x88573,x88574)),f382(x88571,x88572,x88573,x88574)),x88574)+~P104(f334(f334(f250(a1),f2(a1)),x88573))+~P104(f334(f334(f336(a1),x88572),x88571))+~P104(f334(f334(f250(a1),x88574),x88572))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x88574),x88573)),x88572)) % 169.39/169.66 [8937]~P104(f334(x89371,x89372))+~P104(f334(f334(f249(a1),f2(a1)),x89373))+~P104(f334(f334(f250(a1),f2(a1)),x89374))+~P104(f334(x89371,f334(f334(f3(a1),f864(x89373,x89371,x89374)),x89374)))+P104(f334(x89371,f334(f334(f3(a1),x89372),f334(f334(f82(a1),x89373),x89374)))) % 169.39/169.66 [8938]~P104(f334(x89381,x89382))+~P104(f334(f334(f249(a1),f2(a1)),x89383))+~P104(f334(f334(f250(a1),f2(a1)),x89384))+~P104(f334(x89381,f334(f334(f81(a1),f866(x89383,x89381,x89384)),x89384)))+P104(f334(x89381,f334(f334(f81(a1),x89382),f334(f334(f82(a1),x89383),x89384)))) % 169.39/169.66 [9079]~P104(f334(f334(f250(a1),f2(a1)),x90793))+~P104(f334(f334(f336(a1),x90792),x90791))+~P104(f334(f334(f250(a1),x90794),x90792))+P104(f334(f334(f336(a1),f381(x90791,x90792,x90793,x90794)),x90791))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x90794),x90793)),x90792)) % 169.39/169.66 [9099]E(f334(f334(f3(a1),f375(x90991,x90992,x90993,x90994)),f376(x90991,x90992,x90993,x90994)),x90994)+~P104(f334(f334(f250(a1),f2(a1)),x90993))+~P104(f334(f334(f249(a1),x90994),x90992))+~P104(f334(f334(f336(a1),f334(f334(f81(a1),x90992),f79(a1))),x90991))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x90994),x90993)),x90992)) % 169.39/169.66 [9126]~P104(f334(f334(f250(a1),f2(a1)),x91262))+~P104(f334(f334(f336(a1),x91263),x91264))+~P104(f334(f334(f250(a1),x91261),x91263))+P104(f334(f334(f336(a1),f382(x91264,x91263,x91262,x91261)),f305(a1,f79(a1),x91262)))+P104(f334(f334(f250(a1),f334(f334(f81(a1),x91261),x91262)),x91263)) % 169.39/169.66 [9213]~P104(f334(f334(f250(a1),f2(a1)),x92133))+~P104(f334(f334(f249(a1),x92134),x92132))+P104(f334(f334(f336(a1),f375(x92131,x92132,x92133,x92134)),x92131))+~P104(f334(f334(f336(a1),f334(f334(f81(a1),x92132),f79(a1))),x92131))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x92134),x92133)),x92132)) % 169.39/169.66 [9253]~P104(f334(f334(f250(a1),f2(a1)),x92532))+~P104(f334(f334(f249(a1),x92531),x92533))+P104(f334(f334(f336(a1),f376(x92534,x92533,x92532,x92531)),f305(a1,f79(a1),x92532)))+~P104(f334(f334(f336(a1),f334(f334(f81(a1),x92533),f79(a1))),x92534))+P104(f334(f334(f249(a1),f334(f334(f81(a1),x92531),x92532)),x92533)) % 169.39/169.66 [9525]~P39(x95251,x95253)+~P22(x95251,x95254)+P39(x95251,f334(f334(f113(f886(f885(x95251,x95251),a871)),x95252),x95253))+~P104(f334(f334(f249(f886(f885(x95251,x95251),a871)),x95252),f334(f268(f886(f885(x95251,x95251),a871),f886(f885(x95251,x95251),a871)),x95254)))+~P104(f334(f334(f249(f886(f885(x95251,x95251),a871)),x95253),f334(f272(f886(f885(x95251,x95251),a871),f886(f885(x95251,x95251),a871)),x95254))) % 169.39/169.66 [9819]~E(f334(f513(x98191,x98194,x98193,x98192),f515(x98191,x98194,x98193,x98192)),f198(f878(a330)))+P104(f334(f334(f250(a1),f514(x98191,x98194,x98193,x98192)),f515(x98191,x98194,x98193,x98192)))+P104(f334(f334(f334(x98191,x98192),x98193),x98194))+P104(f334(f334(f334(x98191,f513(x98191,x98194,x98193,x98192)),f514(x98191,x98194,x98193,x98192)),f334(f334(f81(a1),f515(x98191,x98194,x98193,x98192)),f79(a1))))+~P104(f334(f322(f885(f886(a1,f881(f878(a330))),f885(a1,a1)),a320),f334(f334(f269(f886(a1,f881(f878(a330))),f885(a1,a1)),x98192),f334(f334(f269(a1,a1),x98193),x98194)))) % 169.39/169.66 [9917]~P14(x99172,x99174,x99173)+E(x99171,f195(f886(x99172,a871)))+~P104(f334(f63(x99172),x99171))+P104(f334(f334(f336(x99172),f334(x99173,x99171)),x99171))+~P104(f334(f334(f336(x99172),f334(f334(x99174,f519(x99171,x99173,x99174,x99172)),f531(x99171,x99173,x99174,x99172))),f334(f334(f312(x99172),f519(x99171,x99173,x99174,x99172)),f334(f334(f312(x99172),f531(x99171,x99173,x99174,x99172)),f195(f886(x99172,a871)))))) % 169.39/169.66 [9848]~P108(x98482)+~P58(x98481)+~P104(f334(f334(f249(f886(x98481,x98482)),x98483),x98484))+P104(f334(f334(f250(f886(x98481,x98482)),x98483),x98484))+~P104(f334(f59(x98481),f334(f334(f10(a871,a871,x98481),a329),f334(f334(f20(x98481,x98482,a871),f334(f334(f10(x98482,f886(x98482,a871),x98481),a331),x98483)),x98484)))) % 169.39/169.66 [9445]~P52(x94451,x94451,x94454)+P104(f334(f334(f336(f885(x94451,x94451)),f334(f334(f269(x94451,x94451),x94452),x94453)),f310(x94451,x94454)))+P104(f334(f334(f336(f885(x94451,x94451)),f334(f334(f269(x94451,x94451),x94453),x94452)),f310(x94451,x94454)))+~P104(f334(f334(f336(f885(x94451,x94451)),f334(f334(f269(x94451,x94451),x94455),x94452)),f310(x94451,x94454)))+~P104(f334(f334(f336(f885(x94451,x94451)),f334(f334(f269(x94451,x94451),x94455),x94453)),f310(x94451,x94454))) % 169.39/169.66 [5661]E(x56611,f2(a877))+~E(f334(f39(x56612),x56615),x56611)+E(f334(f39(x56612),x56613),f334(a115,x56611))+~E(x56613,f334(f334(f312(x56612),x56614),x56615))+P104(f334(f334(f336(x56612),x56614),x56615)) % 169.39/169.66 [5787]~P60(x57872)+E(x57871,f2(x57872))+E(x57873,f2(x57872))+~E(f334(f334(f292(x57872),x57874),x57873),f334(f334(f292(x57872),x57875),x57871))+E(f334(f334(f82(x57872),x57874),x57871),f334(f334(f82(x57872),x57875),x57873)) % 169.39/169.66 [5788]~P60(x57882)+E(x57881,f2(x57882))+E(x57883,f2(x57882))+~E(f334(f334(f82(x57882),x57884),x57883),f334(f334(f82(x57882),x57885),x57881))+E(f334(f334(f292(x57882),x57884),x57881),f334(f334(f292(x57882),x57885),x57883)) % 169.39/169.66 [5854]~E(f334(f39(x58541),x58545),x58543)+~E(x58545,f195(f886(x58541,a871)))+E(f334(f39(x58541),x58542),f334(a115,x58543))+~E(x58542,f334(f334(f312(x58541),x58544),x58545))+P104(f334(f334(f336(x58541),x58544),x58545)) % 169.39/169.66 [6079]~P115(x60792)+~E(f334(x60793,x60795),f2(x60792))+E(f334(f334(f11(x60791,x60792),x60793),x60794),f2(x60792))+~P104(f334(f63(x60791),x60794))+~P104(f334(f334(f336(x60791),x60795),x60794)) % 169.39/169.66 [6453]~P107(x64533)+E(x64531,x64532)+~E(f334(f304(x64533,x64534),x64531),f334(f304(x64533,x64535),x64532))+~P104(f334(f334(f250(x64533),x64535),x64532))+~P104(f334(f334(f250(x64533),x64534),x64531)) % 169.39/169.66 [6454]~P107(x64543)+E(x64541,x64542)+~E(f334(f304(x64543,x64541),x64544),f334(f304(x64543,x64542),x64545))+~P104(f334(f334(f250(x64543),x64542),x64545))+~P104(f334(f334(f250(x64543),x64541),x64544)) % 169.39/169.66 [7511]~P107(x75111)+~P30(x75111,f334(f334(f134(x75111),x75114),x75115))+~P104(f334(f334(f336(x75111),x75113),f334(f173(x75111),x75115)))+~P104(f334(f334(f336(x75111),x75112),f334(f173(x75111),x75114)))+P104(f334(f334(f249(x75111),x75112),x75113)) % 169.39/169.66 [8595]~P108(x85951)+~P104(f334(f334(f250(f886(x85951,a871)),f305(x85951,x85955,x85952)),f305(x85951,x85954,x85953)))+~P104(f334(f334(f249(x85951),x85955),x85952))+P104(f334(f334(f250(x85951),x85952),x85953))+P104(f334(f334(f250(x85951),x85954),x85955)) % 169.39/169.66 [9960]~P13(x99602,x99605,x99603)+E(x99601,f195(f886(x99602,a871)))+~E(f334(f334(x99605,f334(x99604,f687(x99601,x99604,x99603,x99605,x99602))),f334(x99604,f695(x99601,x99604,x99603,x99605,x99602))),f334(x99604,f334(f334(x99605,f687(x99601,x99604,x99603,x99605,x99602)),f695(x99601,x99604,x99603,x99605,x99602))))+E(f334(x99603,f334(f313(x99602,x99602,x99604),x99601)),f334(x99604,f334(x99603,x99601)))+~P104(f334(f63(x99602),x99601)) % 169.39/169.66 [6450]~P14(x64502,x64505,x64503)+E(x64501,f195(f886(x64502,a871)))+~P104(f334(f63(x64502),x64501))+E(f334(x64503,f334(f334(f312(x64502),x64504),x64501)),f334(f334(x64505,x64504),f334(x64503,x64501)))+P104(f334(f334(f336(x64502),x64504),x64501)) % 169.39/169.66 [7268]~P13(x72682,x72683,x72684)+E(f334(f334(x72683,f334(x72684,x72681)),f334(x72684,x72685)),f334(x72684,x72685))+E(x72681,f195(f886(x72682,a871)))+~P104(f334(f63(x72682),x72685))+~P104(f334(f334(f249(f886(x72682,a871)),x72681),x72685)) % 169.39/169.66 [7487]~P58(x74874)+~P91(x74875)+E(f334(x74871,x74872),f334(x74873,x74872))+~P104(f334(f334(f336(x74874),x74872),f334(f173(x74874),f57(x74874))))+~P104(f334(f334(f92(f886(x74874,x74875)),x74871),x74873)) % 169.39/169.66 [7647]~P14(x76474,x76475,x76471)+E(f334(x76471,x76472),x76473)+~P104(f334(f63(x76474),x76472))+~E(f334(f334(f3(f886(x76474,a871)),x76472),f334(f334(f312(x76474),x76473),f195(f886(x76474,a871)))),f195(f886(x76474,a871)))+~P104(f334(f334(f336(x76474),x76473),x76472)) % 169.39/169.66 [7733]E(x77331,x77332)+~E(f334(f196(f878(x77333)),x77332),f334(f196(f878(x77334)),x77335))+~E(f334(f196(f878(x77333)),x77331),f334(f196(f878(x77334)),x77335))+~E(f334(f179(x77334,x77333),f334(f334(f183(x77334,x77333),x77335),x77331)),f334(f179(x77334,x77333),f334(f334(f183(x77334,x77333),x77335),x77332)))+~P104(f334(f137(x77334),x77335)) % 169.39/169.66 [8565]E(x85651,x85652)+~P6(x85653,x85654,x85655)+E(f334(f334(f104(f886(x85653,a871)),x85651),x85652),f195(f886(x85653,a871)))+~P104(f334(f334(f336(f886(x85653,a871)),x85652),f334(f334(f62(x85653),x85654),x85655)))+~P104(f334(f334(f336(f886(x85653,a871)),x85651),f334(f334(f62(x85653),x85654),x85655))) % 169.39/169.66 [9330]~P72(x93302)+~E(f334(x93303,f844(x93303,x93304,x93305,x93301,x93302)),f2(x93302))+E(f334(f334(f8(x93301,x93302),x93303),x93304),f334(f334(f8(x93301,x93302),x93303),x93305))+~P104(f334(f63(x93301),x93305))+~P104(f334(f334(f249(f886(x93301,a871)),x93304),x93305)) % 169.39/169.66 [9331]~P72(x93312)+~E(f334(x93313,f847(x93313,x93314,x93315,x93311,x93312)),f2(x93312))+E(f334(f334(f8(x93311,x93312),x93313),x93314),f334(f334(f8(x93311,x93312),x93313),x93315))+~P104(f334(f63(x93311),x93315))+~P104(f334(f334(f249(f886(x93311,a871)),x93314),x93315)) % 169.39/169.66 [9332]~P68(x93322)+~E(f334(x93323,f851(x93323,x93324,x93325,x93321,x93322)),f79(x93322))+E(f334(f334(f11(x93321,x93322),x93323),x93324),f334(f334(f11(x93321,x93322),x93323),x93325))+~P104(f334(f63(x93321),x93325))+~P104(f334(f334(f249(f886(x93321,a871)),x93324),x93325)) % 169.39/169.66 [9333]~P68(x93332)+~E(f334(x93333,f852(x93333,x93334,x93335,x93331,x93332)),f79(x93332))+E(f334(f334(f11(x93331,x93332),x93333),x93334),f334(f334(f11(x93331,x93332),x93333),x93335))+~P104(f334(f63(x93331),x93335))+~P104(f334(f334(f249(f886(x93331,a871)),x93334),x93335)) % 169.39/169.66 [9799]~P85(x97991)+~P104(f334(f63(x97992),x97995))+~P104(f334(f334(f249(x97991),f2(x97991)),f334(x97993,f845(x97993,x97994,x97995,x97992,x97991))))+P104(f334(f334(f249(x97991),f334(f334(f8(x97992,x97991),x97993),x97994)),f334(f334(f8(x97992,x97991),x97993),x97995)))+~P104(f334(f334(f249(f886(x97992,a871)),x97994),x97995)) % 169.39/169.66 [7508]E(x75081,f2(a877))+P104(f334(x75082,x75083))+~E(x75084,f334(f334(f81(a877),f334(f334(f82(a877),x75081),x75083)),x75085))+~P104(f334(f334(f250(a877),x75085),x75081))+~P104(f334(x75082,f334(f334(f40(a877),x75084),x75081))) % 169.39/169.66 [7588]E(x75881,f2(a877))+P104(f334(x75882,x75883))+~P104(f334(x75882,f46(a877,x75884,x75881)))+~E(x75884,f334(f334(f81(a877),f334(f334(f82(a877),x75881),x75885)),x75883))+~P104(f334(f334(f250(a877),x75883),x75881)) % 169.39/169.66 [7877]~P60(x78773)+E(f334(x78771,x78772),f2(x78773))+~P104(f334(f63(x78774),x78775))+E(f334(f334(f11(x78774,x78773),x78771),f334(f334(f3(f886(x78774,a871)),x78775),f334(f334(f312(x78774),x78772),f195(f886(x78774,a871))))),f334(f334(f11(x78774,x78773),x78771),x78775))+P104(f334(f334(f336(x78774),x78772),x78775)) % 169.39/169.66 [8275]~P72(x82751)+~P104(f334(f63(x82752),x82755))+~P104(f334(f63(x82752),x82754))+~E(f334(f334(f104(f886(x82752,a871)),x82754),x82755),f195(f886(x82752,a871)))+E(f334(f334(f81(x82751),f334(f334(f8(x82752,x82751),x82753),x82754)),f334(f334(f8(x82752,x82751),x82753),x82755)),f334(f334(f8(x82752,x82751),x82753),f334(f334(f113(f886(x82752,a871)),x82754),x82755))) % 169.39/169.66 [8277]~P68(x82771)+~P104(f334(f63(x82772),x82775))+~P104(f334(f63(x82772),x82774))+~E(f334(f334(f104(f886(x82772,a871)),x82774),x82775),f195(f886(x82772,a871)))+E(f334(f334(f82(x82771),f334(f334(f11(x82772,x82771),x82773),x82774)),f334(f334(f11(x82772,x82771),x82773),x82775)),f334(f334(f11(x82772,x82771),x82773),f334(f334(f113(f886(x82772,a871)),x82774),x82775))) % 169.39/169.66 [8368]~P60(x83683)+E(f334(x83681,x83682),f2(x83683))+~P104(f334(f63(x83684),x83685))+E(f334(f334(f11(x83684,x83683),x83681),f334(f334(f3(f886(x83684,a871)),x83685),f334(f334(f312(x83684),x83682),f195(f886(x83684,a871))))),f334(f334(f292(x83683),f334(f334(f11(x83684,x83683),x83681),x83685)),f334(x83681,x83682)))+~P104(f334(f334(f336(x83684),x83682),x83685)) % 169.39/169.66 [9058]~P6(x90581,x90585,x90584)+~E(f334(f334(f62(x90581),f334(f334(f312(x90581),x90582),f195(f886(x90581,a871)))),x90584),f334(f334(f62(x90581),f334(f334(f312(x90581),x90583),f195(f886(x90581,a871)))),x90584))+~P104(f334(f334(f336(x90581),x90583),x90585))+~P104(f334(f334(f336(x90581),x90582),x90585))+P104(f334(f334(f336(f885(x90581,x90581)),f334(f334(f269(x90581,x90581),x90582),x90583)),x90584)) % 169.39/169.66 [9078]~P6(x90781,x90785,x90783)+E(f334(f334(f62(x90781),f334(f334(f312(x90781),x90782),f195(f886(x90781,a871)))),x90783),f334(f334(f62(x90781),f334(f334(f312(x90781),x90784),f195(f886(x90781,a871)))),x90783))+~P104(f334(f334(f336(x90781),x90784),x90785))+~P104(f334(f334(f336(x90781),x90782),x90785))+~P104(f334(f334(f336(f885(x90781,x90781)),f334(f334(f269(x90781,x90781),x90782),x90784)),x90783)) % 169.39/169.66 [9358]~P68(x93581)+~P104(f334(f63(x93582),x93585))+~P104(f334(f63(x93582),x93584))+~E(f334(f334(f104(f886(x93582,a871)),x93584),x93585),f195(f886(x93582,a871)))+E(f334(f334(f82(x93581),f334(f334(f334(f67(x93581,x93582,f82(x93581)),x93583),f79(x93581)),x93584)),f334(f334(f334(f67(x93581,x93582,f82(x93581)),x93583),f79(x93581)),x93585)),f334(f334(f334(f67(x93581,x93582,f82(x93581)),x93583),f79(x93581)),f334(f334(f113(f886(x93582,a871)),x93584),x93585))) % 169.39/169.66 [9367]~P72(x93671)+~E(f334(x93673,f432(x93673,x93675,x93674,x93672,x93671)),f2(x93671))+~P104(f334(f63(x93672),x93674))+~P104(f334(f63(x93672),x93675))+E(f334(f334(f81(x93671),f334(f334(f8(x93672,x93671),x93673),x93674)),f334(f334(f8(x93672,x93671),x93673),x93675)),f334(f334(f8(x93672,x93671),x93673),f334(f334(f113(f886(x93672,a871)),x93674),x93675))) % 169.39/169.66 [9368]~P72(x93681)+~E(f334(x93683,f436(x93683,x93685,x93684,x93682,x93681)),f2(x93681))+~P104(f334(f63(x93682),x93684))+~P104(f334(f63(x93682),x93685))+E(f334(f334(f81(x93681),f334(f334(f8(x93682,x93681),x93683),x93684)),f334(f334(f8(x93682,x93681),x93683),x93685)),f334(f334(f8(x93682,x93681),x93683),f334(f334(f113(f886(x93682,a871)),x93684),x93685))) % 169.39/169.66 [9369]~P68(x93691)+~E(f334(x93693,f433(x93693,x93695,x93694,x93692,x93691)),f79(x93691))+~P104(f334(f63(x93692),x93694))+~P104(f334(f63(x93692),x93695))+E(f334(f334(f82(x93691),f334(f334(f11(x93692,x93691),x93693),x93694)),f334(f334(f11(x93692,x93691),x93693),x93695)),f334(f334(f11(x93692,x93691),x93693),f334(f334(f113(f886(x93692,a871)),x93694),x93695))) % 169.39/169.66 [9370]~P68(x93701)+~E(f334(x93703,f435(x93703,x93705,x93704,x93702,x93701)),f79(x93701))+~P104(f334(f63(x93702),x93704))+~P104(f334(f63(x93702),x93705))+E(f334(f334(f82(x93701),f334(f334(f11(x93702,x93701),x93703),x93704)),f334(f334(f11(x93702,x93701),x93703),x93705)),f334(f334(f11(x93702,x93701),x93703),f334(f334(f113(f886(x93702,a871)),x93704),x93705))) % 169.39/169.66 [9569]~P68(x95691)+~E(f334(x95693,f445(x95693,x95695,x95694,x95692,x95691)),f79(x95691))+~P104(f334(f63(x95692),x95694))+~P104(f334(f63(x95692),x95695))+E(f334(f334(f82(x95691),f334(f334(f334(f67(x95691,x95692,f82(x95691)),x95693),f79(x95691)),x95694)),f334(f334(f334(f67(x95691,x95692,f82(x95691)),x95693),f79(x95691)),x95695)),f334(f334(f334(f67(x95691,x95692,f82(x95691)),x95693),f79(x95691)),f334(f334(f113(f886(x95692,a871)),x95694),x95695))) % 169.39/169.66 [9677]~P72(x96772)+E(f334(f334(f8(x96771,x96772),x96773),x96774),f334(f334(f8(x96771,x96772),x96773),x96775))+~P104(f334(f63(x96771),x96775))+~P104(f334(f334(f249(f886(x96771,a871)),x96774),x96775))+P104(f334(f334(f336(x96771),f844(x96773,x96774,x96775,x96771,x96772)),f334(f334(f3(f886(x96771,a871)),x96775),x96774))) % 169.39/169.66 [9678]~P72(x96782)+E(f334(f334(f8(x96781,x96782),x96783),x96784),f334(f334(f8(x96781,x96782),x96783),x96785))+~P104(f334(f63(x96781),x96785))+~P104(f334(f334(f249(f886(x96781,a871)),x96784),x96785))+P104(f334(f334(f336(x96781),f847(x96783,x96784,x96785,x96781,x96782)),f334(f334(f3(f886(x96781,a871)),x96785),x96784))) % 169.39/169.66 [9679]~P68(x96792)+E(f334(f334(f11(x96791,x96792),x96793),x96794),f334(f334(f11(x96791,x96792),x96793),x96795))+~P104(f334(f63(x96791),x96795))+~P104(f334(f334(f249(f886(x96791,a871)),x96794),x96795))+P104(f334(f334(f336(x96791),f851(x96793,x96794,x96795,x96791,x96792)),f334(f334(f3(f886(x96791,a871)),x96795),x96794))) % 169.39/169.66 [9680]~P68(x96802)+E(f334(f334(f11(x96801,x96802),x96803),x96804),f334(f334(f11(x96801,x96802),x96803),x96805))+~P104(f334(f63(x96801),x96805))+~P104(f334(f334(f249(f886(x96801,a871)),x96804),x96805))+P104(f334(f334(f336(x96801),f852(x96803,x96804,x96805,x96801,x96802)),f334(f334(f3(f886(x96801,a871)),x96805),x96804))) % 169.39/169.66 [9697]~P72(x96971)+~P104(f334(f63(x96972),x96974))+~P104(f334(f63(x96972),x96975))+E(f334(f334(f81(x96971),f334(f334(f8(x96972,x96971),x96973),x96974)),f334(f334(f8(x96972,x96971),x96973),x96975)),f334(f334(f8(x96972,x96971),x96973),f334(f334(f113(f886(x96972,a871)),x96974),x96975)))+P104(f334(f334(f336(x96972),f432(x96973,x96975,x96974,x96972,x96971)),f334(f334(f104(f886(x96972,a871)),x96974),x96975))) % 169.39/169.66 [9698]~P72(x96981)+~P104(f334(f63(x96982),x96984))+~P104(f334(f63(x96982),x96985))+E(f334(f334(f81(x96981),f334(f334(f8(x96982,x96981),x96983),x96984)),f334(f334(f8(x96982,x96981),x96983),x96985)),f334(f334(f8(x96982,x96981),x96983),f334(f334(f113(f886(x96982,a871)),x96984),x96985)))+P104(f334(f334(f336(x96982),f436(x96983,x96985,x96984,x96982,x96981)),f334(f334(f104(f886(x96982,a871)),x96984),x96985))) % 169.39/169.66 [9699]~P68(x96991)+~P104(f334(f63(x96992),x96994))+~P104(f334(f63(x96992),x96995))+E(f334(f334(f82(x96991),f334(f334(f11(x96992,x96991),x96993),x96994)),f334(f334(f11(x96992,x96991),x96993),x96995)),f334(f334(f11(x96992,x96991),x96993),f334(f334(f113(f886(x96992,a871)),x96994),x96995)))+P104(f334(f334(f336(x96992),f433(x96993,x96995,x96994,x96992,x96991)),f334(f334(f104(f886(x96992,a871)),x96994),x96995))) % 169.39/169.66 [9700]~P68(x97001)+~P104(f334(f63(x97002),x97004))+~P104(f334(f63(x97002),x97005))+E(f334(f334(f82(x97001),f334(f334(f11(x97002,x97001),x97003),x97004)),f334(f334(f11(x97002,x97001),x97003),x97005)),f334(f334(f11(x97002,x97001),x97003),f334(f334(f113(f886(x97002,a871)),x97004),x97005)))+P104(f334(f334(f336(x97002),f435(x97003,x97005,x97004,x97002,x97001)),f334(f334(f104(f886(x97002,a871)),x97004),x97005))) % 169.39/169.66 [9707]~P85(x97075)+~P104(f334(f63(x97071),x97074))+P104(f334(f334(f249(x97075),f334(f334(f8(x97071,x97075),x97072),x97073)),f334(f334(f8(x97071,x97075),x97072),x97074)))+~P104(f334(f334(f249(f886(x97071,a871)),x97073),x97074))+P104(f334(f334(f336(x97071),f845(x97072,x97073,x97074,x97071,x97075)),f334(f334(f3(f886(x97071,a871)),x97074),x97073))) % 169.39/169.66 [9761]~P68(x97611)+~P104(f334(f63(x97612),x97614))+~P104(f334(f63(x97612),x97615))+E(f334(f334(f82(x97611),f334(f334(f334(f67(x97611,x97612,f82(x97611)),x97613),f79(x97611)),x97614)),f334(f334(f334(f67(x97611,x97612,f82(x97611)),x97613),f79(x97611)),x97615)),f334(f334(f334(f67(x97611,x97612,f82(x97611)),x97613),f79(x97611)),f334(f334(f113(f886(x97612,a871)),x97614),x97615)))+P104(f334(f334(f336(x97612),f445(x97613,x97615,x97614,x97612,x97611)),f334(f334(f104(f886(x97612,a871)),x97614),x97615))) % 169.39/169.66 [8758]~P14(x87581,x87584,x87585)+~P104(f334(f63(x87581),x87582))+E(f334(f334(f3(f886(x87581,a871)),x87582),f334(f334(f312(x87581),x87583),f195(f886(x87581,a871)))),f195(f886(x87581,a871)))+~P104(f334(f334(f336(x87581),x87583),x87582))+E(f334(f334(x87584,x87583),f334(x87585,f334(f334(f3(f886(x87581,a871)),x87582),f334(f334(f312(x87581),x87583),f195(f886(x87581,a871)))))),f334(x87585,x87582)) % 169.39/169.66 [8831]~P14(x88311,x88314,x88315)+~P104(f334(f63(x88311),x88313))+~P104(f334(f63(x88311),x88312))+E(f334(f334(f104(f886(x88311,a871)),x88312),x88313),f195(f886(x88311,a871)))+E(f334(f334(x88314,f334(x88315,f334(f334(f113(f886(x88311,a871)),x88312),x88313))),f334(x88315,f334(f334(f104(f886(x88311,a871)),x88312),x88313))),f334(f334(x88314,f334(x88315,x88312)),f334(x88315,x88313))) % 169.39/169.66 [9372]~P104(f334(f334(f249(a1),x93724),f2(a1)))+~P104(f334(f334(f250(a1),x93723),x93725))+P104(f334(f334(f249(a1),x93721),x93722))+~P104(f334(f334(f250(a1),x93723),x93724))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),f334(f334(f82(a1),x93723),x93722)),x93725)),f334(f334(f81(a1),f334(f334(f82(a1),x93723),x93721)),x93724))) % 169.39/169.66 [9374]~P104(f334(f334(f249(a1),f2(a1)),x93745))+P104(f334(f334(f249(a1),x93741),x93742))+~P104(f334(f334(f250(a1),x93743),x93744))+~P104(f334(f334(f250(a1),x93745),x93744))+~P104(f334(f334(f249(a1),f334(f334(f81(a1),f334(f334(f82(a1),x93744),x93741)),x93745)),f334(f334(f81(a1),f334(f334(f82(a1),x93744),x93742)),x93743))) % 169.39/169.66 [9481]~P60(x94815)+E(f334(x94811,f434(x94811,x94812,x94813,x94814,x94815)),f2(x94815))+~P104(f334(f63(x94814),x94813))+~P104(f334(f63(x94814),x94812))+E(f334(f334(f292(x94815),f334(f334(f82(x94815),f334(f334(f11(x94814,x94815),x94811),x94813)),f334(f334(f11(x94814,x94815),x94811),x94812))),f334(f334(f11(x94814,x94815),x94811),f334(f334(f104(f886(x94814,a871)),x94813),x94812))),f334(f334(f11(x94814,x94815),x94811),f334(f334(f113(f886(x94814,a871)),x94813),x94812))) % 169.39/169.66 [9753]~P60(x97531)+~P104(f334(f63(x97532),x97534))+~P104(f334(f63(x97532),x97535))+E(f334(f334(f292(x97531),f334(f334(f82(x97531),f334(f334(f11(x97532,x97531),x97533),x97534)),f334(f334(f11(x97532,x97531),x97533),x97535))),f334(f334(f11(x97532,x97531),x97533),f334(f334(f104(f886(x97532,a871)),x97534),x97535))),f334(f334(f11(x97532,x97531),x97533),f334(f334(f113(f886(x97532,a871)),x97534),x97535)))+P104(f334(f334(f336(x97532),f434(x97533,x97535,x97534,x97532,x97531)),f334(f334(f104(f886(x97532,a871)),x97534),x97535))) % 169.39/169.66 [9098]E(f334(f334(f134(x90981),x90982),x90983),f334(f334(f134(x90981),x90984),x90985))+~E(f334(f334(f176(x90981),f334(f196(f878(x90981)),x90984)),x90982),x90984)+~E(f334(f334(f176(x90981),f334(f196(f878(x90981)),x90982)),x90984),x90982)+~E(x90985,f334(f334(f134(x90981),f334(f334(f138(x90981),f334(f196(f878(x90981)),x90984)),x90982)),x90983))+~E(f334(f334(f134(x90981),f334(f334(f138(x90981),f334(f196(f878(x90981)),x90982)),x90984)),x90985),x90983) % 169.39/169.66 [9479]~P107(x94792)+E(f334(f334(f148(x94791,x94792,x94793),x94794),f171(x94791,x94794,x94795)),x94795)+~P30(x94792,f334(f334(f154(x94791,x94792),x94793),x94795))+~P104(f334(f334(f336(x94791),x94794),f334(f173(x94791),x94795)))+~E(f334(f141(x94791),f334(f136(x94791,f334(f334(f10(x94792,a871,x94791),f334(a331,f334(x94793,x94794))),x94793)),x94795)),x94794) % 169.39/169.66 [9816]~P65(x98161)+~P104(f334(f68(x98161,x98161,f82(x98161),x98162,x98163),x98165))+~P104(f334(f334(f336(x98161),x98164),x98163))+P104(f334(f334(f336(x98161),x98162),x98163))+P104(f334(f68(x98161,x98161,f82(x98161),x98164,f334(f334(f312(x98161),x98162),f334(f334(f3(f886(x98161,a871)),x98163),f334(f334(f312(x98161),x98164),f195(f886(x98161,a871)))))),x98165)) % 169.39/169.66 [7277]E(x72771,x72772)+~P21(x72774,x72775,x72773,x72776)+~E(f334(x72773,x72771),f334(x72773,x72772))+~P104(f334(f334(f336(x72774),x72772),x72776))+~P104(f334(f334(f336(x72774),x72771),x72776)) % 169.39/169.66 [6541]~P138(x65414)+E(x65411,x65412)+~E(x65415,x65416)+E(x65413,f2(x65414))+~E(f334(f334(f81(x65414),x65415),f334(f334(f82(x65414),x65413),x65411)),f334(f334(f81(x65414),x65416),f334(f334(f82(x65414),x65413),x65412))) % 169.39/169.66 [7568]~P107(x75681)+~P28(x75681)+~P104(f334(f334(f250(x75681),x75682),f334(x75685,x75686)))+~P104(f334(f334(f336(x75683),x75686),x75684))+P104(f334(f334(f250(x75681),x75682),f334(f334(f44(x75683,x75681),x75684),x75685))) % 169.39/169.66 [8245]~P107(x82451)+~P28(x82451)+~P104(f334(f334(f250(x82451),f334(x82454,x82456)),x82455))+~P104(f334(f334(f336(x82452),x82456),x82453))+P104(f334(f334(f250(x82451),f334(f334(f43(x82452,x82451),x82453),x82454)),x82455)) % 169.39/169.66 [8495]~P15(x84952,x84955,x84956,x84951)+~P104(f334(f63(x84952),x84954))+~P104(f334(f63(x84952),x84953))+~E(f334(f334(f104(f886(x84952,a871)),x84953),x84954),f195(f886(x84952,a871)))+E(f334(x84951,f334(f334(f113(f886(x84952,a871)),x84953),x84954)),f334(f74(x84955,x84955,x84955,f334(x84951,x84953)),f334(x84951,x84954))) % 169.39/169.66 [8801]E(x88011,x88012)+~P54(x88014,x88015,x88016,x88013,x88017)+~E(f334(x88013,x88011),f334(x88013,x88012))+~P104(f334(f334(f336(x88015),x88012),x88017))+~P104(f334(f334(f336(x88015),x88011),x88017)) % 169.39/169.66 [10058]~P104(f334(x100582,x100584))+~E(x100585,f334(f136(x100581,x100582),x100587))+E(f334(f136(x100581,x100582),x100583),f334(f334(f151(x100581),x100584),x100585))+~E(x100583,f334(f334(f134(x100581),x100586),f334(f334(f151(x100581),x100584),x100587)))+P104(f334(x100582,f745(x100585,x100584,x100583,x100582,x100581,x100586,x100587))) % 169.39/169.66 [10059]~P104(f334(x100594,x100592))+~E(x100593,f334(f136(x100591,x100594),x100597))+E(f334(f334(f151(x100591),x100592),x100593),f334(f136(x100591,x100594),x100595))+~E(x100595,f334(f334(f134(x100591),x100596),f334(f334(f151(x100591),x100592),x100597)))+P104(f334(x100594,f742(x100595,x100594,x100593,x100592,x100591,x100596,x100597))) % 169.39/169.66 [10092]~P104(f334(x100922,x100924))+~E(x100925,f334(f136(x100921,x100922),x100927))+E(f334(f136(x100921,x100922),x100923),f334(f334(f151(x100921),x100924),x100925))+~E(x100923,f334(f334(f134(x100921),x100926),f334(f334(f151(x100921),x100924),x100927)))+P104(f334(f334(f336(x100921),f745(x100925,x100924,x100923,x100922,x100921,x100926,x100927)),f334(f173(x100921),x100926))) % 169.39/169.66 [10093]~P104(f334(x100934,x100932))+~E(x100933,f334(f136(x100931,x100934),x100937))+E(f334(f334(f151(x100931),x100932),x100933),f334(f136(x100931,x100934),x100935))+~E(x100935,f334(f334(f134(x100931),x100936),f334(f334(f151(x100931),x100932),x100937)))+P104(f334(f334(f336(x100931),f742(x100935,x100934,x100933,x100932,x100931,x100936,x100937)),f334(f173(x100931),x100936))) % 169.39/169.66 [10096]~P6(x100961,x100967,x100966)+~P9(x100961,f886(x100965,a871),x100966,x100964)+P104(f334(f334(f336(x100961),f554(x100962,x100963,x100964,x100965,x100966,x100967,x100961)),x100967))+~P104(f334(f334(f336(f886(x100961,a871)),x100963),f334(f334(f62(x100961),x100967),x100966)))+P104(f334(f334(f336(f886(x100965,a871)),f334(f334(f44(x100961,f886(x100965,a871)),x100963),x100964)),x100962)) % 169.39/169.66 [10144]~P6(x101442,x101446,x101447)+~P9(x101442,f886(x101441,a871),x101447,x101444)+~P104(f334(f334(f336(f886(x101442,a871)),x101443),f334(f334(f62(x101442),x101446),x101447)))+~P104(f334(f334(f336(f886(x101441,a871)),f334(x101444,f554(x101445,x101443,x101444,x101441,x101447,x101446,x101442))),x101445))+P104(f334(f334(f336(f886(x101441,a871)),f334(f334(f44(x101442,f886(x101441,a871)),x101443),x101444)),x101445)) % 169.39/169.66 [8412]~P68(x84122)+~P21(x84121,x84125,x84128,x84124)+~E(x84123,f334(f74(x84125,x84122,x84121,x84126),x84128))+~E(x84127,f334(f313(x84121,x84125,x84128),x84124))+E(f334(f334(f11(x84121,x84122),x84123),x84124),f334(f334(f11(x84125,x84122),x84126),x84127)) % 169.39/169.66 [10148]~P68(x101482)+~P21(x101485,x101481,x101488,x101487)+~E(f334(x101486,f571(x101483,x101486,x101484,x101487,x101488,x101481,x101485,x101482)),f334(f334(f74(x101481,x101482,x101485,x101483),x101488),f571(x101483,x101486,x101484,x101487,x101488,x101481,x101485,x101482)))+~E(x101484,f334(f313(x101485,x101481,x101488),x101487))+E(f334(f334(f11(x101481,x101482),x101483),x101484),f334(f334(f11(x101485,x101482),x101486),x101487)) % 169.39/169.66 [10150]~P72(x101502)+~P21(x101501,x101505,x101508,x101504)+~E(x101507,f334(f313(x101501,x101505,x101508),x101504))+E(f334(f334(f8(x101501,x101502),x101503),x101504),f334(f334(f8(x101505,x101502),x101506),x101507))+P104(f334(f334(f336(x101501),f867(x101506,x101503,x101507,x101504,x101508,x101505,x101501,x101502)),x101504)) % 169.39/169.66 [10151]~P68(x101512)+~P21(x101511,x101515,x101518,x101514)+~E(x101517,f334(f313(x101511,x101515,x101518),x101514))+E(f334(f334(f11(x101511,x101512),x101513),x101514),f334(f334(f11(x101515,x101512),x101516),x101517))+P104(f334(f334(f336(x101511),f571(x101516,x101513,x101517,x101514,x101518,x101515,x101511,x101512)),x101514)) % 169.39/169.66 [10157]~P72(x101572)+~P21(x101575,x101571,x101578,x101577)+~E(x101574,f334(f313(x101575,x101571,x101578),x101577))+~E(f334(x101576,f867(x101573,x101576,x101574,x101577,x101578,x101571,x101575,x101572)),f334(x101573,f334(x101578,f867(x101573,x101576,x101574,x101577,x101578,x101571,x101575,x101572))))+E(f334(f334(f8(x101571,x101572),x101573),x101574),f334(f334(f8(x101575,x101572),x101576),x101577)) % 169.39/169.66 [9531]~E(f334(f196(f878(x95312)),x95315),f334(f196(f878(x95311)),x95313))+~E(f334(f196(f878(x95312)),x95314),f334(f196(f878(x95311)),x95313))+~E(f334(f334(f334(f73(x95311,f881(x95312)),f334(f179(x95311,x95312),f334(f334(f183(x95311,x95312),x95313),x95314))),x95316),f334(f241(x95312),x95317)),f334(f334(f334(f73(x95311,f881(x95312)),f334(f179(x95311,x95312),f334(f334(f183(x95311,x95312),x95313),x95315))),x95316),f334(f241(x95312),x95318)))+E(f334(f179(x95311,x95312),f334(f334(f183(x95311,x95312),x95313),x95314)),f334(f179(x95311,x95312),f334(f334(f183(x95311,x95312),x95313),x95315)))+P104(f334(f334(f336(x95311),x95316),f334(f173(x95311),x95313))) % 169.39/169.66 [9644]~P19(x96446,x96442,x96445,x96447,x96448,x96441)+~P104(f334(f63(x96442),x96444))+~P104(f334(f63(x96442),x96443))+~E(f334(f334(f104(f886(x96442,a871)),x96443),x96444),f195(f886(x96442,a871)))+E(f334(x96441,f334(f334(f113(f886(x96442,a871)),x96443),x96444)),f334(f334(x96445,f334(x96441,x96443)),f334(x96441,x96444))) % 169.39/169.66 [10045]~P19(x100458,x100452,x100455,x100457,x100456,x100451)+~E(f334(x100456,f446(x100454,x100453,x100451,x100456,x100457,x100455,x100452)),x100457)+~P104(f334(f63(x100452),x100453))+~P104(f334(f63(x100452),x100454))+E(f334(x100451,f334(f334(f113(f886(x100452,a871)),x100453),x100454)),f334(f334(x100455,f334(x100451,x100453)),f334(x100451,x100454))) % 169.39/169.66 [10101]~P19(x101018,x101012,x101015,x101017,x101016,x101011)+~P104(f334(f63(x101012),x101013))+~P104(f334(f63(x101012),x101014))+E(f334(x101011,f334(f334(f113(f886(x101012,a871)),x101013),x101014)),f334(f334(x101015,f334(x101011,x101013)),f334(x101011,x101014)))+P104(f334(f334(f336(x101012),f446(x101014,x101013,x101011,x101016,x101017,x101015,x101012)),f334(f334(f104(f886(x101012,a871)),x101013),x101014))) % 169.39/169.66 [9804]~P6(x98044,x98048,x98045)+~P6(x98041,x98049,x98043)+~P10(x98041,x98044,f886(x98042,a871),x98043,x98045,x98047)+P9(x98041,f886(x98042,a871),x98043,f334(f334(f10(f886(x98044,f886(x98042,a871)),f886(x98042,a871),x98041),f334(f44(x98044,f886(x98042,a871)),f334(f288(x98044,x98044,x98045),f334(f334(f312(x98044),x98046),f195(f886(x98044,a871)))))),x98047))+~P104(f334(f334(f336(x98044),x98046),x98048)) % 169.39/169.66 [5466]~P107(x54663)+~P30(x54663,x54661)+E(x54661,f714(x54662,x54663))+~E(f334(f173(x54663),x54661),x54662)+~P104(f334(f63(x54663),x54662))+~P104(f334(f137(x54663),x54661)) % 169.39/169.66 [5083]~P129(x50832)+~P130(x50832)+~P141(x50832)+~P112(x50832)+E(x50831,f2(x50832))+~E(f334(f334(f259(x50832),x50831),x50833),f2(x50832)) % 169.39/169.66 [5084]~P129(x50842)+~P130(x50842)+~P141(x50842)+~P112(x50842)+~E(x50841,f2(a877))+~E(f334(f334(f259(x50842),x50843),x50841),f2(x50842)) % 169.39/169.66 [6523]~P85(x65231)+~E(x65233,f2(x65231))+~E(x65232,f2(x65231))+E(f334(f334(f81(x65231),x65232),x65233),f2(x65231))+~P104(f334(f334(f249(x65231),f2(x65231)),x65233))+~P104(f334(f334(f249(x65231),f2(x65231)),x65232)) % 169.39/169.66 [8862]~E(f334(f268(a877,a877),x88623),f2(a877))+~E(x88621,f334(f334(f81(a877),f334(f334(f82(a877),f334(f268(a877,a877),x88623)),x88622)),f334(f272(a877,a877),x88623)))+P104(f334(f49(x88621,x88622),x88623))+~P104(f334(f334(f249(a877),f334(f272(a877,a877),x88623)),f2(a877)))+P104(f334(f334(f250(a877),f2(a877)),x88622))+~P104(f334(f334(f250(a877),x88622),f334(f272(a877,a877),x88623))) % 169.39/169.66 [8870]E(x88701,f2(a877))+~E(x88702,f334(f334(f81(a877),f334(f334(f82(a877),f334(f268(a877,a877),x88703)),x88701)),f334(f272(a877,a877),x88703)))+P104(f334(f49(x88702,x88701),x88703))+~P104(f334(f334(f250(a877),f2(a877)),x88701))+~P104(f334(f334(f249(a877),f2(a877)),f334(f272(a877,a877),x88703)))+~P104(f334(f334(f250(a877),f334(f272(a877,a877),x88703)),x88701)) % 169.39/169.66 [8888]~E(f334(f268(a877,a877),x88883),f2(a877))+~E(x88881,f334(f334(f81(a877),f334(f334(f82(a877),f334(f268(a877,a877),x88883)),x88882)),f334(f272(a877,a877),x88883)))+P104(f334(f49(x88881,x88882),x88883))+~P104(f334(f334(f250(a877),f2(a877)),x88882))+~P104(f334(f334(f249(a877),f2(a877)),f334(f272(a877,a877),x88883)))+~P104(f334(f334(f250(a877),f334(f272(a877,a877),x88883)),x88882)) % 169.39/169.66 [6903]~P95(x69032)+E(x69031,f195(f886(x69032,a871)))+E(x69033,f195(f886(x69032,a871)))+~P104(f334(f63(x69032),x69031))+~P104(f334(f63(x69032),x69033))+E(f12(x69032,f334(f334(f113(f886(x69032,a871)),x69033),x69031)),f334(f334(f113(x69032),f12(x69032,x69033)),f12(x69032,x69031))) % 169.39/169.66 [6904]~P95(x69042)+E(x69041,f195(f886(x69042,a871)))+E(x69043,f195(f886(x69042,a871)))+~P104(f334(f63(x69042),x69041))+~P104(f334(f63(x69042),x69043))+E(f13(x69042,f334(f334(f113(f886(x69042,a871)),x69043),x69041)),f334(f334(f104(x69042),f13(x69042,x69043)),f13(x69042,x69041))) % 169.39/169.66 [6905]~P107(x69052)+E(x69051,f195(f886(x69052,a871)))+E(x69053,f195(f886(x69052,a871)))+~P104(f334(f63(x69052),x69051))+~P104(f334(f63(x69052),x69053))+E(f16(x69052,f334(f334(f113(f886(x69052,a871)),x69053),x69051)),f334(f334(f247(x69052),f16(x69052,x69053)),f16(x69052,x69051))) % 169.39/169.66 [6906]~P107(x69062)+E(x69061,f195(f886(x69062,a871)))+E(x69063,f195(f886(x69062,a871)))+~P104(f334(f63(x69062),x69061))+~P104(f334(f63(x69062),x69063))+E(f17(x69062,f334(f334(f113(f886(x69062,a871)),x69063),x69061)),f334(f334(f248(x69062),f17(x69062,x69063)),f17(x69062,x69061))) % 169.39/169.66 [7543]~P93(x75432)+E(x75431,f195(f886(x75432,a871)))+E(x75433,f195(f886(x75432,a871)))+~P104(f334(f63(x75432),x75431))+~P104(f334(f63(x75432),x75433))+E(f334(f334(f82(x75432),f334(f65(x75432,f82(x75432)),x75433)),f334(f65(x75432,f82(x75432)),x75431)),f334(f65(x75432,f82(x75432)),f334(f334(f113(f886(x75432,a871)),x75433),x75431))) % 169.39/169.66 [7701]~P107(x77012)+E(x77011,f195(f886(x77012,a871)))+E(x77013,f195(f886(x77012,a871)))+~P104(f334(f63(x77012),x77011))+~P104(f334(f63(x77012),x77013))+E(f334(f334(f247(x77012),f14(x77012,f247(x77012),x77013)),f14(x77012,f247(x77012),x77011)),f14(x77012,f247(x77012),f334(f334(f113(f886(x77012,a871)),x77013),x77011))) % 169.39/169.66 [7702]~P107(x77022)+E(x77021,f195(f886(x77022,a871)))+E(x77023,f195(f886(x77022,a871)))+~P104(f334(f63(x77022),x77021))+~P104(f334(f63(x77022),x77023))+E(f334(f334(f248(x77022),f15(x77022,f248(x77022),x77023)),f15(x77022,f248(x77022),x77021)),f15(x77022,f248(x77022),f334(f334(f113(f886(x77022,a871)),x77023),x77021))) % 169.39/169.66 [8711]~P104(f334(x87111,x87113))+P104(f334(x87111,f396(x87111,x87112)))+P104(f334(x87111,f393(x87111,x87112)))+~P104(f334(f334(f250(a1),f2(a1)),x87112))+~P104(f334(f334(f336(a1),x87113),f305(a1,f79(a1),x87112)))+P104(f334(x87111,f334(f334(f3(a1),f393(x87111,x87112)),f334(f334(f82(a1),f395(x87111,x87112)),x87112)))) % 169.39/169.66 [8999]~P104(f334(x89991,x89993))+~P104(f334(x89991,f393(x89991,x89992)))+P104(f334(x89991,f396(x89991,x89992)))+~P104(f334(f334(f250(a1),f2(a1)),x89992))+~P104(f334(f334(f336(a1),x89993),f305(a1,f79(a1),x89992)))+~P104(f334(x89991,f334(f334(f3(a1),f393(x89991,x89992)),f334(f334(f82(a1),f395(x89991,x89992)),x89992)))) % 169.39/169.66 [10180]~P99(x101802)+E(x101801,f195(f886(x101802,a871)))+E(x101803,f195(f886(x101802,a871)))+~P104(f334(f63(x101802),x101801))+~P104(f334(f63(x101802),x101803))+E(f13(x101802,f334(f254(x101802),f334(f334(f10(f886(x101802,a871),a871,x101802),f88(x101802)),f334(f334(f10(f886(x101802,f886(x101802,a871)),f886(x101802,a871),x101802),f334(f10(f886(x101802,a871),a871,x101802),f88(x101802))),f334(f334(f9(x101802,f886(x101802,f886(x101802,a871)),f886(x101802,f886(x101802,a871))),f334(f334(f10(f886(x101802,f886(f886(x101802,a871),f886(x101802,a871))),f886(f886(x101802,f886(x101802,a871)),f886(x101802,f886(x101802,a871))),x101802),f20(x101802,f886(x101802,a871),f886(x101802,a871))),f334(f334(f10(f886(x101802,f886(x101802,f886(a871,a871))),f886(x101802,f886(f886(x101802,a871),f886(x101802,a871))),x101802),f334(f10(f886(x101802,f886(a871,a871)),f886(f886(x101802,a871),f886(x101802,a871)),x101802),f20(x101802,a871,a871))),f334(f334(f10(f886(x101802,f886(x101802,a871)),f886(x101802,f886(x101802,f886(a871,a871))),x101802),f334(f10(f886(x101802,a871),f886(x101802,f886(a871,a871)),x101802),f334(f10(a871,f886(a871,a871),x101802),a332))),f334(f334(f9(x101802,f886(x101802,f886(x101802,x101802)),f886(x101802,f886(x101802,a871))),f334(f334(f10(f886(f886(x101802,x101802),f886(x101802,a871)),f886(f886(x101802,f886(x101802,x101802)),f886(x101802,f886(x101802,a871))),x101802),f10(f886(x101802,x101802),f886(x101802,a871),x101802)),f334(f334(f10(f886(x101802,a871),f886(f886(x101802,x101802),f886(x101802,a871)),x101802),f10(x101802,a871,x101802)),a331))),f113(x101802)))))),f334(f334(f9(x101802,f886(x101802,a871),f886(x101802,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x101802,a871),f886(x101802,a871)),x101802),f10(a871,a871,x101802)),f334(f334(f10(a871,f886(a871,a871),x101802),a332),f334(f334(f9(x101802,f886(x101802,a871),a871),f336(x101802)),x101803)))),f334(f334(f9(x101802,f886(x101802,a871),a871),f336(x101802)),x101801))))))),f334(f334(f113(x101802),f13(x101802,x101803)),f13(x101802,x101801))) % 169.39/169.66 [10181]~P99(x101812)+E(x101811,f195(f886(x101812,a871)))+E(x101813,f195(f886(x101812,a871)))+~P104(f334(f63(x101812),x101811))+~P104(f334(f63(x101812),x101813))+E(f12(x101812,f334(f254(x101812),f334(f334(f10(f886(x101812,a871),a871,x101812),f88(x101812)),f334(f334(f10(f886(x101812,f886(x101812,a871)),f886(x101812,a871),x101812),f334(f10(f886(x101812,a871),a871,x101812),f88(x101812))),f334(f334(f9(x101812,f886(x101812,f886(x101812,a871)),f886(x101812,f886(x101812,a871))),f334(f334(f10(f886(x101812,f886(f886(x101812,a871),f886(x101812,a871))),f886(f886(x101812,f886(x101812,a871)),f886(x101812,f886(x101812,a871))),x101812),f20(x101812,f886(x101812,a871),f886(x101812,a871))),f334(f334(f10(f886(x101812,f886(x101812,f886(a871,a871))),f886(x101812,f886(f886(x101812,a871),f886(x101812,a871))),x101812),f334(f10(f886(x101812,f886(a871,a871)),f886(f886(x101812,a871),f886(x101812,a871)),x101812),f20(x101812,a871,a871))),f334(f334(f10(f886(x101812,f886(x101812,a871)),f886(x101812,f886(x101812,f886(a871,a871))),x101812),f334(f10(f886(x101812,a871),f886(x101812,f886(a871,a871)),x101812),f334(f10(a871,f886(a871,a871),x101812),a332))),f334(f334(f9(x101812,f886(x101812,f886(x101812,x101812)),f886(x101812,f886(x101812,a871))),f334(f334(f10(f886(f886(x101812,x101812),f886(x101812,a871)),f886(f886(x101812,f886(x101812,x101812)),f886(x101812,f886(x101812,a871))),x101812),f10(f886(x101812,x101812),f886(x101812,a871),x101812)),f334(f334(f10(f886(x101812,a871),f886(f886(x101812,x101812),f886(x101812,a871)),x101812),f10(x101812,a871,x101812)),a331))),f104(x101812)))))),f334(f334(f9(x101812,f886(x101812,a871),f886(x101812,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x101812,a871),f886(x101812,a871)),x101812),f10(a871,a871,x101812)),f334(f334(f10(a871,f886(a871,a871),x101812),a332),f334(f334(f9(x101812,f886(x101812,a871),a871),f336(x101812)),x101813)))),f334(f334(f9(x101812,f886(x101812,a871),a871),f336(x101812)),x101811))))))),f334(f334(f104(x101812),f12(x101812,x101813)),f12(x101812,x101811))) % 169.39/169.66 [10182]~P107(x101822)+E(x101821,f195(f886(x101822,a871)))+E(x101823,f195(f886(x101822,a871)))+~P104(f334(f63(x101822),x101821))+~P104(f334(f63(x101822),x101823))+E(f15(x101822,f248(x101822),f334(f254(x101822),f334(f334(f10(f886(x101822,a871),a871,x101822),f88(x101822)),f334(f334(f10(f886(x101822,f886(x101822,a871)),f886(x101822,a871),x101822),f334(f10(f886(x101822,a871),a871,x101822),f88(x101822))),f334(f334(f9(x101822,f886(x101822,f886(x101822,a871)),f886(x101822,f886(x101822,a871))),f334(f334(f10(f886(x101822,f886(f886(x101822,a871),f886(x101822,a871))),f886(f886(x101822,f886(x101822,a871)),f886(x101822,f886(x101822,a871))),x101822),f20(x101822,f886(x101822,a871),f886(x101822,a871))),f334(f334(f10(f886(x101822,f886(x101822,f886(a871,a871))),f886(x101822,f886(f886(x101822,a871),f886(x101822,a871))),x101822),f334(f10(f886(x101822,f886(a871,a871)),f886(f886(x101822,a871),f886(x101822,a871)),x101822),f20(x101822,a871,a871))),f334(f334(f10(f886(x101822,f886(x101822,a871)),f886(x101822,f886(x101822,f886(a871,a871))),x101822),f334(f10(f886(x101822,a871),f886(x101822,f886(a871,a871)),x101822),f334(f10(a871,f886(a871,a871),x101822),a332))),f334(f334(f9(x101822,f886(x101822,f886(x101822,x101822)),f886(x101822,f886(x101822,a871))),f334(f334(f10(f886(f886(x101822,x101822),f886(x101822,a871)),f886(f886(x101822,f886(x101822,x101822)),f886(x101822,f886(x101822,a871))),x101822),f10(f886(x101822,x101822),f886(x101822,a871),x101822)),f334(f334(f10(f886(x101822,a871),f886(f886(x101822,x101822),f886(x101822,a871)),x101822),f10(x101822,a871,x101822)),a331))),f247(x101822)))))),f334(f334(f9(x101822,f886(x101822,a871),f886(x101822,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x101822,a871),f886(x101822,a871)),x101822),f10(a871,a871,x101822)),f334(f334(f10(a871,f886(a871,a871),x101822),a332),f334(f334(f9(x101822,f886(x101822,a871),a871),f336(x101822)),x101823)))),f334(f334(f9(x101822,f886(x101822,a871),a871),f336(x101822)),x101821))))))),f334(f334(f247(x101822),f15(x101822,f248(x101822),x101823)),f15(x101822,f248(x101822),x101821))) % 169.39/169.66 [10183]~P107(x101832)+E(x101831,f195(f886(x101832,a871)))+E(x101833,f195(f886(x101832,a871)))+~P104(f334(f63(x101832),x101831))+~P104(f334(f63(x101832),x101833))+E(f14(x101832,f247(x101832),f334(f254(x101832),f334(f334(f10(f886(x101832,a871),a871,x101832),f88(x101832)),f334(f334(f10(f886(x101832,f886(x101832,a871)),f886(x101832,a871),x101832),f334(f10(f886(x101832,a871),a871,x101832),f88(x101832))),f334(f334(f9(x101832,f886(x101832,f886(x101832,a871)),f886(x101832,f886(x101832,a871))),f334(f334(f10(f886(x101832,f886(f886(x101832,a871),f886(x101832,a871))),f886(f886(x101832,f886(x101832,a871)),f886(x101832,f886(x101832,a871))),x101832),f20(x101832,f886(x101832,a871),f886(x101832,a871))),f334(f334(f10(f886(x101832,f886(x101832,f886(a871,a871))),f886(x101832,f886(f886(x101832,a871),f886(x101832,a871))),x101832),f334(f10(f886(x101832,f886(a871,a871)),f886(f886(x101832,a871),f886(x101832,a871)),x101832),f20(x101832,a871,a871))),f334(f334(f10(f886(x101832,f886(x101832,a871)),f886(x101832,f886(x101832,f886(a871,a871))),x101832),f334(f10(f886(x101832,a871),f886(x101832,f886(a871,a871)),x101832),f334(f10(a871,f886(a871,a871),x101832),a332))),f334(f334(f9(x101832,f886(x101832,f886(x101832,x101832)),f886(x101832,f886(x101832,a871))),f334(f334(f10(f886(f886(x101832,x101832),f886(x101832,a871)),f886(f886(x101832,f886(x101832,x101832)),f886(x101832,f886(x101832,a871))),x101832),f10(f886(x101832,x101832),f886(x101832,a871),x101832)),f334(f334(f10(f886(x101832,a871),f886(f886(x101832,x101832),f886(x101832,a871)),x101832),f10(x101832,a871,x101832)),a331))),f248(x101832)))))),f334(f334(f9(x101832,f886(x101832,a871),f886(x101832,a871)),f334(f334(f10(f886(a871,a871),f886(f886(x101832,a871),f886(x101832,a871)),x101832),f10(a871,a871,x101832)),f334(f334(f10(a871,f886(a871,a871),x101832),a332),f334(f334(f9(x101832,f886(x101832,a871),a871),f336(x101832)),x101833)))),f334(f334(f9(x101832,f886(x101832,a871),a871),f336(x101832)),x101831))))))),f334(f334(f248(x101832),f14(x101832,f247(x101832),x101833)),f14(x101832,f247(x101832),x101831))) % 169.39/169.66 [7227]~P119(x72273)+E(x72271,x72272)+~E(f334(f334(f259(x72273),x72271),x72274),f334(f334(f259(x72273),x72272),x72274))+~P104(f334(f334(f249(x72273),f2(x72273)),x72272))+~P104(f334(f334(f249(x72273),f2(x72273)),x72271))+~P104(f334(f334(f250(a877),f2(a877)),x72274)) % 169.39/169.66 [7500]~P107(x75002)+E(x75001,f195(f886(x75002,a871)))+~P104(f334(f63(x75002),x75001))+~P104(f334(f334(f336(x75002),x75004),x75001))+P104(f334(f334(f249(x75002),x75003),x75004))+~P104(f334(f334(f249(x75002),x75003),f334(f65(x75002,f247(x75002)),x75001))) % 169.39/169.66 [7501]~P101(x75012)+E(x75011,f195(f886(x75012,a871)))+~P104(f334(f63(x75012),x75011))+~P104(f334(f334(f336(x75012),x75014),x75011))+P104(f334(f334(f249(x75012),x75013),x75014))+~P104(f334(f334(f249(x75012),x75013),f334(f65(x75012,f104(x75012)),x75011))) % 169.39/169.66 [7502]~P107(x75022)+E(x75021,f195(f886(x75022,a871)))+~P104(f334(f63(x75022),x75021))+~P104(f334(f334(f336(x75022),x75024),x75021))+P104(f334(f334(f250(x75022),x75023),x75024))+~P104(f334(f334(f250(x75022),x75023),f334(f65(x75022,f247(x75022)),x75021))) % 169.39/169.66 [7401]E(x74011,f2(a1))+E(f334(f334(f40(a1),x74012),x74011),x74013)+~P104(f334(f334(f249(a1),x74014),f2(a1)))+~E(x74012,f334(f334(f81(a1),f334(f334(f82(a1),x74011),x74013)),x74014))+P104(f334(f334(f250(a1),f2(a1)),x74011))+~P104(f334(f334(f250(a1),x74011),x74014)) % 169.39/169.66 [7417]E(f46(a1,x74172,x74171),x74173)+E(x74171,f2(a1))+~P104(f334(f334(f249(a1),x74173),f2(a1)))+~E(x74172,f334(f334(f81(a1),f334(f334(f82(a1),x74171),x74174)),x74173))+P104(f334(f334(f250(a1),f2(a1)),x74171))+~P104(f334(f334(f250(a1),x74171),x74173)) % 169.39/169.66 [7542]E(x75421,f2(a1))+E(f334(f334(f40(a1),x75422),x75421),x75423)+~E(x75422,f334(f334(f81(a1),f334(f334(f82(a1),x75421),x75423)),x75424))+~P104(f334(f334(f249(a1),f2(a1)),x75424))+~P104(f334(f334(f250(a1),f2(a1)),x75421))+~P104(f334(f334(f250(a1),x75424),x75421)) % 169.39/169.66 [7564]E(f46(a1,x75642,x75641),x75643)+E(x75641,f2(a1))+~E(x75642,f334(f334(f81(a1),f334(f334(f82(a1),x75641),x75644)),x75643))+~P104(f334(f334(f249(a1),f2(a1)),x75643))+~P104(f334(f334(f250(a1),f2(a1)),x75641))+~P104(f334(f334(f250(a1),x75643),x75641)) % 169.39/169.66 [7705]~P107(x77052)+E(x77051,f195(f886(x77052,a871)))+~P104(f334(f63(x77052),x77051))+~P104(f334(f334(f249(x77052),x77054),x77053))+~P104(f334(f334(f336(x77052),x77054),x77051))+P104(f334(f334(f249(x77052),f334(f65(x77052,f247(x77052)),x77051)),x77053)) % 169.39/169.66 [7706]~P107(x77062)+E(x77061,f195(f886(x77062,a871)))+~P104(f334(f63(x77062),x77061))+~P104(f334(f334(f250(x77062),x77064),x77063))+~P104(f334(f334(f336(x77062),x77064),x77061))+P104(f334(f334(f250(x77062),f334(f65(x77062,f247(x77062)),x77061)),x77063)) % 169.39/169.66 [8270]~P104(f334(f334(f249(a1),x82704),f2(a1)))+~E(x82701,f334(f334(f81(a1),f334(f334(f82(a1),x82702),x82703)),x82704))+~P104(f334(f334(f249(a1),f2(a1)),x82704))+~P104(f334(f334(f250(a1),x82704),x82702))+~P104(f334(f334(f250(a1),x82702),x82704))+P104(f334(f50(x82701,x82702),f334(f334(f269(a1,a1),x82703),x82704))) % 169.39/169.66 [9188]~P58(x91883)+~P58(x91884)+E(x91881,x91882)+~E(f334(f196(f878(x91883)),x91882),f334(f196(f878(x91884)),f57(x91884)))+~E(f334(f196(f878(x91883)),x91881),f334(f196(f878(x91884)),f57(x91884)))+~E(f334(f74(f881(x91883),x91883,x91884,f245(x91883)),f334(f179(x91884,x91883),f334(f334(f183(x91884,x91883),f57(x91884)),x91881))),f334(f74(f881(x91883),x91883,x91884,f245(x91883)),f334(f179(x91884,x91883),f334(f334(f183(x91884,x91883),f57(x91884)),x91882)))) % 169.39/169.66 [8430]~P108(x84301)+P104(f334(f334(f250(f886(x84301,a871)),f305(x84301,x84302,x84303)),f305(x84301,x84304,x84305)))+~P104(f334(f334(f249(x84301),x84304),x84302))+~P104(f334(f334(f249(x84301),x84304),x84305))+~P104(f334(f334(f249(x84301),x84303),x84305))+~P104(f334(f334(f250(x84301),x84303),x84305)) % 169.39/169.66 [8431]~P108(x84311)+P104(f334(f334(f250(f886(x84311,a871)),f305(x84311,x84312,x84313)),f305(x84311,x84314,x84315)))+~P104(f334(f334(f249(x84311),x84313),x84315))+~P104(f334(f334(f249(x84311),x84314),x84315))+~P104(f334(f334(f249(x84311),x84314),x84312))+~P104(f334(f334(f250(x84311),x84314),x84312)) % 169.39/169.66 [9248]P56(x92482,x92483,x92484,x92481)+E(x92481,f195(f886(x92482,a871)))+~P104(f334(f63(x92482),x92484))+~P104(f334(f63(x92482),x92481))+~P104(f334(f334(x92483,f682(x92481,x92484,x92483,x92482)),x92485))+~P104(f334(f334(f336(x92482),x92485),x92481)) % 169.39/169.66 [9389]~E(x93893,x93895)+~P68(x93891)+~P72(x93891)+~P41(x93893)+E(f334(f334(f8(a1,x93891),x93892),x93893),f334(f334(f8(a1,x93891),x93894),x93895))+P104(f334(f334(f249(a1),f2(a1)),f678(x93892,x93894,x93893,x93895,x93891))) % 169.39/169.66 [9390]~E(x93903,x93905)+~P68(x93901)+~P72(x93901)+~P41(x93903)+E(f334(f334(f11(a1,x93901),x93902),x93903),f334(f334(f11(a1,x93901),x93904),x93905))+P104(f334(f334(f249(a1),f2(a1)),f551(x93902,x93904,x93903,x93905,x93901))) % 169.39/169.66 [9552]~E(x95525,x95523)+~P68(x95521)+~P72(x95521)+~P41(x95525)+~E(f334(x95522,f678(x95524,x95522,x95525,x95523,x95521)),f334(x95524,f678(x95524,x95522,x95525,x95523,x95521)))+E(f334(f334(f8(a1,x95521),x95522),x95523),f334(f334(f8(a1,x95521),x95524),x95525)) % 169.39/169.66 [9553]~E(x95535,x95533)+~P68(x95531)+~P72(x95531)+~P41(x95535)+~E(f334(x95532,f551(x95534,x95532,x95535,x95533,x95531)),f334(x95534,f551(x95534,x95532,x95535,x95533,x95531)))+E(f334(f334(f11(a1,x95531),x95532),x95533),f334(f334(f11(a1,x95531),x95534),x95535)) % 169.39/169.66 [9641]~P75(x96413)+E(f334(x96411,x96412),f2(x96413))+~E(f334(f334(f8(x96414,x96413),x96411),x96415),f2(x96413))+~P104(f334(f63(x96414),x96415))+P104(f334(f334(f336(x96414),f492(x96412,x96411,x96415,x96414,x96413)),x96415))+~P104(f334(f334(f336(x96414),x96412),x96415)) % 169.39/169.66 [9777]~P75(x97773)+E(f334(x97771,x97772),f2(x97773))+~E(f334(f334(f8(x97774,x97773),x97771),x97775),f2(x97773))+~P104(f334(f63(x97774),x97775))+~P104(f334(f334(f336(x97774),x97772),x97775))+~P104(f334(f334(f249(x97773),f2(x97773)),f334(x97771,f492(x97772,x97771,x97775,x97774,x97773)))) % 169.39/169.66 [8349]~P134(x83491)+~P104(f334(f334(f249(x83491),x83493),x83495))+~P104(f334(f334(f249(x83491),x83492),x83494))+~P104(f334(f334(f249(x83491),f2(x83491)),x83493))+~P104(f334(f334(f249(x83491),f2(x83491)),x83494))+P104(f334(f334(f249(x83491),f334(f334(f82(x83491),x83492),x83493)),f334(f334(f82(x83491),x83494),x83495))) % 169.39/169.66 [8350]~P134(x83501)+~P104(f334(f334(f249(x83501),x83503),x83505))+~P104(f334(f334(f249(x83501),x83502),x83504))+~P104(f334(f334(f249(x83501),f2(x83501)),x83503))+~P104(f334(f334(f249(x83501),f2(x83501)),x83502))+P104(f334(f334(f249(x83501),f334(f334(f82(x83501),x83502),x83503)),f334(f334(f82(x83501),x83504),x83505))) % 169.39/169.66 [8351]~P62(x83511)+~P104(f334(f334(f250(x83511),f2(x83511)),x83515))+~P104(f334(f334(f249(x83511),x83515),x83513))+~P104(f334(f334(f249(x83511),x83512),x83514))+~P104(f334(f334(f249(x83511),f2(x83511)),x83512))+P104(f334(f334(f249(x83511),f334(f334(f292(x83511),x83512),x83513)),f334(f334(f292(x83511),x83514),x83515))) % 169.39/169.66 [8352]~P131(x83521)+~P104(f334(f334(f249(x83521),x83523),x83525))+~P104(f334(f334(f249(x83521),f2(x83521)),x83522))+~P104(f334(f334(f250(x83521),x83522),x83524))+~P104(f334(f334(f250(x83521),f2(x83521)),x83523))+P104(f334(f334(f250(x83521),f334(f334(f82(x83521),x83522),x83523)),f334(f334(f82(x83521),x83524),x83525))) % 169.39/169.66 [8353]~P131(x83531)+~P104(f334(f334(f249(x83531),x83532),x83534))+~P104(f334(f334(f249(x83531),f2(x83531)),x83533))+~P104(f334(f334(f250(x83531),x83533),x83535))+~P104(f334(f334(f250(x83531),f2(x83531)),x83532))+P104(f334(f334(f250(x83531),f334(f334(f82(x83531),x83532),x83533)),f334(f334(f82(x83531),x83534),x83535))) % 169.39/169.66 [8354]~P131(x83541)+~P104(f334(f334(f249(x83541),f2(x83541)),x83543))+~P104(f334(f334(f249(x83541),f2(x83541)),x83542))+~P104(f334(f334(f250(x83541),x83543),x83545))+~P104(f334(f334(f250(x83541),x83542),x83544))+P104(f334(f334(f250(x83541),f334(f334(f82(x83541),x83542),x83543)),f334(f334(f82(x83541),x83544),x83545))) % 169.39/169.66 [8355]~P131(x83551)+~P104(f334(f334(f249(x83551),f2(x83551)),x83553))+~P104(f334(f334(f250(x83551),x83553),x83555))+~P104(f334(f334(f250(x83551),x83552),x83554))+~P104(f334(f334(f250(x83551),f2(x83551)),x83554))+P104(f334(f334(f250(x83551),f334(f334(f82(x83551),x83552),x83553)),f334(f334(f82(x83551),x83554),x83555))) % 169.39/169.66 [8356]~P62(x83561)+~P104(f334(f334(f249(x83561),x83565),x83563))+~P104(f334(f334(f249(x83561),f2(x83561)),x83562))+~P104(f334(f334(f250(x83561),x83562),x83564))+~P104(f334(f334(f250(x83561),f2(x83561)),x83565))+P104(f334(f334(f250(x83561),f334(f334(f292(x83561),x83562),x83563)),f334(f334(f292(x83561),x83564),x83565))) % 169.39/169.66 [8357]~P62(x83571)+~P104(f334(f334(f249(x83571),x83572),x83574))+~P104(f334(f334(f250(x83571),x83575),x83573))+~P104(f334(f334(f250(x83571),f2(x83571)),x83575))+~P104(f334(f334(f250(x83571),f2(x83571)),x83572))+P104(f334(f334(f250(x83571),f334(f334(f292(x83571),x83572),x83573)),f334(f334(f292(x83571),x83574),x83575))) % 169.39/169.66 [9681]~P84(x96815)+~P72(x96815)+E(x96811,f195(f886(x96812,a871)))+~P104(f334(f63(x96812),x96811))+P104(f334(f334(f336(x96812),f848(x96813,x96814,x96811,x96812,x96815)),x96811))+P104(f334(f334(f250(x96815),f334(f334(f8(x96812,x96815),x96814),x96811)),f334(f334(f8(x96812,x96815),x96813),x96811))) % 169.39/169.66 [9800]~P82(x98001)+~P72(x98001)+~P104(f334(f63(x98002),x98005))+~P104(f334(f334(f249(x98001),f2(x98001)),f334(x98003,f846(x98003,x98004,x98005,x98002,x98001))))+P104(f334(f334(f249(x98001),f334(f334(f8(x98002,x98001),x98003),x98004)),f334(f334(f8(x98002,x98001),x98003),x98005)))+~P104(f334(f334(f249(f886(x98002,a871)),x98004),x98005)) % 169.39/169.66 [9965]~P84(x99653)+~P72(x99653)+E(x99651,f195(f886(x99652,a871)))+~P104(f334(f63(x99652),x99651))+~P104(f334(f334(f250(x99653),f334(x99654,f848(x99655,x99654,x99651,x99652,x99653))),f334(x99655,f848(x99655,x99654,x99651,x99652,x99653))))+P104(f334(f334(f250(x99653),f334(f334(f8(x99652,x99653),x99654),x99651)),f334(f334(f8(x99652,x99653),x99655),x99651))) % 169.39/169.66 [7086]~P13(x70862,x70865,x70864)+E(x70861,f195(f886(x70862,a871)))+E(x70863,f195(f886(x70862,a871)))+~P104(f334(f63(x70862),x70861))+~P104(f334(f63(x70862),x70863))+E(f334(x70864,f334(f334(f113(f886(x70862,a871)),x70863),x70861)),f334(f334(x70865,f334(x70864,x70863)),f334(x70864,x70861))) % 169.39/169.66 [7671]~P146(x76711,x76714,x76713)+P104(f334(x76711,x76712))+~P104(f334(f334(f250(a1),x76714),f2(a1)))+~P104(f334(f334(f249(a1),x76715),f2(a1)))+~E(x76713,f334(f334(f81(a1),f334(f334(f82(a1),x76714),x76712)),x76715))+~P104(f334(f334(f250(a1),x76714),x76715)) % 169.39/169.66 [7672]~P145(x76721,x76724,x76723)+P104(f334(x76721,x76722))+~P104(f334(f334(f250(a1),x76724),f2(a1)))+~P104(f334(f334(f249(a1),x76722),f2(a1)))+~E(x76723,f334(f334(f81(a1),f334(f334(f82(a1),x76724),x76725)),x76722))+~P104(f334(f334(f250(a1),x76724),x76722)) % 169.39/169.66 [7714]~P146(x77141,x77144,x77143)+P104(f334(x77141,x77142))+~E(x77143,f334(f334(f81(a1),f334(f334(f82(a1),x77144),x77142)),x77145))+~P104(f334(f334(f249(a1),f2(a1)),x77145))+~P104(f334(f334(f250(a1),f2(a1)),x77144))+~P104(f334(f334(f250(a1),x77145),x77144)) % 169.39/169.66 [7715]~P145(x77151,x77154,x77153)+P104(f334(x77151,x77152))+~E(x77153,f334(f334(f81(a1),f334(f334(f82(a1),x77154),x77155)),x77152))+~P104(f334(f334(f249(a1),f2(a1)),x77152))+~P104(f334(f334(f250(a1),f2(a1)),x77154))+~P104(f334(f334(f250(a1),x77152),x77154)) % 169.39/169.66 [8634]P104(f334(f334(x86341,x86342),x86343))+~P104(f334(f334(x86341,f334(f334(f40(a1),x86344),x86345)),f46(a1,x86344,x86345)))+~P104(f334(f334(f250(a1),x86345),f2(a1)))+~P104(f334(f334(f249(a1),x86343),f2(a1)))+~E(x86344,f334(f334(f81(a1),f334(f334(f82(a1),x86345),x86342)),x86343))+~P104(f334(f334(f250(a1),x86345),x86343)) % 169.39/169.66 [8641]P104(f334(f334(x86411,x86412),x86413))+~P104(f334(f334(x86411,f334(f334(f40(a1),x86414),x86415)),f46(a1,x86414,x86415)))+~E(x86414,f334(f334(f81(a1),f334(f334(f82(a1),x86415),x86412)),x86413))+~P104(f334(f334(f249(a1),f2(a1)),x86413))+~P104(f334(f334(f250(a1),f2(a1)),x86415))+~P104(f334(f334(f250(a1),x86413),x86415)) % 169.39/169.66 [8876]E(x88761,x88762)+~P53(x88763,x88765,x88764)+~P104(f334(f334(f336(x88763),x88762),x88765))+~P104(f334(f334(f336(x88763),x88761),x88765))+P104(f334(f334(f336(f885(x88763,x88763)),f334(f334(f269(x88763,x88763),x88761),x88762)),x88764))+P104(f334(f334(f336(f885(x88763,x88763)),f334(f334(f269(x88763,x88763),x88762),x88761)),x88764)) % 169.39/169.66 [9708]~P82(x97085)+~P72(x97085)+~P104(f334(f63(x97081),x97084))+P104(f334(f334(f249(x97085),f334(f334(f8(x97081,x97085),x97082),x97083)),f334(f334(f8(x97081,x97085),x97082),x97084)))+~P104(f334(f334(f249(f886(x97081,a871)),x97083),x97084))+P104(f334(f334(f336(x97081),f846(x97082,x97083,x97084,x97081,x97085)),f334(f334(f3(f886(x97081,a871)),x97084),x97083))) % 169.39/169.66 [9808]E(x98081,f195(f886(x98082,a871)))+~P104(f334(f63(x98082),x98083))+~P104(f334(f63(x98082),x98081))+P104(f334(f334(f336(f885(f886(x98082,a871),f886(x98082,a871))),f334(f334(f269(f886(x98082,a871),f886(x98082,a871)),x98083),x98081)),f326(x98082,x98084)))+~P104(f334(f334(f336(x98082),x98085),x98081))+~P104(f334(f334(f336(f885(x98082,x98082)),f334(f334(f269(x98082,x98082),f689(x98084,x98081,x98083,x98082)),x98085)),x98084)) % 169.39/169.66 [9809]E(x98091,f195(f886(x98092,a871)))+~P104(f334(f63(x98092),x98093))+~P104(f334(f63(x98092),x98091))+P104(f334(f334(f336(f885(f886(x98092,a871),f886(x98092,a871))),f334(f334(f269(f886(x98092,a871),f886(x98092,a871)),x98093),x98091)),f326(x98092,x98094)))+~P104(f334(f334(f336(x98092),x98095),x98091))+~P104(f334(f334(f336(f885(x98092,x98092)),f334(f334(f269(x98092,x98092),f748(x98094,x98091,x98093,x98092)),x98095)),x98094)) % 169.39/169.66 [9969]~P75(x99691)+~E(f334(f334(f8(x99695,x99691),x99692),x99696),x99694)+~P104(f334(f63(x99695),x99696))+P104(f334(f334(f336(x99695),f512(x99693,x99694,x99692,x99696,x99695,x99691)),x99696))+P104(f334(f334(f249(x99691),f334(x99692,x99693)),x99694))+~P104(f334(f334(f336(x99695),x99693),x99696)) % 169.39/169.66 [10016]~P75(x100161)+~E(f334(f334(f8(x100165,x100161),x100162),x100166),x100164)+~P104(f334(f63(x100165),x100166))+~P104(f334(f334(f336(x100165),x100163),x100166))+~P104(f334(f334(f249(x100161),f2(x100161)),f334(x100162,f512(x100163,x100164,x100162,x100166,x100165,x100161))))+P104(f334(f334(f249(x100161),f334(x100162,x100163)),x100164)) % 169.39/169.66 [10130]~E(x101305,x101308)+~E(x101304,x101307)+~P106(x101301)+~P72(x101302)+E(f334(f334(f8(x101301,x101302),x101303),f334(f304(x101301,x101304),x101305)),f334(f334(f8(x101301,x101302),x101306),f334(f304(x101301,x101307),x101308)))+P104(f334(f334(f249(x101301),x101304),f403(x101303,x101306,x101305,x101308,x101304,x101307,x101301,x101302))) % 169.39/169.66 [10147]~E(x101477,x101474)+~E(x101478,x101475)+~P106(x101471)+~P72(x101472)+~E(f334(x101473,f403(x101476,x101473,x101478,x101475,x101477,x101474,x101471,x101472)),f334(x101476,f403(x101476,x101473,x101478,x101475,x101477,x101474,x101471,x101472)))+E(f334(f334(f8(x101471,x101472),x101473),f334(f304(x101471,x101474),x101475)),f334(f334(f8(x101471,x101472),x101476),f334(f304(x101471,x101477),x101478))) % 169.39/169.66 [10149]~E(x101494,x101497)+~E(x101495,x101498)+~P106(x101491)+~P72(x101492)+E(f334(f334(f8(x101491,x101492),x101493),f334(f304(x101491,x101494),x101495)),f334(f334(f8(x101491,x101492),x101496),f334(f304(x101491,x101497),x101498)))+P104(f334(f334(f250(x101491),f403(x101493,x101496,x101495,x101498,x101494,x101497,x101491,x101492)),x101495)) % 169.39/169.66 [9814]~P6(x98145,x98149,x98146)+~P6(x98141,x981410,x98143)+~P10(x98141,x98145,f886(x98142,a871),x98143,x98146,x98148)+~P104(f334(f334(f336(x98145),x98147),x98149))+~P104(f334(f334(f336(x98141),x98144),x981410))+E(f334(f334(f44(x98141,f886(x98142,a871)),f334(f288(x98141,x98141,x98143),f334(f334(f312(x98141),x98144),f195(f886(x98141,a871))))),f334(f334(f10(f886(x98145,f886(x98142,a871)),f886(x98142,a871),x98141),f334(f44(x98145,f886(x98142,a871)),f334(f288(x98145,x98145,x98146),f334(f334(f312(x98145),x98147),f195(f886(x98145,a871)))))),x98148)),f334(f334(x98148,x98144),x98147)) % 169.39/169.66 [5634]~P107(x56343)+~P30(x56343,x56342)+~P30(x56343,x56341)+E(x56341,x56342)+~E(f334(f173(x56343),x56341),f334(f173(x56343),x56342))+~P104(f334(f137(x56343),x56342))+~P104(f334(f137(x56343),x56341)) % 169.39/169.66 [4965]~P129(x49652)+~P130(x49652)+~P141(x49652)+~P112(x49652)+~E(x49653,f2(x49652))+E(x49651,f2(a877))+E(f334(f334(f259(x49652),x49653),x49651),f2(x49652)) % 169.39/169.66 [9132]E(x91321,f2(a877))+~E(x91322,f334(f334(f81(a877),f334(f334(f82(a877),f334(f268(a877,a877),x91323)),x91321)),f334(f272(a877,a877),x91323)))+P104(f334(f49(x91322,x91321),x91323))+~P104(f334(f334(f249(a877),f334(f272(a877,a877),x91323)),f2(a877)))+~P104(f334(f334(f249(a877),f2(a877)),f334(f272(a877,a877),x91323)))+~P104(f334(f334(f250(a877),x91321),f334(f272(a877,a877),x91323)))+~P104(f334(f334(f250(a877),f334(f272(a877,a877),x91323)),x91321)) % 169.39/169.66 [9141]~E(f334(f268(a877,a877),x91413),f2(a877))+~E(x91411,f334(f334(f81(a877),f334(f334(f82(a877),f334(f268(a877,a877),x91413)),x91412)),f334(f272(a877,a877),x91413)))+P104(f334(f49(x91411,x91412),x91413))+~P104(f334(f334(f249(a877),f334(f272(a877,a877),x91413)),f2(a877)))+~P104(f334(f334(f249(a877),f2(a877)),f334(f272(a877,a877),x91413)))+~P104(f334(f334(f250(a877),x91412),f334(f272(a877,a877),x91413)))+~P104(f334(f334(f250(a877),f334(f272(a877,a877),x91413)),x91412)) % 169.39/169.66 [8024]~P65(x80242)+E(x80241,f195(f886(x80242,a871)))+E(x80243,f195(f886(x80242,a871)))+~P104(f334(f63(x80242),x80241))+~P104(f334(f63(x80242),x80243))+~E(f334(f334(f104(f886(x80242,a871)),x80243),x80241),f195(f886(x80242,a871)))+E(f334(f334(f82(x80242),f334(f65(x80242,f82(x80242)),x80243)),f334(f65(x80242,f82(x80242)),x80241)),f334(f65(x80242,f82(x80242)),f334(f334(f113(f886(x80242,a871)),x80243),x80241))) % 169.39/169.66 [7810]E(x78101,f2(a1))+E(f334(f334(f40(a1),x78102),x78101),x78103)+~P104(f334(f334(f249(a1),x78104),f2(a1)))+~E(x78102,f334(f334(f81(a1),f334(f334(f82(a1),x78101),x78103)),x78104))+~P104(f334(f334(f249(a1),f2(a1)),x78104))+~P104(f334(f334(f250(a1),x78104),x78101))+~P104(f334(f334(f250(a1),x78101),x78104)) % 169.39/169.66 [7819]E(f46(a1,x78192,x78191),x78193)+E(x78191,f2(a1))+~P104(f334(f334(f249(a1),x78193),f2(a1)))+~E(x78192,f334(f334(f81(a1),f334(f334(f82(a1),x78191),x78194)),x78193))+~P104(f334(f334(f249(a1),f2(a1)),x78193))+~P104(f334(f334(f250(a1),x78193),x78191))+~P104(f334(f334(f250(a1),x78191),x78193)) % 169.39/169.66 [7723]~P14(x77232,x77235,x77234)+E(x77231,f195(f886(x77232,a871)))+E(x77233,f195(f886(x77232,a871)))+~P104(f334(f63(x77232),x77231))+~P104(f334(f63(x77232),x77233))+~E(f334(f334(f104(f886(x77232,a871)),x77233),x77231),f195(f886(x77232,a871)))+E(f334(x77234,f334(f334(f113(f886(x77232,a871)),x77233),x77231)),f334(f334(x77235,f334(x77234,x77233)),f334(x77234,x77231))) % 169.39/169.66 [9363]~P21(x93633,x93631,x93635,x93634)+~P21(x93631,x93633,x93636,x93632)+E(f334(f39(x93631),x93632),f334(f39(x93633),x93634))+~P104(f334(f63(x93633),x93634))+~P104(f334(f63(x93631),x93632))+~P104(f334(f334(f249(f886(x93633,a871)),f334(f313(x93631,x93633,x93636),x93632)),x93634))+~P104(f334(f334(f249(f886(x93631,a871)),f334(f313(x93633,x93631,x93635),x93634)),x93632)) % 169.39/169.66 [9308]~P104(f334(f334(f250(a1),f334(f334(f81(a1),f334(f334(f82(a1),x93085),x93081)),x93086)),f2(a1)))+~E(f334(f334(f81(a1),f334(f334(f82(a1),x93083),x93082)),x93084),f334(f334(f81(a1),f334(f334(f82(a1),x93085),x93081)),x93086))+~P104(f334(f334(f249(a1),f2(a1)),x93086))+~P104(f334(f334(f250(a1),f2(a1)),x93085))+~P104(f334(f334(f249(a1),x93085),x93083))+~P104(f334(f334(f250(a1),x93084),x93083))+P104(f334(f334(f249(a1),x93081),x93082)) % 169.39/169.66 [9084]~E(f334(f334(f81(a1),f334(f334(f82(a1),x90843),x90841)),x90844),f334(f334(f81(a1),f334(f334(f82(a1),x90845),x90842)),x90846))+~P104(f334(f334(f249(a1),f2(a1)),x90844))+~P104(f334(f334(f250(a1),f2(a1)),x90845))+~P104(f334(f334(f249(a1),x90845),x90843))+~P104(f334(f334(f250(a1),x90846),x90845))+P104(f334(f334(f249(a1),x90841),x90842))+~P104(f334(f334(f249(a1),f2(a1)),f334(f334(f81(a1),f334(f334(f82(a1),x90845),x90842)),x90846))) % 169.39/169.66 [9254]~P128(x92541)+~E(f334(f334(f81(x92541),x92542),x92544),f79(x92541))+~P104(f334(f334(f249(x92541),x92545),x92546))+~P104(f334(f334(f249(x92541),x92543),x92546))+~P104(f334(f334(f249(x92541),f2(x92541)),x92544))+~P104(f334(f334(f249(x92541),f2(x92541)),x92542))+P104(f334(f334(f249(x92541),f334(f334(f81(x92541),f334(f334(f82(x92541),x92542),x92543)),f334(f334(f82(x92541),x92544),x92545))),x92546)) % 169.39/169.66 [9255]~P126(x92551)+~E(f334(f334(f81(x92551),x92552),x92554),f79(x92551))+~P104(f334(f334(f249(x92551),f2(x92551)),x92554))+~P104(f334(f334(f249(x92551),f2(x92551)),x92552))+~P104(f334(f334(f250(x92551),x92555),x92556))+~P104(f334(f334(f250(x92551),x92553),x92556))+P104(f334(f334(f250(x92551),f334(f334(f81(x92551),f334(f334(f82(x92551),x92552),x92553)),f334(f334(f82(x92551),x92554),x92555))),x92556)) % 169.39/169.66 [10061]~P6(x100617,x100616,x100615)+E(x100611,x100612)+~P9(x100617,f886(x100614,a871),x100615,x100613)+E(f334(x100613,f553(x100611,x100612,x100613,x100614,x100615,x100616,x100617)),f334(x100613,f549(x100611,x100612,x100613,x100614,x100615,x100616,x100617)))+~E(f334(f334(f44(x100617,f886(x100614,a871)),x100611),x100613),f334(f334(f44(x100617,f886(x100614,a871)),x100612),x100613))+~P104(f334(f334(f336(f886(x100617,a871)),x100612),f334(f334(f62(x100617),x100616),x100615)))+~P104(f334(f334(f336(f886(x100617,a871)),x100611),f334(f334(f62(x100617),x100616),x100615))) % 169.39/169.66 [10094]~P6(x100943,x100947,x100946)+E(x100941,x100942)+~P9(x100943,f886(x100945,a871),x100946,x100944)+~E(f334(f334(f44(x100943,f886(x100945,a871)),x100941),x100944),f334(f334(f44(x100943,f886(x100945,a871)),x100942),x100944))+P104(f334(f334(f336(x100943),f549(x100941,x100942,x100944,x100945,x100946,x100947,x100943)),x100947))+~P104(f334(f334(f336(f886(x100943,a871)),x100942),f334(f334(f62(x100943),x100947),x100946)))+~P104(f334(f334(f336(f886(x100943,a871)),x100941),f334(f334(f62(x100943),x100947),x100946))) % 169.39/169.66 [10095]~P6(x100953,x100957,x100956)+E(x100951,x100952)+~P9(x100953,f886(x100955,a871),x100956,x100954)+~E(f334(f334(f44(x100953,f886(x100955,a871)),x100951),x100954),f334(f334(f44(x100953,f886(x100955,a871)),x100952),x100954))+P104(f334(f334(f336(x100953),f553(x100951,x100952,x100954,x100955,x100956,x100957,x100953)),x100957))+~P104(f334(f334(f336(f886(x100953,a871)),x100952),f334(f334(f62(x100953),x100957),x100956)))+~P104(f334(f334(f336(f886(x100953,a871)),x100951),f334(f334(f62(x100953),x100957),x100956))) % 169.39/169.66 [10166]E(x101661,x101662)+~P6(x101663,x101666,x101667)+~P9(x101663,f886(x101664,a871),x101667,x101665)+~E(f334(f334(f44(x101663,f886(x101664,a871)),x101661),x101665),f334(f334(f44(x101663,f886(x101664,a871)),x101662),x101665))+~P104(f334(f334(f336(f885(x101663,x101663)),f334(f334(f269(x101663,x101663),f549(x101661,x101662,x101665,x101664,x101667,x101666,x101663)),f553(x101661,x101662,x101665,x101664,x101667,x101666,x101663))),x101667))+~P104(f334(f334(f336(f886(x101663,a871)),x101662),f334(f334(f62(x101663),x101666),x101667)))+~P104(f334(f334(f336(f886(x101663,a871)),x101661),f334(f334(f62(x101663),x101666),x101667))) % 169.39/169.66 [9083]~P6(x90831,x90837,x90834)+~E(x90835,x90836)+~P104(f334(f334(f336(x90831),x90833),x90836))+~P104(f334(f334(f336(x90831),x90832),x90835))+~P104(f334(f334(f336(f886(x90831,a871)),x90836),f334(f334(f62(x90831),x90837),x90834)))+~P104(f334(f334(f336(f886(x90831,a871)),x90835),f334(f334(f62(x90831),x90837),x90834)))+P104(f334(f334(f336(f885(x90831,x90831)),f334(f334(f269(x90831,x90831),x90832),x90833)),x90834)) % 169.39/169.66 [9216]E(x92161,x92162)+~P6(x92163,x92164,x92165)+~P104(f334(f334(f336(x92163),x92166),x92162))+~P104(f334(f334(f336(x92163),x92167),x92161))+~P104(f334(f334(f336(f886(x92163,a871)),x92162),f334(f334(f62(x92163),x92164),x92165)))+~P104(f334(f334(f336(f886(x92163,a871)),x92161),f334(f334(f62(x92163),x92164),x92165)))+~P104(f334(f334(f336(f885(x92163,x92163)),f334(f334(f269(x92163,x92163),x92167),x92166)),x92165)) % 169.39/169.66 [10185]~P6(x101859,x101858,x101857)+~P6(x101851,x1018511,x1018510)+~P10(x101851,x101859,f886(x101856,a871),x1018510,x101857,x101855)+P104(f334(f334(f336(x101851),f555(x101852,x101853,x101854,x101855,x101856,x101857,x101858,x101859,x1018510,x1018511,x101851)),x1018511))+~P104(f334(f334(f336(f886(x101859,a871)),x101853),f334(f334(f62(x101859),x101858),x101857)))+~P104(f334(f334(f336(f886(x101851,a871)),x101854),f334(f334(f62(x101851),x1018511),x1018510)))+P104(f334(f334(f336(f886(x101856,a871)),f334(f334(f44(x101851,f886(x101856,a871)),x101854),f334(f334(f10(f886(x101859,f886(x101856,a871)),f886(x101856,a871),x101851),f334(f44(x101859,f886(x101856,a871)),x101853)),x101855))),x101852)) % 169.39/169.66 [10186]~P6(x1018611,x1018610,x101869)+~P6(x101861,x101868,x101867)+~P10(x1018611,x101861,f886(x101866,a871),x101869,x101867,x101865)+P104(f334(f334(f336(x101861),f556(x101862,x101863,x101864,x101865,x101866,x101867,x101868,x101861,x101869,x1018610,x1018611)),x101868))+~P104(f334(f334(f336(f886(x1018611,a871)),x101864),f334(f334(f62(x1018611),x1018610),x101869)))+~P104(f334(f334(f336(f886(x101861,a871)),x101863),f334(f334(f62(x101861),x101868),x101867)))+P104(f334(f334(f336(f886(x101866,a871)),f334(f334(f44(x1018611,f886(x101866,a871)),x101864),f334(f334(f10(f886(x101861,f886(x101866,a871)),f886(x101866,a871),x1018611),f334(f44(x101861,f886(x101866,a871)),x101863)),x101865))),x101862)) % 169.39/169.66 [10189]~P6(x101892,x101898,x101899)+~P6(x101894,x1018910,x1018911)+~P10(x101892,x101894,f886(x101891,a871),x101899,x1018911,x101896)+~P104(f334(f334(f336(f886(x101892,a871)),x101893),f334(f334(f62(x101892),x101898),x101899)))+~P104(f334(f334(f336(f886(x101894,a871)),x101895),f334(f334(f62(x101894),x1018910),x1018911)))+~P104(f334(f334(f336(f886(x101891,a871)),f334(f334(x101896,f555(x101897,x101895,x101893,x101896,x101891,x1018911,x1018910,x101894,x101899,x101898,x101892)),f556(x101897,x101895,x101893,x101896,x101891,x1018911,x1018910,x101894,x101899,x101898,x101892))),x101897))+P104(f334(f334(f336(f886(x101891,a871)),f334(f334(f44(x101892,f886(x101891,a871)),x101893),f334(f334(f10(f886(x101894,f886(x101891,a871)),f886(x101891,a871),x101892),f334(f44(x101894,f886(x101891,a871)),x101895)),x101896))),x101897)) % 169.39/169.66 [9119]E(x91191,x91192)+~P107(x91194)+~P21(x91193,x91194,x91195,f334(f334(f113(f886(x91193,a871)),f334(f173(x91193),x91191)),f334(f173(x91193),x91192)))+~E(f334(f173(x91193),x91191),f334(f173(x91193),x91192))+~P30(x91194,f334(f334(f154(x91193,x91194),x91195),x91192))+~P30(x91194,f334(f334(f154(x91193,x91194),x91195),x91191))+~P104(f334(f137(x91194),f334(f334(f154(x91193,x91194),x91195),x91192)))+~P104(f334(f137(x91194),f334(f334(f154(x91193,x91194),x91195),x91191))) % 169.39/169.66 %EqnAxiom % 169.39/169.66 [1]E(x11,x11) % 169.39/169.66 [2]E(x22,x21)+~E(x21,x22) % 169.39/169.