%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW346+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n021.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 18:08:01 EDT 2024 % Result : Theorem 173.51s 173.26s % Output : CNFRefutation 173.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWW346+1 : TPTP v8.2.0. Released v5.2.0. % 0.04/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Jun 19 06:30:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.48/0.62 start to proof:theBenchmark % 173.06/173.11 %------------------------------------------- % 173.06/173.11 % File :CSE---1.7 % 173.06/173.11 % Problem :theBenchmark % 173.06/173.11 % Transform :cnf % 173.06/173.11 % Format :tptp:raw % 173.06/173.11 % Command :java -jar mcs_scs.jar %d %s % 173.06/173.11 % 173.06/173.11 % Result :Theorem 159.030000s % 173.06/173.11 % Output :CNFRefutation 159.030000s % 173.06/173.11 %------------------------------------------- % 173.06/173.12 %------------------------------------------------------------------------------ % 173.06/173.12 % File : SWW346+1 : TPTP v8.2.0. Released v5.2.0. % 173.06/173.12 % Domain : Software Verification % 173.06/173.12 % Problem : Hoare's Logic with Procedures 435233, 5000 axioms selected % 173.06/173.12 % Version : Especial. % 173.06/173.12 % English : % 173.06/173.12 % 173.06/173.12 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 173.06/173.12 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 173.06/173.12 % Source : [Bla11] % 173.06/173.12 % Names : hoare_435233.5000.p [Bla11] % 173.06/173.12 % 173.06/173.12 % Status : ContradictoryAxioms % 173.06/173.12 % Rating : 0.83 v8.2.0, 0.78 v8.1.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.87 v7.0.0, 0.90 v6.4.0, 0.88 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0, 1.00 v5.2.0 % 173.06/173.12 % Syntax : Number of formulae : 5226 (1698 unt; 0 def) % 173.06/173.12 % Number of atoms : 12655 (4445 equ) % 173.06/173.12 % Maximal formula atoms : 13 ( 2 avg) % 173.06/173.12 % Number of connectives : 8433 (1004 ~; 151 |; 713 &) % 173.06/173.12 % ( 890 <=>;5675 =>; 0 <=; 0 <~>) % 173.06/173.12 % Maximal formula depth : 22 ( 6 avg) % 173.06/173.12 % Maximal term depth : 19 ( 2 avg) % 173.06/173.12 % Number of predicates : 147 ( 146 usr; 0 prp; 1-6 aty) % 173.06/173.12 % Number of functors : 391 ( 391 usr; 51 con; 0-10 aty) % 173.06/173.12 % Number of variables : 16732 (16582 !; 150 ?) % 173.06/173.12 % SPC : FOF_CAX_RFO_SEQ % 173.06/173.12 % 173.06/173.12 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 173.06/173.12 % 2011-03-01 12:15:20 % 173.06/173.12 %------------------------------------------------------------------------------ % 173.06/173.12 %----Relevant facts (4985) % 173.06/173.12 fof(fact_ext,axiom, % 173.06/173.12 ! [V_g_2,V_f_2] : % 173.06/173.12 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 173.06/173.12 => V_f_2 = V_g_2 ) ). % 173.06/173.12 % 173.06/173.12 fof(fact_empty,axiom, % 173.06/173.12 ! [V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 173.06/173.12 % 173.06/173.12 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 173.06/173.12 ! [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))) ). % 173.06/173.12 % 173.06/173.12 fof(fact_triple_Oinject,axiom, % 173.06/173.12 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 173.06/173.12 ( 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) % 173.06/173.12 <=> ( V_fun1_2 = V_fun1_H_2 % 173.06/173.12 & V_com_2 = V_com_H_2 % 173.06/173.12 & V_fun2_2 = V_fun2_H_2 ) ) ). % 173.06/173.12 % 173.06/173.12 fof(fact_cut,axiom, % 173.06/173.12 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 173.06/173.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 173.06/173.12 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2) % 173.06/173.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 173.06/173.12 % 173.06/173.12 fof(fact_hoare__derivs_Oinsert,axiom, % 173.06/173.12 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 173.06/173.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.06/173.12 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 173.06/173.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ). % 173.06/173.12 % 173.06/173.12 fof(fact_derivs__insertD,axiom, % 173.06/173.12 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 173.06/173.12 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) % 173.06/173.12 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.06/173.12 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 173.06/173.12 % 173.06/173.12 fof(fact_MGT__def,axiom, % 173.06/173.12 ! [V_ca_2] : c_Hoare__Mirabelle_OMGT(V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ). % 173.06/173.12 % 173.10/173.12 fof(fact_bot__fun__def,axiom, % 173.10/173.12 ! [V_x_2,T_b,T_a] : % 173.10/173.12 ( class_Orderings_Obot(T_a) % 173.10/173.12 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 173.10/173.12 % 173.10/173.12 fof(fact_triple_Orecs,axiom, % 173.10/173.12 ! [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) ). % 173.10/173.12 % 173.10/173.12 fof(fact_triple_Osimps_I2_J,axiom, % 173.10/173.12 ! [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) ). % 173.10/173.12 % 173.10/173.12 fof(fact_empty__not__insert,axiom, % 173.10/173.12 ! [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) ). % 173.10/173.12 % 173.10/173.12 fof(fact_insert__not__empty,axiom, % 173.10/173.12 ! [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)) ). % 173.10/173.12 % 173.10/173.12 fof(fact_doubleton__eq__iff,axiom, % 173.10/173.12 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.10/173.12 ( 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)))) % 173.10/173.12 <=> ( ( V_a_2 = V_ca_2 % 173.10/173.12 & V_b_2 = V_d_2 ) % 173.10/173.12 | ( V_a_2 = V_d_2 % 173.10/173.12 & V_b_2 = V_ca_2 ) ) ) ). % 173.10/173.12 % 173.10/173.12 fof(fact_singleton__inject,axiom, % 173.10/173.12 ! [V_b_2,V_a_2,T_a] : % 173.10/173.12 ( 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))) % 173.10/173.12 => V_a_2 = V_b_2 ) ). % 173.10/173.12 % 173.10/173.12 fof(fact_bot__apply,axiom, % 173.10/173.12 ! [V_x_2,T_b,T_a] : % 173.10/173.12 ( class_Orderings_Obot(T_a) % 173.10/173.12 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 173.10/173.12 % 173.10/173.12 fof(fact_escape,axiom, % 173.10/173.12 ! [V_Q_2,V_ca_2,V_Ga_2,T_a,V_P_2] : % 173.10/173.12 ( ! [B_Z,B_s] : % 173.10/173.12 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 173.10/173.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) % 173.10/173.12 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 173.10/173.12 % 173.10/173.12 fof(fact_hoare__derivs_OSkip,axiom, % 173.10/173.12 ! [V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 173.10/173.12 % 173.10/173.12 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 173.10/173.12 ! [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)))) ). % 173.10/173.12 % 173.10/173.12 fof(fact_insert__code,axiom, % 173.10/173.12 ! [V_x_2,V_A_2,V_y_2,T_a] : % 173.10/173.12 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 173.10/173.12 <=> ( V_y_2 = V_x_2 % 173.10/173.12 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_insert__commute,axiom, % 173.10/173.13 ! [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)) ). % 173.10/173.13 % 173.10/173.13 fof(fact_insert__absorb2,axiom, % 173.10/173.13 ! [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) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc__elim__cases_I1_J,axiom, % 173.10/173.13 ! [V_t,V_s] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 173.10/173.13 => V_t = V_s ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_OSkip,axiom, % 173.10/173.13 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 173.10/173.13 % 173.10/173.13 fof(fact_the__elem__eq,axiom, % 173.10/173.13 ! [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 ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_Oequations_I1_J,axiom, % 173.10/173.13 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 173.10/173.13 % 173.10/173.13 fof(fact_conseq1,axiom, % 173.10/173.13 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_a] : % 173.10/173.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.13 => ( ! [B_Z,B_s] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 173.10/173.13 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 173.10/173.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_conseq2,axiom, % 173.10/173.13 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_Ga_2,T_a] : % 173.10/173.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.13 => ( ! [B_Z,B_s] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 173.10/173.13 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 173.10/173.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_Comp,axiom, % 173.10/173.13 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] : % 173.10/173.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.13 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_LoopF,axiom, % 173.10/173.13 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com__det,axiom, % 173.10/173.13 ! [V_u,V_t,V_s,V_c] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 173.10/173.13 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 173.10/173.13 => V_u = V_t ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_hoare__sound,axiom, % 173.10/173.13 ! [V_ts_2,V_Ga_2,T_a] : % 173.10/173.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 173.10/173.13 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_conseq12,axiom, % 173.10/173.13 ! [V_Q_2,V_P_2,V_Q_H_2,V_ca_2,V_P_H_2,V_Ga_2,T_a] : % 173.10/173.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.13 => ( ! [B_Z,B_s] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 173.10/173.13 => ! [B_s_H] : % 173.10/173.13 ( ! [B_Z_H] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s)) % 173.10/173.13 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) ) % 173.10/173.13 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) % 173.10/173.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 173.10/173.13 ! [V_a4_2,V_a3_2,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),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_OWhileFalse,axiom, % 173.10/173.13 ! [V_ca_2,V_s_2,V_b_2] : % 173.10/173.13 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.13 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_OWhileTrue,axiom, % 173.10/173.13 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] : % 173.10/173.13 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 173.10/173.13 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 173.10/173.13 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2)) % 173.10/173.13 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_OSemi,axiom, % 173.10/173.13 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 173.10/173.13 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 173.10/173.13 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_OAssign,axiom, % 173.10/173.13 ! [V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc__elim__cases_I2_J,axiom, % 173.10/173.13 ! [V_t_2,V_s_2,V_a_2,V_X_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2)) % 173.10/173.13 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_Oequations_I2_J,axiom, % 173.10/173.13 ! [V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_Oequations_I7_J,axiom, % 173.10/173.13 ! [V_a2_2,V_a3_2,V_a1_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 173.10/173.13 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.13 => ? [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 173.10/173.13 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_Oequations_I8_J,axiom, % 173.10/173.13 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 173.10/173.13 <=> ( ( V_a5_2 = V_a2_2 % 173.10/173.13 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 173.10/173.13 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.13 & ? [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 173.10/173.13 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc_Oequations_I4_J,axiom, % 173.10/173.13 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 173.10/173.13 <=> ? [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 173.10/173.13 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_Ass,axiom, % 173.10/173.13 ! [V_a_2,V_X_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I13_J,axiom, % 173.10/173.13 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I12_J,axiom, % 173.10/173.13 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I9_J,axiom, % 173.10/173.13 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I8_J,axiom, % 173.10/173.13 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I25_J,axiom, % 173.10/173.13 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I24_J,axiom, % 173.10/173.13 ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I17_J,axiom, % 173.10/173.13 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I16_J,axiom, % 173.10/173.13 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I47_J,axiom, % 173.10/173.13 ! [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) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I46_J,axiom, % 173.10/173.13 ! [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) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I29_J,axiom, % 173.10/173.13 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I28_J,axiom, % 173.10/173.13 ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I5_J,axiom, % 173.10/173.13 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 173.10/173.13 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 173.10/173.13 <=> ( V_fun_2 = V_fun_H_2 % 173.10/173.13 & V_com_2 = V_com_H_2 ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I1_J,axiom, % 173.10/173.13 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 173.10/173.13 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 173.10/173.13 <=> ( V_vname_2 = V_vname_H_2 % 173.10/173.13 & V_fun_2 = V_fun_H_2 ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I3_J,axiom, % 173.10/173.13 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 173.10/173.13 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 173.10/173.13 <=> ( V_com1_2 = V_com1_H_2 % 173.10/173.13 & V_com2_2 = V_com2_H_2 ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_the__elem__def,axiom, % 173.10/173.13 ! [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))))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_Loop__sound__lemma,axiom, % 173.10/173.13 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 173.10/173.13 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.13 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc__elim__cases_I4_J,axiom, % 173.10/173.13 ! [V_t,V_s,V_c2,V_c1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 173.10/173.13 => ~ ! [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 173.10/173.13 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_Loop,axiom, % 173.10/173.13 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 173.10/173.13 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.13 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evalc__WHILE__case,axiom, % 173.10/173.13 ! [V_t_2,V_s_2,V_ca_2,V_b_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_t_2)) % 173.10/173.13 => ( ( V_t_2 = V_s_2 % 173.10/173.13 => hBOOL(hAPP(V_b_2,V_s_2)) ) % 173.10/173.13 => ~ ( hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.13 => ! [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),B_s1)) % 173.10/173.13 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),B_s1),V_t_2)) ) ) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_OAssign,axiom, % 173.10/173.13 ! [V_n_2,V_s_2,V_a_2,V_X_2] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln__elim__cases_I2_J,axiom, % 173.10/173.13 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_n_2),V_t_2)) % 173.10/173.13 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I64_J,axiom, % 173.10/173.13 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I67_J,axiom, % 173.10/173.13 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I65_J,axiom, % 173.10/173.13 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_Oequations_I2_J,axiom, % 173.10/173.13 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OAss(V_a1_2,V_a2_2)),V_a3_2),V_a4_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2)))) ). % 173.10/173.13 % 173.10/173.13 fof(fact_com_Osimps_I69_J,axiom, % 173.10/173.13 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(V_f6_2,V_fun_2),V_com_2) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_OWhileTrue,axiom, % 173.10/173.13 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] : % 173.10/173.13 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 173.10/173.13 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2)) % 173.10/173.13 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_n_2),V_s2_2)) % 173.10/173.13 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_OWhileFalse,axiom, % 173.10/173.13 ! [V_n_2,V_ca_2,V_s_2,V_b_2] : % 173.10/173.13 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.13 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_s_2)) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_OSemi,axiom, % 173.10/173.13 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 173.10/173.13 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 173.10/173.13 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln__elim__cases_I1_J,axiom, % 173.10/173.13 ! [V_t,V_n,V_s] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 173.10/173.13 => V_t = V_s ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_OSkip,axiom, % 173.10/173.13 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 173.10/173.13 % 173.10/173.13 fof(fact_peek__and__def,axiom, % 173.10/173.13 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 173.10/173.13 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 173.10/173.13 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_eval__eq,axiom, % 173.10/173.13 ! [V_t_2,V_s_2,V_ca_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 173.10/173.13 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln__evalc,axiom, % 173.10/173.13 ! [V_t,V_n,V_s,V_c] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 173.10/173.13 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_Oequations_I8_J,axiom, % 173.10/173.13 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a6_2)) % 173.10/173.13 <=> ( ( V_a6_2 = V_a2_2 % 173.10/173.13 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 173.10/173.13 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.13 & ? [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 173.10/173.13 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a6_2)) ) ) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_Oequations_I7_J,axiom, % 173.10/173.13 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a4_2),V_a2_2)) % 173.10/173.13 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.13 => ? [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 173.10/173.13 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a4_2),V_a2_2)) ) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_Oequations_I4_J,axiom, % 173.10/173.13 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_a1_2,V_a5_2)),V_a2_2),V_a3_2),V_a6_2)) % 173.10/173.13 <=> ? [B_s1] : % 173.10/173.13 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 173.10/173.13 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 173.10/173.13 % 173.10/173.13 fof(fact_evaln_Oequations_I1_J,axiom, % 173.10/173.14 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 173.10/173.14 % 173.10/173.14 fof(fact_hoare__derivs_OIf,axiom, % 173.10/173.14 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 173.10/173.14 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.14 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.14 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_triple__valid__def,axiom, % 173.10/173.14 ! [V_t_2,V_n_2,T_a] : % 173.10/173.14 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 173.10/173.14 <=> hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(T_a,tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_HOL_Obool),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_HOL_OAll(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_COMBS(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),tc_Com_Ocom),c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Com_Ostate,tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Com_Ocom),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies))),hAPP(hAPP(c_COMBC(tc_Com_Ocom,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_Com_Ocom),c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),c_Natural_Oevaln)),V_n_2))))))))),V_t_2)) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_the__eq__trivial,axiom, % 173.10/173.14 ! [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 ). % 173.10/173.14 % 173.10/173.14 fof(fact_the__sym__eq__trivial,axiom, % 173.10/173.14 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 173.10/173.14 % 173.10/173.14 fof(fact_K__record__comp,axiom, % 173.10/173.14 ! [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 ). % 173.10/173.14 % 173.10/173.14 fof(fact_o__def,axiom, % 173.10/173.14 ! [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)) ). % 173.10/173.14 % 173.10/173.14 fof(fact_triple__valid__def2,axiom, % 173.10/173.14 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] : % 173.10/173.14 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)) % 173.10/173.14 <=> ! [B_Z,B_s] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 173.10/173.14 => ! [B_s_H] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H)) % 173.10/173.14 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln__elim__cases_I4_J,axiom, % 173.10/173.14 ! [V_t,V_n,V_s,V_c2,V_c1] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_n),V_t)) % 173.10/173.14 => ~ ! [B_s1] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s),V_n),B_s1)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),B_s1),V_n),V_t)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_o__eq__elim,axiom, % 173.10/173.14 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 173.10/173.14 ( 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) % 173.10/173.14 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_o__eq__dest,axiom, % 173.10/173.14 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 173.10/173.14 ( 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) % 173.10/173.14 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_o__eq__dest__lhs,axiom, % 173.10/173.14 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 173.10/173.14 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 173.10/173.14 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_comp__cong,axiom, % 173.10/173.14 ! [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] : % 173.10/173.14 ( 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)) % 173.10/173.14 => 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) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln__elim__cases_I5_J,axiom, % 173.10/173.14 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_n_2),V_t_2)) % 173.10/173.14 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 173.10/173.14 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln_OIfTrue,axiom, % 173.10/173.14 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 173.10/173.14 ( hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 173.10/173.14 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln_OIfFalse,axiom, % 173.10/173.14 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 173.10/173.14 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 173.10/173.14 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_n_2),V_s1_2)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc__elim__cases_I5_J,axiom, % 173.10/173.14 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2)) % 173.10/173.14 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 173.10/173.14 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc_OIfTrue,axiom, % 173.10/173.14 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 173.10/173.14 ( hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 173.10/173.14 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc_OIfFalse,axiom, % 173.10/173.14 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 173.10/173.14 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 173.10/173.14 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I4_J,axiom, % 173.10/173.14 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 173.10/173.14 ( 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) % 173.10/173.14 <=> ( V_fun_2 = V_fun_H_2 % 173.10/173.14 & V_com1_2 = V_com1_H_2 % 173.10/173.14 & V_com2_2 = V_com2_H_2 ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln_Oequations_I6_J,axiom, % 173.10/173.14 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a6_2,V_a3_2)),V_a2_2),V_a4_2),V_a5_2)) % 173.10/173.14 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 173.10/173.14 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln_Oequations_I5_J,axiom, % 173.10/173.14 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a6_2)),V_a2_2),V_a4_2),V_a5_2)) % 173.10/173.14 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 173.10/173.14 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc_Oequations_I6_J,axiom, % 173.10/173.14 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2)) % 173.10/173.14 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 173.10/173.14 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc_Oequations_I5_J,axiom, % 173.10/173.14 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2)) % 173.10/173.14 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 173.10/173.14 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I53_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I52_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I26_J,axiom, % 173.10/173.14 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I27_J,axiom, % 173.10/173.14 ! [V_fun_2,V_vname_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_OAss(V_vname_2,V_fun_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I44_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I45_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I14_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I15_J,axiom, % 173.10/173.14 ! [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 ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I68_J,axiom, % 173.10/173.14 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_o__assoc,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_o__apply,axiom, % 173.10/173.14 ! [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)) ). % 173.10/173.14 % 173.10/173.14 fof(fact_override__on__emptyset,axiom, % 173.10/173.14 ! [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 ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln__WHILE__case,axiom, % 173.10/173.14 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_b_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_t_2)) % 173.10/173.14 => ( ( V_t_2 = V_s_2 % 173.10/173.14 => hBOOL(hAPP(V_b_2,V_s_2)) ) % 173.10/173.14 => ~ ( hBOOL(hAPP(V_b_2,V_s_2)) % 173.10/173.14 => ! [B_s1] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),V_n_2),B_s1)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),B_s1),V_n_2),V_t_2)) ) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc__evaln,axiom, % 173.10/173.14 ! [V_t,V_s,V_c] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 173.10/173.14 => ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),B_n),V_t)) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_hoare__valids__def,axiom, % 173.10/173.14 ! [V_ts_2,V_Ga_2,T_a] : % 173.10/173.14 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) % 173.10/173.14 <=> ! [B_n] : % 173.10/173.14 ( ! [B_x] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) % 173.10/173.14 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 173.10/173.14 => ! [B_x] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 173.10/173.14 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_the__equality,axiom, % 173.10/173.14 ! [T_a,V_a_2,V_P_2] : % 173.10/173.14 ( hBOOL(hAPP(V_P_2,V_a_2)) % 173.10/173.14 => ( ! [B_x] : % 173.10/173.14 ( hBOOL(hAPP(V_P_2,B_x)) % 173.10/173.14 => B_x = V_a_2 ) % 173.10/173.14 => c_HOL_OThe(T_a,V_P_2) = V_a_2 ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_enum__the__def,axiom, % 173.10/173.14 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_Collect__conv__if,axiom, % 173.10/173.14 ! [T_a,V_a_2,V_P_2] : % 173.10/173.14 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 173.10/173.14 => 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))) ) % 173.10/173.14 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 173.10/173.14 => 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)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_Collect__conv__if2,axiom, % 173.10/173.14 ! [T_a,V_a_2,V_P_2] : % 173.10/173.14 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 173.10/173.14 => 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))) ) % 173.10/173.14 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 173.10/173.14 => 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)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_singleton__conv,axiom, % 173.10/173.14 ! [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))) ). % 173.10/173.14 % 173.10/173.14 fof(fact_singleton__conv2,axiom, % 173.10/173.14 ! [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))) ). % 173.10/173.14 % 173.10/173.14 fof(fact_hoare__derivs_OLocal,axiom, % 173.10/173.14 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] : % 173.10/173.14 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Q_2)),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),c_Natural_Ogetlocs(V_s_H_2,V_X_2))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 173.10/173.14 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj),hAPP(c_fequal,V_s_H_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),c_Com_Ovname_OLoc(V_X_2))),V_a_2)))),c_Com_Ocom_OLocal(V_X_2,V_a_2,V_ca_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln_OLocal,axiom, % 173.10/173.14 ! [V_s1_2,V_n_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_n_2),V_s1_2)) % 173.10/173.14 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s0_2),V_n_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),c_Natural_Ogetlocs(V_s0_2,V_Y_2)))) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc_OLocal,axiom, % 173.10/173.14 ! [V_s1_2,V_a_2,V_Y_2,V_s0_2,V_ca_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s0_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s0_2))),V_s1_2)) % 173.10/173.14 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s0_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s1_2),c_Com_Ovname_OLoc(V_Y_2)),c_Natural_Ogetlocs(V_s0_2,V_Y_2)))) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_vname_Osimps_I2_J,axiom, % 173.10/173.14 ! [V_loc_H_2,V_loc_2] : % 173.10/173.14 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2) % 173.10/173.14 <=> V_loc_2 = V_loc_H_2 ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I2_J,axiom, % 173.10/173.14 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 173.10/173.14 ( 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) % 173.10/173.14 <=> ( V_loc_2 = V_loc_H_2 % 173.10/173.14 & V_fun_2 = V_fun_H_2 % 173.10/173.14 & V_com_2 = V_com_H_2 ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_Collect__def,axiom, % 173.10/173.14 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln_Oequations_I3_J,axiom, % 173.10/173.14 ! [V_a6_2,V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),V_a5_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),c_Natural_Ogetlocs(V_a2_2,V_a3_2)))) % 173.10/173.14 <=> ? [B_s1] : % 173.10/173.14 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a6_2),c_Com_Ovname_OLoc(V_a3_2)),c_Natural_Ogetlocs(V_a2_2,V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),c_Natural_Ogetlocs(V_a2_2,V_a3_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),V_a5_2),B_s1)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc_Oequations_I3_J,axiom, % 173.10/173.14 ! [V_a5_2,V_a2_2,V_a1_2,V_a4_2,V_a3_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_a3_2,V_a4_2,V_a1_2)),V_a2_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),c_Natural_Ogetlocs(V_a2_2,V_a3_2)))) % 173.10/173.14 <=> ? [B_s1] : % 173.10/173.14 ( hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a5_2),c_Com_Ovname_OLoc(V_a3_2)),c_Natural_Ogetlocs(V_a2_2,V_a3_2)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_a3_2)),c_Natural_Ogetlocs(V_a2_2,V_a3_2)) % 173.10/173.14 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a2_2),c_Com_Ovname_OLoc(V_a3_2)),hAPP(V_a4_2,V_a2_2))),B_s1)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_empty__Collect__eq,axiom, % 173.10/173.14 ! [V_P_2,T_a] : % 173.10/173.14 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 173.10/173.14 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_Collect__empty__eq,axiom, % 173.10/173.14 ! [V_P_2,T_a] : % 173.10/173.14 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.10/173.14 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_ball__empty,axiom, % 173.10/173.14 ! [V_P_2,T_a,B_x] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 173.10/173.14 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_empty__def,axiom, % 173.10/173.14 ! [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)) ). % 173.10/173.14 % 173.10/173.14 fof(fact_insert__Collect,axiom, % 173.10/173.14 ! [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)) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I38_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I39_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I37_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I36_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I23_J,axiom, % 173.10/173.14 ! [V_fun_2,V_vname_2,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_OAss(V_vname_2,V_fun_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I22_J,axiom, % 173.10/173.14 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I34_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I35_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I11_J,axiom, % 173.10/173.14 ! [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 ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I10_J,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_com_Osimps_I66_J,axiom, % 173.10/173.14 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_a] : c_Com_Ocom_Ocom__case(T_a,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evalc__elim__cases_I3_J,axiom, % 173.10/173.14 ! [V_t_2,V_s_2,V_ca_2,V_a_2,V_Y_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s_2),V_t_2)) % 173.10/173.14 => ~ ! [B_s1] : % 173.10/173.14 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),c_Natural_Ogetlocs(V_s_2,V_Y_2)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),B_s1)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_evaln__elim__cases_I3_J,axiom, % 173.10/173.14 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_a_2,V_Y_2] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)),V_s_2),V_n_2),V_t_2)) % 173.10/173.14 => ~ ! [B_s1] : % 173.10/173.14 ( V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,B_s1),c_Com_Ovname_OLoc(V_Y_2)),c_Natural_Ogetlocs(V_s_2,V_Y_2)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),c_Com_Ovname_OLoc(V_Y_2)),hAPP(V_a_2,V_s_2))),V_n_2),B_s1)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_vname_Orecs_I2_J,axiom, % 173.10/173.14 ! [V_loc_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__rec(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_vname_Osimps_I6_J,axiom, % 173.10/173.14 ! [V_loc_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__case(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 173.10/173.14 % 173.10/173.14 fof(fact_triples__valid__Suc,axiom, % 173.10/173.14 ! [V_n_2,V_ts_2,T_a] : % 173.10/173.14 ( ! [B_x] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 173.10/173.14 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 173.10/173.14 => ! [B_x] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 173.10/173.14 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_vname_Osimps_I3_J,axiom, % 173.10/173.14 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ). % 173.10/173.14 % 173.10/173.14 fof(fact_vname_Osimps_I4_J,axiom, % 173.10/173.14 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ). % 173.10/173.14 % 173.10/173.14 fof(fact_insert__compr,axiom, % 173.10/173.14 ! [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))) ). % 173.10/173.14 % 173.10/173.14 fof(fact_insert__compr__raw,axiom, % 173.10/173.14 ! [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))) ). % 173.10/173.14 % 173.10/173.14 fof(fact_insert__def,axiom, % 173.10/173.14 ! [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) ). % 173.10/173.14 % 173.10/173.14 fof(fact_image__constant__conv,axiom, % 173.10/173.14 ! [V_ca_2,T_b,T_a,V_A_2] : % 173.10/173.14 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.10/173.14 => 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)) ) % 173.10/173.14 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.10/173.14 => 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))) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_equalityCE,axiom, % 173.10/173.14 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 173.10/173.14 ( V_A_2 = V_B_2 % 173.10/173.14 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.14 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 173.10/173.14 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.14 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_emptyE,axiom, % 173.10/173.14 ! [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)))) ). % 173.10/173.14 % 173.10/173.14 fof(fact_insertCI,axiom, % 173.10/173.14 ! [V_b_2,V_B_2,V_a_2,T_a] : % 173.10/173.14 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 173.10/173.14 => V_a_2 = V_b_2 ) % 173.10/173.14 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_insertE,axiom, % 173.10/173.14 ! [V_A_2,V_b_2,V_a_2,T_a] : % 173.10/173.14 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 173.10/173.14 => ( V_a_2 != V_b_2 % 173.10/173.14 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 173.10/173.14 % 173.10/173.14 fof(fact_image__eqI,axiom, % 173.10/173.14 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 173.10/173.14 ( V_b_2 = hAPP(V_f_2,V_x_2) % 173.10/173.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_UnCI,axiom, % 173.10/173.15 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 173.10/173.15 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 173.10/173.15 => 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))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_UnE,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( 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))) % 173.10/173.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_CollectI,axiom, % 173.10/173.15 ! [T_a,V_a_2,V_P_2] : % 173.10/173.15 ( hBOOL(hAPP(V_P_2,V_a_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_rev__image__eqI,axiom, % 173.10/173.15 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_eq__mem__trans,axiom, % 173.10/173.15 ! [V_A_2,T_a,V_b_2,V_a_2] : % 173.10/173.15 ( V_a_2 = V_b_2 % 173.10/173.15 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_eqelem__imp__iff,axiom, % 173.10/173.15 ! [V_A_2,T_a,V_y_2,V_x_2] : % 173.10/173.15 ( V_x_2 = V_y_2 % 173.10/173.15 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_eqset__imp__iff,axiom, % 173.10/173.15 ! [V_x_2,T_a,V_B_2,V_A_2] : % 173.10/173.15 ( V_A_2 = V_B_2 % 173.10/173.15 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_imageI,axiom, % 173.10/173.15 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 => 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))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_UnI2,axiom, % 173.10/173.15 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 173.10/173.15 => 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))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_UnI1,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 => 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))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_ball__Un,axiom, % 173.10/173.15 ! [V_P_2,V_B_2,V_A_2,T_a] : % 173.10/173.15 ( ! [B_x] : % 173.10/173.15 ( 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))) % 173.10/173.15 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.10/173.15 <=> ( ! [B_x] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.10/173.15 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.10/173.15 & ! [B_x] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 173.10/173.15 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_bex__Un,axiom, % 173.10/173.15 ! [V_P_2,V_B_2,V_A_2,T_a] : % 173.10/173.15 ( ? [B_x] : % 173.10/173.15 ( 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))) % 173.10/173.15 & hBOOL(hAPP(V_P_2,B_x)) ) % 173.10/173.15 <=> ( ? [B_x] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.10/173.15 & hBOOL(hAPP(V_P_2,B_x)) ) % 173.10/173.15 | ? [B_x] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 173.10/173.15 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__assoc,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__iff,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( 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))) % 173.10/173.15 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__Un,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__left__commute,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__iff,axiom, % 173.10/173.15 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 173.10/173.15 <=> ? [B_x] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.10/173.15 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__left__absorb,axiom, % 173.10/173.15 ! [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) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__commute,axiom, % 173.10/173.15 ! [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) ). % 173.10/173.15 % 173.10/173.15 fof(fact_mem__def,axiom, % 173.10/173.15 ! [V_A_2,V_x_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__absorb,axiom, % 173.10/173.15 ! [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 ). % 173.10/173.15 % 173.10/173.15 fof(fact_vname_Osimps_I5_J,axiom, % 173.10/173.15 ! [V_glb_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__case(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vname_Orecs_I1_J,axiom, % 173.10/173.15 ! [V_glb_2,V_f2_2,V_f1_2,T_a] : c_Com_Ovname_Ovname__rec(T_a,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insert__image,axiom, % 173.10/173.15 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vname_Osimps_I1_J,axiom, % 173.10/173.15 ! [V_glb_H_2,V_glb_2] : % 173.10/173.15 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2) % 173.10/173.15 <=> V_glb_2 = V_glb_H_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__ident,axiom, % 173.10/173.15 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__image,axiom, % 173.10/173.15 ! [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) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__def,axiom, % 173.10/173.15 ! [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))) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__is__empty,axiom, % 173.10/173.15 ! [V_A_2,V_f_2,T_a,T_b] : % 173.10/173.15 ( 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)) % 173.10/173.15 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__empty,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_empty__is__image,axiom, % 173.10/173.15 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( 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) % 173.10/173.15 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__insert,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__compose,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__constant,axiom, % 173.10/173.15 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 => 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))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__empty,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.10/173.15 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__empty__right,axiom, % 173.10/173.15 ! [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 ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__empty__left,axiom, % 173.10/173.15 ! [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 ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__insert__left,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__insert__right,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_equals0D,axiom, % 173.10/173.15 ! [V_a_2,T_a,V_A_2] : % 173.10/173.15 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.10/173.15 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_empty__iff,axiom, % 173.10/173.15 ! [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)))) ). % 173.10/173.15 % 173.10/173.15 fof(fact_ex__in__conv,axiom, % 173.10/173.15 ! [V_A_2,T_a] : % 173.10/173.15 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.10/173.15 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_all__not__in__conv,axiom, % 173.10/173.15 ! [V_A_2,T_a] : % 173.10/173.15 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.10/173.15 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insert__absorb,axiom, % 173.10/173.15 ! [V_A_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insertI2,axiom, % 173.10/173.15 ! [V_b_2,V_B_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insert__ident,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_x_2,T_a] : % 173.10/173.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 173.10/173.15 => ( 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) % 173.10/173.15 <=> V_A_2 = V_B_2 ) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insert__iff,axiom, % 173.10/173.15 ! [V_A_2,V_b_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 173.10/173.15 <=> ( V_a_2 = V_b_2 % 173.10/173.15 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insertI1,axiom, % 173.10/173.15 ! [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))) ). % 173.10/173.15 % 173.10/173.15 fof(fact_evaln__Suc,axiom, % 173.10/173.15 ! [V_s_H,V_n,V_s,V_c] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 173.10/173.15 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_triple__valid__Suc,axiom, % 173.10/173.15 ! [V_t,V_n,T_a] : % 173.10/173.15 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 173.10/173.15 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Collect__disj__eq,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Collect__mem__eq,axiom, % 173.10/173.15 ! [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 ). % 173.10/173.15 % 173.10/173.15 fof(fact_mem__Collect__eq,axiom, % 173.10/173.15 ! [V_P_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.10/173.15 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_CollectD,axiom, % 173.10/173.15 ! [V_P_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.10/173.15 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_CollectE,axiom, % 173.10/173.15 ! [V_P_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.10/173.15 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_override__on__apply__in,axiom, % 173.10/173.15 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_override__on__apply__notin,axiom, % 173.10/173.15 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 173.10/173.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insert__is__Un,axiom, % 173.10/173.15 ! [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) ). % 173.10/173.15 % 173.10/173.15 fof(fact_override__on__def,axiom, % 173.10/173.15 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 173.10/173.15 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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) ) % 173.10/173.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_singletonE,axiom, % 173.10/173.15 ! [V_a_2,V_b_2,T_a] : % 173.10/173.15 ( 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))))) % 173.10/173.15 => V_b_2 = V_a_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_singleton__iff,axiom, % 173.10/173.15 ! [V_a_2,V_b_2,T_a] : % 173.10/173.15 ( 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))))) % 173.10/173.15 <=> V_b_2 = V_a_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup1E,axiom, % 173.10/173.15 ! [V_x_2,V_B_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 173.10/173.15 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup1CI,axiom, % 173.10/173.15 ! [T_a,V_A_2,V_x_2,V_B_2] : % 173.10/173.15 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 173.10/173.15 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__fun__def,axiom, % 173.10/173.15 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__Un__eq,axiom, % 173.10/173.15 ! [V_x_2,V_S_2,V_R_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 <=> 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))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_bot__empty__eq,axiom, % 173.10/173.15 ! [V_x_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 173.10/173.15 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__apply,axiom, % 173.10/173.15 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__eq__bot__iff,axiom, % 173.10/173.15 ! [V_y_2,V_x_2,T_a] : % 173.10/173.15 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.10/173.15 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 173.10/173.15 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 173.10/173.15 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__bot__right,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__bot__left,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_pred__equals__eq,axiom, % 173.10/173.15 ! [V_S_2,V_R_2,T_a] : % 173.10/173.15 ( 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) % 173.10/173.15 <=> V_R_2 = V_S_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_eq__mem,axiom, % 173.10/173.15 ! [V_y_2,V_x_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 173.10/173.15 <=> V_x_2 = V_y_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__assoc,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I6_J,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup_Oassoc,axiom, % 173.10/173.15 ! [V_c,V_b,V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__left__commute,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I7_J,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup_Oleft__commute,axiom, % 173.10/173.15 ! [V_c,V_a,V_b,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__left__idem,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I8_J,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup_Oleft__idem,axiom, % 173.10/173.15 ! [V_b,V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__commute,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I5_J,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup_Ocommute,axiom, % 173.10/173.15 ! [V_b,V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__idem,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup_Oidem,axiom, % 173.10/173.15 ! [V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__sup(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup1I2,axiom, % 173.10/173.15 ! [V_A_2,T_a,V_x_2,V_B_2] : % 173.10/173.15 ( hBOOL(hAPP(V_B_2,V_x_2)) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup1I1,axiom, % 173.10/173.15 ! [V_B_2,T_a,V_x_2,V_A_2] : % 173.10/173.15 ( hBOOL(hAPP(V_A_2,V_x_2)) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Powp__def,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 173.10/173.15 <=> ! [B_x] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 173.10/173.15 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_the__inv__into__def,axiom, % 173.10/173.15 ! [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))) ). % 173.10/173.15 % 173.10/173.15 fof(fact_imageE,axiom, % 173.10/173.15 ! [V_A_2,V_f_2,T_b,V_b_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 173.10/173.15 => ~ ! [B_x] : % 173.10/173.15 ( V_b_2 = hAPP(V_f_2,B_x) % 173.10/173.15 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_if__image__distrib,axiom, % 173.10/173.15 ! [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))))) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Suc__inject,axiom, % 173.10/173.15 ! [V_y,V_x] : % 173.10/173.15 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 173.10/173.15 => V_x = V_y ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_nat_Oinject,axiom, % 173.10/173.15 ! [V_nat_H_2,V_nat_2] : % 173.10/173.15 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 173.10/173.15 <=> V_nat_2 = V_nat_H_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Suc__n__not__n,axiom, % 173.10/173.15 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 173.10/173.15 % 173.10/173.15 fof(fact_n__not__Suc__n,axiom, % 173.10/173.15 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Sup__fin_Oidem,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__insert,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__singleton__eq,axiom, % 173.10/173.15 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 173.10/173.15 ( 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)))))) % 173.10/173.15 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf1E,axiom, % 173.10/173.15 ! [V_x_2,V_B_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 173.10/173.15 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf1I,axiom, % 173.10/173.15 ! [T_a,V_B_2,V_x_2,V_A_2] : % 173.10/173.15 ( hBOOL(hAPP(V_A_2,V_x_2)) % 173.10/173.15 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 173.10/173.15 => 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)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_IntE,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( 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))) % 173.10/173.15 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_IntI,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 173.10/173.15 => 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))) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimageI,axiom, % 173.10/173.15 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 173.10/173.15 ( hAPP(V_f_2,V_a_2) = V_b_2 % 173.10/173.15 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__fun__def,axiom, % 173.10/173.15 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf1D2,axiom, % 173.10/173.15 ! [V_x_2,V_B_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf1D1,axiom, % 173.10/173.15 ! [V_x_2,V_B_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__apply,axiom, % 173.10/173.15 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__assoc,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I2_J,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf_Oassoc,axiom, % 173.10/173.15 ! [V_c,V_b,V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__left__commute,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I3_J,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf_Oleft__commute,axiom, % 173.10/173.15 ! [V_c,V_a,V_b,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__left__idem,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I4_J,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf_Oleft__idem,axiom, % 173.10/173.15 ! [V_b,V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__commute,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__aci_I1_J,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf_Ocommute,axiom, % 173.10/173.15 ! [V_b,V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__idem,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf_Oidem,axiom, % 173.10/173.15 ! [V_a,T_a] : % 173.10/173.15 ( class_Lattices_Osemilattice__inf(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Inf__fin_Oidem,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__code,axiom, % 173.10/173.15 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 173.10/173.15 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__assoc,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__Int,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__left__commute,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__left__absorb,axiom, % 173.10/173.15 ! [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) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__commute,axiom, % 173.10/173.15 ! [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) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__absorb,axiom, % 173.10/173.15 ! [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 ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__ident,axiom, % 173.10/173.15 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__bot__right,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__bot__left,axiom, % 173.10/173.15 ! [V_x,T_a] : % 173.10/173.15 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__absorb,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__inf__absorb,axiom, % 173.10/173.15 ! [V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Olattice(T_a) % 173.10/173.15 => 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 ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__distrib1,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Odistrib__lattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__inf__distrib1,axiom, % 173.10/173.15 ! [V_z,V_y,V_x,T_a] : % 173.10/173.15 ( class_Lattices_Odistrib__lattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__sup__distrib2,axiom, % 173.10/173.15 ! [V_x,V_z,V_y,T_a] : % 173.10/173.15 ( class_Lattices_Odistrib__lattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_sup__inf__distrib2,axiom, % 173.10/173.15 ! [V_x,V_z,V_y,T_a] : % 173.10/173.15 ( class_Lattices_Odistrib__lattice(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimageI2,axiom, % 173.10/173.15 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimageD,axiom, % 173.10/173.15 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__eq,axiom, % 173.10/173.15 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 173.10/173.15 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_IntD2,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( 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))) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_IntD1,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( 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))) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__iff,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( 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))) % 173.10/173.15 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__empty,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_disjoint__iff__not__equal,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 <=> ! [B_x] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.10/173.15 => ! [B_xa] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 173.10/173.15 => B_x != B_xa ) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__empty__right,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__empty__left,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_insert__inter__insert,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__Un,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__compose,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__Int__crazy,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__Int__distrib2,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__Un__distrib2,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Un__Int__distrib,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__Un__distrib,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_inf__Int__eq,axiom, % 173.10/173.15 ! [V_x_2,V_S_2,V_R_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 <=> 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))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__Collect__eq,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Collect__conj__eq,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__insert__right,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_a_2,T_a] : % 173.10/173.15 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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)) ) % 173.10/173.