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 169.39/169.66 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 169.39/169.66 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 169.39/169.66 [6]~E(x61,x62)+E(f103(x61),f103(x62)) % 169.39/169.66 [7]~E(x71,x72)+E(f195(x71),f195(x72)) % 169.39/169.66 [8]~E(x81,x82)+E(f334(x81,x83),f334(x82,x83)) % 169.39/169.66 [9]~E(x91,x92)+E(f334(x93,x91),f334(x93,x92)) % 169.39/169.66 [10]~E(x101,x102)+E(f32(x101),f32(x102)) % 169.39/169.66 [11]~E(x111,x112)+E(f44(x111,x113),f44(x112,x113)) % 169.39/169.66 [12]~E(x121,x122)+E(f44(x123,x121),f44(x123,x122)) % 169.39/169.66 [13]~E(x131,x132)+E(f85(x131),f85(x132)) % 169.39/169.66 [14]~E(x141,x142)+E(f886(x141,x143),f886(x142,x143)) % 169.39/169.66 [15]~E(x151,x152)+E(f886(x153,x151),f886(x153,x152)) % 169.39/169.66 [16]~E(x161,x162)+E(f322(x161,x163),f322(x162,x163)) % 169.39/169.66 [17]~E(x171,x172)+E(f322(x173,x171),f322(x173,x172)) % 169.39/169.66 [18]~E(x181,x182)+E(f556(x181,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812),f556(x182,x183,x184,x185,x186,x187,x188,x189,x1810,x1811,x1812)) % 169.39/169.66 [19]~E(x191,x192)+E(f556(x193,x191,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912),f556(x193,x192,x194,x195,x196,x197,x198,x199,x1910,x1911,x1912)) % 169.39/169.66 [20]~E(x201,x202)+E(f556(x203,x204,x201,x205,x206,x207,x208,x209,x2010,x2011,x2012),f556(x203,x204,x202,x205,x206,x207,x208,x209,x2010,x2011,x2012)) % 169.39/169.66 [21]~E(x211,x212)+E(f556(x213,x214,x215,x211,x216,x217,x218,x219,x2110,x2111,x2112),f556(x213,x214,x215,x212,x216,x217,x218,x219,x2110,x2111,x2112)) % 169.39/169.66 [22]~E(x221,x222)+E(f556(x223,x224,x225,x226,x221,x227,x228,x229,x2210,x2211,x2212),f556(x223,x224,x225,x226,x222,x227,x228,x229,x2210,x2211,x2212)) % 169.39/169.66 [23]~E(x231,x232)+E(f556(x233,x234,x235,x236,x237,x231,x238,x239,x2310,x2311,x2312),f556(x233,x234,x235,x236,x237,x232,x238,x239,x2310,x2311,x2312)) % 169.39/169.66 [24]~E(x241,x242)+E(f556(x243,x244,x245,x246,x247,x248,x241,x249,x2410,x2411,x2412),f556(x243,x244,x245,x246,x247,x248,x242,x249,x2410,x2411,x2412)) % 169.39/169.66 [25]~E(x251,x252)+E(f556(x253,x254,x255,x256,x257,x258,x259,x251,x2510,x2511,x2512),f556(x253,x254,x255,x256,x257,x258,x259,x252,x2510,x2511,x2512)) % 169.39/169.66 [26]~E(x261,x262)+E(f556(x263,x264,x265,x266,x267,x268,x269,x2610,x261,x2611,x2612),f556(x263,x264,x265,x266,x267,x268,x269,x2610,x262,x2611,x2612)) % 169.39/169.66 [27]~E(x271,x272)+E(f556(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x271,x2712),f556(x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x272,x2712)) % 169.39/169.66 [28]~E(x281,x282)+E(f556(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x281),f556(x283,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812,x282)) % 169.39/169.66 [29]~E(x291,x292)+E(f104(x291),f104(x292)) % 169.39/169.66 [30]~E(x301,x302)+E(f247(x301),f247(x302)) % 169.39/169.66 [31]~E(x311,x312)+E(f113(x311),f113(x312)) % 169.39/169.66 [32]~E(x321,x322)+E(f248(x321),f248(x322)) % 169.39/169.66 [33]~E(x331,x332)+E(f105(x331),f105(x332)) % 169.39/169.66 [34]~E(x341,x342)+E(f35(x341),f35(x342)) % 169.39/169.66 [35]~E(x351,x352)+E(f79(x351),f79(x352)) % 169.39/169.66 [36]~E(x361,x362)+E(f336(x361),f336(x362)) % 169.39/169.66 [37]~E(x371,x372)+E(f555(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f555(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 169.39/169.66 [38]~E(x381,x382)+E(f555(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f555(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 169.39/169.66 [39]~E(x391,x392)+E(f555(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f555(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 169.39/169.66 [40]~E(x401,x402)+E(f555(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f555(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012)) % 169.39/169.66 [41]~E(x411,x412)+E(f555(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f555(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112)) % 169.39/169.66 [42]~E(x421,x422)+E(f555(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f555(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212)) % 169.39/169.66 [43]~E(x431,x432)+E(f555(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f555(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312)) % 169.39/169.66 [44]~E(x441,x442)+E(f555(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f555(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412)) % 169.39/169.66 [45]~E(x451,x452)+E(f555(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f555(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512)) % 169.39/169.66 [46]~E(x461,x462)+E(f555(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f555(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612)) % 169.39/169.66 [47]~E(x471,x472)+E(f555(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f555(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472)) % 169.39/169.66 [48]~E(x481,x482)+E(f114(x481),f114(x482)) % 169.39/169.66 [49]~E(x491,x492)+E(f249(x491),f249(x492)) % 169.39/169.66 [50]~E(x501,x502)+E(f269(x501,x503),f269(x502,x503)) % 169.39/169.66 [51]~E(x511,x512)+E(f269(x513,x511),f269(x513,x512)) % 169.39/169.66 [52]~E(x521,x522)+E(f6(x521),f6(x522)) % 169.39/169.66 [53]~E(x531,x532)+E(f173(x531),f173(x532)) % 169.39/169.66 [54]~E(x541,x542)+E(f876(x541),f876(x542)) % 169.39/169.66 [55]~E(x551,x552)+E(f881(x551),f881(x552)) % 169.39/169.66 [56]~E(x561,x562)+E(f878(x561),f878(x562)) % 169.39/169.66 [57]~E(x571,x572)+E(f879(x571),f879(x572)) % 169.39/169.66 [58]~E(x581,x582)+E(f275(x581,x583,x584,x585),f275(x582,x583,x584,x585)) % 169.39/169.66 [59]~E(x591,x592)+E(f275(x593,x591,x594,x595),f275(x593,x592,x594,x595)) % 169.39/169.66 [60]~E(x601,x602)+E(f275(x603,x604,x601,x605),f275(x603,x604,x602,x605)) % 169.39/169.66 [61]~E(x611,x612)+E(f275(x613,x614,x615,x611),f275(x613,x614,x615,x612)) % 169.39/169.66 [62]~E(x621,x622)+E(f250(x621),f250(x622)) % 169.39/169.66 [63]~E(x631,x632)+E(f169(x631),f169(x632)) % 169.39/169.66 [64]~E(x641,x642)+E(f81(x641),f81(x642)) % 169.39/169.66 [65]~E(x651,x652)+E(f80(x651),f80(x652)) % 169.39/169.66 [66]~E(x661,x662)+E(f554(x661,x663,x664,x665,x666,x667,x668),f554(x662,x663,x664,x665,x666,x667,x668)) % 169.39/169.66 [67]~E(x671,x672)+E(f554(x673,x671,x674,x675,x676,x677,x678),f554(x673,x672,x674,x675,x676,x677,x678)) % 169.39/169.66 [68]~E(x681,x682)+E(f554(x683,x684,x681,x685,x686,x687,x688),f554(x683,x684,x682,x685,x686,x687,x688)) % 169.39/169.66 [69]~E(x691,x692)+E(f554(x693,x694,x695,x691,x696,x697,x698),f554(x693,x694,x695,x692,x696,x697,x698)) % 169.39/169.66 [70]~E(x701,x702)+E(f554(x703,x704,x705,x706,x701,x707,x708),f554(x703,x704,x705,x706,x702,x707,x708)) % 169.39/169.66 [71]~E(x711,x712)+E(f554(x713,x714,x715,x716,x717,x711,x718),f554(x713,x714,x715,x716,x717,x712,x718)) % 169.39/169.66 [72]~E(x721,x722)+E(f554(x723,x724,x725,x726,x727,x728,x721),f554(x723,x724,x725,x726,x727,x728,x722)) % 169.39/169.66 [73]~E(x731,x732)+E(f196(x731),f196(x732)) % 169.39/169.66 [74]~E(x741,x742)+E(f82(x741),f82(x742)) % 169.39/169.66 [75]~E(x751,x752)+E(f106(x751),f106(x752)) % 169.39/169.66 [76]~E(x761,x762)+E(f62(x761),f62(x762)) % 169.39/169.66 [77]~E(x771,x772)+E(f413(x771,x773),f413(x772,x773)) % 169.39/169.66 [78]~E(x781,x782)+E(f413(x783,x781),f413(x783,x782)) % 169.39/169.66 [79]~E(x791,x792)+E(f885(x791,x793),f885(x792,x793)) % 169.39/169.66 [80]~E(x801,x802)+E(f885(x803,x801),f885(x803,x802)) % 169.39/169.66 [81]~E(x811,x812)+E(f63(x811),f63(x812)) % 169.39/169.66 [82]~E(x821,x822)+E(f8(x821,x823),f8(x822,x823)) % 169.39/169.66 [83]~E(x831,x832)+E(f8(x833,x831),f8(x833,x832)) % 169.39/169.66 [84]~E(x841,x842)+E(f675(x841,x843),f675(x842,x843)) % 169.39/169.66 [85]~E(x851,x852)+E(f675(x853,x851),f675(x853,x852)) % 169.39/169.66 [86]~E(x861,x862)+E(f312(x861),f312(x862)) % 169.39/169.66 [87]~E(x871,x872)+E(f139(x871,x873),f139(x872,x873)) % 169.39/169.66 [88]~E(x881,x882)+E(f139(x883,x881),f139(x883,x882)) % 169.39/169.66 [89]~E(x891,x892)+E(f313(x891,x893,x894),f313(x892,x893,x894)) % 169.39/169.66 [90]~E(x901,x902)+E(f313(x903,x901,x904),f313(x903,x902,x904)) % 169.39/169.66 [91]~E(x911,x912)+E(f313(x913,x914,x911),f313(x913,x914,x912)) % 169.39/169.66 [92]~E(x921,x922)+E(f151(x921),f151(x922)) % 169.39/169.66 [93]~E(x931,x932)+E(f272(x931,x933),f272(x932,x933)) % 169.39/169.66 [94]~E(x941,x942)+E(f272(x943,x941),f272(x943,x942)) % 169.39/169.66 [95]~E(x951,x952)+E(f268(x951,x953),f268(x952,x953)) % 169.39/169.66 [96]~E(x961,x962)+E(f268(x963,x961),f268(x963,x962)) % 169.39/169.66 [97]~E(x971,x972)+E(f10(x971,x973,x974),f10(x972,x973,x974)) % 169.39/169.66 [98]~E(x981,x982)+E(f10(x983,x981,x984),f10(x983,x982,x984)) % 169.39/169.66 [99]~E(x991,x992)+E(f10(x993,x994,x991),f10(x993,x994,x992)) % 169.39/169.66 [100]~E(x1001,x1002)+E(f46(x1001,x1003,x1004),f46(x1002,x1003,x1004)) % 169.39/169.66 [101]~E(x1011,x1012)+E(f46(x1013,x1011,x1014),f46(x1013,x1012,x1014)) % 169.39/169.66 [102]~E(x1021,x1022)+E(f46(x1023,x1024,x1021),f46(x1023,x1024,x1022)) % 169.39/169.66 [103]~E(x1031,x1032)+E(f20(x1031,x1033,x1034),f20(x1032,x1033,x1034)) % 169.39/169.66 [104]~E(x1041,x1042)+E(f20(x1043,x1041,x1044),f20(x1043,x1042,x1044)) % 169.39/169.66 [105]~E(x1051,x1052)+E(f20(x1053,x1054,x1051),f20(x1053,x1054,x1052)) % 169.39/169.66 [106]~E(x1061,x1062)+E(f165(x1061),f165(x1062)) % 169.39/169.66 [107]~E(x1071,x1072)+E(f210(x1071),f210(x1072)) % 169.39/169.66 [108]~E(x1081,x1082)+E(f884(x1081,x1083),f884(x1082,x1083)) % 169.39/169.66 [109]~E(x1091,x1092)+E(f884(x1093,x1091),f884(x1093,x1092)) % 169.39/169.66 [110]~E(x1101,x1102)+E(f273(x1101,x1103,x1104),f273(x1102,x1103,x1104)) % 169.39/169.66 [111]~E(x1111,x1112)+E(f273(x1113,x1111,x1114),f273(x1113,x1112,x1114)) % 169.39/169.66 [112]~E(x1121,x1122)+E(f273(x1123,x1124,x1121),f273(x1123,x1124,x1122)) % 169.39/169.66 [113]~E(x1131,x1132)+E(f11(x1131,x1133),f11(x1132,x1133)) % 169.39/169.66 [114]~E(x1141,x1142)+E(f11(x1143,x1141),f11(x1143,x1142)) % 169.39/169.66 [115]~E(x1151,x1152)+E(f154(x1151,x1153),f154(x1152,x1153)) % 169.39/169.66 [116]~E(x1161,x1162)+E(f154(x1163,x1161),f154(x1163,x1162)) % 169.39/169.66 [117]~E(x1171,x1172)+E(f553(x1171,x1173,x1174,x1175,x1176,x1177,x1178),f553(x1172,x1173,x1174,x1175,x1176,x1177,x1178)) % 169.39/169.66 [118]~E(x1181,x1182)+E(f553(x1183,x1181,x1184,x1185,x1186,x1187,x1188),f553(x1183,x1182,x1184,x1185,x1186,x1187,x1188)) % 169.39/169.66 [119]~E(x1191,x1192)+E(f553(x1193,x1194,x1191,x1195,x1196,x1197,x1198),f553(x1193,x1194,x1192,x1195,x1196,x1197,x1198)) % 169.39/169.66 [120]~E(x1201,x1202)+E(f553(x1203,x1204,x1205,x1201,x1206,x1207,x1208),f553(x1203,x1204,x1205,x1202,x1206,x1207,x1208)) % 169.39/169.66 [121]~E(x1211,x1212)+E(f553(x1213,x1214,x1215,x1216,x1211,x1217,x1218),f553(x1213,x1214,x1215,x1216,x1212,x1217,x1218)) % 169.39/169.66 [122]~E(x1221,x1222)+E(f553(x1223,x1224,x1225,x1226,x1227,x1221,x1228),f553(x1223,x1224,x1225,x1226,x1227,x1222,x1228)) % 169.39/169.66 [123]~E(x1231,x1232)+E(f553(x1233,x1234,x1235,x1236,x1237,x1238,x1231),f553(x1233,x1234,x1235,x1236,x1237,x1238,x1232)) % 169.39/169.66 [124]~E(x1241,x1242)+E(f116(x1241),f116(x1242)) % 169.39/169.66 [125]~E(x1251,x1252)+E(f291(x1251,x1253,x1254),f291(x1252,x1253,x1254)) % 169.39/169.66 [126]~E(x1261,x1262)+E(f291(x1263,x1261,x1264),f291(x1263,x1262,x1264)) % 169.39/169.66 [127]~E(x1271,x1272)+E(f291(x1273,x1274,x1271),f291(x1273,x1274,x1272)) % 169.39/169.66 [128]~E(x1281,x1282)+E(f166(x1281),f166(x1282)) % 169.39/169.66 [129]~E(x1291,x1292)+E(f9(x1291,x1293,x1294),f9(x1292,x1293,x1294)) % 169.39/169.66 [130]~E(x1301,x1302)+E(f9(x1303,x1301,x1304),f9(x1303,x1302,x1304)) % 169.39/169.66 [131]~E(x1311,x1312)+E(f9(x1313,x1314,x1311),f9(x1313,x1314,x1312)) % 169.39/169.66 [132]~E(x1321,x1322)+E(f816(x1321,x1323,x1324),f816(x1322,x1323,x1324)) % 169.39/169.66 [133]~E(x1331,x1332)+E(f816(x1333,x1331,x1334),f816(x1333,x1332,x1334)) % 169.39/169.66 [134]~E(x1341,x1342)+E(f816(x1343,x1344,x1341),f816(x1343,x1344,x1342)) % 169.39/169.66 [135]~E(x1351,x1352)+E(f274(x1351,x1353,x1354,x1355,x1356,x1357),f274(x1352,x1353,x1354,x1355,x1356,x1357)) % 169.39/169.66 [136]~E(x1361,x1362)+E(f274(x1363,x1361,x1364,x1365,x1366,x1367),f274(x1363,x1362,x1364,x1365,x1366,x1367)) % 169.39/169.66 [137]~E(x1371,x1372)+E(f274(x1373,x1374,x1371,x1375,x1376,x1377),f274(x1373,x1374,x1372,x1375,x1376,x1377)) % 169.39/169.66 [138]~E(x1381,x1382)+E(f274(x1383,x1384,x1385,x1381,x1386,x1387),f274(x1383,x1384,x1385,x1382,x1386,x1387)) % 169.39/169.66 [139]~E(x1391,x1392)+E(f274(x1393,x1394,x1395,x1396,x1391,x1397),f274(x1393,x1394,x1395,x1396,x1392,x1397)) % 169.39/169.66 [140]~E(x1401,x1402)+E(f274(x1403,x1404,x1405,x1406,x1407,x1401),f274(x1403,x1404,x1405,x1406,x1407,x1402)) % 169.39/169.66 [141]~E(x1411,x1412)+E(f156(x1411,x1413,x1414,x1415),f156(x1412,x1413,x1414,x1415)) % 169.39/169.66 [142]~E(x1421,x1422)+E(f156(x1423,x1421,x1424,x1425),f156(x1423,x1422,x1424,x1425)) % 169.39/169.66 [143]~E(x1431,x1432)+E(f156(x1433,x1434,x1431,x1435),f156(x1433,x1434,x1432,x1435)) % 169.39/169.66 [144]~E(x1441,x1442)+E(f156(x1443,x1444,x1445,x1441),f156(x1443,x1444,x1445,x1442)) % 169.39/169.66 [145]~E(x1451,x1452)+E(f142(x1451,x1453,x1454,x1455),f142(x1452,x1453,x1454,x1455)) % 169.39/169.66 [146]~E(x1461,x1462)+E(f142(x1463,x1461,x1464,x1465),f142(x1463,x1462,x1464,x1465)) % 169.39/169.66 [147]~E(x1471,x1472)+E(f142(x1473,x1474,x1471,x1475),f142(x1473,x1474,x1472,x1475)) % 169.39/169.66 [148]~E(x1481,x1482)+E(f142(x1483,x1484,x1485,x1481),f142(x1483,x1484,x1485,x1482)) % 169.39/169.66 [149]~E(x1491,x1492)+E(f605(x1491,x1493),f605(x1492,x1493)) % 169.39/169.66 [150]~E(x1501,x1502)+E(f605(x1503,x1501),f605(x1503,x1502)) % 169.39/169.66 [151]~E(x1511,x1512)+E(f134(x1511),f134(x1512)) % 169.39/169.66 [152]~E(x1521,x1522)+E(f259(x1521),f259(x1522)) % 169.39/169.66 [153]~E(x1531,x1532)+E(f304(x1531,x1533),f304(x1532,x1533)) % 169.39/169.66 [154]~E(x1541,x1542)+E(f304(x1543,x1541),f304(x1543,x1542)) % 169.39/169.66 [155]~E(x1551,x1552)+E(f258(x1551,x1553,x1554),f258(x1552,x1553,x1554)) % 169.39/169.66 [156]~E(x1561,x1562)+E(f258(x1563,x1561,x1564),f258(x1563,x1562,x1564)) % 169.39/169.66 [157]~E(x1571,x1572)+E(f258(x1573,x1574,x1571),f258(x1573,x1574,x1572)) % 169.39/169.66 [158]~E(x1581,x1582)+E(f257(x1581),f257(x1582)) % 169.39/169.66 [159]~E(x1591,x1592)+E(f160(x1591,x1593),f160(x1592,x1593)) % 169.39/169.66 [160]~E(x1601,x1602)+E(f160(x1603,x1601),f160(x1603,x1602)) % 169.39/169.66 [161]~E(x1611,x1612)+E(f74(x1611,x1613,x1614,x1615),f74(x1612,x1613,x1614,x1615)) % 169.39/169.66 [162]~E(x1621,x1622)+E(f74(x1623,x1621,x1624,x1625),f74(x1623,x1622,x1624,x1625)) % 169.39/169.66 [163]~E(x1631,x1632)+E(f74(x1633,x1634,x1631,x1635),f74(x1633,x1634,x1632,x1635)) % 169.39/169.66 [164]~E(x1641,x1642)+E(f74(x1643,x1644,x1645,x1641),f74(x1643,x1644,x1645,x1642)) % 169.39/169.66 [165]~E(x1651,x1652)+E(f227(x1651,x1653),f227(x1652,x1653)) % 169.39/169.66 [166]~E(x1661,x1662)+E(f227(x1663,x1661),f227(x1663,x1662)) % 169.39/169.66 [167]~E(x1671,x1672)+E(f255(x1671),f255(x1672)) % 169.39/169.66 [168]~E(x1681,x1682)+E(f108(x1681),f108(x1682)) % 169.39/169.66 [169]~E(x1691,x1692)+E(f109(x1691),f109(x1692)) % 169.39/169.66 [170]~E(x1701,x1702)+E(f335(x1701),f335(x1702)) % 169.39/169.66 [171]~E(x1711,x1712)+E(f51(x1711,x1713),f51(x1712,x1713)) % 169.39/169.66 [172]~E(x1721,x1722)+E(f51(x1723,x1721),f51(x1723,x1722)) % 169.39/169.66 [173]~E(x1731,x1732)+E(f198(x1731),f198(x1732)) % 169.39/169.66 [174]~E(x1741,x1742)+E(f157(x1741,x1743),f157(x1742,x1743)) % 169.39/169.66 [175]~E(x1751,x1752)+E(f157(x1753,x1751),f157(x1753,x1752)) % 169.39/169.66 [176]~E(x1761,x1762)+E(f176(x1761),f176(x1762)) % 169.39/169.66 [177]~E(x1771,x1772)+E(f305(x1771,x1773,x1774),f305(x1772,x1773,x1774)) % 169.39/169.66 [178]~E(x1781,x1782)+E(f305(x1783,x1781,x1784),f305(x1783,x1782,x1784)) % 169.39/169.66 [179]~E(x1791,x1792)+E(f305(x1793,x1794,x1791),f305(x1793,x1794,x1792)) % 169.39/169.66 [180]~E(x1801,x1802)+E(f7(x1801),f7(x1802)) % 169.39/169.66 [181]~E(x1811,x1812)+E(f221(x1811),f221(x1812)) % 169.39/169.66 [182]~E(x1821,x1822)+E(f254(x1821),f254(x1822)) % 169.39/169.66 [183]~E(x1831,x1832)+E(f549(x1831,x1833,x1834,x1835,x1836,x1837,x1838),f549(x1832,x1833,x1834,x1835,x1836,x1837,x1838)) % 169.39/169.66 [184]~E(x1841,x1842)+E(f549(x1843,x1841,x1844,x1845,x1846,x1847,x1848),f549(x1843,x1842,x1844,x1845,x1846,x1847,x1848)) % 169.39/169.66 [185]~E(x1851,x1852)+E(f549(x1853,x1854,x1851,x1855,x1856,x1857,x1858),f549(x1853,x1854,x1852,x1855,x1856,x1857,x1858)) % 169.39/169.66 [186]~E(x1861,x1862)+E(f549(x1863,x1864,x1865,x1861,x1866,x1867,x1868),f549(x1863,x1864,x1865,x1862,x1866,x1867,x1868)) % 169.39/169.66 [187]~E(x1871,x1872)+E(f549(x1873,x1874,x1875,x1876,x1871,x1877,x1878),f549(x1873,x1874,x1875,x1876,x1872,x1877,x1878)) % 169.39/169.66 [188]~E(x1881,x1882)+E(f549(x1883,x1884,x1885,x1886,x1887,x1881,x1888),f549(x1883,x1884,x1885,x1886,x1887,x1882,x1888)) % 169.39/169.66 [189]~E(x1891,x1892)+E(f549(x1893,x1894,x1895,x1896,x1897,x1898,x1891),f549(x1893,x1894,x1895,x1896,x1897,x1898,x1892)) % 169.39/169.66 [190]~E(x1901,x1902)+E(f437(x1901,x1903,x1904),f437(x1902,x1903,x1904)) % 169.39/169.66 [191]~E(x1911,x1912)+E(f437(x1913,x1911,x1914),f437(x1913,x1912,x1914)) % 169.39/169.66 [192]~E(x1921,x1922)+E(f437(x1923,x1924,x1921),f437(x1923,x1924,x1922)) % 169.39/169.66 [193]~E(x1931,x1932)+E(f159(x1931,x1933),f159(x1932,x1933)) % 169.39/169.66 [194]~E(x1941,x1942)+E(f159(x1943,x1941),f159(x1943,x1942)) % 169.39/169.66 [195]~E(x1951,x1952)+E(f178(x1951,x1953,x1954),f178(x1952,x1953,x1954)) % 169.39/169.66 [196]~E(x1961,x1962)+E(f178(x1963,x1961,x1964),f178(x1963,x1962,x1964)) % 169.39/169.66 [197]~E(x1971,x1972)+E(f178(x1973,x1974,x1971),f178(x1973,x1974,x1972)) % 169.39/169.66 [198]~E(x1981,x1982)+E(f181(x1981,x1983),f181(x1982,x1983)) % 169.39/169.66 [199]~E(x1991,x1992)+E(f181(x1993,x1991),f181(x1993,x1992)) % 169.39/169.66 [200]~E(x2001,x2002)+E(f93(x2001),f93(x2002)) % 169.39/169.66 [201]~E(x2011,x2012)+E(f92(x2011),f92(x2012)) % 169.39/169.66 [202]~E(x2021,x2022)+E(f13(x2021,x2023),f13(x2022,x2023)) % 169.39/169.66 [203]~E(x2031,x2032)+E(f13(x2033,x2031),f13(x2033,x2032)) % 169.39/169.66 [204]~E(x2041,x2042)+E(f153(x2041,x2043),f153(x2042,x2043)) % 169.39/169.66 [205]~E(x2051,x2052)+E(f153(x2053,x2051),f153(x2053,x2052)) % 169.39/169.66 [206]~E(x2061,x2062)+E(f288(x2061,x2063,x2064),f288(x2062,x2063,x2064)) % 169.39/169.66 [207]~E(x2071,x2072)+E(f288(x2073,x2071,x2074),f288(x2073,x2072,x2074)) % 169.39/169.66 [208]~E(x2081,x2082)+E(f288(x2083,x2084,x2081),f288(x2083,x2084,x2082)) % 169.39/169.66 [209]~E(x2091,x2092)+E(f136(x2091,x2093),f136(x2092,x2093)) % 169.39/169.66 [210]~E(x2101,x2102)+E(f136(x2103,x2101),f136(x2103,x2102)) % 169.39/169.66 [211]~E(x2111,x2112)+E(f17(x2111,x2113),f17(x2112,x2113)) % 169.39/169.66 [212]~E(x2121,x2122)+E(f17(x2123,x2121),f17(x2123,x2122)) % 169.39/169.66 [213]~E(x2131,x2132)+E(f742(x2131,x2133,x2134,x2135,x2136,x2137,x2138),f742(x2132,x2133,x2134,x2135,x2136,x2137,x2138)) % 169.39/169.66 [214]~E(x2141,x2142)+E(f742(x2143,x2141,x2144,x2145,x2146,x2147,x2148),f742(x2143,x2142,x2144,x2145,x2146,x2147,x2148)) % 169.39/169.66 [215]~E(x2151,x2152)+E(f742(x2153,x2154,x2151,x2155,x2156,x2157,x2158),f742(x2153,x2154,x2152,x2155,x2156,x2157,x2158)) % 169.39/169.66 [216]~E(x2161,x2162)+E(f742(x2163,x2164,x2165,x2161,x2166,x2167,x2168),f742(x2163,x2164,x2165,x2162,x2166,x2167,x2168)) % 169.39/169.66 [217]~E(x2171,x2172)+E(f742(x2173,x2174,x2175,x2176,x2171,x2177,x2178),f742(x2173,x2174,x2175,x2176,x2172,x2177,x2178)) % 169.39/169.66 [218]~E(x2181,x2182)+E(f742(x2183,x2184,x2185,x2186,x2187,x2181,x2188),f742(x2183,x2184,x2185,x2186,x2187,x2182,x2188)) % 169.39/169.66 [219]~E(x2191,x2192)+E(f742(x2193,x2194,x2195,x2196,x2197,x2198,x2191),f742(x2193,x2194,x2195,x2196,x2197,x2198,x2192)) % 169.39/169.66 [220]~E(x2201,x2202)+E(f446(x2201,x2203,x2204,x2205,x2206,x2207,x2208),f446(x2202,x2203,x2204,x2205,x2206,x2207,x2208)) % 169.39/169.66 [221]~E(x2211,x2212)+E(f446(x2213,x2211,x2214,x2215,x2216,x2217,x2218),f446(x2213,x2212,x2214,x2215,x2216,x2217,x2218)) % 169.39/169.66 [222]~E(x2221,x2222)+E(f446(x2223,x2224,x2221,x2225,x2226,x2227,x2228),f446(x2223,x2224,x2222,x2225,x2226,x2227,x2228)) % 169.39/169.66 [223]~E(x2231,x2232)+E(f446(x2233,x2234,x2235,x2231,x2236,x2237,x2238),f446(x2233,x2234,x2235,x2232,x2236,x2237,x2238)) % 169.39/169.66 [224]~E(x2241,x2242)+E(f446(x2243,x2244,x2245,x2246,x2241,x2247,x2248),f446(x2243,x2244,x2245,x2246,x2242,x2247,x2248)) % 169.39/169.66 [225]~E(x2251,x2252)+E(f446(x2253,x2254,x2255,x2256,x2257,x2251,x2258),f446(x2253,x2254,x2255,x2256,x2257,x2252,x2258)) % 169.39/169.66 [226]~E(x2261,x2262)+E(f446(x2263,x2264,x2265,x2266,x2267,x2268,x2261),f446(x2263,x2264,x2265,x2266,x2267,x2268,x2262)) % 169.39/169.66 [227]~E(x2271,x2272)+E(f292(x2271),f292(x2272)) % 169.39/169.66 [228]~E(x2281,x2282)+E(f587(x2281,x2283,x2284,x2285,x2286),f587(x2282,x2283,x2284,x2285,x2286)) % 169.39/169.66 [229]~E(x2291,x2292)+E(f587(x2293,x2291,x2294,x2295,x2296),f587(x2293,x2292,x2294,x2295,x2296)) % 169.39/169.66 [230]~E(x2301,x2302)+E(f587(x2303,x2304,x2301,x2305,x2306),f587(x2303,x2304,x2302,x2305,x2306)) % 169.39/169.66 [231]~E(x2311,x2312)+E(f587(x2313,x2314,x2315,x2311,x2316),f587(x2313,x2314,x2315,x2312,x2316)) % 169.39/169.66 [232]~E(x2321,x2322)+E(f587(x2323,x2324,x2325,x2326,x2321),f587(x2323,x2324,x2325,x2326,x2322)) % 169.39/169.66 [233]~E(x2331,x2332)+E(f15(x2331,x2333,x2334),f15(x2332,x2333,x2334)) % 169.39/169.66 [234]~E(x2341,x2342)+E(f15(x2343,x2341,x2344),f15(x2343,x2342,x2344)) % 169.39/169.66 [235]~E(x2351,x2352)+E(f15(x2353,x2354,x2351),f15(x2353,x2354,x2352)) % 169.39/169.66 [236]~E(x2361,x2362)+E(f39(x2361),f39(x2362)) % 169.39/169.66 [237]~E(x2371,x2372)+E(f43(x2371,x2373),f43(x2372,x2373)) % 169.39/169.66 [238]~E(x2381,x2382)+E(f43(x2383,x2381),f43(x2383,x2382)) % 169.39/169.66 [239]~E(x2391,x2392)+E(f18(x2391,x2393),f18(x2392,x2393)) % 169.39/169.66 [240]~E(x2401,x2402)+E(f18(x2403,x2401),f18(x2403,x2402)) % 169.39/169.66 [241]~E(x2411,x2412)+E(f610(x2411,x2413,x2414,x2415),f610(x2412,x2413,x2414,x2415)) % 169.39/169.66 [242]~E(x2421,x2422)+E(f610(x2423,x2421,x2424,x2425),f610(x2423,x2422,x2424,x2425)) % 169.39/169.66 [243]~E(x2431,x2432)+E(f610(x2433,x2434,x2431,x2435),f610(x2433,x2434,x2432,x2435)) % 169.39/169.66 [244]~E(x2441,x2442)+E(f610(x2443,x2444,x2445,x2441),f610(x2443,x2444,x2445,x2442)) % 169.39/169.66 [245]~E(x2451,x2452)+E(f40(x2451),f40(x2452)) % 169.39/169.66 [246]~E(x2461,x2462)+E(f12(x2461,x2463),f12(x2462,x2463)) % 169.39/169.66 [247]~E(x2471,x2472)+E(f12(x2473,x2471),f12(x2473,x2472)) % 169.39/169.66 [248]~E(x2481,x2482)+E(f789(x2481,x2483,x2484,x2485),f789(x2482,x2483,x2484,x2485)) % 169.39/169.66 [249]~E(x2491,x2492)+E(f789(x2493,x2491,x2494,x2495),f789(x2493,x2492,x2494,x2495)) % 169.39/169.66 [250]~E(x2501,x2502)+E(f789(x2503,x2504,x2501,x2505),f789(x2503,x2504,x2502,x2505)) % 169.39/169.66 [251]~E(x2511,x2512)+E(f789(x2513,x2514,x2515,x2511),f789(x2513,x2514,x2515,x2512)) % 169.39/169.66 [252]~E(x2521,x2522)+E(f186(x2521,x2523,x2524,x2525),f186(x2522,x2523,x2524,x2525)) % 169.39/169.66 [253]~E(x2531,x2532)+E(f186(x2533,x2531,x2534,x2535),f186(x2533,x2532,x2534,x2535)) % 169.39/169.66 [254]~E(x2541,x2542)+E(f186(x2543,x2544,x2541,x2545),f186(x2543,x2544,x2542,x2545)) % 169.39/169.66 [255]~E(x2551,x2552)+E(f186(x2553,x2554,x2555,x2551),f186(x2553,x2554,x2555,x2552)) % 169.39/169.66 [256]~E(x2561,x2562)+E(f183(x2561,x2563),f183(x2562,x2563)) % 169.39/169.66 [257]~E(x2571,x2572)+E(f183(x2573,x2571),f183(x2573,x2572)) % 169.39/169.66 [258]~E(x2581,x2582)+E(f310(x2581,x2583),f310(x2582,x2583)) % 169.39/169.66 [259]~E(x2591,x2592)+E(f310(x2593,x2591),f310(x2593,x2592)) % 169.39/169.66 [260]~E(x2601,x2602)+E(f745(x2601,x2603,x2604,x2605,x2606,x2607,x2608),f745(x2602,x2603,x2604,x2605,x2606,x2607,x2608)) % 169.39/169.66 [261]~E(x2611,x2612)+E(f745(x2613,x2611,x2614,x2615,x2616,x2617,x2618),f745(x2613,x2612,x2614,x2615,x2616,x2617,x2618)) % 169.39/169.66 [262]~E(x2621,x2622)+E(f745(x2623,x2624,x2621,x2625,x2626,x2627,x2628),f745(x2623,x2624,x2622,x2625,x2626,x2627,x2628)) % 169.39/169.66 [263]~E(x2631,x2632)+E(f745(x2633,x2634,x2635,x2631,x2636,x2637,x2638),f745(x2633,x2634,x2635,x2632,x2636,x2637,x2638)) % 169.39/169.66 [264]~E(x2641,x2642)+E(f745(x2643,x2644,x2645,x2646,x2641,x2647,x2648),f745(x2643,x2644,x2645,x2646,x2642,x2647,x2648)) % 169.39/169.66 [265]~E(x2651,x2652)+E(f745(x2653,x2654,x2655,x2656,x2657,x2651,x2658),f745(x2653,x2654,x2655,x2656,x2657,x2652,x2658)) % 169.39/169.66 [266]~E(x2661,x2662)+E(f745(x2663,x2664,x2665,x2666,x2667,x2668,x2661),f745(x2663,x2664,x2665,x2666,x2667,x2668,x2662)) % 169.39/169.66 [267]~E(x2671,x2672)+E(f64(x2671,x2673,x2674),f64(x2672,x2673,x2674)) % 169.39/169.66 [268]~E(x2681,x2682)+E(f64(x2683,x2681,x2684),f64(x2683,x2682,x2684)) % 169.39/169.66 [269]~E(x2691,x2692)+E(f64(x2693,x2694,x2691),f64(x2693,x2694,x2692)) % 169.39/169.66 [270]~E(x2701,x2702)+E(f148(x2701,x2703,x2704),f148(x2702,x2703,x2704)) % 169.39/169.66 [271]~E(x2711,x2712)+E(f148(x2713,x2711,x2714),f148(x2713,x2712,x2714)) % 169.39/169.66 [272]~E(x2721,x2722)+E(f148(x2723,x2724,x2721),f148(x2723,x2724,x2722)) % 169.39/169.66 [273]~E(x2731,x2732)+E(f76(x2731),f76(x2732)) % 169.39/169.66 [274]~E(x2741,x2742)+E(f83(x2741,x2743),f83(x2742,x2743)) % 169.39/169.66 [275]~E(x2751,x2752)+E(f83(x2753,x2751),f83(x2753,x2752)) % 169.39/169.66 [276]~E(x2761,x2762)+E(f323(x2761,x2763),f323(x2762,x2763)) % 169.39/169.66 [277]~E(x2771,x2772)+E(f323(x2773,x2771),f323(x2773,x2772)) % 169.39/169.66 [278]~E(x2781,x2782)+E(f271(x2781,x2783),f271(x2782,x2783)) % 169.39/169.66 [279]~E(x2791,x2792)+E(f271(x2793,x2791),f271(x2793,x2792)) % 169.39/169.66 [280]~E(x2801,x2802)+E(f117(x2801,x2803),f117(x2802,x2803)) % 169.39/169.66 [281]~E(x2811,x2812)+E(f117(x2813,x2811),f117(x2813,x2812)) % 169.39/169.66 [282]~E(x2821,x2822)+E(f267(x2821,x2823),f267(x2822,x2823)) % 169.39/169.66 [283]~E(x2831,x2832)+E(f267(x2833,x2831),f267(x2833,x2832)) % 169.39/169.66 [284]~E(x2841,x2842)+E(f137(x2841),f137(x2842)) % 169.39/169.66 [285]~E(x2851,x2852)+E(f152(x2851,x2853),f152(x2852,x2853)) % 169.39/169.66 [286]~E(x2861,x2862)+E(f152(x2863,x2861),f152(x2863,x2862)) % 169.39/169.66 [287]~E(x2871,x2872)+E(f657(x2871,x2873),f657(x2872,x2873)) % 169.39/169.66 [288]~E(x2881,x2882)+E(f657(x2883,x2881),f657(x2883,x2882)) % 169.39/169.66 [289]~E(x2891,x2892)+E(f199(x2891),f199(x2892)) % 169.39/169.66 [290]~E(x2901,x2902)+E(f161(x2901,x2903),f161(x2902,x2903)) % 169.39/169.66 [291]~E(x2911,x2912)+E(f161(x2913,x2911),f161(x2913,x2912)) % 169.39/169.66 [292]~E(x2921,x2922)+E(f118(x2921),f118(x2922)) % 169.39/169.66 [293]~E(x2931,x2932)+E(f351(x2931,x2933,x2934),f351(x2932,x2933,x2934)) % 169.39/169.66 [294]~E(x2941,x2942)+E(f351(x2943,x2941,x2944),f351(x2943,x2942,x2944)) % 169.39/169.66 [295]~E(x2951,x2952)+E(f351(x2953,x2954,x2951),f351(x2953,x2954,x2952)) % 169.39/169.66 [296]~E(x2961,x2962)+E(f372(x2961,x2963,x2964,x2965),f372(x2962,x2963,x2964,x2965)) % 169.39/169.66 [297]~E(x2971,x2972)+E(f372(x2973,x2971,x2974,x2975),f372(x2973,x2972,x2974,x2975)) % 169.39/169.66 [298]~E(x2981,x2982)+E(f372(x2983,x2984,x2981,x2985),f372(x2983,x2984,x2982,x2985)) % 169.39/169.66 [299]~E(x2991,x2992)+E(f372(x2993,x2994,x2995,x2991),f372(x2993,x2994,x2995,x2992)) % 169.39/169.66 [300]~E(x3001,x3002)+E(f600(x3001,x3003,x3004,x3005,x3006),f600(x3002,x3003,x3004,x3005,x3006)) % 169.39/169.66 [301]~E(x3011,x3012)+E(f600(x3013,x3011,x3014,x3015,x3016),f600(x3013,x3012,x3014,x3015,x3016)) % 169.39/169.66 [302]~E(x3021,x3022)+E(f600(x3023,x3024,x3021,x3025,x3026),f600(x3023,x3024,x3022,x3025,x3026)) % 169.39/169.66 [303]~E(x3031,x3032)+E(f600(x3033,x3034,x3035,x3031,x3036),f600(x3033,x3034,x3035,x3032,x3036)) % 169.39/169.66 [304]~E(x3041,x3042)+E(f600(x3043,x3044,x3045,x3046,x3041),f600(x3043,x3044,x3045,x3046,x3042)) % 169.39/169.66 [305]~E(x3051,x3052)+E(f170(x3051,x3053,x3054),f170(x3052,x3053,x3054)) % 169.39/169.66 [306]~E(x3061,x3062)+E(f170(x3063,x3061,x3064),f170(x3063,x3062,x3064)) % 169.39/169.66 [307]~E(x3071,x3072)+E(f170(x3073,x3074,x3071),f170(x3073,x3074,x3072)) % 169.39/169.66 [308]~E(x3081,x3082)+E(f213(x3081),f213(x3082)) % 169.39/169.66 [309]~E(x3091,x3092)+E(f60(x3091),f60(x3092)) % 169.39/169.66 [310]~E(x3101,x3102)+E(f764(x3101,x3103),f764(x3102,x3103)) % 169.39/169.66 [311]~E(x3111,x3112)+E(f764(x3113,x3111),f764(x3113,x3112)) % 169.39/169.66 [312]~E(x3121,x3122)+E(f407(x3121,x3123,x3124,x3125),f407(x3122,x3123,x3124,x3125)) % 169.39/169.66 [313]~E(x3131,x3132)+E(f407(x3133,x3131,x3134,x3135),f407(x3133,x3132,x3134,x3135)) % 169.39/169.66 [314]~E(x3141,x3142)+E(f407(x3143,x3144,x3141,x3145),f407(x3143,x3144,x3142,x3145)) % 169.39/169.66 [315]~E(x3151,x3152)+E(f407(x3153,x3154,x3155,x3151),f407(x3153,x3154,x3155,x3152)) % 169.39/169.66 [316]~E(x3161,x3162)+E(f882(x3161,x3163),f882(x3162,x3163)) % 169.39/169.66 [317]~E(x3171,x3172)+E(f882(x3173,x3171),f882(x3173,x3172)) % 169.39/169.66 [318]~E(x3181,x3182)+E(f14(x3181,x3183,x3184),f14(x3182,x3183,x3184)) % 169.39/169.66 [319]~E(x3191,x3192)+E(f14(x3193,x3191,x3194),f14(x3193,x3192,x3194)) % 169.39/169.66 [320]~E(x3201,x3202)+E(f14(x3203,x3204,x3201),f14(x3203,x3204,x3202)) % 169.39/169.66 [321]~E(x3211,x3212)+E(f16(x3211,x3213),f16(x3212,x3213)) % 169.39/169.66 [322]~E(x3221,x3222)+E(f16(x3223,x3221),f16(x3223,x3222)) % 169.39/169.66 [323]~E(x3231,x3232)+E(f31(x3231,x3233,x3234),f31(x3232,x3233,x3234)) % 169.39/169.66 [324]~E(x3241,x3242)+E(f31(x3243,x3241,x3244),f31(x3243,x3242,x3244)) % 169.39/169.66 [325]~E(x3251,x3252)+E(f31(x3253,x3254,x3251),f31(x3253,x3254,x3252)) % 169.39/169.66 [326]~E(x3261,x3262)+E(f168(x3261),f168(x3262)) % 169.39/169.66 [327]~E(x3271,x3272)+E(f356(x3271,x3273,x3274),f356(x3272,x3273,x3274)) % 169.39/169.66 [328]~E(x3281,x3282)+E(f356(x3283,x3281,x3284),f356(x3283,x3282,x3284)) % 169.39/169.66 [329]~E(x3291,x3292)+E(f356(x3293,x3294,x3291),f356(x3293,x3294,x3292)) % 169.39/169.66 [330]~E(x3301,x3302)+E(f59(x3301),f59(x3302)) % 169.39/169.66 [331]~E(x3311,x3312)+E(f290(x3311,x3313),f290(x3312,x3313)) % 169.39/169.66 [332]~E(x3321,x3322)+E(f290(x3323,x3321),f290(x3323,x3322)) % 169.39/169.66 [333]~E(x3331,x3332)+E(f172(x3331),f172(x3332)) % 169.39/169.66 [334]~E(x3341,x3342)+E(f519(x3341,x3343,x3344,x3345),f519(x3342,x3343,x3344,x3345)) % 169.39/169.66 [335]~E(x3351,x3352)+E(f519(x3353,x3351,x3354,x3355),f519(x3353,x3352,x3354,x3355)) % 169.39/169.66 [336]~E(x3361,x3362)+E(f519(x3363,x3364,x3361,x3365),f519(x3363,x3364,x3362,x3365)) % 169.39/169.66 [337]~E(x3371,x3372)+E(f519(x3373,x3374,x3375,x3371),f519(x3373,x3374,x3375,x3372)) % 169.39/169.66 [338]~E(x3381,x3382)+E(f138(x3381),f138(x3382)) % 169.39/169.66 [339]~E(x3391,x3392)+E(f69(x3391,x3393,x3394),f69(x3392,x3393,x3394)) % 169.39/169.66 [340]~E(x3401,x3402)+E(f69(x3403,x3401,x3404),f69(x3403,x3402,x3404)) % 169.39/169.66 [341]~E(x3411,x3412)+E(f69(x3413,x3414,x3411),f69(x3413,x3414,x3412)) % 169.39/169.66 [342]~E(x3421,x3422)+E(f67(x3421,x3423,x3424),f67(x3422,x3423,x3424)) % 169.39/169.66 [343]~E(x3431,x3432)+E(f67(x3433,x3431,x3434),f67(x3433,x3432,x3434)) % 169.39/169.66 [344]~E(x3441,x3442)+E(f67(x3443,x3444,x3441),f67(x3443,x3444,x3442)) % 169.39/169.66 [345]~E(x3451,x3452)+E(f311(x3451),f311(x3452)) % 169.39/169.66 [346]~E(x3461,x3462)+E(f601(x3461,x3463,x3464,x3465,x3466),f601(x3462,x3463,x3464,x3465,x3466)) % 169.39/169.66 [347]~E(x3471,x3472)+E(f601(x3473,x3471,x3474,x3475,x3476),f601(x3473,x3472,x3474,x3475,x3476)) % 169.39/169.66 [348]~E(x3481,x3482)+E(f601(x3483,x3484,x3481,x3485,x3486),f601(x3483,x3484,x3482,x3485,x3486)) % 169.39/169.66 [349]~E(x3491,x3492)+E(f601(x3493,x3494,x3495,x3491,x3496),f601(x3493,x3494,x3495,x3492,x3496)) % 169.39/169.66 [350]~E(x3501,x3502)+E(f601(x3503,x3504,x3505,x3506,x3501),f601(x3503,x3504,x3505,x3506,x3502)) % 169.39/169.66 [351]~E(x3511,x3512)+E(f141(x3511),f141(x3512)) % 169.39/169.66 [352]~E(x3521,x3522)+E(f190(x3521,x3523),f190(x3522,x3523)) % 169.39/169.66 [353]~E(x3531,x3532)+E(f190(x3533,x3531),f190(x3533,x3532)) % 169.39/169.66 [354]~E(x3541,x3542)+E(f245(x3541),f245(x3542)) % 169.39/169.66 [355]~E(x3551,x3552)+E(f523(x3551,x3553,x3554,x3555),f523(x3552,x3553,x3554,x3555)) % 169.39/169.66 [356]~E(x3561,x3562)+E(f523(x3563,x3561,x3564,x3565),f523(x3563,x3562,x3564,x3565)) % 169.39/169.66 [357]~E(x3571,x3572)+E(f523(x3573,x3574,x3571,x3575),f523(x3573,x3574,x3572,x3575)) % 169.39/169.66 [358]~E(x3581,x3582)+E(f523(x3583,x3584,x3585,x3581),f523(x3583,x3584,x3585,x3582)) % 169.39/169.66 [359]~E(x3591,x3592)+E(f475(x3591,x3593,x3594),f475(x3592,x3593,x3594)) % 169.39/169.66 [360]~E(x3601,x3602)+E(f475(x3603,x3601,x3604),f475(x3603,x3602,x3604)) % 169.39/169.66 [361]~E(x3611,x3612)+E(f475(x3613,x3614,x3611),f475(x3613,x3614,x3612)) % 169.39/169.66 [362]~E(x3621,x3622)+E(f179(x3621,x3623),f179(x3622,x3623)) % 169.39/169.66 [363]~E(x3631,x3632)+E(f179(x3633,x3631),f179(x3633,x3632)) % 169.39/169.66 [364]~E(x3641,x3642)+E(f34(x3641,x3643),f34(x3642,x3643)) % 169.39/169.66 [365]~E(x3651,x3652)+E(f34(x3653,x3651),f34(x3653,x3652)) % 169.39/169.66 [366]~E(x3661,x3662)+E(f65(x3661,x3663),f65(x3662,x3663)) % 169.39/169.66 [367]~E(x3671,x3672)+E(f65(x3673,x3671),f65(x3673,x3672)) % 169.39/169.66 [368]~E(x3681,x3682)+E(f325(x3681,x3683),f325(x3682,x3683)) % 169.39/169.66 [369]~E(x3691,x3692)+E(f325(x3693,x3691),f325(x3693,x3692)) % 169.39/169.66 [370]~E(x3701,x3702)+E(f87(x3701,x3703),f87(x3702,x3703)) % 169.39/169.66 [371]~E(x3711,x3712)+E(f87(x3713,x3711),f87(x3713,x3712)) % 169.39/169.66 [372]~E(x3721,x3722)+E(f326(x3721,x3723),f326(x3722,x3723)) % 169.39/169.66 [373]~E(x3731,x3732)+E(f326(x3733,x3731),f326(x3733,x3732)) % 169.39/169.66 [374]~E(x3741,x3742)+E(f99(x3741),f99(x3742)) % 169.39/169.66 [375]~E(x3751,x3752)+E(f145(x3751,x3753),f145(x3752,x3753)) % 169.39/169.66 [376]~E(x3761,x3762)+E(f145(x3763,x3761),f145(x3763,x3762)) % 169.39/169.66 [377]~E(x3771,x3772)+E(f371(x3771,x3773,x3774,x3775),f371(x3772,x3773,x3774,x3775)) % 169.39/169.66 [378]~E(x3781,x3782)+E(f371(x3783,x3781,x3784,x3785),f371(x3783,x3782,x3784,x3785)) % 169.39/169.66 [379]~E(x3791,x3792)+E(f371(x3793,x3794,x3791,x3795),f371(x3793,x3794,x3792,x3795)) % 169.39/169.66 [380]~E(x3801,x3802)+E(f371(x3803,x3804,x3805,x3801),f371(x3803,x3804,x3805,x3802)) % 169.39/169.66 [381]~E(x3811,x3812)+E(f769(x3811,x3813,x3814,x3815,x3816),f769(x3812,x3813,x3814,x3815,x3816)) % 169.39/169.66 [382]~E(x3821,x3822)+E(f769(x3823,x3821,x3824,x3825,x3826),f769(x3823,x3822,x3824,x3825,x3826)) % 169.39/169.66 [383]~E(x3831,x3832)+E(f769(x3833,x3834,x3831,x3835,x3836),f769(x3833,x3834,x3832,x3835,x3836)) % 169.39/169.66 [384]~E(x3841,x3842)+E(f769(x3843,x3844,x3845,x3841,x3846),f769(x3843,x3844,x3845,x3842,x3846)) % 169.39/169.66 [385]~E(x3851,x3852)+E(f769(x3853,x3854,x3855,x3856,x3851),f769(x3853,x3854,x3855,x3856,x3852)) % 169.39/169.66 [386]~E(x3861,x3862)+E(f822(x3861,x3863,x3864,x3865),f822(x3862,x3863,x3864,x3865)) % 169.39/169.66 [387]~E(x3871,x3872)+E(f822(x3873,x3871,x3874,x3875),f822(x3873,x3872,x3874,x3875)) % 169.39/169.66 [388]~E(x3881,x3882)+E(f822(x3883,x3884,x3881,x3885),f822(x3883,x3884,x3882,x3885)) % 169.39/169.66 [389]~E(x3891,x3892)+E(f822(x3893,x3894,x3895,x3891),f822(x3893,x3894,x3895,x3892)) % 169.39/169.66 [390]~E(x3901,x3902)+E(f57(x3901),f57(x3902)) % 169.39/169.66 [391]~E(x3911,x3912)+E(f625(x3911,x3913,x3914,x3915),f625(x3912,x3913,x3914,x3915)) % 169.39/169.66 [392]~E(x3921,x3922)+E(f625(x3923,x3921,x3924,x3925),f625(x3923,x3922,x3924,x3925)) % 169.39/169.66 [393]~E(x3931,x3932)+E(f625(x3933,x3934,x3931,x3935),f625(x3933,x3934,x3932,x3935)) % 169.39/169.66 [394]~E(x3941,x3942)+E(f625(x3943,x3944,x3945,x3941),f625(x3943,x3944,x3945,x3942)) % 169.39/169.66 [395]~E(x3951,x3952)+E(f404(x3951,x3953,x3954,x3955),f404(x3952,x3953,x3954,x3955)) % 169.39/169.66 [396]~E(x3961,x3962)+E(f404(x3963,x3961,x3964,x3965),f404(x3963,x3962,x3964,x3965)) % 169.39/169.66 [397]~E(x3971,x3972)+E(f404(x3973,x3974,x3971,x3975),f404(x3973,x3974,x3972,x3975)) % 169.39/169.66 [398]~E(x3981,x3982)+E(f404(x3983,x3984,x3985,x3981),f404(x3983,x3984,x3985,x3982)) % 169.39/169.66 [399]~E(x3991,x3992)+E(f687(x3991,x3993,x3994,x3995,x3996),f687(x3992,x3993,x3994,x3995,x3996)) % 169.39/169.66 [400]~E(x4001,x4002)+E(f687(x4003,x4001,x4004,x4005,x4006),f687(x4003,x4002,x4004,x4005,x4006)) % 169.39/169.66 [401]~E(x4011,x4012)+E(f687(x4013,x4014,x4011,x4015,x4016),f687(x4013,x4014,x4012,x4015,x4016)) % 169.39/169.66 [402]~E(x4021,x4022)+E(f687(x4023,x4024,x4025,x4021,x4026),f687(x4023,x4024,x4025,x4022,x4026)) % 169.39/169.66 [403]~E(x4031,x4032)+E(f687(x4033,x4034,x4035,x4036,x4031),f687(x4033,x4034,x4035,x4036,x4032)) % 169.39/169.66 [404]~E(x4041,x4042)+E(f78(x4041,x4043,x4044,x4045),f78(x4042,x4043,x4044,x4045)) % 169.39/169.66 [405]~E(x4051,x4052)+E(f78(x4053,x4051,x4054,x4055),f78(x4053,x4052,x4054,x4055)) % 169.39/169.66 [406]~E(x4061,x4062)+E(f78(x4063,x4064,x4061,x4065),f78(x4063,x4064,x4062,x4065)) % 169.39/169.66 [407]~E(x4071,x4072)+E(f78(x4073,x4074,x4075,x4071),f78(x4073,x4074,x4075,x4072)) % 169.39/169.66 [408]~E(x4081,x4082)+E(f225(x4081,x4083),f225(x4082,x4083)) % 169.39/169.66 [409]~E(x4091,x4092)+E(f225(x4093,x4091),f225(x4093,x4092)) % 169.39/169.66 [410]~E(x4101,x4102)+E(f845(x4101,x4103,x4104,x4105,x4106),f845(x4102,x4103,x4104,x4105,x4106)) % 169.39/169.66 [411]~E(x4111,x4112)+E(f845(x4113,x4111,x4114,x4115,x4116),f845(x4113,x4112,x4114,x4115,x4116)) % 169.39/169.66 [412]~E(x4121,x4122)+E(f845(x4123,x4124,x4121,x4125,x4126),f845(x4123,x4124,x4122,x4125,x4126)) % 169.39/169.66 [413]~E(x4131,x4132)+E(f845(x4133,x4134,x4135,x4131,x4136),f845(x4133,x4134,x4135,x4132,x4136)) % 169.39/169.66 [414]~E(x4141,x4142)+E(f845(x4143,x4144,x4145,x4146,x4141),f845(x4143,x4144,x4145,x4146,x4142)) % 169.39/169.66 [415]~E(x4151,x4152)+E(f47(x4151,x4153),f47(x4152,x4153)) % 169.39/169.66 [416]~E(x4161,x4162)+E(f47(x4163,x4161),f47(x4163,x4162)) % 169.39/169.66 [417]~E(x4171,x4172)+E(f66(x4171,x4173,x4174),f66(x4172,x4173,x4174)) % 169.39/169.66 [418]~E(x4181,x4182)+E(f66(x4183,x4181,x4184),f66(x4183,x4182,x4184)) % 169.39/169.66 [419]~E(x4191,x4192)+E(f66(x4193,x4194,x4191),f66(x4193,x4194,x4192)) % 169.39/169.66 [420]~E(x4201,x4202)+E(f189(x4201,x4203,x4204,x4205),f189(x4202,x4203,x4204,x4205)) % 169.39/169.66 [421]~E(x4211,x4212)+E(f189(x4213,x4211,x4214,x4215),f189(x4213,x4212,x4214,x4215)) % 169.39/169.66 [422]~E(x4221,x4222)+E(f189(x4223,x4224,x4221,x4225),f189(x4223,x4224,x4222,x4225)) % 169.39/169.66 [423]~E(x4231,x4232)+E(f189(x4233,x4234,x4235,x4231),f189(x4233,x4234,x4235,x4232)) % 169.39/169.66 [424]~E(x4241,x4242)+E(f814(x4241,x4243,x4244),f814(x4242,x4243,x4244)) % 169.39/169.66 [425]~E(x4251,x4252)+E(f814(x4253,x4251,x4254),f814(x4253,x4252,x4254)) % 169.39/169.66 [426]~E(x4261,x4262)+E(f814(x4263,x4264,x4261),f814(x4263,x4264,x4262)) % 169.39/169.66 [427]~E(x4271,x4272)+E(f91(x4271,x4273),f91(x4272,x4273)) % 169.39/169.66 [428]~E(x4281,x4282)+E(f91(x4283,x4281),f91(x4283,x4282)) % 169.39/169.66 [429]~E(x4291,x4292)+E(f144(x4291,x4293),f144(x4292,x4293)) % 169.39/169.66 [430]~E(x4301,x4302)+E(f144(x4303,x4301),f144(x4303,x4302)) % 169.39/169.66 [431]~E(x4311,x4312)+E(f86(x4311,x4313),f86(x4312,x4313)) % 169.39/169.66 [432]~E(x4321,x4322)+E(f86(x4323,x4321),f86(x4323,x4322)) % 169.39/169.66 [433]~E(x4331,x4332)+E(f180(x4331,x4333),f180(x4332,x4333)) % 169.39/169.66 [434]~E(x4341,x4342)+E(f180(x4343,x4341),f180(x4343,x4342)) % 169.39/169.66 [435]~E(x4351,x4352)+E(f577(x4351,x4353,x4354),f577(x4352,x4353,x4354)) % 169.39/169.66 [436]~E(x4361,x4362)+E(f577(x4363,x4361,x4364),f577(x4363,x4362,x4364)) % 169.39/169.66 [437]~E(x4371,x4372)+E(f577(x4373,x4374,x4371),f577(x4373,x4374,x4372)) % 169.39/169.66 [438]~E(x4381,x4382)+E(f700(x4381,x4383,x4384,x4385),f700(x4382,x4383,x4384,x4385)) % 169.39/169.66 [439]~E(x4391,x4392)+E(f700(x4393,x4391,x4394,x4395),f700(x4393,x4392,x4394,x4395)) % 169.39/169.66 [440]~E(x4401,x4402)+E(f700(x4403,x4404,x4401,x4405),f700(x4403,x4404,x4402,x4405)) % 169.39/169.66 [441]~E(x4411,x4412)+E(f700(x4413,x4414,x4415,x4411),f700(x4413,x4414,x4415,x4412)) % 169.39/169.66 [442]~E(x4421,x4422)+E(f112(x4421),f112(x4422)) % 169.39/169.66 [443]~E(x4431,x4432)+E(f482(x4431,x4433),f482(x4432,x4433)) % 169.39/169.66 [444]~E(x4441,x4442)+E(f482(x4443,x4441),f482(x4443,x4442)) % 169.39/169.66 [445]~E(x4451,x4452)+E(f809(x4451,x4453,x4454,x4455),f809(x4452,x4453,x4454,x4455)) % 169.39/169.66 [446]~E(x4461,x4462)+E(f809(x4463,x4461,x4464,x4465),f809(x4463,x4462,x4464,x4465)) % 169.39/169.66 [447]~E(x4471,x4472)+E(f809(x4473,x4474,x4471,x4475),f809(x4473,x4474,x4472,x4475)) % 169.39/169.66 [448]~E(x4481,x4482)+E(f809(x4483,x4484,x4485,x4481),f809(x4483,x4484,x4485,x4482)) % 169.39/169.66 [449]~E(x4491,x4492)+E(f238(x4491,x4493,x4494),f238(x4492,x4493,x4494)) % 169.39/169.66 [450]~E(x4501,x4502)+E(f238(x4503,x4501,x4504),f238(x4503,x4502,x4504)) % 169.39/169.66 [451]~E(x4511,x4512)+E(f238(x4513,x4514,x4511),f238(x4513,x4514,x4512)) % 169.39/169.66 [452]~E(x4521,x4522)+E(f94(x4521),f94(x4522)) % 169.39/169.66 [453]~E(x4531,x4532)+E(f327(x4531,x4533,x4534,x4535),f327(x4532,x4533,x4534,x4535)) % 169.39/169.66 [454]~E(x4541,x4542)+E(f327(x4543,x4541,x4544,x4545),f327(x4543,x4542,x4544,x4545)) % 169.39/169.66 [455]~E(x4551,x4552)+E(f327(x4553,x4554,x4551,x4555),f327(x4553,x4554,x4552,x4555)) % 169.39/169.66 [456]~E(x4561,x4562)+E(f327(x4563,x4564,x4565,x4561),f327(x4563,x4564,x4565,x4562)) % 169.39/169.66 [457]~E(x4571,x4572)+E(f224(x4571,x4573),f224(x4572,x4573)) % 169.39/169.66 [458]~E(x4581,x4582)+E(f224(x4583,x4581),f224(x4583,x4582)) % 169.39/169.66 [459]~E(x4591,x4592)+E(f56(x4591,x4593,x4594),f56(x4592,x4593,x4594)) % 169.39/169.66 [460]~E(x4601,x4602)+E(f56(x4603,x4601,x4604),f56(x4603,x4602,x4604)) % 169.39/169.66 [461]~E(x4611,x4612)+E(f56(x4613,x4614,x4611),f56(x4613,x4614,x4612)) % 169.39/169.66 [462]~E(x4621,x4622)+E(f566(x4621,x4623,x4624,x4625,x4626,x4627),f566(x4622,x4623,x4624,x4625,x4626,x4627)) % 169.39/169.66 [463]~E(x4631,x4632)+E(f566(x4633,x4631,x4634,x4635,x4636,x4637),f566(x4633,x4632,x4634,x4635,x4636,x4637)) % 169.39/169.66 [464]~E(x4641,x4642)+E(f566(x4643,x4644,x4641,x4645,x4646,x4647),f566(x4643,x4644,x4642,x4645,x4646,x4647)) % 169.39/169.66 [465]~E(x4651,x4652)+E(f566(x4653,x4654,x4655,x4651,x4656,x4657),f566(x4653,x4654,x4655,x4652,x4656,x4657)) % 169.39/169.66 [466]~E(x4661,x4662)+E(f566(x4663,x4664,x4665,x4666,x4661,x4667),f566(x4663,x4664,x4665,x4666,x4662,x4667)) % 169.39/169.66 [467]~E(x4671,x4672)+E(f566(x4673,x4674,x4675,x4676,x4677,x4671),f566(x4673,x4674,x4675,x4676,x4677,x4672)) % 169.39/169.66 [468]~E(x4681,x4682)+E(f564(x4681),f564(x4682)) % 169.39/169.66 [469]~E(x4691,x4692)+E(f231(x4691,x4693,x4694),f231(x4692,x4693,x4694)) % 169.39/169.66 [470]~E(x4701,x4702)+E(f231(x4703,x4701,x4704),f231(x4703,x4702,x4704)) % 169.39/169.66 [471]~E(x4711,x4712)+E(f231(x4713,x4714,x4711),f231(x4713,x4714,x4712)) % 169.39/169.66 [472]~E(x4721,x4722)+E(f73(x4721,x4723),f73(x4722,x4723)) % 169.39/169.66 [473]~E(x4731,x4732)+E(f73(x4733,x4731),f73(x4733,x4732)) % 169.39/169.66 [474]~E(x4741,x4742)+E(f50(x4741,x4743),f50(x4742,x4743)) % 169.39/169.66 [475]~E(x4751,x4752)+E(f50(x4753,x4751),f50(x4753,x4752)) % 169.39/169.66 [476]~E(x4761,x4762)+E(f515(x4761,x4763,x4764,x4765),f515(x4762,x4763,x4764,x4765)) % 169.39/169.66 [477]~E(x4771,x4772)+E(f515(x4773,x4771,x4774,x4775),f515(x4773,x4772,x4774,x4775)) % 169.39/169.66 [478]~E(x4781,x4782)+E(f515(x4783,x4784,x4781,x4785),f515(x4783,x4784,x4782,x4785)) % 169.39/169.66 [479]~E(x4791,x4792)+E(f515(x4793,x4794,x4795,x4791),f515(x4793,x4794,x4795,x4792)) % 169.39/169.66 [480]~E(x4801,x4802)+E(f299(x4801,x4803,x4804,x4805,x4806),f299(x4802,x4803,x4804,x4805,x4806)) % 169.39/169.66 [481]~E(x4811,x4812)+E(f299(x4813,x4811,x4814,x4815,x4816),f299(x4813,x4812,x4814,x4815,x4816)) % 169.39/169.66 [482]~E(x4821,x4822)+E(f299(x4823,x4824,x4821,x4825,x4826),f299(x4823,x4824,x4822,x4825,x4826)) % 169.39/169.66 [483]~E(x4831,x4832)+E(f299(x4833,x4834,x4835,x4831,x4836),f299(x4833,x4834,x4835,x4832,x4836)) % 169.39/169.66 [484]~E(x4841,x4842)+E(f299(x4843,x4844,x4845,x4846,x4841),f299(x4843,x4844,x4845,x4846,x4842)) % 169.39/169.66 [485]~E(x4851,x4852)+E(f143(x4851,x4853),f143(x4852,x4853)) % 169.39/169.66 [486]~E(x4861,x4862)+E(f143(x4863,x4861),f143(x4863,x4862)) % 169.39/169.66 [487]~E(x4871,x4872)+E(f673(x4871,x4873,x4874),f673(x4872,x4873,x4874)) % 169.39/169.66 [488]~E(x4881,x4882)+E(f673(x4883,x4881,x4884),f673(x4883,x4882,x4884)) % 169.39/169.66 [489]~E(x4891,x4892)+E(f673(x4893,x4894,x4891),f673(x4893,x4894,x4892)) % 169.39/169.66 [490]~E(x4901,x4902)+E(f187(x4901,x4903,x4904),f187(x4902,x4903,x4904)) % 169.39/169.66 [491]~E(x4911,x4912)+E(f187(x4913,x4911,x4914),f187(x4913,x4912,x4914)) % 169.39/169.66 [492]~E(x4921,x4922)+E(f187(x4923,x4924,x4921),f187(x4923,x4924,x4922)) % 169.39/169.66 [493]~E(x4931,x4932)+E(f88(x4931),f88(x4932)) % 169.39/169.66 [494]~E(x4941,x4942)+E(f158(x4941,x4943),f158(x4942,x4943)) % 169.39/169.66 [495]~E(x4951,x4952)+E(f158(x4953,x4951),f158(x4953,x4952)) % 169.39/169.66 [496]~E(x4961,x4962)+E(f638(x4961,x4963,x4964),f638(x4962,x4963,x4964)) % 169.39/169.66 [497]~E(x4971,x4972)+E(f638(x4973,x4971,x4974),f638(x4973,x4972,x4974)) % 169.39/169.66 [498]~E(x4981,x4982)+E(f638(x4983,x4984,x4981),f638(x4983,x4984,x4982)) % 169.39/169.66 [499]~E(x4991,x4992)+E(f411(x4991,x4993,x4994,x4995),f411(x4992,x4993,x4994,x4995)) % 169.39/169.66 [500]~E(x5001,x5002)+E(f411(x5003,x5001,x5004,x5005),f411(x5003,x5002,x5004,x5005)) % 169.39/169.66 [501]~E(x5011,x5012)+E(f411(x5013,x5014,x5011,x5015),f411(x5013,x5014,x5012,x5015)) % 169.39/169.66 [502]~E(x5021,x5022)+E(f411(x5023,x5024,x5025,x5021),f411(x5023,x5024,x5025,x5022)) % 169.39/169.66 [503]~E(x5031,x5032)+E(f281(x5031,x5033),f281(x5032,x5033)) % 169.39/169.66 [504]~E(x5041,x5042)+E(f281(x5043,x5041),f281(x5043,x5042)) % 169.39/169.66 [505]~E(x5051,x5052)+E(f42(x5051,x5053),f42(x5052,x5053)) % 169.39/169.66 [506]~E(x5061,x5062)+E(f42(x5063,x5061),f42(x5063,x5062)) % 169.39/169.66 [507]~E(x5071,x5072)+E(f119(x5071,x5073,x5074),f119(x5072,x5073,x5074)) % 169.39/169.66 [508]~E(x5081,x5082)+E(f119(x5083,x5081,x5084),f119(x5083,x5082,x5084)) % 169.39/169.66 [509]~E(x5091,x5092)+E(f119(x5093,x5094,x5091),f119(x5093,x5094,x5092)) % 169.39/169.66 [510]~E(x5101,x5102)+E(f41(x5101,x5103),f41(x5102,x5103)) % 169.39/169.66 [511]~E(x5111,x5112)+E(f41(x5113,x5111),f41(x5113,x5112)) % 169.39/169.66 [512]~E(x5121,x5122)+E(f289(x5121,x5123),f289(x5122,x5123)) % 169.39/169.66 [513]~E(x5131,x5132)+E(f289(x5133,x5131),f289(x5133,x5132)) % 169.39/169.66 [514]~E(x5141,x5142)+E(f55(x5141,x5143),f55(x5142,x5143)) % 169.39/169.66 [515]~E(x5151,x5152)+E(f55(x5153,x5151),f55(x5153,x5152)) % 169.39/169.66 [516]~E(x5161,x5162)+E(f309(x5161),f309(x5162)) % 169.39/169.66 [517]~E(x5171,x5172)+E(f521(x5171,x5173,x5174,x5175,x5176),f521(x5172,x5173,x5174,x5175,x5176)) % 169.39/169.66 [518]~E(x5181,x5182)+E(f521(x5183,x5181,x5184,x5185,x5186),f521(x5183,x5182,x5184,x5185,x5186)) % 169.39/169.66 [519]~E(x5191,x5192)+E(f521(x5193,x5194,x5191,x5195,x5196),f521(x5193,x5194,x5192,x5195,x5196)) % 169.39/169.66 [520]~E(x5201,x5202)+E(f521(x5203,x5204,x5205,x5201,x5206),f521(x5203,x5204,x5205,x5202,x5206)) % 169.39/169.66 [521]~E(x5211,x5212)+E(f521(x5213,x5214,x5215,x5216,x5211),f521(x5213,x5214,x5215,x5216,x5212)) % 169.39/169.66 [522]~E(x5221,x5222)+E(f265(x5221,x5223),f265(x5222,x5223)) % 169.39/169.66 [523]~E(x5231,x5232)+E(f265(x5233,x5231),f265(x5233,x5232)) % 169.39/169.66 [524]~E(x5241,x5242)+E(f805(x5241,x5243,x5244),f805(x5242,x5243,x5244)) % 169.39/169.66 [525]~E(x5251,x5252)+E(f805(x5253,x5251,x5254),f805(x5253,x5252,x5254)) % 169.39/169.66 [526]~E(x5261,x5262)+E(f805(x5263,x5264,x5261),f805(x5263,x5264,x5262)) % 169.39/169.66 [527]~E(x5271,x5272)+E(f135(x5271),f135(x5272)) % 169.39/169.66 [528]~E(x5281,x5282)+E(f702(x5281,x5283,x5284,x5285,x5286,x5287),f702(x5282,x5283,x5284,x5285,x5286,x5287)) % 169.39/169.66 [529]~E(x5291,x5292)+E(f702(x5293,x5291,x5294,x5295,x5296,x5297),f702(x5293,x5292,x5294,x5295,x5296,x5297)) % 169.39/169.66 [530]~E(x5301,x5302)+E(f702(x5303,x5304,x5301,x5305,x5306,x5307),f702(x5303,x5304,x5302,x5305,x5306,x5307)) % 169.39/169.66 [531]~E(x5311,x5312)+E(f702(x5313,x5314,x5315,x5311,x5316,x5317),f702(x5313,x5314,x5315,x5312,x5316,x5317)) % 169.39/169.66 [532]~E(x5321,x5322)+E(f702(x5323,x5324,x5325,x5326,x5321,x5327),f702(x5323,x5324,x5325,x5326,x5322,x5327)) % 169.39/169.66 [533]~E(x5331,x5332)+E(f702(x5333,x5334,x5335,x5336,x5337,x5331),f702(x5333,x5334,x5335,x5336,x5337,x5332)) % 169.39/169.66 [534]~E(x5341,x5342)+E(f637(x5341,x5343),f637(x5342,x5343)) % 169.39/169.66 [535]~E(x5351,x5352)+E(f637(x5353,x5351),f637(x5353,x5352)) % 169.39/169.66 [536]~E(x5361,x5362)+E(f644(x5361,x5363,x5364),f644(x5362,x5363,x5364)) % 169.39/169.66 [537]~E(x5371,x5372)+E(f644(x5373,x5371,x5374),f644(x5373,x5372,x5374)) % 169.39/169.66 [538]~E(x5381,x5382)+E(f644(x5383,x5384,x5381),f644(x5383,x5384,x5382)) % 169.39/169.66 [539]~E(x5391,x5392)+E(f256(x5391),f256(x5392)) % 169.39/169.66 [540]~E(x5401,x5402)+E(f298(x5401,x5403,x5404,x5405),f298(x5402,x5403,x5404,x5405)) % 169.39/169.66 [541]~E(x5411,x5412)+E(f298(x5413,x5411,x5414,x5415),f298(x5413,x5412,x5414,x5415)) % 169.39/169.66 [542]~E(x5421,x5422)+E(f298(x5423,x5424,x5421,x5425),f298(x5423,x5424,x5422,x5425)) % 169.39/169.66 [543]~E(x5431,x5432)+E(f298(x5433,x5434,x5435,x5431),f298(x5433,x5434,x5435,x5432)) % 169.39/169.66 [544]~E(x5441,x5442)+E(f308(x5441,x5443,x5444),f308(x5442,x5443,x5444)) % 169.39/169.66 [545]~E(x5451,x5452)+E(f308(x5453,x5451,x5454),f308(x5453,x5452,x5454)) % 169.39/169.66 [546]~E(x5461,x5462)+E(f308(x5463,x5464,x5461),f308(x5463,x5464,x5462)) % 169.39/169.66 [547]~E(x5471,x5472)+E(f785(x5471,x5473,x5474),f785(x5472,x5473,x5474)) % 169.39/169.66 [548]~E(x5481,x5482)+E(f785(x5483,x5481,x5484),f785(x5483,x5482,x5484)) % 169.39/169.66 [549]~E(x5491,x5492)+E(f785(x5493,x5494,x5491),f785(x5493,x5494,x5492)) % 169.39/169.66 [550]~E(x5501,x5502)+E(f193(x5501),f193(x5502)) % 169.39/169.66 [551]~E(x5511,x5512)+E(f817(x5511,x5513,x5514),f817(x5512,x5513,x5514)) % 169.39/169.66 [552]~E(x5521,x5522)+E(f817(x5523,x5521,x5524),f817(x5523,x5522,x5524)) % 169.39/169.66 [553]~E(x5531,x5532)+E(f817(x5533,x5534,x5531),f817(x5533,x5534,x5532)) % 169.39/169.66 [554]~E(x5541,x5542)+E(f627(x5541,x5543,x5544,x5545,x5546),f627(x5542,x5543,x5544,x5545,x5546)) % 169.39/169.66 [555]~E(x5551,x5552)+E(f627(x5553,x5551,x5554,x5555,x5556),f627(x5553,x5552,x5554,x5555,x5556)) % 169.39/169.66 [556]~E(x5561,x5562)+E(f627(x5563,x5564,x5561,x5565,x5566),f627(x5563,x5564,x5562,x5565,x5566)) % 169.39/169.66 [557]~E(x5571,x5572)+E(f627(x5573,x5574,x5575,x5571,x5576),f627(x5573,x5574,x5575,x5572,x5576)) % 169.39/169.66 [558]~E(x5581,x5582)+E(f627(x5583,x5584,x5585,x5586,x5581),f627(x5583,x5584,x5585,x5586,x5582)) % 169.39/169.66 [559]~E(x5591,x5592)+E(f127(x5591,x5593,x5594),f127(x5592,x5593,x5594)) % 169.39/169.66 [560]~E(x5601,x5602)+E(f127(x5603,x5601,x5604),f127(x5603,x5602,x5604)) % 169.39/169.66 [561]~E(x5611,x5612)+E(f127(x5613,x5614,x5611),f127(x5613,x5614,x5612)) % 169.39/169.66 [562]~E(x5621,x5622)+E(f559(x5621,x5623,x5624,x5625,x5626),f559(x5622,x5623,x5624,x5625,x5626)) % 169.39/169.66 [563]~E(x5631,x5632)+E(f559(x5633,x5631,x5634,x5635,x5636),f559(x5633,x5632,x5634,x5635,x5636)) % 169.39/169.66 [564]~E(x5641,x5642)+E(f559(x5643,x5644,x5641,x5645,x5646),f559(x5643,x5644,x5642,x5645,x5646)) % 169.39/169.66 [565]~E(x5651,x5652)+E(f559(x5653,x5654,x5655,x5651,x5656),f559(x5653,x5654,x5655,x5652,x5656)) % 169.39/169.66 [566]~E(x5661,x5662)+E(f559(x5663,x5664,x5665,x5666,x5661),f559(x5663,x5664,x5665,x5666,x5662)) % 169.39/169.66 [567]~E(x5671,x5672)+E(f818(x5671,x5673,x5674),f818(x5672,x5673,x5674)) % 169.39/169.66 [568]~E(x5681,x5682)+E(f818(x5683,x5681,x5684),f818(x5683,x5682,x5684)) % 169.39/169.66 [569]~E(x5691,x5692)+E(f818(x5693,x5694,x5691),f818(x5693,x5694,x5692)) % 169.39/169.66 [570]~E(x5701,x5702)+E(f713(x5701,x5703),f713(x5702,x5703)) % 169.39/169.66 [571]~E(x5711,x5712)+E(f713(x5713,x5711),f713(x5713,x5712)) % 169.39/169.66 [572]~E(x5721,x5722)+E(f517(x5721,x5723,x5724,x5725,x5726),f517(x5722,x5723,x5724,x5725,x5726)) % 169.39/169.66 [573]~E(x5731,x5732)+E(f517(x5733,x5731,x5734,x5735,x5736),f517(x5733,x5732,x5734,x5735,x5736)) % 169.39/169.66 [574]~E(x5741,x5742)+E(f517(x5743,x5744,x5741,x5745,x5746),f517(x5743,x5744,x5742,x5745,x5746)) % 169.39/169.66 [575]~E(x5751,x5752)+E(f517(x5753,x5754,x5755,x5751,x5756),f517(x5753,x5754,x5755,x5752,x5756)) % 169.39/169.66 [576]~E(x5761,x5762)+E(f517(x5763,x5764,x5765,x5766,x5761),f517(x5763,x5764,x5765,x5766,x5762)) % 169.39/169.66 [577]~E(x5771,x5772)+E(f177(x5771,x5773,x5774),f177(x5772,x5773,x5774)) % 169.39/169.66 [578]~E(x5781,x5782)+E(f177(x5783,x5781,x5784),f177(x5783,x5782,x5784)) % 169.39/169.66 [579]~E(x5791,x5792)+E(f177(x5793,x5794,x5791),f177(x5793,x5794,x5792)) % 169.39/169.66 [580]~E(x5801,x5802)+E(f45(x5801),f45(x5802)) % 169.39/169.66 [581]~E(x5811,x5812)+E(f618(x5811,x5813,x5814,x5815,x5816,x5817,x5818,x5819),f618(x5812,x5813,x5814,x5815,x5816,x5817,x5818,x5819)) % 169.39/169.66 [582]~E(x5821,x5822)+E(f618(x5823,x5821,x5824,x5825,x5826,x5827,x5828,x5829),f618(x5823,x5822,x5824,x5825,x5826,x5827,x5828,x5829)) % 169.39/169.66 [583]~E(x5831,x5832)+E(f618(x5833,x5834,x5831,x5835,x5836,x5837,x5838,x5839),f618(x5833,x5834,x5832,x5835,x5836,x5837,x5838,x5839)) % 169.39/169.66 [584]~E(x5841,x5842)+E(f618(x5843,x5844,x5845,x5841,x5846,x5847,x5848,x5849),f618(x5843,x5844,x5845,x5842,x5846,x5847,x5848,x5849)) % 169.39/169.66 [585]~E(x5851,x5852)+E(f618(x5853,x5854,x5855,x5856,x5851,x5857,x5858,x5859),f618(x5853,x5854,x5855,x5856,x5852,x5857,x5858,x5859)) % 169.39/169.66 [586]~E(x5861,x5862)+E(f618(x5863,x5864,x5865,x5866,x5867,x5861,x5868,x5869),f618(x5863,x5864,x5865,x5866,x5867,x5862,x5868,x5869)) % 169.39/169.66 [587]~E(x5871,x5872)+E(f618(x5873,x5874,x5875,x5876,x5877,x5878,x5871,x5879),f618(x5873,x5874,x5875,x5876,x5877,x5878,x5872,x5879)) % 169.39/169.66 [588]~E(x5881,x5882)+E(f618(x5883,x5884,x5885,x5886,x5887,x5888,x5889,x5881),f618(x5883,x5884,x5885,x5886,x5887,x5888,x5889,x5882)) % 169.39/169.66 [589]~E(x5891,x5892)+E(f241(x5891),f241(x5892)) % 169.39/169.66 [590]~E(x5901,x5902)+E(f442(x5901,x5903,x5904),f442(x5902,x5903,x5904)) % 169.39/169.66 [591]~E(x5911,x5912)+E(f442(x5913,x5911,x5914),f442(x5913,x5912,x5914)) % 169.39/169.66 [592]~E(x5921,x5922)+E(f442(x5923,x5924,x5921),f442(x5923,x5924,x5922)) % 169.39/169.66 [593]~E(x5931,x5932)+E(f622(x5931,x5933,x5934,x5935),f622(x5932,x5933,x5934,x5935)) % 169.39/169.66 [594]~E(x5941,x5942)+E(f622(x5943,x5941,x5944,x5945),f622(x5943,x5942,x5944,x5945)) % 169.39/169.66 [595]~E(x5951,x5952)+E(f622(x5953,x5954,x5951,x5955),f622(x5953,x5954,x5952,x5955)) % 169.39/169.66 [596]~E(x5961,x5962)+E(f622(x5963,x5964,x5965,x5961),f622(x5963,x5964,x5965,x5962)) % 169.39/169.66 [597]~E(x5971,x5972)+E(f395(x5971,x5973),f395(x5972,x5973)) % 169.39/169.66 [598]~E(x5981,x5982)+E(f395(x5983,x5981),f395(x5983,x5982)) % 169.39/169.66 [599]~E(x5991,x5992)+E(f240(x5991,x5993),f240(x5992,x5993)) % 169.39/169.66 [600]~E(x6001,x6002)+E(f240(x6003,x6001),f240(x6003,x6002)) % 169.39/169.66 [601]~E(x6011,x6012)+E(f476(x6011,x6013,x6014,x6015),f476(x6012,x6013,x6014,x6015)) % 169.39/169.66 [602]~E(x6021,x6022)+E(f476(x6023,x6021,x6024,x6025),f476(x6023,x6022,x6024,x6025)) % 169.39/169.66 [603]~E(x6031,x6032)+E(f476(x6033,x6034,x6031,x6035),f476(x6033,x6034,x6032,x6035)) % 169.39/169.66 [604]~E(x6041,x6042)+E(f476(x6043,x6044,x6045,x6041),f476(x6043,x6044,x6045,x6042)) % 169.39/169.66 [605]~E(x6051,x6052)+E(f48(x6051,x6053),f48(x6052,x6053)) % 169.39/169.66 [606]~E(x6061,x6062)+E(f48(x6063,x6061),f48(x6063,x6062)) % 169.39/169.66 [607]~E(x6071,x6072)+E(f510(x6071,x6073,x6074),f510(x6072,x6073,x6074)) % 169.39/169.66 [608]~E(x6081,x6082)+E(f510(x6083,x6081,x6084),f510(x6083,x6082,x6084)) % 169.39/169.66 [609]~E(x6091,x6092)+E(f510(x6093,x6094,x6091),f510(x6093,x6094,x6092)) % 169.39/169.66 [610]~E(x6101,x6102)+E(f563(x6101),f563(x6102)) % 169.39/169.66 [611]~E(x6111,x6112)+E(f285(x6111,x6113),f285(x6112,x6113)) % 169.39/169.66 [612]~E(x6121,x6122)+E(f285(x6123,x6121),f285(x6123,x6122)) % 169.39/169.66 [613]~E(x6131,x6132)+E(f287(x6131),f287(x6132)) % 169.39/169.66 [614]~E(x6141,x6142)+E(f552(x6141,x6143,x6144,x6145,x6146),f552(x6142,x6143,x6144,x6145,x6146)) % 169.39/169.66 [615]~E(x6151,x6152)+E(f552(x6153,x6151,x6154,x6155,x6156),f552(x6153,x6152,x6154,x6155,x6156)) % 169.39/169.66 [616]~E(x6161,x6162)+E(f552(x6163,x6164,x6161,x6165,x6166),f552(x6163,x6164,x6162,x6165,x6166)) % 169.39/169.66 [617]~E(x6171,x6172)+E(f552(x6173,x6174,x6175,x6171,x6176),f552(x6173,x6174,x6175,x6172,x6176)) % 169.39/169.66 [618]~E(x6181,x6182)+E(f552(x6183,x6184,x6185,x6186,x6181),f552(x6183,x6184,x6185,x6186,x6182)) % 169.39/169.66 [619]~E(x6191,x6192)+E(f49(x6191,x6193),f49(x6192,x6193)) % 169.39/169.66 [620]~E(x6201,x6202)+E(f49(x6203,x6201),f49(x6203,x6202)) % 169.39/169.66 [621]~E(x6211,x6212)+E(f366(x6211,x6213),f366(x6212,x6213)) % 169.39/169.66 [622]~E(x6221,x6222)+E(f366(x6223,x6221),f366(x6223,x6222)) % 169.39/169.66 [623]~E(x6231,x6232)+E(f471(x6231,x6233),f471(x6232,x6233)) % 169.39/169.66 [624]~E(x6241,x6242)+E(f471(x6243,x6241),f471(x6243,x6242)) % 169.39/169.66 [625]~E(x6251,x6252)+E(f865(x6251,x6253,x6254,x6255,x6256),f865(x6252,x6253,x6254,x6255,x6256)) % 169.39/169.66 [626]~E(x6261,x6262)+E(f865(x6263,x6261,x6264,x6265,x6266),f865(x6263,x6262,x6264,x6265,x6266)) % 169.39/169.66 [627]~E(x6271,x6272)+E(f865(x6273,x6274,x6271,x6275,x6276),f865(x6273,x6274,x6272,x6275,x6276)) % 169.39/169.66 [628]~E(x6281,x6282)+E(f865(x6283,x6284,x6285,x6281,x6286),f865(x6283,x6284,x6285,x6282,x6286)) % 169.39/169.66 [629]~E(x6291,x6292)+E(f865(x6293,x6294,x6295,x6296,x6291),f865(x6293,x6294,x6295,x6296,x6292)) % 169.39/169.66 [630]~E(x6301,x6302)+E(f398(x6301,x6303,x6304,x6305),f398(x6302,x6303,x6304,x6305)) % 169.39/169.66 [631]~E(x6311,x6312)+E(f398(x6313,x6311,x6314,x6315),f398(x6313,x6312,x6314,x6315)) % 169.39/169.66 [632]~E(x6321,x6322)+E(f398(x6323,x6324,x6321,x6325),f398(x6323,x6324,x6322,x6325)) % 169.39/169.66 [633]~E(x6331,x6332)+E(f398(x6333,x6334,x6335,x6331),f398(x6333,x6334,x6335,x6332)) % 169.39/169.66 [634]~E(x6341,x6342)+E(f321(x6341,x6343,x6344,x6345),f321(x6342,x6343,x6344,x6345)) % 169.39/169.66 [635]~E(x6351,x6352)+E(f321(x6353,x6351,x6354,x6355),f321(x6353,x6352,x6354,x6355)) % 169.39/169.66 [636]~E(x6361,x6362)+E(f321(x6363,x6364,x6361,x6365),f321(x6363,x6364,x6362,x6365)) % 169.39/169.66 [637]~E(x6371,x6372)+E(f321(x6373,x6374,x6375,x6371),f321(x6373,x6374,x6375,x6372)) % 169.39/169.66 [638]~E(x6381,x6382)+E(f207(x6381,x6383),f207(x6382,x6383)) % 169.39/169.66 [639]~E(x6391,x6392)+E(f207(x6393,x6391),f207(x6393,x6392)) % 169.39/169.66 [640]~E(x6401,x6402)+E(f237(x6401,x6403,x6404,x6405),f237(x6402,x6403,x6404,x6405)) % 169.39/169.66 [641]~E(x6411,x6412)+E(f237(x6413,x6411,x6414,x6415),f237(x6413,x6412,x6414,x6415)) % 169.39/169.66 [642]~E(x6421,x6422)+E(f237(x6423,x6424,x6421,x6425),f237(x6423,x6424,x6422,x6425)) % 169.39/169.66 [643]~E(x6431,x6432)+E(f237(x6433,x6434,x6435,x6431),f237(x6433,x6434,x6435,x6432)) % 169.39/169.66 [644]~E(x6441,x6442)+E(f747(x6441,x6443,x6444,x6445),f747(x6442,x6443,x6444,x6445)) % 169.39/169.66 [645]~E(x6451,x6452)+E(f747(x6453,x6451,x6454,x6455),f747(x6453,x6452,x6454,x6455)) % 169.39/169.66 [646]~E(x6461,x6462)+E(f747(x6463,x6464,x6461,x6465),f747(x6463,x6464,x6462,x6465)) % 169.39/169.66 [647]~E(x6471,x6472)+E(f747(x6473,x6474,x6475,x6471),f747(x6473,x6474,x6475,x6472)) % 169.39/169.66 [648]~E(x6481,x6482)+E(f542(x6481),f542(x6482)) % 169.39/169.66 [649]~E(x6491,x6492)+E(f812(x6491,x6493,x6494),f812(x6492,x6493,x6494)) % 169.39/169.66 [650]~E(x6501,x6502)+E(f812(x6503,x6501,x6504),f812(x6503,x6502,x6504)) % 169.39/169.66 [651]~E(x6511,x6512)+E(f812(x6513,x6514,x6511),f812(x6513,x6514,x6512)) % 169.39/169.66 [652]~E(x6521,x6522)+E(f306(x6521),f306(x6522)) % 169.39/169.66 [653]~E(x6531,x6532)+E(f263(x6531,x6533,x6534),f263(x6532,x6533,x6534)) % 169.39/169.66 [654]~E(x6541,x6542)+E(f263(x6543,x6541,x6544),f263(x6543,x6542,x6544)) % 169.39/169.66 [655]~E(x6551,x6552)+E(f263(x6553,x6554,x6551),f263(x6553,x6554,x6552)) % 169.39/169.66 [656]~E(x6561,x6562)+E(f768(x6561,x6563,x6564,x6565,x6566),f768(x6562,x6563,x6564,x6565,x6566)) % 169.39/169.66 [657]~E(x6571,x6572)+E(f768(x6573,x6571,x6574,x6575,x6576),f768(x6573,x6572,x6574,x6575,x6576)) % 169.39/169.66 [658]~E(x6581,x6582)+E(f768(x6583,x6584,x6581,x6585,x6586),f768(x6583,x6584,x6582,x6585,x6586)) % 169.39/169.66 [659]~E(x6591,x6592)+E(f768(x6593,x6594,x6595,x6591,x6596),f768(x6593,x6594,x6595,x6592,x6596)) % 169.39/169.66 [660]~E(x6601,x6602)+E(f768(x6603,x6604,x6605,x6606,x6601),f768(x6603,x6604,x6605,x6606,x6602)) % 169.39/169.66 [661]~E(x6611,x6612)+E(f191(x6611,x6613,x6614),f191(x6612,x6613,x6614)) % 169.39/169.66 [662]~E(x6621,x6622)+E(f191(x6623,x6621,x6624),f191(x6623,x6622,x6624)) % 169.39/169.66 [663]~E(x6631,x6632)+E(f191(x6633,x6634,x6631),f191(x6633,x6634,x6632)) % 169.39/169.66 [664]~E(x6641,x6642)+E(f707(x6641,x6643,x6644,x6645,x6646,x6647,x6648,x6649),f707(x6642,x6643,x6644,x6645,x6646,x6647,x6648,x6649)) % 169.39/169.66 [665]~E(x6651,x6652)+E(f707(x6653,x6651,x6654,x6655,x6656,x6657,x6658,x6659),f707(x6653,x6652,x6654,x6655,x6656,x6657,x6658,x6659)) % 169.39/169.66 [666]~E(x6661,x6662)+E(f707(x6663,x6664,x6661,x6665,x6666,x6667,x6668,x6669),f707(x6663,x6664,x6662,x6665,x6666,x6667,x6668,x6669)) % 169.39/169.66 [667]~E(x6671,x6672)+E(f707(x6673,x6674,x6675,x6671,x6676,x6677,x6678,x6679),f707(x6673,x6674,x6675,x6672,x6676,x6677,x6678,x6679)) % 169.39/169.66 [668]~E(x6681,x6682)+E(f707(x6683,x6684,x6685,x6686,x6681,x6687,x6688,x6689),f707(x6683,x6684,x6685,x6686,x6682,x6687,x6688,x6689)) % 169.39/169.66 [669]~E(x6691,x6692)+E(f707(x6693,x6694,x6695,x6696,x6697,x6691,x6698,x6699),f707(x6693,x6694,x6695,x6696,x6697,x6692,x6698,x6699)) % 169.39/169.66 [670]~E(x6701,x6702)+E(f707(x6703,x6704,x6705,x6706,x6707,x6708,x6701,x6709),f707(x6703,x6704,x6705,x6706,x6707,x6708,x6702,x6709)) % 169.39/169.66 [671]~E(x6711,x6712)+E(f707(x6713,x6714,x6715,x6716,x6717,x6718,x6719,x6711),f707(x6713,x6714,x6715,x6716,x6717,x6718,x6719,x6712)) % 169.39/169.66 [672]~E(x6721,x6722)+E(f462(x6721,x6723,x6724),f462(x6722,x6723,x6724)) % 169.39/169.66 [673]~E(x6731,x6732)+E(f462(x6733,x6731,x6734),f462(x6733,x6732,x6734)) % 169.39/169.66 [674]~E(x6741,x6742)+E(f462(x6743,x6744,x6741),f462(x6743,x6744,x6742)) % 169.39/169.66 [675]~E(x6751,x6752)+E(f857(x6751),f857(x6752)) % 169.39/169.66 [676]~E(x6761,x6762)+E(f488(x6761,x6763,x6764),f488(x6762,x6763,x6764)) % 169.39/169.66 [677]~E(x6771,x6772)+E(f488(x6773,x6771,x6774),f488(x6773,x6772,x6774)) % 169.39/169.66 [678]~E(x6781,x6782)+E(f488(x6783,x6784,x6781),f488(x6783,x6784,x6782)) % 169.39/169.66 [679]~E(x6791,x6792)+E(f89(x6791),f89(x6792)) % 169.39/169.66 [680]~E(x6801,x6802)+E(f744(x6801,x6803,x6804,x6805,x6806,x6807),f744(x6802,x6803,x6804,x6805,x6806,x6807)) % 169.39/169.66 [681]~E(x6811,x6812)+E(f744(x6813,x6811,x6814,x6815,x6816,x6817),f744(x6813,x6812,x6814,x6815,x6816,x6817)) % 169.39/169.66 [682]~E(x6821,x6822)+E(f744(x6823,x6824,x6821,x6825,x6826,x6827),f744(x6823,x6824,x6822,x6825,x6826,x6827)) % 169.39/169.66 [683]~E(x6831,x6832)+E(f744(x6833,x6834,x6835,x6831,x6836,x6837),f744(x6833,x6834,x6835,x6832,x6836,x6837)) % 169.39/169.66 [684]~E(x6841,x6842)+E(f744(x6843,x6844,x6845,x6846,x6841,x6847),f744(x6843,x6844,x6845,x6846,x6842,x6847)) % 169.39/169.66 [685]~E(x6851,x6852)+E(f744(x6853,x6854,x6855,x6856,x6857,x6851),f744(x6853,x6854,x6855,x6856,x6857,x6852)) % 169.39/169.66 [686]~E(x6861,x6862)+E(f405(x6861,x6863,x6864,x6865),f405(x6862,x6863,x6864,x6865)) % 169.39/169.66 [687]~E(x6871,x6872)+E(f405(x6873,x6871,x6874,x6875),f405(x6873,x6872,x6874,x6875)) % 169.39/169.66 [688]~E(x6881,x6882)+E(f405(x6883,x6884,x6881,x6885),f405(x6883,x6884,x6882,x6885)) % 169.39/169.66 [689]~E(x6891,x6892)+E(f405(x6893,x6894,x6895,x6891),f405(x6893,x6894,x6895,x6892)) % 169.39/169.66 [690]~E(x6901,x6902)+E(f608(x6901,x6903,x6904,x6905),f608(x6902,x6903,x6904,x6905)) % 169.39/169.66 [691]~E(x6911,x6912)+E(f608(x6913,x6911,x6914,x6915),f608(x6913,x6912,x6914,x6915)) % 169.39/169.66 [692]~E(x6921,x6922)+E(f608(x6923,x6924,x6921,x6925),f608(x6923,x6924,x6922,x6925)) % 169.39/169.66 [693]~E(x6931,x6932)+E(f608(x6933,x6934,x6935,x6931),f608(x6933,x6934,x6935,x6932)) % 169.39/169.66 [694]~E(x6941,x6942)+E(f264(x6941,x6943,x6944),f264(x6942,x6943,x6944)) % 169.39/169.66 [695]~E(x6951,x6952)+E(f264(x6953,x6951,x6954),f264(x6953,x6952,x6954)) % 169.39/169.66 [696]~E(x6961,x6962)+E(f264(x6963,x6964,x6961),f264(x6963,x6964,x6962)) % 169.39/169.66 [697]~E(x6971,x6972)+E(f799(x6971,x6973,x6974),f799(x6972,x6973,x6974)) % 169.39/169.66 [698]~E(x6981,x6982)+E(f799(x6983,x6981,x6984),f799(x6983,x6982,x6984)) % 169.39/169.66 [699]~E(x6991,x6992)+E(f799(x6993,x6994,x6991),f799(x6993,x6994,x6992)) % 169.39/169.66 [700]~E(x7001,x7002)+E(f609(x7001,x7003,x7004,x7005),f609(x7002,x7003,x7004,x7005)) % 169.39/169.66 [701]~E(x7011,x7012)+E(f609(x7013,x7011,x7014,x7015),f609(x7013,x7012,x7014,x7015)) % 169.39/169.66 [702]~E(x7021,x7022)+E(f609(x7023,x7024,x7021,x7025),f609(x7023,x7024,x7022,x7025)) % 169.39/169.66 [703]~E(x7031,x7032)+E(f609(x7033,x7034,x7035,x7031),f609(x7033,x7034,x7035,x7032)) % 169.39/169.66 [704]~E(x7041,x7042)+E(f132(x7041,x7043),f132(x7042,x7043)) % 169.39/169.66 [705]~E(x7051,x7052)+E(f132(x7053,x7051),f132(x7053,x7052)) % 169.39/169.66 [706]~E(x7061,x7062)+E(f33(x7061,x7063),f33(x7062,x7063)) % 169.39/169.66 [707]~E(x7071,x7072)+E(f33(x7073,x7071),f33(x7073,x7072)) % 169.39/169.66 [708]~E(x7081,x7082)+E(f171(x7081,x7083,x7084),f171(x7082,x7083,x7084)) % 169.39/169.66 [709]~E(x7091,x7092)+E(f171(x7093,x7091,x7094),f171(x7093,x7092,x7094)) % 169.39/169.66 [710]~E(x7101,x7102)+E(f171(x7103,x7104,x7101),f171(x7103,x7104,x7102)) % 169.39/169.66 [711]~E(x7111,x7112)+E(f339(x7111),f339(x7112)) % 169.39/169.66 [712]~E(x7121,x7122)+E(f848(x7121,x7123,x7124,x7125,x7126),f848(x7122,x7123,x7124,x7125,x7126)) % 169.39/169.66 [713]~E(x7131,x7132)+E(f848(x7133,x7131,x7134,x7135,x7136),f848(x7133,x7132,x7134,x7135,x7136)) % 169.39/169.66 [714]~E(x7141,x7142)+E(f848(x7143,x7144,x7141,x7145,x7146),f848(x7143,x7144,x7142,x7145,x7146)) % 169.39/169.66 [715]~E(x7151,x7152)+E(f848(x7153,x7154,x7155,x7151,x7156),f848(x7153,x7154,x7155,x7152,x7156)) % 169.39/169.66 [716]~E(x7161,x7162)+E(f848(x7163,x7164,x7165,x7166,x7161),f848(x7163,x7164,x7165,x7166,x7162)) % 169.39/169.66 [717]~E(x7171,x7172)+E(f29(x7171,x7173,x7174),f29(x7172,x7173,x7174)) % 169.39/169.66 [718]~E(x7181,x7182)+E(f29(x7183,x7181,x7184),f29(x7183,x7182,x7184)) % 169.39/169.66 [719]~E(x7191,x7192)+E(f29(x7193,x7194,x7191),f29(x7193,x7194,x7192)) % 169.39/169.66 [720]~E(x7201,x7202)+E(f314(x7201,x7203,x7204),f314(x7202,x7203,x7204)) % 169.39/169.66 [721]~E(x7211,x7212)+E(f314(x7213,x7211,x7214),f314(x7213,x7212,x7214)) % 169.39/169.66 [722]~E(x7221,x7222)+E(f314(x7223,x7224,x7221),f314(x7223,x7224,x7222)) % 169.39/169.66 [723]~E(x7231,x7232)+E(f518(x7231,x7233,x7234,x7235,x7236),f518(x7232,x7233,x7234,x7235,x7236)) % 169.39/169.66 [724]~E(x7241,x7242)+E(f518(x7243,x7241,x7244,x7245,x7246),f518(x7243,x7242,x7244,x7245,x7246)) % 169.39/169.66 [725]~E(x7251,x7252)+E(f518(x7253,x7254,x7251,x7255,x7256),f518(x7253,x7254,x7252,x7255,x7256)) % 169.39/169.66 [726]~E(x7261,x7262)+E(f518(x7263,x7264,x7265,x7261,x7266),f518(x7263,x7264,x7265,x7262,x7266)) % 169.39/169.66 [727]~E(x7271,x7272)+E(f518(x7273,x7274,x7275,x7276,x7271),f518(x7273,x7274,x7275,x7276,x7272)) % 169.39/169.66 [728]~E(x7281,x7282)+E(f714(x7281,x7283),f714(x7282,x7283)) % 169.39/169.66 [729]~E(x7291,x7292)+E(f714(x7293,x7291),f714(x7293,x7292)) % 169.39/169.66 [730]~E(x7301,x7302)+E(f672(x7301,x7303),f672(x7302,x7303)) % 169.39/169.66 [731]~E(x7311,x7312)+E(f672(x7313,x7311),f672(x7313,x7312)) % 169.39/169.66 [732]~E(x7321,x7322)+E(f730(x7321,x7323,x7324),f730(x7322,x7323,x7324)) % 169.39/169.66 [733]~E(x7331,x7332)+E(f730(x7333,x7331,x7334),f730(x7333,x7332,x7334)) % 169.39/169.66 [734]~E(x7341,x7342)+E(f730(x7343,x7344,x7341),f730(x7343,x7344,x7342)) % 169.39/169.66 [735]~E(x7351,x7352)+E(f725(x7351,x7353,x7354,x7355,x7356,x7357),f725(x7352,x7353,x7354,x7355,x7356,x7357)) % 169.39/169.66 [736]~E(x7361,x7362)+E(f725(x7363,x7361,x7364,x7365,x7366,x7367),f725(x7363,x7362,x7364,x7365,x7366,x7367)) % 169.39/169.66 [737]~E(x7371,x7372)+E(f725(x7373,x7374,x7371,x7375,x7376,x7377),f725(x7373,x7374,x7372,x7375,x7376,x7377)) % 169.39/169.66 [738]~E(x7381,x7382)+E(f725(x7383,x7384,x7385,x7381,x7386,x7387),f725(x7383,x7384,x7385,x7382,x7386,x7387)) % 169.39/169.66 [739]~E(x7391,x7392)+E(f725(x7393,x7394,x7395,x7396,x7391,x7397),f725(x7393,x7394,x7395,x7396,x7392,x7397)) % 169.39/169.66 [740]~E(x7401,x7402)+E(f725(x7403,x7404,x7405,x7406,x7407,x7401),f725(x7403,x7404,x7405,x7406,x7407,x7402)) % 169.39/169.66 [741]~E(x7411,x7412)+E(f541(x7411,x7413,x7414,x7415,x7416,x7417,x7418,x7419),f541(x7412,x7413,x7414,x7415,x7416,x7417,x7418,x7419)) % 169.39/169.66 [742]~E(x7421,x7422)+E(f541(x7423,x7421,x7424,x7425,x7426,x7427,x7428,x7429),f541(x7423,x7422,x7424,x7425,x7426,x7427,x7428,x7429)) % 169.39/169.66 [743]~E(x7431,x7432)+E(f541(x7433,x7434,x7431,x7435,x7436,x7437,x7438,x7439),f541(x7433,x7434,x7432,x7435,x7436,x7437,x7438,x7439)) % 169.39/169.66 [744]~E(x7441,x7442)+E(f541(x7443,x7444,x7445,x7441,x7446,x7447,x7448,x7449),f541(x7443,x7444,x7445,x7442,x7446,x7447,x7448,x7449)) % 169.39/169.66 [745]~E(x7451,x7452)+E(f541(x7453,x7454,x7455,x7456,x7451,x7457,x7458,x7459),f541(x7453,x7454,x7455,x7456,x7452,x7457,x7458,x7459)) % 169.39/169.66 [746]~E(x7461,x7462)+E(f541(x7463,x7464,x7465,x7466,x7467,x7461,x7468,x7469),f541(x7463,x7464,x7465,x7466,x7467,x7462,x7468,x7469)) % 169.39/169.66 [747]~E(x7471,x7472)+E(f541(x7473,x7474,x7475,x7476,x7477,x7478,x7471,x7479),f541(x7473,x7474,x7475,x7476,x7477,x7478,x7472,x7479)) % 169.39/169.66 [748]~E(x7481,x7482)+E(f541(x7483,x7484,x7485,x7486,x7487,x7488,x7489,x7481),f541(x7483,x7484,x7485,x7486,x7487,x7488,x7489,x7482)) % 169.39/169.66 [749]~E(x7491,x7492)+E(f724(x7491,x7493,x7494,x7495,x7496,x7497),f724(x7492,x7493,x7494,x7495,x7496,x7497)) % 169.39/169.66 [750]~E(x7501,x7502)+E(f724(x7503,x7501,x7504,x7505,x7506,x7507),f724(x7503,x7502,x7504,x7505,x7506,x7507)) % 169.39/169.66 [751]~E(x7511,x7512)+E(f724(x7513,x7514,x7511,x7515,x7516,x7517),f724(x7513,x7514,x7512,x7515,x7516,x7517)) % 169.39/169.66 [752]~E(x7521,x7522)+E(f724(x7523,x7524,x7525,x7521,x7526,x7527),f724(x7523,x7524,x7525,x7522,x7526,x7527)) % 169.39/169.66 [753]~E(x7531,x7532)+E(f724(x7533,x7534,x7535,x7536,x7531,x7537),f724(x7533,x7534,x7535,x7536,x7532,x7537)) % 169.39/169.66 [754]~E(x7541,x7542)+E(f724(x7543,x7544,x7545,x7546,x7547,x7541),f724(x7543,x7544,x7545,x7546,x7547,x7542)) % 169.39/169.66 [755]~E(x7551,x7552)+E(f522(x7551,x7553,x7554,x7555,x7556,x7557,x7558),f522(x7552,x7553,x7554,x7555,x7556,x7557,x7558)) % 169.39/169.66 [756]~E(x7561,x7562)+E(f522(x7563,x7561,x7564,x7565,x7566,x7567,x7568),f522(x7563,x7562,x7564,x7565,x7566,x7567,x7568)) % 169.39/169.66 [757]~E(x7571,x7572)+E(f522(x7573,x7574,x7571,x7575,x7576,x7577,x7578),f522(x7573,x7574,x7572,x7575,x7576,x7577,x7578)) % 169.39/169.66 [758]~E(x7581,x7582)+E(f522(x7583,x7584,x7585,x7581,x7586,x7587,x7588),f522(x7583,x7584,x7585,x7582,x7586,x7587,x7588)) % 169.39/169.66 [759]~E(x7591,x7592)+E(f522(x7593,x7594,x7595,x7596,x7591,x7597,x7598),f522(x7593,x7594,x7595,x7596,x7592,x7597,x7598)) % 169.39/169.66 [760]~E(x7601,x7602)+E(f522(x7603,x7604,x7605,x7606,x7607,x7601,x7608),f522(x7603,x7604,x7605,x7606,x7607,x7602,x7608)) % 169.39/169.66 [761]~E(x7611,x7612)+E(f522(x7613,x7614,x7615,x7616,x7617,x7618,x7611),f522(x7613,x7614,x7615,x7616,x7617,x7618,x7612)) % 169.39/169.66 [762]~E(x7621,x7622)+E(f434(x7621,x7623,x7624,x7625,x7626),f434(x7622,x7623,x7624,x7625,x7626)) % 169.39/169.66 [763]~E(x7631,x7632)+E(f434(x7633,x7631,x7634,x7635,x7636),f434(x7633,x7632,x7634,x7635,x7636)) % 169.39/169.66 [764]~E(x7641,x7642)+E(f434(x7643,x7644,x7641,x7645,x7646),f434(x7643,x7644,x7642,x7645,x7646)) % 169.39/169.66 [765]~E(x7651,x7652)+E(f434(x7653,x7654,x7655,x7651,x7656),f434(x7653,x7654,x7655,x7652,x7656)) % 169.39/169.66 [766]~E(x7661,x7662)+E(f434(x7663,x7664,x7665,x7666,x7661),f434(x7663,x7664,x7665,x7666,x7662)) % 169.39/169.66 [767]~E(x7671,x7672)+E(f797(x7671,x7673,x7674,x7675,x7676,x7677),f797(x7672,x7673,x7674,x7675,x7676,x7677)) % 169.39/169.66 [768]~E(x7681,x7682)+E(f797(x7683,x7681,x7684,x7685,x7686,x7687),f797(x7683,x7682,x7684,x7685,x7686,x7687)) % 169.39/169.66 [769]~E(x7691,x7692)+E(f797(x7693,x7694,x7691,x7695,x7696,x7697),f797(x7693,x7694,x7692,x7695,x7696,x7697)) % 169.39/169.66 [770]~E(x7701,x7702)+E(f797(x7703,x7704,x7705,x7701,x7706,x7707),f797(x7703,x7704,x7705,x7702,x7706,x7707)) % 169.39/169.66 [771]~E(x7711,x7712)+E(f797(x7713,x7714,x7715,x7716,x7711,x7717),f797(x7713,x7714,x7715,x7716,x7712,x7717)) % 169.39/169.66 [772]~E(x7721,x7722)+E(f797(x7723,x7724,x7725,x7726,x7727,x7721),f797(x7723,x7724,x7725,x7726,x7727,x7722)) % 169.39/169.66 [773]~E(x7731,x7732)+E(f277(x7731,x7733,x7734,x7735,x7736),f277(x7732,x7733,x7734,x7735,x7736)) % 169.39/169.66 [774]~E(x7741,x7742)+E(f277(x7743,x7741,x7744,x7745,x7746),f277(x7743,x7742,x7744,x7745,x7746)) % 169.39/169.66 [775]~E(x7751,x7752)+E(f277(x7753,x7754,x7751,x7755,x7756),f277(x7753,x7754,x7752,x7755,x7756)) % 169.39/169.66 [776]~E(x7761,x7762)+E(f277(x7763,x7764,x7765,x7761,x7766),f277(x7763,x7764,x7765,x7762,x7766)) % 169.39/169.66 [777]~E(x7771,x7772)+E(f277(x7773,x7774,x7775,x7776,x7771),f277(x7773,x7774,x7775,x7776,x7772)) % 169.39/169.66 [778]~E(x7781,x7782)+E(f504(x7781,x7783,x7784),f504(x7782,x7783,x7784)) % 169.39/169.66 [779]~E(x7791,x7792)+E(f504(x7793,x7791,x7794),f504(x7793,x7792,x7794)) % 169.39/169.66 [780]~E(x7801,x7802)+E(f504(x7803,x7804,x7801),f504(x7803,x7804,x7802)) % 169.39/169.66 [781]~E(x7811,x7812)+E(f495(x7811,x7813,x7814),f495(x7812,x7813,x7814)) % 169.39/169.66 [782]~E(x7821,x7822)+E(f495(x7823,x7821,x7824),f495(x7823,x7822,x7824)) % 169.39/169.66 [783]~E(x7831,x7832)+E(f495(x7833,x7834,x7831),f495(x7833,x7834,x7832)) % 169.39/169.66 [784]~E(x7841,x7842)+E(f244(x7841,x7843,x7844,x7845,x7846),f244(x7842,x7843,x7844,x7845,x7846)) % 169.39/169.66 [785]~E(x7851,x7852)+E(f244(x7853,x7851,x7854,x7855,x7856),f244(x7853,x7852,x7854,x7855,x7856)) % 169.39/169.66 [786]~E(x7861,x7862)+E(f244(x7863,x7864,x7861,x7865,x7866),f244(x7863,x7864,x7862,x7865,x7866)) % 169.39/169.66 [787]~E(x7871,x7872)+E(f244(x7873,x7874,x7875,x7871,x7876),f244(x7873,x7874,x7875,x7872,x7876)) % 169.39/169.66 [788]~E(x7881,x7882)+E(f244(x7883,x7884,x7885,x7886,x7881),f244(x7883,x7884,x7885,x7886,x7882)) % 169.39/169.66 [789]~E(x7891,x7892)+E(f603(x7891,x7893,x7894,x7895,x7896),f603(x7892,x7893,x7894,x7895,x7896)) % 169.39/169.66 [790]~E(x7901,x7902)+E(f603(x7903,x7901,x7904,x7905,x7906),f603(x7903,x7902,x7904,x7905,x7906)) % 169.39/169.66 [791]~E(x7911,x7912)+E(f603(x7913,x7914,x7911,x7915,x7916),f603(x7913,x7914,x7912,x7915,x7916)) % 169.39/169.66 [792]~E(x7921,x7922)+E(f603(x7923,x7924,x7925,x7921,x7926),f603(x7923,x7924,x7925,x7922,x7926)) % 169.39/169.66 [793]~E(x7931,x7932)+E(f603(x7933,x7934,x7935,x7936,x7931),f603(x7933,x7934,x7935,x7936,x7932)) % 169.39/169.66 [794]~E(x7941,x7942)+E(f562(x7941),f562(x7942)) % 169.39/169.66 [795]~E(x7951,x7952)+E(f374(x7951,x7953,x7954,x7955),f374(x7952,x7953,x7954,x7955)) % 169.39/169.66 [796]~E(x7961,x7962)+E(f374(x7963,x7961,x7964,x7965),f374(x7963,x7962,x7964,x7965)) % 169.39/169.66 [797]~E(x7971,x7972)+E(f374(x7973,x7974,x7971,x7975),f374(x7973,x7974,x7972,x7975)) % 169.39/169.66 [798]~E(x7981,x7982)+E(f374(x7983,x7984,x7985,x7981),f374(x7983,x7984,x7985,x7982)) % 169.39/169.66 [799]~E(x7991,x7992)+E(f602(x7991,x7993,x7994,x7995,x7996),f602(x7992,x7993,x7994,x7995,x7996)) % 169.39/169.66 [800]~E(x8001,x8002)+E(f602(x8003,x8001,x8004,x8005,x8006),f602(x8003,x8002,x8004,x8005,x8006)) % 169.39/169.66 [801]~E(x8011,x8012)+E(f602(x8013,x8014,x8011,x8015,x8016),f602(x8013,x8014,x8012,x8015,x8016)) % 169.39/169.66 [802]~E(x8021,x8022)+E(f602(x8023,x8024,x8025,x8021,x8026),f602(x8023,x8024,x8025,x8022,x8026)) % 169.39/169.67 [803]~E(x8031,x8032)+E(f602(x8033,x8034,x8035,x8036,x8031),f602(x8033,x8034,x8035,x8036,x8032)) % 169.39/169.67 [804]~E(x8041,x8042)+E(f68(x8041,x8043,x8044,x8045,x8046),f68(x8042,x8043,x8044,x8045,x8046)) % 169.39/169.67 [805]~E(x8051,x8052)+E(f68(x8053,x8051,x8054,x8055,x8056),f68(x8053,x8052,x8054,x8055,x8056)) % 169.39/169.67 [806]~E(x8061,x8062)+E(f68(x8063,x8064,x8061,x8065,x8066),f68(x8063,x8064,x8062,x8065,x8066)) % 169.39/169.67 [807]~E(x8071,x8072)+E(f68(x8073,x8074,x8075,x8071,x8076),f68(x8073,x8074,x8075,x8072,x8076)) % 169.39/169.67 [808]~E(x8081,x8082)+E(f68(x8083,x8084,x8085,x8086,x8081),f68(x8083,x8084,x8085,x8086,x8082)) % 169.39/169.67 [809]~E(x8091,x8092)+E(f355(x8091,x8093,x8094,x8095,x8096,x8097,x8098),f355(x8092,x8093,x8094,x8095,x8096,x8097,x8098)) % 169.39/169.67 [810]~E(x8101,x8102)+E(f355(x8103,x8101,x8104,x8105,x8106,x8107,x8108),f355(x8103,x8102,x8104,x8105,x8106,x8107,x8108)) % 169.39/169.67 [811]~E(x8111,x8112)+E(f355(x8113,x8114,x8111,x8115,x8116,x8117,x8118),f355(x8113,x8114,x8112,x8115,x8116,x8117,x8118)) % 169.39/169.67 [812]~E(x8121,x8122)+E(f355(x8123,x8124,x8125,x8121,x8126,x8127,x8128),f355(x8123,x8124,x8125,x8122,x8126,x8127,x8128)) % 169.39/169.67 [813]~E(x8131,x8132)+E(f355(x8133,x8134,x8135,x8136,x8131,x8137,x8138),f355(x8133,x8134,x8135,x8136,x8132,x8137,x8138)) % 169.39/169.67 [814]~E(x8141,x8142)+E(f355(x8143,x8144,x8145,x8146,x8147,x8141,x8148),f355(x8143,x8144,x8145,x8146,x8147,x8142,x8148)) % 169.39/169.67 [815]~E(x8151,x8152)+E(f355(x8153,x8154,x8155,x8156,x8157,x8158,x8151),f355(x8153,x8154,x8155,x8156,x8157,x8158,x8152)) % 169.39/169.67 [816]~E(x8161,x8162)+E(f164(x8161,x8163,x8164,x8165),f164(x8162,x8163,x8164,x8165)) % 169.39/169.67 [817]~E(x8171,x8172)+E(f164(x8173,x8171,x8174,x8175),f164(x8173,x8172,x8174,x8175)) % 169.39/169.67 [818]~E(x8181,x8182)+E(f164(x8183,x8184,x8181,x8185),f164(x8183,x8184,x8182,x8185)) % 169.39/169.67 [819]~E(x8191,x8192)+E(f164(x8193,x8194,x8195,x8191),f164(x8193,x8194,x8195,x8192)) % 169.39/169.67 [820]~E(x8201,x8202)+E(f581(x8201,x8203,x8204),f581(x8202,x8203,x8204)) % 169.39/169.67 [821]~E(x8211,x8212)+E(f581(x8213,x8211,x8214),f581(x8213,x8212,x8214)) % 169.39/169.67 [822]~E(x8221,x8222)+E(f581(x8223,x8224,x8221),f581(x8223,x8224,x8222)) % 169.39/169.67 [823]~E(x8231,x8232)+E(f163(x8231,x8233,x8234,x8235),f163(x8232,x8233,x8234,x8235)) % 169.39/169.67 [824]~E(x8241,x8242)+E(f163(x8243,x8241,x8244,x8245),f163(x8243,x8242,x8244,x8245)) % 169.39/169.67 [825]~E(x8251,x8252)+E(f163(x8253,x8254,x8251,x8255),f163(x8253,x8254,x8252,x8255)) % 169.39/169.67 [826]~E(x8261,x8262)+E(f163(x8263,x8264,x8265,x8261),f163(x8263,x8264,x8265,x8262)) % 169.39/169.67 [827]~E(x8271,x8272)+E(f806(x8271,x8273,x8274),f806(x8272,x8273,x8274)) % 169.39/169.67 [828]~E(x8281,x8282)+E(f806(x8283,x8281,x8284),f806(x8283,x8282,x8284)) % 169.39/169.67 [829]~E(x8291,x8292)+E(f806(x8293,x8294,x8291),f806(x8293,x8294,x8292)) % 169.39/169.67 [830]~E(x8301,x8302)+E(f586(x8301,x8303,x8304,x8305),f586(x8302,x8303,x8304,x8305)) % 169.39/169.67 [831]~E(x8311,x8312)+E(f586(x8313,x8311,x8314,x8315),f586(x8313,x8312,x8314,x8315)) % 169.39/169.67 [832]~E(x8321,x8322)+E(f586(x8323,x8324,x8321,x8325),f586(x8323,x8324,x8322,x8325)) % 169.39/169.67 [833]~E(x8331,x8332)+E(f586(x8333,x8334,x8335,x8331),f586(x8333,x8334,x8335,x8332)) % 169.39/169.67 [834]~E(x8341,x8342)+E(f652(x8341,x8343),f652(x8342,x8343)) % 169.39/169.67 [835]~E(x8351,x8352)+E(f652(x8353,x8351),f652(x8353,x8352)) % 169.39/169.67 [836]~E(x8361,x8362)+E(f847(x8361,x8363,x8364,x8365,x8366),f847(x8362,x8363,x8364,x8365,x8366)) % 169.39/169.67 [837]~E(x8371,x8372)+E(f847(x8373,x8371,x8374,x8375,x8376),f847(x8373,x8372,x8374,x8375,x8376)) % 169.39/169.67 [838]~E(x8381,x8382)+E(f847(x8383,x8384,x8381,x8385,x8386),f847(x8383,x8384,x8382,x8385,x8386)) % 169.39/169.67 [839]~E(x8391,x8392)+E(f847(x8393,x8394,x8395,x8391,x8396),f847(x8393,x8394,x8395,x8392,x8396)) % 169.39/169.67 [840]~E(x8401,x8402)+E(f847(x8403,x8404,x8405,x8406,x8401),f847(x8403,x8404,x8405,x8406,x8402)) % 169.39/169.67 [841]~E(x8411,x8412)+E(f682(x8411,x8413,x8414,x8415),f682(x8412,x8413,x8414,x8415)) % 169.39/169.67 [842]~E(x8421,x8422)+E(f682(x8423,x8421,x8424,x8425),f682(x8423,x8422,x8424,x8425)) % 169.39/169.67 [843]~E(x8431,x8432)+E(f682(x8433,x8434,x8431,x8435),f682(x8433,x8434,x8432,x8435)) % 169.39/169.67 [844]~E(x8441,x8442)+E(f682(x8443,x8444,x8445,x8441),f682(x8443,x8444,x8445,x8442)) % 169.39/169.67 [845]~E(x8451,x8452)+E(f280(x8451,x8453),f280(x8452,x8453)) % 169.39/169.67 [846]~E(x8461,x8462)+E(f280(x8463,x8461),f280(x8463,x8462)) % 169.39/169.67 [847]~E(x8471,x8472)+E(f185(x8471,x8473,x8474),f185(x8472,x8473,x8474)) % 169.39/169.67 [848]~E(x8481,x8482)+E(f185(x8483,x8481,x8484),f185(x8483,x8482,x8484)) % 169.39/169.67 [849]~E(x8491,x8492)+E(f185(x8493,x8494,x8491),f185(x8493,x8494,x8492)) % 169.39/169.67 [850]~E(x8501,x8502)+E(f202(x8501,x8503),f202(x8502,x8503)) % 169.39/169.67 [851]~E(x8511,x8512)+E(f202(x8513,x8511),f202(x8513,x8512)) % 169.39/169.67 [852]~E(x8521,x8522)+E(f149(x8521,x8523,x8524,x8525,x8526),f149(x8522,x8523,x8524,x8525,x8526)) % 169.39/169.67 [853]~E(x8531,x8532)+E(f149(x8533,x8531,x8534,x8535,x8536),f149(x8533,x8532,x8534,x8535,x8536)) % 169.39/169.67 [854]~E(x8541,x8542)+E(f149(x8543,x8544,x8541,x8545,x8546),f149(x8543,x8544,x8542,x8545,x8546)) % 169.39/169.67 [855]~E(x8551,x8552)+E(f149(x8553,x8554,x8555,x8551,x8556),f149(x8553,x8554,x8555,x8552,x8556)) % 169.39/169.67 [856]~E(x8561,x8562)+E(f149(x8563,x8564,x8565,x8566,x8561),f149(x8563,x8564,x8565,x8566,x8562)) % 169.39/169.67 [857]~E(x8571,x8572)+E(f505(x8571,x8573,x8574),f505(x8572,x8573,x8574)) % 169.39/169.67 [858]~E(x8581,x8582)+E(f505(x8583,x8581,x8584),f505(x8583,x8582,x8584)) % 169.39/169.67 [859]~E(x8591,x8592)+E(f505(x8593,x8594,x8591),f505(x8593,x8594,x8592)) % 169.39/169.67 [860]~E(x8601,x8602)+E(f266(x8601,x8603),f266(x8602,x8603)) % 169.39/169.67 [861]~E(x8611,x8612)+E(f266(x8613,x8611),f266(x8613,x8612)) % 169.39/169.67 [862]~E(x8621,x8622)+E(f192(x8621,x8623,x8624,x8625),f192(x8622,x8623,x8624,x8625)) % 169.39/169.67 [863]~E(x8631,x8632)+E(f192(x8633,x8631,x8634,x8635),f192(x8633,x8632,x8634,x8635)) % 169.39/169.67 [864]~E(x8641,x8642)+E(f192(x8643,x8644,x8641,x8645),f192(x8643,x8644,x8642,x8645)) % 169.39/169.67 [865]~E(x8651,x8652)+E(f192(x8653,x8654,x8655,x8651),f192(x8653,x8654,x8655,x8652)) % 169.39/169.67 [866]~E(x8661,x8662)+E(f347(x8661,x8663,x8664),f347(x8662,x8663,x8664)) % 169.39/169.67 [867]~E(x8671,x8672)+E(f347(x8673,x8671,x8674),f347(x8673,x8672,x8674)) % 169.39/169.67 [868]~E(x8681,x8682)+E(f347(x8683,x8684,x8681),f347(x8683,x8684,x8682)) % 169.39/169.67 [869]~E(x8691,x8692)+E(f167(x8691,x8693,x8694),f167(x8692,x8693,x8694)) % 169.39/169.67 [870]~E(x8701,x8702)+E(f167(x8703,x8701,x8704),f167(x8703,x8702,x8704)) % 169.39/169.67 [871]~E(x8711,x8712)+E(f167(x8713,x8714,x8711),f167(x8713,x8714,x8712)) % 169.39/169.67 [872]~E(x8721,x8722)+E(f693(x8721,x8723,x8724),f693(x8722,x8723,x8724)) % 169.39/169.67 [873]~E(x8731,x8732)+E(f693(x8733,x8731,x8734),f693(x8733,x8732,x8734)) % 169.39/169.67 [874]~E(x8741,x8742)+E(f693(x8743,x8744,x8741),f693(x8743,x8744,x8742)) % 169.39/169.67 [875]~E(x8751,x8752)+E(f668(x8751,x8753,x8754,x8755),f668(x8752,x8753,x8754,x8755)) % 169.39/169.67 [876]~E(x8761,x8762)+E(f668(x8763,x8761,x8764,x8765),f668(x8763,x8762,x8764,x8765)) % 169.39/169.67 [877]~E(x8771,x8772)+E(f668(x8773,x8774,x8771,x8775),f668(x8773,x8774,x8772,x8775)) % 169.39/169.67 [878]~E(x8781,x8782)+E(f668(x8783,x8784,x8785,x8781),f668(x8783,x8784,x8785,x8782)) % 169.39/169.67 [879]~E(x8791,x8792)+E(f440(x8791,x8793,x8794),f440(x8792,x8793,x8794)) % 169.39/169.67 [880]~E(x8801,x8802)+E(f440(x8803,x8801,x8804),f440(x8803,x8802,x8804)) % 169.39/169.67 [881]~E(x8811,x8812)+E(f440(x8813,x8814,x8811),f440(x8813,x8814,x8812)) % 169.39/169.67 [882]~E(x8821,x8822)+E(f353(x8821,x8823,x8824),f353(x8822,x8823,x8824)) % 169.39/169.67 [883]~E(x8831,x8832)+E(f353(x8833,x8831,x8834),f353(x8833,x8832,x8834)) % 169.39/169.67 [884]~E(x8841,x8842)+E(f353(x8843,x8844,x8841),f353(x8843,x8844,x8842)) % 169.39/169.67 [885]~E(x8851,x8852)+E(f30(x8851,x8853,x8854),f30(x8852,x8853,x8854)) % 169.39/169.67 [886]~E(x8861,x8862)+E(f30(x8863,x8861,x8864),f30(x8863,x8862,x8864)) % 169.39/169.67 [887]~E(x8871,x8872)+E(f30(x8873,x8874,x8871),f30(x8873,x8874,x8872)) % 169.39/169.67 [888]~E(x8881,x8882)+E(f234(x8881,x8883,x8884,x8885,x8886),f234(x8882,x8883,x8884,x8885,x8886)) % 169.39/169.67 [889]~E(x8891,x8892)+E(f234(x8893,x8891,x8894,x8895,x8896),f234(x8893,x8892,x8894,x8895,x8896)) % 169.39/169.67 [890]~E(x8901,x8902)+E(f234(x8903,x8904,x8901,x8905,x8906),f234(x8903,x8904,x8902,x8905,x8906)) % 169.39/169.67 [891]~E(x8911,x8912)+E(f234(x8913,x8914,x8915,x8911,x8916),f234(x8913,x8914,x8915,x8912,x8916)) % 169.39/169.67 [892]~E(x8921,x8922)+E(f234(x8923,x8924,x8925,x8926,x8921),f234(x8923,x8924,x8925,x8926,x8922)) % 169.39/169.67 [893]~E(x8931,x8932)+E(f380(x8931,x8933,x8934,x8935),f380(x8932,x8933,x8934,x8935)) % 169.39/169.67 [894]~E(x8941,x8942)+E(f380(x8943,x8941,x8944,x8945),f380(x8943,x8942,x8944,x8945)) % 169.39/169.67 [895]~E(x8951,x8952)+E(f380(x8953,x8954,x8951,x8955),f380(x8953,x8954,x8952,x8955)) % 169.39/169.67 [896]~E(x8961,x8962)+E(f380(x8963,x8964,x8965,x8961),f380(x8963,x8964,x8965,x8962)) % 169.39/169.67 [897]~E(x8971,x8972)+E(f661(x8971,x8973,x8974,x8975),f661(x8972,x8973,x8974,x8975)) % 169.39/169.67 [898]~E(x8981,x8982)+E(f661(x8983,x8981,x8984,x8985),f661(x8983,x8982,x8984,x8985)) % 169.39/169.67 [899]~E(x8991,x8992)+E(f661(x8993,x8994,x8991,x8995),f661(x8993,x8994,x8992,x8995)) % 169.39/169.67 [900]~E(x9001,x9002)+E(f661(x9003,x9004,x9005,x9001),f661(x9003,x9004,x9005,x9002)) % 169.39/169.67 [901]~E(x9011,x9012)+E(f718(x9011,x9013,x9014),f718(x9012,x9013,x9014)) % 169.39/169.67 [902]~E(x9021,x9022)+E(f718(x9023,x9021,x9024),f718(x9023,x9022,x9024)) % 169.39/169.67 [903]~E(x9031,x9032)+E(f718(x9033,x9034,x9031),f718(x9033,x9034,x9032)) % 169.39/169.67 [904]~E(x9041,x9042)+E(f121(x9041,x9043,x9044),f121(x9042,x9043,x9044)) % 169.39/169.67 [905]~E(x9051,x9052)+E(f121(x9053,x9051,x9054),f121(x9053,x9052,x9054)) % 169.39/169.67 [906]~E(x9061,x9062)+E(f121(x9063,x9064,x9061),f121(x9063,x9064,x9062)) % 169.39/169.67 [907]~E(x9071,x9072)+E(f370(x9071,x9073,x9074),f370(x9072,x9073,x9074)) % 169.39/169.67 [908]~E(x9081,x9082)+E(f370(x9083,x9081,x9084),f370(x9083,x9082,x9084)) % 169.39/169.67 [909]~E(x9091,x9092)+E(f370(x9093,x9094,x9091),f370(x9093,x9094,x9092)) % 169.39/169.67 [910]~E(x9101,x9102)+E(f393(x9101,x9103),f393(x9102,x9103)) % 169.39/169.67 [911]~E(x9111,x9112)+E(f393(x9113,x9111),f393(x9113,x9112)) % 169.39/169.67 [912]~E(x9121,x9122)+E(f770(x9121,x9123,x9124,x9125,x9126),f770(x9122,x9123,x9124,x9125,x9126)) % 169.39/169.67 [913]~E(x9131,x9132)+E(f770(x9133,x9131,x9134,x9135,x9136),f770(x9133,x9132,x9134,x9135,x9136)) % 169.39/169.67 [914]~E(x9141,x9142)+E(f770(x9143,x9144,x9141,x9145,x9146),f770(x9143,x9144,x9142,x9145,x9146)) % 169.39/169.67 [915]~E(x9151,x9152)+E(f770(x9153,x9154,x9155,x9151,x9156),f770(x9153,x9154,x9155,x9152,x9156)) % 169.39/169.67 [916]~E(x9161,x9162)+E(f770(x9163,x9164,x9165,x9166,x9161),f770(x9163,x9164,x9165,x9166,x9162)) % 169.39/169.67 [917]~E(x9171,x9172)+E(f858(x9171),f858(x9172)) % 169.39/169.67 [918]~E(x9181,x9182)+E(f354(x9181,x9183,x9184),f354(x9182,x9183,x9184)) % 169.39/169.67 [919]~E(x9191,x9192)+E(f354(x9193,x9191,x9194),f354(x9193,x9192,x9194)) % 169.39/169.67 [920]~E(x9201,x9202)+E(f354(x9203,x9204,x9201),f354(x9203,x9204,x9202)) % 169.39/169.67 [921]~E(x9211,x9212)+E(f481(x9211,x9213),f481(x9212,x9213)) % 169.39/169.67 [922]~E(x9221,x9222)+E(f481(x9223,x9221),f481(x9223,x9222)) % 169.39/169.67 [923]~E(x9231,x9232)+E(f123(x9231,x9233,x9234,x9235),f123(x9232,x9233,x9234,x9235)) % 169.39/169.67 [924]~E(x9241,x9242)+E(f123(x9243,x9241,x9244,x9245),f123(x9243,x9242,x9244,x9245)) % 169.39/169.67 [925]~E(x9251,x9252)+E(f123(x9253,x9254,x9251,x9255),f123(x9253,x9254,x9252,x9255)) % 169.39/169.67 [926]~E(x9261,x9262)+E(f123(x9263,x9264,x9265,x9261),f123(x9263,x9264,x9265,x9262)) % 169.39/169.67 [927]~E(x9271,x9272)+E(f443(x9271,x9273,x9274),f443(x9272,x9273,x9274)) % 169.39/169.67 [928]~E(x9281,x9282)+E(f443(x9283,x9281,x9284),f443(x9283,x9282,x9284)) % 169.39/169.67 [929]~E(x9291,x9292)+E(f443(x9293,x9294,x9291),f443(x9293,x9294,x9292)) % 169.39/169.67 [930]~E(x9301,x9302)+E(f697(x9301,x9303,x9304,x9305),f697(x9302,x9303,x9304,x9305)) % 169.39/169.67 [931]~E(x9311,x9312)+E(f697(x9313,x9311,x9314,x9315),f697(x9313,x9312,x9314,x9315)) % 169.39/169.67 [932]~E(x9321,x9322)+E(f697(x9323,x9324,x9321,x9325),f697(x9323,x9324,x9322,x9325)) % 169.39/169.67 [933]~E(x9331,x9332)+E(f697(x9333,x9334,x9335,x9331),f697(x9333,x9334,x9335,x9332)) % 169.39/169.67 [934]~E(x9341,x9342)+E(f200(x9341,x9343),f200(x9342,x9343)) % 169.39/169.67 [935]~E(x9351,x9352)+E(f200(x9353,x9351),f200(x9353,x9352)) % 169.39/169.67 [936]~E(x9361,x9362)+E(f585(x9361,x9363,x9364,x9365),f585(x9362,x9363,x9364,x9365)) % 169.39/169.67 [937]~E(x9371,x9372)+E(f585(x9373,x9371,x9374,x9375),f585(x9373,x9372,x9374,x9375)) % 169.39/169.67 [938]~E(x9381,x9382)+E(f585(x9383,x9384,x9381,x9385),f585(x9383,x9384,x9382,x9385)) % 169.39/169.67 [939]~E(x9391,x9392)+E(f585(x9393,x9394,x9395,x9391),f585(x9393,x9394,x9395,x9392)) % 169.39/169.67 [940]~E(x9401,x9402)+E(f122(x9401,x9403),f122(x9402,x9403)) % 169.39/169.67 [941]~E(x9411,x9412)+E(f122(x9413,x9411),f122(x9413,x9412)) % 169.39/169.67 [942]~E(x9421,x9422)+E(f636(x9421,x9423),f636(x9422,x9423)) % 169.39/169.67 [943]~E(x9431,x9432)+E(f636(x9433,x9431),f636(x9433,x9432)) % 169.39/169.67 [944]~E(x9441,x9442)+E(f613(x9441,x9443,x9444,x9445),f613(x9442,x9443,x9444,x9445)) % 169.39/169.67 [945]~E(x9451,x9452)+E(f613(x9453,x9451,x9454,x9455),f613(x9453,x9452,x9454,x9455)) % 169.39/169.67 [946]~E(x9461,x9462)+E(f613(x9463,x9464,x9461,x9465),f613(x9463,x9464,x9462,x9465)) % 169.39/169.67 [947]~E(x9471,x9472)+E(f613(x9473,x9474,x9475,x9471),f613(x9473,x9474,x9475,x9472)) % 169.39/169.67 [948]~E(x9481,x9482)+E(f595(x9481,x9483,x9484),f595(x9482,x9483,x9484)) % 169.39/169.67 [949]~E(x9491,x9492)+E(f595(x9493,x9491,x9494),f595(x9493,x9492,x9494)) % 169.39/169.67 [950]~E(x9501,x9502)+E(f595(x9503,x9504,x9501),f595(x9503,x9504,x9502)) % 169.39/169.67 [951]~E(x9511,x9512)+E(f835(x9511,x9513,x9514),f835(x9512,x9513,x9514)) % 169.39/169.67 [952]~E(x9521,x9522)+E(f835(x9523,x9521,x9524),f835(x9523,x9522,x9524)) % 169.39/169.67 [953]~E(x9531,x9532)+E(f835(x9533,x9534,x9531),f835(x9533,x9534,x9532)) % 169.39/169.67 [954]~E(x9541,x9542)+E(f436(x9541,x9543,x9544,x9545,x9546),f436(x9542,x9543,x9544,x9545,x9546)) % 169.39/169.67 [955]~E(x9551,x9552)+E(f436(x9553,x9551,x9554,x9555,x9556),f436(x9553,x9552,x9554,x9555,x9556)) % 169.39/169.67 [956]~E(x9561,x9562)+E(f436(x9563,x9564,x9561,x9565,x9566),f436(x9563,x9564,x9562,x9565,x9566)) % 169.39/169.67 [957]~E(x9571,x9572)+E(f436(x9573,x9574,x9575,x9571,x9576),f436(x9573,x9574,x9575,x9572,x9576)) % 169.39/169.67 [958]~E(x9581,x9582)+E(f436(x9583,x9584,x9585,x9586,x9581),f436(x9583,x9584,x9585,x9586,x9582)) % 169.39/169.67 [959]~E(x9591,x9592)+E(f262(x9591,x9593),f262(x9592,x9593)) % 169.39/169.67 [960]~E(x9601,x9602)+E(f262(x9603,x9601),f262(x9603,x9602)) % 169.39/169.67 [961]~E(x9611,x9612)+E(f500(x9611,x9613,x9614,x9615),f500(x9612,x9613,x9614,x9615)) % 169.39/169.67 [962]~E(x9621,x9622)+E(f500(x9623,x9621,x9624,x9625),f500(x9623,x9622,x9624,x9625)) % 169.39/169.67 [963]~E(x9631,x9632)+E(f500(x9633,x9634,x9631,x9635),f500(x9633,x9634,x9632,x9635)) % 169.39/169.67 [964]~E(x9641,x9642)+E(f500(x9643,x9644,x9645,x9641),f500(x9643,x9644,x9645,x9642)) % 169.39/169.67 [965]~E(x9651,x9652)+E(f544(x9651),f544(x9652)) % 169.39/169.67 [966]~E(x9661,x9662)+E(f635(x9661,x9663),f635(x9662,x9663)) % 169.39/169.67 [967]~E(x9671,x9672)+E(f635(x9673,x9671),f635(x9673,x9672)) % 169.39/169.67 [968]~E(x9681,x9682)+E(f795(x9681,x9683,x9684),f795(x9682,x9683,x9684)) % 169.39/169.67 [969]~E(x9691,x9692)+E(f795(x9693,x9691,x9694),f795(x9693,x9692,x9694)) % 169.39/169.67 [970]~E(x9701,x9702)+E(f795(x9703,x9704,x9701),f795(x9703,x9704,x9702)) % 169.39/169.67 [971]~E(x9711,x9712)+E(f537(x9711,x9713,x9714,x9715),f537(x9712,x9713,x9714,x9715)) % 169.39/169.67 [972]~E(x9721,x9722)+E(f537(x9723,x9721,x9724,x9725),f537(x9723,x9722,x9724,x9725)) % 169.39/169.67 [973]~E(x9731,x9732)+E(f537(x9733,x9734,x9731,x9735),f537(x9733,x9734,x9732,x9735)) % 169.39/169.67 [974]~E(x9741,x9742)+E(f537(x9743,x9744,x9745,x9741),f537(x9743,x9744,x9745,x9742)) % 169.39/169.67 [975]~E(x9751,x9752)+E(f150(x9751,x9753,x9754,x9755),f150(x9752,x9753,x9754,x9755)) % 169.39/169.67 [976]~E(x9761,x9762)+E(f150(x9763,x9761,x9764,x9765),f150(x9763,x9762,x9764,x9765)) % 169.39/169.67 [977]~E(x9771,x9772)+E(f150(x9773,x9774,x9771,x9775),f150(x9773,x9774,x9772,x9775)) % 169.39/169.67 [978]~E(x9781,x9782)+E(f150(x9783,x9784,x9785,x9781),f150(x9783,x9784,x9785,x9782)) % 169.39/169.67 [979]~E(x9791,x9792)+E(f815(x9791,x9793,x9794),f815(x9792,x9793,x9794)) % 169.39/169.67 [980]~E(x9801,x9802)+E(f815(x9803,x9801,x9804),f815(x9803,x9802,x9804)) % 169.39/169.67 [981]~E(x9811,x9812)+E(f815(x9813,x9814,x9811),f815(x9813,x9814,x9812)) % 169.39/169.67 [982]~E(x9821,x9822)+E(f402(x9821,x9823,x9824,x9825),f402(x9822,x9823,x9824,x9825)) % 169.39/169.67 [983]~E(x9831,x9832)+E(f402(x9833,x9831,x9834,x9835),f402(x9833,x9832,x9834,x9835)) % 169.39/169.67 [984]~E(x9841,x9842)+E(f402(x9843,x9844,x9841,x9845),f402(x9843,x9844,x9842,x9845)) % 169.39/169.67 [985]~E(x9851,x9852)+E(f402(x9853,x9854,x9855,x9851),f402(x9853,x9854,x9855,x9852)) % 169.39/169.67 [986]~E(x9861,x9862)+E(f759(x9861,x9863),f759(x9862,x9863)) % 169.39/169.67 [987]~E(x9871,x9872)+E(f759(x9873,x9871),f759(x9873,x9872)) % 169.39/169.67 [988]~E(x9881,x9882)+E(f653(x9881,x9883,x9884,x9885,x9886),f653(x9882,x9883,x9884,x9885,x9886)) % 169.39/169.67 [989]~E(x9891,x9892)+E(f653(x9893,x9891,x9894,x9895,x9896),f653(x9893,x9892,x9894,x9895,x9896)) % 169.39/169.67 [990]~E(x9901,x9902)+E(f653(x9903,x9904,x9901,x9905,x9906),f653(x9903,x9904,x9902,x9905,x9906)) % 169.39/169.67 [991]~E(x9911,x9912)+E(f653(x9913,x9914,x9915,x9911,x9916),f653(x9913,x9914,x9915,x9912,x9916)) % 169.39/169.67 [992]~E(x9921,x9922)+E(f653(x9923,x9924,x9925,x9926,x9921),f653(x9923,x9924,x9925,x9926,x9922)) % 169.39/169.67 [993]~E(x9931,x9932)+E(f302(x9931,x9933,x9934,x9935,x9936),f302(x9932,x9933,x9934,x9935,x9936)) % 169.39/169.67 [994]~E(x9941,x9942)+E(f302(x9943,x9941,x9944,x9945,x9946),f302(x9943,x9942,x9944,x9945,x9946)) % 169.39/169.67 [995]~E(x9951,x9952)+E(f302(x9953,x9954,x9951,x9955,x9956),f302(x9953,x9954,x9952,x9955,x9956)) % 169.39/169.67 [996]~E(x9961,x9962)+E(f302(x9963,x9964,x9965,x9961,x9966),f302(x9963,x9964,x9965,x9962,x9966)) % 169.39/169.67 [997]~E(x9971,x9972)+E(f302(x9973,x9974,x9975,x9976,x9971),f302(x9973,x9974,x9975,x9976,x9972)) % 169.39/169.67 [998]~E(x9981,x9982)+E(f547(x9981),f547(x9982)) % 169.39/169.67 [999]~E(x9991,x9992)+E(f807(x9991,x9993,x9994,x9995),f807(x9992,x9993,x9994,x9995)) % 169.39/169.67 [1000]~E(x10001,x10002)+E(f807(x10003,x10001,x10004,x10005),f807(x10003,x10002,x10004,x10005)) % 169.39/169.67 [1001]~E(x10011,x10012)+E(f807(x10013,x10014,x10011,x10015),f807(x10013,x10014,x10012,x10015)) % 169.39/169.67 [1002]~E(x10021,x10022)+E(f807(x10023,x10024,x10025,x10021),f807(x10023,x10024,x10025,x10022)) % 169.39/169.67 [1003]~E(x10031,x10032)+E(f767(x10031,x10033,x10034,x10035,x10036),f767(x10032,x10033,x10034,x10035,x10036)) % 169.39/169.67 [1004]~E(x10041,x10042)+E(f767(x10043,x10041,x10044,x10045,x10046),f767(x10043,x10042,x10044,x10045,x10046)) % 169.39/169.67 [1005]~E(x10051,x10052)+E(f767(x10053,x10054,x10051,x10055,x10056),f767(x10053,x10054,x10052,x10055,x10056)) % 169.39/169.67 [1006]~E(x10061,x10062)+E(f767(x10063,x10064,x10065,x10061,x10066),f767(x10063,x10064,x10065,x10062,x10066)) % 169.39/169.67 [1007]~E(x10071,x10072)+E(f767(x10073,x10074,x10075,x10076,x10071),f767(x10073,x10074,x10075,x10076,x10072)) % 169.39/169.67 [1008]~E(x10081,x10082)+E(f441(x10081,x10083,x10084),f441(x10082,x10083,x10084)) % 169.39/169.67 [1009]~E(x10091,x10092)+E(f441(x10093,x10091,x10094),f441(x10093,x10092,x10094)) % 169.39/169.67 [1010]~E(x10101,x10102)+E(f441(x10103,x10104,x10101),f441(x10103,x10104,x10102)) % 169.39/169.67 [1011]~E(x10111,x10112)+E(f229(x10111,x10113,x10114,x10115),f229(x10112,x10113,x10114,x10115)) % 169.39/169.67 [1012]~E(x10121,x10122)+E(f229(x10123,x10121,x10124,x10125),f229(x10123,x10122,x10124,x10125)) % 169.39/169.67 [1013]~E(x10131,x10132)+E(f229(x10133,x10134,x10131,x10135),f229(x10133,x10134,x10132,x10135)) % 169.39/169.67 [1014]~E(x10141,x10142)+E(f229(x10143,x10144,x10145,x10141),f229(x10143,x10144,x10145,x10142)) % 169.39/169.67 [1015]~E(x10151,x10152)+E(f279(x10151),f279(x10152)) % 169.39/169.67 [1016]~E(x10161,x10162)+E(f849(x10161,x10163,x10164),f849(x10162,x10163,x10164)) % 169.39/169.67 [1017]~E(x10171,x10172)+E(f849(x10173,x10171,x10174),f849(x10173,x10172,x10174)) % 169.39/169.67 [1018]~E(x10181,x10182)+E(f849(x10183,x10184,x10181),f849(x10183,x10184,x10182)) % 169.39/169.67 [1019]~E(x10191,x10192)+E(f278(x10191,x10193),f278(x10192,x10193)) % 169.39/169.67 [1020]~E(x10201,x10202)+E(f278(x10203,x10201),f278(x10203,x10202)) % 169.39/169.67 [1021]~E(x10211,x10212)+E(f77(x10211,x10213,x10214,x10215,x10216),f77(x10212,x10213,x10214,x10215,x10216)) % 169.39/169.67 [1022]~E(x10221,x10222)+E(f77(x10223,x10221,x10224,x10225,x10226),f77(x10223,x10222,x10224,x10225,x10226)) % 169.39/169.67 [1023]~E(x10231,x10232)+E(f77(x10233,x10234,x10231,x10235,x10236),f77(x10233,x10234,x10232,x10235,x10236)) % 169.39/169.67 [1024]~E(x10241,x10242)+E(f77(x10243,x10244,x10245,x10241,x10246),f77(x10243,x10244,x10245,x10242,x10246)) % 169.39/169.67 [1025]~E(x10251,x10252)+E(f77(x10253,x10254,x10255,x10256,x10251),f77(x10253,x10254,x10255,x10256,x10252)) % 169.39/169.67 [1026]~E(x10261,x10262)+E(f545(x10261,x10263,x10264),f545(x10262,x10263,x10264)) % 169.39/169.67 [1027]~E(x10271,x10272)+E(f545(x10273,x10271,x10274),f545(x10273,x10272,x10274)) % 169.39/169.67 [1028]~E(x10281,x10282)+E(f545(x10283,x10284,x10281),f545(x10283,x10284,x10282)) % 169.39/169.67 [1029]~E(x10291,x10292)+E(f188(x10291,x10293,x10294,x10295,x10296),f188(x10292,x10293,x10294,x10295,x10296)) % 169.39/169.67 [1030]~E(x10301,x10302)+E(f188(x10303,x10301,x10304,x10305,x10306),f188(x10303,x10302,x10304,x10305,x10306)) % 169.39/169.67 [1031]~E(x10311,x10312)+E(f188(x10313,x10314,x10311,x10315,x10316),f188(x10313,x10314,x10312,x10315,x10316)) % 169.39/169.67 [1032]~E(x10321,x10322)+E(f188(x10323,x10324,x10325,x10321,x10326),f188(x10323,x10324,x10325,x10322,x10326)) % 169.39/169.67 [1033]~E(x10331,x10332)+E(f188(x10333,x10334,x10335,x10336,x10331),f188(x10333,x10334,x10335,x10336,x10332)) % 169.39/169.67 [1034]~E(x10341,x10342)+E(f591(x10341,x10343,x10344,x10345,x10346),f591(x10342,x10343,x10344,x10345,x10346)) % 169.39/169.67 [1035]~E(x10351,x10352)+E(f591(x10353,x10351,x10354,x10355,x10356),f591(x10353,x10352,x10354,x10355,x10356)) % 169.39/169.67 [1036]~E(x10361,x10362)+E(f591(x10363,x10364,x10361,x10365,x10366),f591(x10363,x10364,x10362,x10365,x10366)) % 169.39/169.67 [1037]~E(x10371,x10372)+E(f591(x10373,x10374,x10375,x10371,x10376),f591(x10373,x10374,x10375,x10372,x10376)) % 169.39/169.67 [1038]~E(x10381,x10382)+E(f591(x10383,x10384,x10385,x10386,x10381),f591(x10383,x10384,x10385,x10386,x10382)) % 169.39/169.67 [1039]~E(x10391,x10392)+E(f307(x10391,x10393,x10394),f307(x10392,x10393,x10394)) % 169.39/169.67 [1040]~E(x10401,x10402)+E(f307(x10403,x10401,x10404),f307(x10403,x10402,x10404)) % 169.39/169.67 [1041]~E(x10411,x10412)+E(f307(x10413,x10414,x10411),f307(x10413,x10414,x10412)) % 169.39/169.67 [1042]~E(x10421,x10422)+E(f729(x10421,x10423,x10424,x10425,x10426),f729(x10422,x10423,x10424,x10425,x10426)) % 169.39/169.67 [1043]~E(x10431,x10432)+E(f729(x10433,x10431,x10434,x10435,x10436),f729(x10433,x10432,x10434,x10435,x10436)) % 169.39/169.67 [1044]~E(x10441,x10442)+E(f729(x10443,x10444,x10441,x10445,x10446),f729(x10443,x10444,x10442,x10445,x10446)) % 169.39/169.67 [1045]~E(x10451,x10452)+E(f729(x10453,x10454,x10455,x10451,x10456),f729(x10453,x10454,x10455,x10452,x10456)) % 169.39/169.67 [1046]~E(x10461,x10462)+E(f729(x10463,x10464,x10465,x10466,x10461),f729(x10463,x10464,x10465,x10466,x10462)) % 169.39/169.67 [1047]~E(x10471,x10472)+E(f301(x10471,x10473,x10474,x10475),f301(x10472,x10473,x10474,x10475)) % 169.39/169.67 [1048]~E(x10481,x10482)+E(f301(x10483,x10481,x10484,x10485),f301(x10483,x10482,x10484,x10485)) % 169.39/169.67 [1049]~E(x10491,x10492)+E(f301(x10493,x10494,x10491,x10495),f301(x10493,x10494,x10492,x10495)) % 169.39/169.67 [1050]~E(x10501,x10502)+E(f301(x10503,x10504,x10505,x10501),f301(x10503,x10504,x10505,x10502)) % 169.39/169.67 [1051]~E(x10511,x10512)+E(f401(x10511,x10513,x10514,x10515),f401(x10512,x10513,x10514,x10515)) % 169.39/169.67 [1052]~E(x10521,x10522)+E(f401(x10523,x10521,x10524,x10525),f401(x10523,x10522,x10524,x10525)) % 169.39/169.67 [1053]~E(x10531,x10532)+E(f401(x10533,x10534,x10531,x10535),f401(x10533,x10534,x10532,x10535)) % 169.39/169.67 [1054]~E(x10541,x10542)+E(f401(x10543,x10544,x10545,x10541),f401(x10543,x10544,x10545,x10542)) % 169.39/169.67 [1055]~E(x10551,x10552)+E(f120(x10551,x10553,x10554),f120(x10552,x10553,x10554)) % 169.39/169.67 [1056]~E(x10561,x10562)+E(f120(x10563,x10561,x10564),f120(x10563,x10562,x10564)) % 169.39/169.67 [1057]~E(x10571,x10572)+E(f120(x10573,x10574,x10571),f120(x10573,x10574,x10572)) % 169.39/169.67 [1058]~E(x10581,x10582)+E(f125(x10581,x10583),f125(x10582,x10583)) % 169.39/169.67 [1059]~E(x10591,x10592)+E(f125(x10593,x10591),f125(x10593,x10592)) % 169.39/169.67 [1060]~E(x10601,x10602)+E(f528(x10601,x10603,x10604,x10605,x10606),f528(x10602,x10603,x10604,x10605,x10606)) % 169.39/169.67 [1061]~E(x10611,x10612)+E(f528(x10613,x10611,x10614,x10615,x10616),f528(x10613,x10612,x10614,x10615,x10616)) % 169.39/169.67 [1062]~E(x10621,x10622)+E(f528(x10623,x10624,x10621,x10625,x10626),f528(x10623,x10624,x10622,x10625,x10626)) % 169.39/169.67 [1063]~E(x10631,x10632)+E(f528(x10633,x10634,x10635,x10631,x10636),f528(x10633,x10634,x10635,x10632,x10636)) % 169.39/169.67 [1064]~E(x10641,x10642)+E(f528(x10643,x10644,x10645,x10646,x10641),f528(x10643,x10644,x10645,x10646,x10642)) % 169.39/169.67 [1065]~E(x10651,x10652)+E(f525(x10651,x10653),f525(x10652,x10653)) % 169.39/169.67 [1066]~E(x10661,x10662)+E(f525(x10663,x10661),f525(x10663,x10662)) % 169.39/169.67 [1067]~E(x10671,x10672)+E(f851(x10671,x10673,x10674,x10675,x10676),f851(x10672,x10673,x10674,x10675,x10676)) % 169.39/169.67 [1068]~E(x10681,x10682)+E(f851(x10683,x10681,x10684,x10685,x10686),f851(x10683,x10682,x10684,x10685,x10686)) % 169.39/169.67 [1069]~E(x10691,x10692)+E(f851(x10693,x10694,x10691,x10695,x10696),f851(x10693,x10694,x10692,x10695,x10696)) % 169.39/169.67 [1070]~E(x10701,x10702)+E(f851(x10703,x10704,x10705,x10701,x10706),f851(x10703,x10704,x10705,x10702,x10706)) % 169.39/169.67 [1071]~E(x10711,x10712)+E(f851(x10713,x10714,x10715,x10716,x10711),f851(x10713,x10714,x10715,x10716,x10712)) % 169.39/169.67 [1072]~E(x10721,x10722)+E(f420(x10721,x10723,x10724,x10725,x10726),f420(x10722,x10723,x10724,x10725,x10726)) % 169.39/169.67 [1073]~E(x10731,x10732)+E(f420(x10733,x10731,x10734,x10735,x10736),f420(x10733,x10732,x10734,x10735,x10736)) % 169.39/169.67 [1074]~E(x10741,x10742)+E(f420(x10743,x10744,x10741,x10745,x10746),f420(x10743,x10744,x10742,x10745,x10746)) % 169.39/169.67 [1075]~E(x10751,x10752)+E(f420(x10753,x10754,x10755,x10751,x10756),f420(x10753,x10754,x10755,x10752,x10756)) % 169.39/169.67 [1076]~E(x10761,x10762)+E(f420(x10763,x10764,x10765,x10766,x10761),f420(x10763,x10764,x10765,x10766,x10762)) % 169.39/169.67 [1077]~E(x10771,x10772)+E(f394(x10771,x10773),f394(x10772,x10773)) % 169.39/169.67 [1078]~E(x10781,x10782)+E(f394(x10783,x10781),f394(x10783,x10782)) % 169.39/169.67 [1079]~E(x10791,x10792)+E(f823(x10791,x10793,x10794,x10795),f823(x10792,x10793,x10794,x10795)) % 169.39/169.67 [1080]~E(x10801,x10802)+E(f823(x10803,x10801,x10804,x10805),f823(x10803,x10802,x10804,x10805)) % 169.39/169.67 [1081]~E(x10811,x10812)+E(f823(x10813,x10814,x10811,x10815),f823(x10813,x10814,x10812,x10815)) % 169.39/169.67 [1082]~E(x10821,x10822)+E(f823(x10823,x10824,x10825,x10821),f823(x10823,x10824,x10825,x10822)) % 169.39/169.67 [1083]~E(x10831,x10832)+E(f342(x10831),f342(x10832)) % 169.39/169.67 [1084]~E(x10841,x10842)+E(f589(x10841,x10843,x10844,x10845,x10846),f589(x10842,x10843,x10844,x10845,x10846)) % 169.39/169.67 [1085]~E(x10851,x10852)+E(f589(x10853,x10851,x10854,x10855,x10856),f589(x10853,x10852,x10854,x10855,x10856)) % 169.39/169.67 [1086]~E(x10861,x10862)+E(f589(x10863,x10864,x10861,x10865,x10866),f589(x10863,x10864,x10862,x10865,x10866)) % 169.39/169.67 [1087]~E(x10871,x10872)+E(f589(x10873,x10874,x10875,x10871,x10876),f589(x10873,x10874,x10875,x10872,x10876)) % 169.39/169.67 [1088]~E(x10881,x10882)+E(f589(x10883,x10884,x10885,x10886,x10881),f589(x10883,x10884,x10885,x10886,x10882)) % 169.39/169.67 [1089]~E(x10891,x10892)+E(f791(x10891,x10893),f791(x10892,x10893)) % 169.39/169.67 [1090]~E(x10901,x10902)+E(f791(x10903,x10901),f791(x10903,x10902)) % 169.39/169.67 [1091]~E(x10911,x10912)+E(f466(x10911,x10913,x10914),f466(x10912,x10913,x10914)) % 169.39/169.67 [1092]~E(x10921,x10922)+E(f466(x10923,x10921,x10924),f466(x10923,x10922,x10924)) % 169.39/169.67 [1093]~E(x10931,x10932)+E(f466(x10933,x10934,x10931),f466(x10933,x10934,x10932)) % 169.39/169.67 [1094]~E(x10941,x10942)+E(f147(x10941,x10943),f147(x10942,x10943)) % 169.39/169.67 [1095]~E(x10951,x10952)+E(f147(x10953,x10951),f147(x10953,x10952)) % 169.39/169.67 [1096]~E(x10961,x10962)+E(f670(x10961,x10963,x10964,x10965,x10966),f670(x10962,x10963,x10964,x10965,x10966)) % 169.39/169.67 [1097]~E(x10971,x10972)+E(f670(x10973,x10971,x10974,x10975,x10976),f670(x10973,x10972,x10974,x10975,x10976)) % 169.39/169.67 [1098]~E(x10981,x10982)+E(f670(x10983,x10984,x10981,x10985,x10986),f670(x10983,x10984,x10982,x10985,x10986)) % 169.39/169.67 [1099]~E(x10991,x10992)+E(f670(x10993,x10994,x10995,x10991,x10996),f670(x10993,x10994,x10995,x10992,x10996)) % 169.39/169.67 [1100]~E(x11001,x11002)+E(f670(x11003,x11004,x11005,x11006,x11001),f670(x11003,x11004,x11005,x11006,x11002)) % 169.39/169.67 [1101]~E(x11011,x11012)+E(f473(x11011,x11013),f473(x11012,x11013)) % 169.39/169.67 [1102]~E(x11021,x11022)+E(f473(x11023,x11021),f473(x11023,x11022)) % 169.39/169.67 [1103]~E(x11031,x11032)+E(f450(x11031,x11033),f450(x11032,x11033)) % 169.39/169.67 [1104]~E(x11041,x11042)+E(f450(x11043,x11041),f450(x11043,x11042)) % 169.39/169.67 [1105]~E(x11051,x11052)+E(f546(x11051,x11053,x11054,x11055),f546(x11052,x11053,x11054,x11055)) % 169.39/169.67 [1106]~E(x11061,x11062)+E(f546(x11063,x11061,x11064,x11065),f546(x11063,x11062,x11064,x11065)) % 169.39/169.67 [1107]~E(x11071,x11072)+E(f546(x11073,x11074,x11071,x11075),f546(x11073,x11074,x11072,x11075)) % 169.39/169.67 [1108]~E(x11081,x11082)+E(f546(x11083,x11084,x11085,x11081),f546(x11083,x11084,x11085,x11082)) % 169.39/169.67 [1109]~E(x11091,x11092)+E(f737(x11091,x11093,x11094),f737(x11092,x11093,x11094)) % 169.39/169.67 [1110]~E(x11101,x11102)+E(f737(x11103,x11101,x11104),f737(x11103,x11102,x11104)) % 169.39/169.67 [1111]~E(x11111,x11112)+E(f737(x11113,x11114,x11111),f737(x11113,x11114,x11112)) % 169.39/169.67 [1112]~E(x11121,x11122)+E(f403(x11121,x11123,x11124,x11125,x11126,x11127,x11128,x11129),f403(x11122,x11123,x11124,x11125,x11126,x11127,x11128,x11129)) % 169.39/169.67 [1113]~E(x11131,x11132)+E(f403(x11133,x11131,x11134,x11135,x11136,x11137,x11138,x11139),f403(x11133,x11132,x11134,x11135,x11136,x11137,x11138,x11139)) % 169.39/169.67 [1114]~E(x11141,x11142)+E(f403(x11143,x11144,x11141,x11145,x11146,x11147,x11148,x11149),f403(x11143,x11144,x11142,x11145,x11146,x11147,x11148,x11149)) % 169.39/169.67 [1115]~E(x11151,x11152)+E(f403(x11153,x11154,x11155,x11151,x11156,x11157,x11158,x11159),f403(x11153,x11154,x11155,x11152,x11156,x11157,x11158,x11159)) % 169.39/169.67 [1116]~E(x11161,x11162)+E(f403(x11163,x11164,x11165,x11166,x11161,x11167,x11168,x11169),f403(x11163,x11164,x11165,x11166,x11162,x11167,x11168,x11169)) % 169.39/169.67 [1117]~E(x11171,x11172)+E(f403(x11173,x11174,x11175,x11176,x11177,x11171,x11178,x11179),f403(x11173,x11174,x11175,x11176,x11177,x11172,x11178,x11179)) % 169.39/169.67 [1118]~E(x11181,x11182)+E(f403(x11183,x11184,x11185,x11186,x11187,x11188,x11181,x11189),f403(x11183,x11184,x11185,x11186,x11187,x11188,x11182,x11189)) % 169.39/169.67 [1119]~E(x11191,x11192)+E(f403(x11193,x11194,x11195,x11196,x11197,x11198,x11199,x11191),f403(x11193,x11194,x11195,x11196,x11197,x11198,x11199,x11192)) % 169.39/169.67 [1120]~E(x11201,x11202)+E(f639(x11201,x11203,x11204),f639(x11202,x11203,x11204)) % 169.39/169.67 [1121]~E(x11211,x11212)+E(f639(x11213,x11211,x11214),f639(x11213,x11212,x11214)) % 169.39/169.67 [1122]~E(x11221,x11222)+E(f639(x11223,x11224,x11221),f639(x11223,x11224,x11222)) % 169.39/169.67 [1123]~E(x11231,x11232)+E(f449(x11231,x11233,x11234,x11235,x11236,x11237),f449(x11232,x11233,x11234,x11235,x11236,x11237)) % 169.39/169.67 [1124]~E(x11241,x11242)+E(f449(x11243,x11241,x11244,x11245,x11246,x11247),f449(x11243,x11242,x11244,x11245,x11246,x11247)) % 169.39/169.67 [1125]~E(x11251,x11252)+E(f449(x11253,x11254,x11251,x11255,x11256,x11257),f449(x11253,x11254,x11252,x11255,x11256,x11257)) % 169.39/169.67 [1126]~E(x11261,x11262)+E(f449(x11263,x11264,x11265,x11261,x11266,x11267),f449(x11263,x11264,x11265,x11262,x11266,x11267)) % 169.39/169.67 [1127]~E(x11271,x11272)+E(f449(x11273,x11274,x11275,x11276,x11271,x11277),f449(x11273,x11274,x11275,x11276,x11272,x11277)) % 169.39/169.67 [1128]~E(x11281,x11282)+E(f449(x11283,x11284,x11285,x11286,x11287,x11281),f449(x11283,x11284,x11285,x11286,x11287,x11282)) % 169.39/169.67 [1129]~E(x11291,x11292)+E(f782(x11291,x11293,x11294),f782(x11292,x11293,x11294)) % 169.39/169.67 [1130]~E(x11301,x11302)+E(f782(x11303,x11301,x11304),f782(x11303,x11302,x11304)) % 169.39/169.67 [1131]~E(x11311,x11312)+E(f782(x11313,x11314,x11311),f782(x11313,x11314,x11312)) % 169.39/169.67 [1132]~E(x11321,x11322)+E(f303(x11321),f303(x11322)) % 169.39/169.67 [1133]~E(x11331,x11332)+E(f283(x11331,x11333,x11334,x11335),f283(x11332,x11333,x11334,x11335)) % 169.39/169.67 [1134]~E(x11341,x11342)+E(f283(x11343,x11341,x11344,x11345),f283(x11343,x11342,x11344,x11345)) % 169.39/169.67 [1135]~E(x11351,x11352)+E(f283(x11353,x11354,x11351,x11355),f283(x11353,x11354,x11352,x11355)) % 169.39/169.67 [1136]~E(x11361,x11362)+E(f283(x11363,x11364,x11365,x11361),f283(x11363,x11364,x11365,x11362)) % 169.39/169.67 [1137]~E(x11371,x11372)+E(f558(x11371,x11373,x11374,x11375,x11376),f558(x11372,x11373,x11374,x11375,x11376)) % 169.39/169.67 [1138]~E(x11381,x11382)+E(f558(x11383,x11381,x11384,x11385,x11386),f558(x11383,x11382,x11384,x11385,x11386)) % 169.39/169.67 [1139]~E(x11391,x11392)+E(f558(x11393,x11394,x11391,x11395,x11396),f558(x11393,x11394,x11392,x11395,x11396)) % 169.39/169.67 [1140]~E(x11401,x11402)+E(f558(x11403,x11404,x11405,x11401,x11406),f558(x11403,x11404,x11405,x11402,x11406)) % 169.39/169.67 [1141]~E(x11411,x11412)+E(f558(x11413,x11414,x11415,x11416,x11411),f558(x11413,x11414,x11415,x11416,x11412)) % 169.39/169.67 [1142]~E(x11421,x11422)+E(f472(x11421,x11423),f472(x11422,x11423)) % 169.39/169.67 [1143]~E(x11431,x11432)+E(f472(x11433,x11431),f472(x11433,x11432)) % 169.39/169.67 [1144]~E(x11441,x11442)+E(f732(x11441),f732(x11442)) % 169.39/169.67 [1145]~E(x11451,x11452)+E(f129(x11451,x11453),f129(x11452,x11453)) % 169.39/169.67 [1146]~E(x11461,x11462)+E(f129(x11463,x11461),f129(x11463,x11462)) % 169.39/169.67 [1147]~E(x11471,x11472)+E(f509(x11471,x11473,x11474),f509(x11472,x11473,x11474)) % 169.39/169.67 [1148]~E(x11481,x11482)+E(f509(x11483,x11481,x11484),f509(x11483,x11482,x11484)) % 169.39/169.67 [1149]~E(x11491,x11492)+E(f509(x11493,x11494,x11491),f509(x11493,x11494,x11492)) % 169.39/169.67 [1150]~E(x11501,x11502)+E(f499(x11501,x11503,x11504,x11505),f499(x11502,x11503,x11504,x11505)) % 169.39/169.67 [1151]~E(x11511,x11512)+E(f499(x11513,x11511,x11514,x11515),f499(x11513,x11512,x11514,x11515)) % 169.39/169.67 [1152]~E(x11521,x11522)+E(f499(x11523,x11524,x11521,x11525),f499(x11523,x11524,x11522,x11525)) % 169.39/169.67 [1153]~E(x11531,x11532)+E(f499(x11533,x11534,x11535,x11531),f499(x11533,x11534,x11535,x11532)) % 169.39/169.67 [1154]~E(x11541,x11542)+E(f270(x11541,x11543,x11544,x11545,x11546),f270(x11542,x11543,x11544,x11545,x11546)) % 169.39/169.67 [1155]~E(x11551,x11552)+E(f270(x11553,x11551,x11554,x11555,x11556),f270(x11553,x11552,x11554,x11555,x11556)) % 169.39/169.67 [1156]~E(x11561,x11562)+E(f270(x11563,x11564,x11561,x11565,x11566),f270(x11563,x11564,x11562,x11565,x11566)) % 169.39/169.67 [1157]~E(x11571,x11572)+E(f270(x11573,x11574,x11575,x11571,x11576),f270(x11573,x11574,x11575,x11572,x11576)) % 169.39/169.67 [1158]~E(x11581,x11582)+E(f270(x11583,x11584,x11585,x11586,x11581),f270(x11583,x11584,x11585,x11586,x11582)) % 169.39/169.67 [1159]~E(x11591,x11592)+E(f491(x11591,x11593,x11594),f491(x11592,x11593,x11594)) % 169.39/169.67 [1160]~E(x11601,x11602)+E(f491(x11603,x11601,x11604),f491(x11603,x11602,x11604)) % 169.39/169.67 [1161]~E(x11611,x11612)+E(f491(x11613,x11614,x11611),f491(x11613,x11614,x11612)) % 169.39/169.67 [1162]~E(x11621,x11622)+E(f463(x11621,x11623,x11624),f463(x11622,x11623,x11624)) % 169.39/169.67 [1163]~E(x11631,x11632)+E(f463(x11633,x11631,x11634),f463(x11633,x11632,x11634)) % 169.39/169.67 [1164]~E(x11641,x11642)+E(f463(x11643,x11644,x11641),f463(x11643,x11644,x11642)) % 169.39/169.67 [1165]~E(x11651,x11652)+E(f140(x11651,x11653,x11654),f140(x11652,x11653,x11654)) % 169.39/169.67 [1166]~E(x11661,x11662)+E(f140(x11663,x11661,x11664),f140(x11663,x11662,x11664)) % 169.39/169.67 [1167]~E(x11671,x11672)+E(f140(x11673,x11674,x11671),f140(x11673,x11674,x11672)) % 169.39/169.67 [1168]~E(x11681,x11682)+E(f677(x11681,x11683),f677(x11682,x11683)) % 169.39/169.67 [1169]~E(x11691,x11692)+E(f677(x11693,x11691),f677(x11693,x11692)) % 169.39/169.67 [1170]~E(x11701,x11702)+E(f427(x11701,x11703,x11704),f427(x11702,x11703,x11704)) % 169.39/169.67 [1171]~E(x11711,x11712)+E(f427(x11713,x11711,x11714),f427(x11713,x11712,x11714)) % 169.39/169.67 [1172]~E(x11721,x11722)+E(f427(x11723,x11724,x11721),f427(x11723,x11724,x11722)) % 169.39/169.67 [1173]~E(x11731,x11732)+E(f594(x11731,x11733,x11734,x11735),f594(x11732,x11733,x11734,x11735)) % 169.39/169.67 [1174]~E(x11741,x11742)+E(f594(x11743,x11741,x11744,x11745),f594(x11743,x11742,x11744,x11745)) % 169.39/169.67 [1175]~E(x11751,x11752)+E(f594(x11753,x11754,x11751,x11755),f594(x11753,x11754,x11752,x11755)) % 169.39/169.67 [1176]~E(x11761,x11762)+E(f594(x11763,x11764,x11765,x11761),f594(x11763,x11764,x11765,x11762)) % 169.39/169.67 [1177]~E(x11771,x11772)+E(f341(x11771),f341(x11772)) % 169.39/169.67 [1178]~E(x11781,x11782)+E(f756(x11781,x11783,x11784),f756(x11782,x11783,x11784)) % 169.39/169.67 [1179]~E(x11791,x11792)+E(f756(x11793,x11791,x11794),f756(x11793,x11792,x11794)) % 169.39/169.67 [1180]~E(x11801,x11802)+E(f756(x11803,x11804,x11801),f756(x11803,x11804,x11802)) % 169.39/169.67 [1181]~E(x11811,x11812)+E(f243(x11811,x11813,x11814,x11815),f243(x11812,x11813,x11814,x11815)) % 169.39/169.67 [1182]~E(x11821,x11822)+E(f243(x11823,x11821,x11824,x11825),f243(x11823,x11822,x11824,x11825)) % 169.39/169.67 [1183]~E(x11831,x11832)+E(f243(x11833,x11834,x11831,x11835),f243(x11833,x11834,x11832,x11835)) % 169.39/169.67 [1184]~E(x11841,x11842)+E(f243(x11843,x11844,x11845,x11841),f243(x11843,x11844,x11845,x11842)) % 169.39/169.67 [1185]~E(x11851,x11852)+E(f260(x11851,x11853,x11854),f260(x11852,x11853,x11854)) % 169.39/169.67 [1186]~E(x11861,x11862)+E(f260(x11863,x11861,x11864),f260(x11863,x11862,x11864)) % 169.39/169.67 [1187]~E(x11871,x11872)+E(f260(x11873,x11874,x11871),f260(x11873,x11874,x11872)) % 169.39/169.67 [1188]~E(x11881,x11882)+E(f490(x11881,x11883,x11884),f490(x11882,x11883,x11884)) % 169.39/169.67 [1189]~E(x11891,x11892)+E(f490(x11893,x11891,x11894),f490(x11893,x11892,x11894)) % 169.39/169.67 [1190]~E(x11901,x11902)+E(f490(x11903,x11904,x11901),f490(x11903,x11904,x11902)) % 169.39/169.67 [1191]~E(x11911,x11912)+E(f350(x11911,x11913,x11914),f350(x11912,x11913,x11914)) % 169.39/169.67 [1192]~E(x11921,x11922)+E(f350(x11923,x11921,x11924),f350(x11923,x11922,x11924)) % 169.39/169.67 [1193]~E(x11931,x11932)+E(f350(x11933,x11934,x11931),f350(x11933,x11934,x11932)) % 169.39/169.67 [1194]~E(x11941,x11942)+E(f655(x11941,x11943,x11944),f655(x11942,x11943,x11944)) % 169.39/169.67 [1195]~E(x11951,x11952)+E(f655(x11953,x11951,x11954),f655(x11953,x11952,x11954)) % 169.39/169.67 [1196]~E(x11961,x11962)+E(f655(x11963,x11964,x11961),f655(x11963,x11964,x11962)) % 169.39/169.67 [1197]~E(x11971,x11972)+E(f439(x11971,x11973),f439(x11972,x11973)) % 169.39/169.67 [1198]~E(x11981,x11982)+E(f439(x11983,x11981),f439(x11983,x11982)) % 169.39/169.67 [1199]~E(x11991,x11992)+E(f775(x11991,x11993,x11994,x11995,x11996),f775(x11992,x11993,x11994,x11995,x11996)) % 169.39/169.67 [1200]~E(x12001,x12002)+E(f775(x12003,x12001,x12004,x12005,x12006),f775(x12003,x12002,x12004,x12005,x12006)) % 169.39/169.67 [1201]~E(x12011,x12012)+E(f775(x12013,x12014,x12011,x12015,x12016),f775(x12013,x12014,x12012,x12015,x12016)) % 169.39/169.67 [1202]~E(x12021,x12022)+E(f775(x12023,x12024,x12025,x12021,x12026),f775(x12023,x12024,x12025,x12022,x12026)) % 169.39/169.67 [1203]~E(x12031,x12032)+E(f775(x12033,x12034,x12035,x12036,x12031),f775(x12033,x12034,x12035,x12036,x12032)) % 169.39/169.67 [1204]~E(x12041,x12042)+E(f826(x12041),f826(x12042)) % 169.39/169.67 [1205]~E(x12051,x12052)+E(f474(x12051,x12053,x12054),f474(x12052,x12053,x12054)) % 169.39/169.67 [1206]~E(x12061,x12062)+E(f474(x12063,x12061,x12064),f474(x12063,x12062,x12064)) % 169.39/169.67 [1207]~E(x12071,x12072)+E(f474(x12073,x12074,x12071),f474(x12073,x12074,x12072)) % 169.39/169.67 [1208]~E(x12081,x12082)+E(f710(x12081,x12083,x12084,x12085),f710(x12082,x12083,x12084,x12085)) % 169.39/169.67 [1209]~E(x12091,x12092)+E(f710(x12093,x12091,x12094,x12095),f710(x12093,x12092,x12094,x12095)) % 169.39/169.67 [1210]~E(x12101,x12102)+E(f710(x12103,x12104,x12101,x12105),f710(x12103,x12104,x12102,x12105)) % 169.39/169.67 [1211]~E(x12111,x12112)+E(f710(x12113,x12114,x12115,x12111),f710(x12113,x12114,x12115,x12112)) % 169.39/169.67 [1212]~E(x12121,x12122)+E(f596(x12121,x12123,x12124),f596(x12122,x12123,x12124)) % 169.39/169.67 [1213]~E(x12131,x12132)+E(f596(x12133,x12131,x12134),f596(x12133,x12132,x12134)) % 169.39/169.67 [1214]~E(x12141,x12142)+E(f596(x12143,x12144,x12141),f596(x12143,x12144,x12142)) % 169.39/169.67 [1215]~E(x12151,x12152)+E(f753(x12151,x12153),f753(x12152,x12153)) % 169.39/169.67 [1216]~E(x12161,x12162)+E(f753(x12163,x12161),f753(x12163,x12162)) % 169.39/169.67 [1217]~E(x12171,x12172)+E(f382(x12171,x12173,x12174,x12175),f382(x12172,x12173,x12174,x12175)) % 169.39/169.67 [1218]~E(x12181,x12182)+E(f382(x12183,x12181,x12184,x12185),f382(x12183,x12182,x12184,x12185)) % 169.39/169.67 [1219]~E(x12191,x12192)+E(f382(x12193,x12194,x12191,x12195),f382(x12193,x12194,x12192,x12195)) % 169.39/169.67 [1220]~E(x12201,x12202)+E(f382(x12203,x12204,x12205,x12201),f382(x12203,x12204,x12205,x12202)) % 169.39/169.67 [1221]~E(x12211,x12212)+E(f61(x12211,x12213,x12214,x12215),f61(x12212,x12213,x12214,x12215)) % 169.39/169.67 [1222]~E(x12221,x12222)+E(f61(x12223,x12221,x12224,x12225),f61(x12223,x12222,x12224,x12225)) % 169.39/169.67 [1223]~E(x12231,x12232)+E(f61(x12233,x12234,x12231,x12235),f61(x12233,x12234,x12232,x12235)) % 169.39/169.67 [1224]~E(x12241,x12242)+E(f61(x12243,x12244,x12245,x12241),f61(x12243,x12244,x12245,x12242)) % 169.39/169.67 [1225]~E(x12251,x12252)+E(f820(x12251,x12253,x12254),f820(x12252,x12253,x12254)) % 169.39/169.67 [1226]~E(x12261,x12262)+E(f820(x12263,x12261,x12264),f820(x12263,x12262,x12264)) % 169.39/169.67 [1227]~E(x12271,x12272)+E(f820(x12273,x12274,x12271),f820(x12273,x12274,x12272)) % 169.39/169.67 [1228]~E(x12281,x12282)+E(f423(x12281,x12283,x12284),f423(x12282,x12283,x12284)) % 169.39/169.67 [1229]~E(x12291,x12292)+E(f423(x12293,x12291,x12294),f423(x12293,x12292,x12294)) % 169.39/169.67 [1230]~E(x12301,x12302)+E(f423(x12303,x12304,x12301),f423(x12303,x12304,x12302)) % 169.39/169.67 [1231]~E(x12311,x12312)+E(f565(x12311,x12313,x12314,x12315,x12316),f565(x12312,x12313,x12314,x12315,x12316)) % 169.39/169.67 [1232]~E(x12321,x12322)+E(f565(x12323,x12321,x12324,x12325,x12326),f565(x12323,x12322,x12324,x12325,x12326)) % 169.39/169.67 [1233]~E(x12331,x12332)+E(f565(x12333,x12334,x12331,x12335,x12336),f565(x12333,x12334,x12332,x12335,x12336)) % 169.39/169.67 [1234]~E(x12341,x12342)+E(f565(x12343,x12344,x12345,x12341,x12346),f565(x12343,x12344,x12345,x12342,x12346)) % 169.39/169.67 [1235]~E(x12351,x12352)+E(f565(x12353,x12354,x12355,x12356,x12351),f565(x12353,x12354,x12355,x12356,x12352)) % 169.39/169.67 [1236]~E(x12361,x12362)+E(f800(x12361,x12363,x12364),f800(x12362,x12363,x12364)) % 169.39/169.67 [1237]~E(x12371,x12372)+E(f800(x12373,x12371,x12374),f800(x12373,x12372,x12374)) % 169.39/169.67 [1238]~E(x12381,x12382)+E(f800(x12383,x12384,x12381),f800(x12383,x12384,x12382)) % 169.39/169.67 [1239]~E(x12391,x12392)+E(f454(x12391,x12393,x12394),f454(x12392,x12393,x12394)) % 169.39/169.67 [1240]~E(x12401,x12402)+E(f454(x12403,x12401,x12404),f454(x12403,x12402,x12404)) % 169.39/169.67 [1241]~E(x12411,x12412)+E(f454(x12413,x12414,x12411),f454(x12413,x12414,x12412)) % 169.39/169.67 [1242]~E(x12421,x12422)+E(f208(x12421,x12423),f208(x12422,x12423)) % 169.39/169.67 [1243]~E(x12431,x12432)+E(f208(x12433,x12431),f208(x12433,x12432)) % 169.39/169.67 [1244]~E(x12441,x12442)+E(f497(x12441,x12443,x12444,x12445),f497(x12442,x12443,x12444,x12445)) % 169.39/169.67 [1245]~E(x12451,x12452)+E(f497(x12453,x12451,x12454,x12455),f497(x12453,x12452,x12454,x12455)) % 169.39/169.67 [1246]~E(x12461,x12462)+E(f497(x12463,x12464,x12461,x12465),f497(x12463,x12464,x12462,x12465)) % 169.39/169.67 [1247]~E(x12471,x12472)+E(f497(x12473,x12474,x12475,x12471),f497(x12473,x12474,x12475,x12472)) % 169.39/169.67 [1248]~E(x12481,x12482)+E(f126(x12481),f126(x12482)) % 169.39/169.67 [1249]~E(x12491,x12492)+E(f695(x12491,x12493,x12494,x12495,x12496),f695(x12492,x12493,x12494,x12495,x12496)) % 169.39/169.67 [1250]~E(x12501,x12502)+E(f695(x12503,x12501,x12504,x12505,x12506),f695(x12503,x12502,x12504,x12505,x12506)) % 169.39/169.67 [1251]~E(x12511,x12512)+E(f695(x12513,x12514,x12511,x12515,x12516),f695(x12513,x12514,x12512,x12515,x12516)) % 169.39/169.67 [1252]~E(x12521,x12522)+E(f695(x12523,x12524,x12525,x12521,x12526),f695(x12523,x12524,x12525,x12522,x12526)) % 169.39/169.67 [1253]~E(x12531,x12532)+E(f695(x12533,x12534,x12535,x12536,x12531),f695(x12533,x12534,x12535,x12536,x12532)) % 169.39/169.67 [1254]~E(x12541,x12542)+E(f174(x12541,x12543,x12544),f174(x12542,x12543,x12544)) % 169.39/169.67 [1255]~E(x12551,x12552)+E(f174(x12553,x12551,x12554),f174(x12553,x12552,x12554)) % 169.39/169.67 [1256]~E(x12561,x12562)+E(f174(x12563,x12564,x12561),f174(x12563,x12564,x12562)) % 169.39/169.67 [1257]~E(x12571,x12572)+E(f378(x12571,x12573,x12574),f378(x12572,x12573,x12574)) % 169.39/169.67 [1258]~E(x12581,x12582)+E(f378(x12583,x12581,x12584),f378(x12583,x12582,x12584)) % 169.39/169.67 [1259]~E(x12591,x12592)+E(f378(x12593,x12594,x12591),f378(x12593,x12594,x12592)) % 169.39/169.67 [1260]~E(x12601,x12602)+E(f239(x12601,x12603,x12604,x12605),f239(x12602,x12603,x12604,x12605)) % 169.39/169.67 [1261]~E(x12611,x12612)+E(f239(x12613,x12611,x12614,x12615),f239(x12613,x12612,x12614,x12615)) % 169.39/169.67 [1262]~E(x12621,x12622)+E(f239(x12623,x12624,x12621,x12625),f239(x12623,x12624,x12622,x12625)) % 169.39/169.67 [1263]~E(x12631,x12632)+E(f239(x12633,x12634,x12635,x12631),f239(x12633,x12634,x12635,x12632)) % 169.39/169.67 [1264]~E(x12641,x12642)+E(f379(x12641,x12643,x12644,x12645),f379(x12642,x12643,x12644,x12645)) % 169.39/169.67 [1265]~E(x12651,x12652)+E(f379(x12653,x12651,x12654,x12655),f379(x12653,x12652,x12654,x12655)) % 169.39/169.67 [1266]~E(x12661,x12662)+E(f379(x12663,x12664,x12661,x12665),f379(x12663,x12664,x12662,x12665)) % 169.39/169.67 [1267]~E(x12671,x12672)+E(f379(x12673,x12674,x12675,x12671),f379(x12673,x12674,x12675,x12672)) % 169.39/169.67 [1268]~E(x12681,x12682)+E(f802(x12681,x12683),f802(x12682,x12683)) % 169.39/169.67 [1269]~E(x12691,x12692)+E(f802(x12693,x12691),f802(x12693,x12692)) % 169.39/169.67 [1270]~E(x12701,x12702)+E(f841(x12701,x12703,x12704,x12705),f841(x12702,x12703,x12704,x12705)) % 169.39/169.67 [1271]~E(x12711,x12712)+E(f841(x12713,x12711,x12714,x12715),f841(x12713,x12712,x12714,x12715)) % 169.39/169.67 [1272]~E(x12721,x12722)+E(f841(x12723,x12724,x12721,x12725),f841(x12723,x12724,x12722,x12725)) % 169.39/169.67 [1273]~E(x12731,x12732)+E(f841(x12733,x12734,x12735,x12731),f841(x12733,x12734,x12735,x12732)) % 169.39/169.67 [1274]~E(x12741,x12742)+E(f478(x12741,x12743,x12744),f478(x12742,x12743,x12744)) % 169.39/169.67 [1275]~E(x12751,x12752)+E(f478(x12753,x12751,x12754),f478(x12753,x12752,x12754)) % 169.39/169.67 [1276]~E(x12761,x12762)+E(f478(x12763,x12764,x12761),f478(x12763,x12764,x12762)) % 169.39/169.67 [1277]~E(x12771,x12772)+E(f794(x12771,x12773,x12774),f794(x12772,x12773,x12774)) % 169.39/169.67 [1278]~E(x12781,x12782)+E(f794(x12783,x12781,x12784),f794(x12783,x12782,x12784)) % 169.39/169.67 [1279]~E(x12791,x12792)+E(f794(x12793,x12794,x12791),f794(x12793,x12794,x12792)) % 169.39/169.67 [1280]~E(x12801,x12802)+E(f484(x12801,x12803,x12804),f484(x12802,x12803,x12804)) % 169.39/169.67 [1281]~E(x12811,x12812)+E(f484(x12813,x12811,x12814),f484(x12813,x12812,x12814)) % 169.39/169.67 [1282]~E(x12821,x12822)+E(f484(x12823,x12824,x12821),f484(x12823,x12824,x12822)) % 169.39/169.67 [1283]~E(x12831,x12832)+E(f445(x12831,x12833,x12834,x12835,x12836),f445(x12832,x12833,x12834,x12835,x12836)) % 169.39/169.67 [1284]~E(x12841,x12842)+E(f445(x12843,x12841,x12844,x12845,x12846),f445(x12843,x12842,x12844,x12845,x12846)) % 169.39/169.67 [1285]~E(x12851,x12852)+E(f445(x12853,x12854,x12851,x12855,x12856),f445(x12853,x12854,x12852,x12855,x12856)) % 169.39/169.67 [1286]~E(x12861,x12862)+E(f445(x12863,x12864,x12865,x12861,x12866),f445(x12863,x12864,x12865,x12862,x12866)) % 169.39/169.67 [1287]~E(x12871,x12872)+E(f445(x12873,x12874,x12875,x12876,x12871),f445(x12873,x12874,x12875,x12876,x12872)) % 169.39/169.67 [1288]~E(x12881,x12882)+E(f748(x12881,x12883,x12884,x12885),f748(x12882,x12883,x12884,x12885)) % 169.39/169.67 [1289]~E(x12891,x12892)+E(f748(x12893,x12891,x12894,x12895),f748(x12893,x12892,x12894,x12895)) % 169.39/169.67 [1290]~E(x12901,x12902)+E(f748(x12903,x12904,x12901,x12905),f748(x12903,x12904,x12902,x12905)) % 169.39/169.67 [1291]~E(x12911,x12912)+E(f748(x12913,x12914,x12915,x12911),f748(x12913,x12914,x12915,x12912)) % 169.39/169.67 [1292]~E(x12921,x12922)+E(f300(x12921,x12923,x12924),f300(x12922,x12923,x12924)) % 169.39/169.67 [1293]~E(x12931,x12932)+E(f300(x12933,x12931,x12934),f300(x12933,x12932,x12934)) % 169.39/169.67 [1294]~E(x12941,x12942)+E(f300(x12943,x12944,x12941),f300(x12943,x12944,x12942)) % 169.39/169.67 [1295]~E(x12951,x12952)+E(f719(x12951,x12953,x12954),f719(x12952,x12953,x12954)) % 169.39/169.67 [1296]~E(x12961,x12962)+E(f719(x12963,x12961,x12964),f719(x12963,x12962,x12964)) % 169.39/169.67 [1297]~E(x12971,x12972)+E(f719(x12973,x12974,x12971),f719(x12973,x12974,x12972)) % 169.39/169.67 [1298]~E(x12981,x12982)+E(f790(x12981,x12983,x12984,x12985),f790(x12982,x12983,x12984,x12985)) % 169.39/169.67 [1299]~E(x12991,x12992)+E(f790(x12993,x12991,x12994,x12995),f790(x12993,x12992,x12994,x12995)) % 169.39/169.67 [1300]~E(x13001,x13002)+E(f790(x13003,x13004,x13001,x13005),f790(x13003,x13004,x13002,x13005)) % 