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__insert__left,axiom, % 173.10/173.15 ! [V_B_2,V_C_2,V_a_2,T_a] : % 173.10/173.15 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 173.10/173.15 => 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)) ) % 173.10/173.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 173.10/173.15 => 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) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__insert__right__if0,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_a_2,T_a] : % 173.10/173.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__insert__left__if0,axiom, % 173.10/173.15 ! [V_B_2,V_C_2,V_a_2,T_a] : % 173.10/173.15 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 173.10/173.15 => 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) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__insert__right__if1,axiom, % 173.10/173.15 ! [V_B_2,V_A_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__insert__left__if1,axiom, % 173.10/173.15 ! [V_B_2,V_C_2,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__def,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__def,axiom, % 173.10/173.15 ! [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))) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Int__Collect,axiom, % 173.10/173.15 ! [V_P_2,V_A_2,V_x_2,T_a] : % 173.10/173.15 ( 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)))) % 173.10/173.15 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.15 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__inter__cong,axiom, % 173.10/173.15 ! [V_y_2,T_b,V_g_2,V_f_2,V_S_2,T_a] : % 173.10/173.15 ( ! [B_w] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),B_w),V_S_2)) % 173.10/173.15 => hAPP(V_f_2,B_w) = hAPP(V_g_2,B_w) ) % 173.10/173.15 => 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_y_2)),V_S_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_g_2),V_y_2)),V_S_2) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_the__inv__into__comp,axiom, % 173.10/173.15 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 173.10/173.15 => ( 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)))) % 173.10/173.15 => 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) ) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_Powp__Pow__eq,axiom, % 173.10/173.15 ! [V_x_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimage__const,axiom, % 173.10/173.15 ! [T_b,V_A_2,V_ca_2,T_a] : % 173.10/173.15 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 => 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)) ) % 173.10/173.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.15 => 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)) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_vimageE,axiom, % 173.10/173.15 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 173.10/173.15 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 173.10/173.15 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_funpow_Osimps_I2_J,axiom, % 173.10/173.15 ! [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)) ). % 173.10/173.15 % 173.10/173.15 fof(fact_image__vimage__eq,axiom, % 173.10/173.15 ! [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)))) ). % 173.10/173.15 % 173.10/173.15 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 173.10/173.15 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 173.10/173.15 ( class_Rings_Osemiring__1(T_a) % 173.10/173.15 => 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)) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_f__the__inv__into__f,axiom, % 173.10/173.15 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 173.10/173.15 => 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 ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_bij__betw__Disj__Un,axiom, % 173.10/173.15 ! [V_f_2,V_B_H_2,V_A_H_2,T_b,V_B_2,V_A_2,T_a] : % 173.10/173.15 ( 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)) % 173.10/173.15 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.10/173.15 => ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_A_H_2) % 173.10/173.15 => ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_B_2,V_B_H_2) % 173.10/173.15 => c_Fun_Obij__betw(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ). % 173.10/173.15 % 173.10/173.15 fof(fact_bij__betw__combine,axiom, % 173.10/173.15 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.15 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.10/173.15 => ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_C_2,V_D_2) % 173.10/173.15 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.10/173.16 => c_Fun_Obij__betw(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_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_top1I,axiom, % 173.10/173.16 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_UNIV__I,axiom, % 173.10/173.16 ! [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)))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__empty,axiom, % 173.10/173.16 ! [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))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_funpow__swap1,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__top,axiom, % 173.10/173.16 ! [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))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bijI,axiom, % 173.10/173.16 ! [V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_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)) % 173.10/173.16 => c_Fun_Obij__betw(T_a,T_b,V_f_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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__def,axiom, % 173.10/173.16 ! [V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.10/173.16 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 & hAPP(c_Set_Oimage(T_a,T_b,V_f_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)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Cantors__paradox,axiom, % 173.10/173.16 ! [V_A_2,T_a] : % 173.10/173.16 ~ ? [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) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__def,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 <=> ! [B_x] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.10/173.16 => ! [B_xa] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 173.10/173.16 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 173.10/173.16 => B_x = B_xa ) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__fun,axiom, % 173.10/173.16 ! [T_c,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => 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))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__eq,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.10/173.16 <=> V_x_2 = V_y_2 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_injD,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.10/173.16 => V_x_2 = V_y_2 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__is__inj,axiom, % 173.10/173.16 ! [V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.10/173.16 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__imp__inj__on,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.10/173.16 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__not__empty,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__UNIV,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_top__apply,axiom, % 173.10/173.16 ! [V_x_2,T_b,T_a] : % 173.10/173.16 ( class_Orderings_Otop(T_a) % 173.10/173.16 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__imp__bij__betw,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__def,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.10/173.16 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 & hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = V_B_2 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__image__eq__iff,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( 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) % 173.10/173.16 <=> V_A_2 = V_B_2 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__comp,axiom, % 173.10/173.16 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 173.10/173.16 => 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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__id2,axiom, % 173.10/173.16 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__is__surj,axiom, % 173.10/173.16 ! [V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.10/173.16 => hAPP(c_Set_Oimage(T_a,T_b,V_f_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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__imp__surj,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.10/173.16 => hAPP(c_Set_Oimage(T_a,T_b,V_f_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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__comp,axiom, % 173.10/173.16 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.10/173.16 => ( c_Fun_Obij__betw(T_b,T_c,V_g_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))) % 173.10/173.16 => c_Fun_Obij__betw(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_the__inv__f__f,axiom, % 173.10/173.16 ! [V_x_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => 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 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_comp__funpow,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_range__ex1__eq,axiom, % 173.10/173.16 ! [V_b_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( 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))))) % 173.10/173.16 <=> ? [B_x] : % 173.10/173.16 ( V_b_2 = hAPP(V_f_2,B_x) % 173.10/173.16 & ! [B_y] : % 173.10/173.16 ( V_b_2 = hAPP(V_f_2,B_y) % 173.10/173.16 => B_y = B_x ) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__image__mem__iff,axiom, % 173.10/173.16 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( 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))) % 173.10/173.16 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_image__Int,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__contraD,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( V_x_2 != V_y_2 % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 173.10/173.16 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__iff,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 173.10/173.16 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.10/173.16 <=> V_x_2 = V_y_2 ) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__onD,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 173.10/173.16 => V_x_2 = V_y_2 ) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__vimage__image__eq,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => 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 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__Suc,axiom, % 173.10/173.16 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__Int,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.10/173.16 => 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)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__imageI2,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 173.10/173.16 ( 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) % 173.10/173.16 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__singleton,axiom, % 173.10/173.16 ! [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))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__empty1,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 173.10/173.16 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__empty2,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 173.10/173.16 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__trans,axiom, % 173.10/173.16 ! [V_C_2,V_g_2,T_c,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.10/173.16 => ( c_Fun_Obij__betw(T_b,T_c,V_g_2,V_B_2,V_C_2) % 173.10/173.16 => c_Fun_Obij__betw(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__comp__iff,axiom, % 173.10/173.16 ! [V_A_H_H_2,V_f_H_2,T_c,V_A_H_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_A_H_2) % 173.10/173.16 => ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) % 173.10/173.16 <=> c_Fun_Obij__betw(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_iso__tuple__UNIV__I,axiom, % 173.10/173.16 ! [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)))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_UNIV__not__empty,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Un__UNIV__left,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Un__UNIV__right,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Int__UNIV__left,axiom, % 173.10/173.16 ! [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 ). % 173.10/173.16 % 173.10/173.16 fof(fact_Int__UNIV__right,axiom, % 173.10/173.16 ! [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 ). % 173.10/173.16 % 173.10/173.16 fof(fact_vimage__UNIV,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__empty,axiom, % 173.10/173.16 ! [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))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__bottom,axiom, % 173.10/173.16 ! [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))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__insert,axiom, % 173.10/173.16 ! [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))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_image__Pow__surj,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 173.10/173.16 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 173.10/173.16 => 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) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__Int__eq,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_bij__betw__the__inv__into,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.10/173.16 => c_Fun_Obij__betw(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_UNIV__def,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_range__composition,axiom, % 173.10/173.16 ! [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)))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_sup__top__right,axiom, % 173.10/173.16 ! [V_x,T_a] : % 173.10/173.16 ( class_Lattices_Obounded__lattice__top(T_a) % 173.10/173.16 => 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) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_sup__top__left,axiom, % 173.10/173.16 ! [V_x,T_a] : % 173.10/173.16 ( class_Lattices_Obounded__lattice__top(T_a) % 173.10/173.16 => 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) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inf__top__left,axiom, % 173.10/173.16 ! [V_x,T_a] : % 173.10/173.16 ( class_Lattices_Obounded__lattice__top(T_a) % 173.10/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inf__top__right,axiom, % 173.10/173.16 ! [V_x,T_a] : % 173.10/173.16 ( class_Lattices_Obounded__lattice__top(T_a) % 173.10/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inf__eq__top__iff,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,T_a] : % 173.10/173.16 ( class_Lattices_Obounded__lattice__top(T_a) % 173.10/173.16 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 173.10/173.16 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 173.10/173.16 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__Un__image__eq__iff,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( 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)) % 173.10/173.16 => ( 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) % 173.10/173.16 <=> V_A_2 = V_B_2 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_comp__inj__on__iff,axiom, % 173.10/173.16 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( 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)) % 173.10/173.16 <=> 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) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_comp__inj__on,axiom, % 173.10/173.16 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( 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)) % 173.10/173.16 => 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) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__imageI,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 173.10/173.16 ( 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) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_the__inv__into__f__f,axiom, % 173.10/173.16 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.16 => 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 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_the__inv__into__f__eq,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.10/173.16 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_rangeI,axiom, % 173.10/173.16 ! [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))))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_range__eqI,axiom, % 173.10/173.16 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 173.10/173.16 ( V_b_2 = hAPP(V_f_2,V_x_2) % 173.10/173.16 => 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))))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__the__inv__into,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_the__inv__into__onto,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => 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 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_ball__UNIV,axiom, % 173.10/173.16 ! [V_P_2,T_a] : % 173.10/173.16 ( ! [B_x] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.10/173.16 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.10/173.16 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_comp__surj,axiom, % 173.10/173.16 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 173.10/173.16 ( 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)) % 173.10/173.16 => ( 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)) % 173.10/173.16 => 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)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_surj__image__vimage__eq,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_a,T_b] : % 173.10/173.16 ( 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)) % 173.10/173.16 => 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 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_funpow__code__def,axiom, % 173.10/173.16 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__vimage__singleton,axiom, % 173.10/173.16 ! [V_a_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => 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))))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__Un,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( 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)) % 173.10/173.16 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.10/173.16 & 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)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__insert,axiom, % 173.10/173.16 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 173.10/173.16 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 & ~ 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))))))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_the__inv__into__into,axiom, % 173.10/173.16 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => 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)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_vimage__subset__eq,axiom, % 173.10/173.16 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.10/173.16 => ( 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)) % 173.10/173.16 <=> 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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_vimage__subsetI,axiom, % 173.10/173.16 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.10/173.16 => ( 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))) % 173.10/173.16 => 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)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_vimage__if,axiom, % 173.10/173.16 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 173.10/173.16 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.16 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 173.10/173.16 => 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)) ) % 173.10/173.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 173.10/173.16 => 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 ) ) ) % 173.10/173.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.16 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 173.10/173.16 => 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) ) % 173.10/173.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 173.10/173.16 => 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)) ) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_rangeE,axiom, % 173.10/173.16 ! [V_f_2,T_b,V_b_2,T_a] : % 173.10/173.16 ( 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))))) % 173.10/173.16 => ~ ! [B_x] : V_b_2 != hAPP(V_f_2,B_x) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__fun__updI,axiom, % 173.10/173.16 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.10/173.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 173.10/173.16 => c_Fun_Oinj__on(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_order__refl,axiom, % 173.10/173.16 ! [V_x,T_a] : % 173.10/173.16 ( class_Orderings_Opreorder(T_a) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_equalityI,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.10/173.16 => V_A_2 = V_B_2 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__triv,axiom, % 173.10/173.16 ! [V_x_2,V_f_2,T_b,T_a] : c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ). % 173.10/173.16 % 173.10/173.16 fof(fact_subsetD,axiom, % 173.10/173.16 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_empty__subsetI,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_DiffE,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.16 ( 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))) % 173.10/173.16 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_DiffI,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 173.10/173.16 => 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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__uminus,axiom, % 173.10/173.16 ! [V_A_2,T_a] : % 173.10/173.16 ( class_Groups_Oordered__ab__group__add(T_a) % 173.10/173.16 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_ComplI,axiom, % 173.10/173.16 ! [V_A_2,V_ca_2,T_a] : % 173.10/173.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.10/173.16 => 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))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_PowI,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_diff__eq,axiom, % 173.10/173.16 ! [V_y,V_x,T_a] : % 173.10/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Compl__eq__Diff__UNIV,axiom, % 173.10/173.16 ! [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) ). % 173.10/173.16 % 173.10/173.16 fof(fact_subset__Compl__self__eq,axiom, % 173.10/173.16 ! [V_A_2,T_a] : % 173.10/173.16 ( 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))) % 173.10/173.16 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Compl__Diff__eq,axiom, % 173.10/173.16 ! [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) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Diff__eq,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Diff__Compl,axiom, % 173.10/173.16 ! [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) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__Compl__def,axiom, % 173.10/173.16 ! [V_x_2,V_A_2,T_b,T_a] : % 173.10/173.16 ( class_Groups_Ouminus(T_a) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__diff__def,axiom, % 173.10/173.16 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 173.10/173.16 ( class_Groups_Ominus(T_a) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_predicate1D,axiom, % 173.10/173.16 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 173.10/173.16 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.10/173.16 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_compl__mono,axiom, % 173.10/173.16 ! [V_y,V_x,T_a] : % 173.10/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.10/173.16 => 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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_rev__predicate1D,axiom, % 173.10/173.16 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 173.10/173.16 ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 173.10/173.16 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_minus__apply,axiom, % 173.10/173.16 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 173.10/173.16 ( class_Groups_Ominus(T_a) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_compl__le__compl__iff,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,T_a] : % 173.10/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.10/173.16 => ( 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))) % 173.10/173.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_compl__eq__compl__iff,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,T_a] : % 173.10/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.10/173.16 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 173.10/173.16 <=> V_x_2 = V_y_2 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_uminus__apply,axiom, % 173.10/173.16 ! [V_x_2,V_A_2,T_b,T_a] : % 173.10/173.16 ( class_Groups_Ouminus(T_a) % 173.10/173.16 => 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)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_double__compl,axiom, % 173.10/173.16 ! [V_x,T_a] : % 173.10/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.10/173.