169.39/169.67 [1301]~E(x13011,x13012)+E(f790(x13013,x13014,x13015,x13011),f790(x13013,x13014,x13015,x13012)) % 169.39/169.67 [1302]~E(x13021,x13022)+E(f455(x13021,x13023,x13024),f455(x13022,x13023,x13024)) % 169.39/169.67 [1303]~E(x13031,x13032)+E(f455(x13033,x13031,x13034),f455(x13033,x13032,x13034)) % 169.39/169.67 [1304]~E(x13041,x13042)+E(f455(x13043,x13044,x13041),f455(x13043,x13044,x13042)) % 169.39/169.67 [1305]~E(x13051,x13052)+E(f643(x13051,x13053),f643(x13052,x13053)) % 169.39/169.67 [1306]~E(x13061,x13062)+E(f643(x13063,x13061),f643(x13063,x13062)) % 169.39/169.67 [1307]~E(x13071,x13072)+E(f203(x13071,x13073,x13074,x13075),f203(x13072,x13073,x13074,x13075)) % 169.39/169.67 [1308]~E(x13081,x13082)+E(f203(x13083,x13081,x13084,x13085),f203(x13083,x13082,x13084,x13085)) % 169.39/169.67 [1309]~E(x13091,x13092)+E(f203(x13093,x13094,x13091,x13095),f203(x13093,x13094,x13092,x13095)) % 169.39/169.67 [1310]~E(x13101,x13102)+E(f203(x13103,x13104,x13105,x13101),f203(x13103,x13104,x13105,x13102)) % 169.39/169.67 [1311]~E(x13111,x13112)+E(f502(x13111,x13113,x13114,x13115),f502(x13112,x13113,x13114,x13115)) % 169.39/169.67 [1312]~E(x13121,x13122)+E(f502(x13123,x13121,x13124,x13125),f502(x13123,x13122,x13124,x13125)) % 169.39/169.67 [1313]~E(x13131,x13132)+E(f502(x13133,x13134,x13131,x13135),f502(x13133,x13134,x13132,x13135)) % 169.39/169.67 [1314]~E(x13141,x13142)+E(f502(x13143,x13144,x13145,x13141),f502(x13143,x13144,x13145,x13142)) % 169.39/169.67 [1315]~E(x13151,x13152)+E(f788(x13151,x13153,x13154),f788(x13152,x13153,x13154)) % 169.39/169.67 [1316]~E(x13161,x13162)+E(f788(x13163,x13161,x13164),f788(x13163,x13162,x13164)) % 169.39/169.67 [1317]~E(x13171,x13172)+E(f788(x13173,x13174,x13171),f788(x13173,x13174,x13172)) % 169.39/169.67 [1318]~E(x13181,x13182)+E(f711(x13181,x13183,x13184,x13185),f711(x13182,x13183,x13184,x13185)) % 169.39/169.67 [1319]~E(x13191,x13192)+E(f711(x13193,x13191,x13194,x13195),f711(x13193,x13192,x13194,x13195)) % 169.39/169.67 [1320]~E(x13201,x13202)+E(f711(x13203,x13204,x13201,x13205),f711(x13203,x13204,x13202,x13205)) % 169.39/169.67 [1321]~E(x13211,x13212)+E(f711(x13213,x13214,x13215,x13211),f711(x13213,x13214,x13215,x13212)) % 169.39/169.67 [1322]~E(x13221,x13222)+E(f296(x13221,x13223,x13224),f296(x13222,x13223,x13224)) % 169.39/169.67 [1323]~E(x13231,x13232)+E(f296(x13233,x13231,x13234),f296(x13233,x13232,x13234)) % 169.39/169.67 [1324]~E(x13241,x13242)+E(f296(x13243,x13244,x13241),f296(x13243,x13244,x13242)) % 169.39/169.67 [1325]~E(x13251,x13252)+E(f852(x13251,x13253,x13254,x13255,x13256),f852(x13252,x13253,x13254,x13255,x13256)) % 169.39/169.67 [1326]~E(x13261,x13262)+E(f852(x13263,x13261,x13264,x13265,x13266),f852(x13263,x13262,x13264,x13265,x13266)) % 169.39/169.67 [1327]~E(x13271,x13272)+E(f852(x13273,x13274,x13271,x13275,x13276),f852(x13273,x13274,x13272,x13275,x13276)) % 169.39/169.67 [1328]~E(x13281,x13282)+E(f852(x13283,x13284,x13285,x13281,x13286),f852(x13283,x13284,x13285,x13282,x13286)) % 169.39/169.67 [1329]~E(x13291,x13292)+E(f852(x13293,x13294,x13295,x13296,x13291),f852(x13293,x13294,x13295,x13296,x13292)) % 169.39/169.67 [1330]~E(x13301,x13302)+E(f568(x13301,x13303,x13304,x13305),f568(x13302,x13303,x13304,x13305)) % 169.39/169.67 [1331]~E(x13311,x13312)+E(f568(x13313,x13311,x13314,x13315),f568(x13313,x13312,x13314,x13315)) % 169.39/169.67 [1332]~E(x13321,x13322)+E(f568(x13323,x13324,x13321,x13325),f568(x13323,x13324,x13322,x13325)) % 169.39/169.67 [1333]~E(x13331,x13332)+E(f568(x13333,x13334,x13335,x13331),f568(x13333,x13334,x13335,x13332)) % 169.39/169.67 [1334]~E(x13341,x13342)+E(f415(x13341,x13343,x13344),f415(x13342,x13343,x13344)) % 169.39/169.67 [1335]~E(x13351,x13352)+E(f415(x13353,x13351,x13354),f415(x13353,x13352,x13354)) % 169.39/169.67 [1336]~E(x13361,x13362)+E(f415(x13363,x13364,x13361),f415(x13363,x13364,x13362)) % 169.39/169.67 [1337]~E(x13371,x13372)+E(f435(x13371,x13373,x13374,x13375,x13376),f435(x13372,x13373,x13374,x13375,x13376)) % 169.39/169.67 [1338]~E(x13381,x13382)+E(f435(x13383,x13381,x13384,x13385,x13386),f435(x13383,x13382,x13384,x13385,x13386)) % 169.39/169.67 [1339]~E(x13391,x13392)+E(f435(x13393,x13394,x13391,x13395,x13396),f435(x13393,x13394,x13392,x13395,x13396)) % 169.39/169.67 [1340]~E(x13401,x13402)+E(f435(x13403,x13404,x13405,x13401,x13406),f435(x13403,x13404,x13405,x13402,x13406)) % 169.39/169.67 [1341]~E(x13411,x13412)+E(f435(x13413,x13414,x13415,x13416,x13411),f435(x13413,x13414,x13415,x13416,x13412)) % 169.39/169.67 [1342]~E(x13421,x13422)+E(f390(x13421,x13423,x13424,x13425),f390(x13422,x13423,x13424,x13425)) % 169.39/169.67 [1343]~E(x13431,x13432)+E(f390(x13433,x13431,x13434,x13435),f390(x13433,x13432,x13434,x13435)) % 169.39/169.67 [1344]~E(x13441,x13442)+E(f390(x13443,x13444,x13441,x13445),f390(x13443,x13444,x13442,x13445)) % 169.39/169.67 [1345]~E(x13451,x13452)+E(f390(x13453,x13454,x13455,x13451),f390(x13453,x13454,x13455,x13452)) % 169.39/169.67 [1346]~E(x13461,x13462)+E(f242(x13461,x13463,x13464),f242(x13462,x13463,x13464)) % 169.39/169.67 [1347]~E(x13471,x13472)+E(f242(x13473,x13471,x13474),f242(x13473,x13472,x13474)) % 169.39/169.67 [1348]~E(x13481,x13482)+E(f242(x13483,x13484,x13481),f242(x13483,x13484,x13482)) % 169.39/169.67 [1349]~E(x13491,x13492)+E(f631(x13491,x13493,x13494,x13495),f631(x13492,x13493,x13494,x13495)) % 169.39/169.67 [1350]~E(x13501,x13502)+E(f631(x13503,x13501,x13504,x13505),f631(x13503,x13502,x13504,x13505)) % 169.39/169.67 [1351]~E(x13511,x13512)+E(f631(x13513,x13514,x13511,x13515),f631(x13513,x13514,x13512,x13515)) % 169.39/169.67 [1352]~E(x13521,x13522)+E(f631(x13523,x13524,x13525,x13521),f631(x13523,x13524,x13525,x13522)) % 169.39/169.67 [1353]~E(x13531,x13532)+E(f611(x13531,x13533,x13534,x13535,x13536),f611(x13532,x13533,x13534,x13535,x13536)) % 169.39/169.67 [1354]~E(x13541,x13542)+E(f611(x13543,x13541,x13544,x13545,x13546),f611(x13543,x13542,x13544,x13545,x13546)) % 169.39/169.67 [1355]~E(x13551,x13552)+E(f611(x13553,x13554,x13551,x13555,x13556),f611(x13553,x13554,x13552,x13555,x13556)) % 169.39/169.67 [1356]~E(x13561,x13562)+E(f611(x13563,x13564,x13565,x13561,x13566),f611(x13563,x13564,x13565,x13562,x13566)) % 169.39/169.67 [1357]~E(x13571,x13572)+E(f611(x13573,x13574,x13575,x13576,x13571),f611(x13573,x13574,x13575,x13576,x13572)) % 169.39/169.67 [1358]~E(x13581,x13582)+E(f620(x13581,x13583,x13584),f620(x13582,x13583,x13584)) % 169.39/169.67 [1359]~E(x13591,x13592)+E(f620(x13593,x13591,x13594),f620(x13593,x13592,x13594)) % 169.39/169.67 [1360]~E(x13601,x13602)+E(f620(x13603,x13604,x13601),f620(x13603,x13604,x13602)) % 169.39/169.67 [1361]~E(x13611,x13612)+E(f641(x13611,x13613,x13614),f641(x13612,x13613,x13614)) % 169.39/169.67 [1362]~E(x13621,x13622)+E(f641(x13623,x13621,x13624),f641(x13623,x13622,x13624)) % 169.39/169.67 [1363]~E(x13631,x13632)+E(f641(x13633,x13634,x13631),f641(x13633,x13634,x13632)) % 169.39/169.67 [1364]~E(x13641,x13642)+E(f752(x13641,x13643,x13644),f752(x13642,x13643,x13644)) % 169.39/169.67 [1365]~E(x13651,x13652)+E(f752(x13653,x13651,x13654),f752(x13653,x13652,x13654)) % 169.39/169.67 [1366]~E(x13661,x13662)+E(f752(x13663,x13664,x13661),f752(x13663,x13664,x13662)) % 169.39/169.67 [1367]~E(x13671,x13672)+E(f778(x13671,x13673,x13674,x13675),f778(x13672,x13673,x13674,x13675)) % 169.39/169.67 [1368]~E(x13681,x13682)+E(f778(x13683,x13681,x13684,x13685),f778(x13683,x13682,x13684,x13685)) % 169.39/169.67 [1369]~E(x13691,x13692)+E(f778(x13693,x13694,x13691,x13695),f778(x13693,x13694,x13692,x13695)) % 169.39/169.67 [1370]~E(x13701,x13702)+E(f778(x13703,x13704,x13705,x13701),f778(x13703,x13704,x13705,x13702)) % 169.39/169.67 [1371]~E(x13711,x13712)+E(f508(x13711,x13713,x13714),f508(x13712,x13713,x13714)) % 169.39/169.67 [1372]~E(x13721,x13722)+E(f508(x13723,x13721,x13724),f508(x13723,x13722,x13724)) % 169.39/169.67 [1373]~E(x13731,x13732)+E(f508(x13733,x13734,x13731),f508(x13733,x13734,x13732)) % 169.39/169.67 [1374]~E(x13741,x13742)+E(f358(x13741,x13743,x13744),f358(x13742,x13743,x13744)) % 169.39/169.67 [1375]~E(x13751,x13752)+E(f358(x13753,x13751,x13754),f358(x13753,x13752,x13754)) % 169.39/169.67 [1376]~E(x13761,x13762)+E(f358(x13763,x13764,x13761),f358(x13763,x13764,x13762)) % 169.39/169.67 [1377]~E(x13771,x13772)+E(f839(x13771,x13773,x13774,x13775),f839(x13772,x13773,x13774,x13775)) % 169.39/169.67 [1378]~E(x13781,x13782)+E(f839(x13783,x13781,x13784,x13785),f839(x13783,x13782,x13784,x13785)) % 169.39/169.67 [1379]~E(x13791,x13792)+E(f839(x13793,x13794,x13791,x13795),f839(x13793,x13794,x13792,x13795)) % 169.39/169.67 [1380]~E(x13801,x13802)+E(f839(x13803,x13804,x13805,x13801),f839(x13803,x13804,x13805,x13802)) % 169.39/169.67 [1381]~E(x13811,x13812)+E(f648(x13811,x13813,x13814),f648(x13812,x13813,x13814)) % 169.39/169.67 [1382]~E(x13821,x13822)+E(f648(x13823,x13821,x13824),f648(x13823,x13822,x13824)) % 169.39/169.67 [1383]~E(x13831,x13832)+E(f648(x13833,x13834,x13831),f648(x13833,x13834,x13832)) % 169.39/169.67 [1384]~E(x13841,x13842)+E(f813(x13841,x13843,x13844,x13845,x13846),f813(x13842,x13843,x13844,x13845,x13846)) % 169.39/169.67 [1385]~E(x13851,x13852)+E(f813(x13853,x13851,x13854,x13855,x13856),f813(x13853,x13852,x13854,x13855,x13856)) % 169.39/169.67 [1386]~E(x13861,x13862)+E(f813(x13863,x13864,x13861,x13865,x13866),f813(x13863,x13864,x13862,x13865,x13866)) % 169.39/169.67 [1387]~E(x13871,x13872)+E(f813(x13873,x13874,x13875,x13871,x13876),f813(x13873,x13874,x13875,x13872,x13876)) % 169.39/169.67 [1388]~E(x13881,x13882)+E(f813(x13883,x13884,x13885,x13886,x13881),f813(x13883,x13884,x13885,x13886,x13882)) % 169.39/169.67 [1389]~E(x13891,x13892)+E(f421(x13891,x13893),f421(x13892,x13893)) % 169.39/169.67 [1390]~E(x13901,x13902)+E(f421(x13903,x13901),f421(x13903,x13902)) % 169.39/169.67 [1391]~E(x13911,x13912)+E(f780(x13911,x13913,x13914,x13915,x13916),f780(x13912,x13913,x13914,x13915,x13916)) % 169.39/169.67 [1392]~E(x13921,x13922)+E(f780(x13923,x13921,x13924,x13925,x13926),f780(x13923,x13922,x13924,x13925,x13926)) % 169.39/169.67 [1393]~E(x13931,x13932)+E(f780(x13933,x13934,x13931,x13935,x13936),f780(x13933,x13934,x13932,x13935,x13936)) % 169.39/169.67 [1394]~E(x13941,x13942)+E(f780(x13943,x13944,x13945,x13941,x13946),f780(x13943,x13944,x13945,x13942,x13946)) % 169.39/169.67 [1395]~E(x13951,x13952)+E(f780(x13953,x13954,x13955,x13956,x13951),f780(x13953,x13954,x13955,x13956,x13952)) % 169.39/169.67 [1396]~E(x13961,x13962)+E(f349(x13961,x13963,x13964),f349(x13962,x13963,x13964)) % 169.39/169.67 [1397]~E(x13971,x13972)+E(f349(x13973,x13971,x13974),f349(x13973,x13972,x13974)) % 169.39/169.67 [1398]~E(x13981,x13982)+E(f349(x13983,x13984,x13981),f349(x13983,x13984,x13982)) % 169.39/169.67 [1399]~E(x13991,x13992)+E(f352(x13991,x13993,x13994),f352(x13992,x13993,x13994)) % 169.39/169.67 [1400]~E(x14001,x14002)+E(f352(x14003,x14001,x14004),f352(x14003,x14002,x14004)) % 169.39/169.67 [1401]~E(x14011,x14012)+E(f352(x14013,x14014,x14011),f352(x14013,x14014,x14012)) % 169.39/169.67 [1402]~E(x14021,x14022)+E(f503(x14021,x14023,x14024),f503(x14022,x14023,x14024)) % 169.39/169.67 [1403]~E(x14031,x14032)+E(f503(x14033,x14031,x14034),f503(x14033,x14032,x14034)) % 169.39/169.67 [1404]~E(x14041,x14042)+E(f503(x14043,x14044,x14041),f503(x14043,x14044,x14042)) % 169.39/169.67 [1405]~E(x14051,x14052)+E(f155(x14051,x14053,x14054),f155(x14052,x14053,x14054)) % 169.39/169.67 [1406]~E(x14061,x14062)+E(f155(x14063,x14061,x14064),f155(x14063,x14062,x14064)) % 169.39/169.67 [1407]~E(x14071,x14072)+E(f155(x14073,x14074,x14071),f155(x14073,x14074,x14072)) % 169.39/169.67 [1408]~E(x14081,x14082)+E(f438(x14081,x14083),f438(x14082,x14083)) % 169.39/169.67 [1409]~E(x14091,x14092)+E(f438(x14093,x14091),f438(x14093,x14092)) % 169.39/169.67 [1410]~E(x14101,x14102)+E(f409(x14101,x14103),f409(x14102,x14103)) % 169.39/169.67 [1411]~E(x14111,x14112)+E(f409(x14113,x14111),f409(x14113,x14112)) % 169.39/169.67 [1412]~E(x14121,x14122)+E(f570(x14121,x14123,x14124,x14125,x14126,x14127),f570(x14122,x14123,x14124,x14125,x14126,x14127)) % 169.39/169.67 [1413]~E(x14131,x14132)+E(f570(x14133,x14131,x14134,x14135,x14136,x14137),f570(x14133,x14132,x14134,x14135,x14136,x14137)) % 169.39/169.67 [1414]~E(x14141,x14142)+E(f570(x14143,x14144,x14141,x14145,x14146,x14147),f570(x14143,x14144,x14142,x14145,x14146,x14147)) % 169.39/169.67 [1415]~E(x14151,x14152)+E(f570(x14153,x14154,x14155,x14151,x14156,x14157),f570(x14153,x14154,x14155,x14152,x14156,x14157)) % 169.39/169.67 [1416]~E(x14161,x14162)+E(f570(x14163,x14164,x14165,x14166,x14161,x14167),f570(x14163,x14164,x14165,x14166,x14162,x14167)) % 169.39/169.67 [1417]~E(x14171,x14172)+E(f570(x14173,x14174,x14175,x14176,x14177,x14171),f570(x14173,x14174,x14175,x14176,x14177,x14172)) % 169.39/169.67 [1418]~E(x14181,x14182)+E(f425(x14181,x14183,x14184),f425(x14182,x14183,x14184)) % 169.39/169.67 [1419]~E(x14191,x14192)+E(f425(x14193,x14191,x14194),f425(x14193,x14192,x14194)) % 169.39/169.67 [1420]~E(x14201,x14202)+E(f425(x14203,x14204,x14201),f425(x14203,x14204,x14202)) % 169.39/169.67 [1421]~E(x14211,x14212)+E(f615(x14211,x14213,x14214,x14215),f615(x14212,x14213,x14214,x14215)) % 169.39/169.67 [1422]~E(x14221,x14222)+E(f615(x14223,x14221,x14224,x14225),f615(x14223,x14222,x14224,x14225)) % 169.39/169.67 [1423]~E(x14231,x14232)+E(f615(x14233,x14234,x14231,x14235),f615(x14233,x14234,x14232,x14235)) % 169.39/169.67 [1424]~E(x14241,x14242)+E(f615(x14243,x14244,x14245,x14241),f615(x14243,x14244,x14245,x14242)) % 169.39/169.67 [1425]~E(x14251,x14252)+E(f628(x14251,x14253,x14254,x14255),f628(x14252,x14253,x14254,x14255)) % 169.39/169.67 [1426]~E(x14261,x14262)+E(f628(x14263,x14261,x14264,x14265),f628(x14263,x14262,x14264,x14265)) % 169.39/169.67 [1427]~E(x14271,x14272)+E(f628(x14273,x14274,x14271,x14275),f628(x14273,x14274,x14272,x14275)) % 169.39/169.67 [1428]~E(x14281,x14282)+E(f628(x14283,x14284,x14285,x14281),f628(x14283,x14284,x14285,x14282)) % 169.39/169.67 [1429]~E(x14291,x14292)+E(f217(x14291),f217(x14292)) % 169.39/169.67 [1430]~E(x14301,x14302)+E(f468(x14301,x14303,x14304),f468(x14302,x14303,x14304)) % 169.39/169.67 [1431]~E(x14311,x14312)+E(f468(x14313,x14311,x14314),f468(x14313,x14312,x14314)) % 169.39/169.67 [1432]~E(x14321,x14322)+E(f468(x14323,x14324,x14321),f468(x14323,x14324,x14322)) % 169.39/169.67 [1433]~E(x14331,x14332)+E(f459(x14331,x14333,x14334,x14335),f459(x14332,x14333,x14334,x14335)) % 169.39/169.67 [1434]~E(x14341,x14342)+E(f459(x14343,x14341,x14344,x14345),f459(x14343,x14342,x14344,x14345)) % 169.39/169.67 [1435]~E(x14351,x14352)+E(f459(x14353,x14354,x14351,x14355),f459(x14353,x14354,x14352,x14355)) % 169.39/169.67 [1436]~E(x14361,x14362)+E(f459(x14363,x14364,x14365,x14361),f459(x14363,x14364,x14365,x14362)) % 169.39/169.67 [1437]~E(x14371,x14372)+E(f743(x14371,x14373),f743(x14372,x14373)) % 169.39/169.67 [1438]~E(x14381,x14382)+E(f743(x14383,x14381),f743(x14383,x14382)) % 169.39/169.67 [1439]~E(x14391,x14392)+E(f824(x14391,x14393,x14394,x14395),f824(x14392,x14393,x14394,x14395)) % 169.39/169.67 [1440]~E(x14401,x14402)+E(f824(x14403,x14401,x14404,x14405),f824(x14403,x14402,x14404,x14405)) % 169.39/169.67 [1441]~E(x14411,x14412)+E(f824(x14413,x14414,x14411,x14415),f824(x14413,x14414,x14412,x14415)) % 169.39/169.67 [1442]~E(x14421,x14422)+E(f824(x14423,x14424,x14425,x14421),f824(x14423,x14424,x14425,x14422)) % 169.39/169.67 [1443]~E(x14431,x14432)+E(f376(x14431,x14433,x14434,x14435),f376(x14432,x14433,x14434,x14435)) % 169.39/169.67 [1444]~E(x14441,x14442)+E(f376(x14443,x14441,x14444,x14445),f376(x14443,x14442,x14444,x14445)) % 169.39/169.67 [1445]~E(x14451,x14452)+E(f376(x14453,x14454,x14451,x14455),f376(x14453,x14454,x14452,x14455)) % 169.39/169.67 [1446]~E(x14461,x14462)+E(f376(x14463,x14464,x14465,x14461),f376(x14463,x14464,x14465,x14462)) % 169.39/169.67 [1447]~E(x14471,x14472)+E(f282(x14471,x14473),f282(x14472,x14473)) % 169.39/169.67 [1448]~E(x14481,x14482)+E(f282(x14483,x14481),f282(x14483,x14482)) % 169.39/169.67 [1449]~E(x14491,x14492)+E(f428(x14491,x14493,x14494),f428(x14492,x14493,x14494)) % 169.39/169.67 [1450]~E(x14501,x14502)+E(f428(x14503,x14501,x14504),f428(x14503,x14502,x14504)) % 169.39/169.67 [1451]~E(x14511,x14512)+E(f428(x14513,x14514,x14511),f428(x14513,x14514,x14512)) % 169.39/169.67 [1452]~E(x14521,x14522)+E(f761(x14521,x14523,x14524),f761(x14522,x14523,x14524)) % 169.39/169.67 [1453]~E(x14531,x14532)+E(f761(x14533,x14531,x14534),f761(x14533,x14532,x14534)) % 169.39/169.67 [1454]~E(x14541,x14542)+E(f761(x14543,x14544,x14541),f761(x14543,x14544,x14542)) % 169.39/169.67 [1455]~E(x14551,x14552)+E(f843(x14551,x14553,x14554,x14555),f843(x14552,x14553,x14554,x14555)) % 169.39/169.67 [1456]~E(x14561,x14562)+E(f843(x14563,x14561,x14564,x14565),f843(x14563,x14562,x14564,x14565)) % 169.39/169.67 [1457]~E(x14571,x14572)+E(f843(x14573,x14574,x14571,x14575),f843(x14573,x14574,x14572,x14575)) % 169.39/169.67 [1458]~E(x14581,x14582)+E(f843(x14583,x14584,x14585,x14581),f843(x14583,x14584,x14585,x14582)) % 169.39/169.67 [1459]~E(x14591,x14592)+E(f833(x14591,x14593,x14594,x14595,x14596,x14597,x14598),f833(x14592,x14593,x14594,x14595,x14596,x14597,x14598)) % 169.39/169.67 [1460]~E(x14601,x14602)+E(f833(x14603,x14601,x14604,x14605,x14606,x14607,x14608),f833(x14603,x14602,x14604,x14605,x14606,x14607,x14608)) % 169.39/169.67 [1461]~E(x14611,x14612)+E(f833(x14613,x14614,x14611,x14615,x14616,x14617,x14618),f833(x14613,x14614,x14612,x14615,x14616,x14617,x14618)) % 169.39/169.67 [1462]~E(x14621,x14622)+E(f833(x14623,x14624,x14625,x14621,x14626,x14627,x14628),f833(x14623,x14624,x14625,x14622,x14626,x14627,x14628)) % 169.39/169.67 [1463]~E(x14631,x14632)+E(f833(x14633,x14634,x14635,x14636,x14631,x14637,x14638),f833(x14633,x14634,x14635,x14636,x14632,x14637,x14638)) % 169.39/169.67 [1464]~E(x14641,x14642)+E(f833(x14643,x14644,x14645,x14646,x14647,x14641,x14648),f833(x14643,x14644,x14645,x14646,x14647,x14642,x14648)) % 169.39/169.67 [1465]~E(x14651,x14652)+E(f833(x14653,x14654,x14655,x14656,x14657,x14658,x14651),f833(x14653,x14654,x14655,x14656,x14657,x14658,x14652)) % 169.39/169.67 [1466]~E(x14661,x14662)+E(f840(x14661,x14663,x14664),f840(x14662,x14663,x14664)) % 169.39/169.67 [1467]~E(x14671,x14672)+E(f840(x14673,x14671,x14674),f840(x14673,x14672,x14674)) % 169.39/169.67 [1468]~E(x14681,x14682)+E(f840(x14683,x14684,x14681),f840(x14683,x14684,x14682)) % 169.39/169.67 [1469]~E(x14691,x14692)+E(f869(x14691),f869(x14692)) % 169.39/169.67 [1470]~E(x14701,x14702)+E(f493(x14701,x14703,x14704,x14705,x14706,x14707,x14708,x14709,x147010),f493(x14702,x14703,x14704,x14705,x14706,x14707,x14708,x14709,x147010)) % 169.39/169.67 [1471]~E(x14711,x14712)+E(f493(x14713,x14711,x14714,x14715,x14716,x14717,x14718,x14719,x147110),f493(x14713,x14712,x14714,x14715,x14716,x14717,x14718,x14719,x147110)) % 169.39/169.67 [1472]~E(x14721,x14722)+E(f493(x14723,x14724,x14721,x14725,x14726,x14727,x14728,x14729,x147210),f493(x14723,x14724,x14722,x14725,x14726,x14727,x14728,x14729,x147210)) % 169.39/169.67 [1473]~E(x14731,x14732)+E(f493(x14733,x14734,x14735,x14731,x14736,x14737,x14738,x14739,x147310),f493(x14733,x14734,x14735,x14732,x14736,x14737,x14738,x14739,x147310)) % 169.39/169.67 [1474]~E(x14741,x14742)+E(f493(x14743,x14744,x14745,x14746,x14741,x14747,x14748,x14749,x147410),f493(x14743,x14744,x14745,x14746,x14742,x14747,x14748,x14749,x147410)) % 169.39/169.67 [1475]~E(x14751,x14752)+E(f493(x14753,x14754,x14755,x14756,x14757,x14751,x14758,x14759,x147510),f493(x14753,x14754,x14755,x14756,x14757,x14752,x14758,x14759,x147510)) % 169.39/169.67 [1476]~E(x14761,x14762)+E(f493(x14763,x14764,x14765,x14766,x14767,x14768,x14761,x14769,x147610),f493(x14763,x14764,x14765,x14766,x14767,x14768,x14762,x14769,x147610)) % 169.39/169.67 [1477]~E(x14771,x14772)+E(f493(x14773,x14774,x14775,x14776,x14777,x14778,x14779,x14771,x147710),f493(x14773,x14774,x14775,x14776,x14777,x14778,x14779,x14772,x147710)) % 169.39/169.67 [1478]~E(x14781,x14782)+E(f493(x14783,x14784,x14785,x14786,x14787,x14788,x14789,x147810,x14781),f493(x14783,x14784,x14785,x14786,x14787,x14788,x14789,x147810,x14782)) % 169.39/169.67 [1479]~E(x14791,x14792)+E(f175(x14791,x14793,x14794),f175(x14792,x14793,x14794)) % 169.39/169.67 [1480]~E(x14801,x14802)+E(f175(x14803,x14801,x14804),f175(x14803,x14802,x14804)) % 169.39/169.67 [1481]~E(x14811,x14812)+E(f175(x14813,x14814,x14811),f175(x14813,x14814,x14812)) % 169.39/169.67 [1482]~E(x14821,x14822)+E(f406(x14821,x14823,x14824,x14825),f406(x14822,x14823,x14824,x14825)) % 169.39/169.67 [1483]~E(x14831,x14832)+E(f406(x14833,x14831,x14834,x14835),f406(x14833,x14832,x14834,x14835)) % 169.39/169.67 [1484]~E(x14841,x14842)+E(f406(x14843,x14844,x14841,x14845),f406(x14843,x14844,x14842,x14845)) % 169.39/169.67 [1485]~E(x14851,x14852)+E(f406(x14853,x14854,x14855,x14851),f406(x14853,x14854,x14855,x14852)) % 169.39/169.67 [1486]~E(x14861,x14862)+E(f457(x14861,x14863,x14864,x14865),f457(x14862,x14863,x14864,x14865)) % 169.39/169.67 [1487]~E(x14871,x14872)+E(f457(x14873,x14871,x14874,x14875),f457(x14873,x14872,x14874,x14875)) % 169.39/169.67 [1488]~E(x14881,x14882)+E(f457(x14883,x14884,x14881,x14885),f457(x14883,x14884,x14882,x14885)) % 169.39/169.67 [1489]~E(x14891,x14892)+E(f457(x14893,x14894,x14895,x14891),f457(x14893,x14894,x14895,x14892)) % 169.39/169.67 [1490]~E(x14901,x14902)+E(f447(x14901,x14903,x14904),f447(x14902,x14903,x14904)) % 169.39/169.67 [1491]~E(x14911,x14912)+E(f447(x14913,x14911,x14914),f447(x14913,x14912,x14914)) % 169.39/169.67 [1492]~E(x14921,x14922)+E(f447(x14923,x14924,x14921),f447(x14923,x14924,x14922)) % 169.39/169.67 [1493]~E(x14931,x14932)+E(f632(x14931,x14933,x14934),f632(x14932,x14933,x14934)) % 169.39/169.67 [1494]~E(x14941,x14942)+E(f632(x14943,x14941,x14944),f632(x14943,x14942,x14944)) % 169.39/169.67 [1495]~E(x14951,x14952)+E(f632(x14953,x14954,x14951),f632(x14953,x14954,x14952)) % 169.39/169.67 [1496]~E(x14961,x14962)+E(f588(x14961,x14963,x14964,x14965,x14966),f588(x14962,x14963,x14964,x14965,x14966)) % 169.39/169.67 [1497]~E(x14971,x14972)+E(f588(x14973,x14971,x14974,x14975,x14976),f588(x14973,x14972,x14974,x14975,x14976)) % 169.39/169.67 [1498]~E(x14981,x14982)+E(f588(x14983,x14984,x14981,x14985,x14986),f588(x14983,x14984,x14982,x14985,x14986)) % 169.39/169.67 [1499]~E(x14991,x14992)+E(f588(x14993,x14994,x14995,x14991,x14996),f588(x14993,x14994,x14995,x14992,x14996)) % 169.39/169.67 [1500]~E(x15001,x15002)+E(f588(x15003,x15004,x15005,x15006,x15001),f588(x15003,x15004,x15005,x15006,x15002)) % 169.39/169.67 [1501]~E(x15011,x15012)+E(f649(x15011,x15013,x15014),f649(x15012,x15013,x15014)) % 169.39/169.67 [1502]~E(x15021,x15022)+E(f649(x15023,x15021,x15024),f649(x15023,x15022,x15024)) % 169.39/169.67 [1503]~E(x15031,x15032)+E(f649(x15033,x15034,x15031),f649(x15033,x15034,x15032)) % 169.39/169.67 [1504]~E(x15041,x15042)+E(f417(x15041,x15043,x15044),f417(x15042,x15043,x15044)) % 169.39/169.67 [1505]~E(x15051,x15052)+E(f417(x15053,x15051,x15054),f417(x15053,x15052,x15054)) % 169.39/169.67 [1506]~E(x15061,x15062)+E(f417(x15063,x15064,x15061),f417(x15063,x15064,x15062)) % 169.39/169.67 [1507]~E(x15071,x15072)+E(f804(x15071,x15073,x15074),f804(x15072,x15073,x15074)) % 169.39/169.67 [1508]~E(x15081,x15082)+E(f804(x15083,x15081,x15084),f804(x15083,x15082,x15084)) % 169.39/169.67 [1509]~E(x15091,x15092)+E(f804(x15093,x15094,x15091),f804(x15093,x15094,x15092)) % 169.39/169.67 [1510]~E(x15101,x15102)+E(f786(x15101,x15103,x15104,x15105),f786(x15102,x15103,x15104,x15105)) % 169.39/169.67 [1511]~E(x15111,x15112)+E(f786(x15113,x15111,x15114,x15115),f786(x15113,x15112,x15114,x15115)) % 169.39/169.67 [1512]~E(x15121,x15122)+E(f786(x15123,x15124,x15121,x15125),f786(x15123,x15124,x15122,x15125)) % 169.39/169.67 [1513]~E(x15131,x15132)+E(f786(x15133,x15134,x15135,x15131),f786(x15133,x15134,x15135,x15132)) % 169.39/169.67 [1514]~E(x15141,x15142)+E(f867(x15141,x15143,x15144,x15145,x15146,x15147,x15148,x15149),f867(x15142,x15143,x15144,x15145,x15146,x15147,x15148,x15149)) % 169.39/169.67 [1515]~E(x15151,x15152)+E(f867(x15153,x15151,x15154,x15155,x15156,x15157,x15158,x15159),f867(x15153,x15152,x15154,x15155,x15156,x15157,x15158,x15159)) % 169.39/169.67 [1516]~E(x15161,x15162)+E(f867(x15163,x15164,x15161,x15165,x15166,x15167,x15168,x15169),f867(x15163,x15164,x15162,x15165,x15166,x15167,x15168,x15169)) % 169.39/169.67 [1517]~E(x15171,x15172)+E(f867(x15173,x15174,x15175,x15171,x15176,x15177,x15178,x15179),f867(x15173,x15174,x15175,x15172,x15176,x15177,x15178,x15179)) % 169.39/169.67 [1518]~E(x15181,x15182)+E(f867(x15183,x15184,x15185,x15186,x15181,x15187,x15188,x15189),f867(x15183,x15184,x15185,x15186,x15182,x15187,x15188,x15189)) % 169.39/169.67 [1519]~E(x15191,x15192)+E(f867(x15193,x15194,x15195,x15196,x15197,x15191,x15198,x15199),f867(x15193,x15194,x15195,x15196,x15197,x15192,x15198,x15199)) % 169.39/169.67 [1520]~E(x15201,x15202)+E(f867(x15203,x15204,x15205,x15206,x15207,x15208,x15201,x15209),f867(x15203,x15204,x15205,x15206,x15207,x15208,x15202,x15209)) % 169.39/169.67 [1521]~E(x15211,x15212)+E(f867(x15213,x15214,x15215,x15216,x15217,x15218,x15219,x15211),f867(x15213,x15214,x15215,x15216,x15217,x15218,x15219,x15212)) % 169.39/169.67 [1522]~E(x15221,x15222)+E(f348(x15221,x15223,x15224),f348(x15222,x15223,x15224)) % 169.39/169.67 [1523]~E(x15231,x15232)+E(f348(x15233,x15231,x15234),f348(x15233,x15232,x15234)) % 169.39/169.67 [1524]~E(x15241,x15242)+E(f348(x15243,x15244,x15241),f348(x15243,x15244,x15242)) % 169.39/169.67 [1525]~E(x15251,x15252)+E(f606(x15251,x15253,x15254),f606(x15252,x15253,x15254)) % 169.39/169.67 [1526]~E(x15261,x15262)+E(f606(x15263,x15261,x15264),f606(x15263,x15262,x15264)) % 169.39/169.67 [1527]~E(x15271,x15272)+E(f606(x15273,x15274,x15271),f606(x15273,x15274,x15272)) % 169.39/169.67 [1528]~E(x15281,x15282)+E(f480(x15281,x15283),f480(x15282,x15283)) % 169.39/169.67 [1529]~E(x15291,x15292)+E(f480(x15293,x15291),f480(x15293,x15292)) % 169.39/169.67 [1530]~E(x15301,x15302)+E(f293(x15301,x15303),f293(x15302,x15303)) % 169.39/169.67 [1531]~E(x15311,x15312)+E(f293(x15313,x15311),f293(x15313,x15312)) % 169.39/169.67 [1532]~E(x15321,x15322)+E(f821(x15321,x15323,x15324),f821(x15322,x15323,x15324)) % 169.39/169.67 [1533]~E(x15331,x15332)+E(f821(x15333,x15331,x15334),f821(x15333,x15332,x15334)) % 169.39/169.67 [1534]~E(x15341,x15342)+E(f821(x15343,x15344,x15341),f821(x15343,x15344,x15342)) % 169.39/169.67 [1535]~E(x15351,x15352)+E(f95(x15351,x15353,x15354),f95(x15352,x15353,x15354)) % 169.39/169.67 [1536]~E(x15361,x15362)+E(f95(x15363,x15361,x15364),f95(x15363,x15362,x15364)) % 169.39/169.67 [1537]~E(x15371,x15372)+E(f95(x15373,x15374,x15371),f95(x15373,x15374,x15372)) % 169.39/169.67 [1538]~E(x15381,x15382)+E(f676(x15381,x15383),f676(x15382,x15383)) % 169.39/169.67 [1539]~E(x15391,x15392)+E(f676(x15393,x15391),f676(x15393,x15392)) % 169.39/169.67 [1540]~E(x15401,x15402)+E(f284(x15401,x15403,x15404),f284(x15402,x15403,x15404)) % 169.39/169.67 [1541]~E(x15411,x15412)+E(f284(x15413,x15411,x15414),f284(x15413,x15412,x15414)) % 169.39/169.67 [1542]~E(x15421,x15422)+E(f284(x15423,x15424,x15421),f284(x15423,x15424,x15422)) % 169.39/169.67 [1543]~E(x15431,x15432)+E(f460(x15431,x15433,x15434,x15435),f460(x15432,x15433,x15434,x15435)) % 169.39/169.67 [1544]~E(x15441,x15442)+E(f460(x15443,x15441,x15444,x15445),f460(x15443,x15442,x15444,x15445)) % 169.39/169.67 [1545]~E(x15451,x15452)+E(f460(x15453,x15454,x15451,x15455),f460(x15453,x15454,x15452,x15455)) % 169.39/169.67 [1546]~E(x15461,x15462)+E(f460(x15463,x15464,x15465,x15461),f460(x15463,x15464,x15465,x15462)) % 169.39/169.67 [1547]~E(x15471,x15472)+E(f465(x15471,x15473,x15474),f465(x15472,x15473,x15474)) % 169.39/169.67 [1548]~E(x15481,x15482)+E(f465(x15483,x15481,x15484),f465(x15483,x15482,x15484)) % 169.39/169.67 [1549]~E(x15491,x15492)+E(f465(x15493,x15494,x15491),f465(x15493,x15494,x15492)) % 169.39/169.67 [1550]~E(x15501,x15502)+E(f560(x15501,x15503,x15504,x15505,x15506,x15507,x15508),f560(x15502,x15503,x15504,x15505,x15506,x15507,x15508)) % 169.39/169.67 [1551]~E(x15511,x15512)+E(f560(x15513,x15511,x15514,x15515,x15516,x15517,x15518),f560(x15513,x15512,x15514,x15515,x15516,x15517,x15518)) % 169.39/169.67 [1552]~E(x15521,x15522)+E(f560(x15523,x15524,x15521,x15525,x15526,x15527,x15528),f560(x15523,x15524,x15522,x15525,x15526,x15527,x15528)) % 169.39/169.67 [1553]~E(x15531,x15532)+E(f560(x15533,x15534,x15535,x15531,x15536,x15537,x15538),f560(x15533,x15534,x15535,x15532,x15536,x15537,x15538)) % 169.39/169.67 [1554]~E(x15541,x15542)+E(f560(x15543,x15544,x15545,x15546,x15541,x15547,x15548),f560(x15543,x15544,x15545,x15546,x15542,x15547,x15548)) % 169.39/169.67 [1555]~E(x15551,x15552)+E(f560(x15553,x15554,x15555,x15556,x15557,x15551,x15558),f560(x15553,x15554,x15555,x15556,x15557,x15552,x15558)) % 169.39/169.67 [1556]~E(x15561,x15562)+E(f560(x15563,x15564,x15565,x15566,x15567,x15568,x15561),f560(x15563,x15564,x15565,x15566,x15567,x15568,x15562)) % 169.39/169.67 [1557]~E(x15571,x15572)+E(f361(x15571,x15573,x15574),f361(x15572,x15573,x15574)) % 169.39/169.67 [1558]~E(x15581,x15582)+E(f361(x15583,x15581,x15584),f361(x15583,x15582,x15584)) % 169.39/169.67 [1559]~E(x15591,x15592)+E(f361(x15593,x15594,x15591),f361(x15593,x15594,x15592)) % 169.39/169.67 [1560]~E(x15601,x15602)+E(f629(x15601,x15603,x15604),f629(x15602,x15603,x15604)) % 169.39/169.67 [1561]~E(x15611,x15612)+E(f629(x15613,x15611,x15614),f629(x15613,x15612,x15614)) % 169.39/169.67 [1562]~E(x15621,x15622)+E(f629(x15623,x15624,x15621),f629(x15623,x15624,x15622)) % 169.39/169.67 [1563]~E(x15631,x15632)+E(f538(x15631,x15633,x15634,x15635),f538(x15632,x15633,x15634,x15635)) % 169.39/169.67 [1564]~E(x15641,x15642)+E(f538(x15643,x15641,x15644,x15645),f538(x15643,x15642,x15644,x15645)) % 169.39/169.67 [1565]~E(x15651,x15652)+E(f538(x15653,x15654,x15651,x15655),f538(x15653,x15654,x15652,x15655)) % 169.39/169.67 [1566]~E(x15661,x15662)+E(f538(x15663,x15664,x15665,x15661),f538(x15663,x15664,x15665,x15662)) % 169.39/169.67 [1567]~E(x15671,x15672)+E(f567(x15671,x15673,x15674,x15675,x15676,x15677),f567(x15672,x15673,x15674,x15675,x15676,x15677)) % 169.39/169.67 [1568]~E(x15681,x15682)+E(f567(x15683,x15681,x15684,x15685,x15686,x15687),f567(x15683,x15682,x15684,x15685,x15686,x15687)) % 169.39/169.67 [1569]~E(x15691,x15692)+E(f567(x15693,x15694,x15691,x15695,x15696,x15697),f567(x15693,x15694,x15692,x15695,x15696,x15697)) % 169.39/169.67 [1570]~E(x15701,x15702)+E(f567(x15703,x15704,x15705,x15701,x15706,x15707),f567(x15703,x15704,x15705,x15702,x15706,x15707)) % 169.39/169.67 [1571]~E(x15711,x15712)+E(f567(x15713,x15714,x15715,x15716,x15711,x15717),f567(x15713,x15714,x15715,x15716,x15712,x15717)) % 169.39/169.67 [1572]~E(x15721,x15722)+E(f567(x15723,x15724,x15725,x15726,x15727,x15721),f567(x15723,x15724,x15725,x15726,x15727,x15722)) % 169.39/169.67 [1573]~E(x15731,x15732)+E(f735(x15731,x15733,x15734),f735(x15732,x15733,x15734)) % 169.39/169.67 [1574]~E(x15741,x15742)+E(f735(x15743,x15741,x15744),f735(x15743,x15742,x15744)) % 169.39/169.67 [1575]~E(x15751,x15752)+E(f735(x15753,x15754,x15751),f735(x15753,x15754,x15752)) % 169.39/169.67 [1576]~E(x15761,x15762)+E(f359(x15761,x15763,x15764),f359(x15762,x15763,x15764)) % 169.39/169.67 [1577]~E(x15771,x15772)+E(f359(x15773,x15771,x15774),f359(x15773,x15772,x15774)) % 169.39/169.67 [1578]~E(x15781,x15782)+E(f359(x15783,x15784,x15781),f359(x15783,x15784,x15782)) % 169.39/169.67 [1579]~E(x15791,x15792)+E(f514(x15791,x15793,x15794,x15795),f514(x15792,x15793,x15794,x15795)) % 169.39/169.67 [1580]~E(x15801,x15802)+E(f514(x15803,x15801,x15804,x15805),f514(x15803,x15802,x15804,x15805)) % 169.39/169.67 [1581]~E(x15811,x15812)+E(f514(x15813,x15814,x15811,x15815),f514(x15813,x15814,x15812,x15815)) % 169.39/169.67 [1582]~E(x15821,x15822)+E(f514(x15823,x15824,x15825,x15821),f514(x15823,x15824,x15825,x15822)) % 169.39/169.67 [1583]~E(x15831,x15832)+E(f647(x15831,x15833,x15834),f647(x15832,x15833,x15834)) % 169.39/169.67 [1584]~E(x15841,x15842)+E(f647(x15843,x15841,x15844),f647(x15843,x15842,x15844)) % 169.39/169.67 [1585]~E(x15851,x15852)+E(f647(x15853,x15854,x15851),f647(x15853,x15854,x15852)) % 169.39/169.67 [1586]~E(x15861,x15862)+E(f803(x15861,x15863,x15864),f803(x15862,x15863,x15864)) % 169.39/169.67 [1587]~E(x15871,x15872)+E(f803(x15873,x15871,x15874),f803(x15873,x15872,x15874)) % 169.39/169.67 [1588]~E(x15881,x15882)+E(f803(x15883,x15884,x15881),f803(x15883,x15884,x15882)) % 169.39/169.67 [1589]~E(x15891,x15892)+E(f583(x15891,x15893,x15894),f583(x15892,x15893,x15894)) % 169.39/169.67 [1590]~E(x15901,x15902)+E(f583(x15903,x15901,x15904),f583(x15903,x15902,x15904)) % 169.39/169.67 [1591]~E(x15911,x15912)+E(f583(x15913,x15914,x15911),f583(x15913,x15914,x15912)) % 169.39/169.67 [1592]~E(x15921,x15922)+E(f206(x15921,x15923,x15924,x15925),f206(x15922,x15923,x15924,x15925)) % 169.39/169.67 [1593]~E(x15931,x15932)+E(f206(x15933,x15931,x15934,x15935),f206(x15933,x15932,x15934,x15935)) % 169.39/169.67 [1594]~E(x15941,x15942)+E(f206(x15943,x15944,x15941,x15945),f206(x15943,x15944,x15942,x15945)) % 169.39/169.67 [1595]~E(x15951,x15952)+E(f206(x15953,x15954,x15955,x15951),f206(x15953,x15954,x15955,x15952)) % 169.39/169.67 [1596]~E(x15961,x15962)+E(f530(x15961,x15963,x15964,x15965,x15966),f530(x15962,x15963,x15964,x15965,x15966)) % 169.39/169.67 [1597]~E(x15971,x15972)+E(f530(x15973,x15971,x15974,x15975,x15976),f530(x15973,x15972,x15974,x15975,x15976)) % 169.39/169.67 [1598]~E(x15981,x15982)+E(f530(x15983,x15984,x15981,x15985,x15986),f530(x15983,x15984,x15982,x15985,x15986)) % 169.39/169.67 [1599]~E(x15991,x15992)+E(f530(x15993,x15994,x15995,x15991,x15996),f530(x15993,x15994,x15995,x15992,x15996)) % 169.39/169.67 [1600]~E(x16001,x16002)+E(f530(x16003,x16004,x16005,x16006,x16001),f530(x16003,x16004,x16005,x16006,x16002)) % 169.39/169.67 [1601]~E(x16011,x16012)+E(f844(x16011,x16013,x16014,x16015,x16016),f844(x16012,x16013,x16014,x16015,x16016)) % 169.39/169.67 [1602]~E(x16021,x16022)+E(f844(x16023,x16021,x16024,x16025,x16026),f844(x16023,x16022,x16024,x16025,x16026)) % 169.39/169.67 [1603]~E(x16031,x16032)+E(f844(x16033,x16034,x16031,x16035,x16036),f844(x16033,x16034,x16032,x16035,x16036)) % 169.39/169.67 [1604]~E(x16041,x16042)+E(f844(x16043,x16044,x16045,x16041,x16046),f844(x16043,x16044,x16045,x16042,x16046)) % 169.39/169.67 [1605]~E(x16051,x16052)+E(f844(x16053,x16054,x16055,x16056,x16051),f844(x16053,x16054,x16055,x16056,x16052)) % 169.39/169.67 [1606]~E(x16061,x16062)+E(f796(x16061,x16063,x16064),f796(x16062,x16063,x16064)) % 169.39/169.67 [1607]~E(x16071,x16072)+E(f796(x16073,x16071,x16074),f796(x16073,x16072,x16074)) % 169.39/169.67 [1608]~E(x16081,x16082)+E(f796(x16083,x16084,x16081),f796(x16083,x16084,x16082)) % 169.39/169.67 [1609]~E(x16091,x16092)+E(f656(x16091,x16093),f656(x16092,x16093)) % 169.39/169.67 [1610]~E(x16101,x16102)+E(f656(x16103,x16101),f656(x16103,x16102)) % 169.39/169.67 [1611]~E(x16111,x16112)+E(f317(x16111,x16113,x16114),f317(x16112,x16113,x16114)) % 169.39/169.67 [1612]~E(x16121,x16122)+E(f317(x16123,x16121,x16124),f317(x16123,x16122,x16124)) % 169.39/169.67 [1613]~E(x16131,x16132)+E(f317(x16133,x16134,x16131),f317(x16133,x16134,x16132)) % 169.39/169.67 [1614]~E(x16141,x16142)+E(f400(x16141,x16143,x16144,x16145),f400(x16142,x16143,x16144,x16145)) % 169.39/169.67 [1615]~E(x16151,x16152)+E(f400(x16153,x16151,x16154,x16155),f400(x16153,x16152,x16154,x16155)) % 169.39/169.67 [1616]~E(x16161,x16162)+E(f400(x16163,x16164,x16161,x16165),f400(x16163,x16164,x16162,x16165)) % 169.39/169.67 [1617]~E(x16171,x16172)+E(f400(x16173,x16174,x16175,x16171),f400(x16173,x16174,x16175,x16172)) % 169.39/169.67 [1618]~E(x16181,x16182)+E(f492(x16181,x16183,x16184,x16185,x16186),f492(x16182,x16183,x16184,x16185,x16186)) % 169.39/169.67 [1619]~E(x16191,x16192)+E(f492(x16193,x16191,x16194,x16195,x16196),f492(x16193,x16192,x16194,x16195,x16196)) % 169.39/169.67 [1620]~E(x16201,x16202)+E(f492(x16203,x16204,x16201,x16205,x16206),f492(x16203,x16204,x16202,x16205,x16206)) % 169.39/169.67 [1621]~E(x16211,x16212)+E(f492(x16213,x16214,x16215,x16211,x16216),f492(x16213,x16214,x16215,x16212,x16216)) % 169.39/169.67 [1622]~E(x16221,x16222)+E(f492(x16223,x16224,x16225,x16226,x16221),f492(x16223,x16224,x16225,x16226,x16222)) % 169.39/169.67 [1623]~E(x16231,x16232)+E(f722(x16231,x16233),f722(x16232,x16233)) % 169.39/169.67 [1624]~E(x16241,x16242)+E(f722(x16243,x16241),f722(x16243,x16242)) % 169.39/169.67 [1625]~E(x16251,x16252)+E(f444(x16251,x16253,x16254),f444(x16252,x16253,x16254)) % 169.39/169.67 [1626]~E(x16261,x16262)+E(f444(x16263,x16261,x16264),f444(x16263,x16262,x16264)) % 169.39/169.67 [1627]~E(x16271,x16272)+E(f444(x16273,x16274,x16271),f444(x16273,x16274,x16272)) % 169.39/169.67 [1628]~E(x16281,x16282)+E(f569(x16281,x16283,x16284,x16285,x16286,x16287),f569(x16282,x16283,x16284,x16285,x16286,x16287)) % 169.39/169.67 [1629]~E(x16291,x16292)+E(f569(x16293,x16291,x16294,x16295,x16296,x16297),f569(x16293,x16292,x16294,x16295,x16296,x16297)) % 169.39/169.67 [1630]~E(x16301,x16302)+E(f569(x16303,x16304,x16301,x16305,x16306,x16307),f569(x16303,x16304,x16302,x16305,x16306,x16307)) % 169.39/169.67 [1631]~E(x16311,x16312)+E(f569(x16313,x16314,x16315,x16311,x16316,x16317),f569(x16313,x16314,x16315,x16312,x16316,x16317)) % 169.39/169.67 [1632]~E(x16321,x16322)+E(f569(x16323,x16324,x16325,x16326,x16321,x16327),f569(x16323,x16324,x16325,x16326,x16322,x16327)) % 169.39/169.67 [1633]~E(x16331,x16332)+E(f569(x16333,x16334,x16335,x16336,x16337,x16331),f569(x16333,x16334,x16335,x16336,x16337,x16332)) % 169.39/169.67 [1634]~E(x16341,x16342)+E(f810(x16341,x16343,x16344,x16345),f810(x16342,x16343,x16344,x16345)) % 169.39/169.67 [1635]~E(x16351,x16352)+E(f810(x16353,x16351,x16354,x16355),f810(x16353,x16352,x16354,x16355)) % 169.39/169.67 [1636]~E(x16361,x16362)+E(f810(x16363,x16364,x16361,x16365),f810(x16363,x16364,x16362,x16365)) % 169.39/169.67 [1637]~E(x16371,x16372)+E(f810(x16373,x16374,x16375,x16371),f810(x16373,x16374,x16375,x16372)) % 169.39/169.67 [1638]~E(x16381,x16382)+E(f853(x16381,x16383,x16384,x16385,x16386,x16387),f853(x16382,x16383,x16384,x16385,x16386,x16387)) % 169.39/169.67 [1639]~E(x16391,x16392)+E(f853(x16393,x16391,x16394,x16395,x16396,x16397),f853(x16393,x16392,x16394,x16395,x16396,x16397)) % 169.39/169.67 [1640]~E(x16401,x16402)+E(f853(x16403,x16404,x16401,x16405,x16406,x16407),f853(x16403,x16404,x16402,x16405,x16406,x16407)) % 169.39/169.67 [1641]~E(x16411,x16412)+E(f853(x16413,x16414,x16415,x16411,x16416,x16417),f853(x16413,x16414,x16415,x16412,x16416,x16417)) % 169.39/169.67 [1642]~E(x16421,x16422)+E(f853(x16423,x16424,x16425,x16426,x16421,x16427),f853(x16423,x16424,x16425,x16426,x16422,x16427)) % 169.39/169.67 [1643]~E(x16431,x16432)+E(f853(x16433,x16434,x16435,x16436,x16437,x16431),f853(x16433,x16434,x16435,x16436,x16437,x16432)) % 169.39/169.67 [1644]~E(x16441,x16442)+E(f529(x16441,x16443,x16444,x16445,x16446),f529(x16442,x16443,x16444,x16445,x16446)) % 169.39/169.67 [1645]~E(x16451,x16452)+E(f529(x16453,x16451,x16454,x16455,x16456),f529(x16453,x16452,x16454,x16455,x16456)) % 169.39/169.67 [1646]~E(x16461,x16462)+E(f529(x16463,x16464,x16461,x16465,x16466),f529(x16463,x16464,x16462,x16465,x16466)) % 169.39/169.67 [1647]~E(x16471,x16472)+E(f529(x16473,x16474,x16475,x16471,x16476),f529(x16473,x16474,x16475,x16472,x16476)) % 169.39/169.67 [1648]~E(x16481,x16482)+E(f529(x16483,x16484,x16485,x16486,x16481),f529(x16483,x16484,x16485,x16486,x16482)) % 169.39/169.67 [1649]~E(x16491,x16492)+E(f751(x16491,x16493,x16494),f751(x16492,x16493,x16494)) % 169.39/169.67 [1650]~E(x16501,x16502)+E(f751(x16503,x16501,x16504),f751(x16503,x16502,x16504)) % 169.39/169.67 [1651]~E(x16511,x16512)+E(f751(x16513,x16514,x16511),f751(x16513,x16514,x16512)) % 169.39/169.67 [1652]~E(x16521,x16522)+E(f345(x16521,x16523),f345(x16522,x16523)) % 169.39/169.67 [1653]~E(x16531,x16532)+E(f345(x16533,x16531),f345(x16533,x16532)) % 169.39/169.67 [1654]~E(x16541,x16542)+E(f582(x16541,x16543,x16544),f582(x16542,x16543,x16544)) % 169.39/169.67 [1655]~E(x16551,x16552)+E(f582(x16553,x16551,x16554),f582(x16553,x16552,x16554)) % 169.39/169.67 [1656]~E(x16561,x16562)+E(f582(x16563,x16564,x16561),f582(x16563,x16564,x16562)) % 169.39/169.67 [1657]~E(x16571,x16572)+E(f787(x16571,x16573,x16574,x16575,x16576,x16577),f787(x16572,x16573,x16574,x16575,x16576,x16577)) % 169.39/169.67 [1658]~E(x16581,x16582)+E(f787(x16583,x16581,x16584,x16585,x16586,x16587),f787(x16583,x16582,x16584,x16585,x16586,x16587)) % 169.39/169.67 [1659]~E(x16591,x16592)+E(f787(x16593,x16594,x16591,x16595,x16596,x16597),f787(x16593,x16594,x16592,x16595,x16596,x16597)) % 169.39/169.67 [1660]~E(x16601,x16602)+E(f787(x16603,x16604,x16605,x16601,x16606,x16607),f787(x16603,x16604,x16605,x16602,x16606,x16607)) % 169.39/169.67 [1661]~E(x16611,x16612)+E(f787(x16613,x16614,x16615,x16616,x16611,x16617),f787(x16613,x16614,x16615,x16616,x16612,x16617)) % 169.39/169.67 [1662]~E(x16621,x16622)+E(f787(x16623,x16624,x16625,x16626,x16627,x16621),f787(x16623,x16624,x16625,x16626,x16627,x16622)) % 169.39/169.67 [1663]~E(x16631,x16632)+E(f612(x16631,x16633,x16634,x16635),f612(x16632,x16633,x16634,x16635)) % 169.39/169.67 [1664]~E(x16641,x16642)+E(f612(x16643,x16641,x16644,x16645),f612(x16643,x16642,x16644,x16645)) % 169.39/169.67 [1665]~E(x16651,x16652)+E(f612(x16653,x16654,x16651,x16655),f612(x16653,x16654,x16652,x16655)) % 169.39/169.67 [1666]~E(x16661,x16662)+E(f612(x16663,x16664,x16665,x16661),f612(x16663,x16664,x16665,x16662)) % 169.39/169.67 [1667]~E(x16671,x16672)+E(f860(x16671),f860(x16672)) % 169.39/169.67 [1668]~E(x16681,x16682)+E(f294(x16681,x16683),f294(x16682,x16683)) % 169.39/169.67 [1669]~E(x16691,x16692)+E(f294(x16693,x16691),f294(x16693,x16692)) % 169.39/169.67 [1670]~E(x16701,x16702)+E(f97(x16701,x16703,x16704,x16705),f97(x16702,x16703,x16704,x16705)) % 169.39/169.67 [1671]~E(x16711,x16712)+E(f97(x16713,x16711,x16714,x16715),f97(x16713,x16712,x16714,x16715)) % 169.39/169.67 [1672]~E(x16721,x16722)+E(f97(x16723,x16724,x16721,x16725),f97(x16723,x16724,x16722,x16725)) % 169.39/169.67 [1673]~E(x16731,x16732)+E(f97(x16733,x16734,x16735,x16731),f97(x16733,x16734,x16735,x16732)) % 169.39/169.67 [1674]~E(x16741,x16742)+E(f626(x16741,x16743,x16744),f626(x16742,x16743,x16744)) % 169.39/169.67 [1675]~E(x16751,x16752)+E(f626(x16753,x16751,x16754),f626(x16753,x16752,x16754)) % 169.39/169.67 [1676]~E(x16761,x16762)+E(f626(x16763,x16764,x16761),f626(x16763,x16764,x16762)) % 169.39/169.67 [1677]~E(x16771,x16772)+E(f640(x16771,x16773,x16774),f640(x16772,x16773,x16774)) % 169.39/169.67 [1678]~E(x16781,x16782)+E(f640(x16783,x16781,x16784),f640(x16783,x16782,x16784)) % 169.39/169.67 [1679]~E(x16791,x16792)+E(f640(x16793,x16794,x16791),f640(x16793,x16794,x16792)) % 169.39/169.67 [1680]~E(x16801,x16802)+E(f760(x16801,x16803,x16804),f760(x16802,x16803,x16804)) % 169.39/169.67 [1681]~E(x16811,x16812)+E(f760(x16813,x16811,x16814),f760(x16813,x16812,x16814)) % 169.39/169.67 [1682]~E(x16821,x16822)+E(f760(x16823,x16824,x16821),f760(x16823,x16824,x16822)) % 169.39/169.67 [1683]~E(x16831,x16832)+E(f373(x16831,x16833,x16834,x16835),f373(x16832,x16833,x16834,x16835)) % 169.39/169.67 [1684]~E(x16841,x16842)+E(f373(x16843,x16841,x16844,x16845),f373(x16843,x16842,x16844,x16845)) % 169.39/169.67 [1685]~E(x16851,x16852)+E(f373(x16853,x16854,x16851,x16855),f373(x16853,x16854,x16852,x16855)) % 169.39/169.67 [1686]~E(x16861,x16862)+E(f373(x16863,x16864,x16865,x16861),f373(x16863,x16864,x16865,x16862)) % 169.39/169.67 [1687]~E(x16871,x16872)+E(f381(x16871,x16873,x16874,x16875),f381(x16872,x16873,x16874,x16875)) % 169.39/169.67 [1688]~E(x16881,x16882)+E(f381(x16883,x16881,x16884,x16885),f381(x16883,x16882,x16884,x16885)) % 169.39/169.67 [1689]~E(x16891,x16892)+E(f381(x16893,x16894,x16891,x16895),f381(x16893,x16894,x16892,x16895)) % 169.39/169.67 [1690]~E(x16901,x16902)+E(f381(x16903,x16904,x16905,x16901),f381(x16903,x16904,x16905,x16902)) % 169.39/169.67 [1691]~E(x16911,x16912)+E(f516(x16911,x16913,x16914,x16915,x16916),f516(x16912,x16913,x16914,x16915,x16916)) % 169.39/169.67 [1692]~E(x16921,x16922)+E(f516(x16923,x16921,x16924,x16925,x16926),f516(x16923,x16922,x16924,x16925,x16926)) % 169.39/169.67 [1693]~E(x16931,x16932)+E(f516(x16933,x16934,x16931,x16935,x16936),f516(x16933,x16934,x16932,x16935,x16936)) % 169.39/169.67 [1694]~E(x16941,x16942)+E(f516(x16943,x16944,x16945,x16941,x16946),f516(x16943,x16944,x16945,x16942,x16946)) % 169.39/169.67 [1695]~E(x16951,x16952)+E(f516(x16953,x16954,x16955,x16956,x16951),f516(x16953,x16954,x16955,x16956,x16952)) % 169.39/169.67 [1696]~E(x16961,x16962)+E(f316(x16961,x16963,x16964),f316(x16962,x16963,x16964)) % 169.39/169.67 [1697]~E(x16971,x16972)+E(f316(x16973,x16971,x16974),f316(x16973,x16972,x16974)) % 169.39/169.67 [1698]~E(x16981,x16982)+E(f316(x16983,x16984,x16981),f316(x16983,x16984,x16982)) % 169.39/169.67 [1699]~E(x16991,x16992)+E(f667(x16991,x16993,x16994,x16995),f667(x16992,x16993,x16994,x16995)) % 169.39/169.67 [1700]~E(x17001,x17002)+E(f667(x17003,x17001,x17004,x17005),f667(x17003,x17002,x17004,x17005)) % 169.39/169.67 [1701]~E(x17011,x17012)+E(f667(x17013,x17014,x17011,x17015),f667(x17013,x17014,x17012,x17015)) % 169.39/169.67 [1702]~E(x17021,x17022)+E(f667(x17023,x17024,x17025,x17021),f667(x17023,x17024,x17025,x17022)) % 169.39/169.67 [1703]~E(x17031,x17032)+E(f686(x17031,x17033,x17034,x17035,x17036),f686(x17032,x17033,x17034,x17035,x17036)) % 169.39/169.67 [1704]~E(x17041,x17042)+E(f686(x17043,x17041,x17044,x17045,x17046),f686(x17043,x17042,x17044,x17045,x17046)) % 169.39/169.67 [1705]~E(x17051,x17052)+E(f686(x17053,x17054,x17051,x17055,x17056),f686(x17053,x17054,x17052,x17055,x17056)) % 169.39/169.67 [1706]~E(x17061,x17062)+E(f686(x17063,x17064,x17065,x17061,x17066),f686(x17063,x17064,x17065,x17062,x17066)) % 169.39/169.67 [1707]~E(x17071,x17072)+E(f686(x17073,x17074,x17075,x17076,x17071),f686(x17073,x17074,x17075,x17076,x17072)) % 169.39/169.67 [1708]~E(x17081,x17082)+E(f728(x17081,x17083,x17084,x17085),f728(x17082,x17083,x17084,x17085)) % 169.39/169.67 [1709]~E(x17091,x17092)+E(f728(x17093,x17091,x17094,x17095),f728(x17093,x17092,x17094,x17095)) % 169.39/169.67 [1710]~E(x17101,x17102)+E(f728(x17103,x17104,x17101,x17105),f728(x17103,x17104,x17102,x17105)) % 169.39/169.67 [1711]~E(x17111,x17112)+E(f728(x17113,x17114,x17115,x17111),f728(x17113,x17114,x17115,x17112)) % 169.39/169.67 [1712]~E(x17121,x17122)+E(f855(x17121,x17123,x17124),f855(x17122,x17123,x17124)) % 169.39/169.67 [1713]~E(x17131,x17132)+E(f855(x17133,x17131,x17134),f855(x17133,x17132,x17134)) % 169.39/169.67 [1714]~E(x17141,x17142)+E(f855(x17143,x17144,x17141),f855(x17143,x17144,x17142)) % 169.39/169.67 [1715]~E(x17151,x17152)+E(f204(x17151,x17153,x17154,x17155),f204(x17152,x17153,x17154,x17155)) % 169.39/169.67 [1716]~E(x17161,x17162)+E(f204(x17163,x17161,x17164,x17165),f204(x17163,x17162,x17164,x17165)) % 169.39/169.67 [1717]~E(x17171,x17172)+E(f204(x17173,x17174,x17171,x17175),f204(x17173,x17174,x17172,x17175)) % 169.39/169.67 [1718]~E(x17181,x17182)+E(f204(x17183,x17184,x17185,x17181),f204(x17183,x17184,x17185,x17182)) % 169.39/169.67 [1719]~E(x17191,x17192)+E(f487(x17191,x17193,x17194),f487(x17192,x17193,x17194)) % 169.39/169.67 [1720]~E(x17201,x17202)+E(f487(x17203,x17201,x17204),f487(x17203,x17202,x17204)) % 169.39/169.67 [1721]~E(x17211,x17212)+E(f487(x17213,x17214,x17211),f487(x17213,x17214,x17212)) % 169.39/169.67 [1722]~E(x17221,x17222)+E(f762(x17221,x17223,x17224,x17225),f762(x17222,x17223,x17224,x17225)) % 169.39/169.67 [1723]~E(x17231,x17232)+E(f762(x17233,x17231,x17234,x17235),f762(x17233,x17232,x17234,x17235)) % 169.39/169.67 [1724]~E(x17241,x17242)+E(f762(x17243,x17244,x17241,x17245),f762(x17243,x17244,x17242,x17245)) % 169.39/169.67 [1725]~E(x17251,x17252)+E(f762(x17253,x17254,x17255,x17251),f762(x17253,x17254,x17255,x17252)) % 169.39/169.67 [1726]~E(x17261,x17262)+E(f793(x17261,x17263,x17264,x17265,x17266,x17267),f793(x17262,x17263,x17264,x17265,x17266,x17267)) % 169.39/169.67 [1727]~E(x17271,x17272)+E(f793(x17273,x17271,x17274,x17275,x17276,x17277),f793(x17273,x17272,x17274,x17275,x17276,x17277)) % 169.39/169.67 [1728]~E(x17281,x17282)+E(f793(x17283,x17284,x17281,x17285,x17286,x17287),f793(x17283,x17284,x17282,x17285,x17286,x17287)) % 169.39/169.67 [1729]~E(x17291,x17292)+E(f793(x17293,x17294,x17295,x17291,x17296,x17297),f793(x17293,x17294,x17295,x17292,x17296,x17297)) % 169.39/169.67 [1730]~E(x17301,x17302)+E(f793(x17303,x17304,x17305,x17306,x17301,x17307),f793(x17303,x17304,x17305,x17306,x17302,x17307)) % 169.39/169.67 [1731]~E(x17311,x17312)+E(f793(x17313,x17314,x17315,x17316,x17317,x17311),f793(x17313,x17314,x17315,x17316,x17317,x17312)) % 169.39/169.67 [1732]~E(x17321,x17322)+E(f295(x17321,x17323,x17324),f295(x17322,x17323,x17324)) % 169.39/169.67 [1733]~E(x17331,x17332)+E(f295(x17333,x17331,x17334),f295(x17333,x17332,x17334)) % 169.39/169.67 [1734]~E(x17341,x17342)+E(f295(x17343,x17344,x17341),f295(x17343,x17344,x17342)) % 169.39/169.67 [1735]~E(x17351,x17352)+E(f551(x17351,x17353,x17354,x17355,x17356),f551(x17352,x17353,x17354,x17355,x17356)) % 169.39/169.67 [1736]~E(x17361,x17362)+E(f551(x17363,x17361,x17364,x17365,x17366),f551(x17363,x17362,x17364,x17365,x17366)) % 169.39/169.67 [1737]~E(x17371,x17372)+E(f551(x17373,x17374,x17371,x17375,x17376),f551(x17373,x17374,x17372,x17375,x17376)) % 169.39/169.67 [1738]~E(x17381,x17382)+E(f551(x17383,x17384,x17385,x17381,x17386),f551(x17383,x17384,x17385,x17382,x17386)) % 169.39/169.67 [1739]~E(x17391,x17392)+E(f551(x17393,x17394,x17395,x17396,x17391),f551(x17393,x17394,x17395,x17396,x17392)) % 169.39/169.67 [1740]~E(x17401,x17402)+E(f579(x17401,x17403,x17404),f579(x17402,x17403,x17404)) % 169.39/169.67 [1741]~E(x17411,x17412)+E(f579(x17413,x17411,x17414),f579(x17413,x17412,x17414)) % 169.39/169.67 [1742]~E(x17421,x17422)+E(f579(x17423,x17424,x17421),f579(x17423,x17424,x17422)) % 169.39/169.67 [1743]~E(x17431,x17432)+E(f286(x17431,x17433,x17434,x17435),f286(x17432,x17433,x17434,x17435)) % 169.39/169.67 [1744]~E(x17441,x17442)+E(f286(x17443,x17441,x17444,x17445),f286(x17443,x17442,x17444,x17445)) % 169.39/169.67 [1745]~E(x17451,x17452)+E(f286(x17453,x17454,x17451,x17455),f286(x17453,x17454,x17452,x17455)) % 169.39/169.67 [1746]~E(x17461,x17462)+E(f286(x17463,x17464,x17465,x17461),f286(x17463,x17464,x17465,x17462)) % 169.39/169.67 [1747]~E(x17471,x17472)+E(f218(x17471,x17473,x17474,x17475),f218(x17472,x17473,x17474,x17475)) % 169.39/169.67 [1748]~E(x17481,x17482)+E(f218(x17483,x17481,x17484,x17485),f218(x17483,x17482,x17484,x17485)) % 169.39/169.67 [1749]~E(x17491,x17492)+E(f218(x17493,x17494,x17491,x17495),f218(x17493,x17494,x17492,x17495)) % 169.39/169.67 [1750]~E(x17501,x17502)+E(f218(x17503,x17504,x17505,x17501),f218(x17503,x17504,x17505,x17502)) % 169.39/169.67 [1751]~E(x17511,x17512)+E(f548(x17511,x17513,x17514),f548(x17512,x17513,x17514)) % 169.39/169.67 [1752]~E(x17521,x17522)+E(f548(x17523,x17521,x17524),f548(x17523,x17522,x17524)) % 169.39/169.67 [1753]~E(x17531,x17532)+E(f548(x17533,x17534,x17531),f548(x17533,x17534,x17532)) % 169.39/169.67 [1754]~E(x17541,x17542)+E(f75(x17541,x17543),f75(x17542,x17543)) % 169.39/169.67 [1755]~E(x17551,x17552)+E(f75(x17553,x17551),f75(x17553,x17552)) % 169.39/169.67 [1756]~E(x17561,x17562)+E(f733(x17561,x17563,x17564),f733(x17562,x17563,x17564)) % 169.39/169.67 [1757]~E(x17571,x17572)+E(f733(x17573,x17571,x17574),f733(x17573,x17572,x17574)) % 169.39/169.67 [1758]~E(x17581,x17582)+E(f733(x17583,x17584,x17581),f733(x17583,x17584,x17582)) % 169.39/169.67 [1759]~E(x17591,x17592)+E(f367(x17591,x17593),f367(x17592,x17593)) % 169.39/169.67 [1760]~E(x17601,x17602)+E(f367(x17603,x17601),f367(x17603,x17602)) % 169.39/169.67 [1761]~E(x17611,x17612)+E(f660(x17611,x17613,x17614),f660(x17612,x17613,x17614)) % 169.39/169.67 [1762]~E(x17621,x17622)+E(f660(x17623,x17621,x17624),f660(x17623,x17622,x17624)) % 169.39/169.67 [1763]~E(x17631,x17632)+E(f660(x17633,x17634,x17631),f660(x17633,x17634,x17632)) % 169.39/169.67 [1764]~E(x17641,x17642)+E(f479(x17641,x17643),f479(x17642,x17643)) % 169.39/169.67 [1765]~E(x17651,x17652)+E(f479(x17653,x17651),f479(x17653,x17652)) % 169.39/169.67 [1766]~E(x17661,x17662)+E(f825(x17661),f825(x17662)) % 169.39/169.67 [1767]~E(x17671,x17672)+E(f571(x17671,x17673,x17674,x17675,x17676,x17677,x17678,x17679),f571(x17672,x17673,x17674,x17675,x17676,x17677,x17678,x17679)) % 169.39/169.67 [1768]~E(x17681,x17682)+E(f571(x17683,x17681,x17684,x17685,x17686,x17687,x17688,x17689),f571(x17683,x17682,x17684,x17685,x17686,x17687,x17688,x17689)) % 169.39/169.67 [1769]~E(x17691,x17692)+E(f571(x17693,x17694,x17691,x17695,x17696,x17697,x17698,x17699),f571(x17693,x17694,x17692,x17695,x17696,x17697,x17698,x17699)) % 169.39/169.67 [1770]~E(x17701,x17702)+E(f571(x17703,x17704,x17705,x17701,x17706,x17707,x17708,x17709),f571(x17703,x17704,x17705,x17702,x17706,x17707,x17708,x17709)) % 169.39/169.67 [1771]~E(x17711,x17712)+E(f571(x17713,x17714,x17715,x17716,x17711,x17717,x17718,x17719),f571(x17713,x17714,x17715,x17716,x17712,x17717,x17718,x17719)) % 169.39/169.67 [1772]~E(x17721,x17722)+E(f571(x17723,x17724,x17725,x17726,x17727,x17721,x17728,x17729),f571(x17723,x17724,x17725,x17726,x17727,x17722,x17728,x17729)) % 169.39/169.67 [1773]~E(x17731,x17732)+E(f571(x17733,x17734,x17735,x17736,x17737,x17738,x17731,x17739),f571(x17733,x17734,x17735,x17736,x17737,x17738,x17732,x17739)) % 169.39/169.67 [1774]~E(x17741,x17742)+E(f571(x17743,x17744,x17745,x17746,x17747,x17748,x17749,x17741),f571(x17743,x17744,x17745,x17746,x17747,x17748,x17749,x17742)) % 169.39/169.67 [1775]~E(x17751,x17752)+E(f418(x17751,x17753,x17754,x17755),f418(x17752,x17753,x17754,x17755)) % 169.39/169.67 [1776]~E(x17761,x17762)+E(f418(x17763,x17761,x17764,x17765),f418(x17763,x17762,x17764,x17765)) % 169.39/169.67 [1777]~E(x17771,x17772)+E(f418(x17773,x17774,x17771,x17775),f418(x17773,x17774,x17772,x17775)) % 169.39/169.67 [1778]~E(x17781,x17782)+E(f418(x17783,x17784,x17785,x17781),f418(x17783,x17784,x17785,x17782)) % 169.39/169.67 [1779]~E(x17791,x17792)+E(f750(x17791,x17793,x17794),f750(x17792,x17793,x17794)) % 169.39/169.67 [1780]~E(x17801,x17802)+E(f750(x17803,x17801,x17804),f750(x17803,x17802,x17804)) % 169.39/169.67 [1781]~E(x17811,x17812)+E(f750(x17813,x17814,x17811),f750(x17813,x17814,x17812)) % 169.39/169.67 [1782]~E(x17821,x17822)+E(f23(x17821,x17823),f23(x17822,x17823)) % 169.39/169.67 [1783]~E(x17831,x17832)+E(f23(x17833,x17831),f23(x17833,x17832)) % 169.39/169.67 [1784]~E(x17841,x17842)+E(f328(x17841,x17843,x17844),f328(x17842,x17843,x17844)) % 169.39/169.67 [1785]~E(x17851,x17852)+E(f328(x17853,x17851,x17854),f328(x17853,x17852,x17854)) % 169.39/169.67 [1786]~E(x17861,x17862)+E(f328(x17863,x17864,x17861),f328(x17863,x17864,x17862)) % 169.39/169.67 [1787]~E(x17871,x17872)+E(f694(x17871,x17873,x17874,x17875),f694(x17872,x17873,x17874,x17875)) % 169.39/169.67 [1788]~E(x17881,x17882)+E(f694(x17883,x17881,x17884,x17885),f694(x17883,x17882,x17884,x17885)) % 169.39/169.67 [1789]~E(x17891,x17892)+E(f694(x17893,x17894,x17891,x17895),f694(x17893,x17894,x17892,x17895)) % 169.39/169.67 [1790]~E(x17901,x17902)+E(f694(x17903,x17904,x17905,x17901),f694(x17903,x17904,x17905,x17902)) % 169.39/169.67 [1791]~E(x17911,x17912)+E(f819(x17911,x17913,x17914),f819(x17912,x17913,x17914)) % 169.39/169.67 [1792]~E(x17921,x17922)+E(f819(x17923,x17921,x17924),f819(x17923,x17922,x17924)) % 169.39/169.67 [1793]~E(x17931,x17932)+E(f819(x17933,x17934,x17931),f819(x17933,x17934,x17932)) % 169.39/169.67 [1794]~E(x17941,x17942)+E(f539(x17941,x17943,x17944,x17945,x17946),f539(x17942,x17943,x17944,x17945,x17946)) % 169.39/169.67 [1795]~E(x17951,x17952)+E(f539(x17953,x17951,x17954,x17955,x17956),f539(x17953,x17952,x17954,x17955,x17956)) % 169.39/169.67 [1796]~E(x17961,x17962)+E(f539(x17963,x17964,x17961,x17965,x17966),f539(x17963,x17964,x17962,x17965,x17966)) % 169.39/169.67 [1797]~E(x17971,x17972)+E(f539(x17973,x17974,x17975,x17971,x17976),f539(x17973,x17974,x17975,x17972,x17976)) % 169.39/169.67 [1798]~E(x17981,x17982)+E(f539(x17983,x17984,x17985,x17986,x17981),f539(x17983,x17984,x17985,x17986,x17982)) % 169.39/169.67 [1799]~E(x17991,x17992)+E(f252(x17991,x17993),f252(x17992,x17993)) % 169.39/169.67 [1800]~E(x18001,x18002)+E(f252(x18003,x18001),f252(x18003,x18002)) % 169.39/169.67 [1801]~E(x18011,x18012)+E(f422(x18011,x18013),f422(x18012,x18013)) % 169.39/169.67 [1802]~E(x18021,x18022)+E(f422(x18023,x18021),f422(x18023,x18022)) % 169.39/169.67 [1803]~E(x18031,x18032)+E(f584(x18031,x18033,x18034),f584(x18032,x18033,x18034)) % 169.39/169.67 [1804]~E(x18041,x18042)+E(f584(x18043,x18041,x18044),f584(x18043,x18042,x18044)) % 169.39/169.67 [1805]~E(x18051,x18052)+E(f584(x18053,x18054,x18051),f584(x18053,x18054,x18052)) % 169.39/169.67 [1806]~E(x18061,x18062)+E(f801(x18061,x18063),f801(x18062,x18063)) % 169.39/169.67 [1807]~E(x18071,x18072)+E(f801(x18073,x18071),f801(x18073,x18072)) % 169.39/169.67 [1808]~E(x18081,x18082)+E(f384(x18081,x18083,x18084,x18085),f384(x18082,x18083,x18084,x18085)) % 169.39/169.67 [1809]~E(x18091,x18092)+E(f384(x18093,x18091,x18094,x18095),f384(x18093,x18092,x18094,x18095)) % 169.39/169.67 [1810]~E(x18101,x18102)+E(f384(x18103,x18104,x18101,x18105),f384(x18103,x18104,x18102,x18105)) % 169.39/169.67 [1811]~E(x18111,x18112)+E(f384(x18113,x18114,x18115,x18111),f384(x18113,x18114,x18115,x18112)) % 169.39/169.67 [1812]~E(x18121,x18122)+E(f699(x18121,x18123,x18124,x18125,x18126,x18127),f699(x18122,x18123,x18124,x18125,x18126,x18127)) % 169.39/169.67 [1813]~E(x18131,x18132)+E(f699(x18133,x18131,x18134,x18135,x18136,x18137),f699(x18133,x18132,x18134,x18135,x18136,x18137)) % 169.39/169.67 [1814]~E(x18141,x18142)+E(f699(x18143,x18144,x18141,x18145,x18146,x18147),f699(x18143,x18144,x18142,x18145,x18146,x18147)) % 169.39/169.67 [1815]~E(x18151,x18152)+E(f699(x18153,x18154,x18155,x18151,x18156,x18157),f699(x18153,x18154,x18155,x18152,x18156,x18157)) % 169.39/169.67 [1816]~E(x18161,x18162)+E(f699(x18163,x18164,x18165,x18166,x18161,x18167),f699(x18163,x18164,x18165,x18166,x18162,x18167)) % 169.39/169.67 [1817]~E(x18171,x18172)+E(f699(x18173,x18174,x18175,x18176,x18177,x18171),f699(x18173,x18174,x18175,x18176,x18177,x18172)) % 169.39/169.67 [1818]~E(x18181,x18182)+E(f771(x18181,x18183,x18184,x18185,x18186),f771(x18182,x18183,x18184,x18185,x18186)) % 169.39/169.67 [1819]~E(x18191,x18192)+E(f771(x18193,x18191,x18194,x18195,x18196),f771(x18193,x18192,x18194,x18195,x18196)) % 169.39/169.67 [1820]~E(x18201,x18202)+E(f771(x18203,x18204,x18201,x18205,x18206),f771(x18203,x18204,x18202,x18205,x18206)) % 169.39/169.67 [1821]~E(x18211,x18212)+E(f771(x18213,x18214,x18215,x18211,x18216),f771(x18213,x18214,x18215,x18212,x18216)) % 169.39/169.67 [1822]~E(x18221,x18222)+E(f771(x18223,x18224,x18225,x18226,x18221),f771(x18223,x18224,x18225,x18226,x18222)) % 169.39/169.67 [1823]~E(x18231,x18232)+E(f318(x18231,x18233,x18234),f318(x18232,x18233,x18234)) % 169.39/169.67 [1824]~E(x18241,x18242)+E(f318(x18243,x18241,x18244),f318(x18243,x18242,x18244)) % 169.39/169.67 [1825]~E(x18251,x18252)+E(f318(x18253,x18254,x18251),f318(x18253,x18254,x18252)) % 169.39/169.67 [1826]~E(x18261,x18262)+E(f532(x18261,x18263,x18264,x18265,x18266),f532(x18262,x18263,x18264,x18265,x18266)) % 169.39/169.67 [1827]~E(x18271,x18272)+E(f532(x18273,x18271,x18274,x18275,x18276),f532(x18273,x18272,x18274,x18275,x18276)) % 169.39/169.67 [1828]~E(x18281,x18282)+E(f532(x18283,x18284,x18281,x18285,x18286),f532(x18283,x18284,x18282,x18285,x18286)) % 169.39/169.67 [1829]~E(x18291,x18292)+E(f532(x18293,x18294,x18295,x18291,x18296),f532(x18293,x18294,x18295,x18292,x18296)) % 169.39/169.67 [1830]~E(x18301,x18302)+E(f532(x18303,x18304,x18305,x18306,x18301),f532(x18303,x18304,x18305,x18306,x18302)) % 169.39/169.67 [1831]~E(x18311,x18312)+E(f98(x18311,x18313,x18314,x18315),f98(x18312,x18313,x18314,x18315)) % 169.39/169.67 [1832]~E(x18321,x18322)+E(f98(x18323,x18321,x18324,x18325),f98(x18323,x18322,x18324,x18325)) % 169.39/169.67 [1833]~E(x18331,x18332)+E(f98(x18333,x18334,x18331,x18335),f98(x18333,x18334,x18332,x18335)) % 169.39/169.67 [1834]~E(x18341,x18342)+E(f98(x18343,x18344,x18345,x18341),f98(x18343,x18344,x18345,x18342)) % 169.39/169.67 [1835]~E(x18351,x18352)+E(f870(x18351,x18353,x18354,x18355,x18356,x18357,x18358),f870(x18352,x18353,x18354,x18355,x18356,x18357,x18358)) % 169.39/169.67 [1836]~E(x18361,x18362)+E(f870(x18363,x18361,x18364,x18365,x18366,x18367,x18368),f870(x18363,x18362,x18364,x18365,x18366,x18367,x18368)) % 169.39/169.67 [1837]~E(x18371,x18372)+E(f870(x18373,x18374,x18371,x18375,x18376,x18377,x18378),f870(x18373,x18374,x18372,x18375,x18376,x18377,x18378)) % 169.39/169.67 [1838]~E(x18381,x18382)+E(f870(x18383,x18384,x18385,x18381,x18386,x18387,x18388),f870(x18383,x18384,x18385,x18382,x18386,x18387,x18388)) % 169.39/169.67 [1839]~E(x18391,x18392)+E(f870(x18393,x18394,x18395,x18396,x18391,x18397,x18398),f870(x18393,x18394,x18395,x18396,x18392,x18397,x18398)) % 169.39/169.67 [1840]~E(x18401,x18402)+E(f870(x18403,x18404,x18405,x18406,x18407,x18401,x18408),f870(x18403,x18404,x18405,x18406,x18407,x18402,x18408)) % 169.39/169.67 [1841]~E(x18411,x18412)+E(f870(x18413,x18414,x18415,x18416,x18417,x18418,x18411),f870(x18413,x18414,x18415,x18416,x18417,x18418,x18412)) % 169.39/169.67 [1842]~E(x18421,x18422)+E(f708(x18421,x18423),f708(x18422,x18423)) % 169.39/169.67 [1843]~E(x18431,x18432)+E(f708(x18433,x18431),f708(x18433,x18432)) % 169.39/169.67 [1844]~E(x18441,x18442)+E(f386(x18441,x18443,x18444,x18445),f386(x18442,x18443,x18444,x18445)) % 169.39/169.67 [1845]~E(x18451,x18452)+E(f386(x18453,x18451,x18454,x18455),f386(x18453,x18452,x18454,x18455)) % 169.39/169.67 [1846]~E(x18461,x18462)+E(f386(x18463,x18464,x18461,x18465),f386(x18463,x18464,x18462,x18465)) % 169.39/169.67 [1847]~E(x18471,x18472)+E(f386(x18473,x18474,x18475,x18471),f386(x18473,x18474,x18475,x18472)) % 169.39/169.67 [1848]~E(x18481,x18482)+E(f498(x18481,x18483,x18484),f498(x18482,x18483,x18484)) % 169.39/169.67 [1849]~E(x18491,x18492)+E(f498(x18493,x18491,x18494),f498(x18493,x18492,x18494)) % 169.39/169.67 [1850]~E(x18501,x18502)+E(f498(x18503,x18504,x18501),f498(x18503,x18504,x18502)) % 169.39/169.67 [1851]~E(x18511,x18512)+E(f19(x18511,x18513,x18514,x18515),f19(x18512,x18513,x18514,x18515)) % 169.39/169.67 [1852]~E(x18521,x18522)+E(f19(x18523,x18521,x18524,x18525),f19(x18523,x18522,x18524,x18525)) % 169.39/169.67 [1853]~E(x18531,x18532)+E(f19(x18533,x18534,x18531,x18535),f19(x18533,x18534,x18532,x18535)) % 169.39/169.67 [1854]~E(x18541,x18542)+E(f19(x18543,x18544,x18545,x18541),f19(x18543,x18544,x18545,x18542)) % 169.39/169.67 [1855]~E(x18551,x18552)+E(f726(x18551,x18553,x18554,x18555,x18556,x18557),f726(x18552,x18553,x18554,x18555,x18556,x18557)) % 169.39/169.67 [1856]~E(x18561,x18562)+E(f726(x18563,x18561,x18564,x18565,x18566,x18567),f726(x18563,x18562,x18564,x18565,x18566,x18567)) % 169.39/169.67 [1857]~E(x18571,x18572)+E(f726(x18573,x18574,x18571,x18575,x18576,x18577),f726(x18573,x18574,x18572,x18575,x18576,x18577)) % 169.39/169.67 [1858]~E(x18581,x18582)+E(f726(x18583,x18584,x18585,x18581,x18586,x18587),f726(x18583,x18584,x18585,x18582,x18586,x18587)) % 169.39/169.67 [1859]~E(x18591,x18592)+E(f726(x18593,x18594,x18595,x18596,x18591,x18597),f726(x18593,x18594,x18595,x18596,x18592,x18597)) % 169.39/169.67 [1860]~E(x18601,x18602)+E(f726(x18603,x18604,x18605,x18606,x18607,x18601),f726(x18603,x18604,x18605,x18606,x18607,x18602)) % 169.39/169.67 [1861]~E(x18611,x18612)+E(f599(x18611,x18613,x18614,x18615),f599(x18612,x18613,x18614,x18615)) % 169.39/169.67 [1862]~E(x18621,x18622)+E(f599(x18623,x18621,x18624,x18625),f599(x18623,x18622,x18624,x18625)) % 169.39/169.67 [1863]~E(x18631,x18632)+E(f599(x18633,x18634,x18631,x18635),f599(x18633,x18634,x18632,x18635)) % 169.39/169.67 [1864]~E(x18641,x18642)+E(f599(x18643,x18644,x18645,x18641),f599(x18643,x18644,x18645,x18642)) % 169.39/169.67 [1865]~E(x18651,x18652)+E(f651(x18651,x18653,x18654,x18655,x18656),f651(x18652,x18653,x18654,x18655,x18656)) % 169.39/169.67 [1866]~E(x18661,x18662)+E(f651(x18663,x18661,x18664,x18665,x18666),f651(x18663,x18662,x18664,x18665,x18666)) % 169.39/169.67 [1867]~E(x18671,x18672)+E(f651(x18673,x18674,x18671,x18675,x18676),f651(x18673,x18674,x18672,x18675,x18676)) % 169.39/169.67 [1868]~E(x18681,x18682)+E(f651(x18683,x18684,x18685,x18681,x18686),f651(x18683,x18684,x18685,x18682,x18686)) % 169.39/169.67 [1869]~E(x18691,x18692)+E(f651(x18693,x18694,x18695,x18696,x18691),f651(x18693,x18694,x18695,x18696,x18692)) % 169.39/169.67 [1870]~E(x18701,x18702)+E(f408(x18701,x18703),f408(x18702,x18703)) % 169.39/169.67 [1871]~E(x18711,x18712)+E(f408(x18713,x18711),f408(x18713,x18712)) % 169.39/169.67 [1872]~E(x18721,x18722)+E(f683(x18721,x18723),f683(x18722,x18723)) % 169.39/169.67 [1873]~E(x18731,x18732)+E(f683(x18733,x18731),f683(x18733,x18732)) % 169.39/169.67 [1874]~E(x18741,x18742)+E(f738(x18741,x18743,x18744,x18745,x18746),f738(x18742,x18743,x18744,x18745,x18746)) % 169.39/169.67 [1875]~E(x18751,x18752)+E(f738(x18753,x18751,x18754,x18755,x18756),f738(x18753,x18752,x18754,x18755,x18756)) % 169.39/169.67 [1876]~E(x18761,x18762)+E(f738(x18763,x18764,x18761,x18765,x18766),f738(x18763,x18764,x18762,x18765,x18766)) % 169.39/169.67 [1877]~E(x18771,x18772)+E(f738(x18773,x18774,x18775,x18771,x18776),f738(x18773,x18774,x18775,x18772,x18776)) % 169.39/169.67 [1878]~E(x18781,x18782)+E(f738(x18783,x18784,x18785,x18786,x18781),f738(x18783,x18784,x18785,x18786,x18782)) % 169.39/169.67 [1879]~E(x18791,x18792)+E(f674(x18791,x18793),f674(x18792,x18793)) % 169.39/169.67 [1880]~E(x18801,x18802)+E(f674(x18803,x18801),f674(x18803,x18802)) % 169.39/169.67 [1881]~E(x18811,x18812)+E(f432(x18811,x18813,x18814,x18815,x18816),f432(x18812,x18813,x18814,x18815,x18816)) % 169.39/169.67 [1882]~E(x18821,x18822)+E(f432(x18823,x18821,x18824,x18825,x18826),f432(x18823,x18822,x18824,x18825,x18826)) % 169.39/169.67 [1883]~E(x18831,x18832)+E(f432(x18833,x18834,x18831,x18835,x18836),f432(x18833,x18834,x18832,x18835,x18836)) % 169.39/169.67 [1884]~E(x18841,x18842)+E(f432(x18843,x18844,x18845,x18841,x18846),f432(x18843,x18844,x18845,x18842,x18846)) % 169.39/169.67 [1885]~E(x18851,x18852)+E(f432(x18853,x18854,x18855,x18856,x18851),f432(x18853,x18854,x18855,x18856,x18852)) % 169.39/169.67 [1886]~E(x18861,x18862)+E(f531(x18861,x18863,x18864,x18865),f531(x18862,x18863,x18864,x18865)) % 169.39/169.67 [1887]~E(x18871,x18872)+E(f531(x18873,x18871,x18874,x18875),f531(x18873,x18872,x18874,x18875)) % 169.39/169.67 [1888]~E(x18881,x18882)+E(f531(x18883,x18884,x18881,x18885),f531(x18883,x18884,x18882,x18885)) % 169.39/169.67 [1889]~E(x18891,x18892)+E(f531(x18893,x18894,x18895,x18891),f531(x18893,x18894,x18895,x18892)) % 169.39/169.67 [1890]~E(x18901,x18902)+E(f765(x18901,x18903,x18904),f765(x18902,x18903,x18904)) % 