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_linorder__le__cases,axiom, % 173.10/173.16 ! [V_y,V_x,T_a] : % 173.10/173.16 ( class_Orderings_Olinorder(T_a) % 173.10/173.16 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_le__funE,axiom, % 173.10/173.16 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 173.10/173.16 ( class_Orderings_Oord(T_b) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.10/173.16 => 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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_equalityE,axiom, % 173.10/173.16 ! [T_a,V_B_2,V_A_2] : % 173.10/173.16 ( V_A_2 = V_B_2 % 173.10/173.16 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_double__diff,axiom, % 173.10/173.16 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.10/173.16 => 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 ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Diff__mono,axiom, % 173.10/173.16 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 173.10/173.16 => 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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_xt1_I6_J,axiom, % 173.10/173.16 ! [V_z,V_x,V_y,T_a] : % 173.10/173.16 ( class_Orderings_Oorder(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_xt1_I5_J,axiom, % 173.10/173.16 ! [V_x,V_y,T_a] : % 173.10/173.16 ( class_Orderings_Oorder(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.10/173.16 => V_x = V_y ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_order__trans,axiom, % 173.10/173.16 ! [V_z,V_y,V_x,T_a] : % 173.10/173.16 ( class_Orderings_Opreorder(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_order__antisym,axiom, % 173.10/173.16 ! [V_y,V_x,T_a] : % 173.10/173.16 ( class_Orderings_Oorder(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.10/173.16 => V_x = V_y ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_xt1_I4_J,axiom, % 173.10/173.16 ! [V_c,V_a,V_b,T_a] : % 173.10/173.16 ( class_Orderings_Oorder(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.10/173.16 => ( V_b = V_c % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_ord__le__eq__trans,axiom, % 173.10/173.16 ! [V_c,V_b,V_a,T_a] : % 173.10/173.16 ( class_Orderings_Oord(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.10/173.16 => ( V_b = V_c % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_subset__trans,axiom, % 173.10/173.16 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_xt1_I3_J,axiom, % 173.10/173.16 ! [V_c,V_b,V_a,T_a] : % 173.10/173.16 ( class_Orderings_Oorder(T_a) % 173.10/173.16 => ( V_a = V_b % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_ord__eq__le__trans,axiom, % 173.10/173.16 ! [V_c,V_b,V_a,T_a] : % 173.10/173.16 ( class_Orderings_Oord(T_a) % 173.10/173.16 => ( V_a = V_b % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_order__antisym__conv,axiom, % 173.10/173.16 ! [V_x_2,V_y_2,T_a] : % 173.10/173.16 ( class_Orderings_Oorder(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.10/173.16 <=> V_x_2 = V_y_2 ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_le__funD,axiom, % 173.10/173.16 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 173.10/173.16 ( class_Orderings_Oord(T_b) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.10/173.16 => 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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Compl__anti__mono,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => 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))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_order__eq__refl,axiom, % 173.10/173.16 ! [V_y,V_x,T_a] : % 173.10/173.16 ( class_Orderings_Opreorder(T_a) % 173.10/173.16 => ( V_x = V_y % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_equalityD2,axiom, % 173.10/173.16 ! [T_a,V_B_2,V_A_2] : % 173.10/173.16 ( V_A_2 = V_B_2 % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_equalityD1,axiom, % 173.10/173.16 ! [T_a,V_B_2,V_A_2] : % 173.10/173.16 ( V_A_2 = V_B_2 % 173.10/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Diff__idemp,axiom, % 173.10/173.16 ! [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) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Compl__subset__Compl__iff,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( 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))) % 173.10/173.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Compl__eq__Compl__iff,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( 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) % 173.10/173.16 <=> V_A_2 = V_B_2 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_order__eq__iff,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,T_a] : % 173.10/173.16 ( class_Orderings_Oorder(T_a) % 173.10/173.16 => ( V_x_2 = V_y_2 % 173.10/173.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.10/173.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_set__eq__subset,axiom, % 173.10/173.16 ! [T_a,V_B_2,V_A_2] : % 173.10/173.16 ( V_A_2 = V_B_2 % 173.10/173.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_linorder__linear,axiom, % 173.10/173.16 ! [V_y,V_x,T_a] : % 173.10/173.16 ( class_Orderings_Olinorder(T_a) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.10/173.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_le__fun__def,axiom, % 173.10/173.16 ! [V_g_2,V_f_2,T_a,T_b] : % 173.10/173.16 ( class_Orderings_Oord(T_b) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.10/173.16 <=> ! [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))) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Diff__subset,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_double__complement,axiom, % 173.10/173.16 ! [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 ). % 173.10/173.16 % 173.10/173.16 fof(fact_subset__refl,axiom, % 173.10/173.16 ! [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)) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__idem,axiom, % 173.10/173.16 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 173.10/173.16 ( hAPP(V_f_2,V_x_2) = V_y_2 % 173.10/173.16 => c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2) = V_f_2 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__other,axiom, % 173.10/173.16 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 173.10/173.16 ( V_z_2 != V_x_2 % 173.10/173.16 => 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) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__twist,axiom, % 173.10/173.16 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 173.10/173.16 ( V_a_2 != V_ca_2 % 173.10/173.16 => c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_a_2,V_b_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__apply,axiom, % 173.10/173.16 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 173.10/173.16 ( ( V_z_2 = V_x_2 % 173.10/173.16 => hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) % 173.10/173.16 & ( V_z_2 != V_x_2 % 173.10/173.16 => 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) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__same,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(c_Fun_Ofun__upd(T_b,T_a,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__upd,axiom, % 173.10/173.16 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : c_Fun_Ofun__upd(T_a,T_b,c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_z_2) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__idem__iff,axiom, % 173.10/173.16 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 % 173.10/173.16 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_image__diff__subset,axiom, % 173.10/173.16 ! [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)))) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Diff__partition,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => 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 ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Diff__subset__conv,axiom, % 173.10/173.16 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.10/173.16 ( 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)) % 173.10/173.16 <=> 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))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Pow__mono,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => 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))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_fun__upd__def,axiom, % 173.10/173.16 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 173.10/173.16 ( ( V_x_2 = V_a_2 % 173.10/173.16 => hAPP(c_Fun_Ofun__upd(T_a,T_b,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) % 173.10/173.16 & ( V_x_2 != V_a_2 % 173.10/173.16 => 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) ) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_Powp__mono,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.10/173.16 => 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))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_disjoint__eq__subset__Compl,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,T_a] : % 173.10/173.16 ( 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)) % 173.10/173.16 <=> 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))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_surj__Compl__image__subset,axiom, % 173.10/173.16 ! [V_A_2,V_f_2,T_a,T_b] : % 173.10/173.16 ( 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)) % 173.10/173.16 => 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)))) ) ). % 173.10/173.16 % 173.10/173.16 fof(fact_inj__on__image__set__diff,axiom, % 173.10/173.16 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 173.10/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 173.10/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.22/173.16 => 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)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_ComplE,axiom, % 173.22/173.16 ! [V_A_2,V_ca_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_ComplD,axiom, % 173.22/173.16 ! [V_A_2,V_ca_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__iff,axiom, % 173.22/173.16 ! [V_A_2,V_ca_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_DiffD2,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_DiffD1,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__iff,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.22/173.16 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_image__Pow__mono,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( 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)) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__cancel,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__empty,axiom, % 173.22/173.16 ! [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 ). % 173.22/173.16 % 173.22/173.16 fof(fact_empty__Diff,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__Diff,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__Diff__cancel2,axiom, % 173.22/173.16 ! [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) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__Diff__cancel,axiom, % 173.22/173.16 ! [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) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__Int2,axiom, % 173.22/173.16 ! [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) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__Int__distrib2,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Int__Diff,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__Int__distrib,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_set__mp,axiom, % 173.22/173.16 ! [V_x_2,V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_set__rev__mp,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_x_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_in__mono,axiom, % 173.22/173.16 ! [V_x_2,V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_bot__least,axiom, % 173.22/173.16 ! [V_x,T_a] : % 173.22/173.16 ( class_Orderings_Obot(T_a) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inj__on__diff,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__empty,axiom, % 173.22/173.16 ! [V_A_2,T_a] : % 173.22/173.16 ( 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)))) % 173.22/173.16 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__sup__ord_I3_J,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Olattice(T_a) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_sup__ge1,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__sup__ord_I4_J,axiom, % 173.22/173.16 ! [V_x,V_y,T_a] : % 173.22/173.16 ( class_Lattices_Olattice(T_a) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_sup__ge2,axiom, % 173.22/173.16 ! [V_x,V_y,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__iff__sup,axiom, % 173.22/173.16 ! [V_y_2,V_x_2,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.16 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__sup__iff,axiom, % 173.22/173.16 ! [V_z_2,V_y_2,V_x_2,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( 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)) % 173.22/173.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 173.22/173.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__supI1,axiom, % 173.22/173.16 ! [V_b,V_a,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.22/173.16 => 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))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__supI2,axiom, % 173.22/173.16 ! [V_a,V_b,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.22/173.16 => 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))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_sup__absorb2,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_sup__absorb1,axiom, % 173.22/173.16 ! [V_x,V_y,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__supI,axiom, % 173.22/173.16 ! [V_b,V_x,V_a,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.22/173.16 => 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)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_sup__least,axiom, % 173.22/173.16 ! [V_z,V_x,V_y,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 173.22/173.16 => 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)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_sup__mono,axiom, % 173.22/173.16 ! [V_d,V_b,V_c,V_a,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.22/173.16 => 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))) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__supE,axiom, % 173.22/173.16 ! [V_x,V_b,V_a,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.16 => ( 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)) % 173.22/173.16 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.22/173.16 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__infE,axiom, % 173.22/173.16 ! [V_b,V_a,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( 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))) % 173.22/173.16 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.22/173.16 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__mono,axiom, % 173.22/173.16 ! [V_d,V_b,V_c,V_a,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.22/173.16 => 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))) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__greatest,axiom, % 173.22/173.16 ! [V_z,V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 173.22/173.16 => 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))) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__infI,axiom, % 173.22/173.16 ! [V_b,V_a,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.22/173.16 => 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))) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__absorb2,axiom, % 173.22/173.16 ! [V_x,V_y,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__absorb1,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__infI2,axiom, % 173.22/173.16 ! [V_a,V_x,V_b,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.22/173.16 => 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)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__infI1,axiom, % 173.22/173.16 ! [V_b,V_x,V_a,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.22/173.16 => 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)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__inf__iff,axiom, % 173.22/173.16 ! [V_z_2,V_y_2,V_x_2,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( 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))) % 173.22/173.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_le__iff__inf,axiom, % 173.22/173.16 ! [V_y_2,V_x_2,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.16 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__le2,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__sup__ord_I2_J,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Olattice(T_a) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__le1,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__sup__ord_I1_J,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Olattice(T_a) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_top__greatest,axiom, % 173.22/173.16 ! [V_x,T_a] : % 173.22/173.16 ( class_Orderings_Otop(T_a) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_insert__mono,axiom, % 173.22/173.16 ! [V_a_2,V_D_2,V_C_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__insertI2,axiom, % 173.22/173.16 ! [V_b_2,V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__insertI,axiom, % 173.22/173.16 ! [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))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__UNIV,axiom, % 173.22/173.16 ! [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)))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_image__mono,axiom, % 173.22/173.16 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__image__iff,axiom, % 173.22/173.16 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 <=> ? [B_AA] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 173.22/173.16 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__mono,axiom, % 173.22/173.16 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 173.22/173.16 => 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))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__least,axiom, % 173.22/173.16 ! [V_B_2,V_C_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.22/173.16 => 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)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__absorb2,axiom, % 173.22/173.16 ! [V_A_2,V_B_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__absorb1,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__Un__eq,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__upper2,axiom, % 173.22/173.16 ! [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))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__upper1,axiom, % 173.22/173.16 ! [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))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Int__mono,axiom, % 173.22/173.16 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 173.22/173.16 => 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))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Int__greatest,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_C_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 173.22/173.16 => 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))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Int__absorb1,axiom, % 173.22/173.16 ! [V_A_2,V_B_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Int__absorb2,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Int__lower2,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Int__lower1,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_vimage__Compl,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__inj__on,axiom, % 173.22/173.16 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_vimage__Diff,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_vimage__mono,axiom, % 173.22/173.16 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.16 => 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))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_thin,axiom, % 173.22/173.16 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 173.22/173.16 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) % 173.22/173.16 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_weaken,axiom, % 173.22/173.16 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] : % 173.22/173.16 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2) % 173.22/173.16 => ( 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)) % 173.22/173.16 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_asm,axiom, % 173.22/173.16 ! [V_Ga_2,V_ts_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_Ga_2)) % 173.22/173.16 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_diff__single__insert,axiom, % 173.22/173.16 ! [V_B_2,V_x_2,V_A_2,T_a] : % 173.22/173.16 ( 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)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => 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))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__insert__iff,axiom, % 173.22/173.16 ! [V_B_2,V_x_2,V_A_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => 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)) ) % 173.22/173.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Collect__neg__eq,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inj__image__Compl__subset,axiom, % 173.22/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.16 => 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)))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_pred__subset__eq,axiom, % 173.22/173.16 ! [V_S_2,V_R_2,T_a] : % 173.22/173.16 ( 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))) % 173.22/173.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_fun__upd__comp,axiom, % 173.22/173.16 ! [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),c_Fun_Ofun__upd(T_a,T_c,V_g_2,V_x_2,V_y_2)) = 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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Pow__def,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inf__compl__bot,axiom, % 173.22/173.16 ! [V_x,T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => 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) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_compl__inf__bot,axiom, % 173.22/173.16 ! [V_x,T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => 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) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_compl__top__eq,axiom, % 173.22/173.16 ! [T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_compl__bot__eq,axiom, % 173.22/173.16 ! [T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_compl__sup,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_compl__inf,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_compl__sup__top,axiom, % 173.22/173.16 ! [V_x,T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => 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) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_sup__compl__top,axiom, % 173.22/173.16 ! [V_x,T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => 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) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_insert__Diff__if,axiom, % 173.22/173.16 ! [V_A_2,V_B_2,V_x_2,T_a] : % 173.22/173.16 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 173.22/173.16 => 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) ) % 173.22/173.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 173.22/173.16 => 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)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_insert__Diff1,axiom, % 173.22/173.16 ! [V_A_2,V_B_2,V_x_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 173.22/173.16 => 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) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__empty__eq,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__UNIV__eq,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__disjoint,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__disjoint2,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_insert__Diff__single,axiom, % 173.22/173.16 ! [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) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__insert2,axiom, % 173.22/173.16 ! [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) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__insert,axiom, % 173.22/173.16 ! [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)))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__UNIV,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__disjoint,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__triv,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,T_a] : % 173.22/173.16 ( 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)) % 173.22/173.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__partition2,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__partition,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__Un,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__Int,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__Diff__Int,axiom, % 173.22/173.16 ! [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 ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__Un,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__Int,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_insert__subset,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_x_2,T_a] : % 173.22/173.16 ( 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)) % 173.22/173.16 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 173.22/173.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__insert,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_x_2,T_a] : % 173.22/173.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => ( 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))) % 173.22/173.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_distrib__inf__le,axiom, % 173.22/173.16 ! [V_z,V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Olattice(T_a) % 173.22/173.16 => 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)))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_distrib__sup__le,axiom, % 173.22/173.16 ! [V_z,V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Olattice(T_a) % 173.22/173.16 => 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)))) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_fun__upd__image,axiom, % 173.22/173.16 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 173.22/173.16 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => hAPP(c_Set_Oimage(T_a,T_b,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)))))) ) % 173.22/173.16 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => hAPP(c_Set_Oimage(T_a,T_b,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) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_subset__singletonD,axiom, % 173.22/173.16 ! [V_x_2,V_A_2,T_a] : % 173.22/173.16 ( 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))))) % 173.22/173.16 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.16 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_image__Int__subset,axiom, % 173.22/173.16 ! [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)))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__Int__assoc__eq,axiom, % 173.22/173.16 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.22/173.16 ( 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)) % 173.22/173.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_bij__betw__subset,axiom, % 173.22/173.16 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_A_H_2) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.16 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) = V_B_H_2 % 173.22/173.16 => c_Fun_Obij__betw(T_a,T_b,V_f_2,V_B_2,V_B_H_2) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_image__vimage__subset,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Compl__eq,axiom, % 173.22/173.16 ! [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))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Un__Pow__subset,axiom, % 173.22/173.16 ! [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)))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Pow__iff,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 173.22/173.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_PowD,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 173.22/173.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_set__diff__eq,axiom, % 173.22/173.16 ! [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)))) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Collect__imp__eq,axiom, % 173.22/173.16 ! [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)) ). % 173.22/173.16 % 173.22/173.16 fof(fact_insert__Diff,axiom, % 173.22/173.16 ! [V_A_2,V_a_2,T_a] : % 173.22/173.16 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.16 => 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 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_Diff__insert__absorb,axiom, % 173.22/173.16 ! [V_A_2,V_x_2,T_a] : % 173.22/173.16 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.16 => 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 ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_image__set__diff,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_bij__image__Compl__eq,axiom, % 173.22/173.16 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.22/173.16 => 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)) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inj__image__subset__iff,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.16 => ( 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))) % 173.22/173.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inj__on__image__Int,axiom, % 173.22/173.16 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.22/173.16 => 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)) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_vimage__subsetD,axiom, % 173.22/173.16 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 173.22/173.16 ( 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)) % 173.22/173.16 => ( 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)) % 173.22/173.16 => 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))) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_bij__betw__comp__iff2,axiom, % 173.22/173.16 ! [V_A_2,V_f_2,T_c,V_A_H_H_2,V_A_H_2,V_f_H_2,T_b,T_a] : % 173.22/173.16 ( c_Fun_Obij__betw(T_a,T_b,V_f_H_2,V_A_H_2,V_A_H_H_2) % 173.22/173.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),V_A_H_2)) % 173.22/173.16 => ( c_Fun_Obij__betw(T_c,T_a,V_f_2,V_A_2,V_A_H_2) % 173.22/173.16 <=> c_Fun_Obij__betw(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_compl__unique,axiom, % 173.22/173.16 ! [V_y,V_x,T_a] : % 173.22/173.16 ( class_Lattices_Oboolean__algebra(T_a) % 173.22/173.16 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 173.22/173.16 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 173.22/173.