169.39/169.67 [1891]~E(x18911,x18912)+E(f765(x18913,x18911,x18914),f765(x18913,x18912,x18914)) % 169.39/169.67 [1892]~E(x18921,x18922)+E(f765(x18923,x18924,x18921),f765(x18923,x18924,x18922)) % 169.39/169.67 [1893]~E(x18931,x18932)+E(f829(x18931,x18933,x18934,x18935,x18936,x18937),f829(x18932,x18933,x18934,x18935,x18936,x18937)) % 169.39/169.67 [1894]~E(x18941,x18942)+E(f829(x18943,x18941,x18944,x18945,x18946,x18947),f829(x18943,x18942,x18944,x18945,x18946,x18947)) % 169.39/169.67 [1895]~E(x18951,x18952)+E(f829(x18953,x18954,x18951,x18955,x18956,x18957),f829(x18953,x18954,x18952,x18955,x18956,x18957)) % 169.39/169.67 [1896]~E(x18961,x18962)+E(f829(x18963,x18964,x18965,x18961,x18966,x18967),f829(x18963,x18964,x18965,x18962,x18966,x18967)) % 169.39/169.67 [1897]~E(x18971,x18972)+E(f829(x18973,x18974,x18975,x18976,x18971,x18977),f829(x18973,x18974,x18975,x18976,x18972,x18977)) % 169.39/169.67 [1898]~E(x18981,x18982)+E(f829(x18983,x18984,x18985,x18986,x18987,x18981),f829(x18983,x18984,x18985,x18986,x18987,x18982)) % 169.39/169.67 [1899]~E(x18991,x18992)+E(f766(x18991,x18993,x18994),f766(x18992,x18993,x18994)) % 169.39/169.67 [1900]~E(x19001,x19002)+E(f766(x19003,x19001,x19004),f766(x19003,x19002,x19004)) % 169.39/169.67 [1901]~E(x19011,x19012)+E(f766(x19013,x19014,x19011),f766(x19013,x19014,x19012)) % 169.39/169.67 [1902]~E(x19021,x19022)+E(f507(x19021,x19023,x19024),f507(x19022,x19023,x19024)) % 169.39/169.67 [1903]~E(x19031,x19032)+E(f507(x19033,x19031,x19034),f507(x19033,x19032,x19034)) % 169.39/169.67 [1904]~E(x19041,x19042)+E(f507(x19043,x19044,x19041),f507(x19043,x19044,x19042)) % 169.39/169.67 [1905]~E(x19051,x19052)+E(f854(x19051,x19053,x19054),f854(x19052,x19053,x19054)) % 169.39/169.67 [1906]~E(x19061,x19062)+E(f854(x19063,x19061,x19064),f854(x19063,x19062,x19064)) % 169.39/169.67 [1907]~E(x19071,x19072)+E(f854(x19073,x19074,x19071),f854(x19073,x19074,x19072)) % 169.39/169.67 [1908]~E(x19081,x19082)+E(f645(x19081,x19083),f645(x19082,x19083)) % 169.39/169.67 [1909]~E(x19091,x19092)+E(f645(x19093,x19091),f645(x19093,x19092)) % 169.39/169.67 [1910]~E(x19101,x19102)+E(f681(x19101,x19103,x19104,x19105),f681(x19102,x19103,x19104,x19105)) % 169.39/169.67 [1911]~E(x19111,x19112)+E(f681(x19113,x19111,x19114,x19115),f681(x19113,x19112,x19114,x19115)) % 169.39/169.67 [1912]~E(x19121,x19122)+E(f681(x19123,x19124,x19121,x19125),f681(x19123,x19124,x19122,x19125)) % 169.39/169.67 [1913]~E(x19131,x19132)+E(f681(x19133,x19134,x19135,x19131),f681(x19133,x19134,x19135,x19132)) % 169.39/169.67 [1914]~E(x19141,x19142)+E(f389(x19141,x19143,x19144,x19145),f389(x19142,x19143,x19144,x19145)) % 169.39/169.67 [1915]~E(x19151,x19152)+E(f389(x19153,x19151,x19154,x19155),f389(x19153,x19152,x19154,x19155)) % 169.39/169.67 [1916]~E(x19161,x19162)+E(f389(x19163,x19164,x19161,x19165),f389(x19163,x19164,x19162,x19165)) % 169.39/169.67 [1917]~E(x19171,x19172)+E(f389(x19173,x19174,x19175,x19171),f389(x19173,x19174,x19175,x19172)) % 169.39/169.67 [1918]~E(x19181,x19182)+E(f811(x19181,x19183,x19184),f811(x19182,x19183,x19184)) % 169.39/169.67 [1919]~E(x19191,x19192)+E(f811(x19193,x19191,x19194),f811(x19193,x19192,x19194)) % 169.39/169.67 [1920]~E(x19201,x19202)+E(f811(x19203,x19204,x19201),f811(x19203,x19204,x19202)) % 169.39/169.67 [1921]~E(x19211,x19212)+E(f506(x19211,x19213,x19214),f506(x19212,x19213,x19214)) % 169.39/169.67 [1922]~E(x19221,x19222)+E(f506(x19223,x19221,x19224),f506(x19223,x19222,x19224)) % 169.39/169.67 [1923]~E(x19231,x19232)+E(f506(x19233,x19234,x19231),f506(x19233,x19234,x19232)) % 169.39/169.67 [1924]~E(x19241,x19242)+E(f363(x19241),f363(x19242)) % 169.39/169.67 [1925]~E(x19251,x19252)+E(f385(x19251,x19253,x19254,x19255),f385(x19252,x19253,x19254,x19255)) % 169.39/169.67 [1926]~E(x19261,x19262)+E(f385(x19263,x19261,x19264,x19265),f385(x19263,x19262,x19264,x19265)) % 169.39/169.67 [1927]~E(x19271,x19272)+E(f385(x19273,x19274,x19271,x19275),f385(x19273,x19274,x19272,x19275)) % 169.39/169.67 [1928]~E(x19281,x19282)+E(f385(x19283,x19284,x19285,x19281),f385(x19283,x19284,x19285,x19282)) % 169.39/169.67 [1929]~E(x19291,x19292)+E(f781(x19291,x19293,x19294),f781(x19292,x19293,x19294)) % 169.39/169.67 [1930]~E(x19301,x19302)+E(f781(x19303,x19301,x19304),f781(x19303,x19302,x19304)) % 169.39/169.67 [1931]~E(x19311,x19312)+E(f781(x19313,x19314,x19311),f781(x19313,x19314,x19312)) % 169.39/169.67 [1932]~E(x19321,x19322)+E(f576(x19321,x19323,x19324,x19325,x19326,x19327,x19328),f576(x19322,x19323,x19324,x19325,x19326,x19327,x19328)) % 169.39/169.67 [1933]~E(x19331,x19332)+E(f576(x19333,x19331,x19334,x19335,x19336,x19337,x19338),f576(x19333,x19332,x19334,x19335,x19336,x19337,x19338)) % 169.39/169.67 [1934]~E(x19341,x19342)+E(f576(x19343,x19344,x19341,x19345,x19346,x19347,x19348),f576(x19343,x19344,x19342,x19345,x19346,x19347,x19348)) % 169.39/169.67 [1935]~E(x19351,x19352)+E(f576(x19353,x19354,x19355,x19351,x19356,x19357,x19358),f576(x19353,x19354,x19355,x19352,x19356,x19357,x19358)) % 169.39/169.67 [1936]~E(x19361,x19362)+E(f576(x19363,x19364,x19365,x19366,x19361,x19367,x19368),f576(x19363,x19364,x19365,x19366,x19362,x19367,x19368)) % 169.39/169.67 [1937]~E(x19371,x19372)+E(f576(x19373,x19374,x19375,x19376,x19377,x19371,x19378),f576(x19373,x19374,x19375,x19376,x19377,x19372,x19378)) % 169.39/169.67 [1938]~E(x19381,x19382)+E(f576(x19383,x19384,x19385,x19386,x19387,x19388,x19381),f576(x19383,x19384,x19385,x19386,x19387,x19388,x19382)) % 169.39/169.67 [1939]~E(x19391,x19392)+E(f863(x19391,x19393,x19394,x19395,x19396,x19397,x19398),f863(x19392,x19393,x19394,x19395,x19396,x19397,x19398)) % 169.39/169.67 [1940]~E(x19401,x19402)+E(f863(x19403,x19401,x19404,x19405,x19406,x19407,x19408),f863(x19403,x19402,x19404,x19405,x19406,x19407,x19408)) % 169.39/169.67 [1941]~E(x19411,x19412)+E(f863(x19413,x19414,x19411,x19415,x19416,x19417,x19418),f863(x19413,x19414,x19412,x19415,x19416,x19417,x19418)) % 169.39/169.67 [1942]~E(x19421,x19422)+E(f863(x19423,x19424,x19425,x19421,x19426,x19427,x19428),f863(x19423,x19424,x19425,x19422,x19426,x19427,x19428)) % 169.39/169.67 [1943]~E(x19431,x19432)+E(f863(x19433,x19434,x19435,x19436,x19431,x19437,x19438),f863(x19433,x19434,x19435,x19436,x19432,x19437,x19438)) % 169.39/169.67 [1944]~E(x19441,x19442)+E(f863(x19443,x19444,x19445,x19446,x19447,x19441,x19448),f863(x19443,x19444,x19445,x19446,x19447,x19442,x19448)) % 169.39/169.67 [1945]~E(x19451,x19452)+E(f863(x19453,x19454,x19455,x19456,x19457,x19458,x19451),f863(x19453,x19454,x19455,x19456,x19457,x19458,x19452)) % 169.39/169.67 [1946]~E(x19461,x19462)+E(f315(x19461,x19463),f315(x19462,x19463)) % 169.39/169.67 [1947]~E(x19471,x19472)+E(f315(x19473,x19471),f315(x19473,x19472)) % 169.39/169.67 [1948]~E(x19481,x19482)+E(f776(x19481,x19483),f776(x19482,x19483)) % 169.39/169.67 [1949]~E(x19491,x19492)+E(f776(x19493,x19491),f776(x19493,x19492)) % 169.39/169.67 [1950]~E(x19501,x19502)+E(f777(x19501,x19503,x19504,x19505),f777(x19502,x19503,x19504,x19505)) % 169.39/169.67 [1951]~E(x19511,x19512)+E(f777(x19513,x19511,x19514,x19515),f777(x19513,x19512,x19514,x19515)) % 169.39/169.67 [1952]~E(x19521,x19522)+E(f777(x19523,x19524,x19521,x19525),f777(x19523,x19524,x19522,x19525)) % 169.39/169.67 [1953]~E(x19531,x19532)+E(f777(x19533,x19534,x19535,x19531),f777(x19533,x19534,x19535,x19532)) % 169.39/169.67 [1954]~E(x19541,x19542)+E(f859(x19541),f859(x19542)) % 169.39/169.67 [1955]~E(x19551,x19552)+E(f205(x19551,x19553,x19554,x19555),f205(x19552,x19553,x19554,x19555)) % 169.39/169.67 [1956]~E(x19561,x19562)+E(f205(x19563,x19561,x19564,x19565),f205(x19563,x19562,x19564,x19565)) % 169.39/169.67 [1957]~E(x19571,x19572)+E(f205(x19573,x19574,x19571,x19575),f205(x19573,x19574,x19572,x19575)) % 169.39/169.67 [1958]~E(x19581,x19582)+E(f205(x19583,x19584,x19585,x19581),f205(x19583,x19584,x19585,x19582)) % 169.39/169.67 [1959]~E(x19591,x19592)+E(f680(x19591,x19593),f680(x19592,x19593)) % 169.39/169.67 [1960]~E(x19601,x19602)+E(f680(x19603,x19601),f680(x19603,x19602)) % 169.39/169.67 [1961]~E(x19611,x19612)+E(f709(x19611),f709(x19612)) % 169.39/169.67 [1962]~E(x19621,x19622)+E(f836(x19621,x19623,x19624),f836(x19622,x19623,x19624)) % 169.39/169.67 [1963]~E(x19631,x19632)+E(f836(x19633,x19631,x19634),f836(x19633,x19632,x19634)) % 169.39/169.67 [1964]~E(x19641,x19642)+E(f836(x19643,x19644,x19641),f836(x19643,x19644,x19642)) % 169.39/169.67 [1965]~E(x19651,x19652)+E(f633(x19651,x19653),f633(x19652,x19653)) % 169.39/169.67 [1966]~E(x19661,x19662)+E(f633(x19663,x19661),f633(x19663,x19662)) % 169.39/169.67 [1967]~E(x19671,x19672)+E(f834(x19671,x19673),f834(x19672,x19673)) % 169.39/169.67 [1968]~E(x19681,x19682)+E(f834(x19683,x19681),f834(x19683,x19682)) % 169.39/169.67 [1969]~E(x19691,x19692)+E(f850(x19691,x19693,x19694,x19695),f850(x19692,x19693,x19694,x19695)) % 169.39/169.67 [1970]~E(x19701,x19702)+E(f850(x19703,x19701,x19704,x19705),f850(x19703,x19702,x19704,x19705)) % 169.39/169.67 [1971]~E(x19711,x19712)+E(f850(x19713,x19714,x19711,x19715),f850(x19713,x19714,x19712,x19715)) % 169.39/169.67 [1972]~E(x19721,x19722)+E(f850(x19723,x19724,x19725,x19721),f850(x19723,x19724,x19725,x19722)) % 169.39/169.67 [1973]~E(x19731,x19732)+E(f749(x19731,x19733,x19734,x19735,x19736),f749(x19732,x19733,x19734,x19735,x19736)) % 169.39/169.67 [1974]~E(x19741,x19742)+E(f749(x19743,x19741,x19744,x19745,x19746),f749(x19743,x19742,x19744,x19745,x19746)) % 169.39/169.67 [1975]~E(x19751,x19752)+E(f749(x19753,x19754,x19751,x19755,x19756),f749(x19753,x19754,x19752,x19755,x19756)) % 169.39/169.67 [1976]~E(x19761,x19762)+E(f749(x19763,x19764,x19765,x19761,x19766),f749(x19763,x19764,x19765,x19762,x19766)) % 169.39/169.67 [1977]~E(x19771,x19772)+E(f749(x19773,x19774,x19775,x19776,x19771),f749(x19773,x19774,x19775,x19776,x19772)) % 169.39/169.67 [1978]~E(x19781,x19782)+E(f572(x19781,x19783),f572(x19782,x19783)) % 169.39/169.67 [1979]~E(x19791,x19792)+E(f572(x19793,x19791),f572(x19793,x19792)) % 169.39/169.67 [1980]~E(x19801,x19802)+E(f453(x19801,x19803,x19804),f453(x19802,x19803,x19804)) % 169.39/169.67 [1981]~E(x19811,x19812)+E(f453(x19813,x19811,x19814),f453(x19813,x19812,x19814)) % 169.39/169.67 [1982]~E(x19821,x19822)+E(f453(x19823,x19824,x19821),f453(x19823,x19824,x19822)) % 169.39/169.67 [1983]~E(x19831,x19832)+E(f706(x19831,x19833,x19834,x19835,x19836),f706(x19832,x19833,x19834,x19835,x19836)) % 169.39/169.67 [1984]~E(x19841,x19842)+E(f706(x19843,x19841,x19844,x19845,x19846),f706(x19843,x19842,x19844,x19845,x19846)) % 169.39/169.67 [1985]~E(x19851,x19852)+E(f706(x19853,x19854,x19851,x19855,x19856),f706(x19853,x19854,x19852,x19855,x19856)) % 169.39/169.67 [1986]~E(x19861,x19862)+E(f706(x19863,x19864,x19865,x19861,x19866),f706(x19863,x19864,x19865,x19862,x19866)) % 169.39/169.67 [1987]~E(x19871,x19872)+E(f706(x19873,x19874,x19875,x19876,x19871),f706(x19873,x19874,x19875,x19876,x19872)) % 169.39/169.67 [1988]~E(x19881,x19882)+E(f691(x19881,x19883,x19884,x19885),f691(x19882,x19883,x19884,x19885)) % 169.39/169.67 [1989]~E(x19891,x19892)+E(f691(x19893,x19891,x19894,x19895),f691(x19893,x19892,x19894,x19895)) % 169.39/169.67 [1990]~E(x19901,x19902)+E(f691(x19903,x19904,x19901,x19905),f691(x19903,x19904,x19902,x19905)) % 169.39/169.67 [1991]~E(x19911,x19912)+E(f691(x19913,x19914,x19915,x19911),f691(x19913,x19914,x19915,x19912)) % 169.39/169.67 [1992]~E(x19921,x19922)+E(f731(x19921,x19923),f731(x19922,x19923)) % 169.39/169.67 [1993]~E(x19931,x19932)+E(f731(x19933,x19931),f731(x19933,x19932)) % 169.39/169.67 [1994]~E(x19941,x19942)+E(f392(x19941,x19943),f392(x19942,x19943)) % 169.39/169.67 [1995]~E(x19951,x19952)+E(f392(x19953,x19951),f392(x19953,x19952)) % 169.39/169.67 [1996]~E(x19961,x19962)+E(f779(x19961,x19963,x19964,x19965,x19966),f779(x19962,x19963,x19964,x19965,x19966)) % 169.39/169.67 [1997]~E(x19971,x19972)+E(f779(x19973,x19971,x19974,x19975,x19976),f779(x19973,x19972,x19974,x19975,x19976)) % 169.39/169.67 [1998]~E(x19981,x19982)+E(f779(x19983,x19984,x19981,x19985,x19986),f779(x19983,x19984,x19982,x19985,x19986)) % 169.39/169.67 [1999]~E(x19991,x19992)+E(f779(x19993,x19994,x19995,x19991,x19996),f779(x19993,x19994,x19995,x19992,x19996)) % 169.39/169.67 [2000]~E(x20001,x20002)+E(f779(x20003,x20004,x20005,x20006,x20001),f779(x20003,x20004,x20005,x20006,x20002)) % 169.39/169.67 [2001]~E(x20011,x20012)+E(f182(x20011),f182(x20012)) % 169.39/169.67 [2002]~E(x20021,x20022)+E(f842(x20021,x20023,x20024,x20025,x20026,x20027),f842(x20022,x20023,x20024,x20025,x20026,x20027)) % 169.39/169.67 [2003]~E(x20031,x20032)+E(f842(x20033,x20031,x20034,x20035,x20036,x20037),f842(x20033,x20032,x20034,x20035,x20036,x20037)) % 169.39/169.67 [2004]~E(x20041,x20042)+E(f842(x20043,x20044,x20041,x20045,x20046,x20047),f842(x20043,x20044,x20042,x20045,x20046,x20047)) % 169.39/169.67 [2005]~E(x20051,x20052)+E(f842(x20053,x20054,x20055,x20051,x20056,x20057),f842(x20053,x20054,x20055,x20052,x20056,x20057)) % 169.39/169.67 [2006]~E(x20061,x20062)+E(f842(x20063,x20064,x20065,x20066,x20061,x20067),f842(x20063,x20064,x20065,x20066,x20062,x20067)) % 169.39/169.67 [2007]~E(x20071,x20072)+E(f842(x20073,x20074,x20075,x20076,x20077,x20071),f842(x20073,x20074,x20075,x20076,x20077,x20072)) % 169.39/169.67 [2008]~E(x20081,x20082)+E(f416(x20081,x20083,x20084),f416(x20082,x20083,x20084)) % 169.39/169.67 [2009]~E(x20091,x20092)+E(f416(x20093,x20091,x20094),f416(x20093,x20092,x20094)) % 169.39/169.67 [2010]~E(x20101,x20102)+E(f416(x20103,x20104,x20101),f416(x20103,x20104,x20102)) % 169.39/169.67 [2011]~E(x20111,x20112)+E(f496(x20111,x20113,x20114),f496(x20112,x20113,x20114)) % 169.39/169.67 [2012]~E(x20121,x20122)+E(f496(x20123,x20121,x20124),f496(x20123,x20122,x20124)) % 169.39/169.67 [2013]~E(x20131,x20132)+E(f496(x20133,x20134,x20131),f496(x20133,x20134,x20132)) % 169.39/169.67 [2014]~E(x20141,x20142)+E(f663(x20141,x20143,x20144,x20145,x20146),f663(x20142,x20143,x20144,x20145,x20146)) % 169.39/169.67 [2015]~E(x20151,x20152)+E(f663(x20153,x20151,x20154,x20155,x20156),f663(x20153,x20152,x20154,x20155,x20156)) % 169.39/169.67 [2016]~E(x20161,x20162)+E(f663(x20163,x20164,x20161,x20165,x20166),f663(x20163,x20164,x20162,x20165,x20166)) % 169.39/169.67 [2017]~E(x20171,x20172)+E(f663(x20173,x20174,x20175,x20171,x20176),f663(x20173,x20174,x20175,x20172,x20176)) % 169.39/169.67 [2018]~E(x20181,x20182)+E(f663(x20183,x20184,x20185,x20186,x20181),f663(x20183,x20184,x20185,x20186,x20182)) % 169.39/169.67 [2019]~E(x20191,x20192)+E(f211(x20191,x20193),f211(x20192,x20193)) % 169.39/169.67 [2020]~E(x20201,x20202)+E(f211(x20203,x20201),f211(x20203,x20202)) % 169.39/169.67 [2021]~E(x20211,x20212)+E(f774(x20211,x20213,x20214,x20215,x20216),f774(x20212,x20213,x20214,x20215,x20216)) % 169.39/169.67 [2022]~E(x20221,x20222)+E(f774(x20223,x20221,x20224,x20225,x20226),f774(x20223,x20222,x20224,x20225,x20226)) % 169.39/169.67 [2023]~E(x20231,x20232)+E(f774(x20233,x20234,x20231,x20235,x20236),f774(x20233,x20234,x20232,x20235,x20236)) % 169.39/169.67 [2024]~E(x20241,x20242)+E(f774(x20243,x20244,x20245,x20241,x20246),f774(x20243,x20244,x20245,x20242,x20246)) % 169.39/169.67 [2025]~E(x20251,x20252)+E(f774(x20253,x20254,x20255,x20256,x20251),f774(x20253,x20254,x20255,x20256,x20252)) % 169.39/169.67 [2026]~E(x20261,x20262)+E(f678(x20261,x20263,x20264,x20265,x20266),f678(x20262,x20263,x20264,x20265,x20266)) % 169.39/169.67 [2027]~E(x20271,x20272)+E(f678(x20273,x20271,x20274,x20275,x20276),f678(x20273,x20272,x20274,x20275,x20276)) % 169.39/169.67 [2028]~E(x20281,x20282)+E(f678(x20283,x20284,x20281,x20285,x20286),f678(x20283,x20284,x20282,x20285,x20286)) % 169.39/169.67 [2029]~E(x20291,x20292)+E(f678(x20293,x20294,x20295,x20291,x20296),f678(x20293,x20294,x20295,x20292,x20296)) % 169.39/169.67 [2030]~E(x20301,x20302)+E(f678(x20303,x20304,x20305,x20306,x20301),f678(x20303,x20304,x20305,x20306,x20302)) % 169.39/169.67 [2031]~E(x20311,x20312)+E(f387(x20311,x20313,x20314,x20315),f387(x20312,x20313,x20314,x20315)) % 169.39/169.67 [2032]~E(x20321,x20322)+E(f387(x20323,x20321,x20324,x20325),f387(x20323,x20322,x20324,x20325)) % 169.39/169.67 [2033]~E(x20331,x20332)+E(f387(x20333,x20334,x20331,x20335),f387(x20333,x20334,x20332,x20335)) % 169.39/169.67 [2034]~E(x20341,x20342)+E(f387(x20343,x20344,x20345,x20341),f387(x20343,x20344,x20345,x20342)) % 169.39/169.67 [2035]~E(x20351,x20352)+E(f616(x20351,x20353,x20354,x20355,x20356),f616(x20352,x20353,x20354,x20355,x20356)) % 169.39/169.67 [2036]~E(x20361,x20362)+E(f616(x20363,x20361,x20364,x20365,x20366),f616(x20363,x20362,x20364,x20365,x20366)) % 169.39/169.67 [2037]~E(x20371,x20372)+E(f616(x20373,x20374,x20371,x20375,x20376),f616(x20373,x20374,x20372,x20375,x20376)) % 169.39/169.67 [2038]~E(x20381,x20382)+E(f616(x20383,x20384,x20385,x20381,x20386),f616(x20383,x20384,x20385,x20382,x20386)) % 169.39/169.67 [2039]~E(x20391,x20392)+E(f616(x20393,x20394,x20395,x20396,x20391),f616(x20393,x20394,x20395,x20396,x20392)) % 169.39/169.67 [2040]~E(x20401,x20402)+E(f214(x20401,x20403,x20404,x20405),f214(x20402,x20403,x20404,x20405)) % 169.39/169.67 [2041]~E(x20411,x20412)+E(f214(x20413,x20411,x20414,x20415),f214(x20413,x20412,x20414,x20415)) % 169.39/169.67 [2042]~E(x20421,x20422)+E(f214(x20423,x20424,x20421,x20425),f214(x20423,x20424,x20422,x20425)) % 169.39/169.67 [2043]~E(x20431,x20432)+E(f214(x20433,x20434,x20435,x20431),f214(x20433,x20434,x20435,x20432)) % 169.39/169.67 [2044]~E(x20441,x20442)+E(f827(x20441,x20443),f827(x20442,x20443)) % 169.39/169.67 [2045]~E(x20451,x20452)+E(f827(x20453,x20451),f827(x20453,x20452)) % 169.39/169.67 [2046]~E(x20461,x20462)+E(f614(x20461,x20463,x20464,x20465),f614(x20462,x20463,x20464,x20465)) % 169.39/169.67 [2047]~E(x20471,x20472)+E(f614(x20473,x20471,x20474,x20475),f614(x20473,x20472,x20474,x20475)) % 169.39/169.67 [2048]~E(x20481,x20482)+E(f614(x20483,x20484,x20481,x20485),f614(x20483,x20484,x20482,x20485)) % 169.39/169.67 [2049]~E(x20491,x20492)+E(f614(x20493,x20494,x20495,x20491),f614(x20493,x20494,x20495,x20492)) % 169.39/169.67 [2050]~E(x20501,x20502)+E(f642(x20501,x20503,x20504,x20505,x20506),f642(x20502,x20503,x20504,x20505,x20506)) % 169.39/169.67 [2051]~E(x20511,x20512)+E(f642(x20513,x20511,x20514,x20515,x20516),f642(x20513,x20512,x20514,x20515,x20516)) % 169.39/169.67 [2052]~E(x20521,x20522)+E(f642(x20523,x20524,x20521,x20525,x20526),f642(x20523,x20524,x20522,x20525,x20526)) % 169.39/169.67 [2053]~E(x20531,x20532)+E(f642(x20533,x20534,x20535,x20531,x20536),f642(x20533,x20534,x20535,x20532,x20536)) % 169.39/169.67 [2054]~E(x20541,x20542)+E(f642(x20543,x20544,x20545,x20546,x20541),f642(x20543,x20544,x20545,x20546,x20542)) % 169.39/169.67 [2055]~E(x20551,x20552)+E(f574(x20551,x20553),f574(x20552,x20553)) % 169.39/169.67 [2056]~E(x20561,x20562)+E(f574(x20563,x20561),f574(x20563,x20562)) % 169.39/169.67 [2057]~E(x20571,x20572)+E(f233(x20571,x20573,x20574,x20575,x20576),f233(x20572,x20573,x20574,x20575,x20576)) % 169.39/169.67 [2058]~E(x20581,x20582)+E(f233(x20583,x20581,x20584,x20585,x20586),f233(x20583,x20582,x20584,x20585,x20586)) % 169.39/169.67 [2059]~E(x20591,x20592)+E(f233(x20593,x20594,x20591,x20595,x20596),f233(x20593,x20594,x20592,x20595,x20596)) % 169.39/169.67 [2060]~E(x20601,x20602)+E(f233(x20603,x20604,x20605,x20601,x20606),f233(x20603,x20604,x20605,x20602,x20606)) % 169.39/169.67 [2061]~E(x20611,x20612)+E(f233(x20613,x20614,x20615,x20616,x20611),f233(x20613,x20614,x20615,x20616,x20612)) % 169.39/169.67 [2062]~E(x20621,x20622)+E(f536(x20621,x20623,x20624,x20625,x20626),f536(x20622,x20623,x20624,x20625,x20626)) % 169.39/169.67 [2063]~E(x20631,x20632)+E(f536(x20633,x20631,x20634,x20635,x20636),f536(x20633,x20632,x20634,x20635,x20636)) % 169.39/169.67 [2064]~E(x20641,x20642)+E(f536(x20643,x20644,x20641,x20645,x20646),f536(x20643,x20644,x20642,x20645,x20646)) % 169.39/169.67 [2065]~E(x20651,x20652)+E(f536(x20653,x20654,x20655,x20651,x20656),f536(x20653,x20654,x20655,x20652,x20656)) % 169.39/169.67 [2066]~E(x20661,x20662)+E(f536(x20663,x20664,x20665,x20666,x20661),f536(x20663,x20664,x20665,x20666,x20662)) % 169.39/169.67 [2067]~E(x20671,x20672)+E(f692(x20671,x20673,x20674,x20675),f692(x20672,x20673,x20674,x20675)) % 169.39/169.67 [2068]~E(x20681,x20682)+E(f692(x20683,x20681,x20684,x20685),f692(x20683,x20682,x20684,x20685)) % 169.39/169.67 [2069]~E(x20691,x20692)+E(f692(x20693,x20694,x20691,x20695),f692(x20693,x20694,x20692,x20695)) % 169.39/169.67 [2070]~E(x20701,x20702)+E(f692(x20703,x20704,x20705,x20701),f692(x20703,x20704,x20705,x20702)) % 169.39/169.67 [2071]~E(x20711,x20712)+E(f716(x20711,x20713),f716(x20712,x20713)) % 169.39/169.67 [2072]~E(x20721,x20722)+E(f716(x20723,x20721),f716(x20723,x20722)) % 169.39/169.67 [2073]~E(x20731,x20732)+E(f458(x20731,x20733,x20734,x20735),f458(x20732,x20733,x20734,x20735)) % 169.39/169.67 [2074]~E(x20741,x20742)+E(f458(x20743,x20741,x20744,x20745),f458(x20743,x20742,x20744,x20745)) % 169.39/169.67 [2075]~E(x20751,x20752)+E(f458(x20753,x20754,x20751,x20755),f458(x20753,x20754,x20752,x20755)) % 169.39/169.67 [2076]~E(x20761,x20762)+E(f458(x20763,x20764,x20765,x20761),f458(x20763,x20764,x20765,x20762)) % 169.39/169.67 [2077]~E(x20771,x20772)+E(f54(x20771,x20773),f54(x20772,x20773)) % 169.39/169.67 [2078]~E(x20781,x20782)+E(f54(x20783,x20781),f54(x20783,x20782)) % 169.39/169.67 [2079]~E(x20791,x20792)+E(f365(x20791,x20793),f365(x20792,x20793)) % 169.39/169.67 [2080]~E(x20801,x20802)+E(f365(x20803,x20801),f365(x20803,x20802)) % 169.39/169.67 [2081]~E(x20811,x20812)+E(f346(x20811,x20813,x20814),f346(x20812,x20813,x20814)) % 169.39/169.67 [2082]~E(x20821,x20822)+E(f346(x20823,x20821,x20824),f346(x20823,x20822,x20824)) % 169.39/169.67 [2083]~E(x20831,x20832)+E(f346(x20833,x20834,x20831),f346(x20833,x20834,x20832)) % 169.39/169.67 [2084]~E(x20841,x20842)+E(f456(x20841,x20843,x20844,x20845),f456(x20842,x20843,x20844,x20845)) % 169.39/169.67 [2085]~E(x20851,x20852)+E(f456(x20853,x20851,x20854,x20855),f456(x20853,x20852,x20854,x20855)) % 169.39/169.67 [2086]~E(x20861,x20862)+E(f456(x20863,x20864,x20861,x20865),f456(x20863,x20864,x20862,x20865)) % 169.39/169.67 [2087]~E(x20871,x20872)+E(f456(x20873,x20874,x20875,x20871),f456(x20873,x20874,x20875,x20872)) % 169.39/169.67 [2088]~E(x20881,x20882)+E(f727(x20881,x20883,x20884,x20885,x20886,x20887),f727(x20882,x20883,x20884,x20885,x20886,x20887)) % 169.39/169.67 [2089]~E(x20891,x20892)+E(f727(x20893,x20891,x20894,x20895,x20896,x20897),f727(x20893,x20892,x20894,x20895,x20896,x20897)) % 169.39/169.67 [2090]~E(x20901,x20902)+E(f727(x20903,x20904,x20901,x20905,x20906,x20907),f727(x20903,x20904,x20902,x20905,x20906,x20907)) % 169.39/169.67 [2091]~E(x20911,x20912)+E(f727(x20913,x20914,x20915,x20911,x20916,x20917),f727(x20913,x20914,x20915,x20912,x20916,x20917)) % 169.39/169.67 [2092]~E(x20921,x20922)+E(f727(x20923,x20924,x20925,x20926,x20921,x20927),f727(x20923,x20924,x20925,x20926,x20922,x20927)) % 169.39/169.67 [2093]~E(x20931,x20932)+E(f727(x20933,x20934,x20935,x20936,x20937,x20931),f727(x20933,x20934,x20935,x20936,x20937,x20932)) % 169.39/169.67 [2094]~E(x20941,x20942)+E(f494(x20941,x20943),f494(x20942,x20943)) % 169.39/169.67 [2095]~E(x20951,x20952)+E(f494(x20953,x20951),f494(x20953,x20952)) % 169.39/169.67 [2096]~E(x20961,x20962)+E(f856(x20961),f856(x20962)) % 169.39/169.67 [2097]~E(x20971,x20972)+E(f383(x20971,x20973,x20974,x20975),f383(x20972,x20973,x20974,x20975)) % 169.39/169.67 [2098]~E(x20981,x20982)+E(f383(x20983,x20981,x20984,x20985),f383(x20983,x20982,x20984,x20985)) % 169.39/169.67 [2099]~E(x20991,x20992)+E(f383(x20993,x20994,x20991,x20995),f383(x20993,x20994,x20992,x20995)) % 169.39/169.67 [2100]~E(x21001,x21002)+E(f383(x21003,x21004,x21005,x21001),f383(x21003,x21004,x21005,x21002)) % 169.39/169.67 [2101]~E(x21011,x21012)+E(f470(x21011,x21013),f470(x21012,x21013)) % 169.39/169.67 [2102]~E(x21021,x21022)+E(f470(x21023,x21021),f470(x21023,x21022)) % 169.39/169.67 [2103]~E(x21031,x21032)+E(f590(x21031,x21033,x21034,x21035,x21036,x21037),f590(x21032,x21033,x21034,x21035,x21036,x21037)) % 169.39/169.67 [2104]~E(x21041,x21042)+E(f590(x21043,x21041,x21044,x21045,x21046,x21047),f590(x21043,x21042,x21044,x21045,x21046,x21047)) % 169.39/169.67 [2105]~E(x21051,x21052)+E(f590(x21053,x21054,x21051,x21055,x21056,x21057),f590(x21053,x21054,x21052,x21055,x21056,x21057)) % 169.39/169.67 [2106]~E(x21061,x21062)+E(f590(x21063,x21064,x21065,x21061,x21066,x21067),f590(x21063,x21064,x21065,x21062,x21066,x21067)) % 169.39/169.67 [2107]~E(x21071,x21072)+E(f590(x21073,x21074,x21075,x21076,x21071,x21077),f590(x21073,x21074,x21075,x21076,x21072,x21077)) % 169.39/169.67 [2108]~E(x21081,x21082)+E(f590(x21083,x21084,x21085,x21086,x21087,x21081),f590(x21083,x21084,x21085,x21086,x21087,x21082)) % 169.39/169.67 [2109]~E(x21091,x21092)+E(f580(x21091,x21093),f580(x21092,x21093)) % 169.39/169.67 [2110]~E(x21101,x21102)+E(f580(x21103,x21101),f580(x21103,x21102)) % 169.39/169.67 [2111]~E(x21111,x21112)+E(f837(x21111,x21113,x21114,x21115,x21116,x21117,x21118),f837(x21112,x21113,x21114,x21115,x21116,x21117,x21118)) % 169.39/169.67 [2112]~E(x21121,x21122)+E(f837(x21123,x21121,x21124,x21125,x21126,x21127,x21128),f837(x21123,x21122,x21124,x21125,x21126,x21127,x21128)) % 169.39/169.67 [2113]~E(x21131,x21132)+E(f837(x21133,x21134,x21131,x21135,x21136,x21137,x21138),f837(x21133,x21134,x21132,x21135,x21136,x21137,x21138)) % 169.39/169.67 [2114]~E(x21141,x21142)+E(f837(x21143,x21144,x21145,x21141,x21146,x21147,x21148),f837(x21143,x21144,x21145,x21142,x21146,x21147,x21148)) % 169.39/169.67 [2115]~E(x21151,x21152)+E(f837(x21153,x21154,x21155,x21156,x21151,x21157,x21158),f837(x21153,x21154,x21155,x21156,x21152,x21157,x21158)) % 169.39/169.67 [2116]~E(x21161,x21162)+E(f837(x21163,x21164,x21165,x21166,x21167,x21161,x21168),f837(x21163,x21164,x21165,x21166,x21167,x21162,x21168)) % 169.39/169.67 [2117]~E(x21171,x21172)+E(f837(x21173,x21174,x21175,x21176,x21177,x21178,x21171),f837(x21173,x21174,x21175,x21176,x21177,x21178,x21172)) % 169.39/169.67 [2118]~E(x21181,x21182)+E(f410(x21181,x21183),f410(x21182,x21183)) % 169.39/169.67 [2119]~E(x21191,x21192)+E(f410(x21193,x21191),f410(x21193,x21192)) % 169.39/169.67 [2120]~E(x21201,x21202)+E(f426(x21201,x21203,x21204),f426(x21202,x21203,x21204)) % 169.39/169.67 [2121]~E(x21211,x21212)+E(f426(x21213,x21211,x21214),f426(x21213,x21212,x21214)) % 169.39/169.67 [2122]~E(x21221,x21222)+E(f426(x21223,x21224,x21221),f426(x21223,x21224,x21222)) % 169.39/169.67 [2123]~E(x21231,x21232)+E(f433(x21231,x21233,x21234,x21235,x21236),f433(x21232,x21233,x21234,x21235,x21236)) % 169.39/169.67 [2124]~E(x21241,x21242)+E(f433(x21243,x21241,x21244,x21245,x21246),f433(x21243,x21242,x21244,x21245,x21246)) % 169.39/169.67 [2125]~E(x21251,x21252)+E(f433(x21253,x21254,x21251,x21255,x21256),f433(x21253,x21254,x21252,x21255,x21256)) % 169.39/169.67 [2126]~E(x21261,x21262)+E(f433(x21263,x21264,x21265,x21261,x21266),f433(x21263,x21264,x21265,x21262,x21266)) % 169.39/169.67 [2127]~E(x21271,x21272)+E(f433(x21273,x21274,x21275,x21276,x21271),f433(x21273,x21274,x21275,x21276,x21272)) % 169.39/169.67 [2128]~E(x21281,x21282)+E(f212(x21281,x21283,x21284),f212(x21282,x21283,x21284)) % 169.39/169.67 [2129]~E(x21291,x21292)+E(f212(x21293,x21291,x21294),f212(x21293,x21292,x21294)) % 169.39/169.67 [2130]~E(x21301,x21302)+E(f212(x21303,x21304,x21301),f212(x21303,x21304,x21302)) % 169.39/169.67 [2131]~E(x21311,x21312)+E(f866(x21311,x21313,x21314),f866(x21312,x21313,x21314)) % 169.39/169.67 [2132]~E(x21321,x21322)+E(f866(x21323,x21321,x21324),f866(x21323,x21322,x21324)) % 169.39/169.67 [2133]~E(x21331,x21332)+E(f866(x21333,x21334,x21331),f866(x21333,x21334,x21332)) % 169.39/169.67 [2134]~E(x21341,x21342)+E(f573(x21341,x21343),f573(x21342,x21343)) % 169.39/169.67 [2135]~E(x21351,x21352)+E(f573(x21353,x21351),f573(x21353,x21352)) % 169.39/169.67 [2136]~E(x21361,x21362)+E(f540(x21361,x21363,x21364),f540(x21362,x21363,x21364)) % 169.39/169.67 [2137]~E(x21371,x21372)+E(f540(x21373,x21371,x21374),f540(x21373,x21372,x21374)) % 169.39/169.67 [2138]~E(x21381,x21382)+E(f540(x21383,x21384,x21381),f540(x21383,x21384,x21382)) % 169.39/169.67 [2139]~E(x21391,x21392)+E(f578(x21391,x21393,x21394),f578(x21392,x21393,x21394)) % 169.39/169.67 [2140]~E(x21401,x21402)+E(f578(x21403,x21401,x21404),f578(x21403,x21402,x21404)) % 169.39/169.67 [2141]~E(x21411,x21412)+E(f578(x21413,x21414,x21411),f578(x21413,x21414,x21412)) % 169.39/169.67 [2142]~E(x21421,x21422)+E(f360(x21421,x21423,x21424),f360(x21422,x21423,x21424)) % 169.39/169.67 [2143]~E(x21431,x21432)+E(f360(x21433,x21431,x21434),f360(x21433,x21432,x21434)) % 169.39/169.67 [2144]~E(x21441,x21442)+E(f360(x21443,x21444,x21441),f360(x21443,x21444,x21442)) % 169.39/169.67 [2145]~E(x21451,x21452)+E(f607(x21451,x21453,x21454),f607(x21452,x21453,x21454)) % 169.39/169.67 [2146]~E(x21461,x21462)+E(f607(x21463,x21461,x21464),f607(x21463,x21462,x21464)) % 169.39/169.67 [2147]~E(x21471,x21472)+E(f607(x21473,x21474,x21471),f607(x21473,x21474,x21472)) % 169.39/169.67 [2148]~E(x21481,x21482)+E(f375(x21481,x21483,x21484,x21485),f375(x21482,x21483,x21484,x21485)) % 169.39/169.67 [2149]~E(x21491,x21492)+E(f375(x21493,x21491,x21494,x21495),f375(x21493,x21492,x21494,x21495)) % 169.39/169.67 [2150]~E(x21501,x21502)+E(f375(x21503,x21504,x21501,x21505),f375(x21503,x21504,x21502,x21505)) % 169.39/169.67 [2151]~E(x21511,x21512)+E(f375(x21513,x21514,x21515,x21511),f375(x21513,x21514,x21515,x21512)) % 169.39/169.67 [2152]~E(x21521,x21522)+E(f746(x21521,x21523,x21524),f746(x21522,x21523,x21524)) % 169.39/169.67 [2153]~E(x21531,x21532)+E(f746(x21533,x21531,x21534),f746(x21533,x21532,x21534)) % 169.39/169.67 [2154]~E(x21541,x21542)+E(f746(x21543,x21544,x21541),f746(x21543,x21544,x21542)) % 169.39/169.67 [2155]~E(x21551,x21552)+E(f597(x21551,x21553,x21554),f597(x21552,x21553,x21554)) % 169.39/169.67 [2156]~E(x21561,x21562)+E(f597(x21563,x21561,x21564),f597(x21563,x21562,x21564)) % 169.39/169.67 [2157]~E(x21571,x21572)+E(f597(x21573,x21574,x21571),f597(x21573,x21574,x21572)) % 169.39/169.67 [2158]~E(x21581,x21582)+E(f96(x21581,x21583,x21584),f96(x21582,x21583,x21584)) % 169.39/169.67 [2159]~E(x21591,x21592)+E(f96(x21593,x21591,x21594),f96(x21593,x21592,x21594)) % 169.39/169.67 [2160]~E(x21601,x21602)+E(f96(x21603,x21604,x21601),f96(x21603,x21604,x21602)) % 169.39/169.67 [2161]~E(x21611,x21612)+E(f557(x21611,x21613,x21614,x21615,x21616),f557(x21612,x21613,x21614,x21615,x21616)) % 169.39/169.67 [2162]~E(x21621,x21622)+E(f557(x21623,x21621,x21624,x21625,x21626),f557(x21623,x21622,x21624,x21625,x21626)) % 169.39/169.67 [2163]~E(x21631,x21632)+E(f557(x21633,x21634,x21631,x21635,x21636),f557(x21633,x21634,x21632,x21635,x21636)) % 169.39/169.67 [2164]~E(x21641,x21642)+E(f557(x21643,x21644,x21645,x21641,x21646),f557(x21643,x21644,x21645,x21642,x21646)) % 169.39/169.67 [2165]~E(x21651,x21652)+E(f557(x21653,x21654,x21655,x21656,x21651),f557(x21653,x21654,x21655,x21656,x21652)) % 169.39/169.67 [2166]~E(x21661,x21662)+E(f513(x21661,x21663,x21664,x21665),f513(x21662,x21663,x21664,x21665)) % 169.39/169.67 [2167]~E(x21671,x21672)+E(f513(x21673,x21671,x21674,x21675),f513(x21673,x21672,x21674,x21675)) % 169.39/169.67 [2168]~E(x21681,x21682)+E(f513(x21683,x21684,x21681,x21685),f513(x21683,x21684,x21682,x21685)) % 169.39/169.67 [2169]~E(x21691,x21692)+E(f513(x21693,x21694,x21695,x21691),f513(x21693,x21694,x21695,x21692)) % 169.39/169.67 [2170]~E(x21701,x21702)+E(f469(x21701,x21703,x21704),f469(x21702,x21703,x21704)) % 169.39/169.67 [2171]~E(x21711,x21712)+E(f469(x21713,x21711,x21714),f469(x21713,x21712,x21714)) % 169.39/169.67 [2172]~E(x21721,x21722)+E(f469(x21723,x21724,x21721),f469(x21723,x21724,x21722)) % 169.39/169.67 [2173]~E(x21731,x21732)+E(f483(x21731,x21733,x21734),f483(x21732,x21733,x21734)) % 169.39/169.67 [2174]~E(x21741,x21742)+E(f483(x21743,x21741,x21744),f483(x21743,x21742,x21744)) % 169.39/169.67 [2175]~E(x21751,x21752)+E(f483(x21753,x21754,x21751),f483(x21753,x21754,x21752)) % 169.39/169.67 [2176]~E(x21761,x21762)+E(f624(x21761,x21763,x21764),f624(x21762,x21763,x21764)) % 169.39/169.67 [2177]~E(x21771,x21772)+E(f624(x21773,x21771,x21774),f624(x21773,x21772,x21774)) % 169.39/169.67 [2178]~E(x21781,x21782)+E(f624(x21783,x21784,x21781),f624(x21783,x21784,x21782)) % 169.39/169.67 [2179]~E(x21791,x21792)+E(f658(x21791,x21793,x21794),f658(x21792,x21793,x21794)) % 169.39/169.67 [2180]~E(x21801,x21802)+E(f658(x21803,x21801,x21804),f658(x21803,x21802,x21804)) % 169.39/169.67 [2181]~E(x21811,x21812)+E(f658(x21813,x21814,x21811),f658(x21813,x21814,x21812)) % 169.39/169.67 [2182]~E(x21821,x21822)+E(f838(x21821,x21823,x21824),f838(x21822,x21823,x21824)) % 169.39/169.67 [2183]~E(x21831,x21832)+E(f838(x21833,x21831,x21834),f838(x21833,x21832,x21834)) % 169.39/169.67 [2184]~E(x21841,x21842)+E(f838(x21843,x21844,x21841),f838(x21843,x21844,x21842)) % 169.39/169.67 [2185]~E(x21851,x21852)+E(f369(x21851,x21853,x21854),f369(x21852,x21853,x21854)) % 169.39/169.67 [2186]~E(x21861,x21862)+E(f369(x21863,x21861,x21864),f369(x21863,x21862,x21864)) % 169.39/169.67 [2187]~E(x21871,x21872)+E(f369(x21873,x21874,x21871),f369(x21873,x21874,x21872)) % 169.39/169.67 [2188]~E(x21881,x21882)+E(f621(x21881,x21883,x21884),f621(x21882,x21883,x21884)) % 169.39/169.67 [2189]~E(x21891,x21892)+E(f621(x21893,x21891,x21894),f621(x21893,x21892,x21894)) % 169.39/169.67 [2190]~E(x21901,x21902)+E(f621(x21903,x21904,x21901),f621(x21903,x21904,x21902)) % 169.39/169.67 [2191]~E(x21911,x21912)+E(f701(x21911,x21913,x21914,x21915,x21916,x21917),f701(x21912,x21913,x21914,x21915,x21916,x21917)) % 169.39/169.67 [2192]~E(x21921,x21922)+E(f701(x21923,x21921,x21924,x21925,x21926,x21927),f701(x21923,x21922,x21924,x21925,x21926,x21927)) % 169.39/169.67 [2193]~E(x21931,x21932)+E(f701(x21933,x21934,x21931,x21935,x21936,x21937),f701(x21933,x21934,x21932,x21935,x21936,x21937)) % 169.39/169.67 [2194]~E(x21941,x21942)+E(f701(x21943,x21944,x21945,x21941,x21946,x21947),f701(x21943,x21944,x21945,x21942,x21946,x21947)) % 169.39/169.67 [2195]~E(x21951,x21952)+E(f701(x21953,x21954,x21955,x21956,x21951,x21957),f701(x21953,x21954,x21955,x21956,x21952,x21957)) % 169.39/169.67 [2196]~E(x21961,x21962)+E(f701(x21963,x21964,x21965,x21966,x21967,x21961),f701(x21963,x21964,x21965,x21966,x21967,x21962)) % 169.39/169.67 [2197]~E(x21971,x21972)+E(f739(x21971,x21973,x21974,x21975,x21976),f739(x21972,x21973,x21974,x21975,x21976)) % 169.39/169.67 [2198]~E(x21981,x21982)+E(f739(x21983,x21981,x21984,x21985,x21986),f739(x21983,x21982,x21984,x21985,x21986)) % 169.39/169.67 [2199]~E(x21991,x21992)+E(f739(x21993,x21994,x21991,x21995,x21996),f739(x21993,x21994,x21992,x21995,x21996)) % 169.39/169.67 [2200]~E(x22001,x22002)+E(f739(x22003,x22004,x22005,x22001,x22006),f739(x22003,x22004,x22005,x22002,x22006)) % 169.39/169.67 [2201]~E(x22011,x22012)+E(f739(x22013,x22014,x22015,x22016,x22011),f739(x22013,x22014,x22015,x22016,x22012)) % 169.39/169.67 [2202]~E(x22021,x22022)+E(f755(x22021,x22023,x22024,x22025,x22026),f755(x22022,x22023,x22024,x22025,x22026)) % 169.39/169.67 [2203]~E(x22031,x22032)+E(f755(x22033,x22031,x22034,x22035,x22036),f755(x22033,x22032,x22034,x22035,x22036)) % 169.39/169.67 [2204]~E(x22041,x22042)+E(f755(x22043,x22044,x22041,x22045,x22046),f755(x22043,x22044,x22042,x22045,x22046)) % 169.39/169.67 [2205]~E(x22051,x22052)+E(f755(x22053,x22054,x22055,x22051,x22056),f755(x22053,x22054,x22055,x22052,x22056)) % 169.39/169.67 [2206]~E(x22061,x22062)+E(f755(x22063,x22064,x22065,x22066,x22061),f755(x22063,x22064,x22065,x22066,x22062)) % 169.39/169.67 [2207]~E(x22071,x22072)+E(f235(x22071,x22073),f235(x22072,x22073)) % 169.39/169.67 [2208]~E(x22081,x22082)+E(f235(x22083,x22081),f235(x22083,x22082)) % 169.39/169.67 [2209]~E(x22091,x22092)+E(f671(x22091,x22093,x22094,x22095,x22096),f671(x22092,x22093,x22094,x22095,x22096)) % 169.39/169.67 [2210]~E(x22101,x22102)+E(f671(x22103,x22101,x22104,x22105,x22106),f671(x22103,x22102,x22104,x22105,x22106)) % 169.39/169.67 [2211]~E(x22111,x22112)+E(f671(x22113,x22114,x22111,x22115,x22116),f671(x22113,x22114,x22112,x22115,x22116)) % 169.39/169.67 [2212]~E(x22121,x22122)+E(f671(x22123,x22124,x22125,x22121,x22126),f671(x22123,x22124,x22125,x22122,x22126)) % 169.39/169.67 [2213]~E(x22131,x22132)+E(f671(x22133,x22134,x22135,x22136,x22131),f671(x22133,x22134,x22135,x22136,x22132)) % 169.39/169.67 [2214]~E(x22141,x22142)+E(f688(x22141,x22143,x22144,x22145),f688(x22142,x22143,x22144,x22145)) % 169.39/169.67 [2215]~E(x22151,x22152)+E(f688(x22153,x22151,x22154,x22155),f688(x22153,x22152,x22154,x22155)) % 169.39/169.67 [2216]~E(x22161,x22162)+E(f688(x22163,x22164,x22161,x22165),f688(x22163,x22164,x22162,x22165)) % 169.39/169.67 [2217]~E(x22171,x22172)+E(f688(x22173,x22174,x22175,x22171),f688(x22173,x22174,x22175,x22172)) % 169.39/169.67 [2218]~E(x22181,x22182)+E(f575(x22181,x22183,x22184,x22185,x22186),f575(x22182,x22183,x22184,x22185,x22186)) % 169.39/169.67 [2219]~E(x22191,x22192)+E(f575(x22193,x22191,x22194,x22195,x22196),f575(x22193,x22192,x22194,x22195,x22196)) % 169.39/169.67 [2220]~E(x22201,x22202)+E(f575(x22203,x22204,x22201,x22205,x22206),f575(x22203,x22204,x22202,x22205,x22206)) % 169.39/169.67 [2221]~E(x22211,x22212)+E(f575(x22213,x22214,x22215,x22211,x22216),f575(x22213,x22214,x22215,x22212,x22216)) % 169.39/169.67 [2222]~E(x22221,x22222)+E(f575(x22223,x22224,x22225,x22226,x22221),f575(x22223,x22224,x22225,x22226,x22222)) % 169.39/169.67 [2223]~E(x22231,x22232)+E(f758(x22231,x22233),f758(x22232,x22233)) % 169.39/169.67 [2224]~E(x22241,x22242)+E(f758(x22243,x22241),f758(x22243,x22242)) % 169.39/169.67 [2225]~E(x22251,x22252)+E(f128(x22251),f128(x22252)) % 169.39/169.67 [2226]~E(x22261,x22262)+E(f669(x22261,x22263,x22264,x22265,x22266),f669(x22262,x22263,x22264,x22265,x22266)) % 169.39/169.67 [2227]~E(x22271,x22272)+E(f669(x22273,x22271,x22274,x22275,x22276),f669(x22273,x22272,x22274,x22275,x22276)) % 169.39/169.67 [2228]~E(x22281,x22282)+E(f669(x22283,x22284,x22281,x22285,x22286),f669(x22283,x22284,x22282,x22285,x22286)) % 169.39/169.67 [2229]~E(x22291,x22292)+E(f669(x22293,x22294,x22295,x22291,x22296),f669(x22293,x22294,x22295,x22292,x22296)) % 169.39/169.67 [2230]~E(x22301,x22302)+E(f669(x22303,x22304,x22305,x22306,x22301),f669(x22303,x22304,x22305,x22306,x22302)) % 169.39/169.67 [2231]~E(x22311,x22312)+E(f593(x22311,x22313,x22314),f593(x22312,x22313,x22314)) % 169.39/169.67 [2232]~E(x22321,x22322)+E(f593(x22323,x22321,x22324),f593(x22323,x22322,x22324)) % 169.39/169.67 [2233]~E(x22331,x22332)+E(f593(x22333,x22334,x22331),f593(x22333,x22334,x22332)) % 169.39/169.67 [2234]~E(x22341,x22342)+E(f501(x22341,x22343,x22344,x22345),f501(x22342,x22343,x22344,x22345)) % 169.39/169.67 [2235]~E(x22351,x22352)+E(f501(x22353,x22351,x22354,x22355),f501(x22353,x22352,x22354,x22355)) % 169.39/169.67 [2236]~E(x22361,x22362)+E(f501(x22363,x22364,x22361,x22365),f501(x22363,x22364,x22362,x22365)) % 169.39/169.67 [2237]~E(x22371,x22372)+E(f501(x22373,x22374,x22375,x22371),f501(x22373,x22374,x22375,x22372)) % 169.39/169.67 [2238]~E(x22381,x22382)+E(f736(x22381,x22383,x22384),f736(x22382,x22383,x22384)) % 169.39/169.67 [2239]~E(x22391,x22392)+E(f736(x22393,x22391,x22394),f736(x22393,x22392,x22394)) % 169.39/169.67 [2240]~E(x22401,x22402)+E(f736(x22403,x22404,x22401),f736(x22403,x22404,x22402)) % 169.39/169.67 [2241]~E(x22411,x22412)+E(f391(x22411,x22413,x22414,x22415),f391(x22412,x22413,x22414,x22415)) % 169.39/169.67 [2242]~E(x22421,x22422)+E(f391(x22423,x22421,x22424,x22425),f391(x22423,x22422,x22424,x22425)) % 169.39/169.67 [2243]~E(x22431,x22432)+E(f391(x22433,x22434,x22431,x22435),f391(x22433,x22434,x22432,x22435)) % 169.39/169.67 [2244]~E(x22441,x22442)+E(f391(x22443,x22444,x22445,x22441),f391(x22443,x22444,x22445,x22442)) % 169.39/169.67 [2245]~E(x22451,x22452)+E(f623(x22451,x22453,x22454),f623(x22452,x22453,x22454)) % 169.39/169.67 [2246]~E(x22461,x22462)+E(f623(x22463,x22461,x22464),f623(x22463,x22462,x22464)) % 169.39/169.67 [2247]~E(x22471,x22472)+E(f623(x22473,x22474,x22471),f623(x22473,x22474,x22472)) % 169.39/169.67 [2248]~E(x22481,x22482)+E(f703(x22481,x22483,x22484,x22485,x22486),f703(x22482,x22483,x22484,x22485,x22486)) % 169.39/169.67 [2249]~E(x22491,x22492)+E(f703(x22493,x22491,x22494,x22495,x22496),f703(x22493,x22492,x22494,x22495,x22496)) % 169.39/169.67 [2250]~E(x22501,x22502)+E(f703(x22503,x22504,x22501,x22505,x22506),f703(x22503,x22504,x22502,x22505,x22506)) % 169.39/169.67 [2251]~E(x22511,x22512)+E(f703(x22513,x22514,x22515,x22511,x22516),f703(x22513,x22514,x22515,x22512,x22516)) % 169.39/169.67 [2252]~E(x22521,x22522)+E(f703(x22523,x22524,x22525,x22526,x22521),f703(x22523,x22524,x22525,x22526,x22522)) % 169.39/169.67 [2253]~E(x22531,x22532)+E(f630(x22531,x22533,x22534,x22535,x22536),f630(x22532,x22533,x22534,x22535,x22536)) % 169.39/169.67 [2254]~E(x22541,x22542)+E(f630(x22543,x22541,x22544,x22545,x22546),f630(x22543,x22542,x22544,x22545,x22546)) % 169.39/169.67 [2255]~E(x22551,x22552)+E(f630(x22553,x22554,x22551,x22555,x22556),f630(x22553,x22554,x22552,x22555,x22556)) % 169.39/169.67 [2256]~E(x22561,x22562)+E(f630(x22563,x22564,x22565,x22561,x22566),f630(x22563,x22564,x22565,x22562,x22566)) % 169.39/169.67 [2257]~E(x22571,x22572)+E(f630(x22573,x22574,x22575,x22576,x22571),f630(x22573,x22574,x22575,x22576,x22572)) % 169.39/169.67 [2258]~E(x22581,x22582)+E(f489(x22581,x22583,x22584,x22585),f489(x22582,x22583,x22584,x22585)) % 169.39/169.67 [2259]~E(x22591,x22592)+E(f489(x22593,x22591,x22594,x22595),f489(x22593,x22592,x22594,x22595)) % 169.39/169.67 [2260]~E(x22601,x22602)+E(f489(x22603,x22604,x22601,x22605),f489(x22603,x22604,x22602,x22605)) % 169.39/169.67 [2261]~E(x22611,x22612)+E(f489(x22613,x22614,x22615,x22611),f489(x22613,x22614,x22615,x22612)) % 169.39/169.67 [2262]~E(x22621,x22622)+E(f527(x22621,x22623,x22624,x22625,x22626),f527(x22622,x22623,x22624,x22625,x22626)) % 169.39/169.67 [2263]~E(x22631,x22632)+E(f527(x22633,x22631,x22634,x22635,x22636),f527(x22633,x22632,x22634,x22635,x22636)) % 169.39/169.67 [2264]~E(x22641,x22642)+E(f527(x22643,x22644,x22641,x22645,x22646),f527(x22643,x22644,x22642,x22645,x22646)) % 169.39/169.67 [2265]~E(x22651,x22652)+E(f527(x22653,x22654,x22655,x22651,x22656),f527(x22653,x22654,x22655,x22652,x22656)) % 169.39/169.67 [2266]~E(x22661,x22662)+E(f527(x22663,x22664,x22665,x22666,x22661),f527(x22663,x22664,x22665,x22666,x22662)) % 169.39/169.67 [2267]~E(x22671,x22672)+E(f784(x22671,x22673,x22674),f784(x22672,x22673,x22674)) % 169.39/169.67 [2268]~E(x22681,x22682)+E(f784(x22683,x22681,x22684),f784(x22683,x22682,x22684)) % 169.39/169.67 [2269]~E(x22691,x22692)+E(f784(x22693,x22694,x22691),f784(x22693,x22694,x22692)) % 169.39/169.67 [2270]~E(x22701,x22702)+E(f741(x22701,x22703,x22704,x22705,x22706),f741(x22702,x22703,x22704,x22705,x22706)) % 169.39/169.67 [2271]~E(x22711,x22712)+E(f741(x22713,x22711,x22714,x22715,x22716),f741(x22713,x22712,x22714,x22715,x22716)) % 169.39/169.67 [2272]~E(x22721,x22722)+E(f741(x22723,x22724,x22721,x22725,x22726),f741(x22723,x22724,x22722,x22725,x22726)) % 169.39/169.67 [2273]~E(x22731,x22732)+E(f741(x22733,x22734,x22735,x22731,x22736),f741(x22733,x22734,x22735,x22732,x22736)) % 169.39/169.67 [2274]~E(x22741,x22742)+E(f741(x22743,x22744,x22745,x22746,x22741),f741(x22743,x22744,x22745,x22746,x22742)) % 169.39/169.67 [2275]~E(x22751,x22752)+E(f868(x22751),f868(x22752)) % 169.39/169.67 [2276]~E(x22761,x22762)+E(f740(x22761,x22763,x22764,x22765,x22766),f740(x22762,x22763,x22764,x22765,x22766)) % 169.39/169.67 [2277]~E(x22771,x22772)+E(f740(x22773,x22771,x22774,x22775,x22776),f740(x22773,x22772,x22774,x22775,x22776)) % 169.39/169.67 [2278]~E(x22781,x22782)+E(f740(x22783,x22784,x22781,x22785,x22786),f740(x22783,x22784,x22782,x22785,x22786)) % 169.39/169.67 [2279]~E(x22791,x22792)+E(f740(x22793,x22794,x22795,x22791,x22796),f740(x22793,x22794,x22795,x22792,x22796)) % 169.39/169.67 [2280]~E(x22801,x22802)+E(f740(x22803,x22804,x22805,x22806,x22801),f740(x22803,x22804,x22805,x22806,x22802)) % 169.39/169.67 [2281]~E(x22811,x22812)+E(f451(x22811,x22813),f451(x22812,x22813)) % 169.39/169.67 [2282]~E(x22821,x22822)+E(f451(x22823,x22821),f451(x22823,x22822)) % 169.39/169.67 [2283]~E(x22831,x22832)+E(f319(x22831),f319(x22832)) % 169.39/169.67 [2284]~E(x22841,x22842)+E(f862(x22841,x22843),f862(x22842,x22843)) % 169.39/169.67 [2285]~E(x22851,x22852)+E(f862(x22853,x22851),f862(x22853,x22852)) % 169.39/169.67 [2286]~E(x22861,x22862)+E(f197(x22861,x22863,x22864,x22865),f197(x22862,x22863,x22864,x22865)) % 169.39/169.67 [2287]~E(x22871,x22872)+E(f197(x22873,x22871,x22874,x22875),f197(x22873,x22872,x22874,x22875)) % 169.39/169.67 [2288]~E(x22881,x22882)+E(f197(x22883,x22884,x22881,x22885),f197(x22883,x22884,x22882,x22885)) % 169.39/169.67 [2289]~E(x22891,x22892)+E(f197(x22893,x22894,x22895,x22891),f197(x22893,x22894,x22895,x22892)) % 169.39/169.67 [2290]~E(x22901,x22902)+E(f397(x22901,x22903),f397(x22902,x22903)) % 169.39/169.67 [2291]~E(x22911,x22912)+E(f397(x22913,x22911),f397(x22913,x22912)) % 169.39/169.67 [2292]~E(x22921,x22922)+E(f485(x22921,x22923,x22924),f485(x22922,x22923,x22924)) % 169.39/169.67 [2293]~E(x22931,x22932)+E(f485(x22933,x22931,x22934),f485(x22933,x22932,x22934)) % 169.39/169.67 [2294]~E(x22941,x22942)+E(f485(x22943,x22944,x22941),f485(x22943,x22944,x22942)) % 169.39/169.67 [2295]~E(x22951,x22952)+E(f399(x22951,x22953,x22954,x22955),f399(x22952,x22953,x22954,x22955)) % 169.39/169.67 [2296]~E(x22961,x22962)+E(f399(x22963,x22961,x22964,x22965),f399(x22963,x22962,x22964,x22965)) % 169.39/169.67 [2297]~E(x22971,x22972)+E(f399(x22973,x22974,x22971,x22975),f399(x22973,x22974,x22972,x22975)) % 169.39/169.67 [2298]~E(x22981,x22982)+E(f399(x22983,x22984,x22985,x22981),f399(x22983,x22984,x22985,x22982)) % 169.39/169.67 [2299]~E(x22991,x22992)+E(f216(x22991,x22993,x22994,x22995,x22996,x22997,x22998),f216(x22992,x22993,x22994,x22995,x22996,x22997,x22998)) % 169.39/169.67 [2300]~E(x23001,x23002)+E(f216(x23003,x23001,x23004,x23005,x23006,x23007,x23008),f216(x23003,x23002,x23004,x23005,x23006,x23007,x23008)) % 169.39/169.67 [2301]~E(x23011,x23012)+E(f216(x23013,x23014,x23011,x23015,x23016,x23017,x23018),f216(x23013,x23014,x23012,x23015,x23016,x23017,x23018)) % 169.39/169.67 [2302]~E(x23021,x23022)+E(f216(x23023,x23024,x23025,x23021,x23026,x23027,x23028),f216(x23023,x23024,x23025,x23022,x23026,x23027,x23028)) % 169.39/169.67 [2303]~E(x23031,x23032)+E(f216(x23033,x23034,x23035,x23036,x23031,x23037,x23038),f216(x23033,x23034,x23035,x23036,x23032,x23037,x23038)) % 169.39/169.67 [2304]~E(x23041,x23042)+E(f216(x23043,x23044,x23045,x23046,x23047,x23041,x23048),f216(x23043,x23044,x23045,x23046,x23047,x23042,x23048)) % 169.39/169.67 [2305]~E(x23051,x23052)+E(f216(x23053,x23054,x23055,x23056,x23057,x23058,x23051),f216(x23053,x23054,x23055,x23056,x23057,x23058,x23052)) % 169.39/169.67 [2306]~E(x23061,x23062)+E(f419(x23061,x23063,x23064),f419(x23062,x23063,x23064)) % 169.39/169.67 [2307]~E(x23071,x23072)+E(f419(x23073,x23071,x23074),f419(x23073,x23072,x23074)) % 169.39/169.67 [2308]~E(x23081,x23082)+E(f419(x23083,x23084,x23081),f419(x23083,x23084,x23082)) % 169.39/169.67 [2309]~E(x23091,x23092)+E(f396(x23091,x23093),f396(x23092,x23093)) % 169.39/169.67 [2310]~E(x23101,x23102)+E(f396(x23103,x23101),f396(x23103,x23102)) % 169.39/169.67 [2311]~E(x23111,x23112)+E(f721(x23111,x23113,x23114,x23115),f721(x23112,x23113,x23114,x23115)) % 169.39/169.67 [2312]~E(x23121,x23122)+E(f721(x23123,x23121,x23124,x23125),f721(x23123,x23122,x23124,x23125)) % 169.39/169.67 [2313]~E(x23131,x23132)+E(f721(x23133,x23134,x23131,x23135),f721(x23133,x23134,x23132,x23135)) % 169.39/169.67 [2314]~E(x23141,x23142)+E(f721(x23143,x23144,x23145,x23141),f721(x23143,x23144,x23145,x23142)) % 169.39/169.67 [2315]~E(x23151,x23152)+E(f534(x23151,x23153,x23154,x23155,x23156,x23157,x23158),f534(x23152,x23153,x23154,x23155,x23156,x23157,x23158)) % 169.39/169.67 [2316]~E(x23161,x23162)+E(f534(x23163,x23161,x23164,x23165,x23166,x23167,x23168),f534(x23163,x23162,x23164,x23165,x23166,x23167,x23168)) % 169.39/169.67 [2317]~E(x23171,x23172)+E(f534(x23173,x23174,x23171,x23175,x23176,x23177,x23178),f534(x23173,x23174,x23172,x23175,x23176,x23177,x23178)) % 169.39/169.67 [2318]~E(x23181,x23182)+E(f534(x23183,x23184,x23185,x23181,x23186,x23187,x23188),f534(x23183,x23184,x23185,x23182,x23186,x23187,x23188)) % 169.39/169.67 [2319]~E(x23191,x23192)+E(f534(x23193,x23194,x23195,x23196,x23191,x23197,x23198),f534(x23193,x23194,x23195,x23196,x23192,x23197,x23198)) % 169.39/169.67 [2320]~E(x23201,x23202)+E(f534(x23203,x23204,x23205,x23206,x23207,x23201,x23208),f534(x23203,x23204,x23205,x23206,x23207,x23202,x23208)) % 169.39/169.67 [2321]~E(x23211,x23212)+E(f534(x23213,x23214,x23215,x23216,x23217,x23218,x23211),f534(x23213,x23214,x23215,x23216,x23217,x23218,x23212)) % 169.39/169.67 [2322]~E(x23221,x23222)+E(f808(x23221,x23223,x23224,x23225),f808(x23222,x23223,x23224,x23225)) % 169.39/169.67 [2323]~E(x23231,x23232)+E(f808(x23233,x23231,x23234,x23235),f808(x23233,x23232,x23234,x23235)) % 169.39/169.67 [2324]~E(x23241,x23242)+E(f808(x23243,x23244,x23241,x23245),f808(x23243,x23244,x23242,x23245)) % 169.39/169.67 [2325]~E(x23251,x23252)+E(f808(x23253,x23254,x23255,x23251),f808(x23253,x23254,x23255,x23252)) % 169.39/169.67 [2326]~E(x23261,x23262)+E(f604(x23261,x23263,x23264),f604(x23262,x23263,x23264)) % 169.39/169.67 [2327]~E(x23271,x23272)+E(f604(x23273,x23271,x23274),f604(x23273,x23272,x23274)) % 169.39/169.67 [2328]~E(x23281,x23282)+E(f604(x23283,x23284,x23281),f604(x23283,x23284,x23282)) % 169.39/169.67 [2329]~E(x23291,x23292)+E(f131(x23291,x23293,x23294,x23295),f131(x23292,x23293,x23294,x23295)) % 169.39/169.67 [2330]~E(x23301,x23302)+E(f131(x23303,x23301,x23304,x23305),f131(x23303,x23302,x23304,x23305)) % 169.39/169.67 [2331]~E(x23311,x23312)+E(f131(x23313,x23314,x23311,x23315),f131(x23313,x23314,x23312,x23315)) % 169.39/169.67 [2332]~E(x23321,x23322)+E(f131(x23323,x23324,x23325,x23321),f131(x23323,x23324,x23325,x23322)) % 169.39/169.67 [2333]~E(x23331,x23332)+E(f705(x23331,x23333),f705(x23332,x23333)) % 169.39/169.67 [2334]~E(x23341,x23342)+E(f705(x23343,x23341),f705(x23343,x23342)) % 169.39/169.67 [2335]~E(x23351,x23352)+E(f343(x23351,x23353),f343(x23352,x23353)) % 169.39/169.67 [2336]~E(x23361,x23362)+E(f343(x23363,x23361),f343(x23363,x23362)) % 169.39/169.67 [2337]~E(x23371,x23372)+E(f619(x23371,x23373,x23374,x23375,x23376,x23377,x23378,x23379),f619(x23372,x23373,x23374,x23375,x23376,x23377,x23378,x23379)) % 169.39/169.67 [2338]~E(x23381,x23382)+E(f619(x23383,x23381,x23384,x23385,x23386,x23387,x23388,x23389),f619(x23383,x23382,x23384,x23385,x23386,x23387,x23388,x23389)) % 169.39/169.67 [2339]~E(x23391,x23392)+E(f619(x23393,x23394,x23391,x23395,x23396,x23397,x23398,x23399),f619(x23393,x23394,x23392,x23395,x23396,x23397,x23398,x23399)) % 169.39/169.67 [2340]~E(x23401,x23402)+E(f619(x23403,x23404,x23405,x23401,x23406,x23407,x23408,x23409),f619(x23403,x23404,x23405,x23402,x23406,x23407,x23408,x23409)) % 169.39/169.67 [2341]~E(x23411,x23412)+E(f619(x23413,x23414,x23415,x23416,x23411,x23417,x23418,x23419),f619(x23413,x23414,x23415,x23416,x23412,x23417,x23418,x23419)) % 169.39/169.67 [2342]~E(x23421,x23422)+E(f619(x23423,x23424,x23425,x23426,x23427,x23421,x23428,x23429),f619(x23423,x23424,x23425,x23426,x23427,x23422,x23428,x23429)) % 169.39/169.67 [2343]~E(x23431,x23432)+E(f619(x23433,x23434,x23435,x23436,x23437,x23438,x23431,x23439),f619(x23433,x23434,x23435,x23436,x23437,x23438,x23432,x23439)) % 169.39/169.67 [2344]~E(x23441,x23442)+E(f619(x23443,x23444,x23445,x23446,x23447,x23448,x23449,x23441),f619(x23443,x23444,x23445,x23446,x23447,x23448,x23449,x23442)) % 169.39/169.67 [2345]~E(x23451,x23452)+E(f723(x23451,x23453,x23454,x23455,x23456),f723(x23452,x23453,x23454,x23455,x23456)) % 169.39/169.67 [2346]~E(x23461,x23462)+E(f723(x23463,x23461,x23464,x23465,x23466),f723(x23463,x23462,x23464,x23465,x23466)) % 169.39/169.67 [2347]~E(x23471,x23472)+E(f723(x23473,x23474,x23471,x23475,x23476),f723(x23473,x23474,x23472,x23475,x23476)) % 169.39/169.67 [2348]~E(x23481,x23482)+E(f723(x23483,x23484,x23485,x23481,x23486),f723(x23483,x23484,x23485,x23482,x23486)) % 169.39/169.67 [2349]~E(x23491,x23492)+E(f723(x23493,x23494,x23495,x23496,x23491),f723(x23493,x23494,x23495,x23496,x23492)) % 169.39/169.67 [2350]~E(x23501,x23502)+E(f236(x23501,x23503,x23504),f236(x23502,x23503,x23504)) % 169.39/169.67 [2351]~E(x23511,x23512)+E(f236(x23513,x23511,x23514),f236(x23513,x23512,x23514)) % 169.39/169.67 [2352]~E(x23521,x23522)+E(f236(x23523,x23524,x23521),f236(x23523,x23524,x23522)) % 169.39/169.67 [2353]~E(x23531,x23532)+E(f772(x23531,x23533,x23534,x23535,x23536),f772(x23532,x23533,x23534,x23535,x23536)) % 169.39/169.67 [2354]~E(x23541,x23542)+E(f772(x23543,x23541,x23544,x23545,x23546),f772(x23543,x23542,x23544,x23545,x23546)) % 169.39/169.67 [2355]~E(x23551,x23552)+E(f772(x23553,x23554,x23551,x23555,x23556),f772(x23553,x23554,x23552,x23555,x23556)) % 169.39/169.67 [2356]~E(x23561,x23562)+E(f772(x23563,x23564,x23565,x23561,x23566),f772(x23563,x23564,x23565,x23562,x23566)) % 169.39/169.67 [2357]~E(x23571,x23572)+E(f772(x23573,x23574,x23575,x23576,x23571),f772(x23573,x23574,x23575,x23576,x23572)) % 169.39/169.67 [2358]~E(x23581,x23582)+E(f388(x23581,x23583,x23584,x23585),f388(x23582,x23583,x23584,x23585)) % 169.39/169.67 [2359]~E(x23591,x23592)+E(f388(x23593,x23591,x23594,x23595),f388(x23593,x23592,x23594,x23595)) % 169.39/169.67 [2360]~E(x23601,x23602)+E(f388(x23603,x23604,x23601,x23605),f388(x23603,x23604,x23602,x23605)) % 169.39/169.67 [2361]~E(x23611,x23612)+E(f388(x23613,x23614,x23615,x23611),f388(x23613,x23614,x23615,x23612)) % 169.39/169.67 [2362]~E(x23621,x23622)+E(f364(x23621,x23623),f364(x23622,x23623)) % 169.39/169.67 [2363]~E(x23631,x23632)+E(f364(x23633,x23631),f364(x23633,x23632)) % 169.39/169.67 [2364]~E(x23641,x23642)+E(f412(x23641,x23643,x23644),f412(x23642,x23643,x23644)) % 169.39/169.67 [2365]~E(x23651,x23652)+E(f412(x23653,x23651,x23654),f412(x23653,x23652,x23654)) % 169.39/169.67 [2366]~E(x23661,x23662)+E(f412(x23663,x23664,x23661),f412(x23663,x23664,x23662)) % 169.39/169.67 [2367]~E(x23671,x23672)+E(f734(x23671,x23673,x23674),f734(x23672,x23673,x23674)) % 169.39/169.67 [2368]~E(x23681,x23682)+E(f734(x23683,x23681,x23684),f734(x23683,x23682,x23684)) % 169.39/169.67 [2369]~E(x23691,x23692)+E(f734(x23693,x23694,x23691),f734(x23693,x23694,x23692)) % 169.39/169.67 [2370]~E(x23701,x23702)+E(f219(x23701,x23703,x23704,x23705),f219(x23702,x23703,x23704,x23705)) % 169.39/169.67 [2371]~E(x23711,x23712)+E(f219(x23713,x23711,x23714,x23715),f219(x23713,x23712,x23714,x23715)) % 169.39/169.67 [2372]~E(x23721,x23722)+E(f219(x23723,x23724,x23721,x23725),f219(x23723,x23724,x23722,x23725)) % 169.39/169.67 [2373]~E(x23731,x23732)+E(f219(x23733,x23734,x23735,x23731),f219(x23733,x23734,x23735,x23732)) % 169.39/169.67 [2374]~E(x23741,x23742)+E(f448(x23741,x23743,x23744,x23745),f448(x23742,x23743,x23744,x23745)) % 169.39/169.67 [2375]~E(x23751,x23752)+E(f448(x23753,x23751,x23754,x23755),f448(x23753,x23752,x23754,x23755)) % 169.39/169.67 [2376]~E(x23761,x23762)+E(f448(x23763,x23764,x23761,x23765),f448(x23763,x23764,x23762,x23765)) % 169.39/169.67 [2377]~E(x23771,x23772)+E(f448(x23773,x23774,x23775,x23771),f448(x23773,x23774,x23775,x23772)) % 169.39/169.67 [2378]~E(x23781,x23782)+E(f461(x23781,x23783,x23784),f461(x23782,x23783,x23784)) % 169.39/169.67 [2379]~E(x23791,x23792)+E(f461(x23793,x23791,x23794),f461(x23793,x23792,x23794)) % 169.39/169.67 [2380]~E(x23801,x23802)+E(f461(x23803,x23804,x23801),f461(x23803,x23804,x23802)) % 169.39/169.67 [2381]~E(x23811,x23812)+E(f511(x23811,x23813,x23814),f511(x23812,x23813,x23814)) % 169.39/169.67 [2382]~E(x23821,x23822)+E(f511(x23823,x23821,x23824),f511(x23823,x23822,x23824)) % 169.39/169.67 [2383]~E(x23831,x23832)+E(f511(x23833,x23834,x23831),f511(x23833,x23834,x23832)) % 169.39/169.67 [2384]~E(x23841,x23842)+E(f698(x23841,x23843,x23844),f698(x23842,x23843,x23844)) % 169.39/169.67 [2385]~E(x23851,x23852)+E(f698(x23853,x23851,x23854),f698(x23853,x23852,x23854)) % 169.39/169.67 [2386]~E(x23861,x23862)+E(f698(x23863,x23864,x23861),f698(x23863,x23864,x23862)) % 169.39/169.67 [2387]~E(x23871,x23872)+E(f617(x23871,x23873,x23874,x23875),f617(x23872,x23873,x23874,x23875)) % 169.39/169.67 [2388]~E(x23881,x23882)+E(f617(x23883,x23881,x23884,x23885),f617(x23883,x23882,x23884,x23885)) % 169.39/169.67 [2389]~E(x23891,x23892)+E(f617(x23893,x23894,x23891,x23895),f617(x23893,x23894,x23892,x23895)) % 169.39/169.67 [2390]~E(x23901,x23902)+E(f617(x23903,x23904,x23905,x23901),f617(x23903,x23904,x23905,x23902)) % 169.39/169.67 [2391]~E(x23911,x23912)+E(f832(x23911,x23913),f832(x23912,x23913)) % 169.39/169.67 [2392]~E(x23921,x23922)+E(f832(x23923,x23921),f832(x23923,x23922)) % 169.39/169.67 [2393]~E(x23931,x23932)+E(f431(x23931,x23933,x23934),f431(x23932,x23933,x23934)) % 169.39/169.67 [2394]~E(x23941,x23942)+E(f431(x23943,x23941,x23944),f431(x23943,x23942,x23944)) % 169.39/169.67 [2395]~E(x23951,x23952)+E(f431(x23953,x23954,x23951),f431(x23953,x23954,x23952)) % 169.39/169.67 [2396]~E(x23961,x23962)+E(f864(x23961,x23963,x23964),f864(x23962,x23963,x23964)) % 169.39/169.67 [2397]~E(x23971,x23972)+E(f864(x23973,x23971,x23974),f864(x23973,x23972,x23974)) % 169.39/169.67 [2398]~E(x23981,x23982)+E(f864(x23983,x23984,x23981),f864(x23983,x23984,x23982)) % 169.39/169.67 [2399]~E(x23991,x23992)+E(f720(x23991,x23993,x23994),f720(x23992,x23993,x23994)) % 169.39/169.67 [2400]~E(x24001,x24002)+E(f720(x24003,x24001,x24004),f720(x24003,x24002,x24004)) % 169.39/169.67 [2401]~E(x24011,x24012)+E(f720(x24013,x24014,x24011),f720(x24013,x24014,x24012)) % 169.39/169.67 [2402]~E(x24021,x24022)+E(f535(x24021,x24023,x24024,x24025,x24026),f535(x24022,x24023,x24024,x24025,x24026)) % 169.39/169.67 [2403]~E(x24031,x24032)+E(f535(x24033,x24031,x24034,x24035,x24036),f535(x24033,x24032,x24034,x24035,x24036)) % 169.39/169.67 [2404]~E(x24041,x24042)+E(f535(x24043,x24044,x24041,x24045,x24046),f535(x24043,x24044,x24042,x24045,x24046)) % 169.39/169.67 [2405]~E(x24051,x24052)+E(f535(x24053,x24054,x24055,x24051,x24056),f535(x24053,x24054,x24055,x24052,x24056)) % 169.39/169.67 [2406]~E(x24061,x24062)+E(f535(x24063,x24064,x24065,x24066,x24061),f535(x24063,x24064,x24065,x24066,x24062)) % 169.39/169.67 [2407]~E(x24071,x24072)+E(f685(x24071,x24073,x24074),f685(x24072,x24073,x24074)) % 169.39/169.67 [2408]~E(x24081,x24082)+E(f685(x24083,x24081,x24084),f685(x24083,x24082,x24084)) % 169.39/169.67 [2409]~E(x24091,x24092)+E(f685(x24093,x24094,x24091),f685(x24093,x24094,x24092)) % 169.39/169.67 [2410]~E(x24101,x24102)+E(f690(x24101,x24103,x24104,x24105),f690(x24102,x24103,x24104,x24105)) % 169.39/169.67 [2411]~E(x24111,x24112)+E(f690(x24113,x24111,x24114,x24115),f690(x24113,x24112,x24114,x24115)) % 169.39/169.67 [2412]~E(x24121,x24122)+E(f690(x24123,x24124,x24121,x24125),f690(x24123,x24124,x24122,x24125)) % 169.39/169.67 [2413]~E(x24131,x24132)+E(f690(x24133,x24134,x24135,x24131),f690(x24133,x24134,x24135,x24132)) % 169.39/169.67 [2414]~E(x24141,x24142)+E(f464(x24141,x24143,x24144),f464(x24142,x24143,x24144)) % 169.39/169.67 [2415]~E(x24151,x24152)+E(f464(x24153,x24151,x24154),f464(x24153,x24152,x24154)) % 169.39/169.67 [2416]~E(x24161,x24162)+E(f464(x24163,x24164,x24161),f464(x24163,x24164,x24162)) % 169.39/169.67 [2417]~E(x24171,x24172)+E(f477(x24171,x24173,x24174),f477(x24172,x24173,x24174)) % 169.39/169.67 [2418]~E(x24181,x24182)+E(f477(x24183,x24181,x24184),f477(x24183,x24182,x24184)) % 169.39/169.67 [2419]~E(x24191,x24192)+E(f477(x24193,x24194,x24191),f477(x24193,x24194,x24192)) % 169.39/169.67 [2420]~E(x24201,x24202)+E(f430(x24201,x24203,x24204),f430(x24202,x24203,x24204)) % 169.39/169.67 [2421]~E(x24211,x24212)+E(f430(x24213,x24211,x24214),f430(x24213,x24212,x24214)) % 169.39/169.67 [2422]~E(x24221,x24222)+E(f430(x24223,x24224,x24221),f430(x24223,x24224,x24222)) % 169.39/169.67 [2423]~E(x24231,x24232)+E(f261(x24231,x24233,x24234),f261(x24232,x24233,x24234)) % 169.39/169.67 [2424]~E(x24241,x24242)+E(f261(x24243,x24241,x24244),f261(x24243,x24242,x24244)) % 169.39/169.67 [2425]~E(x24251,x24252)+E(f261(x24253,x24254,x24251),f261(x24253,x24254,x24252)) % 169.39/169.67 [2426]~E(x24261,x24262)+E(f467(x24261,x24263,x24264),f467(x24262,x24263,x24264)) % 169.39/169.67 [2427]~E(x24271,x24272)+E(f467(x24273,x24271,x24274),f467(x24273,x24272,x24274)) % 169.39/169.67 [2428]~E(x24281,x24282)+E(f467(x24283,x24284,x24281),f467(x24283,x24284,x24282)) % 169.39/169.67 [2429]~E(x24291,x24292)+E(f665(x24291,x24293),f665(x24292,x24293)) % 169.39/169.67 [2430]~E(x24301,x24302)+E(f665(x24303,x24301),f665(x24303,x24302)) % 169.39/169.67 [2431]~E(x24311,x24312)+E(f650(x24311,x24313,x24314),f650(x24312,x24313,x24314)) % 169.39/169.67 [2432]~E(x24321,x24322)+E(f650(x24323,x24321,x24324),f650(x24323,x24322,x24324)) % 169.39/169.67 [2433]~E(x24331,x24332)+E(f650(x24333,x24334,x24331),f650(x24333,x24334,x24332)) % 169.39/169.67 [2434]~E(x24341,x24342)+E(f338(x24341,x24343,x24344,x24345),f338(x24342,x24343,x24344,x24345)) % 169.39/169.67 [2435]~E(x24351,x24352)+E(f338(x24353,x24351,x24354,x24355),f338(x24353,x24352,x24354,x24355)) % 169.39/169.67 [2436]~E(x24361,x24362)+E(f338(x24363,x24364,x24361,x24365),f338(x24363,x24364,x24362,x24365)) % 169.39/169.67 [2437]~E(x24371,x24372)+E(f338(x24373,x24374,x24375,x24371),f338(x24373,x24374,x24375,x24372)) % 169.39/169.67 [2438]~E(x24381,x24382)+E(f251(x24381,x24383),f251(x24382,x24383)) % 169.39/169.67 [2439]~E(x24391,x24392)+E(f251(x24393,x24391),f251(x24393,x24392)) % 169.39/169.67 [2440]~E(x24401,x24402)+E(f377(x24401,x24403,x24404),f377(x24402,x24403,x24404)) % 169.39/169.67 [2441]~E(x24411,x24412)+E(f377(x24413,x24411,x24414),f377(x24413,x24412,x24414)) % 169.39/169.67 [2442]~E(x24421,x24422)+E(f377(x24423,x24424,x24421),f377(x24423,x24424,x24422)) % 169.39/169.67 [2443]~E(x24431,x24432)+E(f830(x24431,x24433),f830(x24432,x24433)) % 169.39/169.67 [2444]~E(x24441,x24442)+E(f830(x24443,x24441),f830(x24443,x24442)) % 169.39/169.67 [2445]~E(x24451,x24452)+E(f146(x24451,x24453),f146(x24452,x24453)) % 169.39/169.67 [2446]~E(x24461,x24462)+E(f146(x24463,x24461),f146(x24463,x24462)) % 169.39/169.67 [2447]~E(x24471,x24472)+E(f712(x24471,x24473,x24474,x24475,x24476,x24477),f712(x24472,x24473,x24474,x24475,x24476,x24477)) % 169.39/169.67 [2448]~E(x24481,x24482)+E(f712(x24483,x24481,x24484,x24485,x24486,x24487),f712(x24483,x24482,x24484,x24485,x24486,x24487)) % 169.39/169.67 [2449]~E(x24491,x24492)+E(f712(x24493,x24494,x24491,x24495,x24496,x24497),f712(x24493,x24494,x24492,x24495,x24496,x24497)) % 169.39/169.67 [2450]~E(x24501,x24502)+E(f712(x24503,x24504,x24505,x24501,x24506,x24507),f712(x24503,x24504,x24505,x24502,x24506,x24507)) % 169.39/169.67 [2451]~E(x24511,x24512)+E(f712(x24513,x24514,x24515,x24516,x24511,x24517),f712(x24513,x24514,x24515,x24516,x24512,x24517)) % 169.39/169.67 [2452]~E(x24521,x24522)+E(f712(x24523,x24524,x24525,x24526,x24527,x24521),f712(x24523,x24524,x24525,x24526,x24527,x24522)) % 169.39/169.67 [2453]~E(x24531,x24532)+E(f526(x24531,x24533,x24534,x24535),f526(x24532,x24533,x24534,x24535)) % 169.39/169.67 [2454]~E(x24541,x24542)+E(f526(x24543,x24541,x24544,x24545),f526(x24543,x24542,x24544,x24545)) % 169.39/169.67 [2455]~E(x24551,x24552)+E(f526(x24553,x24554,x24551,x24555),f526(x24553,x24554,x24552,x24555)) % 169.39/169.67 [2456]~E(x24561,x24562)+E(f526(x24563,x24564,x24565,x24561),f526(x24563,x24564,x24565,x24562)) % 169.39/169.67 [2457]~E(x24571,x24572)+E(f424(x24571,x24573,x24574),f424(x24572,x24573,x24574)) % 169.39/169.67 [2458]~E(x24581,x24582)+E(f424(x24583,x24581,x24584),f424(x24583,x24582,x24584)) % 169.39/169.67 [2459]~E(x24591,x24592)+E(f424(x24593,x24594,x24591),f424(x24593,x24594,x24592)) % 169.39/169.67 [2460]~E(x24601,x24602)+E(f679(x24601,x24603),f679(x24602,x24603)) % 169.39/169.67 [2461]~E(x24611,x24612)+E(f679(x24613,x24611),f679(x24613,x24612)) % 169.39/169.67 [2462]~E(x24621,x24622)+E(f861(x24621,x24623),f861(x24622,x24623)) % 169.39/169.67 [2463]~E(x24631,x24632)+E(f861(x24633,x24631),f861(x24633,x24632)) % 169.39/169.67 [2464]~E(x24641,x24642)+E(f414(x24641,x24643),f414(x24642,x24643)) % 169.39/169.67 [2465]~E(x24651,x24652)+E(f414(x24653,x24651),f414(x24653,x24652)) % 169.39/169.67 [2466]~E(x24661,x24662)+E(f162(x24661,x24663),f162(x24662,x24663)) % 169.39/169.67 [2467]~E(x24671,x24672)+E(f162(x24673,x24671),f162(x24673,x24672)) % 169.39/169.67 [2468]~E(x24681,x24682)+E(f512(x24681,x24683,x24684,x24685,x24686,x24687),f512(x24682,x24683,x24684,x24685,x24686,x24687)) % 169.39/169.67 [2469]~E(x24691,x24692)+E(f512(x24693,x24691,x24694,x24695,x24696,x24697),f512(x24693,x24692,x24694,x24695,x24696,x24697)) % 169.39/169.67 [2470]~E(x24701,x24702)+E(f512(x24703,x24704,x24701,x24705,x24706,x24707),f512(x24703,x24704,x24702,x24705,x24706,x24707)) % 169.39/169.67 [2471]~E(x24711,x24712)+E(f512(x24713,x24714,x24715,x24711,x24716,x24717),f512(x24713,x24714,x24715,x24712,x24716,x24717)) % 169.39/169.67 [2472]~E(x24721,x24722)+E(f512(x24723,x24724,x24725,x24726,x24721,x24727),f512(x24723,x24724,x24725,x24726,x24722,x24727)) % 169.39/169.67 [2473]~E(x24731,x24732)+E(f512(x24733,x24734,x24735,x24736,x24737,x24731),f512(x24733,x24734,x24735,x24736,x24737,x24732)) % 169.39/169.67 [2474]~E(x24741,x24742)+E(f798(x24741,x24743,x24744,x24745,x24746,x24747),f798(x24742,x24743,x24744,x24745,x24746,x24747)) % 169.39/169.67 [2475]~E(x24751,x24752)+E(f798(x24753,x24751,x24754,x24755,x24756,x24757),f798(x24753,x24752,x24754,x24755,x24756,x24757)) % 169.39/169.67 [2476]~E(x24761,x24762)+E(f798(x24763,x24764,x24761,x24765,x24766,x24767),f798(x24763,x24764,x24762,x24765,x24766,x24767)) % 169.39/169.67 [2477]~E(x24771,x24772)+E(f798(x24773,x24774,x24775,x24771,x24776,x24777),f798(x24773,x24774,x24775,x24772,x24776,x24777)) % 169.39/169.67 [2478]~E(x24781,x24782)+E(f798(x24783,x24784,x24785,x24786,x24781,x24787),f798(x24783,x24784,x24785,x24786,x24782,x24787)) % 169.39/169.67 [2479]~E(x24791,x24792)+E(f798(x24793,x24794,x24795,x24796,x24797,x24791),f798(x24793,x24794,x24795,x24796,x24797,x24792)) % 169.39/169.67 [2480]~E(x24801,x24802)+E(f124(x24801),f124(x24802)) % 169.39/169.67 [2481]~E(x24811,x24812)+E(f524(x24811,x24813,x24814),f524(x24812,x24813,x24814)) % 169.39/169.67 [2482]~E(x24821,x24822)+E(f524(x24823,x24821,x24824),f524(x24823,x24822,x24824)) % 169.39/169.67 [2483]~E(x24831,x24832)+E(f524(x24833,x24834,x24831),f524(x24833,x24834,x24832)) % 169.39/169.67 [2484]~E(x24841,x24842)+E(f598(x24841,x24843,x24844,x24845,x24846,x24847,x24848),f598(x24842,x24843,x24844,x24845,x24846,x24847,x24848)) % 169.39/169.67 [2485]~E(x24851,x24852)+E(f598(x24853,x24851,x24854,x24855,x24856,x24857,x24858),f598(x24853,x24852,x24854,x24855,x24856,x24857,x24858)) % 169.39/169.67 [2486]~E(x24861,x24862)+E(f598(x24863,x24864,x24861,x24865,x24866,x24867,x24868),f598(x24863,x24864,x24862,x24865,x24866,x24867,x24868)) % 