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_inj__on__iff__surj,axiom, % 173.22/173.16 ! [V_A_H_2,T_b,T_a,V_A_2] : % 173.22/173.16 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.16 => ( ? [B_f] : % 173.22/173.16 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 173.22/173.16 & 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)) ) % 173.22/173.16 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 173.22/173.16 % 173.22/173.16 fof(fact_flat__lub__def,axiom, % 173.22/173.16 ! [V_b_2,V_A_2,T_a] : % 173.22/173.16 ( ( 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))))) % 173.22/173.16 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 173.22/173.16 & ( ~ 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))))) % 173.22/173.17 => 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)))))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_minus__diff__eq,axiom, % 173.22/173.17 ! [V_b,V_a,T_a] : % 173.22/173.17 ( class_Groups_Oab__group__add(T_a) % 173.22/173.17 => 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) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__minus__iff,axiom, % 173.22/173.17 ! [V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( 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))) % 173.22/173.17 <=> 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_minus__le__iff,axiom, % 173.22/173.17 ! [V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( 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)) % 173.22/173.17 <=> 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_neg__le__iff__le,axiom, % 173.22/173.17 ! [V_a_2,V_b_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( 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))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__imp__neg__le,axiom, % 173.22/173.17 ! [V_b,V_a,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.17 => 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__eq__diff__less__eq,axiom, % 173.22/173.17 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( 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) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__fun_I1_J,axiom, % 173.22/173.17 ! [V_g_2,V_f_2,T_a,T_b] : % 173.22/173.17 ( ( class_Orderings_Oorder(T_b) % 173.22/173.17 & class_Enum_Oenum(T_a) ) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.22/173.17 <=> 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_psubset__insert__iff,axiom, % 173.22/173.17 ! [V_B_2,V_x_2,V_A_2,T_a] : % 173.22/173.17 ( 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))) % 173.22/173.17 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 173.22/173.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 173.22/173.17 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.17 => 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)) ) % 173.22/173.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__diff__le,axiom, % 173.22/173.17 ! [V_m,V_n] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.17 => 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)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__irrefl,axiom, % 173.22/173.17 ! [V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__neq__iff,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( V_x_2 != V_y_2 % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_not__less__iff__gr__or__eq,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 173.22/173.17 | V_x_2 = V_y_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__less__linear,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 | V_x = V_y % 173.22/173.17 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__antisym__conv3,axiom, % 173.22/173.17 ! [V_x_2,V_y_2,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> V_x_2 = V_y_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__neqE,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( V_x != V_y % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__imp__neq,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => V_x != V_y ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__not__sym,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__imp__not__less,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__imp__not__eq,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => V_x != V_y ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__imp__not__eq2,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => V_y != V_x ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__asym_H,axiom, % 173.22/173.17 ! [V_b,V_a,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I9_J,axiom, % 173.22/173.17 ! [V_a,V_b,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.22/173.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_ord__eq__less__trans,axiom, % 173.22/173.17 ! [V_c,V_b,V_a,T_a] : % 173.22/173.17 ( class_Orderings_Oord(T_a) % 173.22/173.17 => ( V_a = V_b % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I1_J,axiom, % 173.22/173.17 ! [V_c,V_b,V_a,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( V_a = V_b % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_psubset__trans,axiom, % 173.22/173.17 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_ord__less__eq__trans,axiom, % 173.22/173.17 ! [V_c,V_b,V_a,T_a] : % 173.22/173.17 ( class_Orderings_Oord(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.17 => ( V_b = V_c % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I2_J,axiom, % 173.22/173.17 ! [V_c,V_a,V_b,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.22/173.17 => ( V_b = V_c % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__trans,axiom, % 173.22/173.17 ! [V_z,V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I10_J,axiom, % 173.22/173.17 ! [V_z,V_x,V_y,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__asym,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__cases,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => ( V_x != V_y % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_all__code,axiom, % 173.22/173.17 ! [V_P_2,T_a] : % 173.22/173.17 ( class_Enum_Oenum(T_a) % 173.22/173.17 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.17 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_enum__all,axiom, % 173.22/173.17 ! [V_P_2,T_a] : % 173.22/173.17 ( class_Enum_Oenum(T_a) % 173.22/173.17 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 173.22/173.17 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__eq__diff__less,axiom, % 173.22/173.17 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( 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) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_neg__less__iff__less,axiom, % 173.22/173.17 ! [V_a_2,V_b_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( 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))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_minus__less__iff,axiom, % 173.22/173.17 ! [V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__minus__iff,axiom, % 173.22/173.17 ! [V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__fun__def,axiom, % 173.22/173.17 ! [V_g_2,V_f_2,T_a,T_b] : % 173.22/173.17 ( class_Orderings_Oord(T_b) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.22/173.17 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__not__less,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__not__le,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__le__less__linear,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.17 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__le,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.17 & V_x_2 != V_y_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__le__not__le,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.17 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__le__less,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 | V_x_2 = V_y_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_leI,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_not__leE,axiom, % 173.22/173.17 ! [V_x,V_y,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__antisym__conv1,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> V_x_2 = V_y_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__neq__le__trans,axiom, % 173.22/173.17 ! [V_b,V_a,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( V_a != V_b % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I12_J,axiom, % 173.22/173.17 ! [V_b,V_a,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( V_a != V_b % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_leD,axiom, % 173.22/173.17 ! [V_x,V_y,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__imp__le,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__antisym__conv2,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,T_a] : % 173.22/173.17 ( class_Orderings_Olinorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 173.22/173.17 <=> V_x_2 = V_y_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__le__imp__less__or__eq,axiom, % 173.22/173.17 ! [V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 | V_x = V_y ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__le__neq__trans,axiom, % 173.22/173.17 ! [V_b,V_a,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.17 => ( V_a != V_b % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I11_J,axiom, % 173.22/173.17 ! [V_a,V_b,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.22/173.17 => ( V_a != V_b % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__less__le__trans,axiom, % 173.22/173.17 ! [V_z,V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I7_J,axiom, % 173.22/173.17 ! [V_z,V_x,V_y,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__le__less__trans,axiom, % 173.22/173.17 ! [V_z,V_y,V_x,T_a] : % 173.22/173.17 ( class_Orderings_Opreorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_xt1_I8_J,axiom, % 173.22/173.17 ! [V_z,V_x,V_y,T_a] : % 173.22/173.17 ( class_Orderings_Oorder(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_psubsetD,axiom, % 173.22/173.17 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__diff__diff,axiom, % 173.22/173.17 ! [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) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__Suc__Suc,axiom, % 173.22/173.17 ! [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) ). % 173.22/173.17 % 173.22/173.17 fof(fact_not__psubset__empty,axiom, % 173.22/173.17 ! [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)))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__supI2,axiom, % 173.22/173.17 ! [V_a,V_b,V_x,T_a] : % 173.22/173.17 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 173.22/173.17 => 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__supI1,axiom, % 173.22/173.17 ! [V_b,V_a,V_x,T_a] : % 173.22/173.17 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 173.22/173.17 => 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__infI1,axiom, % 173.22/173.17 ! [V_b,V_x,V_a,T_a] : % 173.22/173.17 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 173.22/173.17 => 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__infI2,axiom, % 173.22/173.17 ! [V_a,V_x,V_b,T_a] : % 173.22/173.17 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 173.22/173.17 => 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_psubset__eq,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 & V_A_2 != V_B_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_subset__iff__psubset__eq,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 | V_A_2 = V_B_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_psubset__imp__subset,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_psubset__subset__trans,axiom, % 173.22/173.17 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_subset__psubset__trans,axiom, % 173.22/173.17 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__leD,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__SucE,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__SucI,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__le__mono,axiom, % 173.22/173.17 ! [V_m_2,V_n_2] : % 173.22/173.17 ( 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))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__Suc__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_not__less__eq__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__n__not__le__n,axiom, % 173.22/173.17 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 173.22/173.17 % 173.22/173.17 fof(fact_evaln__nonstrict,axiom, % 173.22/173.17 ! [V_m,V_t,V_n,V_s,V_c] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.17 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__on__strict__subset,axiom, % 173.22/173.17 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__eq__diff__eq,axiom, % 173.22/173.17 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Oab__group__add(T_a) % 173.22/173.17 => ( 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) % 173.22/173.17 => ( V_a_2 = V_b_2 % 173.22/173.17 <=> V_ca_2 = V_d_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_neg__equal__iff__equal,axiom, % 173.22/173.17 ! [V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Ogroup__add(T_a) % 173.22/173.17 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 173.22/173.17 <=> V_a_2 = V_b_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_minus__equation__iff,axiom, % 173.22/173.17 ! [V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Ogroup__add(T_a) % 173.22/173.17 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 173.22/173.17 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_equation__minus__iff,axiom, % 173.22/173.17 ! [V_b_2,V_a_2,T_a] : % 173.22/173.17 ( class_Groups_Ogroup__add(T_a) % 173.22/173.17 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 173.22/173.17 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_minus__minus,axiom, % 173.22/173.17 ! [V_a,T_a] : % 173.22/173.17 ( class_Groups_Ogroup__add(T_a) % 173.22/173.17 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_order__fun_I2_J,axiom, % 173.22/173.17 ! [V_g_2,V_f_2,T_a,T_b] : % 173.22/173.17 ( ( class_Orderings_Oorder(T_b) % 173.22/173.17 & class_Enum_Oenum(T_a) ) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 173.22/173.17 & 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)))) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Cantor__Bernstein,axiom, % 173.22/173.17 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.17 => ( 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)) % 173.22/173.17 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 173.22/173.17 => ( 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)) % 173.22/173.17 => ? [B_h] : c_Fun_Obij__betw(T_a,T_b,B_h,V_A_2,V_B_2) ) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Int__Collect__mono,axiom, % 173.22/173.17 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => ( ! [B_x] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.17 => ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.17 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 173.22/173.17 => 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)))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 173.22/173.17 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.17 => ( 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) % 173.22/173.17 => 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Pow__Compl,axiom, % 173.22/173.17 ! [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))))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__image__Collect__eq,axiom, % 173.22/173.17 ! [V_P_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.22/173.17 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),V_P_2),c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__vimage__eq__inv__image,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.22/173.17 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2)),V_A_2) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__into__comp,axiom, % 173.22/173.17 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 173.22/173.17 ( 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)) % 173.22/173.17 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 173.22/173.17 => ( 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)))) % 173.22/173.17 => hAPP(c_Hilbert__Choice_Oinv__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_Hilbert__Choice_Oinv__into(T_c,T_a,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__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) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_mk__less__def,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,V_R_2,T_a] : % 173.22/173.17 ( c_Partial__Function_Omk__less(T_a,V_R_2,V_x_2,V_y_2) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 173.22/173.17 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_lessI,axiom, % 173.22/173.17 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__mono,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_termination__basic__simps_I5_J,axiom, % 173.22/173.17 ! [V_y,V_x] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__or__eq__imp__le,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 | V_m = V_n ) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__diff__iff,axiom, % 173.22/173.17 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 173.22/173.17 => ( 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))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__diff__iff,axiom, % 173.22/173.17 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 173.22/173.17 => ( 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))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Nat_Odiff__diff__eq,axiom, % 173.22/173.17 ! [V_n,V_m,V_k] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 173.22/173.17 => 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) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_eq__diff__iff,axiom, % 173.22/173.17 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 173.22/173.17 => ( 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) % 173.22/173.17 <=> V_m_2 = V_n_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__less__mono2,axiom, % 173.22/173.17 ! [V_l,V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 173.22/173.17 => 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__less__mono,axiom, % 173.22/173.17 ! [V_c,V_b,V_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 173.22/173.17 => 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))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__antisym,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.17 => V_m = V_n ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__trans,axiom, % 173.22/173.17 ! [V_k,V_j,V_i] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__neq__implies__less,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => ( V_m != V_n % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__diff__cancel,axiom, % 173.22/173.17 ! [V_n,V_i] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 173.22/173.17 => 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 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__le__mono,axiom, % 173.22/173.17 ! [V_l,V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => 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))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__le__mono2,axiom, % 173.22/173.17 ! [V_l,V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => 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))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__imp__diff__less,axiom, % 173.22/173.17 ! [V_n,V_k,V_j] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 173.22/173.17 => 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)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__imp__le__nat,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_eq__imp__le,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( V_m = V_n % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__commute,axiom, % 173.22/173.17 ! [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) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__eq__less__or__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 | V_m_2 = V_n_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_nat__less__le,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 & V_m_2 != V_n_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_nat__le__linear,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__le__self,axiom, % 173.22/173.17 ! [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)) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__refl,axiom, % 173.22/173.17 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 173.22/173.17 % 173.22/173.17 fof(fact_exists__code,axiom, % 173.22/173.17 ! [V_P_2,T_a] : % 173.22/173.17 ( class_Enum_Oenum(T_a) % 173.22/173.17 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.17 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_enum__ex,axiom, % 173.22/173.17 ! [V_P_2,T_a] : % 173.22/173.17 ( class_Enum_Oenum(T_a) % 173.22/173.17 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 173.22/173.17 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 173.22/173.17 ! [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) ). % 173.22/173.17 % 173.22/173.17 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 173.22/173.17 ! [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) ). % 173.22/173.17 % 173.22/173.17 fof(fact_not__less__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__Suc__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 | V_m_2 = V_n_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__less__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( 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))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_not__less__less__Suc__eq,axiom, % 173.22/173.17 ! [V_m_2,V_n_2] : % 173.22/173.17 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 173.22/173.17 <=> V_n_2 = V_m_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__antisym,axiom, % 173.22/173.17 ! [V_m,V_n] : % 173.22/173.17 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 173.22/173.17 => V_m = V_n ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__SucI,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__lessI,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__trans__Suc,axiom, % 173.22/173.17 ! [V_k,V_j,V_i] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__SucE,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => V_m = V_n ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__lessD,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__less__SucD,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__eq__Suc__le,axiom, % 173.22/173.17 ! [V_m_2,V_n_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__Suc__eq__le,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__le__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 173.22/173.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__imp__less__Suc,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__leI,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_le__less__Suc__eq,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 173.22/173.17 <=> V_n_2 = V_m_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_Suc__le__lessD,axiom, % 173.22/173.17 ! [V_n,V_m] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_diff__less__Suc,axiom, % 173.22/173.17 ! [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))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__betw__inv__into,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.22/173.17 => c_Fun_Obij__betw(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__eq__Suc__le__raw,axiom, % 173.22/173.17 ! [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)) ). % 173.22/173.17 % 173.22/173.17 fof(fact_f__inv__into__f,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_b,V_y_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 173.22/173.17 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__into__into,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_b,V_x_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__into__injective,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_b,T_a] : % 173.22/173.17 ( hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 173.22/173.17 => V_x_2 = V_y_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__into__f__eq,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.17 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 173.22/173.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__into__f__f,axiom, % 173.22/173.17 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_image__inv__into__cancel,axiom, % 173.22/173.17 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 173.22/173.17 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) % 173.22/173.17 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_image__surj__f__inv__f,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_a,T_b] : % 173.22/173.17 ( 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)) % 173.22/173.17 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_surj__f__inv__f,axiom, % 173.22/173.17 ! [V_y_2,V_f_2,T_a,T_b] : % 173.22/173.17 ( 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)) % 173.22/173.17 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_surj__iff__all,axiom, % 173.22/173.17 ! [V_f_2,T_a,T_b] : % 173.22/173.17 ( 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)) % 173.22/173.17 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__f__f,axiom, % 173.22/173.17 ! [V_x_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => hAPP(c_Hilbert__Choice_Oinv__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 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__f__eq,axiom, % 173.22/173.17 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 173.22/173.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__into__inv__into__eq,axiom, % 173.22/173.17 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_A_H_2) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.17 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__inv__eq,axiom, % 173.22/173.17 ! [V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.22/173.17 => c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__imp__bij__inv,axiom, % 173.22/173.17 ! [V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.22/173.17 => c_Fun_Obij__betw(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),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))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__on__inv__into,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 173.22/173.17 ( 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))) % 173.22/173.17 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_2) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__into__image__cancel,axiom, % 173.22/173.17 ! [V_S_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_A_2)) % 173.22/173.17 => hAPP(c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = V_S_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_surj__imp__inj__inv,axiom, % 173.22/173.17 ! [V_f_2,T_a,T_b] : % 173.22/173.17 ( 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)) % 173.22/173.17 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__image__comp,axiom, % 173.22/173.17 ! [V_X_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => hAPP(c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_X_2)) = V_X_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_image__inv__f__f,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => hAPP(c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__imp__surj__inv,axiom, % 173.22/173.17 ! [V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => hAPP(c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),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)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_o__inv__o__cancel,axiom, % 173.22/173.17 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => hAPP(c_Fun_Ocomp(T_b,T_c,T_a,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_o__inv__distrib,axiom, % 173.22/173.17 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.22/173.17 => ( c_Fun_Obij__betw(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Hilbert__Choice_Oinv__into(T_c,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 173.22/173.17 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 173.22/173.17 ( 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)) % 173.22/173.17 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.17 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 173.22/173.17 | ? [B_x,B_y] : % 173.22/173.17 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 173.22/173.17 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 173.22/173.17 & 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) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__transfer,axiom, % 173.22/173.17 ! [V_x_2,V_P_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => ( ! [B_y] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) % 173.22/173.17 => hBOOL(hAPP(V_P_2,hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),B_y))) ) % 173.22/173.17 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__on__diff__nat,axiom, % 173.22/173.17 ! [V_k_2,V_N_2] : % 173.22/173.17 ( ! [B_x] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 173.22/173.17 => 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) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 173.22/173.17 <=> 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)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__diff1__nat,axiom, % 173.22/173.17 ! [V_f_2,V_A_2,V_a_2,T_a] : % 173.22/173.17 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.17 => 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)) ) % 173.22/173.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.17 => 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) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__iff,axiom, % 173.22/173.17 ! [V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 <=> hAPP(c_Fun_Ocomp(T_b,T_a,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_a) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__o__cancel,axiom, % 173.22/173.17 ! [V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => hAPP(c_Fun_Ocomp(T_b,T_a,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_a) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_surj__iff,axiom, % 173.22/173.17 ! [V_f_2,T_a,T_b] : % 173.22/173.17 ( 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)) % 173.22/173.17 <=> hAPP(c_Fun_Ocomp(T_b,T_a,T_a,V_f_2),c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_a) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__betw__id,axiom, % 173.22/173.17 ! [V_A_2,T_a] : c_Fun_Obij__betw(T_a,T_a,c_Fun_Oid(T_a),V_A_2,V_A_2) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__not__refl,axiom, % 173.22/173.17 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 173.22/173.17 % 173.22/173.17 fof(fact_nat__neq__iff,axiom, % 173.22/173.17 ! [V_n_2,V_m_2] : % 173.22/173.17 ( V_m_2 != V_n_2 % 173.22/173.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_linorder__neqE__nat,axiom, % 173.22/173.17 ! [V_y,V_x] : % 173.22/173.17 ( V_x != V_y % 173.22/173.17 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__irrefl__nat,axiom, % 173.22/173.17 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__not__refl2,axiom, % 173.22/173.17 ! [V_m,V_n] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 173.22/173.17 => V_m != V_n ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_less__not__refl3,axiom, % 173.22/173.17 ! [V_t,V_s] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 173.22/173.17 => V_s != V_t ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_nat__less__cases,axiom, % 173.22/173.17 ! [V_P_2,V_n_2,V_m_2] : % 173.22/173.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 173.22/173.17 => ( ( V_m_2 = V_n_2 % 173.22/173.17 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 173.22/173.17 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 173.22/173.17 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_id__apply,axiom, % 173.22/173.17 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__commute,axiom, % 173.22/173.17 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 173.22/173.17 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.17 => 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) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_id__def,axiom, % 173.22/173.17 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__reindex__id,axiom, % 173.22/173.17 ! [V_B_2,V_f_2,T_a,T_b] : % 173.22/173.17 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.17 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.22/173.17 => 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_image__id,axiom, % 173.22/173.17 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 173.22/173.17 % 173.22/173.17 fof(fact_o__eq__id__dest,axiom, % 173.22/173.17 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 173.22/173.17 ( 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) % 173.22/173.17 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_o__id,axiom, % 173.22/173.17 ! [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 ). % 173.22/173.17 % 173.22/173.17 fof(fact_id__o,axiom, % 173.22/173.17 ! [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 ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__on__id,axiom, % 173.22/173.17 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__subtractf,axiom, % 173.22/173.17 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( class_Groups_Oab__group__add(T_a) % 173.22/173.17 => 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)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__betw__id__iff,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_a,c_Fun_Oid(T_a),V_A_2,V_B_2) % 173.22/173.17 <=> V_A_2 = V_B_2 ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_vimage__id,axiom, % 173.22/173.17 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__negf,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( class_Groups_Oab__group__add(T_a) % 173.22/173.17 => 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)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_surj__id,axiom, % 173.22/173.17 ! [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)) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__id,axiom, % 173.22/173.17 ! [T_a] : c_Fun_Obij__betw(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))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inv__id,axiom, % 173.22/173.17 ! [T_a] : c_Hilbert__Choice_Oinv__into(T_a,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Fun_Oid(T_a)) = c_Fun_Oid(T_a) ). % 173.22/173.17 % 173.22/173.17 fof(fact_nat__case__Suc,axiom, % 173.22/173.17 ! [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) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__reindex,axiom, % 173.22/173.17 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 173.22/173.17 ( class_Groups_Ocomm__monoid__add(T_c) % 173.22/173.17 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.22/173.17 => 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) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__diff1,axiom, % 173.22/173.17 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 173.22/173.17 ( class_Groups_Oab__group__add(T_b) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.17 => 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)) ) % 173.22/173.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.17 => 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) ) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__diff1__ring,axiom, % 173.22/173.17 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 173.22/173.17 ( class_Rings_Oring(T_b) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.17 => 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)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__reindex__cong,axiom, % 173.22/173.17 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 173.22/173.17 ( class_Groups_Ocomm__monoid__add(T_c) % 173.22/173.17 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.17 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 173.22/173.17 => ( ! [B_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 173.22/173.17 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 173.22/173.17 => 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) ) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__diff__nat,axiom, % 173.22/173.17 ! [V_f_2,V_A_2,V_B_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.17 => 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum_Oreindex,axiom, % 173.22/173.17 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 173.22/173.17 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 173.22/173.17 => 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) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__diff,axiom, % 173.22/173.17 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.17 ( class_Groups_Oab__group__add(T_b) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.17 => 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)) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__mono,axiom, % 173.22/173.17 ! [V_g_2,V_f_2,V_K_2,T_a,T_b] : % 173.22/173.17 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.17 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 173.22/173.17 => ( ! [B_i] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_K_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),hAPP(V_g_2,B_i))) ) % 173.22/173.17 => 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_K_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_K_2))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_inj__imp__inv__eq,axiom, % 173.22/173.17 ! [V_g_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => ( ! [B_x] : hAPP(V_f_2,hAPP(V_g_2,B_x)) = B_x % 173.22/173.17 => c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2) = V_g_2 ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Collect__subsets,axiom, % 173.22/173.17 ! [V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => 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)))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Collect__conjI,axiom, % 173.22/173.17 ! [V_Q_2,V_P_2,T_a] : % 173.22/173.17 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.22/173.17 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 173.22/173.17 => 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)))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_setsum__image__gen,axiom, % 173.22/173.17 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 173.22/173.17 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.17 => 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Diff,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => 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))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Int,axiom, % 173.22/173.17 ! [V_Ga_2,V_F_2,T_a] : % 173.22/173.17 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.17 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__imageI,axiom, % 173.22/173.17 ! [V_h_2,T_b,V_F_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite_OinsertI,axiom, % 173.22/173.17 ! [V_a_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite_OemptyI,axiom, % 173.22/173.17 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Collect__less__nat,axiom, % 173.22/173.17 ! [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)))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Collect__le__nat,axiom, % 173.22/173.17 ! [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)))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__code,axiom, % 173.22/173.17 ! [V_A_2,T_a] : % 173.22/173.17 ( class_Finite__Set_Ofinite(T_a) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite,axiom, % 173.22/173.17 ! [V_A_2,T_a] : % 173.22/173.17 ( class_Finite__Set_Ofinite(T_a) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__nat__set__iff__bounded,axiom, % 173.22/173.17 ! [V_N_2] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 173.22/173.17 <=> ? [B_m] : % 173.22/173.17 ! [B_x] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 173.22/173.17 ! [V_N_2] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 173.22/173.17 <=> ? [B_m] : % 173.22/173.17 ! [B_x] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 173.22/173.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__M__bounded__by__nat,axiom, % 173.22/173.17 ! [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))))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite_Oequations_I1_J,axiom, % 173.22/173.17 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__insert,axiom, % 173.22/173.17 ! [V_A_2,V_a_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 173.22/173.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_rev__finite__subset,axiom, % 173.22/173.17 ! [V_A_2,V_B_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__subset,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__UNIV,axiom, % 173.22/173.17 ! [T_a] : % 173.22/173.17 ( class_Finite__Set_Ofinite(T_a) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Prod__UNIV,axiom, % 173.22/173.17 ! [T_b,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.22/173.17 => 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)))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Plus__UNIV__iff,axiom, % 173.22/173.17 ! [T_b,T_a] : % 173.22/173.17 ( 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)))) % 173.22/173.17 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.17 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__option__UNIV,axiom, % 173.22/173.17 ! [T_a] : % 173.22/173.17 ( 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)))) % 173.22/173.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Un,axiom, % 173.22/173.17 ! [V_Ga_2,V_F_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) % 173.22/173.17 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.17 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__UnI,axiom, % 173.22/173.17 ! [V_Ga_2,V_F_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Diff2,axiom, % 173.22/173.17 ! [V_A_2,V_B_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.17 => ( 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))) % 173.22/173.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_bij__betw__finite,axiom, % 173.22/173.17 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Pow__iff,axiom, % 173.22/173.17 ! [V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 173.22/173.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_nat__seg__image__imp__finite,axiom, % 173.22/173.17 ! [V_n_2,V_f_2,T_a,V_A_2] : % 173.22/173.17 ( 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))) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Collect__disjI,axiom, % 173.22/173.17 ! [V_Q_2,V_P_2,T_a] : % 173.22/173.17 ( 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)))) % 173.22/173.17 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.22/173.17 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__surj,axiom, % 173.22/173.17 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( 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))) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Diff__insert,axiom, % 173.22/173.17 ! [V_B_2,V_a_2,V_A_2,T_a] : % 173.22/173.17 ( 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)))) % 173.22/173.17 <=> 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))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__imageD,axiom, % 173.22/173.17 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 173.22/173.17 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__compl,axiom, % 173.22/173.17 ! [V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 173.22/173.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__image__set,axiom, % 173.22/173.17 ! [V_f_2,T_b,V_P_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.22/173.17 => 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))))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Collect__bounded__ex,axiom, % 173.22/173.17 ! [V_Q_2,T_b,V_P_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.22/173.17 => ( 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))))) % 173.22/173.17 <=> ! [B_y] : % 173.22/173.17 ( hBOOL(hAPP(V_P_2,B_y)) % 173.22/173.17 => 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)))) ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__Collect__not,axiom, % 173.22/173.17 ! [V_P_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 173.22/173.17 => ( 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)))) % 173.22/173.17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__range__imageI,axiom, % 173.22/173.17 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 173.22/173.17 ( 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))))) % 173.22/173.17 => 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))))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__fun__UNIVD2,axiom, % 173.22/173.17 ! [T_b,T_a] : % 173.22/173.17 ( 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)))) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__surj__inj,axiom, % 173.22/173.17 ! [V_f_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( 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))) % 173.22/173.17 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_endo__inj__surj,axiom, % 173.22/173.17 ! [V_f_2,V_A_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.17 => ( 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)) % 173.22/173.17 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 173.22/173.17 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__UNIV__inj__surj,axiom, % 173.22/173.17 ! [V_f_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.17 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.17 => 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)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__UNIV__surj__inj,axiom, % 173.22/173.17 ! [V_f_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.17 => ( 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)) % 173.22/173.17 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__vimageD,axiom, % 173.22/173.17 ! [V_F_2,V_h_2,T_b,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 173.22/173.17 => ( 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)) % 173.22/173.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 173.22/173.17 % 173.22/173.17 fof(fact_finite__vimageI,axiom, % 173.22/173.17 ! [V_h_2,T_b,V_F_2,T_a] : % 173.22/173.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.17 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.22/173.18 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_finite__vimage__iff,axiom, % 173.22/173.18 ! [V_F_2,V_h_2,T_b,T_a] : % 173.22/173.18 ( c_Fun_Obij__betw(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))) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 173.22/173.18 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__setsum__restrict,axiom, % 173.22/173.18 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_c) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Oremove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one_Oremove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 173.22/173.18 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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)))))) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image__simple_Oremove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.22/173.18 => 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)))))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image_Oreindex,axiom, % 173.22/173.18 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ounion,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Oinsert__remove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 173.22/173.18 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 173.22/173.18 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OatLeastLessThan__iff,axiom, % 173.22/173.18 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 173.22/173.18 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_infinite__UNIV__nat,axiom, % 173.22/173.18 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 173.22/173.18 ! [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] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ocommute__comp,axiom, % 173.22/173.18 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ocommute__left__comp,axiom, % 173.22/173.18 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image__simple_Oempty,axiom, % 173.22/173.18 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.18 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image_Odistrib,axiom, % 173.22/173.18 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ocommute__comp_H,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ocommute__left__comp_H,axiom, % 173.22/173.18 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ocommute__comp_H_H,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 173.22/173.18 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Oempty,axiom, % 173.22/173.18 ! [V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one_Osingleton,axiom, % 173.22/173.18 ! [V_x_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image__simple_Oinsert,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image__simple_Ounion__inter,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Oinsert,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding_Ounion__inter,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one_Oinsert,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => 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)))))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one_Oinsert__remove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 173.22/173.18 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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)))))) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one_Ounion__disjoint,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one_Ounion__inter,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OatMost__iff,axiom, % 173.22/173.18 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OatLeast__iff,axiom, % 173.22/173.18 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OlessThan__iff,axiom, % 173.22/173.18 ! [V_k_2,V_less_2,V_i_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OgreaterThan__iff,axiom, % 173.22/173.18 ! [V_k_2,V_less_2,V_i_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OatLeastAtMost__iff,axiom, % 173.22/173.18 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 173.22/173.18 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 173.22/173.18 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 173.22/173.18 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_finite__pointwise,axiom, % 173.22/173.18 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_b,V_U_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 173.22/173.18 => ( ! [B_p] : % 173.22/173.18 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 173.22/173.18 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) % 173.22/173.18 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2)) % 173.22/173.18 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_inf__Sup2__distrib,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Odistrib__lattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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))))))) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Osingleton,axiom, % 173.22/173.18 ! [V_x_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Oin__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_inf__Sup__absorb,axiom, % 173.22/173.18 ! [V_a_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.18 => 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 ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Oinsert__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Osubset__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Ounion__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Oinsert,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Oinsert__remove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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 ) % 173.22/173.18 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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)))))) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Ounion__inter,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Oremove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 173.22/173.18 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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)))))) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_inf__Sup1__distrib,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Odistrib__lattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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))))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Oclosed,axiom, % 173.22/173.18 ! [V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( ! [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)))))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_sup__Inf1__distrib,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Odistrib__lattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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))))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_sup__Inf2__distrib,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Odistrib__lattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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))))))) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Oremove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 173.22/173.18 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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)))))) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__idem_Ounion__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__idem_Oinsert__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one_Oclosed,axiom, % 173.22/173.18 ! [V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( ! [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)))))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Osingleton,axiom, % 173.22/173.18 ! [V_x_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__idem_Oidem__comp,axiom, % 173.22/173.18 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__idem_Oidem__left__comp,axiom, % 173.22/173.18 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_sup__Inf__absorb,axiom, % 173.22/173.18 ! [V_a_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.18 => 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 ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Oin__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Oinsert__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Osubset__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Ounion__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__le__Sup,axiom, % 173.22/173.18 ! [V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Oinsert,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Oinsert__remove,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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 ) % 173.22/173.18 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.18 => 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)))))) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Ounion__inter,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__idem_Oin__comp__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Oclosed,axiom, % 173.22/173.18 ! [V_A_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( ! [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)))))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Inf__fin_Ohom__commute,axiom, % 173.22/173.18 ! [V_N_2,V_h_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( ! [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)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Sup__fin_Ohom__commute,axiom, % 173.22/173.18 ! [V_N_2,V_h_2,T_a] : % 173.22/173.18 ( class_Lattices_Olattice(T_a) % 173.22/173.18 => ( ! [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)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_finite__empty__induct,axiom, % 173.22/173.18 ! [V_P_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 173.22/173.18 => ( ! [B_a,B_A] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 173.22/173.18 => ( hBOOL(hAPP(V_P_2,B_A)) % 173.22/173.18 => 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)))))) ) ) ) % 173.22/173.18 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one__idem_Ounion__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_finite__subset__induct,axiom, % 173.22/173.18 ! [V_P_2,V_A_2,V_F_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.18 => ( ! [B_a,B_F] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 173.22/173.18 => ( hBOOL(hAPP(V_P_2,B_F)) % 173.22/173.18 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 173.22/173.18 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one__idem_Osubset__idem,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__strict__mono,axiom, % 173.22/173.18 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => ( ! [B_x] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 173.22/173.18 => 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))) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one__idem_Oidem,axiom, % 173.22/173.18 ! [V_x_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 173.22/173.18 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one__idem_Oin__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_finite__conv__nat__seg__image,axiom, % 173.22/173.18 ! [V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 <=> ? [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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__diff1_H,axiom, % 173.22/173.18 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.18 => 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)))))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum_Oremove,axiom, % 173.22/173.18 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)))))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_image__eq__fold__image,axiom, % 173.22/173.18 ! [V_f_2,T_b,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Diff2__less,axiom, % 173.22/173.18 ! [V_y_2,V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Diff1__less,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Suc__Diff1,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__one__idem_Ohom__commute,axiom, % 173.22/173.18 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 173.22/173.18 => ( ! [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)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__right__imp__eq,axiom, % 173.22/173.18 ! [V_c,V_a,V_b,T_a] : % 173.22/173.18 ( class_Groups_Ocancel__semigroup__add(T_a) % 173.22/173.18 => ( 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) % 