169.39/169.67 [2487]~E(x24871,x24872)+E(f598(x24873,x24874,x24875,x24871,x24876,x24877,x24878),f598(x24873,x24874,x24875,x24872,x24876,x24877,x24878)) % 169.39/169.67 [2488]~E(x24881,x24882)+E(f598(x24883,x24884,x24885,x24886,x24881,x24887,x24888),f598(x24883,x24884,x24885,x24886,x24882,x24887,x24888)) % 169.39/169.67 [2489]~E(x24891,x24892)+E(f598(x24893,x24894,x24895,x24896,x24897,x24891,x24898),f598(x24893,x24894,x24895,x24896,x24897,x24892,x24898)) % 169.39/169.67 [2490]~E(x24901,x24902)+E(f598(x24903,x24904,x24905,x24906,x24907,x24908,x24901),f598(x24903,x24904,x24905,x24906,x24907,x24908,x24902)) % 169.39/169.67 [2491]~E(x24911,x24912)+E(f666(x24911,x24913),f666(x24912,x24913)) % 169.39/169.67 [2492]~E(x24921,x24922)+E(f666(x24923,x24921),f666(x24923,x24922)) % 169.39/169.67 [2493]~E(x24931,x24932)+E(f130(x24931,x24933,x24934,x24935,x24936),f130(x24932,x24933,x24934,x24935,x24936)) % 169.39/169.67 [2494]~E(x24941,x24942)+E(f130(x24943,x24941,x24944,x24945,x24946),f130(x24943,x24942,x24944,x24945,x24946)) % 169.39/169.67 [2495]~E(x24951,x24952)+E(f130(x24953,x24954,x24951,x24955,x24956),f130(x24953,x24954,x24952,x24955,x24956)) % 169.39/169.67 [2496]~E(x24961,x24962)+E(f130(x24963,x24964,x24965,x24961,x24966),f130(x24963,x24964,x24965,x24962,x24966)) % 169.39/169.67 [2497]~E(x24971,x24972)+E(f130(x24973,x24974,x24975,x24976,x24971),f130(x24973,x24974,x24975,x24976,x24972)) % 169.39/169.67 [2498]~E(x24981,x24982)+E(f662(x24981,x24983,x24984,x24985),f662(x24982,x24983,x24984,x24985)) % 169.39/169.67 [2499]~E(x24991,x24992)+E(f662(x24993,x24991,x24994,x24995),f662(x24993,x24992,x24994,x24995)) % 169.39/169.67 [2500]~E(x25001,x25002)+E(f662(x25003,x25004,x25001,x25005),f662(x25003,x25004,x25002,x25005)) % 169.39/169.67 [2501]~E(x25011,x25012)+E(f662(x25013,x25014,x25015,x25011),f662(x25013,x25014,x25015,x25012)) % 169.39/169.67 [2502]~E(x25021,x25022)+E(f357(x25021,x25023,x25024),f357(x25022,x25023,x25024)) % 169.39/169.67 [2503]~E(x25031,x25032)+E(f357(x25033,x25031,x25034),f357(x25033,x25032,x25034)) % 169.39/169.67 [2504]~E(x25041,x25042)+E(f357(x25043,x25044,x25041),f357(x25043,x25044,x25042)) % 169.39/169.67 [2505]~E(x25051,x25052)+E(f684(x25051,x25053,x25054,x25055),f684(x25052,x25053,x25054,x25055)) % 169.39/169.67 [2506]~E(x25061,x25062)+E(f684(x25063,x25061,x25064,x25065),f684(x25063,x25062,x25064,x25065)) % 169.39/169.67 [2507]~E(x25071,x25072)+E(f684(x25073,x25074,x25071,x25075),f684(x25073,x25074,x25072,x25075)) % 169.39/169.67 [2508]~E(x25081,x25082)+E(f684(x25083,x25084,x25085,x25081),f684(x25083,x25084,x25085,x25082)) % 169.39/169.67 [2509]~E(x25091,x25092)+E(f486(x25091,x25093,x25094,x25095),f486(x25092,x25093,x25094,x25095)) % 169.39/169.67 [2510]~E(x25101,x25102)+E(f486(x25103,x25101,x25104,x25105),f486(x25103,x25102,x25104,x25105)) % 169.39/169.67 [2511]~E(x25111,x25112)+E(f486(x25113,x25114,x25111,x25115),f486(x25113,x25114,x25112,x25115)) % 169.39/169.67 [2512]~E(x25121,x25122)+E(f486(x25123,x25124,x25125,x25121),f486(x25123,x25124,x25125,x25122)) % 169.39/169.67 [2513]~E(x25131,x25132)+E(f452(x25131,x25133,x25134),f452(x25132,x25133,x25134)) % 169.39/169.67 [2514]~E(x25141,x25142)+E(f452(x25143,x25141,x25144),f452(x25143,x25142,x25144)) % 169.39/169.67 [2515]~E(x25151,x25152)+E(f452(x25153,x25154,x25151),f452(x25153,x25154,x25152)) % 169.39/169.67 [2516]~E(x25161,x25162)+E(f715(x25161,x25163),f715(x25162,x25163)) % 169.39/169.67 [2517]~E(x25171,x25172)+E(f715(x25173,x25171),f715(x25173,x25172)) % 169.39/169.67 [2518]~E(x25181,x25182)+E(f533(x25181,x25183,x25184,x25185,x25186),f533(x25182,x25183,x25184,x25185,x25186)) % 169.39/169.67 [2519]~E(x25191,x25192)+E(f533(x25193,x25191,x25194,x25195,x25196),f533(x25193,x25192,x25194,x25195,x25196)) % 169.39/169.67 [2520]~E(x25201,x25202)+E(f533(x25203,x25204,x25201,x25205,x25206),f533(x25203,x25204,x25202,x25205,x25206)) % 169.39/169.67 [2521]~E(x25211,x25212)+E(f533(x25213,x25214,x25215,x25211,x25216),f533(x25213,x25214,x25215,x25212,x25216)) % 169.39/169.67 [2522]~E(x25221,x25222)+E(f533(x25223,x25224,x25225,x25226,x25221),f533(x25223,x25224,x25225,x25226,x25222)) % 169.39/169.67 [2523]~E(x25231,x25232)+E(f276(x25231,x25233,x25234,x25235,x25236),f276(x25232,x25233,x25234,x25235,x25236)) % 169.39/169.67 [2524]~E(x25241,x25242)+E(f276(x25243,x25241,x25244,x25245,x25246),f276(x25243,x25242,x25244,x25245,x25246)) % 169.39/169.67 [2525]~E(x25251,x25252)+E(f276(x25253,x25254,x25251,x25255,x25256),f276(x25253,x25254,x25252,x25255,x25256)) % 169.39/169.67 [2526]~E(x25261,x25262)+E(f276(x25263,x25264,x25265,x25261,x25266),f276(x25263,x25264,x25265,x25262,x25266)) % 169.39/169.67 [2527]~E(x25271,x25272)+E(f276(x25273,x25274,x25275,x25276,x25271),f276(x25273,x25274,x25275,x25276,x25272)) % 169.39/169.67 [2528]~E(x25281,x25282)+E(f831(x25281),f831(x25282)) % 169.39/169.67 [2529]~E(x25291,x25292)+E(f717(x25291,x25293,x25294,x25295),f717(x25292,x25293,x25294,x25295)) % 169.39/169.67 [2530]~E(x25301,x25302)+E(f717(x25303,x25301,x25304,x25305),f717(x25303,x25302,x25304,x25305)) % 169.39/169.67 [2531]~E(x25311,x25312)+E(f717(x25313,x25314,x25311,x25315),f717(x25313,x25314,x25312,x25315)) % 169.39/169.67 [2532]~E(x25321,x25322)+E(f717(x25323,x25324,x25325,x25321),f717(x25323,x25324,x25325,x25322)) % 169.39/169.67 [2533]~E(x25331,x25332)+E(f689(x25331,x25333,x25334,x25335),f689(x25332,x25333,x25334,x25335)) % 169.39/169.67 [2534]~E(x25341,x25342)+E(f689(x25343,x25341,x25344,x25345),f689(x25343,x25342,x25344,x25345)) % 169.39/169.67 [2535]~E(x25351,x25352)+E(f689(x25353,x25354,x25351,x25355),f689(x25353,x25354,x25352,x25355)) % 169.39/169.67 [2536]~E(x25361,x25362)+E(f689(x25363,x25364,x25365,x25361),f689(x25363,x25364,x25365,x25362)) % 169.39/169.67 [2537]~E(x25371,x25372)+E(f429(x25371),f429(x25372)) % 169.39/169.67 [2538]~E(x25381,x25382)+E(f664(x25381,x25383,x25384,x25385,x25386),f664(x25382,x25383,x25384,x25385,x25386)) % 169.39/169.67 [2539]~E(x25391,x25392)+E(f664(x25393,x25391,x25394,x25395,x25396),f664(x25393,x25392,x25394,x25395,x25396)) % 169.39/169.67 [2540]~E(x25401,x25402)+E(f664(x25403,x25404,x25401,x25405,x25406),f664(x25403,x25404,x25402,x25405,x25406)) % 169.39/169.67 [2541]~E(x25411,x25412)+E(f664(x25413,x25414,x25415,x25411,x25416),f664(x25413,x25414,x25415,x25412,x25416)) % 169.39/169.67 [2542]~E(x25421,x25422)+E(f664(x25423,x25424,x25425,x25426,x25421),f664(x25423,x25424,x25425,x25426,x25422)) % 169.39/169.67 [2543]~E(x25431,x25432)+E(f773(x25431,x25433,x25434,x25435,x25436),f773(x25432,x25433,x25434,x25435,x25436)) % 169.39/169.67 [2544]~E(x25441,x25442)+E(f773(x25443,x25441,x25444,x25445,x25446),f773(x25443,x25442,x25444,x25445,x25446)) % 169.39/169.67 [2545]~E(x25451,x25452)+E(f773(x25453,x25454,x25451,x25455,x25456),f773(x25453,x25454,x25452,x25455,x25456)) % 169.39/169.67 [2546]~E(x25461,x25462)+E(f773(x25463,x25464,x25465,x25461,x25466),f773(x25463,x25464,x25465,x25462,x25466)) % 169.39/169.67 [2547]~E(x25471,x25472)+E(f773(x25473,x25474,x25475,x25476,x25471),f773(x25473,x25474,x25475,x25476,x25472)) % 169.39/169.67 [2548]~E(x25481,x25482)+E(f846(x25481,x25483,x25484,x25485,x25486),f846(x25482,x25483,x25484,x25485,x25486)) % 169.39/169.67 [2549]~E(x25491,x25492)+E(f846(x25493,x25491,x25494,x25495,x25496),f846(x25493,x25492,x25494,x25495,x25496)) % 169.39/169.67 [2550]~E(x25501,x25502)+E(f846(x25503,x25504,x25501,x25505,x25506),f846(x25503,x25504,x25502,x25505,x25506)) % 169.39/169.67 [2551]~E(x25511,x25512)+E(f846(x25513,x25514,x25515,x25511,x25516),f846(x25513,x25514,x25515,x25512,x25516)) % 169.39/169.67 [2552]~E(x25521,x25522)+E(f846(x25523,x25524,x25525,x25526,x25521),f846(x25523,x25524,x25525,x25526,x25522)) % 169.39/169.67 [2553]~E(x25531,x25532)+E(f757(x25531,x25533,x25534),f757(x25532,x25533,x25534)) % 169.39/169.67 [2554]~E(x25541,x25542)+E(f757(x25543,x25541,x25544),f757(x25543,x25542,x25544)) % 169.39/169.67 [2555]~E(x25551,x25552)+E(f757(x25553,x25554,x25551),f757(x25553,x25554,x25552)) % 169.39/169.67 [2556]~E(x25561,x25562)+E(f634(x25561,x25563),f634(x25562,x25563)) % 169.39/169.67 [2557]~E(x25571,x25572)+E(f634(x25573,x25571),f634(x25573,x25572)) % 169.39/169.67 [2558]~E(x25581,x25582)+E(f232(x25581,x25583,x25584,x25585,x25586),f232(x25582,x25583,x25584,x25585,x25586)) % 169.39/169.67 [2559]~E(x25591,x25592)+E(f232(x25593,x25591,x25594,x25595,x25596),f232(x25593,x25592,x25594,x25595,x25596)) % 169.39/169.67 [2560]~E(x25601,x25602)+E(f232(x25603,x25604,x25601,x25605,x25606),f232(x25603,x25604,x25602,x25605,x25606)) % 169.39/169.67 [2561]~E(x25611,x25612)+E(f232(x25613,x25614,x25615,x25611,x25616),f232(x25613,x25614,x25615,x25612,x25616)) % 169.39/169.67 [2562]~E(x25621,x25622)+E(f232(x25623,x25624,x25625,x25626,x25621),f232(x25623,x25624,x25625,x25626,x25622)) % 169.39/169.67 [2563]~E(x25631,x25632)+E(f209(x25631),f209(x25632)) % 169.39/169.67 [2564]~E(x25641,x25642)+E(f654(x25641,x25643,x25644),f654(x25642,x25643,x25644)) % 169.39/169.67 [2565]~E(x25651,x25652)+E(f654(x25653,x25651,x25654),f654(x25653,x25652,x25654)) % 169.39/169.67 [2566]~E(x25661,x25662)+E(f654(x25663,x25664,x25661),f654(x25663,x25664,x25662)) % 169.39/169.67 [2567]~E(x25671,x25672)+E(f368(x25671,x25673),f368(x25672,x25673)) % 169.39/169.67 [2568]~E(x25681,x25682)+E(f368(x25683,x25681),f368(x25683,x25682)) % 169.39/169.67 [2569]~E(x25691,x25692)+E(f520(x25691,x25693,x25694,x25695,x25696),f520(x25692,x25693,x25694,x25695,x25696)) % 169.39/169.67 [2570]~E(x25701,x25702)+E(f520(x25703,x25701,x25704,x25705,x25706),f520(x25703,x25702,x25704,x25705,x25706)) % 169.39/169.67 [2571]~E(x25711,x25712)+E(f520(x25713,x25714,x25711,x25715,x25716),f520(x25713,x25714,x25712,x25715,x25716)) % 169.39/169.67 [2572]~E(x25721,x25722)+E(f520(x25723,x25724,x25725,x25721,x25726),f520(x25723,x25724,x25725,x25722,x25726)) % 169.39/169.67 [2573]~E(x25731,x25732)+E(f520(x25733,x25734,x25735,x25736,x25731),f520(x25733,x25734,x25735,x25736,x25732)) % 169.39/169.67 [2574]~E(x25741,x25742)+E(f215(x25741,x25743,x25744,x25745),f215(x25742,x25743,x25744,x25745)) % 169.39/169.67 [2575]~E(x25751,x25752)+E(f215(x25753,x25751,x25754,x25755),f215(x25753,x25752,x25754,x25755)) % 169.39/169.67 [2576]~E(x25761,x25762)+E(f215(x25763,x25764,x25761,x25765),f215(x25763,x25764,x25762,x25765)) % 169.39/169.67 [2577]~E(x25771,x25772)+E(f215(x25773,x25774,x25775,x25771),f215(x25773,x25774,x25775,x25772)) % 169.39/169.67 [2578]~E(x25781,x25782)+E(f646(x25781,x25783),f646(x25782,x25783)) % 169.39/169.67 [2579]~E(x25791,x25792)+E(f646(x25793,x25791),f646(x25793,x25792)) % 169.39/169.67 [2580]~E(x25801,x25802)+E(f362(x25801,x25803),f362(x25802,x25803)) % 169.39/169.67 [2581]~E(x25811,x25812)+E(f362(x25813,x25811),f362(x25813,x25812)) % 169.39/169.67 [2582]~E(x25821,x25822)+E(f297(x25821,x25823,x25824),f297(x25822,x25823,x25824)) % 169.39/169.67 [2583]~E(x25831,x25832)+E(f297(x25833,x25831,x25834),f297(x25833,x25832,x25834)) % 169.39/169.67 [2584]~E(x25841,x25842)+E(f297(x25843,x25844,x25841),f297(x25843,x25844,x25842)) % 169.39/169.67 [2585]~E(x25851,x25852)+E(f344(x25851,x25853),f344(x25852,x25853)) % 169.39/169.67 [2586]~E(x25861,x25862)+E(f344(x25863,x25861),f344(x25863,x25862)) % 169.39/169.67 [2587]~E(x25871,x25872)+E(f792(x25871,x25873,x25874,x25875,x25876),f792(x25872,x25873,x25874,x25875,x25876)) % 169.39/169.67 [2588]~E(x25881,x25882)+E(f792(x25883,x25881,x25884,x25885,x25886),f792(x25883,x25882,x25884,x25885,x25886)) % 169.39/169.67 [2589]~E(x25891,x25892)+E(f792(x25893,x25894,x25891,x25895,x25896),f792(x25893,x25894,x25892,x25895,x25896)) % 169.39/169.67 [2590]~E(x25901,x25902)+E(f792(x25903,x25904,x25905,x25901,x25906),f792(x25903,x25904,x25905,x25902,x25906)) % 169.39/169.67 [2591]~E(x25911,x25912)+E(f792(x25913,x25914,x25915,x25916,x25911),f792(x25913,x25914,x25915,x25916,x25912)) % 169.39/169.67 [2592]~E(x25921,x25922)+E(f704(x25921,x25923),f704(x25922,x25923)) % 169.39/169.67 [2593]~E(x25931,x25932)+E(f704(x25933,x25931),f704(x25933,x25932)) % 169.39/169.67 [2594]~E(x25941,x25942)+E(f340(x25941),f340(x25942)) % 169.39/169.67 [2595]~E(x25951,x25952)+E(f659(x25951,x25953,x25954,x25955),f659(x25952,x25953,x25954,x25955)) % 169.39/169.67 [2596]~E(x25961,x25962)+E(f659(x25963,x25961,x25964,x25965),f659(x25963,x25962,x25964,x25965)) % 169.39/169.67 [2597]~E(x25971,x25972)+E(f659(x25973,x25974,x25971,x25975),f659(x25973,x25974,x25972,x25975)) % 169.39/169.67 [2598]~E(x25981,x25982)+E(f659(x25983,x25984,x25985,x25981),f659(x25983,x25984,x25985,x25982)) % 169.39/169.67 [2599]~E(x25991,x25992)+E(f763(x25991,x25993,x25994),f763(x25992,x25993,x25994)) % 169.39/169.67 [2600]~E(x26001,x26002)+E(f763(x26003,x26001,x26004),f763(x26003,x26002,x26004)) % 169.39/169.67 [2601]~E(x26011,x26012)+E(f763(x26013,x26014,x26011),f763(x26013,x26014,x26012)) % 169.39/169.67 [2602]~E(x26021,x26022)+E(f696(x26021,x26023),f696(x26022,x26023)) % 169.39/169.67 [2603]~E(x26031,x26032)+E(f696(x26033,x26031),f696(x26033,x26032)) % 169.39/169.67 [2604]~E(x26041,x26042)+E(f754(x26041,x26043,x26044),f754(x26042,x26043,x26044)) % 169.39/169.67 [2605]~E(x26051,x26052)+E(f754(x26053,x26051,x26054),f754(x26053,x26052,x26054)) % 169.39/169.67 [2606]~E(x26061,x26062)+E(f754(x26063,x26064,x26061),f754(x26063,x26064,x26062)) % 169.39/169.67 [2607]~E(x26071,x26072)+E(f828(x26071),f828(x26072)) % 169.39/169.67 [2608]~E(x26081,x26082)+E(f223(x26081,x26083),f223(x26082,x26083)) % 169.39/169.67 [2609]~E(x26091,x26092)+E(f223(x26093,x26091),f223(x26093,x26092)) % 169.39/169.67 [2610]~E(x26101,x26102)+E(f550(x26101,x26103,x26104,x26105,x26106),f550(x26102,x26103,x26104,x26105,x26106)) % 169.39/169.67 [2611]~E(x26111,x26112)+E(f550(x26113,x26111,x26114,x26115,x26116),f550(x26113,x26112,x26114,x26115,x26116)) % 169.39/169.67 [2612]~E(x26121,x26122)+E(f550(x26123,x26124,x26121,x26125,x26126),f550(x26123,x26124,x26122,x26125,x26126)) % 169.39/169.67 [2613]~E(x26131,x26132)+E(f550(x26133,x26134,x26135,x26131,x26136),f550(x26133,x26134,x26135,x26132,x26136)) % 169.39/169.67 [2614]~E(x26141,x26142)+E(f550(x26143,x26144,x26145,x26146,x26141),f550(x26143,x26144,x26145,x26146,x26142)) % 169.39/169.67 [2615]~E(x26151,x26152)+E(f783(x26151,x26153,x26154),f783(x26152,x26153,x26154)) % 169.39/169.67 [2616]~E(x26161,x26162)+E(f783(x26163,x26161,x26164),f783(x26163,x26162,x26164)) % 169.39/169.67 [2617]~E(x26171,x26172)+E(f783(x26173,x26174,x26171),f783(x26173,x26174,x26172)) % 169.39/169.67 [2618]~E(x26181,x26182)+E(f220(x26181,x26183,x26184,x26185,x26186,x26187,x26188),f220(x26182,x26183,x26184,x26185,x26186,x26187,x26188)) % 169.39/169.67 [2619]~E(x26191,x26192)+E(f220(x26193,x26191,x26194,x26195,x26196,x26197,x26198),f220(x26193,x26192,x26194,x26195,x26196,x26197,x26198)) % 169.39/169.67 [2620]~E(x26201,x26202)+E(f220(x26203,x26204,x26201,x26205,x26206,x26207,x26208),f220(x26203,x26204,x26202,x26205,x26206,x26207,x26208)) % 169.39/169.67 [2621]~E(x26211,x26212)+E(f220(x26213,x26214,x26215,x26211,x26216,x26217,x26218),f220(x26213,x26214,x26215,x26212,x26216,x26217,x26218)) % 169.39/169.67 [2622]~E(x26221,x26222)+E(f220(x26223,x26224,x26225,x26226,x26221,x26227,x26228),f220(x26223,x26224,x26225,x26226,x26222,x26227,x26228)) % 169.39/169.67 [2623]~E(x26231,x26232)+E(f220(x26233,x26234,x26235,x26236,x26237,x26231,x26238),f220(x26233,x26234,x26235,x26236,x26237,x26232,x26238)) % 169.39/169.67 [2624]~E(x26241,x26242)+E(f220(x26243,x26244,x26245,x26246,x26247,x26248,x26241),f220(x26243,x26244,x26245,x26246,x26247,x26248,x26242)) % 169.39/169.67 [2625]~P1(x26251)+P1(x26252)+~E(x26251,x26252) % 169.39/169.67 [2626]~P2(x26261)+P2(x26262)+~E(x26261,x26262) % 169.39/169.67 [2627]~P24(x26271)+P24(x26272)+~E(x26271,x26272) % 169.39/169.67 [2628]~P104(x26281)+P104(x26282)+~E(x26281,x26282) % 169.39/169.67 [2629]P10(x26292,x26293,x26294,x26295,x26296,x26297)+~E(x26291,x26292)+~P10(x26291,x26293,x26294,x26295,x26296,x26297) % 169.39/169.67 [2630]P10(x26303,x26302,x26304,x26305,x26306,x26307)+~E(x26301,x26302)+~P10(x26303,x26301,x26304,x26305,x26306,x26307) % 169.39/169.67 [2631]P10(x26313,x26314,x26312,x26315,x26316,x26317)+~E(x26311,x26312)+~P10(x26313,x26314,x26311,x26315,x26316,x26317) % 169.39/169.67 [2632]P10(x26323,x26324,x26325,x26322,x26326,x26327)+~E(x26321,x26322)+~P10(x26323,x26324,x26325,x26321,x26326,x26327) % 169.39/169.67 [2633]P10(x26333,x26334,x26335,x26336,x26332,x26337)+~E(x26331,x26332)+~P10(x26333,x26334,x26335,x26336,x26331,x26337) % 169.39/169.67 [2634]P10(x26343,x26344,x26345,x26346,x26347,x26342)+~E(x26341,x26342)+~P10(x26343,x26344,x26345,x26346,x26347,x26341) % 169.39/169.67 [2635]~P105(x26351)+P105(x26352)+~E(x26351,x26352) % 169.39/169.67 [2636]P146(x26362,x26363,x26364)+~E(x26361,x26362)+~P146(x26361,x26363,x26364) % 169.39/169.67 [2637]P146(x26373,x26372,x26374)+~E(x26371,x26372)+~P146(x26373,x26371,x26374) % 169.39/169.67 [2638]P146(x26383,x26384,x26382)+~E(x26381,x26382)+~P146(x26383,x26384,x26381) % 169.39/169.67 [2639]P145(x26392,x26393,x26394)+~E(x26391,x26392)+~P145(x26391,x26393,x26394) % 169.39/169.67 [2640]P145(x26403,x26402,x26404)+~E(x26401,x26402)+~P145(x26403,x26401,x26404) % 169.39/169.67 [2641]P145(x26413,x26414,x26412)+~E(x26411,x26412)+~P145(x26413,x26414,x26411) % 169.39/169.67 [2642]~P107(x26421)+P107(x26422)+~E(x26421,x26422) % 169.39/169.67 [2643]~P106(x26431)+P106(x26432)+~E(x26431,x26432) % 169.39/169.67 [2644]~P124(x26441)+P124(x26442)+~E(x26441,x26442) % 169.39/169.67 [2645]P21(x26452,x26453,x26454,x26455)+~E(x26451,x26452)+~P21(x26451,x26453,x26454,x26455) % 169.39/169.67 [2646]P21(x26463,x26462,x26464,x26465)+~E(x26461,x26462)+~P21(x26463,x26461,x26464,x26465) % 169.39/169.67 [2647]P21(x26473,x26474,x26472,x26475)+~E(x26471,x26472)+~P21(x26473,x26474,x26471,x26475) % 169.39/169.67 [2648]P21(x26483,x26484,x26485,x26482)+~E(x26481,x26482)+~P21(x26483,x26484,x26485,x26481) % 169.39/169.67 [2649]~P83(x26491)+P83(x26492)+~E(x26491,x26492) % 169.39/169.67 [2650]P39(x26502,x26503)+~E(x26501,x26502)+~P39(x26501,x26503) % 169.39/169.67 [2651]P39(x26513,x26512)+~E(x26511,x26512)+~P39(x26513,x26511) % 169.39/169.67 [2652]~P92(x26521)+P92(x26522)+~E(x26521,x26522) % 169.39/169.67 [2653]~P120(x26531)+P120(x26532)+~E(x26531,x26532) % 169.39/169.67 [2654]~P108(x26541)+P108(x26542)+~E(x26541,x26542) % 169.39/169.67 [2655]~P119(x26551)+P119(x26552)+~E(x26551,x26552) % 169.39/169.67 [2656]~P61(x26561)+P61(x26562)+~E(x26561,x26562) % 169.39/169.67 [2657]P36(x26572,x26573,x26574,x26575,x26576)+~E(x26571,x26572)+~P36(x26571,x26573,x26574,x26575,x26576) % 169.39/169.67 [2658]P36(x26583,x26582,x26584,x26585,x26586)+~E(x26581,x26582)+~P36(x26583,x26581,x26584,x26585,x26586) % 169.39/169.67 [2659]P36(x26593,x26594,x26592,x26595,x26596)+~E(x26591,x26592)+~P36(x26593,x26594,x26591,x26595,x26596) % 169.39/169.67 [2660]P36(x26603,x26604,x26605,x26602,x26606)+~E(x26601,x26602)+~P36(x26603,x26604,x26605,x26601,x26606) % 169.39/169.67 [2661]P36(x26613,x26614,x26615,x26616,x26612)+~E(x26611,x26612)+~P36(x26613,x26614,x26615,x26616,x26611) % 169.39/169.67 [2662]~P25(x26621)+P25(x26622)+~E(x26621,x26622) % 169.39/169.67 [2663]P13(x26632,x26633,x26634)+~E(x26631,x26632)+~P13(x26631,x26633,x26634) % 169.39/169.67 [2664]P13(x26643,x26642,x26644)+~E(x26641,x26642)+~P13(x26643,x26641,x26644) % 169.39/169.67 [2665]P13(x26653,x26654,x26652)+~E(x26651,x26652)+~P13(x26653,x26654,x26651) % 169.39/169.67 [2666]~P63(x26661)+P63(x26662)+~E(x26661,x26662) % 169.39/169.67 [2667]P30(x26672,x26673)+~E(x26671,x26672)+~P30(x26671,x26673) % 169.39/169.67 [2668]P30(x26683,x26682)+~E(x26681,x26682)+~P30(x26683,x26681) % 169.39/169.67 [2669]~P142(x26691)+P142(x26692)+~E(x26691,x26692) % 169.39/169.67 [2670]~P62(x26701)+P62(x26702)+~E(x26701,x26702) % 169.39/169.67 [2671]~P75(x26711)+P75(x26712)+~E(x26711,x26712) % 169.39/169.67 [2672]~P64(x26721)+P64(x26722)+~E(x26721,x26722) % 169.39/169.67 [2673]~P65(x26731)+P65(x26732)+~E(x26731,x26732) % 169.39/169.67 [2674]P9(x26742,x26743,x26744,x26745)+~E(x26741,x26742)+~P9(x26741,x26743,x26744,x26745) % 169.39/169.67 [2675]P9(x26753,x26752,x26754,x26755)+~E(x26751,x26752)+~P9(x26753,x26751,x26754,x26755) % 169.39/169.67 [2676]P9(x26763,x26764,x26762,x26765)+~E(x26761,x26762)+~P9(x26763,x26764,x26761,x26765) % 169.39/169.67 [2677]P9(x26773,x26774,x26775,x26772)+~E(x26771,x26772)+~P9(x26773,x26774,x26775,x26771) % 169.39/169.67 [2678]P54(x26782,x26783,x26784,x26785,x26786)+~E(x26781,x26782)+~P54(x26781,x26783,x26784,x26785,x26786) % 169.39/169.67 [2679]P54(x26793,x26792,x26794,x26795,x26796)+~E(x26791,x26792)+~P54(x26793,x26791,x26794,x26795,x26796) % 169.39/169.67 [2680]P54(x26803,x26804,x26802,x26805,x26806)+~E(x26801,x26802)+~P54(x26803,x26804,x26801,x26805,x26806) % 169.39/169.67 [2681]P54(x26813,x26814,x26815,x26812,x26816)+~E(x26811,x26812)+~P54(x26813,x26814,x26815,x26811,x26816) % 169.39/169.67 [2682]P54(x26823,x26824,x26825,x26826,x26822)+~E(x26821,x26822)+~P54(x26823,x26824,x26825,x26826,x26821) % 169.39/169.67 [2683]~P79(x26831)+P79(x26832)+~E(x26831,x26832) % 169.39/169.67 [2684]~P67(x26841)+P67(x26842)+~E(x26841,x26842) % 169.39/169.67 [2685]~P80(x26851)+P80(x26852)+~E(x26851,x26852) % 169.39/169.67 [2686]~P115(x26861)+P115(x26862)+~E(x26861,x26862) % 169.39/169.67 [2687]~P109(x26871)+P109(x26872)+~E(x26871,x26872) % 169.39/169.67 [2688]~P110(x26881)+P110(x26882)+~E(x26881,x26882) % 169.39/169.67 [2689]~P76(x26891)+P76(x26892)+~E(x26891,x26892) % 169.39/169.67 [2690]P37(x26902,x26903,x26904)+~E(x26901,x26902)+~P37(x26901,x26903,x26904) % 169.39/169.67 [2691]P37(x26913,x26912,x26914)+~E(x26911,x26912)+~P37(x26913,x26911,x26914) % 169.39/169.67 [2692]P37(x26923,x26924,x26922)+~E(x26921,x26922)+~P37(x26923,x26924,x26921) % 169.39/169.67 [2693]P33(x26932,x26933,x26934)+~E(x26931,x26932)+~P33(x26931,x26933,x26934) % 169.39/169.67 [2694]P33(x26943,x26942,x26944)+~E(x26941,x26942)+~P33(x26943,x26941,x26944) % 169.39/169.67 [2695]P33(x26953,x26954,x26952)+~E(x26951,x26952)+~P33(x26953,x26954,x26951) % 169.39/169.67 [2696]~P77(x26961)+P77(x26962)+~E(x26961,x26962) % 169.39/169.67 [2697]~P29(x26971)+P29(x26972)+~E(x26971,x26972) % 169.39/169.67 [2698]~P81(x26981)+P81(x26982)+~E(x26981,x26982) % 169.39/169.67 [2699]~P68(x26991)+P68(x26992)+~E(x26991,x26992) % 169.39/169.67 [2700]~P95(x27001)+P95(x27002)+~E(x27001,x27002) % 169.39/169.67 [2701]~P59(x27011)+P59(x27012)+~E(x27011,x27012) % 169.39/169.67 [2702]~P90(x27021)+P90(x27022)+~E(x27021,x27022) % 169.39/169.67 [2703]~P123(x27031)+P123(x27032)+~E(x27031,x27032) % 169.39/169.67 [2704]P11(x27042,x27043,x27044)+~E(x27041,x27042)+~P11(x27041,x27043,x27044) % 169.39/169.67 [2705]P11(x27053,x27052,x27054)+~E(x27051,x27052)+~P11(x27053,x27051,x27054) % 169.39/169.67 [2706]P11(x27063,x27064,x27062)+~E(x27061,x27062)+~P11(x27063,x27064,x27061) % 169.39/169.67 [2707]~P136(x27071)+P136(x27072)+~E(x27071,x27072) % 169.39/169.67 [2708]~P100(x27081)+P100(x27082)+~E(x27081,x27082) % 169.39/169.67 [2709]~P111(x27091)+P111(x27092)+~E(x27091,x27092) % 169.39/169.67 [2710]~P112(x27101)+P112(x27102)+~E(x27101,x27102) % 169.39/169.67 [2711]~P72(x27111)+P72(x27112)+~E(x27111,x27112) % 169.39/169.67 [2712]~P85(x27121)+P85(x27122)+~E(x27121,x27122) % 169.39/169.67 [2713]~P66(x27131)+P66(x27132)+~E(x27131,x27132) % 169.39/169.67 [2714]P49(x27142,x27143,x27144)+~E(x27141,x27142)+~P49(x27141,x27143,x27144) % 169.39/169.67 [2715]P49(x27153,x27152,x27154)+~E(x27151,x27152)+~P49(x27153,x27151,x27154) % 169.39/169.67 [2716]P49(x27163,x27164,x27162)+~E(x27161,x27162)+~P49(x27163,x27164,x27161) % 169.39/169.67 [2717]P16(x27172,x27173,x27174,x27175)+~E(x27171,x27172)+~P16(x27171,x27173,x27174,x27175) % 169.39/169.67 [2718]P16(x27183,x27182,x27184,x27185)+~E(x27181,x27182)+~P16(x27183,x27181,x27184,x27185) % 169.39/169.67 [2719]P16(x27193,x27194,x27192,x27195)+~E(x27191,x27192)+~P16(x27193,x27194,x27191,x27195) % 169.39/169.67 [2720]P16(x27203,x27204,x27205,x27202)+~E(x27201,x27202)+~P16(x27203,x27204,x27205,x27201) % 169.39/169.67 [2721]~P69(x27211)+P69(x27212)+~E(x27211,x27212) % 169.39/169.67 [2722]P6(x27222,x27223,x27224)+~E(x27221,x27222)+~P6(x27221,x27223,x27224) % 169.39/169.67 [2723]P6(x27233,x27232,x27234)+~E(x27231,x27232)+~P6(x27233,x27231,x27234) % 169.39/169.67 [2724]P6(x27243,x27244,x27242)+~E(x27241,x27242)+~P6(x27243,x27244,x27241) % 169.39/169.67 [2725]~P101(x27251)+P101(x27252)+~E(x27251,x27252) % 169.39/169.67 [2726]~P70(x27261)+P70(x27262)+~E(x27261,x27262) % 169.39/169.67 [2727]~P26(x27271)+P26(x27272)+~E(x27271,x27272) % 169.39/169.67 [2728]~P41(x27281)+P41(x27282)+~E(x27281,x27282) % 169.39/169.67 [2729]~P138(x27291)+P138(x27292)+~E(x27291,x27292) % 169.39/169.67 [2730]P53(x27302,x27303,x27304)+~E(x27301,x27302)+~P53(x27301,x27303,x27304) % 169.39/169.67 [2731]P53(x27313,x27312,x27314)+~E(x27311,x27312)+~P53(x27313,x27311,x27314) % 169.39/169.67 [2732]P53(x27323,x27324,x27322)+~E(x27321,x27322)+~P53(x27323,x27324,x27321) % 169.39/169.67 [2733]~P137(x27331)+P137(x27332)+~E(x27331,x27332) % 169.39/169.67 [2734]P57(x27342,x27343)+~E(x27341,x27342)+~P57(x27341,x27343) % 169.39/169.67 [2735]P57(x27353,x27352)+~E(x27351,x27352)+~P57(x27353,x27351) % 169.39/169.67 [2736]P17(x27362,x27363,x27364,x27365,x27366)+~E(x27361,x27362)+~P17(x27361,x27363,x27364,x27365,x27366) % 169.39/169.67 [2737]P17(x27373,x27372,x27374,x27375,x27376)+~E(x27371,x27372)+~P17(x27373,x27371,x27374,x27375,x27376) % 169.39/169.67 [2738]P17(x27383,x27384,x27382,x27385,x27386)+~E(x27381,x27382)+~P17(x27383,x27384,x27381,x27385,x27386) % 169.39/169.67 [2739]P17(x27393,x27394,x27395,x27392,x27396)+~E(x27391,x27392)+~P17(x27393,x27394,x27395,x27391,x27396) % 169.39/169.67 [2740]P17(x27403,x27404,x27405,x27406,x27402)+~E(x27401,x27402)+~P17(x27403,x27404,x27405,x27406,x27401) % 169.39/169.67 [2741]~P82(x27411)+P82(x27412)+~E(x27411,x27412) % 169.39/169.67 [2742]P20(x27422,x27423,x27424)+~E(x27421,x27422)+~P20(x27421,x27423,x27424) % 169.39/169.67 [2743]P20(x27433,x27432,x27434)+~E(x27431,x27432)+~P20(x27433,x27431,x27434) % 169.39/169.67 [2744]P20(x27443,x27444,x27442)+~E(x27441,x27442)+~P20(x27443,x27444,x27441) % 169.39/169.67 [2745]P35(x27452,x27453,x27454)+~E(x27451,x27452)+~P35(x27451,x27453,x27454) % 169.39/169.67 [2746]P35(x27463,x27462,x27464)+~E(x27461,x27462)+~P35(x27463,x27461,x27464) % 169.39/169.67 [2747]P35(x27473,x27474,x27472)+~E(x27471,x27472)+~P35(x27473,x27474,x27471) % 169.39/169.67 [2748]~P84(x27481)+P84(x27482)+~E(x27481,x27482) % 169.39/169.67 [2749]P32(x27492,x27493)+~E(x27491,x27492)+~P32(x27491,x27493) % 169.39/169.67 [2750]P32(x27503,x27502)+~E(x27501,x27502)+~P32(x27503,x27501) % 169.39/169.67 [2751]~P58(x27511)+P58(x27512)+~E(x27511,x27512) % 169.39/169.67 [2752]~P139(x27521)+P139(x27522)+~E(x27521,x27522) % 169.39/169.67 [2753]~P60(x27531)+P60(x27532)+~E(x27531,x27532) % 169.39/169.67 [2754]~P28(x27541)+P28(x27542)+~E(x27541,x27542) % 169.39/169.67 [2755]~P116(x27551)+P116(x27552)+~E(x27551,x27552) % 169.39/169.67 [2756]~P117(x27561)+P117(x27562)+~E(x27561,x27562) % 169.39/169.67 [2757]P4(x27572,x27573,x27574,x27575,x27576)+~E(x27571,x27572)+~P4(x27571,x27573,x27574,x27575,x27576) % 169.39/169.67 [2758]P4(x27583,x27582,x27584,x27585,x27586)+~E(x27581,x27582)+~P4(x27583,x27581,x27584,x27585,x27586) % 169.39/169.67 [2759]P4(x27593,x27594,x27592,x27595,x27596)+~E(x27591,x27592)+~P4(x27593,x27594,x27591,x27595,x27596) % 169.39/169.67 [2760]P4(x27603,x27604,x27605,x27602,x27606)+~E(x27601,x27602)+~P4(x27603,x27604,x27605,x27601,x27606) % 169.39/169.67 [2761]P4(x27613,x27614,x27615,x27616,x27612)+~E(x27611,x27612)+~P4(x27613,x27614,x27615,x27616,x27611) % 169.39/169.67 [2762]~P125(x27621)+P125(x27622)+~E(x27621,x27622) % 169.39/169.67 [2763]~P126(x27631)+P126(x27632)+~E(x27631,x27632) % 169.39/169.67 [2764]~P88(x27641)+P88(x27642)+~E(x27641,x27642) % 169.39/169.67 [2765]~P131(x27651)+P131(x27652)+~E(x27651,x27652) % 169.39/169.67 [2766]P12(x27662,x27663,x27664)+~E(x27661,x27662)+~P12(x27661,x27663,x27664) % 169.39/169.67 [2767]P12(x27673,x27672,x27674)+~E(x27671,x27672)+~P12(x27673,x27671,x27674) % 169.39/169.67 [2768]P12(x27683,x27684,x27682)+~E(x27681,x27682)+~P12(x27683,x27684,x27681) % 169.39/169.67 [2769]~P78(x27691)+P78(x27692)+~E(x27691,x27692) % 169.39/169.67 [2770]P31(x27702,x27703,x27704)+~E(x27701,x27702)+~P31(x27701,x27703,x27704) % 169.39/169.67 [2771]P31(x27713,x27712,x27714)+~E(x27711,x27712)+~P31(x27713,x27711,x27714) % 169.39/169.67 [2772]P31(x27723,x27724,x27722)+~E(x27721,x27722)+~P31(x27723,x27724,x27721) % 169.39/169.67 [2773]P43(x27732,x27733,x27734,x27735,x27736,x27737)+~E(x27731,x27732)+~P43(x27731,x27733,x27734,x27735,x27736,x27737) % 169.39/169.67 [2774]P43(x27743,x27742,x27744,x27745,x27746,x27747)+~E(x27741,x27742)+~P43(x27743,x27741,x27744,x27745,x27746,x27747) % 169.39/169.67 [2775]P43(x27753,x27754,x27752,x27755,x27756,x27757)+~E(x27751,x27752)+~P43(x27753,x27754,x27751,x27755,x27756,x27757) % 169.39/169.67 [2776]P43(x27763,x27764,x27765,x27762,x27766,x27767)+~E(x27761,x27762)+~P43(x27763,x27764,x27765,x27761,x27766,x27767) % 169.39/169.67 [2777]P43(x27773,x27774,x27775,x27776,x27772,x27777)+~E(x27771,x27772)+~P43(x27773,x27774,x27775,x27776,x27771,x27777) % 169.39/169.67 [2778]P43(x27783,x27784,x27785,x27786,x27787,x27782)+~E(x27781,x27782)+~P43(x27783,x27784,x27785,x27786,x27787,x27781) % 169.39/169.67 [2779]P7(x27792,x27793,x27794)+~E(x27791,x27792)+~P7(x27791,x27793,x27794) % 169.39/169.67 [2780]P7(x27803,x27802,x27804)+~E(x27801,x27802)+~P7(x27803,x27801,x27804) % 169.39/169.67 [2781]P7(x27813,x27814,x27812)+~E(x27811,x27812)+~P7(x27813,x27814,x27811) % 169.39/169.67 [2782]~P93(x27821)+P93(x27822)+~E(x27821,x27822) % 169.39/169.67 [2783]P18(x27832,x27833,x27834,x27835,x27836,x27837)+~E(x27831,x27832)+~P18(x27831,x27833,x27834,x27835,x27836,x27837) % 169.39/169.67 [2784]P18(x27843,x27842,x27844,x27845,x27846,x27847)+~E(x27841,x27842)+~P18(x27843,x27841,x27844,x27845,x27846,x27847) % 169.39/169.67 [2785]P18(x27853,x27854,x27852,x27855,x27856,x27857)+~E(x27851,x27852)+~P18(x27853,x27854,x27851,x27855,x27856,x27857) % 169.39/169.67 [2786]P18(x27863,x27864,x27865,x27862,x27866,x27867)+~E(x27861,x27862)+~P18(x27863,x27864,x27865,x27861,x27866,x27867) % 169.39/169.67 [2787]P18(x27873,x27874,x27875,x27876,x27872,x27877)+~E(x27871,x27872)+~P18(x27873,x27874,x27875,x27876,x27871,x27877) % 169.39/169.67 [2788]P18(x27883,x27884,x27885,x27886,x27887,x27882)+~E(x27881,x27882)+~P18(x27883,x27884,x27885,x27886,x27887,x27881) % 169.39/169.67 [2789]~P73(x27891)+P73(x27892)+~E(x27891,x27892) % 169.39/169.67 [2790]~P129(x27901)+P129(x27902)+~E(x27901,x27902) % 169.39/169.67 [2791]~P27(x27911)+P27(x27912)+~E(x27911,x27912) % 169.39/169.67 [2792]P15(x27922,x27923,x27924,x27925)+~E(x27921,x27922)+~P15(x27921,x27923,x27924,x27925) % 169.39/169.67 [2793]P15(x27933,x27932,x27934,x27935)+~E(x27931,x27932)+~P15(x27933,x27931,x27934,x27935) % 169.39/169.67 [2794]P15(x27943,x27944,x27942,x27945)+~E(x27941,x27942)+~P15(x27943,x27944,x27941,x27945) % 169.39/169.67 [2795]P15(x27953,x27954,x27955,x27952)+~E(x27951,x27952)+~P15(x27953,x27954,x27955,x27951) % 169.39/169.67 [2796]~P140(x27961)+P140(x27962)+~E(x27961,x27962) % 169.39/169.67 [2797]~P130(x27971)+P130(x27972)+~E(x27971,x27972) % 169.39/169.67 [2798]P8(x27982,x27983,x27984)+~E(x27981,x27982)+~P8(x27981,x27983,x27984) % 169.39/169.67 [2799]P8(x27993,x27992,x27994)+~E(x27991,x27992)+~P8(x27993,x27991,x27994) % 169.39/169.67 [2800]P8(x28003,x28004,x28002)+~E(x28001,x28002)+~P8(x28003,x28004,x28001) % 169.39/169.67 [2801]P23(x28012,x28013,x28014)+~E(x28011,x28012)+~P23(x28011,x28013,x28014) % 169.39/169.67 [2802]P23(x28023,x28022,x28024)+~E(x28021,x28022)+~P23(x28023,x28021,x28024) % 169.39/169.67 [2803]P23(x28033,x28034,x28032)+~E(x28031,x28032)+~P23(x28033,x28034,x28031) % 169.39/169.67 [2804]~P141(x28041)+P141(x28042)+~E(x28041,x28042) % 169.39/169.67 [2805]P55(x28052,x28053)+~E(x28051,x28052)+~P55(x28051,x28053) % 169.39/169.67 [2806]P55(x28063,x28062)+~E(x28061,x28062)+~P55(x28063,x28061) % 169.39/169.67 [2807]~P143(x28071)+P143(x28072)+~E(x28071,x28072) % 169.39/169.67 [2808]P52(x28082,x28083,x28084)+~E(x28081,x28082)+~P52(x28081,x28083,x28084) % 169.39/169.67 [2809]P52(x28093,x28092,x28094)+~E(x28091,x28092)+~P52(x28093,x28091,x28094) % 169.39/169.67 [2810]P52(x28103,x28104,x28102)+~E(x28101,x28102)+~P52(x28103,x28104,x28101) % 169.39/169.67 [2811]~P118(x28111)+P118(x28112)+~E(x28111,x28112) % 169.39/169.67 [2812]P5(x28122,x28123)+~E(x28121,x28122)+~P5(x28121,x28123) % 169.39/169.67 [2813]P5(x28133,x28132)+~E(x28131,x28132)+~P5(x28133,x28131) % 169.39/169.67 [2814]~P132(x28141)+P132(x28142)+~E(x28141,x28142) % 169.39/169.67 [2815]P56(x28152,x28153,x28154,x28155)+~E(x28151,x28152)+~P56(x28151,x28153,x28154,x28155) % 169.39/169.67 [2816]P56(x28163,x28162,x28164,x28165)+~E(x28161,x28162)+~P56(x28163,x28161,x28164,x28165) % 169.39/169.67 [2817]P56(x28173,x28174,x28172,x28175)+~E(x28171,x28172)+~P56(x28173,x28174,x28171,x28175) % 169.39/169.67 [2818]P56(x28183,x28184,x28185,x28182)+~E(x28181,x28182)+~P56(x28183,x28184,x28185,x28181) % 169.39/169.67 [2819]P50(x28192,x28193)+~E(x28191,x28192)+~P50(x28191,x28193) % 169.39/169.67 [2820]P50(x28203,x28202)+~E(x28201,x28202)+~P50(x28203,x28201) % 169.39/169.67 [2821]~P134(x28211)+P134(x28212)+~E(x28211,x28212) % 169.39/169.67 [2822]~P86(x28221)+P86(x28222)+~E(x28221,x28222) % 169.39/169.67 [2823]~P91(x28231)+P91(x28232)+~E(x28231,x28232) % 169.39/169.67 [2824]~P133(x28241)+P133(x28242)+~E(x28241,x28242) % 169.39/169.67 [2825]P14(x28252,x28253,x28254)+~E(x28251,x28252)+~P14(x28251,x28253,x28254) % 169.39/169.67 [2826]P14(x28263,x28262,x28264)+~E(x28261,x28262)+~P14(x28263,x28261,x28264) % 169.39/169.67 [2827]P14(x28273,x28274,x28272)+~E(x28271,x28272)+~P14(x28273,x28274,x28271) % 169.39/169.67 [2828]P42(x28282,x28283,x28284,x28285)+~E(x28281,x28282)+~P42(x28281,x28283,x28284,x28285) % 169.39/169.67 [2829]P42(x28293,x28292,x28294,x28295)+~E(x28291,x28292)+~P42(x28293,x28291,x28294,x28295) % 169.39/169.67 [2830]P42(x28303,x28304,x28302,x28305)+~E(x28301,x28302)+~P42(x28303,x28304,x28301,x28305) % 169.39/169.67 [2831]P42(x28313,x28314,x28315,x28312)+~E(x28311,x28312)+~P42(x28313,x28314,x28315,x28311) % 169.39/169.67 [2832]~P144(x28321)+P144(x28322)+~E(x28321,x28322) % 169.39/169.67 [2833]~P98(x28331)+P98(x28332)+~E(x28331,x28332) % 169.39/169.67 [2834]~P121(x28341)+P121(x28342)+~E(x28341,x28342) % 169.39/169.67 [2835]~P99(x28351)+P99(x28352)+~E(x28351,x28352) % 169.39/169.67 [2836]~P122(x28361)+P122(x28362)+~E(x28361,x28362) % 169.39/169.67 [2837]P44(x28372,x28373)+~E(x28371,x28372)+~P44(x28371,x28373) % 169.39/169.67 [2838]P44(x28383,x28382)+~E(x28381,x28382)+~P44(x28383,x28381) % 169.39/169.67 [2839]P51(x28392,x28393)+~E(x28391,x28392)+~P51(x28391,x28393) % 169.39/169.67 [2840]P51(x28403,x28402)+~E(x28401,x28402)+~P51(x28403,x28401) % 169.39/169.67 [2841]~P97(x28411)+P97(x28412)+~E(x28411,x28412) % 169.39/169.67 [2842]~P127(x28421)+P127(x28422)+~E(x28421,x28422) % 169.39/169.67 [2843]P34(x28432,x28433,x28434,x28435)+~E(x28431,x28432)+~P34(x28431,x28433,x28434,x28435) % 169.39/169.67 [2844]P34(x28443,x28442,x28444,x28445)+~E(x28441,x28442)+~P34(x28443,x28441,x28444,x28445) % 169.39/169.67 [2845]P34(x28453,x28454,x28452,x28455)+~E(x28451,x28452)+~P34(x28453,x28454,x28451,x28455) % 169.39/169.67 [2846]P34(x28463,x28464,x28465,x28462)+~E(x28461,x28462)+~P34(x28463,x28464,x28465,x28461) % 169.39/169.67 [2847]P19(x28472,x28473,x28474,x28475,x28476,x28477)+~E(x28471,x28472)+~P19(x28471,x28473,x28474,x28475,x28476,x28477) % 169.39/169.67 [2848]P19(x28483,x28482,x28484,x28485,x28486,x28487)+~E(x28481,x28482)+~P19(x28483,x28481,x28484,x28485,x28486,x28487) % 169.39/169.67 [2849]P19(x28493,x28494,x28492,x28495,x28496,x28497)+~E(x28491,x28492)+~P19(x28493,x28494,x28491,x28495,x28496,x28497) % 169.39/169.67 [2850]P19(x28503,x28504,x28505,x28502,x28506,x28507)+~E(x28501,x28502)+~P19(x28503,x28504,x28505,x28501,x28506,x28507) % 169.39/169.67 [2851]P19(x28513,x28514,x28515,x28516,x28512,x28517)+~E(x28511,x28512)+~P19(x28513,x28514,x28515,x28516,x28511,x28517) % 169.39/169.67 [2852]P19(x28523,x28524,x28525,x28526,x28527,x28522)+~E(x28521,x28522)+~P19(x28523,x28524,x28525,x28526,x28527,x28521) % 169.39/169.67 [2853]~P128(x28531)+P128(x28532)+~E(x28531,x28532) % 169.39/169.67 [2854]~P71(x28541)+P71(x28542)+~E(x28541,x28542) % 169.39/169.67 [2855]P22(x28552,x28553)+~E(x28551,x28552)+~P22(x28551,x28553) % 169.39/169.67 [2856]P22(x28563,x28562)+~E(x28561,x28562)+~P22(x28563,x28561) % 169.39/169.67 [2857]~P89(x28571)+P89(x28572)+~E(x28571,x28572) % 169.39/169.67 [2858]~P102(x28581)+P102(x28582)+~E(x28581,x28582) % 169.39/169.67 [2859]~P135(x28591)+P135(x28592)+~E(x28591,x28592) % 169.39/169.67 [2860]~P103(x28601)+P103(x28602)+~E(x28601,x28602) % 169.39/169.67 [2861]P40(x28612,x28613)+~E(x28611,x28612)+~P40(x28611,x28613) % 169.39/169.67 [2862]P40(x28623,x28622)+~E(x28621,x28622)+~P40(x28623,x28621) % 169.39/169.67 [2863]~P94(x28631)+P94(x28632)+~E(x28631,x28632) % 169.39/169.67 [2864]~P87(x28641)+P87(x28642)+~E(x28641,x28642) % 169.39/169.67 [2865]~P74(x28651)+P74(x28652)+~E(x28651,x28652) % 169.39/169.67 [2866]~P96(x28661)+P96(x28662)+~E(x28661,x28662) % 169.39/169.67 [2867]~P45(x28671)+P45(x28672)+~E(x28671,x28672) % 169.39/169.67 [2868]P46(x28682,x28683)+~E(x28681,x28682)+~P46(x28681,x28683) % 169.39/169.67 [2869]P46(x28693,x28692)+~E(x28691,x28692)+~P46(x28693,x28691) % 169.39/169.67 [2870]P47(x28702,x28703,x28704)+~E(x28701,x28702)+~P47(x28701,x28703,x28704) % 169.39/169.67 [2871]P47(x28713,x28712,x28714)+~E(x28711,x28712)+~P47(x28713,x28711,x28714) % 169.39/169.67 [2872]P47(x28723,x28724,x28722)+~E(x28721,x28722)+~P47(x28723,x28724,x28721) % 169.39/169.67 [2873]~P114(x28731)+P114(x28732)+~E(x28731,x28732) % 169.39/169.67 [2874]~P38(x28741)+P38(x28742)+~E(x28741,x28742) % 169.39/169.67 [2875]~P113(x28751)+P113(x28752)+~E(x28751,x28752) % 169.39/169.67 [2876]P48(x28762,x28763,x28764)+~E(x28761,x28762)+~P48(x28761,x28763,x28764) % 169.39/169.67 [2877]P48(x28773,x28772,x28774)+~E(x28771,x28772)+~P48(x28773,x28771,x28774) % 169.39/169.67 [2878]P48(x28783,x28784,x28782)+~E(x28781,x28782)+~P48(x28783,x28784,x28781) % 169.39/169.67 [2879]P3(x28792,x28793,x28794)+~E(x28791,x28792)+~P3(x28791,x28793,x28794) % 169.39/169.67 [2880]P3(x28803,x28802,x28804)+~E(x28801,x28802)+~P3(x28803,x28801,x28804) % 169.39/169.67 [2881]P3(x28813,x28814,x28812)+~E(x28811,x28812)+~P3(x28813,x28814,x28811) % 169.39/169.67 % 169.39/169.67 %------------------------------------------- % 169.42/169.72 cnf(10194,plain, % 169.42/169.72 (E(f334(f265(x101941,x101941),f266(x101941,x101942)),x101942)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(10197,plain, % 169.42/169.72 (~E(f334(a115,x101971),x101971)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10200,plain, % 169.42/169.72 (~E(f334(a115,x102001),x102001)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10203,plain, % 169.42/169.72 (E(f334(f265(x102031,x102031),f266(x102031,x102032)),x102032)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(10210,plain, % 169.42/169.72 (~E(f334(a115,x102101),x102101)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10223,plain, % 169.42/169.72 (~E(f334(a115,x102231),x102231)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10228,plain, % 169.42/169.72 (~P104(f334(f64(x102281,x102282,f195(f886(x102281,a871))),x102283))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(10231,plain, % 169.42/169.72 (~P104(f334(f64(x102311,x102312,f195(f886(x102311,a871))),x102313))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(10234,plain, % 169.42/169.72 (~E(f334(a115,x102341),x102341)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10237,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x102371),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(10240,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x102401),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(10253,plain, % 169.42/169.72 (~P104(f334(f195(f886(x102531,a871)),x102532))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,2882,3085,3259,10194,3129,3193,3137,3285,4568,10237,4565,4514,4575,3276,4555,4593,10228,4597,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075])). % 169.42/169.72 cnf(10257,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x102571)),x102571))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(10260,plain, % 169.42/169.72 (~E(f334(f334(f151(x102601),x102602),x102603),x102603)), % 169.42/169.72 inference(rename_variables,[],[4520])). % 169.42/169.72 cnf(10266,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x102661),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(10269,plain, % 169.42/169.72 (E(f334(f265(x102691,x102691),f266(x102691,x102692)),x102692)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(10272,plain, % 169.42/169.72 (E(f334(f265(x102721,x102721),f266(x102721,x102722)),x102722)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(10279,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x102791),x102792)),x102792))), % 169.42/169.72 inference(rename_variables,[],[4595])). % 169.42/169.72 cnf(10282,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x102821),x102822)),x102822))), % 169.42/169.72 inference(rename_variables,[],[4595])). % 169.42/169.72 cnf(10289,plain, % 169.42/169.72 (~E(x102891,f334(a115,x102891))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,2882,3085,3259,10194,10203,10269,3129,3193,3160,3137,4520,3372,3285,4568,10237,10240,4565,4514,4577,4145,4575,3276,4555,4593,10228,4597,4595,10279,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217])). % 169.42/169.72 cnf(10303,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x103031),x103031))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(10306,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f46(a877,x103061,x103062)),x103061))), % 169.42/169.72 inference(rename_variables,[],[3767])). % 169.42/169.72 cnf(10329,plain, % 169.42/169.72 (E(f334(f39(a877),f334(f255(a877),x103291)),x103291)), % 169.42/169.72 inference(rename_variables,[],[3191])). % 169.42/169.72 cnf(10337,plain, % 169.42/169.72 (~E(f334(a115,x103371),x103371)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10340,plain, % 169.42/169.72 (~E(f334(a115,x103401),x103401)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10343,plain, % 169.42/169.72 (~E(f334(a115,x103431),x103431)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10345,plain, % 169.42/169.72 (P104(f334(a201,a100))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,10234,10337,10340,2882,3085,3259,10194,10203,10269,3129,3193,3160,3137,3229,4520,3191,4602,3211,3372,3285,4568,10237,10240,3902,3304,4565,4514,4564,10303,3398,3832,3767,4577,10257,4145,4575,4554,3276,4555,4559,4593,10228,4597,4595,10279,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365])). % 169.42/169.72 cnf(10348,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x103481),f334(a115,x103481)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10357,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x103571),x103571))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10364,plain, % 169.42/169.72 (E(f334(f265(x103641,x103641),f266(x103641,x103642)),x103642)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(10367,plain, % 169.42/169.72 (E(f334(f265(x103671,x103671),f266(x103671,x103672)),x103672)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(10386,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x103861),x103861))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(10395,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x103951),x103951))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(10400,plain, % 169.42/169.72 (~E(f334(f334(f334(f73(x104001,f881(x104002)),x104003),x104004),f334(f241(x104002),x104005)),f334(f18(f881(x104002),x104001),f198(x104002)))), % 169.42/169.72 inference(rename_variables,[],[4589])). % 169.42/169.72 cnf(10427,plain, % 169.42/169.72 (~E(f334(f334(f151(x104271),x104272),x104273),x104273)), % 169.42/169.72 inference(rename_variables,[],[4520])). % 169.42/169.72 cnf(10430,plain, % 169.42/169.72 (~E(f334(a26,x104301),f34(x104302,x104303))), % 169.42/169.72 inference(rename_variables,[],[4509])). % 169.42/169.72 cnf(10441,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x104411),x104411))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(10446,plain, % 169.42/169.72 (~E(f334(a115,x104461),x104461)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10453,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x104531),x104531))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10466,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x104661),f334(a115,x104661)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10487,plain, % 169.42/169.72 (~P104(f334(f64(x104871,x104872,f195(f886(x104871,a871))),x104873))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(10506,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x105061),x105061))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(10521,plain, % 169.42/169.72 (~E(f334(a26,x105211),f34(x105212,x105213))), % 169.42/169.72 inference(rename_variables,[],[4509])). % 169.42/169.72 cnf(10530,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x105301),x105301))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(10535,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x105351),f334(a115,x105351)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10538,plain, % 169.42/169.72 (~P104(f334(f64(x105381,x105382,f195(f886(x105381,a871))),x105383))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(10541,plain, % 169.42/169.72 (~P104(f334(f64(x105411,x105412,f195(f886(x105411,a871))),x105413))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(10546,plain, % 169.42/169.72 (~P104(f334(f64(x105461,x105462,f195(f886(x105461,a871))),x105463))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(10556,plain, % 169.42/169.72 (~E(f334(f169(x105561),f334(a115,f334(f334(f134(x105561),f334(f169(x105561),x105562)),f334(f334(f151(x105561),x105563),f116(x105561))))),f334(f334(f151(x105561),x105563),x105562))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,3129,3193,3160,3137,3782,3229,4589,4520,10260,3191,4101,4602,3211,3672,3372,10348,10466,10535,3285,4568,10237,10240,10266,4584,3749,3902,3329,3331,3304,4565,4514,4052,3301,10357,10453,3302,10386,3303,4564,10303,10395,10506,3398,3832,3767,10306,4577,10257,4145,4575,4554,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4597,3791,4595,10279,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046])). % 169.42/169.72 cnf(10557,plain, % 169.42/169.72 (~E(f334(a115,x105571),x105571)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10575,plain, % 169.42/169.72 (P104(f334(f334(f250(a102),f334(a5,x105751)),f334(a5,f334(a115,x105751))))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,3129,3193,3160,3137,3782,3229,4589,4520,10260,3191,4101,4602,3211,3672,3372,10348,10466,10535,3762,3285,4568,10237,10240,10266,4584,3749,3902,3329,3331,3304,4565,4514,4052,3301,10357,10453,3302,10386,3303,4564,10303,10395,10506,3398,3832,3767,10306,4577,10257,4145,4575,4554,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4597,3791,4595,10279,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129])). % 169.42/169.72 cnf(10582,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x105821),x105821))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10585,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x105851),f334(f334(f82(a877),x105851),x105851)))), % 169.42/169.72 inference(rename_variables,[],[3573])). % 169.42/169.72 cnf(10588,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x105881),f334(f334(f82(a877),x105881),x105881)))), % 169.42/169.72 inference(rename_variables,[],[3573])). % 169.42/169.72 cnf(10591,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x105911),f334(a115,f334(f334(f81(a877),x105912),x105911))))), % 169.42/169.72 inference(rename_variables,[],[3760])). % 169.42/169.72 cnf(10596,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x105961),f334(a115,x105961)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10599,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x105991),f334(a115,x105991)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10602,plain, % 169.42/169.72 (P104(f334(f334(f336(x106021),x106022),f257(f886(x106021,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(10621,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x106211)),x106211))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(10624,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x106241)),x106241))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(10627,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x106271),x106272)),x106272))), % 169.42/169.72 inference(rename_variables,[],[4595])). % 169.42/169.72 cnf(10630,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x106301),x106302)),x106302))), % 169.42/169.72 inference(rename_variables,[],[4595])). % 169.42/169.72 cnf(10633,plain, % 169.42/169.72 (P104(f334(f257(f886(x106331,a871)),x106332))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(10636,plain, % 169.42/169.72 (E(f334(f39(a877),f334(f255(a877),x106361)),x106361)), % 169.42/169.72 inference(rename_variables,[],[3191])). % 169.42/169.72 cnf(10639,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x106391),f334(a115,x106391)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10646,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x106461),x106461))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10651,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x106511),x106511))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(10660,plain, % 169.42/169.72 (E(f334(f265(x106601,x106601),f266(x106601,x106602)),x106602)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(10663,plain, % 169.42/169.72 (P104(f334(f257(f886(x106631,a871)),x106632))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(10666,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x106661))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(10669,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x106691,a871)),f195(f886(x106691,a871))),x106692))), % 169.42/169.72 inference(rename_variables,[],[3758])). % 169.42/169.72 cnf(10672,plain, % 169.42/169.72 (P104(f334(f257(f886(x106721,a871)),x106722))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(10674,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(f334(f82(a877),f334(a115,x106741)),f334(a115,x106741))),x106741))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,10367,3129,3193,3160,3137,3782,3229,4589,4520,10260,3191,10329,4101,4602,3211,3672,3611,3372,10348,10466,10535,10596,10599,3762,3285,4568,10237,10240,10266,4584,3749,3517,3902,3329,3331,3304,4565,4514,4052,3301,10357,10453,10582,3302,10386,10441,3303,4564,10303,10395,10506,3462,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,3323,4145,4575,4554,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4600,3758,3573,10585,10588,4597,3791,4595,10279,10282,10627,3760,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363])). % 169.42/169.72 cnf(10675,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x106751),f334(f334(f82(a877),x106751),x106751)))), % 169.42/169.72 inference(rename_variables,[],[3573])). % 169.42/169.72 cnf(10679,plain, % 169.42/169.72 (E(f334(f169(x106791),f174(x106792,f334(f334(f134(x106791),f334(f169(x106791),x106793)),f334(f334(f151(x106791),x106794),f116(x106791))),f116(x106792))),f334(f334(f151(x106791),x106794),x106793))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,10367,3236,3129,3193,3160,3137,3782,3229,4589,4520,10260,3191,10329,4101,4602,3211,3672,3611,3372,10348,10466,10535,10596,10599,3762,3285,4568,10237,10240,10266,4584,3749,3517,3902,3329,3331,3304,4565,4514,4052,3301,10357,10453,10582,3302,10386,10441,3303,4564,10303,10395,10506,3462,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,3323,4145,4575,4554,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4600,3758,3573,10585,10588,4597,3791,4595,10279,10282,10627,3760,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404])). % 169.42/169.72 cnf(10684,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,f334(a115,f334(f334(f81(a877),x106841),x106842)))),f334(a115,x106842)))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,10367,3236,3129,3193,3160,3137,3782,3229,4589,4520,10260,3191,10329,4101,4602,3211,3672,3611,3372,10348,10466,10535,10596,10599,10639,3762,3285,4568,10237,10240,10266,4584,3749,3517,3902,3329,3331,3304,4565,4514,4052,3301,10357,10453,10582,3302,10386,10441,3303,4564,10303,10395,10506,3462,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,3323,4145,4575,4554,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4600,3758,3573,10585,10588,4597,3791,4595,10279,10282,10627,3760,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408])). % 169.42/169.72 cnf(10715,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x107151),x107151))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10726,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x107261,f886(x107262,a871))),x107263),x107264))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(10733,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x107331),f334(a115,x107331)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10735,plain, % 169.42/169.72 (P104(f334(f334(f250(a1),f334(f334(f3(a1),x107351),f79(a1))),x107351))), % 169.42/169.72 inference(scs_inference,[],[4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,10367,3236,3129,3193,3160,3137,3782,3229,4589,4520,10260,3191,10329,4101,3954,4602,3211,3672,3611,3372,10348,10466,10535,10596,10599,10639,3762,3285,4568,10237,10240,10266,4584,3749,3517,3902,3329,3331,3304,4565,4514,4052,3301,10357,10453,10582,10646,10715,3302,10386,10441,10651,3303,4564,10303,10395,10506,3462,4580,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,3323,4145,4575,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4600,3758,3573,10585,10588,4597,4598,3791,4595,10279,10282,10627,3760,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667])). % 169.42/169.72 cnf(10736,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x107361),x107361))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(10741,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x107411),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(10754,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x107541),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(10757,plain, % 169.42/169.72 (~P104(f334(f334(f250(f886(x107571,a871)),x107572),f195(f886(x107571,a871))))), % 169.42/169.72 inference(rename_variables,[],[4591])). % 169.42/169.72 cnf(10760,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x107601),x107601))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10763,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x107631),x107631))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10778,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x107781),x107781))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(10787,plain, % 169.42/169.72 (~P104(f334(f334(f336(x107871),x107872),f195(f886(x107871,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(10796,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x107961),x107961))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10799,plain, % 169.42/169.72 (~P104(f334(f334(f336(x107991),x107992),f195(f886(x107991,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(10802,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x108021,a871)),f334(f313(x108022,x108021,x108023),f334(f314(x108022,x108021,x108023),x108024))),x108024))), % 169.42/169.72 inference(rename_variables,[],[4205])). % 169.42/169.72 cnf(10809,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x108091,a871)),f334(f173(x108091),f334(f136(x108091,x108092),x108093))),f334(f173(x108091),x108093)))), % 169.42/169.72 inference(rename_variables,[],[3964])). % 169.42/169.72 cnf(10812,plain, % 169.42/169.72 (E(f334(f313(x108121,x108121,f7(x108121)),x108122),x108122)), % 169.42/169.72 inference(rename_variables,[],[3361])). % 169.42/169.72 cnf(10819,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x108191))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(10822,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x108221),x108221))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10825,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x108251),x108251))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(10828,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x108281,f886(x108282,a871))),x108283),x108284))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(10835,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x108351),x108351))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(10846,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x108461),f334(f334(f82(a877),x108461),x108461)))), % 169.42/169.72 inference(rename_variables,[],[3573])). % 169.42/169.72 cnf(10852,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x108521),f334(a115,f334(f334(f81(a877),x108522),x108521))))), % 169.42/169.72 inference(rename_variables,[],[3760])). % 169.42/169.72 cnf(10859,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x108591),x108591))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10862,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x108621),x108621))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(10865,plain, % 169.42/169.72 (~E(f334(a115,x108651),x108651)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(10870,plain, % 169.42/169.72 (P104(f334(f334(f336(x108701),x108702),f257(f886(x108701,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(10875,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x108751),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(10890,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x108901))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(10897,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x108971),x108971))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10906,plain, % 169.42/169.72 (~P104(f334(f334(f336(x109061),x109062),f195(f886(x109061,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(10910,plain, % 169.42/169.72 (E(f334(f334(f104(f886(x109101,a871)),f334(f334(f104(f886(x109101,a871)),x109102),f334(f80(f886(x109101,a871)),x109103))),x109103),f195(f886(x109101,a871)))), % 169.42/169.72 inference(scs_inference,[],[4590,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,10367,3236,3129,3193,3160,3137,3782,3361,3229,4589,4520,10260,3191,10329,4101,3954,4602,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,3762,3285,4568,10237,10240,10266,10741,10754,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,3673,4052,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,4580,10787,10799,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4600,3758,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814])). % 169.42/169.72 cnf(10914,plain, % 169.42/169.72 (P104(f334(f334(f336(x109141),x109142),f257(f886(x109141,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(10917,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x109171),f878(x109171))),f334(f334(f269(f878(x109171),f878(x109171)),x109172),f116(x109171))),f145(x109171,x109173)))), % 169.42/169.72 inference(rename_variables,[],[4602])). % 169.42/169.72 cnf(10923,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(x109231,x109231)),x109232),f266(x109231,f195(f886(x109231,a871)))))), % 169.42/169.72 inference(scs_inference,[],[4590,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,10367,3236,3129,3193,3160,3137,3782,3361,3229,4589,4520,10260,3191,10329,4101,3954,4602,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,3762,3285,4568,10237,10240,10266,10741,10754,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,3673,4052,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,4580,10787,10799,10906,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4600,3758,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952])). % 169.42/169.72 cnf(10924,plain, % 169.42/169.72 (~P104(f334(f334(f336(x109241),x109242),f195(f886(x109241,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(10926,plain, % 169.42/169.72 (~P104(f334(f334(f336(x109261),x109262),f334(f314(x109261,x109263,x109264),f195(f886(x109263,a871)))))), % 169.42/169.72 inference(scs_inference,[],[4590,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,4509,10430,2882,3085,3259,10194,10203,10269,10272,10364,10367,3236,3129,3193,3160,3137,3782,3361,3229,4589,4520,10260,3191,10329,4101,3954,4602,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,3762,3285,4568,10237,10240,10266,10741,10754,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,3673,4052,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,4580,10787,10799,10906,10924,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,4600,3758,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987])). % 169.42/169.72 cnf(10927,plain, % 169.42/169.72 (~P104(f334(f334(f336(x109271),x109272),f195(f886(x109271,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(10930,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x109301,a871)),x109302),f334(f334(f312(x109301),x109303),x109302)))), % 169.42/169.72 inference(rename_variables,[],[3756])). % 169.42/169.72 cnf(10933,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x109331),x109331))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(10936,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x109361,a871)),x109362),f334(f334(f312(x109361),x109363),x109362)))), % 169.42/169.72 inference(rename_variables,[],[3756])). % 169.42/169.72 cnf(10951,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x109511,a871)),x109512),f334(f334(f312(x109511),x109513),x109512)))), % 169.42/169.72 inference(rename_variables,[],[3756])). % 169.42/169.72 cnf(10956,plain, % 169.42/169.72 (~P104(f334(f64(x109561,x109562,f195(f886(x109561,a871))),x109563))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(10960,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(a877,a877)),f334(f334(f269(a877,a877),f334(a115,x109601)),x109601)),f310(a877,a324)))), % 169.42/169.72 inference(scs_inference,[],[4590,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,4509,10430,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3129,3193,3160,3137,3782,3361,3229,4589,4520,10260,3191,10329,4101,3954,4602,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,3762,3285,4568,10237,10240,10266,10741,10754,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,3673,4052,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3758,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409])). % 169.42/169.72 cnf(10969,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x109691),f334(a115,x109691)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(10979,plain, % 169.42/169.72 (~E(f334(f313(x109791,f886(x109791,a871),x109792),x109793),f334(f311(x109791),x109793))), % 169.42/169.72 inference(rename_variables,[],[4578])). % 169.42/169.72 cnf(10982,plain, % 169.42/169.72 (~P104(f334(f334(f336(x109821),x109822),f195(f886(x109821,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(10985,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x109851,x109851)),f334(f334(f269(x109851,x109851),x109852),x109852)),f310(x109851,x109853)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(10988,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x109881,a871)),x109882),f257(f886(x109881,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(10991,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x109911,a871)),f334(f173(x109911),f171(x109911,x109912,x109913))),f334(f173(x109911),x109913)))), % 169.42/169.72 inference(rename_variables,[],[4015])). % 169.42/169.72 cnf(11007,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x110071,a871)),f195(f886(x110071,a871))),x110072))), % 169.42/169.72 inference(rename_variables,[],[3758])). % 169.42/169.72 cnf(11018,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x110181),f878(x110181))),f334(f334(f269(f878(x110181),f878(x110181)),x110182),f116(x110181))),f147(x110181,x110183)))), % 169.42/169.72 inference(rename_variables,[],[4603])). % 169.42/169.72 cnf(11029,plain, % 169.42/169.72 (~E(f334(a115,x110291),x110291)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11032,plain, % 169.42/169.72 (~E(f334(a115,x110321),x110321)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11044,plain, % 169.42/169.72 (P21(x110441,x110441,f7(x110441),x110442)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(11049,plain, % 169.42/169.72 (~E(f334(f313(x110491,f886(x110491,a871),x110492),x110493),f334(f311(x110491),x110493))), % 169.42/169.72 inference(rename_variables,[],[4578])). % 169.42/169.72 cnf(11054,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x110541,a871)),x110542),f257(f886(x110541,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(11068,plain, % 169.42/169.72 (~P104(f334(f334(f336(x110681),x110682),f195(f886(x110681,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11071,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x110711)),x110711))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11076,plain, % 169.42/169.72 (~P104(f334(f334(f336(x110761),x110762),f195(f886(x110761,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11088,plain, % 169.42/169.72 (~P104(f334(f334(f336(a877),f334(a115,f334(f142(a877,a877,f81(a877),f2(a877)),x110881))),f334(f173(a877),x110881)))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,4602,10917,4603,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3758,10669,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846])). % 169.42/169.72 cnf(11089,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x110891)),x110891))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11092,plain, % 169.42/169.72 (~P104(f334(f334(f336(x110921),x110922),f195(f886(x110921,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11100,plain, % 169.42/169.72 (E(f334(f136(x111001,f257(f886(x111002,a871))),f738(x111003,x111004,f334(f334(f151(x111001),x111004),x111003),f257(f886(x111002,a871)),x111001)),x111003)), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,4602,10917,4603,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3758,10669,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920])). % 169.42/169.72 cnf(11102,plain, % 169.42/169.72 (E(f334(x111021,f565(f334(x111021,x111022),f334(f241(x111023),x111022),x111021,x111024,x111023)),f334(x111021,x111022))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,4602,10917,4603,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3758,10669,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922])). % 