173.22/173.18 => V_b = V_c ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__imp__eq,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 173.22/173.18 => ( 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) % 173.22/173.18 => V_b = V_c ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__left__imp__eq,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ocancel__semigroup__add(T_a) % 173.22/173.18 => ( 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) % 173.22/173.18 => V_b = V_c ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__right__cancel,axiom, % 173.22/173.18 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 173.22/173.18 ( class_Groups_Ocancel__semigroup__add(T_a) % 173.22/173.18 => ( 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) % 173.22/173.18 <=> V_b_2 = V_ca_2 ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__left__cancel,axiom, % 173.22/173.18 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Ocancel__semigroup__add(T_a) % 173.22/173.18 => ( 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) % 173.22/173.18 <=> V_b_2 = V_ca_2 ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oab__semigroup__add(T_a) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__le__cancel__right,axiom, % 173.22/173.18 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__le__cancel__left,axiom, % 173.22/173.18 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__right__mono,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__left__mono,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__mono,axiom, % 173.22/173.18 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__le__imp__le__right,axiom, % 173.22/173.18 ! [V_b,V_c,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__le__imp__le__left,axiom, % 173.22/173.18 ! [V_b,V_a,V_c,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__less__cancel__right,axiom, % 173.22/173.18 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__less__cancel__left,axiom, % 173.22/173.18 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__strict__right__mono,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__strict__left__mono,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__strict__mono,axiom, % 173.22/173.18 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__less__imp__less__right,axiom, % 173.22/173.18 ! [V_b,V_c,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__less__imp__less__left,axiom, % 173.22/173.18 ! [V_b,V_a,V_c,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__add__cancel,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__diff__cancel,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_minus__add__distrib,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oab__group__add(T_a) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_minus__add,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__minus__cancel,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_minus__add__cancel,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__Suc__right,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__Suc,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__Suc__shift,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_termination__basic__simps_I2_J,axiom, % 173.22/173.18 ! [V_y,V_z,V_x] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_termination__basic__simps_I1_J,axiom, % 173.22/173.18 ! [V_z,V_y,V_x] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__lessD1,axiom, % 173.22/173.18 ! [V_k,V_j,V_i] : % 173.22/173.18 ( 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)) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__add__eq__less,axiom, % 173.22/173.18 ! [V_n,V_m,V_l,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 173.22/173.18 => ( 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) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__less__mono,axiom, % 173.22/173.18 ! [V_l,V_k,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__less__mono1,axiom, % 173.22/173.18 ! [V_k,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_trans__less__add2,axiom, % 173.22/173.18 ! [V_m,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_trans__less__add1,axiom, % 173.22/173.18 ! [V_m,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__add__left__cancel__less,axiom, % 173.22/173.18 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_not__add__less2,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_not__add__less1,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_bij__betw__same__card,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Fun_Obij__betw(T_a,T_b,V_f_2,V_A_2,V_B_2) % 173.22/173.18 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_termination__basic__simps_I4_J,axiom, % 173.22/173.18 ! [V_y,V_z,V_x] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_termination__basic__simps_I3_J,axiom, % 173.22/173.18 ! [V_z,V_y,V_x] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__leE,axiom, % 173.22/173.18 ! [V_n,V_k,V_m] : % 173.22/173.18 ( 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)) % 173.22/173.18 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__leD1,axiom, % 173.22/173.18 ! [V_n,V_k,V_m] : % 173.22/173.18 ( 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)) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__leD2,axiom, % 173.22/173.18 ! [V_n,V_k,V_m] : % 173.22/173.18 ( 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)) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__le__mono,axiom, % 173.22/173.18 ! [V_l,V_k,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__le__mono1,axiom, % 173.22/173.18 ! [V_k,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_trans__le__add2,axiom, % 173.22/173.18 ! [V_m,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_trans__le__add1,axiom, % 173.22/173.18 ! [V_m,V_j,V_i] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__add__left__cancel__le,axiom, % 173.22/173.18 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__iff__add,axiom, % 173.22/173.18 ! [V_n_2,V_m_2] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.18 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__add1,axiom, % 173.22/173.18 ! [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))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__add2,axiom, % 173.22/173.18 ! [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))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__cancel2,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__cancel,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__diff__left,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__add__inverse,axiom, % 173.22/173.18 ! [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 ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__add__inverse2,axiom, % 173.22/173.18 ! [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 ). % 173.22/173.18 % 173.22/173.18 fof(fact_fold__image__empty,axiom, % 173.22/173.18 ! [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 ). % 173.22/173.18 % 173.22/173.18 fof(fact_card_Ounion__inter,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Un__Int,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__addf,axiom, % 173.22/173.18 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Un__disjoint,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 173.22/173.18 ! [V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.18 => ( 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))) % 173.22/173.18 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__le__less__mono,axiom, % 173.22/173.18 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__less__le__mono,axiom, % 173.22/173.18 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__image,axiom, % 173.22/173.18 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_BIJ,axiom, % 173.22/173.18 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.18 => ( ? [B_f] : c_Fun_Obij__betw(T_a,T_b,B_f,V_A_2,V_B_2) % 173.22/173.18 <=> hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__def,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_ab__diff__minus,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oab__group__add(T_a) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__minus__eq__add,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__iff__Suc__add,axiom, % 173.22/173.18 ! [V_n_2,V_m_2] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.18 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__add__Suc2,axiom, % 173.22/173.18 ! [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)))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__add__Suc1,axiom, % 173.22/173.18 ! [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)))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__diff__inverse,axiom, % 173.22/173.18 ! [V_n,V_m] : % 173.22/173.18 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__diff__conv,axiom, % 173.22/173.18 ! [V_k_2,V_j_2,V_i_2] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__add__assoc2,axiom, % 173.22/173.18 ! [V_i,V_j,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__diff__assoc2,axiom, % 173.22/173.18 ! [V_i,V_j,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__add__assoc,axiom, % 173.22/173.18 ! [V_i,V_j,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__imp__diff__is__add,axiom, % 173.22/173.18 ! [V_k_2,V_j_2,V_i_2] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.22/173.18 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 173.22/173.18 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__add__diff__inverse2,axiom, % 173.22/173.18 ! [V_m,V_n] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__diff__conv2,axiom, % 173.22/173.18 ! [V_i_2,V_j_2,V_k_2] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__diff__assoc,axiom, % 173.22/173.18 ! [V_i,V_j,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__add__diff__inverse,axiom, % 173.22/173.18 ! [V_m,V_n] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__add__diff,axiom, % 173.22/173.18 ! [V_m,V_n,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__diff__conv,axiom, % 173.22/173.18 ! [V_i_2,V_k_2,V_j_2] : % 173.22/173.18 ( 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)) % 173.22/173.18 <=> 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__diff__right,axiom, % 173.22/173.18 ! [V_i,V_j,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_funpow__add,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_inj__on__add__nat,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum_Odistrib,axiom, % 173.22/173.18 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 173.22/173.18 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => 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) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_folding__image_Oeq__fold,axiom, % 173.22/173.18 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => 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) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__insert__le,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__mono,axiom, % 173.22/173.18 ! [V_A_2,V_B_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__seteq,axiom, % 173.22/173.18 ! [V_A_2,V_B_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.18 => ( 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))) % 173.22/173.18 => V_A_2 = V_B_2 ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__image__le,axiom, % 173.22/173.18 ! [V_f_2,T_b,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_eq__card__imp__inj__on,axiom, % 173.22/173.18 ! [V_f_2,T_b,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( 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) % 173.22/173.18 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_inj__on__iff__eq__card,axiom, % 173.22/173.18 ! [V_f_2,T_b,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.18 <=> 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) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_pigeonhole,axiom, % 173.22/173.18 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( 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))) % 173.22/173.18 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_psubset__card__mono,axiom, % 173.22/173.18 ! [V_A_2,V_B_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__Suc__diff__eq2,axiom, % 173.22/173.18 ! [V_m,V_j,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__Suc__diff__eq1,axiom, % 173.22/173.18 ! [V_m,V_j,V_k] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__insert__disjoint,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__insert__if,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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) ) % 173.22/173.18 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__bij__eq,axiom, % 173.22/173.18 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.18 => ( 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)) % 173.22/173.18 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 173.22/173.18 => ( 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)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.18 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Diff__subset,axiom, % 173.22/173.18 ! [V_A_2,V_B_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Diff__subset__Int,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,T_a] : % 173.22/173.18 ( 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))) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__card__le__card__Diff,axiom, % 173.22/173.18 ! [V_A_2,V_B_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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)))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__insert,axiom, % 173.22/173.18 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum_Oinsert,axiom, % 173.22/173.18 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__psubset,axiom, % 173.22/173.18 ! [V_A_2,V_B_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.18 => ( 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))) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__Un__Int,axiom, % 173.22/173.18 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__insert,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)))))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Diff1__le,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_inj__on__iff__card__le,axiom, % 173.22/173.18 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.18 => ( ? [B_f] : % 173.22/173.18 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 173.22/173.18 & 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)) ) % 173.22/173.18 <=> 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__inj__on__le,axiom, % 173.22/173.18 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.18 => ( 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)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum_Oinsert__remove,axiom, % 173.22/173.18 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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)))))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__Un__disjoint,axiom, % 173.22/173.18 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => ( 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)) % 173.22/173.18 => 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)) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__Un,axiom, % 173.22/173.18 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Oab__group__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__Un__nat,axiom, % 173.22/173.18 ! [V_f_2,V_B_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.18 => 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__cases,axiom, % 173.22/173.18 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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))))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 173.22/173.18 ! [V_y,V_x,T_a] : % 173.22/173.18 ( class_Rings_Ocomm__ring__1(T_a) % 173.22/173.18 => 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)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_comm__monoid__big_OF__eq,axiom, % 173.22/173.18 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.18 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 173.22/173.18 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => 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) ) % 173.22/173.18 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.18 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_finite__fun__UNIVD1,axiom, % 173.22/173.18 ! [T_b,T_a] : % 173.22/173.18 ( 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)))) % 173.22/173.18 => ( 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)) % 173.22/173.18 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Diff__singleton,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__Diff__singleton__if,axiom, % 173.22/173.18 ! [V_x_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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)) ) % 173.22/173.18 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__Min__commute,axiom, % 173.22/173.18 ! [V_k_2,V_N_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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))))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__Max__commute,axiom, % 173.22/173.18 ! [V_k_2,V_N_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.18 => 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))))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__multicount__gen,axiom, % 173.22/173.18 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 173.22/173.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 173.22/173.18 => ( ! [B_x] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 173.22/173.18 => 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) ) % 173.22/173.18 => 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) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__zeroE,axiom, % 173.22/173.18 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le0,axiom, % 173.22/173.18 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_zero__less__Suc,axiom, % 173.22/173.18 ! [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))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__UNIV__unit,axiom, % 173.22/173.18 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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__0__iff,axiom, % 173.22/173.18 ! [V_a_2,V_b_2,T_a] : % 173.22/173.18 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 173.22/173.18 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 173.22/173.18 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__eq__self__zero,axiom, % 173.22/173.18 ! [V_n,V_m] : % 173.22/173.18 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 173.22/173.18 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__add__right__cancel,axiom, % 173.22/173.18 ! [V_n_2,V_k_2,V_m_2] : % 173.22/173.18 ( 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) % 173.22/173.18 <=> V_m_2 = V_n_2 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__add__left__cancel,axiom, % 173.22/173.18 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.18 ( 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) % 173.22/173.18 <=> V_m_2 = V_n_2 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__add__assoc,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__is__0,axiom, % 173.22/173.18 ! [V_n_2,V_m_2] : % 173.22/173.18 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__add__left__commute,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__add__commute,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Nat_Oadd__0__right,axiom, % 173.22/173.18 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 173.22/173.18 % 173.22/173.18 fof(fact_plus__nat_Oadd__0,axiom, % 173.22/173.18 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 173.22/173.18 % 173.22/173.18 fof(fact_bot__nat__def,axiom, % 173.22/173.18 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.18 % 173.22/173.18 fof(fact_One__nat__def,axiom, % 173.22/173.18 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_one__reorient,axiom, % 173.22/173.18 ! [V_x_2,T_a] : % 173.22/173.18 ( class_Groups_Oone(T_a) % 173.22/173.18 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 173.22/173.18 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_zero__reorient,axiom, % 173.22/173.18 ! [V_x_2,T_a] : % 173.22/173.18 ( class_Groups_Ozero(T_a) % 173.22/173.18 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 173.22/173.18 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card_Oeq__fold__g,axiom, % 173.22/173.18 ! [V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_card__def,axiom, % 173.22/173.18 ! [V_A_2,T_a] : % 173.22/173.18 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => 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) ) % 173.22/173.18 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__eq__if,axiom, % 173.22/173.18 ! [V_n,V_m] : % 173.22/173.18 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 173.22/173.18 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 => 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)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__eq__1__iff,axiom, % 173.22/173.18 ! [V_f_2,V_A_2,T_a] : % 173.22/173.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.18 => ( 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) % 173.22/173.18 <=> ? [B_x] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.18 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.22/173.18 & ! [B_xa] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 173.22/173.18 => ( B_x != B_xa % 173.22/173.18 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Suc__eq__plus1,axiom, % 173.22/173.18 ! [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)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Suc__eq__plus1__left,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__0__left,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Groups_Omonoid__add(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__0,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_double__zero__sym,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 173.22/173.18 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__0__right,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Groups_Omonoid__add(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add_Ocomm__neutral,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_right__minus__eq,axiom, % 173.22/173.18 ! [V_b_2,V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.18 <=> V_a_2 = V_b_2 ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_eq__iff__diff__eq__0,axiom, % 173.22/173.18 ! [V_b_2,V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Oab__group__add(T_a) % 173.22/173.18 => ( V_a_2 = V_b_2 % 173.22/173.18 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__self,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__0__right,axiom, % 173.22/173.18 ! [V_a,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_neg__equal__zero,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 173.22/173.18 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_neg__equal__0__iff__equal,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.18 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_equal__neg__zero,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 173.22/173.18 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_neg__0__equal__iff__equal,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 173.22/173.18 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_minus__zero,axiom, % 173.22/173.18 ! [T_a] : % 173.22/173.18 ( class_Groups_Ogroup__add(T_a) % 173.22/173.18 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Suc__neq__Zero,axiom, % 173.22/173.18 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Zero__neq__Suc,axiom, % 173.22/173.18 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat_Osimps_I3_J,axiom, % 173.22/173.18 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Suc__not__Zero,axiom, % 173.22/173.18 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat_Osimps_I2_J,axiom, % 173.22/173.18 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Zero__not__Suc,axiom, % 173.22/173.18 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__is__1,axiom, % 173.22/173.18 ! [V_n_2,V_m_2] : % 173.22/173.18 ( 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)) % 173.22/173.18 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.22/173.18 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.18 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_one__is__add,axiom, % 173.22/173.18 ! [V_n_2,V_m_2] : % 173.22/173.18 ( 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) % 173.22/173.18 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.22/173.18 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.18 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_not__less0,axiom, % 173.22/173.18 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_neq0__conv,axiom, % 173.22/173.18 ! [V_n_2] : % 173.22/173.18 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__nat__zero__code,axiom, % 173.22/173.18 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 173.22/173.18 % 173.22/173.18 fof(fact_gr__implies__not0,axiom, % 173.22/173.18 ! [V_n,V_m] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.18 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_gr0I,axiom, % 173.22/173.18 ! [V_n] : % 173.22/173.18 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__gr__0,axiom, % 173.22/173.18 ! [V_n_2,V_m_2] : % 173.22/173.18 ( 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))) % 173.22/173.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 173.22/173.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 173.22/173.18 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__0__eq,axiom, % 173.22/173.18 ! [V_n_2] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 173.22/173.18 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__0__eq__0,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_minus__nat_Odiff__0,axiom, % 173.22/173.18 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__self__eq__0,axiom, % 173.22/173.18 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diffs0__imp__equal,axiom, % 173.22/173.18 ! [V_n,V_m] : % 173.22/173.18 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.18 => V_m = V_n ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__add__0,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.18 fof(fact_nat__case__0,axiom, % 173.22/173.18 ! [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 ). % 173.22/173.18 % 173.22/173.18 fof(fact_Suc__diff__1,axiom, % 173.22/173.18 ! [V_n] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_Suc__pred_H,axiom, % 173.22/173.18 ! [V_n] : % 173.22/173.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.18 => 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))) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_setsum__0,axiom, % 173.22/173.18 ! [V_A_2,T_b,T_a] : % 173.22/173.18 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.18 => 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) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 173.22/173.18 ! [V_i_2,V_inc_2,T_a] : % 173.22/173.18 ( class_Rings_Osemiring__1(T_a) % 173.22/173.18 => 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 ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__nonneg__nonneg,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__nonneg__eq__0__iff,axiom, % 173.22/173.18 ! [V_y_2,V_x_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 173.22/173.18 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.18 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.18 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__increasing,axiom, % 173.22/173.18 ! [V_c,V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__increasing2,axiom, % 173.22/173.18 ! [V_a,V_b,V_c,T_a] : % 173.22/173.18 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__nonpos__nonpos,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__pos__pos,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_add__neg__neg,axiom, % 173.22/173.18 ! [V_b,V_a,T_a] : % 173.22/173.18 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.18 => 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))) ) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__iff__diff__le__0,axiom, % 173.22/173.18 ! [V_b_2,V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 173.22/173.18 <=> 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_less__iff__diff__less__0,axiom, % 173.22/173.18 ! [V_b_2,V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 173.22/173.18 <=> 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))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_minus__le__self__iff,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( 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)) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_neg__le__0__iff__le,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_le__minus__self__iff,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_neg__0__le__iff__le,axiom, % 173.22/173.18 ! [V_a_2,T_a] : % 173.22/173.18 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.18 => ( 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))) % 173.22/173.