169.42/169.72 cnf(11111,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x111111,x111111)),f334(f334(f269(x111111,x111111),x111112),x111112)),f310(x111111,x111113)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(11116,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x111161),f878(x111161))),f334(f334(f269(f878(x111161),f878(x111161)),x111162),f116(x111161))),f145(x111161,x111163)))), % 169.42/169.72 inference(rename_variables,[],[4602])). % 169.42/169.72 cnf(11119,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x111191),f878(x111191))),f334(f334(f269(f878(x111191),f878(x111191)),x111192),f116(x111191))),f147(x111191,x111193)))), % 169.42/169.72 inference(rename_variables,[],[4603])). % 169.42/169.72 cnf(11122,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x111221),f878(x111221))),f334(f334(f269(f878(x111221),f878(x111221)),x111222),f116(x111221))),f157(x111221,x111223)))), % 169.42/169.72 inference(rename_variables,[],[4604])). % 169.42/169.72 cnf(11124,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x111241),f878(x111241))),f334(f334(f269(f878(x111241),f878(x111241)),f116(x111241)),x111242)),f334(f289(f878(x111241),f878(x111241)),f145(x111241,x111243))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,4602,10917,11116,4603,11018,4604,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,4591,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3758,10669,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057])). % 169.42/169.72 cnf(11127,plain, % 169.42/169.72 (~P104(f334(f334(f250(f886(x111271,a871)),x111272),f195(f886(x111271,a871))))), % 169.42/169.72 inference(rename_variables,[],[4591])). % 169.42/169.72 cnf(11129,plain, % 169.42/169.72 (~P104(f334(f334(f336(x111291),x111292),f334(f313(x111293,x111291,x111294),f195(f886(x111293,a871)))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,4602,10917,11116,4603,11018,4604,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,4591,10757,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3758,10669,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080])). % 169.42/169.72 cnf(11130,plain, % 169.42/169.72 (~P104(f334(f334(f336(x111301),x111302),f195(f886(x111301,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11135,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111351,a871)),x111352),f257(f886(x111351,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(11144,plain, % 169.42/169.72 (~P104(f334(f334(f336(x111441),x111442),f195(f886(x111441,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11147,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(x111471,x111471)),f334(f334(f269(x111471,x111471),x111472),x111473)),f153(x111471,f116(f886(x111471,a877)))))), % 169.42/169.72 inference(rename_variables,[],[4600])). % 169.42/169.72 cnf(11150,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111501,a871)),x111502),x111502))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(11153,plain, % 169.42/169.72 (~P104(f334(f334(f336(x111531),x111532),f195(f886(x111531,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11155,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111551,a871)),f334(f288(x111552,x111551,f195(f886(f885(x111552,x111551),a871))),x111553)),x111554))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,4602,10917,11116,4603,11018,4604,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,11054,4591,10757,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3607,3758,10669,11007,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273])). % 169.42/169.72 cnf(11156,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111561,a871)),f195(f886(x111561,a871))),x111562))), % 169.42/169.72 inference(rename_variables,[],[3758])). % 169.42/169.72 cnf(11159,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x111591,x111591)),f334(f334(f269(x111591,x111591),x111592),x111592)),f310(x111591,x111593)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(11161,plain, % 169.42/169.72 (~P36(x111611,x111612,x111613,f334(f334(f154(x111614,x111611),x111615),f334(a115,f116(x111614))),f116(x111612))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,11111,4602,10917,11116,4603,11018,4604,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,11054,4591,10757,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3607,3758,10669,11007,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279])). % 169.42/169.72 cnf(11165,plain, % 169.42/169.72 (P36(x111651,x111652,x111653,f334(f334(f154(x111654,x111651),x111655),f117(x111654,f116(x111654))),f116(x111652))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,11111,4602,10917,11116,4603,11018,4604,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,11054,4591,10757,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3607,3758,10669,11007,3573,10585,10588,10675,10846,4597,4598,10726,4205,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300])). % 169.42/169.72 cnf(11170,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x111701),f878(x111701))),f334(f334(f269(f878(x111701),f878(x111701)),x111702),f116(x111701))),f157(x111701,x111703)))), % 169.42/169.72 inference(rename_variables,[],[4604])). % 169.42/169.72 cnf(11173,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x111731),f878(x111731))),f334(f334(f269(f878(x111731),f878(x111731)),f116(x111731)),x111732)),f145(x111731,x111733)))), % 169.42/169.72 inference(rename_variables,[],[4605])). % 169.42/169.72 cnf(11181,plain, % 169.42/169.72 (P104(f334(f334(f336(x111811),x111812),f257(f886(x111811,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(11186,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111861,a871)),f195(f886(x111861,a871))),x111862))), % 169.42/169.72 inference(rename_variables,[],[3758])). % 169.42/169.72 cnf(11189,plain, % 169.42/169.72 (~P104(f334(f334(f336(x111891),x111892),f195(f886(x111891,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11192,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111921,a871)),x111922),f257(f886(x111921,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(11196,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111961,a871)),f334(f288(x111962,x111961,x111963),f195(f886(x111962,a871)))),x111964))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,4578,10979,3409,3191,10329,4101,3954,10985,11111,4602,10917,11116,4603,11018,4604,11122,4605,4606,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4063,3964,10809,4015,3673,4052,3691,10988,11054,11135,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,3365,10633,10663,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3607,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,4598,10726,4205,4106,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524])). % 169.42/169.72 cnf(11197,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x111971,a871)),f195(f886(x111971,a871))),x111972))), % 169.42/169.72 inference(rename_variables,[],[3758])). % 169.42/169.72 cnf(11210,plain, % 169.42/169.72 (P104(f334(f257(f886(x112101,a871)),x112102))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(11218,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x112181),f878(x112181))),f334(f334(f269(f878(x112181),f878(x112181)),x112182),f116(x112181))),f145(x112181,x112183)))), % 169.42/169.72 inference(rename_variables,[],[4602])). % 169.42/169.72 cnf(11221,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x112211),f878(x112211))),f334(f334(f269(f878(x112211),f878(x112211)),x112212),f116(x112211))),f147(x112211,x112213)))), % 169.42/169.72 inference(rename_variables,[],[4603])). % 169.42/169.72 cnf(11224,plain, % 169.42/169.72 (~E(f334(f334(f151(x112241),x112242),x112243),x112243)), % 169.42/169.72 inference(rename_variables,[],[4520])). % 169.42/169.72 cnf(11227,plain, % 169.42/169.72 (~E(f334(a115,x112271),x112271)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11230,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112301),x112302),f195(f886(x112301,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11235,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112351),x112352),f195(f886(x112351,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11238,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(f878(x112381),f878(x112381))),f334(f334(f269(f878(x112381),f878(x112381)),x112382),x112382)),f158(x112381,f310(x112381,x112383))))), % 169.42/169.72 inference(rename_variables,[],[4095])). % 169.42/169.72 cnf(11243,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x112431),f878(x112431))),f334(f334(f269(f878(x112431),f878(x112431)),x112432),f116(x112431))),f145(x112431,x112433)))), % 169.42/169.72 inference(rename_variables,[],[4602])). % 169.42/169.72 cnf(11252,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112521),x112522),f187(x112523,x112521,f189(x112523,x112521,x112524,f195(f886(x112523,a871))))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,10427,4578,10979,3409,3191,10329,4101,3954,10985,11111,4602,10917,11116,11218,4603,11018,11119,4604,11122,4605,11173,4606,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4095,11238,4063,3964,10809,4015,3673,4052,3691,10988,11054,11135,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,3365,10633,10663,10672,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,3919,3756,10930,10936,3607,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,4598,10726,4205,4106,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740])). % 169.42/169.72 cnf(11253,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112531),x112532),f195(f886(x112531,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11256,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112561),x112562),f195(f886(x112561,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11259,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112591),x112592),f195(f886(x112591,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11262,plain, % 169.42/169.72 (P104(f334(f334(f336(x112621),x112622),f257(f886(x112621,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(11265,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x112651),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(11270,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(x112701,x112701)),f334(f334(f269(x112701,x112701),x112702),x112703)),f153(x112701,f116(f886(x112701,a877)))))), % 169.42/169.72 inference(rename_variables,[],[4600])). % 169.42/169.72 cnf(11273,plain, % 169.42/169.72 (~E(f334(f313(x112731,f886(x112731,a871),x112732),x112733),f334(f311(x112731),x112733))), % 169.42/169.72 inference(rename_variables,[],[4578])). % 169.42/169.72 cnf(11276,plain, % 169.42/169.72 (~E(f334(f313(x112761,f886(x112761,a871),x112762),x112763),f334(f311(x112761),x112763))), % 169.42/169.72 inference(rename_variables,[],[4578])). % 169.42/169.72 cnf(11281,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x112811),f878(x112811))),f334(f334(f269(f878(x112811),f878(x112811)),x112812),f116(x112811))),f145(x112811,x112813)))), % 169.42/169.72 inference(rename_variables,[],[4602])). % 169.42/169.72 cnf(11287,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x112871),f878(x112871))),f334(f334(f269(f878(x112871),f878(x112871)),x112872),f116(x112871))),f145(x112871,x112873)))), % 169.42/169.72 inference(rename_variables,[],[4602])). % 169.42/169.72 cnf(11290,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112901),x112902),f195(f886(x112901,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11294,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x112941,x112942)),f334(f334(f269(x112941,x112942),f334(x112943,x112944)),f334(x112945,x112944))),f334(f313(f885(x112946,x112946),f885(x112941,x112942),f274(x112946,x112941,x112946,x112942,x112943,x112945)),f310(x112946,x112947))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,4509,10430,10521,2882,3085,3139,3259,10194,10203,10269,10272,10364,10367,3236,3770,3129,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,10427,4578,10979,11049,11273,3409,3191,10329,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,3672,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,4584,3749,3517,3902,3329,3331,3304,4565,4514,4095,11238,4063,3964,10809,4015,3673,4052,3691,10988,11054,11135,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,11181,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,3365,10633,10663,10672,3398,3832,3767,10306,4577,10257,10621,10624,11071,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4593,10228,10231,10487,10538,10541,10546,4600,11147,3919,3756,10930,10936,3607,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,4598,10726,4205,4106,3791,4595,10279,10282,10627,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037])). % 169.42/169.72 cnf(11297,plain, % 169.42/169.72 (~P104(f334(f334(f336(x112971),x112972),f195(f886(x112971,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11300,plain, % 169.42/169.72 (~P104(f334(f334(f336(x113001),x113002),f195(f886(x113001,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11303,plain, % 169.42/169.72 (P104(f334(f334(f336(x113031),f334(x113032,x113033)),f334(f313(x113034,x113031,x113032),f257(f886(x113034,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(11306,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(x113061,x113061)),f334(f334(f269(x113061,x113061),x113062),x113063)),f153(x113061,f116(f886(x113061,a877)))))), % 169.42/169.72 inference(rename_variables,[],[4600])). % 169.42/169.72 cnf(11314,plain, % 169.42/169.72 (E(f117(x113141,f116(x113141)),f116(x113141))), % 169.42/169.72 inference(rename_variables,[],[3139])). % 169.42/169.72 cnf(11317,plain, % 169.42/169.72 (~E(f334(a115,x113171),x113171)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11324,plain, % 169.42/169.72 (~E(f334(a115,x113241),x113241)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11329,plain, % 169.42/169.72 (E(f334(f265(x113291,x113291),f266(x113291,x113292)),x113292)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(11332,plain, % 169.42/169.72 (E(f334(f265(x113321,x113321),f266(x113321,x113322)),x113322)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(11338,plain, % 169.42/169.72 (~E(f334(a115,x113381),x113381)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11345,plain, % 169.42/169.72 (~E(f334(f334(f81(a1),x113451),x113451),a100)), % 169.42/169.72 inference(rename_variables,[],[4517])). % 169.42/169.72 cnf(11354,plain, % 169.42/169.72 (E(f334(f334(f3(a877),f2(a877)),x113541),f2(a877))), % 169.42/169.72 inference(rename_variables,[],[3212])). % 169.42/169.72 cnf(11357,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x113571),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(11364,plain, % 169.42/169.72 (E(f334(f334(f81(a1),f334(f334(f82(a1),x113641),f334(f334(f40(a1),x113642),x113641))),f46(a1,x113642,x113641)),x113642)), % 169.42/169.72 inference(rename_variables,[],[3865])). % 169.42/169.72 cnf(11390,plain, % 169.42/169.72 (~E(f334(a115,x113901),x113901)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11393,plain, % 169.42/169.72 (~E(f334(a115,x113931),x113931)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11419,plain, % 169.42/169.72 (~P104(f334(f64(x114191,x114192,f195(f886(x114191,a871))),x114193))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(11422,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x114221,f886(x114222,a871))),x114223),x114224))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(11425,plain, % 169.42/169.72 (P104(f334(f334(f336(x114251),x114252),f257(f886(x114251,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(11437,plain, % 169.42/169.72 (~E(f334(a115,x114371),x114371)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11440,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x114401),x114401))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11447,plain, % 169.42/169.72 (P104(f334(f68(x114471,x114472,x114473,x114474,f195(f886(x114471,a871))),x114474))), % 169.42/169.72 inference(rename_variables,[],[4245])). % 169.42/169.72 cnf(11448,plain, % 169.42/169.72 (E(f334(f265(x114481,x114481),f266(x114481,x114482)),x114482)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(11453,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x114531,f886(x114532,a871))),x114533),x114534))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(11464,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x114641),x114642)),x114642))), % 169.42/169.72 inference(rename_variables,[],[4595])). % 169.42/169.72 cnf(11467,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f103(a1),x114671)),f2(a1)))), % 169.42/169.72 inference(rename_variables,[],[4584])). % 169.42/169.72 cnf(11483,plain, % 169.42/169.72 (~E(f334(f334(f104(a877),f334(a115,x114831)),x114831),f334(a115,x114831))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,4509,10430,10521,3216,2882,2892,2898,2902,2903,2912,2916,2917,2928,2935,2943,2949,2950,2974,2977,3013,3022,3023,3027,3039,3042,3049,3062,3068,3085,4490,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,3236,3770,3129,3865,11364,3193,3160,3137,3782,3361,3229,3408,4589,3952,4520,10260,10427,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3107,3212,11354,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,11287,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,3672,4517,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,3285,4568,10237,10240,10266,10741,10754,10875,11265,11357,4584,3749,3517,3902,3329,3331,3304,4565,4514,3500,4585,4095,11238,3632,4063,3964,10809,4015,3673,4052,3691,10988,11054,11135,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,3302,10386,10441,10651,10736,10862,3303,4564,10303,10395,10506,10530,10778,10825,3462,10602,10870,10914,11181,11262,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,3365,10633,10663,10672,3398,3832,3767,10306,4577,10257,10621,10624,11071,11089,3323,10666,10819,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,4245,4593,10228,10231,10487,10538,10541,10546,10956,4600,11147,11270,3919,3756,10930,10936,3607,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,4586,4598,10726,10828,11422,4205,4106,3791,4595,10279,10282,10627,10630,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411])). % 169.42/169.72 cnf(11490,plain, % 169.42/169.72 (E(f334(f265(x114901,x114901),f266(x114901,x114902)),x114902)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(11495,plain, % 169.42/169.72 (E(f334(f265(x114951,x114951),f266(x114951,x114952)),x114952)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(11498,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f103(a1),x114981)),f2(a1)))), % 169.42/169.72 inference(rename_variables,[],[4584])). % 169.42/169.72 cnf(11503,plain, % 169.42/169.72 (~E(f334(a115,x115031),x115031)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11512,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x115121),x115121))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11533,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f103(a1),x115331)),f2(a1)))), % 169.42/169.72 inference(rename_variables,[],[4584])). % 169.42/169.72 cnf(11548,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x115481)),x115481))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11549,plain, % 169.42/169.72 (~E(f334(a115,x115491),x115491)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11559,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x115591),x115592)),x115591))), % 169.42/169.72 inference(rename_variables,[],[4596])). % 169.42/169.72 cnf(11562,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f103(a1),x115621)),f2(a1)))), % 169.42/169.72 inference(rename_variables,[],[4584])). % 169.42/169.72 cnf(11565,plain, % 169.42/169.72 (~E(f334(a115,x115651),x115651)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11578,plain, % 169.42/169.72 (P104(f334(f334(f336(x115781),x115782),f334(f334(f312(x115781),x115782),x115783)))), % 169.42/169.72 inference(rename_variables,[],[3622])). % 169.42/169.72 cnf(11579,plain, % 169.42/169.72 (~P104(f334(f334(f249(a1),f2(a1)),f334(f80(a1),f334(f103(a1),f334(a115,x115791)))))), % 169.42/169.72 inference(rename_variables,[],[4597])). % 169.42/169.72 cnf(11582,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),f334(f334(f3(a877),x115821),x115822)),f334(a115,x115821)))), % 169.42/169.72 inference(rename_variables,[],[3762])). % 169.42/169.72 cnf(11585,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f46(a877,x115851,x115852)),x115851))), % 169.42/169.72 inference(rename_variables,[],[3767])). % 169.42/169.72 cnf(11591,plain, % 169.42/169.72 (E(f334(f265(x115911,x115911),f266(x115911,x115912)),x115912)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(11596,plain, % 169.42/169.72 (E(f334(f334(f134(x115961),f170(x115961,x115962,x115963)),f170(x115961,x115964,x115963)),f334(f334(f134(x115961),f170(x115961,x115964,x115963)),f170(x115961,x115962,x115963)))), % 169.42/169.72 inference(rename_variables,[],[3880])). % 169.42/169.72 cnf(11601,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x116011)),x116011))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11610,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x116101),x116101))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11613,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f46(a877,x116131,x116132)),x116131))), % 169.42/169.72 inference(rename_variables,[],[3767])). % 169.42/169.72 cnf(11614,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x116141))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(11631,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x116311),x116311))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11634,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x116341),x116341))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11637,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x116371),x116371))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11640,plain, % 169.42/169.72 (P104(f334(f334(f336(x116401),f334(x116402,x116403)),f334(f313(x116404,x116401,x116402),f257(f886(x116404,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(11641,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x116411)),x116411))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11644,plain, % 169.42/169.72 (P104(f334(f334(f336(x116441),f334(x116442,x116443)),f334(f313(x116444,x116441,x116442),f257(f886(x116444,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(11645,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x116451),x116452)),x116452))), % 169.42/169.72 inference(rename_variables,[],[4595])). % 169.42/169.72 cnf(11650,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x116501),x116502)),x116501))), % 169.42/169.72 inference(rename_variables,[],[4596])). % 169.42/169.72 cnf(11653,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x116531),x116531))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11656,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x116561),x116561))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11662,plain, % 169.42/169.72 (~P37(x116621,x116622,f116(x116621))), % 169.42/169.72 inference(rename_variables,[],[4531])). % 169.42/169.72 cnf(11665,plain, % 169.42/169.72 (P104(f334(f334(f336(x116651),x116652),f257(f886(x116651,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(11666,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x116661)),x116661))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11669,plain, % 169.42/169.72 (~P104(f334(f64(x116691,x116692,f195(f886(x116691,a871))),x116693))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(11682,plain, % 169.42/169.72 (~P104(f334(f334(f336(x116821),x116822),f195(f886(x116821,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11685,plain, % 169.42/169.72 (E(f334(f334(f18(x116851,x116852),x116853),x116854),x116853)), % 169.42/169.72 inference(rename_variables,[],[3292])). % 169.42/169.72 cnf(11688,plain, % 169.42/169.72 (E(f334(f334(f18(x116881,x116882),x116883),x116884),x116883)), % 169.42/169.72 inference(rename_variables,[],[3292])). % 169.42/169.72 cnf(11700,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),f2(a877)),f334(a115,x117001)))), % 169.42/169.72 inference(rename_variables,[],[3384])). % 169.42/169.72 cnf(11703,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x117031),x117031))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11706,plain, % 169.42/169.72 (P104(f334(f334(f336(x117061),f334(x117062,x117063)),f334(f313(x117064,x117061,x117062),f257(f886(x117064,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(11709,plain, % 169.42/169.72 (P104(f334(f63(x117091),f334(f173(x117091),x117092)))), % 169.42/169.72 inference(rename_variables,[],[3343])). % 169.42/169.72 cnf(11712,plain, % 169.42/169.72 (P104(f334(f63(x117121),f334(f173(x117121),x117122)))), % 169.42/169.72 inference(rename_variables,[],[3343])). % 169.42/169.72 cnf(11715,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),f334(f80(a1),f334(f103(a1),x117151))),f334(f103(a1),x117152)))), % 169.42/169.72 inference(rename_variables,[],[3792])). % 169.42/169.72 cnf(11718,plain, % 169.42/169.72 (~P104(f334(f334(f336(x117181),x117182),f195(f886(x117181,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11732,plain, % 169.42/169.72 (~P104(f334(f334(f336(a877),f2(a877)),f334(f306(a877),x117321)))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4530,4531,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,4509,10430,10521,3216,2882,2891,2892,2895,2898,2899,2902,2903,2912,2916,2917,2928,2935,2943,2949,2950,2974,2977,3013,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,3085,4490,3880,11596,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,3236,3770,3129,3510,3865,11364,3193,3160,3155,3137,3138,3782,3361,3229,3408,4589,3952,4520,10260,10427,3292,11685,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3467,3107,3212,11354,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,11287,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,3672,4385,4386,4517,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,11582,3285,3384,4568,10237,10240,10266,10741,10754,10875,11265,11357,4584,11467,11498,11533,3749,3517,3902,3329,3331,3304,4565,4514,3500,4585,4095,11238,3632,3343,11709,4063,3964,10809,4015,3673,4052,3691,10988,11054,11135,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,3302,10386,10441,10651,10736,10862,3303,3380,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,3462,10602,10870,10914,11181,11262,11425,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,3365,10633,10663,10672,3404,3398,3832,3767,10306,11585,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,3323,10666,10819,10890,3792,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,3622,4245,4593,10228,10231,10487,10538,10541,10546,10956,11419,4600,11147,11270,4029,3919,11303,11640,11644,3756,10930,10936,3607,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,4205,4106,3791,3735,4595,10279,10282,10627,10630,11464,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182])). % 169.42/169.72 cnf(11734,plain, % 169.42/169.72 (~P104(f334(f334(f336(a877),x117341),f334(f255(a877),f2(a877))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4530,4531,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,4509,10430,10521,3216,2882,2891,2892,2895,2898,2899,2902,2903,2912,2916,2917,2928,2935,2943,2949,2950,2974,2977,3013,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,3085,4490,3880,11596,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,3236,3770,3129,3510,3865,11364,3193,3160,3155,3137,3138,3782,3361,3229,3408,4589,3952,4520,10260,10427,3292,11685,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3467,3107,3212,11354,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,11287,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,3672,4385,4386,4517,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,3762,11582,3285,3384,4568,10237,10240,10266,10741,10754,10875,11265,11357,4584,11467,11498,11533,3749,3517,3902,3329,3331,3304,4565,4514,3500,4585,4095,11238,3632,3343,11709,4063,3964,10809,4015,3673,4052,3691,10988,11054,11135,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,3302,10386,10441,10651,10736,10862,3303,3380,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,3462,10602,10870,10914,11181,11262,11425,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,3365,10633,10663,10672,3404,3398,3832,3767,10306,11585,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,3323,10666,10819,10890,3792,4145,4575,3840,4554,4557,3276,3280,4556,4555,4559,3622,4245,4593,10228,10231,10487,10538,10541,10546,10956,11419,4600,11147,11270,4029,3919,11303,11640,11644,3756,10930,10936,3607,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,4205,4106,3791,3735,4595,10279,10282,10627,10630,11464,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183])). % 169.42/169.72 cnf(11737,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x117371),x117371))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11740,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x117401),x117401))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11749,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x117491),x117491))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11752,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x117521),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(11757,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x117571),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(11764,plain, % 169.42/169.72 (P104(f334(f257(f886(x117641,a871)),x117642))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(11769,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x117691))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(11770,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x117701)),x117701))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11773,plain, % 169.42/169.72 (~P104(f334(f64(x117731,x117732,f195(f886(x117731,a871))),x117733))), % 169.42/169.72 inference(rename_variables,[],[4593])). % 169.42/169.72 cnf(11795,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x117951)),x117951))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11798,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x117981)),x117981))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11801,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x118011)),x118011))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11804,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x118041)),x118041))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(11807,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x118071),x118071))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11810,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x118101),x118101))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11813,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x118131),x118131))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11816,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x118161),x118161))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11833,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x118331),x118331))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11839,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x118391),x118391))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11850,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x118501),x118501))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11853,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(f885(f878(x118531),f878(x118531)),a871)),f158(x118531,x118532)),f310(f878(x118531),f157(x118531,x118532))))), % 169.42/169.72 inference(rename_variables,[],[4020])). % 169.42/169.72 cnf(11860,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x118601),f334(a115,x118601)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(11863,plain, % 169.42/169.72 (P104(f334(f334(f336(f886(x118631,a871)),x118632),f334(f311(x118631),x118632)))), % 169.42/169.72 inference(rename_variables,[],[3673])). % 169.42/169.72 cnf(11864,plain, % 169.42/169.72 (~E(f334(a115,x118641),x118641)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11869,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x118691),x118691))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11874,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x118741),x118741))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11885,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x118851,a871)),x118852),f334(f334(f312(x118851),x118853),x118852)))), % 169.42/169.72 inference(rename_variables,[],[3756])). % 169.42/169.72 cnf(11888,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x118881),x118881))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11889,plain, % 169.42/169.72 (~E(f334(a115,x118891),x118891)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11900,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119001),x119001))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11901,plain, % 169.42/169.72 (~E(f334(a115,x119011),x119011)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11904,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x119041),x119041))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11907,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x119071),x119071))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11910,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x119101),x119101))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11913,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x119131),x119131))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(11916,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x119161),x119161))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11919,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119191),x119191))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11922,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119221),x119221))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11923,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x119231),f334(a115,x119231)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(11930,plain, % 169.42/169.72 (~E(f334(a115,x119301),x119301)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11935,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119351),x119351))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11936,plain, % 169.42/169.72 (~E(f334(a115,x119361),x119361)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(11939,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x119391),x119391))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11956,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x119561),x119561))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(11961,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x119611))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(11978,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119781),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(11981,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119811),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(11984,plain, % 169.42/169.72 (~P104(f334(f334(f336(x119841),x119842),f195(f886(x119841,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11987,plain, % 169.42/169.72 (~P104(f334(f334(f336(x119871),x119872),f195(f886(x119871,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(11989,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119891),f334(f334(f104(a877),x119892),x119891)))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,4530,4531,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,4509,10430,10521,3516,3216,2882,2891,2892,2895,2898,2899,2902,2903,2911,2912,2916,2917,2928,2931,2935,2943,2949,2950,2974,2977,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,3085,4490,3880,11596,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,3236,3244,3770,4088,3129,3510,3865,11364,3193,3160,3155,3137,3138,3782,3361,3229,3408,4589,3952,4520,10260,10427,3292,11685,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3467,3107,3212,11354,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,11287,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,3672,4385,4386,4517,3611,3828,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,3762,11582,3285,3384,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,4584,11467,11498,11533,11562,3749,3517,3902,3329,3331,3304,4565,4514,3500,4585,4095,11238,3632,3343,11709,4063,4020,3964,10809,4015,3673,4052,3691,10988,11054,11135,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,3462,10602,10870,10914,11181,11262,11425,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,3365,10633,10663,10672,11210,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,3323,10666,10819,10890,11614,11769,3792,4145,4575,3803,3840,4554,4557,3276,3280,4556,4555,4559,3811,3622,4245,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,4029,3919,11303,11640,11644,3756,10930,10936,10951,3607,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,4205,4106,3791,3735,4595,10279,10282,10627,10630,11464,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066])). % 169.42/169.72 cnf(11990,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119901),x119901))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11993,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119931),x119931))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11996,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119961),x119961))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(11999,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x119991),x119991))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12002,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x120021),f334(a115,x120021)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12009,plain, % 169.42/169.72 (P104(f334(f334(f336(f886(x120091,a871)),x120092),f334(f311(x120091),x120092)))), % 169.42/169.72 inference(rename_variables,[],[3673])). % 169.42/169.72 cnf(12014,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x120141,a871)),x120142),f334(f334(f312(x120141),x120143),x120142)))), % 169.42/169.72 inference(rename_variables,[],[3756])). % 169.42/169.72 cnf(12021,plain, % 169.42/169.72 (~P104(f334(f334(f336(x120211),x120212),f195(f886(x120211,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12030,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x120301,a871)),x120302),f257(f886(x120301,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(12031,plain, % 169.42/169.72 (~E(f334(a115,x120311),x120311)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12034,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x120341,a871)),f334(f313(x120342,x120341,x120343),f334(f314(x120342,x120341,x120343),x120344))),x120344))), % 169.42/169.72 inference(rename_variables,[],[4205])). % 169.42/169.72 cnf(12037,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x120371,a871)),f334(f173(x120371),f334(f136(x120371,x120372),x120373))),f334(f173(x120371),x120373)))), % 169.42/169.72 inference(rename_variables,[],[3964])). % 169.42/169.72 cnf(12043,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x120431),f334(a115,x120431)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12052,plain, % 169.42/169.72 (E(f334(f265(x120521,x120521),f266(x120521,x120522)),x120522)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12063,plain, % 169.42/169.72 (~P104(f334(f334(f249(a877),f334(a115,x120631)),x120631))), % 169.42/169.72 inference(rename_variables,[],[4577])). % 169.42/169.72 cnf(12064,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x120641),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12067,plain, % 169.42/169.72 (P104(f334(f63(x120671),f195(f886(x120671,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12068,plain, % 169.42/169.72 (~P104(f334(f334(f336(x120681),x120682),f195(f886(x120681,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12073,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x120731),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12074,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x120741),x120741))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12079,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x120791,a871)),f334(f173(x120791),f171(x120791,x120792,x120793))),f334(f173(x120791),x120793)))), % 169.42/169.72 inference(rename_variables,[],[4015])). % 169.42/169.72 cnf(12082,plain, % 169.42/169.72 (P21(x120821,x120821,f7(x120821),x120822)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12087,plain, % 169.42/169.72 (P104(f334(f334(f336(f886(x120871,a871)),x120872),f334(f311(x120871),x120872)))), % 169.42/169.72 inference(rename_variables,[],[3673])). % 169.42/169.72 cnf(12094,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x120941),x120941))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12097,plain, % 169.42/169.72 (~P104(f334(f334(f336(x120971),x120972),f195(f886(x120971,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12100,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x121001,a871)),x121002),f334(f334(f312(x121001),x121003),x121002)))), % 169.42/169.72 inference(rename_variables,[],[3756])). % 169.42/169.72 cnf(12101,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x121011,a871)),x121012),f257(f886(x121011,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(12108,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x121081),x121081))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12111,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x121111),x121111))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12114,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x121141),x121141))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12117,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x121171),x121171))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12120,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x121201),f334(a115,x121201)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12123,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x121231),f334(a115,x121231)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12126,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x121261,a871)),x121262),x121262))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12128,plain, % 169.42/169.72 (~P104(f334(f334(f249(a1),f334(f334(f3(a1),a84),a100)),f2(a1)))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,11044,4530,4531,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,4509,10430,10521,3516,3216,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2916,2917,2928,2931,2935,2943,2949,2950,2974,2977,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,3085,4490,3880,11596,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,3236,3244,3770,4088,3129,3510,3865,11364,3193,3160,3155,3137,3138,3782,3361,3229,3408,4589,3952,4520,10260,10427,3292,11685,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3467,3107,3212,11354,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,11287,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,3672,4385,4386,4517,3611,3828,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,3762,11582,3285,3384,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,4584,11467,11498,11533,11562,3749,3517,3902,3329,3331,3304,4565,4514,3500,4585,4095,11238,3632,3343,11709,11712,4063,4020,3964,10809,4015,10991,3673,11863,12009,4052,3691,10988,11054,11135,11192,12030,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,12067,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,3462,10602,10870,10914,11181,11262,11425,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,3365,10633,10663,10672,11210,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,3323,10666,10819,10890,11614,11769,3792,4145,4575,3803,3840,4554,4557,3276,3280,4556,4555,4559,3811,3622,4245,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,4029,3919,11303,11640,11644,3756,10930,10936,10951,11885,12014,3607,11150,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,4205,10802,4106,3791,3735,4595,10279,10282,10627,10630,11464,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675])). % 169.42/169.72 cnf(12133,plain, % 169.42/169.72 (P104(f334(f334(f336(f886(x121331,a871)),x121332),f334(f311(x121331),x121332)))), % 169.42/169.72 inference(rename_variables,[],[3673])). % 169.42/169.72 cnf(12139,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f334(f81(a1),a84),a84)),f2(a1)))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,11044,4530,4531,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,4509,10430,10521,3516,3216,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2916,2917,2928,2931,2935,2943,2949,2950,2974,2977,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,3085,4490,3880,11596,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,3236,3244,3770,4088,3129,3510,3865,11364,3193,3160,3155,3137,3138,3782,3361,3229,3408,4589,3952,4520,10260,10427,3292,11685,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3467,3107,3212,11354,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,11287,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,3672,4385,4386,4517,3611,3828,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,3762,11582,3285,3384,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,4584,11467,11498,11533,11562,3749,3517,3902,3329,3331,3304,4565,4514,3500,4585,4095,11238,3632,3343,11709,11712,4063,4020,3964,10809,4015,10991,3673,11863,12009,12087,4052,3691,10988,11054,11135,11192,12030,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,12067,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,3462,10602,10870,10914,11181,11262,11425,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,3365,10633,10663,10672,11210,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,3323,10666,10819,10890,11614,11769,3792,4145,4575,3803,3840,4554,4557,3276,3280,4556,4555,4559,3811,3622,4245,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,4029,3919,11303,11640,11644,3756,10930,10936,10951,11885,12014,3607,11150,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,4205,10802,4106,3791,3735,4595,10279,10282,10627,10630,11464,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712])). % 169.42/169.72 cnf(12142,plain, % 169.42/169.72 (~E(f334(a115,x121421),x121421)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12143,plain, % 169.42/169.72 (E(f334(f313(x121431,x121431,f7(x121431)),x121432),x121432)), % 169.42/169.72 inference(rename_variables,[],[3361])). % 169.42/169.72 cnf(12146,plain, % 169.42/169.72 (P34(x121461,x121462,f116(x121461),f116(x121461))), % 169.42/169.72 inference(rename_variables,[],[3556])). % 169.42/169.72 cnf(12149,plain, % 169.42/169.72 (~E(f334(a115,x121491),x121491)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12152,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x121521,a871)),f334(f173(x121521),f171(x121521,x121522,x121523))),f334(f173(x121521),x121523)))), % 169.42/169.72 inference(rename_variables,[],[4015])). % 169.42/169.72 cnf(12153,plain, % 169.42/169.72 (P104(f334(f63(x121531),f334(f173(x121531),x121532)))), % 169.42/169.72 inference(rename_variables,[],[3343])). % 169.42/169.72 cnf(12164,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x121641),x121641))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12167,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x121671),x121671))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12172,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x121721))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(12179,plain, % 169.42/169.72 (P30(a877,f334(f169(a877),f334(f334(f154(f878(x121791),a877),f196(f878(x121791))),f181(x121791,x121792))))), % 169.42/169.72 inference(rename_variables,[],[3875])). % 169.42/169.72 cnf(12182,plain, % 169.42/169.72 (P21(x121821,x121821,f7(x121821),x121822)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12185,plain, % 169.42/169.72 (P104(f334(f334(f336(f878(x121851)),f116(x121851)),f161(x121851,x121852)))), % 169.42/169.72 inference(rename_variables,[],[3508])). % 169.42/169.72 cnf(12188,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x121881,f886(x121882,a871))),x121883),x121884))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(12193,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x121931),x121931))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12194,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x121941))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(12197,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x121971,f886(x121972,a871))),x121973),x121974))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(12200,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(f885(f878(x122001),f878(x122001)),a871)),f158(x122001,x122002)),f310(f878(x122001),f157(x122001,x122002))))), % 169.42/169.72 inference(rename_variables,[],[4020])). % 169.42/169.72 cnf(12206,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x122061,a871)),f334(f173(x122061),f171(x122061,x122062,x122063))),f334(f173(x122061),x122063)))), % 169.42/169.72 inference(rename_variables,[],[4015])). % 169.42/169.72 cnf(12207,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x122071,a871)),f334(f173(x122071),f334(f136(x122071,x122072),x122073))),f334(f173(x122071),x122073)))), % 169.42/169.72 inference(rename_variables,[],[3964])). % 169.42/169.72 cnf(12210,plain, % 169.42/169.72 (~P104(f334(f334(f250(f886(x122101,a871)),x122102),f195(f886(x122101,a871))))), % 169.42/169.72 inference(rename_variables,[],[4591])). % 169.42/169.72 cnf(12213,plain, % 169.42/169.72 (P21(x122131,f881(x122131),f241(x122131),x122132)), % 169.42/169.72 inference(rename_variables,[],[3557])). % 169.42/169.72 cnf(12218,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x122181,a871)),f334(f313(x122182,x122181,x122183),f334(f314(x122182,x122181,x122183),x122184))),x122184))), % 169.42/169.72 inference(rename_variables,[],[4205])). % 169.42/169.72 cnf(12221,plain, % 169.42/169.72 (P104(f334(f63(f881(x122211)),f334(f313(x122212,f881(x122211),f334(f179(x122212,x122211),x122213)),f257(f886(x122212,a871)))))), % 169.42/169.72 inference(rename_variables,[],[4029])). % 169.42/169.72 cnf(12226,plain, % 169.42/169.72 (P104(f334(f334(f336(f878(x122261)),f116(x122261)),f161(x122261,x122262)))), % 169.42/169.72 inference(rename_variables,[],[3508])). % 169.42/169.72 cnf(12229,plain, % 169.42/169.72 (~P104(f334(f334(f336(f885(f878(x122291),f878(x122291))),f334(f334(f269(f878(x122291),f878(x122291)),x122292),f116(x122291))),f145(x122291,x122293)))), % 169.42/169.72 inference(rename_variables,[],[4602])). % 169.42/169.72 cnf(12232,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x122321),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12234,plain, % 169.42/169.72 (~P104(f334(f63(x122341),f257(f886(x122341,a871))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,11044,12082,3556,3557,3270,4530,4531,3169,4512,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,4509,10430,10521,3516,3216,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2916,2917,2928,2931,2935,2943,2949,2950,2951,2974,2977,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,3085,4490,3880,11596,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,3236,3244,3770,4088,3129,3510,3865,11364,3193,3160,3155,3137,3138,3143,3782,3175,3361,10812,3229,3408,4589,3952,4520,10260,10427,3292,11685,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3467,3107,3212,11354,4101,3954,10985,11111,11159,4602,10917,11116,11218,11243,11281,11287,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,3672,4385,4386,4517,3611,3828,3875,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,3762,11582,3285,3384,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,4584,11467,11498,11533,11562,3749,3517,3902,3329,3331,3304,4565,4514,3500,4585,4095,11238,3632,3343,11709,11712,4063,4020,11853,12200,3964,10809,12037,4015,10991,12079,12152,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,12067,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,3462,10602,10870,10914,11181,11262,11425,11665,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,3365,10633,10663,10672,11210,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,3323,10666,10819,10890,11614,11769,11961,12172,3792,4145,4575,3803,3840,4554,4557,3276,3280,4556,4555,4559,3811,3622,4245,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,4029,3919,11303,11640,11644,3756,10930,10936,10951,11885,12014,3607,11150,12126,3758,10669,11007,11156,11186,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,11453,12188,4205,10802,12034,4106,3791,3735,4595,10279,10282,10627,10630,11464,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9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% 169.42/169.72 cnf(12235,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x122351,a871)),x122352),x122352))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12238,plain, % 169.42/169.72 (~P104(f334(f334(f336(x122381),x122382),f195(f886(x122381,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12241,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x122411,f886(x122412,a871))),x122413),x122414))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(12244,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x122441,a871)),f334(f313(x122442,x122441,x122443),f334(f314(x122442,x122441,x122443),x122444))),x122444))), % 169.42/169.72 inference(rename_variables,[],[4205])). % 169.42/169.72 cnf(12245,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x122451,a871)),x122452),x122452))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12250,plain, % 169.42/169.72 (E(f334(f265(x122501,x122501),f266(x122501,x122502)),x122502)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12253,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x122531,a871)),f334(f173(x122531),f171(x122531,x122532,x122533))),f334(f173(x122531),x122533)))), % 169.42/169.72 inference(rename_variables,[],[4015])). % 169.42/169.72 cnf(12254,plain, % 169.42/169.72 (P104(f334(f63(x122541),f334(f173(x122541),x122542)))), % 169.42/169.72 inference(rename_variables,[],[3343])). % 169.42/169.72 cnf(12257,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x122571),x122571))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12260,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x122601),x122601))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12263,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x122631),x122631))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12274,plain, % 169.42/169.72 (P21(x122741,x122741,f7(x122741),x122742)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12279,plain, % 169.42/169.72 (~P104(f334(f334(f336(x122791),x122792),f195(f886(x122791,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12282,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x122821,x122821)),f334(f334(f269(x122821,x122821),x122822),x122822)),f310(x122821,x122823)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(12285,plain, % 169.42/169.72 (~P104(f334(f334(f336(x122851),x122852),f195(f886(x122851,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12288,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x122881,x122881)),f334(f334(f269(x122881,x122881),x122882),x122882)),f310(x122881,x122883)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(12298,plain, % 169.42/169.72 (~E(f334(f334(f151(x122981),x122982),x122983),x122983)), % 169.42/169.72 inference(rename_variables,[],[4520])). % 169.42/169.72 cnf(12301,plain, % 169.42/169.72 (P104(f334(f334(f336(x123011),x123012),f257(f886(x123011,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(12302,plain, % 169.42/169.72 (~E(f334(a115,x123021),x123021)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12305,plain, % 169.42/169.72 (P104(f334(f334(f336(f878(x123051)),f116(x123051)),f161(x123051,x123052)))), % 169.42/169.72 inference(rename_variables,[],[3508])). % 169.42/169.72 cnf(12306,plain, % 169.42/169.72 (~E(f334(f334(f151(x123061),x123062),x123063),f116(x123061))), % 169.42/169.72 inference(rename_variables,[],[4529])). % 169.42/169.72 cnf(12309,plain, % 169.42/169.72 (P104(f334(f334(f336(x123091),f334(x123092,x123093)),f334(f313(x123094,x123091,x123092),f257(f886(x123094,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(12310,plain, % 169.42/169.72 (P21(x123101,x123101,f7(x123101),x123102)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12313,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x123131,a871)),f195(f886(x123131,a871))),x123132))), % 169.42/169.72 inference(rename_variables,[],[3758])). % 169.42/169.72 cnf(12314,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x123141,a871)),x123142),x123142))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12317,plain, % 169.42/169.72 (P104(f334(f334(f336(x123171),f334(x123172,x123173)),f334(f313(x123174,x123171,x123172),f257(f886(x123174,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(12318,plain, % 169.42/169.72 (P21(x123181,x123181,f7(x123181),x123182)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12321,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(f878(x123211),f878(x123211))),f334(f334(f269(f878(x123211),f878(x123211)),f116(x123211)),f116(x123211))),f158(x123211,x123212)))), % 169.42/169.72 inference(rename_variables,[],[4101])). % 169.42/169.72 cnf(12324,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x123241),x123241))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12325,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x123251),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12331,plain, % 169.42/169.72 (E(f334(f334(f134(x123311),x123312),f116(x123311)),x123312)), % 169.42/169.72 inference(rename_variables,[],[3230])). % 169.42/169.72 cnf(12332,plain, % 169.42/169.72 (~E(f334(f334(f151(x123321),x123322),x123323),x123323)), % 169.42/169.72 inference(rename_variables,[],[4520])). % 169.42/169.72 cnf(12335,plain, % 169.42/169.72 (E(f334(f334(f134(x123351),x123352),f116(x123351)),x123352)), % 169.42/169.72 inference(rename_variables,[],[3230])). % 169.42/169.72 cnf(12336,plain, % 169.42/169.72 (~E(f334(f334(f151(x123361),x123362),x123363),x123363)), % 169.42/169.72 inference(rename_variables,[],[4520])). % 169.42/169.72 cnf(12339,plain, % 169.42/169.72 (E(f334(f334(f134(x123391),x123392),f116(x123391)),x123392)), % 169.42/169.72 inference(rename_variables,[],[3230])). % 169.42/169.72 cnf(12348,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x123481,a871)),x123482),f257(f886(x123481,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(12352,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x123521),x123521))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12353,plain, % 169.42/169.72 (~E(f334(a115,x123531),x123531)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12356,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x123561,a871)),f195(f886(x123561,a871))),x123562))), % 169.42/169.72 inference(rename_variables,[],[3758])). % 169.42/169.72 cnf(12359,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x123591),x123591))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12362,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x123621,a871)),x123622),x123622))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12367,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x123671,a871)),x123672),f334(f334(f312(x123671),x123673),x123672)))), % 169.42/169.72 inference(rename_variables,[],[3756])). % 169.42/169.72 cnf(12370,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x123701,a871)),x123702),x123702))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12371,plain, % 169.42/169.72 (~P104(f334(f334(f336(x123711),x123712),f195(f886(x123711,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12374,plain, % 169.42/169.72 (~P104(f334(f334(f336(x123741),x123742),f195(f886(x123741,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12382,plain, % 169.42/169.72 (~P104(f334(f334(f249(f886(f885(x123821,x123821),a871)),f334(f313(f885(x123821,x123821),f885(x123821,x123821),f7(f885(x123821,x123821))),f257(f886(f885(x123821,x123821),a871)))),f334(f313(f885(x123821,x123821),f885(x123821,x123821),f7(f885(x123821,x123821))),f195(f886(f885(x123821,x123821),a871)))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,3556,3557,3270,4530,4531,3169,4512,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,4509,10430,10521,3360,3516,3216,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2916,2917,2920,2928,2931,2935,2943,2949,2950,2951,2974,2977,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,3085,4490,3880,11596,3139,11314,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,3230,12331,12335,3236,3244,3770,4088,3129,4506,3510,3865,11364,3193,3160,3155,3137,3138,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,3952,4520,10260,10427,11224,12298,12332,4529,12306,3292,11685,4578,10979,11049,11273,11276,3409,3190,3191,10329,10636,3467,3107,3212,11354,4101,12321,3954,10985,11111,11159,12282,12288,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3828,3875,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,3762,11582,3285,3384,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,4584,11467,11498,11533,11562,3749,3517,3902,3329,3331,3304,4565,4514,3700,3500,4585,4095,11238,3632,3343,11709,11712,12153,4063,4020,11853,12200,3964,10809,12037,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,12067,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,3462,10602,10870,10914,11181,11262,11425,11665,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,3365,10633,10663,10672,11210,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,3323,10666,10819,10890,11614,11769,11961,12172,3792,4145,4575,3803,3840,4554,4557,3276,3280,4556,4555,4559,3811,3622,4245,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,3919,11303,11640,11644,11706,12309,3756,10930,10936,10951,11885,12014,12100,3607,11150,12126,12235,12245,12314,12362,3758,10669,11007,11156,11186,11197,12313,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,11453,12188,12197,4205,10802,12034,12218,4106,3791,3735,4595,10279,10282,10627,10630,11464,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,88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% 169.42/169.72 cnf(12383,plain, % 169.42/169.72 (P21(x123831,x123831,f7(x123831),x123832)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12386,plain, % 169.42/169.72 (E(f334(f196(f878(x123861)),f170(x123861,x123862,x123863)),x123862)), % 169.42/169.72 inference(rename_variables,[],[3371])). % 169.42/169.72 cnf(12389,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x123891),x123891))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12390,plain, % 169.42/169.72 (P104(f334(f257(f886(x123901,a871)),x123902))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(12393,plain, % 169.42/169.72 (~P104(f334(f334(f336(x123931),x123932),f195(f886(x123931,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12396,plain, % 169.42/169.72 (P104(f334(f334(f336(x123961),f334(x123962,x123963)),f334(f313(x123964,x123961,x123962),f257(f886(x123964,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(12397,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x123971,x123971)),f334(f334(f269(x123971,x123971),x123972),x123972)),f310(x123971,x123973)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(12400,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x124001,x124001)),f334(f334(f269(x124001,x124001),x124002),x124002)),f310(x124001,x124003)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(12403,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x124031),x124031))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12404,plain, % 169.42/169.72 (P104(f334(f257(f886(x124041,a871)),x124042))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(12407,plain, % 169.42/169.72 (P104(f334(f63(x124071),f334(f173(x124071),x124072)))), % 169.42/169.72 inference(rename_variables,[],[3343])). % 169.42/169.72 cnf(12417,plain, % 169.42/169.72 (~P104(f334(f334(f195(f886(x124171,f886(x124172,a871))),x124173),x124174))), % 169.42/169.72 inference(rename_variables,[],[4598])). % 169.42/169.72 cnf(12420,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x124201,a871)),x124202),f257(f886(x124201,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(12423,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(x124231,x124231)),f334(f334(f269(x124231,x124231),x124232),x124232)),f310(x124231,x124233)))), % 169.42/169.72 inference(rename_variables,[],[3954])). % 169.42/169.72 cnf(12426,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),f334(f334(f81(a877),x124261),x124262)),x124262))), % 169.42/169.72 inference(rename_variables,[],[4595])). % 169.42/169.72 cnf(12427,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x124271),f334(a115,x124271)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12430,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x124301,a871)),f334(f173(x124301),f334(f136(x124301,x124302),x124303))),f334(f173(x124301),x124303)))), % 169.42/169.72 inference(rename_variables,[],[3964])). % 169.42/169.72 cnf(12433,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x124331,a871)),x124332),f257(f886(x124331,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(12436,plain, % 169.42/169.72 (E(f334(f265(x124361,x124361),f266(x124361,x124362)),x124362)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12447,plain, % 169.42/169.72 (~P104(f334(f334(f336(x124471),x124472),f195(f886(x124471,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12448,plain, % 169.42/169.72 (P104(f334(f334(f336(f885(f878(x124481),f878(x124481))),f334(f334(f269(f878(x124481),f878(x124481)),f116(x124481)),f116(x124481))),f158(x124481,x124482)))), % 169.42/169.72 inference(rename_variables,[],[4101])). % 169.42/169.72 cnf(12453,plain, % 169.42/169.72 (~P104(f334(f334(f336(x124531),x124532),f195(f886(x124531,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12456,plain, % 169.42/169.72 (P33(x124561,x124562,f116(x124561))), % 169.42/169.72 inference(rename_variables,[],[3235])). % 169.42/169.72 cnf(12459,plain, % 169.42/169.72 (E(f334(f196(f878(x124591)),f170(x124591,x124592,x124593)),x124592)), % 169.42/169.72 inference(rename_variables,[],[3371])). % 169.42/169.72 cnf(12462,plain, % 169.42/169.72 (~P104(f334(f334(f336(x124621),x124622),f195(f886(x124621,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12468,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x124681),x124681))), % 169.42/169.72 inference(rename_variables,[],[4564])). % 169.42/169.72 cnf(12471,plain, % 169.42/169.72 (P104(f334(f334(f336(x124711),x124712),f257(f886(x124711,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(12479,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x124791,a871)),x124792),x124792))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12482,plain, % 169.42/169.72 (~P104(f334(f334(f336(x124821),x124822),f195(f886(x124821,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12485,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),f2(a1)),f334(f334(f259(a1),f334(f76(a1),x124851)),x124852)))), % 169.42/169.72 inference(rename_variables,[],[3791])). % 169.42/169.72 cnf(12488,plain, % 169.42/169.72 (~E(f334(a115,x124881),x124881)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12490,plain, % 169.42/169.72 (E(f334(f265(x124901,x124901),f266(x124901,x124902)),x124902)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12498,plain, % 169.42/169.72 (P21(x124981,x124981,f7(x124981),x124982)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12500,plain, % 169.42/169.72 (P21(x125001,x125001,f7(x125001),x125002)), % 169.42/169.72 inference(rename_variables,[],[3547])). % 169.42/169.72 cnf(12506,plain, % 169.42/169.72 (P39(x125061,f153(x125061,x125062))), % 169.42/169.72 inference(rename_variables,[],[3169])). % 169.42/169.72 cnf(12510,plain, % 169.42/169.72 (E(f334(f265(x125101,x125101),f266(x125101,x125102)),x125102)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12516,plain, % 169.42/169.72 (E(f334(f265(x125161,x125161),f266(x125161,x125162)),x125162)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12520,plain, % 169.42/169.72 (E(f334(f265(x125201,x125201),f266(x125201,x125202)),x125202)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12522,plain, % 169.42/169.72 (E(f334(f265(x125221,x125221),f266(x125221,x125222)),x125222)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12528,plain, % 169.42/169.72 (E(f334(f265(x125281,x125281),f266(x125281,x125282)),x125282)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12538,plain, % 169.42/169.72 (E(f334(f265(x125381,x125381),f266(x125381,x125382)),x125382)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12540,plain, % 169.42/169.72 (P11(x125401,f886(x125401,a871),f312(x125401))), % 169.42/169.72 inference(rename_variables,[],[3273])). % 169.42/169.72 cnf(12544,plain, % 169.42/169.72 (P49(x125441,x125442,f266(x125441,x125442))), % 169.42/169.72 inference(rename_variables,[],[3269])). % 169.42/169.72 cnf(12546,plain, % 169.42/169.72 (P49(x125461,x125462,f266(x125461,x125462))), % 169.42/169.72 inference(rename_variables,[],[3269])). % 169.42/169.72 cnf(12552,plain, % 169.42/169.72 (E(f195(f886(f885(x125521,x125521),a871)),f266(x125521,f195(f886(x125521,a871))))), % 169.42/169.72 inference(rename_variables,[],[3375])). % 169.42/169.72 cnf(12554,plain, % 169.42/169.72 (E(f334(f265(x125541,x125541),f266(x125541,x125542)),x125542)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12556,plain, % 169.42/169.72 (P53(x125561,f195(f886(x125561,a871)),x125562)), % 169.42/169.72 inference(rename_variables,[],[3321])). % 169.42/169.72 cnf(12562,plain, % 169.42/169.72 (P20(x125621,x125622,f195(f886(f876(x125621),a871)))), % 169.42/169.72 inference(rename_variables,[],[3359])). % 169.42/169.72 cnf(12569,plain, % 169.42/169.72 (E(f334(f265(x125691,x125691),f266(x125691,x125692)),x125692)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12571,plain, % 169.42/169.72 (P31(x125711,f2(a877),f334(f334(f334(f93(x125711),x125712),f334(a26,x125713)),x125714))), % 169.42/169.72 inference(rename_variables,[],[3684])). % 169.42/169.72 cnf(12577,plain, % 169.42/169.72 (P43(x125771,x125772,x125773,x125774,f195(f886(x125771,a871)),x125774)), % 169.42/169.72 inference(rename_variables,[],[4269])). % 169.42/169.72 cnf(12580,plain, % 169.42/169.72 (P43(x125801,x125802,x125803,x125804,f195(f886(x125801,a871)),x125804)), % 169.42/169.72 inference(rename_variables,[],[4269])). % 169.42/169.72 cnf(12585,plain, % 169.42/169.72 (P52(x125851,x125851,f266(x125851,x125852))), % 169.42/169.72 inference(rename_variables,[],[3270])). % 169.42/169.72 cnf(12596,plain, % 169.42/169.72 (P34(x125961,x125962,f116(x125961),f116(x125961))), % 169.42/169.72 inference(rename_variables,[],[3556])). % 169.42/169.72 cnf(12598,plain, % 169.42/169.72 (P34(x125981,x125982,f116(x125981),f116(x125981))), % 169.42/169.72 inference(rename_variables,[],[3556])). % 169.42/169.72 cnf(12602,plain, % 169.42/169.72 (P40(x126021,f198(x126021))), % 169.42/169.72 inference(rename_variables,[],[3126])). % 169.42/169.72 cnf(12607,plain, % 169.42/169.72 (E(f334(f265(x126071,x126071),f266(x126071,x126072)),x126072)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12609,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),f2(a877)),f334(a115,x126091)))), % 169.42/169.72 inference(rename_variables,[],[3384])). % 169.42/169.72 cnf(12610,plain, % 169.42/169.72 (~E(f334(a115,x126101),x126101)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12616,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x126161),f334(a115,x126161)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12621,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x126211),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12623,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),a84),f2(a1)))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,4509,10430,10521,3360,3321,12556,3516,3216,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2916,2917,2920,2928,2931,2935,2943,2949,2950,2951,2974,2977,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3689,4473,3137,3138,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,4529,12306,3292,11685,4578,10979,11049,11273,11276,3709,3409,3633,3375,12552,3190,3191,10329,10636,3467,3183,3107,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3828,3875,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,4584,11467,11498,11533,11562,3749,3517,3902,3329,3331,3304,4565,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,4063,4020,11853,12200,3964,10809,12037,12207,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,12067,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,3462,10602,10870,10914,11181,11262,11425,11665,12301,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,3365,10633,10663,10672,11210,11764,12390,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,3323,10666,10819,10890,11614,11769,11961,12172,3792,4145,4575,3803,3840,4554,4557,3276,3280,4556,4555,4559,3811,3622,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,3919,11303,11640,11644,11706,12309,12317,3756,10930,10936,10951,11885,12014,12100,3607,11150,12126,12235,12245,12314,12362,12370,4099,3758,10669,11007,11156,11186,11197,12313,3573,10585,10588,10675,10846,4597,11579,4586,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,4106,3791,3735,4595,10279,10282,10627,10630,11464,11645,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7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% 169.42/169.72 cnf(12630,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f103(a1),x126301)),f334(f80(a1),f334(f103(a1),x126302))))), % 169.42/169.72 inference(rename_variables,[],[4592])). % 169.42/169.72 cnf(12640,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x126401),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12643,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x126431),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12646,plain, % 169.42/169.72 (P104(f334(f63(a877),f307(a877,x126461,x126462)))), % 169.42/169.72 inference(rename_variables,[],[3519])). % 169.42/169.72 cnf(12649,plain, % 169.42/169.72 (P104(f334(f63(a877),f307(a877,x126491,x126492)))), % 169.42/169.72 inference(rename_variables,[],[3519])). % 169.42/169.72 cnf(12652,plain, % 169.42/169.72 (P104(f334(f63(a877),f307(a877,x126521,x126522)))), % 169.42/169.72 inference(rename_variables,[],[3519])). % 169.42/169.72 cnf(12655,plain, % 169.42/169.72 (P104(f334(f63(a877),f307(a877,x126551,x126552)))), % 169.42/169.72 inference(rename_variables,[],[3519])). % 169.42/169.72 cnf(12662,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),f334(f80(a1),f334(f103(a1),x126621))),f334(f103(a1),x126622)))), % 169.42/169.72 inference(rename_variables,[],[3792])). % 169.42/169.72 cnf(12667,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x126671),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12668,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x126681),x126681))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12675,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x126751),f334(a115,x126751)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12677,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),f2(a1)),a84))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,4509,10430,10521,3360,3321,12556,3516,3216,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2916,2917,2920,2928,2931,2935,2943,2949,2950,2951,2974,2977,3012,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,4529,12306,3292,11685,4578,10979,11049,11273,11276,3709,3409,3633,3375,12552,3190,3191,10329,10636,3467,3183,3107,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3649,3828,3875,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,4584,11467,11498,11533,11562,3749,3517,3519,12646,12649,12652,3902,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,4063,4020,11853,12200,3964,10809,12037,12207,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,12067,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,3462,10602,10870,10914,11181,11262,11425,11665,12301,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,3365,10633,10663,10672,11210,11764,12390,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,3323,10666,10819,10890,11614,11769,11961,12172,3792,11715,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,3811,3622,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,3919,11303,11640,11644,11706,12309,12317,3756,10930,10936,10951,11885,12014,12100,3607,11150,12126,12235,12245,12314,12362,12370,4099,3758,10669,11007,11156,11186,11197,12313,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,4106,3791,3735,3736,4595,10279,10282,10627,10630,11464,11645,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156])). % 169.42/169.72 cnf(12680,plain, % 169.42/169.72 (P104(f334(f334(f336(x126801),f334(x126802,x126803)),f334(f313(x126804,x126801,x126802),f257(f886(x126804,a871)))))), % 169.42/169.72 inference(rename_variables,[],[3919])). % 169.42/169.72 cnf(12681,plain, % 169.42/169.72 (~E(f334(a115,x126811),f2(a877))), % 169.42/169.72 inference(rename_variables,[],[4504])). % 169.42/169.72 cnf(12683,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f2(a1)),f334(f106(a1),f2(a1))))), % 169.42/169.72 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,4509,10430,10521,3360,3321,12556,3516,3216,4504,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2916,2917,2920,2928,2931,2935,2943,2949,2950,2951,2974,2977,3012,3013,3018,3022,3023,3025,3027,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,4529,12306,3292,11685,4578,10979,11049,11273,11276,3709,3409,3633,3375,12552,3190,3191,10329,10636,3467,3183,3107,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3649,3828,3875,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,4584,11467,11498,11533,11562,3749,3517,3519,12646,12649,12652,3902,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,4063,4020,11853,12200,3964,10809,12037,12207,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,3303,3380,12067,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,3462,10602,10870,10914,11181,11262,11425,11665,12301,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,3365,10633,10663,10672,11210,11764,12390,3404,3398,3832,3767,10306,11585,11613,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,3323,10666,10819,10890,11614,11769,11961,12172,3792,11715,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,3811,3622,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,3756,10930,10936,10951,11885,12014,12100,3607,11150,12126,12235,12245,12314,12362,12370,4099,3758,10669,11007,11156,11186,11197,12313,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,4106,3791,3735,3736,4595,10279,10282,10627,10630,11464,11645,4596,11559,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308])). % 169.42/169.72 cnf(12686,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x126861),x126861))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(12689,plain, % 169.42/169.72 (P104(f334(f63(a877),f307(a877,x126891,x126892)))), % 169.42/169.72 inference(rename_variables,[],[3519])). % 169.42/169.72 cnf(12692,plain, % 169.42/169.72 (P104(f334(f63(a877),f307(a877,x126921,x126922)))), % 169.42/169.72 inference(rename_variables,[],[3519])). % 169.42/169.72 cnf(12695,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x126951),x126951))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12696,plain, % 169.42/169.72 (~E(f334(a115,x126961),f2(a877))), % 169.42/169.72 inference(rename_variables,[],[4504])). % 169.42/169.72 cnf(12713,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f46(a877,x127131,x127132)),x127131))), % 169.42/169.72 inference(rename_variables,[],[3767])). % 169.42/169.72 cnf(12718,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x127181),f334(a115,x127181)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12721,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x127211),f334(a115,x127211)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12722,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x127221),f2(a877)))), % 169.42/169.72 inference(rename_variables,[],[4568])). % 169.42/169.72 cnf(12731,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f103(a1),x127311)),f2(a1)))), % 169.42/169.72 inference(rename_variables,[],[4584])). % 169.42/169.72 cnf(12732,plain, % 169.42/169.72 (P104(f334(f257(f886(x127321,a871)),x127322))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(12735,plain, % 169.42/169.72 (~P104(f334(f334(f250(a1),f334(f103(a1),x127351)),f2(a1)))), % 169.42/169.72 inference(rename_variables,[],[4584])). % 169.42/169.72 cnf(12736,plain, % 169.42/169.72 (P104(f334(f257(f886(x127361,a871)),x127362))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(12739,plain, % 169.42/169.72 (P104(f334(f257(f886(x127391,a871)),x127392))), % 169.42/169.72 inference(rename_variables,[],[3365])). % 169.42/169.72 cnf(12750,plain, % 169.42/169.72 (~P104(f334(f334(f336(x127501),x127502),f195(f886(x127501,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12751,plain, % 169.42/169.72 (P104(f334(f63(x127511),f195(f886(x127511,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12760,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),f2(a877)),x127601))), % 169.42/169.72 inference(rename_variables,[],[3323])). % 169.42/169.72 cnf(12763,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x127631),f334(a115,x127631)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12764,plain, % 169.42/169.72 (~E(f334(a115,x127641),x127641)), % 169.42/169.72 inference(rename_variables,[],[4494])). % 169.42/169.72 cnf(12767,plain, % 169.42/169.72 (~P104(f334(f334(f336(x127671),x127672),f195(f886(x127671,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12770,plain, % 169.42/169.72 (~P104(f334(f334(f336(x127701),x127702),f195(f886(x127701,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12773,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x127731),x127731))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12781,plain, % 169.42/169.72 (P104(f334(f334(f250(a877),x127811),f334(a115,x127811)))), % 169.42/169.72 inference(rename_variables,[],[3372])). % 169.42/169.72 cnf(12784,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x127841),x127841))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12789,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x127891),x127891))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12792,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x127921),x127921))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12795,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x127951),x127951))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12798,plain, % 169.42/169.72 (E(f334(f334(f3(f886(x127981,a871)),f195(f886(x127981,a871))),x127982),f195(f886(x127981,a871)))), % 169.42/169.72 inference(rename_variables,[],[3577])). % 169.42/169.72 cnf(12799,plain, % 169.42/169.72 (P104(f334(f63(x127991),f195(f886(x127991,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12802,plain, % 169.42/169.72 (E(f334(f334(f3(f886(x128021,a871)),f195(f886(x128021,a871))),x128022),f195(f886(x128021,a871)))), % 169.42/169.72 inference(rename_variables,[],[3577])). % 169.42/169.72 cnf(12803,plain, % 169.42/169.72 (P104(f334(f63(x128031),f195(f886(x128031,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12806,plain, % 169.42/169.72 (E(f334(f334(f3(f886(x128061,a871)),f195(f886(x128061,a871))),x128062),f195(f886(x128061,a871)))), % 169.42/169.72 inference(rename_variables,[],[3577])). % 169.42/169.72 cnf(12807,plain, % 169.42/169.72 (P104(f334(f63(x128071),f195(f886(x128071,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12810,plain, % 169.42/169.72 (E(f334(f334(f3(f886(x128101,a871)),f195(f886(x128101,a871))),x128102),f195(f886(x128101,a871)))), % 169.42/169.72 inference(rename_variables,[],[3577])). % 169.42/169.72 cnf(12811,plain, % 169.42/169.72 (P104(f334(f63(x128111),f195(f886(x128111,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12815,plain, % 169.42/169.72 (E(f334(f265(x128151,x128151),f266(x128151,x128152)),x128152)), % 169.42/169.72 inference(rename_variables,[],[3259])). % 169.42/169.72 cnf(12820,plain, % 169.42/169.72 (E(f334(f334(f3(f886(x128201,a871)),f195(f886(x128201,a871))),x128202),f195(f886(x128201,a871)))), % 169.42/169.72 inference(rename_variables,[],[3577])). % 169.42/169.72 cnf(12821,plain, % 169.42/169.72 (P104(f334(f63(x128211),f195(f886(x128211,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12825,plain, % 169.42/169.72 (P104(f334(f63(x128251),f195(f886(x128251,a871))))), % 169.42/169.72 inference(rename_variables,[],[3380])). % 169.42/169.72 cnf(12828,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x128281),x128281))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12832,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x128321),x128321))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(12839,plain, % 169.42/169.72 (P104(f334(f334(f249(a877),x128391),x128391))), % 169.42/169.72 inference(rename_variables,[],[3301])). % 169.42/169.72 cnf(12852,plain, % 169.42/169.72 (P104(f334(f334(f249(a1),x128521),x128521))), % 169.42/169.72 inference(rename_variables,[],[3302])). % 169.42/169.72 cnf(12861,plain, % 169.42/169.72 (~P104(f334(f334(f336(x128611),x128612),f195(f886(x128611,a871))))), % 169.42/169.72 inference(rename_variables,[],[4580])). % 169.42/169.72 cnf(12872,plain, % 169.42/169.72 (P104(f334(f334(f336(x128721),x128722),f257(f886(x128721,a871))))), % 169.42/169.72 inference(rename_variables,[],[3462])). % 169.42/169.72 cnf(12876,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x128761,a871)),x128762),f257(f886(x128761,a871))))), % 169.42/169.72 inference(rename_variables,[],[3691])). % 169.42/169.72 cnf(12879,plain, % 169.42/169.72 (P104(f334(f334(f249(f886(x128791,a871)),x128792),x128792))), % 169.42/169.72 inference(rename_variables,[],[3607])). % 169.42/169.72 cnf(12885,plain, % 169.42/169.72 (~P104(f334(f334(f250(a877),x128851),f2(a877)))), % 169.42/169.73 inference(rename_variables,[],[4568])). % 169.42/169.73 cnf(12886,plain, % 169.42/169.73 (P104(f334(f334(f249(a1),x128861),x128861))), % 169.42/169.73 inference(rename_variables,[],[3302])). % 169.42/169.73 cnf(12890,plain, % 169.42/169.73 (~P104(f334(f334(f250(a877),x128901),f2(a877)))), % 169.42/169.73 inference(rename_variables,[],[4568])). % 169.42/169.73 cnf(12891,plain, % 169.42/169.73 (P104(f334(f334(f249(a1),x128911),x128911))), % 169.42/169.73 inference(rename_variables,[],[3302])). % 169.42/169.73 cnf(12896,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),x128961),x128961))), % 169.42/169.73 inference(rename_variables,[],[3301])). % 169.42/169.73 cnf(12903,plain, % 169.42/169.73 (E(f334(f334(f18(x129031,x129032),x129033),x129034),x129033)), % 169.42/169.73 inference(rename_variables,[],[3292])). % 169.42/169.73 cnf(12906,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x129061,a871)),f334(f173(x129061),f171(x129061,x129062,x129063))),f334(f173(x129061),x129063)))), % 169.42/169.73 inference(rename_variables,[],[4015])). % 169.42/169.73 cnf(12910,plain, % 169.42/169.73 (~P104(f334(f334(f250(a877),x129101),f2(a877)))), % 169.42/169.73 inference(rename_variables,[],[4568])). % 169.42/169.73 cnf(12911,plain, % 169.42/169.73 (P104(f334(f334(f249(a1),x129111),x129111))), % 169.42/169.73 inference(rename_variables,[],[3302])). % 169.42/169.73 cnf(12915,plain, % 169.42/169.73 (~P104(f334(f334(f250(a877),x129151),f2(a877)))), % 169.42/169.73 inference(rename_variables,[],[4568])). % 169.42/169.73 cnf(12916,plain, % 169.42/169.73 (P104(f334(f334(f249(a1),x129161),x129161))), % 169.42/169.73 inference(rename_variables,[],[3302])). % 169.42/169.73 cnf(12920,plain, % 169.42/169.73 (~P104(f334(f334(f249(f886(a877,a871)),f305(a877,f334(a115,x129201),f334(a115,x129201))),f305(a877,x129202,x129201)))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2943,2949,2950,2951,2957,2974,2977,2988,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,4529,12306,3292,11685,11688,4578,10979,11049,11273,11276,3709,3409,3633,3375,12552,3190,3191,10329,10636,3467,3183,3107,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,3902,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,3323,10666,10819,10890,11614,11769,11961,12172,12194,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,3811,3622,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,3756,10930,10936,10951,11885,12014,12100,3607,11150,12126,12235,12245,12314,12362,12370,12479,4099,3758,10669,11007,11156,11186,11197,12313,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523])). % 169.42/169.73 cnf(12921,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),x129211),x129211))), % 169.42/169.73 inference(rename_variables,[],[3301])). % 169.42/169.73 cnf(12923,plain, % 169.42/169.73 (~P104(f334(f334(f250(f886(a877,a871)),f305(a877,f334(a115,x129231),f334(a115,x129231))),f305(a877,x129232,x129231)))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2943,2949,2950,2951,2957,2974,2977,2988,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,4529,12306,3292,11685,11688,4578,10979,11049,11273,11276,3709,3409,3633,3375,12552,3190,3191,10329,10636,3467,3183,3107,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,3902,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,3323,10666,10819,10890,11614,11769,11961,12172,12194,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,3811,3622,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,3756,10930,10936,10951,11885,12014,12100,3607,11150,12126,12235,12245,12314,12362,12370,12479,4099,3758,10669,11007,11156,11186,11197,12313,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523,8524])). % 169.42/169.73 cnf(12924,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),x129241),x129241))), % 169.42/169.73 inference(rename_variables,[],[3301])). % 169.42/169.73 cnf(12927,plain, % 169.42/169.73 (~P104(f334(f334(f249(a877),f334(a115,x129271)),x129271))), % 169.42/169.73 inference(rename_variables,[],[4577])). % 169.42/169.73 cnf(12932,plain, % 169.42/169.73 (E(x129321,f418(f334(f7(x129322),f334(f7(x129322),x129321)),f7(x129322),x129322,x129322))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2943,2949,2950,2951,2957,2974,2977,2988,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,4529,12306,3292,11685,11688,4578,10979,11049,11273,11276,3709,3409,3633,3375,12552,3190,3191,10329,10636,3467,3183,3107,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,3902,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,4591,10757,11127,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,3811,3622,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,3756,10930,10936,10951,11885,12014,12100,3607,11150,12126,12235,12245,12314,12362,12370,12479,4099,3758,10669,11007,11156,11186,11197,12313,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,598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% 169.42/169.73 cnf(12933,plain, % 169.42/169.73 (P104(f334(f334(f336(x129331),f334(x129332,x129333)),f334(f313(x129334,x129331,x129332),f257(f886(x129334,a871)))))), % 169.42/169.73 inference(rename_variables,[],[3919])). % 169.42/169.73 cnf(12934,plain, % 169.42/169.73 (P21(x129341,x129341,f7(x129341),x129342)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(12939,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x129391,a871)),x129392),f257(f886(x129391,a871))))), % 169.42/169.73 inference(rename_variables,[],[3691])). % 169.42/169.73 cnf(12940,plain, % 169.42/169.73 (P21(x129401,x129401,f7(x129401),x129402)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(12944,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x129441,a871)),x129442),f257(f886(x129441,a871))))), % 169.42/169.73 inference(rename_variables,[],[3691])). % 169.42/169.73 cnf(12945,plain, % 169.42/169.73 (P21(x129451,x129451,f7(x129451),x129452)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(12949,plain, % 169.42/169.73 (P21(x129491,x129491,f7(x129491),x129492)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(12952,plain, % 169.42/169.73 (~P104(f334(f334(f250(f886(x129521,a871)),x129522),f195(f886(x129521,a871))))), % 169.42/169.73 inference(rename_variables,[],[4591])). % 169.42/169.73 cnf(12955,plain, % 169.42/169.73 (P21(x129551,x129551,f7(x129551),x129552)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(12958,plain, % 169.42/169.73 (P21(x129581,x129581,f7(x129581),x129582)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(12969,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x129691,a871)),f195(f886(x129691,a871))),x129692))), % 169.42/169.73 inference(rename_variables,[],[3758])). % 169.42/169.73 cnf(12973,plain, % 169.42/169.73 (E(f334(f265(x129731,x129731),f266(x129731,x129732)),x129732)), % 169.42/169.73 inference(rename_variables,[],[3259])). % 169.42/169.73 cnf(12977,plain, % 169.42/169.73 (~P104(f334(f334(f336(x129771),x129772),f195(f886(x129771,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(12981,plain, % 169.42/169.73 (P104(f334(f334(f336(x129811),f334(x129812,x129813)),f334(f313(x129814,x129811,x129812),f257(f886(x129814,a871)))))), % 169.42/169.73 inference(rename_variables,[],[3919])). % 169.42/169.73 cnf(12982,plain, % 169.42/169.73 (P21(x129821,x129821,f7(x129821),x129822)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(12985,plain, % 169.42/169.73 (P104(f334(f334(f336(x129851),x129852),f257(f886(x129851,a871))))), % 169.42/169.73 inference(rename_variables,[],[3462])). % 169.42/169.73 cnf(12992,plain, % 169.42/169.73 (~P104(f334(f334(f336(x129921),x129922),f195(f886(x129921,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(12995,plain, % 169.42/169.73 (~P104(f334(f334(f336(x129951),x129952),f195(f886(x129951,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(12999,plain, % 169.42/169.73 (E(f334(f334(f18(x129991,x129992),x129993),x129994),x129993)), % 169.42/169.73 inference(rename_variables,[],[3292])). % 169.42/169.73 cnf(13002,plain, % 169.42/169.73 (P104(f334(f334(f250(a877),x130021),f334(a115,x130021)))), % 169.42/169.73 inference(rename_variables,[],[3372])). % 169.42/169.73 cnf(13003,plain, % 169.42/169.73 (~E(f334(a115,x130031),x130031)), % 169.42/169.73 inference(rename_variables,[],[4494])). % 169.42/169.73 cnf(13006,plain, % 169.42/169.73 (P104(f334(f334(f250(a877),x130061),f334(a115,f334(f334(f81(a877),x130062),x130061))))), % 169.42/169.73 inference(rename_variables,[],[3760])). % 169.42/169.73 cnf(13007,plain, % 169.42/169.73 (P104(f334(f334(f250(a877),x130071),f334(a115,x130071)))), % 169.42/169.73 inference(rename_variables,[],[3372])). % 169.42/169.73 cnf(13009,plain, % 169.42/169.73 (~E(f334(f334(f82(a877),f334(a115,f2(a877))),f34(x130091,x130092)),f334(f334(f82(a877),f334(a115,f2(a877))),f33(x130093,x130094)))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,12934,12940,12945,12949,12955,12958,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,12764,13003,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2937,2943,2949,2950,2951,2957,2974,2977,2988,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,12815,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3176,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,12336,4529,12306,3292,11685,11688,12903,4578,10979,11049,11273,11276,3709,3289,3409,3633,3375,12552,3190,3191,10329,10636,4562,3467,3183,3107,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,11170,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,13002,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,3902,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,4015,10991,12079,12152,12206,12253,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,12876,12939,12944,4591,10757,11127,12210,12952,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,12872,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,12861,12977,12992,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,3811,3622,11578,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,12933,12981,3756,10930,10936,10951,11885,12014,12100,12367,3607,11150,12126,12235,12245,12314,12362,12370,12479,4099,3758,10669,11007,11156,11186,11197,12313,12356,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,12244,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,10852,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724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53,6454,6541])). % 169.42/169.73 cnf(13016,plain, % 169.42/169.73 (P104(f334(f334(f249(a1),f2(a1)),f334(f103(a1),x130161)))), % 169.42/169.73 inference(rename_variables,[],[3404])). % 169.42/169.73 cnf(13019,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),f2(a877)),x130191))), % 169.42/169.73 inference(rename_variables,[],[3323])). % 169.42/169.73 cnf(13023,plain, % 169.42/169.73 (~E(f334(a115,x130231),f2(a877))), % 169.42/169.73 inference(rename_variables,[],[4504])). % 169.42/169.73 cnf(13032,plain, % 169.42/169.73 (~P104(f334(f334(f336(x130321),x130322),f195(f886(x130321,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(13035,plain, % 169.42/169.73 (P104(f334(f63(a877),f307(a877,x130351,x130352)))), % 169.42/169.73 inference(rename_variables,[],[3519])). % 169.42/169.73 cnf(13036,plain, % 169.42/169.73 (E(f334(f334(f247(a877),f334(a115,x130361)),f334(a115,x130362)),f334(a115,f334(f334(f247(a877),x130361),x130362)))), % 169.42/169.73 inference(rename_variables,[],[3479])). % 169.42/169.73 cnf(13039,plain, % 169.42/169.73 (P104(f334(f63(a877),f307(a877,x130391,x130392)))), % 169.42/169.73 inference(rename_variables,[],[3519])). % 169.42/169.73 cnf(13040,plain, % 169.42/169.73 (E(f334(f334(f248(a877),f334(a115,x130401)),f334(a115,x130402)),f334(a115,f334(f334(f248(a877),x130401),x130402)))), % 169.42/169.73 inference(rename_variables,[],[3480])). % 169.42/169.73 cnf(13043,plain, % 169.42/169.73 (P104(f334(f63(a877),f307(a877,x130431,x130432)))), % 169.42/169.73 inference(rename_variables,[],[3519])). % 169.42/169.73 cnf(13051,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x130511,a871)),f334(f173(x130511),f334(f136(x130511,x130512),x130513))),f334(f173(x130511),x130513)))), % 169.42/169.73 inference(rename_variables,[],[3964])). % 169.42/169.73 cnf(13052,plain, % 169.42/169.73 (E(f334(f334(f18(x130521,x130522),x130523),x130524),x130523)), % 169.42/169.73 inference(rename_variables,[],[3292])). % 169.42/169.73 cnf(13055,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x130551,a871)),f334(f173(x130551),f334(f334(f176(x130551),x130552),x130553))),f334(f173(x130551),x130553)))), % 169.42/169.73 inference(rename_variables,[],[4009])). % 169.42/169.73 cnf(13056,plain, % 169.42/169.73 (E(f334(f334(f18(x130561,x130562),x130563),x130564),x130563)), % 169.42/169.73 inference(rename_variables,[],[3292])). % 169.42/169.73 cnf(13060,plain, % 169.42/169.73 (E(f334(f334(f18(x130601,x130602),x130603),x130604),x130603)), % 169.42/169.73 inference(rename_variables,[],[3292])). % 169.42/169.73 cnf(13073,plain, % 169.42/169.73 (P104(f334(f334(f249(a1),f2(a1)),f334(f103(a1),x130731)))), % 169.42/169.73 inference(rename_variables,[],[3404])). % 169.42/169.73 cnf(13076,plain, % 169.42/169.73 (~P104(f334(f334(f336(x130761),x130762),f195(f886(x130761,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(13079,plain, % 169.42/169.73 (~P104(f334(f334(f336(x130791),x130792),f195(f886(x130791,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(13080,plain, % 169.42/169.73 (E(f334(f265(x130801,x130801),f266(x130801,x130802)),x130802)), % 169.42/169.73 inference(rename_variables,[],[3259])). % 169.42/169.73 cnf(13081,plain, % 169.42/169.73 (P21(x130811,x130811,f7(x130811),x130812)), % 169.42/169.73 inference(rename_variables,[],[3547])). % 169.42/169.73 cnf(13085,plain, % 169.42/169.73 (E(f334(f265(x130851,x130851),f266(x130851,x130852)),x130852)), % 169.42/169.73 inference(rename_variables,[],[3259])). % 169.42/169.73 cnf(13092,plain, % 169.42/169.73 (P104(f334(f334(f250(f886(a1,a871)),f305(a1,f2(a1),f2(a1))),f305(a1,f334(f80(a1),f334(f103(a1),f334(a115,x130921))),f2(a1))))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,12934,12940,12945,12949,12955,12958,12982,13081,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,12764,13003,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,12696,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2937,2943,2949,2950,2951,2957,2974,2977,2978,2988,2989,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,12815,12973,13080,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3176,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,12336,4529,12306,3292,11685,11688,12903,12999,13052,13056,13060,4578,10979,11049,11273,11276,3709,3289,3409,3633,3401,3375,12552,3190,3191,10329,10636,4562,3467,3183,3107,3297,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,11170,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,13002,3762,11582,3285,3384,11700,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,12692,13035,13039,13043,3902,3479,13036,3480,13040,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,12430,13051,4009,13055,4015,10991,12079,12152,12206,12253,12906,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,12876,12939,12944,4591,10757,11127,12210,12952,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,12916,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,12872,12985,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,12861,12977,12992,12995,13032,13076,13079,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,13016,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,12760,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,4322,3811,3622,11578,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,12933,12981,3756,10930,10936,10951,11885,12014,12100,12367,3607,11150,12126,12235,12245,12314,12362,12370,12479,12879,4099,3758,10669,11007,11156,11186,11197,12313,12356,12969,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,12244,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,10852,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523,8524,8525,8526,8669,8905,8906,8977,8991,9044,9045,9160,9194,9217,9246,9284,9470,9727,9918,9974,9976,6079,6453,6454,6541,6561,6562,6975,7191,8595,8628,8821,9002,9003,9071,9072,9330,9331,9332,9333,9525,9799,10096,10150,10151,6523,8430,8431])). % 169.42/169.73 cnf(13099,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),f2(a877)),x130991))), % 169.42/169.73 inference(rename_variables,[],[3323])). % 169.42/169.73 cnf(13100,plain, % 169.42/169.73 (P104(f334(f334(f250(a877),f2(a877)),f334(a115,x131001)))), % 169.42/169.73 inference(rename_variables,[],[3384])). % 169.42/169.73 cnf(13101,plain, % 169.42/169.73 (E(f334(f265(x131011,x131011),f266(x131011,x131012)),x131012)), % 169.42/169.73 inference(rename_variables,[],[3259])). % 169.42/169.73 cnf(13120,plain, % 169.42/169.73 (E(f334(f334(f81(a877),f2(a877)),f715(f334(a115,f2(a877)),f2(a877))),f2(a877))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,12934,12940,12945,12949,12955,12958,12982,13081,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,12764,13003,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,12696,13023,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2937,2943,2949,2950,2951,2955,2957,2974,2975,2977,2978,2988,2989,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,12815,12973,13080,13085,13101,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3176,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,12336,4529,12306,3292,11685,11688,12903,12999,13052,13056,13060,4578,10979,11049,11273,11276,3709,3289,3409,3633,3401,3375,12552,3190,3191,10329,10636,4562,3467,3183,3107,3297,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,11170,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,3490,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,13002,13007,3762,11582,3285,3384,11700,12609,13100,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,12915,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,12692,13035,13039,13043,3902,3479,13036,3480,13040,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,12430,13051,4009,13055,4015,10991,12079,12152,12206,12253,12906,4016,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,12876,12939,12944,4591,10757,11127,12210,12952,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,12916,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,12872,12985,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,12861,12977,12992,12995,13032,13076,13079,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,13016,13073,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,12760,13019,13099,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,4322,3811,3622,11578,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,12933,12981,3756,10930,10936,10951,11885,12014,12100,12367,3607,11150,12126,12235,12245,12314,12362,12370,12479,12879,4099,3758,10669,11007,11156,11186,11197,12313,12356,12969,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,12244,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,10852,13006,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523,8524,8525,8526,8669,8905,8906,8977,8991,9044,9045,9160,9194,9217,9246,9284,9470,9727,9918,9974,9976,6079,6453,6454,6541,6561,6562,6975,7191,8595,8628,8821,9002,9003,9071,9072,9330,9331,9332,9333,9525,9799,10096,10150,10151,6523,8430,8431,8870,8888,9800,10149,4689,4691])). % 169.42/169.73 cnf(13168,plain, % 169.42/169.73 (~P104(f334(f334(f250(a1),f2(a1)),f2(a1)))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,12934,12940,12945,12949,12955,12958,12982,13081,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,12764,13003,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,12696,13023,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2937,2943,2949,2950,2951,2955,2957,2974,2975,2977,2978,2988,2989,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,12815,12973,13080,13085,13101,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3176,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,12336,4529,12306,3292,11685,11688,12903,12999,13052,13056,13060,4578,10979,11049,11273,11276,3709,3289,3409,3633,3401,3375,12552,3190,3191,10329,10636,4562,3467,3183,3107,3297,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,11170,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,3490,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,13002,13007,3762,11582,3285,3384,11700,12609,13100,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,12915,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,12692,13035,13039,13043,3902,3479,13036,3480,13040,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,12430,13051,4009,13055,4015,10991,12079,12152,12206,12253,12906,4016,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,12876,12939,12944,4591,10757,11127,12210,12952,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,12916,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,12872,12985,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,12861,12977,12992,12995,13032,13076,13079,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,13016,13073,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,12760,13019,13099,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,4322,3811,3622,11578,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,12933,12981,3756,10930,10936,10951,11885,12014,12100,12367,3607,11150,12126,12235,12245,12314,12362,12370,12479,12879,4099,3758,10669,11007,11156,11186,11197,12313,12356,12969,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,12244,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,10852,13006,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523,8524,8525,8526,8669,8905,8906,8977,8991,9044,9045,9160,9194,9217,9246,9284,9470,9727,9918,9974,9976,6079,6453,6454,6541,6561,6562,6975,7191,8595,8628,8821,9002,9003,9071,9072,9330,9331,9332,9333,9525,9799,10096,10150,10151,6523,8430,8431,8870,8888,9800,10149,4689,4691,4692,4748,4756,4894,4910,4911,4939,4940,4971,5026,5089,5225,5261,5263,5272,5273,5299,5377,5398,5532,5600,5601,5602,5719])). % 169.42/169.73 cnf(13170,plain, % 169.42/169.73 (P104(f334(f334(f250(a1),f2(a1)),f334(f76(a1),f79(a1))))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,12934,12940,12945,12949,12955,12958,12982,13081,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,12764,13003,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,12696,13023,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2937,2943,2949,2950,2951,2955,2957,2974,2975,2977,2978,2988,2989,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,12815,12973,13080,13085,13101,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3176,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,12336,4529,12306,3292,11685,11688,12903,12999,13052,13056,13060,4578,10979,11049,11273,11276,3709,3289,3409,3633,3401,3375,12552,3190,3191,10329,10636,4562,3467,3183,3107,3297,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,11170,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,3490,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,13002,13007,3762,11582,3285,3384,11700,12609,13100,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,12915,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,12692,13035,13039,13043,3902,3479,13036,3480,13040,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,12430,13051,4009,13055,4015,10991,12079,12152,12206,12253,12906,4016,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,12876,12939,12944,4591,10757,11127,12210,12952,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,12916,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,12872,12985,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,12861,12977,12992,12995,13032,13076,13079,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,13016,13073,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,12760,13019,13099,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,4322,3811,3622,11578,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,12933,12981,3756,10930,10936,10951,11885,12014,12100,12367,3607,11150,12126,12235,12245,12314,12362,12370,12479,12879,4099,3758,10669,11007,11156,11186,11197,12313,12356,12969,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,12244,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,10852,13006,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523,8524,8525,8526,8669,8905,8906,8977,8991,9044,9045,9160,9194,9217,9246,9284,9470,9727,9918,9974,9976,6079,6453,6454,6541,6561,6562,6975,7191,8595,8628,8821,9002,9003,9071,9072,9330,9331,9332,9333,9525,9799,10096,10150,10151,6523,8430,8431,8870,8888,9800,10149,4689,4691,4692,4748,4756,4894,4910,4911,4939,4940,4971,5026,5089,5225,5261,5263,5272,5273,5299,5377,5398,5532,5600,5601,5602,5719,5720])). % 169.42/169.73 cnf(13188,plain, % 169.42/169.73 (~E(f334(f189(x131881,f886(x131882,a871),x131883,f195(f886(x131881,a871))),x131884),f334(f241(f886(x131882,a871)),f334(f334(f44(f46(a1,x131885,x131885),f886(x131882,a871)),x131886),a115)))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,12934,12940,12945,12949,12955,12958,12982,13081,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,12764,13003,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,12696,13023,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2937,2943,2949,2950,2951,2955,2957,2974,2975,2977,2978,2988,2989,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,12815,12973,13080,13085,13101,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3176,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,12336,4529,12306,3292,11685,11688,12903,12999,13052,13056,13060,4578,10979,11049,11273,11276,3709,3289,3409,3633,3401,3375,12552,3190,3191,10329,10636,4562,3467,3183,3107,3297,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,11170,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,3490,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,13002,13007,3762,11582,3285,3384,11700,12609,13100,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,12915,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,12692,13035,13039,13043,3902,3479,13036,3480,13040,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,12430,13051,4009,13055,4015,10991,12079,12152,12206,12253,12906,4016,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,12876,12939,12944,4591,10757,11127,12210,12952,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,12916,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,12872,12985,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,12861,12977,12992,12995,13032,13076,13079,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,13016,13073,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,12760,13019,13099,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,4322,3811,3622,11578,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,12933,12981,3756,10930,10936,10951,11885,12014,12100,12367,3607,11150,12126,12235,12245,12314,12362,12370,12479,12879,4099,3758,10669,11007,11156,11186,11197,12313,12356,12969,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,12244,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,10852,13006,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523,8524,8525,8526,8669,8905,8906,8977,8991,9044,9045,9160,9194,9217,9246,9284,9470,9727,9918,9974,9976,6079,6453,6454,6541,6561,6562,6975,7191,8595,8628,8821,9002,9003,9071,9072,9330,9331,9332,9333,9525,9799,10096,10150,10151,6523,8430,8431,8870,8888,9800,10149,4689,4691,4692,4748,4756,4894,4910,4911,4939,4940,4971,5026,5089,5225,5261,5263,5272,5273,5299,5377,5398,5532,5600,5601,5602,5719,5720,5746,5750,5810,5812,5821,5827,5899,5977,6102])). % 169.42/169.73 cnf(13192,plain, % 169.42/169.73 (~P104(f334(f63(x131921),f41(f886(x131921,a871),f257(f886(f886(x131921,a871),a871)))))), % 169.42/169.73 inference(scs_inference,[],[4590,3547,11044,12082,12182,12274,12310,12318,12383,12498,12500,12934,12940,12945,12949,12955,12958,12982,13081,3556,12146,12596,12598,3557,12213,3269,12544,12546,3270,12585,3235,12456,4530,4531,11662,4269,12577,12580,3273,12540,3106,3126,12602,3169,12506,4512,3609,4494,10197,10200,10210,10223,10234,10337,10340,10343,10446,10557,10865,11029,11032,11227,11317,11324,11338,11390,11393,11437,11503,11549,11565,11864,11889,11901,11930,11936,12031,12142,12149,12302,12353,12488,12610,12764,13003,4509,10430,10521,3360,3321,12556,3516,3216,4504,12681,12696,13023,2882,2891,2892,2894,2895,2898,2899,2901,2902,2903,2911,2912,2913,2916,2917,2920,2928,2931,2935,2937,2943,2949,2950,2951,2955,2957,2974,2975,2977,2978,2988,2989,2992,3000,3006,3012,3013,3015,3018,3022,3023,3025,3026,3027,3038,3039,3042,3043,3047,3049,3050,3062,3068,4489,3085,3168,4490,3646,3880,11596,3139,11314,3283,3256,3259,10194,10203,10269,10272,10364,10367,10660,11329,11332,11448,11490,11495,11591,12052,12250,12436,12490,12510,12516,12520,12522,12528,12538,12554,12569,12607,12815,12973,13080,13085,13101,3893,3230,12331,12335,12339,3236,3244,3770,4088,3371,12386,12459,3128,3129,4506,4518,3510,3865,11364,3359,12562,3193,3160,3684,12571,3155,3986,3176,3689,4473,3137,3138,3116,3143,3782,3175,3361,10812,12143,3228,3229,3408,4589,10400,3952,4520,10260,10427,11224,12298,12332,12336,4529,12306,3292,11685,11688,12903,12999,13052,13056,13060,4578,10979,11049,11273,11276,3709,3289,3409,3633,3401,3375,12552,3190,3191,10329,10636,4562,3467,3183,3107,3297,3212,11354,4101,12321,12448,3954,10985,11111,11159,12282,12288,12397,12400,12423,4602,10917,11116,11218,11243,11281,11287,12229,4603,11018,11119,11221,4604,11122,11170,4605,11173,4606,3211,3508,12185,12226,12305,3672,4385,4386,3490,4517,11345,3611,3649,3828,3577,12798,12802,12806,12810,12820,3875,12179,3493,3751,3372,10348,10466,10535,10596,10599,10639,10733,10969,11860,11923,12002,12043,12120,12123,12427,12616,12675,12718,12721,12763,12781,13002,13007,3762,11582,3285,3384,11700,12609,13100,3572,4568,10237,10240,10266,10741,10754,10875,11265,11357,11752,11757,11978,11981,12064,12073,12232,12325,12621,12640,12643,12667,12722,12885,12890,12910,12915,4584,11467,11498,11533,11562,12731,12735,3749,3517,3519,12646,12649,12652,12655,12689,12692,13035,13039,13043,3902,3479,13036,3480,13040,3329,3331,3304,4565,3189,4514,3700,4239,4021,3500,4585,4095,11238,3632,3343,11709,11712,12153,12254,12407,4063,4020,11853,12200,3964,10809,12037,12207,12430,13051,4009,13055,4015,10991,12079,12152,12206,12253,12906,4016,3673,11863,12009,12087,12133,4052,3691,10988,11054,11135,11192,12030,12101,12348,12420,12433,12876,12939,12944,4591,10757,11127,12210,12952,3301,10357,10453,10582,10646,10715,10760,10763,10796,10822,10859,10897,10933,11656,11703,11833,11888,11904,11907,11910,11913,12094,12108,12111,12114,12117,12193,12257,12359,12403,12668,12695,12773,12784,12789,12792,12795,12828,12839,12896,12921,12924,3302,10386,10441,10651,10736,10862,11440,11737,11740,11749,11839,11850,11869,11874,11916,11939,11956,12686,12832,12852,12886,12891,12911,12916,3303,3380,12067,12751,12799,12803,12807,12811,12821,12825,4564,10303,10395,10506,10530,10778,10825,10835,11512,11610,11631,11634,11637,11653,11807,11810,11813,11816,11900,11919,11922,11935,11990,11993,11996,11999,12074,12164,12167,12260,12263,12324,12352,12389,12468,3462,10602,10870,10914,11181,11262,11425,11665,12301,12471,12872,12985,4580,10787,10799,10906,10924,10927,10982,11068,11076,11092,11130,11144,11153,11189,11230,11235,11253,11256,11259,11290,11297,11300,11682,11718,11984,11987,12021,12068,12097,12238,12279,12285,12371,12374,12393,12447,12453,12462,12482,12750,12767,12770,12861,12977,12992,12995,13032,13076,13079,3365,10633,10663,10672,11210,11764,12390,12404,12732,12736,12739,3404,13016,13073,3398,3832,3767,10306,11585,11613,12713,4577,10257,10621,10624,11071,11089,11548,11601,11641,11666,11770,11795,11798,11801,11804,12063,12927,3323,10666,10819,10890,11614,11769,11961,12172,12194,12760,13019,13099,3792,11715,12662,4145,3523,4575,3803,3840,4554,4557,4558,3276,3280,4556,4555,4559,4322,3811,3622,11578,4245,11447,4593,10228,10231,10487,10538,10541,10546,10956,11419,11669,11773,4600,11147,11270,11306,4029,12221,3919,11303,11640,11644,11706,12309,12317,12396,12680,12933,12981,3756,10930,10936,10951,11885,12014,12100,12367,3607,11150,12126,12235,12245,12314,12362,12370,12479,12879,4099,3758,10669,11007,11156,11186,11197,12313,12356,12969,3573,10585,10588,10675,10846,3575,4597,11579,4586,4592,12630,4598,10726,10828,11422,11453,12188,12197,12241,12417,4205,10802,12034,12218,12244,4106,3791,12485,3735,3736,4595,10279,10282,10627,10630,11464,11645,12426,4596,11559,11650,3760,10591,10852,13006,4036,4611,4620,4625,4632,4648,4697,4699,4730,4747,4754,4755,4791,4796,4826,4832,4916,4941,4942,4957,5004,5005,5027,5028,5041,5045,5068,5075,5093,5096,5097,5098,5103,5104,5126,5151,5152,5162,5167,5173,5217,5218,5226,5236,5240,5242,5252,5254,5260,5264,5265,5280,5287,5290,5291,5292,5296,5335,5348,5356,5358,5359,5363,5364,5365,5373,5376,5380,5381,5382,5389,5393,5394,5395,5403,5407,5408,5409,5414,5427,5436,5448,5450,5458,5459,5463,5467,5492,5498,5508,5509,5524,5536,5558,5564,5582,5583,5586,5605,5613,5614,5619,5620,5630,5632,5644,5648,5657,5658,5660,5675,5680,5690,5691,5703,5710,5724,5728,5731,5737,5738,5739,5742,5747,5785,5786,5789,5791,5794,5795,5796,5798,5800,5802,5807,5814,5829,5843,5848,5849,5862,5863,5868,5872,5874,5879,5920,5932,5941,5945,5956,5960,5961,5969,5982,5988,6006,6009,6018,6046,6060,6085,6105,6106,6109,6123,6125,6127,6129,6142,6143,6146,6148,6151,6152,6164,6170,6171,6172,6174,6176,6219,6220,6225,6228,6234,6238,6274,6276,6278,6280,6289,6291,6293,6299,6301,6306,6309,6317,6324,6325,6326,6331,6353,6354,6355,6357,6363,6368,6404,6405,6408,6409,6410,6412,6413,6414,6415,6422,6455,6456,6465,6486,6487,6507,6510,6521,6522,6528,6558,6560,6574,6610,6613,6614,6667,6691,6733,6753,6762,6763,6764,6765,6784,6785,6791,6804,6807,6809,6811,6812,6813,6815,6829,6840,6842,6843,6856,6860,6911,6922,6924,6928,6945,6946,6980,6992,7023,7042,7055,7109,7137,7192,7213,7222,7225,7281,7291,7349,7351,7366,7376,7377,7378,7394,7400,7402,7452,7462,7465,7481,7532,7534,7537,7581,7582,7600,7667,7686,7709,7732,7747,7761,7772,7781,7782,7809,7812,7814,7823,7859,7870,7895,7952,7987,8020,8059,8075,8091,8092,8165,8218,8237,8261,8281,8305,8401,8403,8409,8423,8427,8443,8465,8473,8475,8486,8492,8496,8516,8530,8531,8547,8549,8553,8554,8555,8556,8557,8575,8576,8577,8586,8600,8602,8614,8618,8620,8621,8622,8630,8635,8661,8662,8693,8706,8710,8728,8750,8751,8752,8753,8765,8766,8788,8798,8808,8809,8810,8811,8813,8834,8835,8846,8890,8896,8903,8915,8920,8922,8924,8925,8929,8939,9010,9041,9042,9043,9057,9075,9080,9108,9109,9153,9177,9222,9223,9224,9234,9259,9273,9276,9279,9299,9300,9328,9387,9422,9423,9424,9448,9449,9467,9484,9490,9501,9524,9546,9554,9555,9556,9557,9572,9574,9579,9610,9611,9617,9618,9662,9663,9672,9695,9704,9714,9716,9717,9726,9740,9743,9771,9805,9807,9811,9865,9906,9907,9909,9919,9920,9940,9945,9986,10037,10108,10109,10165,10179,2,8,9,4635,4636,4654,4685,4686,4688,4716,4722,4723,4734,4783,4785,4817,4831,4860,4958,4959,4972,4992,5048,5049,5052,5053,5055,5057,5058,5067,5071,5072,5082,5094,5095,5101,5121,5122,5139,5144,5145,5146,5147,5150,5158,5161,5168,5232,5238,5239,5246,5277,5288,5294,5313,5333,5334,5341,5342,5343,5352,5362,5369,5371,5372,5378,5385,5386,5399,5400,5401,5402,5404,5405,5410,5411,5412,5413,5444,5445,5446,5454,5455,5456,5457,5500,5505,5507,5543,5545,5546,5548,5549,5551,5552,5554,5563,5568,5570,5571,5572,5573,5574,5575,5584,5594,5597,5608,5624,5625,5628,5638,5640,5641,5642,5667,5677,5693,5694,5704,5705,5707,5709,5714,5749,5754,5756,5816,5850,5851,5855,5861,5864,5865,5866,5867,5873,5884,5885,5887,5888,5896,5917,5948,5964,5967,5968,5970,5979,5996,6000,6003,6004,6005,6020,6030,6031,6062,6063,6067,6087,6090,6094,6113,6118,6119,6144,6147,6155,6163,6169,6173,6180,6181,6182,6183,6222,6239,6292,6327,6329,6350,6351,6356,6360,6361,6364,6370,6379,6396,6417,6418,6423,6433,6448,6468,6474,6476,6491,6492,6495,6496,6498,6500,6501,6502,6504,6506,6509,6514,6515,6517,6518,6524,6526,6568,6573,6587,6589,6590,6591,6625,6630,6632,6637,6638,6646,6650,6662,6686,6687,6689,6690,6701,6707,6724,6727,6746,6779,6780,6781,6786,6800,6819,6821,6823,6825,6830,6836,6838,6853,6858,6861,6897,6898,6899,6913,6914,6916,6917,6936,6938,6952,6978,7000,7011,7013,7015,7017,7018,7019,7052,7053,7058,7059,7066,7067,7069,7071,7090,7099,7100,7112,7122,7161,7171,7175,7182,7193,7199,7201,7207,7215,7216,7229,7246,7264,7266,7284,7335,7336,7337,7339,7341,7345,7350,7373,7416,7448,7463,7480,7512,7515,7541,7565,7583,7586,7587,7597,7616,7618,7620,7622,7623,7624,7649,7675,7676,7708,7710,7711,7712,7717,7739,7748,7758,7763,7769,7771,7777,7789,7790,7792,7815,7821,7842,7908,7909,7955,7963,7964,7989,7990,8007,8008,8066,8067,8094,8122,8133,8135,8144,8156,8187,8193,8200,8213,8232,8238,8260,8303,8331,8343,8361,8364,8394,8417,8476,8477,8480,8481,8579,8580,8581,8582,8609,8638,8665,8709,8727,8782,8827,8830,8843,8850,8887,8935,8936,8951,8952,9082,9086,9106,9117,9140,9142,9145,9149,9151,9152,9163,9164,9184,9190,9202,9245,9263,9312,9313,9320,9380,9384,9419,9426,9429,9432,9433,9447,9463,9472,9483,9491,9492,9494,9496,9522,9645,9690,9691,9733,9778,9892,9949,10014,10087,10100,10105,3,2628,2636,2637,2638,2639,2640,2641,2645,2646,2647,2648,2650,2651,2653,2657,2658,2660,2661,2662,2668,2671,2672,2674,2676,2680,2681,2684,2690,2691,2692,2693,2694,2695,2697,2704,2706,2714,2715,2716,2722,2723,2724,2728,2730,2731,2734,2742,2743,2744,2750,2754,2770,2771,2772,2773,2776,2777,2778,2801,2808,2809,2810,2813,2819,2820,2843,2845,2846,2861,2862,2868,2875,5269,5332,5430,5516,5517,5518,5595,5692,5723,5757,5773,5775,5781,5844,5845,5846,5847,5853,5886,6015,6052,6061,6084,6121,6156,6161,6308,6313,6348,6349,6369,6372,6374,6381,6382,6383,6384,6385,6386,6387,6388,6470,6538,6539,6624,6657,6658,6698,6699,6837,6852,6925,6926,6933,6953,6976,6984,6986,7033,7056,7057,7075,7076,7111,7155,7156,7253,7317,7318,7319,7320,7334,7367,7421,7422,7431,7438,7439,7451,7483,7484,7485,7486,7631,7633,7634,7635,7641,7642,7850,7856,7857,7867,7906,7985,8025,8078,8099,8100,8172,8274,8341,8342,8344,8379,8439,8440,8505,8523,8524,8525,8526,8669,8905,8906,8977,8991,9044,9045,9160,9194,9217,9246,9284,9470,9727,9918,9974,9976,6079,6453,6454,6541,6561,6562,6975,7191,8595,8628,8821,9002,9003,9071,9072,9330,9331,9332,9333,9525,9799,10096,10150,10151,6523,8430,8431,8870,8888,9800,10149,4689,4691,4692,4748,4756,4894,4910,4911,4939,4940,4971,5026,5089,5225,5261,5263,5272,5273,5299,5377,5398,5532,5600,5601,5602,5719,5720,5746,5750,5810,5812,5821,5827,5899,5977,6102,6128,6295])). % 169.42/169.73 cnf(13354,plain, % 169.42/169.73 (~P104(f334(f334(f250(a877),x133541),x133541))), % 169.42/169.73 inference(rename_variables,[],[4564])). % 169.42/169.73 cnf(13359,plain, % 169.42/169.73 (~E(f334(f334(f151(x133591),x133592),x133593),x133593)), % 169.42/169.73 inference(rename_variables,[],[4520])). % 169.42/169.73 cnf(13362,plain, % 169.42/169.73 (~P104(f334(f334(f249(a877),f334(a115,x133621)),x133621))), % 169.42/169.73 inference(rename_variables,[],[4577])). % 169.42/169.73 cnf(13376,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x133761,a871)),x133762),x133762))), % 169.42/169.73 inference(rename_variables,[],[3607])). % 169.42/169.73 cnf(13385,plain, % 169.42/169.73 (~P104(f334(f334(f336(x133851),x133852),f334(f314(x133851,x133853,x133854),f195(f886(x133853,a871)))))), % 169.42/169.73 inference(rename_variables,[],[10926])). % 169.42/169.73 cnf(13401,plain, % 169.42/169.73 (~P104(f334(f334(f336(x134011),x134012),f195(f886(x134011,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(13409,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x134091,a871)),x134092),x134092))), % 169.42/169.73 inference(rename_variables,[],[3607])). % 169.42/169.73 cnf(13416,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),x134161),f334(f334(f82(a877),x134161),x134161)))), % 169.42/169.73 inference(rename_variables,[],[3573])). % 169.42/169.73 cnf(13425,plain, % 169.42/169.73 (~P104(f334(f334(f249(a877),f334(a115,x134251)),x134251))), % 169.42/169.73 inference(rename_variables,[],[4577])). % 169.42/169.73 cnf(13428,plain, % 169.42/169.73 (~P104(f334(f334(f336(f885(x134281,x134281)),x134282),f266(x134281,f195(f886(x134281,a871)))))), % 169.42/169.73 inference(rename_variables,[],[10923])). % 169.42/169.73 cnf(13433,plain, % 169.42/169.73 (~P104(f334(f334(f336(x134331),x134332),f195(f886(x134331,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(13440,plain, % 169.42/169.73 (~E(f334(a115,x134401),f2(a877))), % 169.42/169.73 inference(rename_variables,[],[4504])). % 169.42/169.73 cnf(13443,plain, % 169.42/169.73 (~P104(f334(f334(f336(a877),x134431),f334(f255(a877),f2(a877))))), % 169.42/169.73 inference(rename_variables,[],[11734])). % 169.42/169.73 cnf(13455,plain, % 169.42/169.73 (~P104(f334(f334(f336(f885(x134551,x134551)),x134552),f266(x134551,f195(f886(x134551,a871)))))), % 169.42/169.73 inference(rename_variables,[],[10923])). % 169.42/169.73 cnf(13461,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),x134611),f334(f334(f82(a877),x134611),x134611)))), % 169.42/169.73 inference(rename_variables,[],[3573])). % 169.42/169.73 cnf(13464,plain, % 169.42/169.73 (~P104(f334(f334(f336(x134641),x134642),f334(f314(x134641,x134643,x134644),f195(f886(x134643,a871)))))), % 169.42/169.73 inference(rename_variables,[],[10926])). % 169.42/169.73 cnf(13467,plain, % 169.42/169.73 (~P36(x134671,x134672,x134673,f334(f334(f154(x134674,x134671),x134675),f334(a115,f116(x134674))),f116(x134672))), % 169.42/169.73 inference(rename_variables,[],[11161])). % 169.42/169.73 cnf(13470,plain, % 169.42/169.73 (P104(f334(f334(f249(a877),f2(a877)),x134701))), % 169.42/169.73 inference(rename_variables,[],[3323])). % 169.42/169.73 cnf(13478,plain, % 169.42/169.73 (~P104(f334(f334(f336(a877),x134781),f334(f255(a877),f2(a877))))), % 169.42/169.73 inference(rename_variables,[],[11734])). % 169.42/169.73 cnf(13487,plain, % 169.42/169.73 (~P104(f334(f334(f249(a877),f334(a115,x134871)),x134871))), % 169.42/169.73 inference(rename_variables,[],[4577])). % 169.42/169.73 cnf(13498,plain, % 169.42/169.73 (~P104(f334(f334(f195(f886(x134981,f886(x134982,a871))),x134983),x134984))), % 169.42/169.73 inference(rename_variables,[],[4598])). % 169.42/169.73 cnf(13507,plain, % 169.42/169.73 (~P104(f334(f334(f195(f886(x135071,f886(x135072,a871))),x135073),x135074))), % 169.42/169.73 inference(rename_variables,[],[4598])). % 169.42/169.73 cnf(13522,plain, % 169.42/169.73 (~P104(f334(f334(f249(a877),f334(f334(f82(a877),f334(a115,x135221)),f334(a115,x135221))),x135221))), % 169.42/169.73 inference(rename_variables,[],[10674])). % 169.42/169.73 cnf(13540,plain, % 169.42/169.73 (P104(f334(f334(f336(x135401),f334(x135402,x135403)),f334(f313(x135404,x135401,x135402),f257(f886(x135404,a871)))))), % 169.42/169.73 inference(rename_variables,[],[3919])). % 169.42/169.73 cnf(13543,plain, % 169.42/169.73 (~E(f334(f334(f104(a877),f334(a115,x135431)),x135431),f334(a115,x135431))), % 169.42/169.73 inference(rename_variables,[],[11483])). % 169.42/169.73 cnf(13561,plain, % 169.42/169.73 (~P104(f334(f334(f336(x135611),x135612),f195(f886(x135611,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(13579,plain, % 169.42/169.73 (P104(f334(f334(f336(x135791),f334(x135792,x135793)),f334(f313(x135794,x135791,x135792),f257(f886(x135794,a871)))))), % 169.42/169.73 inference(rename_variables,[],[3919])). % 169.42/169.73 cnf(13588,plain, % 169.42/169.73 (~E(f334(f334(f151(x135881),x135882),x135883),x135883)), % 169.42/169.73 inference(rename_variables,[],[4520])). % 169.42/169.73 cnf(13594,plain, % 169.42/169.73 (~P104(f334(f334(f336(a877),x135941),f334(f255(a877),f2(a877))))), % 169.42/169.73 inference(rename_variables,[],[11734])). % 169.42/169.73 cnf(13610,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x136101,a871)),f334(f173(x136101),f171(x136101,x136102,x136103))),f334(f173(x136101),x136103)))), % 169.42/169.73 inference(rename_variables,[],[4015])). % 169.42/169.73 cnf(13615,plain, % 169.42/169.73 (E(f334(x136151,f565(f334(x136151,x136152),f334(f241(x136153),x136152),x136151,x136154,x136153)),f334(x136151,x136152))), % 169.42/169.73 inference(rename_variables,[],[11102])). % 169.42/169.73 cnf(13629,plain, % 169.42/169.73 (P104(f334(f334(f249(f886(x136291,a871)),f334(f173(x136291),f171(x136291,x136292,x136293))),f334(f173(x136291),x136293)))), % 169.42/169.73 inference(rename_variables,[],[4015])). % 169.42/169.73 cnf(13632,plain, % 169.42/169.73 (~P104(f334(f334(f336(a877),x136321),f334(f255(a877),f2(a877))))), % 169.42/169.73 inference(rename_variables,[],[11734])). % 169.42/169.73 cnf(13662,plain, % 169.42/169.73 (~P104(f334(f334(f336(f885(x136621,x136621)),x136622),f266(x136621,f195(f886(x136621,a871)))))), % 169.42/169.73 inference(rename_variables,[],[10923])). % 169.42/169.73 cnf(13674,plain, % 169.42/169.73 (~P104(f334(f334(f336(x136741),x136742),f195(f886(x136741,a871))))), % 169.42/169.73 inference(rename_variables,[],[4580])). % 169.42/169.73 cnf(13717,plain, % 169.42/169.73 (~E(f334(f334(f151(x137171),x137172),x137173),x137173)), % 169.42/169.73 inference(rename_variables,[],[4520])). % 169.42/169.73 cnf(13743,plain, % 169.42/169.73 (~P104(f334(f334(f336(f885(x137431,x137431)),x137432),f266(x137431,f195(f886(x137431,a871)))))), % 169.42/169.73 inference(rename_variables,[],[10923])). % 169.42/169.73 cnf(13773,plain, % 169.42/169.73 ($false), % 169.42/169.73 inference(scs_inference,[],[3749,3331,4063,3902,4101,3085,4597,3304,3954,3380,4602,4556,3398,3762,4580,13401,13433,13561,13674,4015,13610,13629,3919,13540,13579,3791,4504,13440,4589,4520,13359,13588,13717,4517,3285,3384,4095,3302,3767,3323,13470,3756,3607,13376,13409,3573,13416,13461,3575,4205,3760,3259,3893,3254,4603,4604,4564,13354,4577,13362,13425,13487,4598,13498,13507,4595,4596,11483,13543,10289,13009,10556,13188,10345,12623,11294,13170,13092,10575,12677,10735,11196,11155,11102,13615,13120,12932,10910,10679,3243,11100,10960,12920,12923,10684,13168,12139,12128,11124,12234,10253,12683,11732,11734,13443,13478,13594,13632,11088,10923,13428,13455,13662,13743,10926,13385,13464,11129,10674,13522,11989,11252,12382,13192,11161,13467,11165,2905,2,5509,7534,5299,5364,5467,5524,7491,5026,6128,8427,9501,7782,4894,6006,7809,8557,7197,7213,5096,5644,6733,6354,5956,9273,5750,6129,6804,6812,9074,9555,5252,10109,7781,9423,4755,5287,5874,8810,9490,4796,7351,6987,9222,5703,6924,9223,9279,6289,6928,7400,9080,8939,9986,7281,5152,8614,5532,4941,4957,5265,5691,5794,8473,5746,8465,6234,6295,8798,5068,6220,7814,5296,9,5292,6060,8475,8492,9524,6228,6151,5335,8059,8549,9611,5564,6325,6404,4942,8920,7423,9276,5848,6170,6691,8622,6274,6856,8618,9556,7812,6018,6613,6763,8602,8662,8486,5945,6143,6306,6528,9805,8661,8828,5600,6560,8,5738,5796,7686,5264,8423,9424,9714,4692,6291,8890,6422,7394,9422,5728,6785,8261,5613,8165,7895,4625,6102,7859,8553,7462,5977,5941,6614,8305,7600,9108,9726,5151,5261,6046,6811,8575,8809,4748,5737,6125,6238,7667,9610,5376,5602,8496,8835,5614,5028,5358,5742,9259,6840,6815,4648,9224,4730]), % 169.42/169.73 ['proof']). % 169.42/169.73 % SZS output end Proof % 169.42/169.73 % Total time :154.380000s %------------------------------------------------------------------------------