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__Suc__1,axiom, % 173.22/173.18 ! [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 ). % 173.22/173.18 % 173.22/173.18 fof(fact_diff__Suc__eq__diff__pred,axiom, % 173.22/173.18 ! [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) ). % 173.22/173.18 % 173.22/173.19 fof(fact_neg__0__less__iff__less,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_neg__less__0__iff__less,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_neg__less__nonneg,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_minus__Max__eq__Min,axiom, % 173.22/173.19 ! [V_S_2,T_a] : % 173.22/173.19 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_minus__Min__eq__Max,axiom, % 173.22/173.19 ! [V_S_2,T_a] : % 173.22/173.19 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_minus__unique,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Ogroup__add(T_a) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_ab__left__minus,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Oab__group__add(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_left__minus,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Ogroup__add(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_eq__neg__iff__add__eq__0,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Groups_Ogroup__add(T_a) % 173.22/173.19 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 173.22/173.19 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_right__minus,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Ogroup__add(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__0,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Ogroup__add(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__empty,axiom, % 173.22/173.19 ! [V_f_2,T_b,T_a] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum_Oempty,axiom, % 173.22/173.19 ! [V_g_2,T_b,T_a] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum_Oinfinite,axiom, % 173.22/173.19 ! [V_g_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__infinite,axiom, % 173.22/173.19 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_less__Suc__eq__0__disj,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.22/173.19 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 | ? [B_j] : % 173.22/173.19 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_less__Suc0,axiom, % 173.22/173.19 ! [V_n_2] : % 173.22/173.19 ( 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)))) % 173.22/173.19 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_gr0__conv__Suc,axiom, % 173.22/173.19 ! [V_n_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.22/173.19 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card_Oempty,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__infinite,axiom, % 173.22/173.19 ! [V_A_2,T_a] : % 173.22/173.19 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__less__diff,axiom, % 173.22/173.19 ! [V_m_2,V_n_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__less,axiom, % 173.22/173.19 ! [V_m,V_n] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.22/173.19 => 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__diff__split,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_P_2] : % 173.22/173.19 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 173.22/173.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 173.22/173.19 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.22/173.19 & ! [B_d] : % 173.22/173.19 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 173.22/173.19 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__diff__split__asm,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_P_2] : % 173.22/173.19 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 173.22/173.19 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 173.22/173.19 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.22/173.19 | ? [B_d] : % 173.22/173.19 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 173.22/173.19 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__is__0__eq,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__is__0__eq_H,axiom, % 173.22/173.19 ! [V_n,V_m] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.19 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Max_Osingleton,axiom, % 173.22/173.19 ! [V_x_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => 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 ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Min_Osingleton,axiom, % 173.22/173.19 ! [V_x_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => 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 ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__eq__0__iff,axiom, % 173.22/173.19 ! [V_f_2,V_F_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> ! [B_x] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 173.22/173.19 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_funpow_Osimps_I1_J,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__Suc,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__eq__setsum,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__pos__nonneg,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__nonneg__pos,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__strict__increasing,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__strict__increasing2,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__neg__nonpos,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__nonpos__neg,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 173.22/173.19 ! [V_d,V_c,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 173.22/173.19 ! [V_d,V_c,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 173.22/173.19 ! [V_c,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__eq__0__iff,axiom, % 173.22/173.19 ! [V_A_2,T_a] : % 173.22/173.19 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__ge__0__finite,axiom, % 173.22/173.19 ! [V_A_2,T_a] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__Suc__less,axiom, % 173.22/173.19 ! [V_i,V_n] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Suc__pred,axiom, % 173.22/173.19 ! [V_n] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.19 => 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 ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Max__ge,axiom, % 173.22/173.19 ! [V_x_2,V_A_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Min__le,axiom, % 173.22/173.19 ! [V_x_2,V_A_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Max__in,axiom, % 173.22/173.19 ! [V_A_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Min__in,axiom, % 173.22/173.19 ! [V_A_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__eq__Suc0__iff,axiom, % 173.22/173.19 ! [V_f_2,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( 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)) % 173.22/173.19 <=> ? [B_x] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.19 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.22/173.19 & ! [B_xa] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 173.22/173.19 => ( B_x != B_xa % 173.22/173.19 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__delta,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.19 => 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) ) % 173.22/173.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.19 => 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) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__delta_H,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.19 => 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) ) % 173.22/173.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.19 => 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) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__less__Suc,axiom, % 173.22/173.19 ! [V_i_2,V_M_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 173.22/173.19 => 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))))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__less,axiom, % 173.22/173.19 ! [V_i_2,V_M_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__less__Suc2,axiom, % 173.22/173.19 ! [V_i_2,V_M_2] : % 173.22/173.19 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 173.22/173.19 => 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))))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card_Oinsert,axiom, % 173.22/173.19 ! [V_x_2,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.19 => 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__gt__0__iff,axiom, % 173.22/173.19 ! [V_A_2,T_a] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_finite__UNIV__card__ge__0,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.19 => 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))))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum_OF__eq,axiom, % 173.22/173.19 ! [V_g_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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) ) % 173.22/173.19 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum_Oeq__fold,axiom, % 173.22/173.19 ! [V_g_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Min__antimono,axiom, % 173.22/173.19 ! [V_N_2,V_M_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 173.22/173.19 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.19 => 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))) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Max__mono,axiom, % 173.22/173.19 ! [V_N_2,V_M_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 173.22/173.19 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.19 => 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))) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__monoid__big_Oinfinite,axiom, % 173.22/173.19 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.19 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 173.22/173.19 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.19 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__restrict__set_H,axiom, % 173.22/173.19 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__restrict__set,axiom, % 173.22/173.19 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card_Oinsert__remove,axiom, % 173.22/173.19 ! [V_x_2,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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)))))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card_Oremove,axiom, % 173.22/173.19 ! [V_x_2,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.19 => 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)))))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__Diff__insert,axiom, % 173.22/173.19 ! [V_B_2,V_a_2,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_triple_Osize_I1_J,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__less__two,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => 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)))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_less__add__one,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => 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)))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_less__minus__self__iff,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_not__one__less__zero,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__less__one,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_vname_Osize_I1_J,axiom, % 173.22/173.19 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_linorder__neqE__linordered__idom,axiom, % 173.22/173.19 ! [V_y,V_x,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( V_x != V_y % 173.22/173.19 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_one__neq__zero,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Ozero__neq__one(T_a) % 173.22/173.19 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__neq__one,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Ozero__neq__one(T_a) % 173.22/173.19 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_vname_Osize_I2_J,axiom, % 173.22/173.19 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_pos__add__strict,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__le__one,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_not__one__le__zero,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => ~ 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_even__less__0__iff,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_triple_Osize_I2_J,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card_Ounion__inter__neutral,axiom, % 173.22/173.19 ! [V_B_2,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.19 => ( ( ? [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))) % 173.22/173.19 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__mono2,axiom, % 173.22/173.19 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Oordered__comm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.19 => ( ! [B_b] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 173.22/173.19 => 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))) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_vname_Osize_I3_J,axiom, % 173.22/173.19 ! [V_glb] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__Un__zero,axiom, % 173.22/173.19 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 173.22/173.19 => 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)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum_Ounion__inter__neutral,axiom, % 173.22/173.19 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 173.22/173.19 => 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)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_double__eq__0__iff,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_vname_Osize_I4_J,axiom, % 173.22/173.19 ! [V_loc] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__Suc__eq,axiom, % 173.22/173.19 ! [V_k_2,V_A_2,T_a] : % 173.22/173.19 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 173.22/173.19 <=> ? [B_b,B_B] : % 173.22/173.19 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 173.22/173.19 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 173.22/173.19 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 173.22/173.19 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__mono3,axiom, % 173.22/173.19 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 173.22/173.19 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 173.22/173.19 => 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))) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__reindex__nonzero,axiom, % 173.22/173.19 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_c) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 173.22/173.19 => ! [B_y] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 173.22/173.19 => ( B_x != B_y % 173.22/173.19 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 173.22/173.19 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 173.22/173.19 => 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) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__odd__less__0,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I4_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I3_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I5_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__0,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Oring__1(T_a) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__add,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oring__1(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__diff,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oring__1(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__1,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Rings_Oring__1(T_a) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__minus,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oring__1(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I2_J,axiom, % 173.22/173.19 ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I1_J,axiom, % 173.22/173.19 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__double__eq__0__iff,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Int_Oring__char__0(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__odd__nonzero,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Int_Oring__char__0(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I6_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__Plus__conv__if,axiom, % 173.22/173.19 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.19 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 173.22/173.19 => 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)) ) % 173.22/173.19 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 173.22/173.19 => 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I11_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I12_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I13_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I14_J,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__nonneg__leq__bound,axiom, % 173.22/173.19 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Oordered__ab__group__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 173.22/173.19 => ( ! [B_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 173.22/173.19 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__nonneg__0,axiom, % 173.22/173.19 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Oordered__ab__group__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 173.22/173.19 => ( ! [B_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 173.22/173.19 => ( 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) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 173.22/173.19 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I10_J,axiom, % 173.22/173.19 ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_com_Osize_I9_J,axiom, % 173.22/173.19 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.19 % 173.22/173.19 fof(fact_finite__PlusD_I2_J,axiom, % 173.22/173.19 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_finite__PlusD_I1_J,axiom, % 173.22/173.19 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_finite__Plus,axiom, % 173.22/173.19 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_finite__Plus__iff,axiom, % 173.22/173.19 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__Plus,axiom, % 173.22/173.19 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.19 => 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_UNIV__Plus__UNIV,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Plus__eq__empty__conv,axiom, % 173.22/173.19 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.19 ( 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)) % 173.22/173.19 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.19 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_ex__least__nat__less,axiom, % 173.22/173.19 ! [V_n_2,V_P_2] : % 173.22/173.19 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 173.22/173.19 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 173.22/173.19 => ? [B_k] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 173.22/173.19 & ! [B_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 173.22/173.19 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 173.22/173.19 & 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)))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__mono__zero__right,axiom, % 173.22/173.19 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 173.22/173.19 => 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) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__mono__zero__left,axiom, % 173.22/173.19 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 173.22/173.19 => 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) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_fold__Un__disjoint,axiom, % 173.22/173.19 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.19 => ( 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)) % 173.22/173.19 => 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)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 173.22/173.19 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 173.22/173.19 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 173.22/173.19 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 173.22/173.19 ! [V_rx,V_ly,V_lx,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 173.22/173.19 ! [V_rx,V_ly,V_lx,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 173.22/173.19 ! [V_ry,V_rx,V_lx,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 173.22/173.19 ! [V_ry,V_rx,V_lx,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__left__idem,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__idem,axiom, % 173.22/173.19 ! [V_x,T_a] : % 173.22/173.19 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_times_Oidem,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_divisors__zero,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ono__zero__divisors(T_a) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_no__zero__divisors,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ono__zero__divisors(T_a) % 173.22/173.19 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__eq__0__iff,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oring__no__zero__divisors(T_a) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__zero__right,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Omult__zero(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__zero__left,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Omult__zero(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__class_Odistrib,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_combine__common__factor,axiom, % 173.22/173.19 ! [V_c,V_b,V_e,V_a,T_a] : % 173.22/173.19 ( class_Rings_Osemiring(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_crossproduct__eq,axiom, % 173.22/173.19 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 173.22/173.19 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 173.22/173.19 => ( 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)) % 173.22/173.19 <=> ( V_w_2 = V_x_2 % 173.22/173.19 | V_y_2 = V_z_2 ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 173.22/173.19 ! [V_b,V_m,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_crossproduct__noteq,axiom, % 173.22/173.19 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 173.22/173.19 => ( ( V_a_2 != V_b_2 % 173.22/173.19 & V_ca_2 != V_d_2 ) % 173.22/173.19 <=> 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 173.22/173.19 ! [V_z,V_y,V_x,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult_Ocomm__neutral,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__1__right,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__1,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__1__left,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__cancel2,axiom, % 173.22/173.19 ! [V_n_2,V_k_2,V_m_2] : % 173.22/173.19 ( 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) % 173.22/173.19 <=> ( V_m_2 = V_n_2 % 173.22/173.19 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( 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) % 173.22/173.19 <=> ( V_m_2 = V_n_2 % 173.22/173.19 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__is__0,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__0__right,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__0,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_square__eq__iff,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oidom(T_a) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> ( V_a_2 = V_b_2 % 173.22/173.19 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_minus__mult__minus,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oring(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_minus__mult__commute,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oring(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_minus__mult__left,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oring(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_minus__mult__right,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oring(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Suc__mult__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( 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) % 173.22/173.19 <=> V_m_2 = V_n_2 ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__mult__distrib2,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__mult__distrib,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__mono,axiom, % 173.22/173.19 ! [V_l,V_k,V_j,V_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__mono2,axiom, % 173.22/173.19 ! [V_k,V_j,V_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.19 => 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__mono1,axiom, % 173.22/173.19 ! [V_k,V_j,V_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.19 => 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_le__cube,axiom, % 173.22/173.19 ! [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)))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_le__square,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__mult__distrib,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_diff__mult__distrib2,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__eq__1__iff,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.22/173.19 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.22/173.19 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__1__right,axiom, % 173.22/173.19 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__1__eq__mult__iff,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 173.22/173.19 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.22/173.19 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__1,axiom, % 173.22/173.19 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 173.22/173.19 % 173.22/173.19 fof(fact_funpow__mult,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__right__distrib,axiom, % 173.22/173.19 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 173.22/173.19 ( class_Rings_Osemiring__0(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__left__distrib,axiom, % 173.22/173.19 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.19 ( class_Rings_Osemiring__0(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__product,axiom, % 173.22/173.19 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.19 ( class_Rings_Osemiring__0(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_split__mult__neg__le,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.22/173.19 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 173.22/173.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_split__mult__pos__le,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 173.22/173.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__mono,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__mono_H,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__left__mono__neg,axiom, % 173.22/173.19 ! [V_c,V_a,V_b,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__right__mono__neg,axiom, % 173.22/173.19 ! [V_c,V_a,V_b,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__mult__left__mono,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__comm__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__left__mono,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__right__mono,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__nonpos__nonpos,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__nonpos__nonneg,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__nonneg__nonpos2,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__nonneg__nonpos,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__nonneg__nonneg,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__0__iff,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 173.22/173.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__le__mult__iff,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 173.22/173.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__le__square,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring(T_a) % 173.22/173.19 => 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__strict__left__mono__neg,axiom, % 173.22/173.19 ! [V_c,V_a,V_b,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__strict__right__mono__neg,axiom, % 173.22/173.19 ! [V_c,V_a,V_b,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__mult__strict__left__mono,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__strict__left__mono,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__strict__right__mono,axiom, % 173.22/173.19 ! [V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__neg__neg,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__neg__pos,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__cancel__left__neg,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__less__mult__pos2,axiom, % 173.22/173.19 ! [V_a,V_b,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_zero__less__mult__pos,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__pos__neg2,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__pos__neg,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__pos__pos,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__cancel__left__pos,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__cancel__left__disj,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 173.22/173.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__cancel__right__disj,axiom, % 173.22/173.19 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 173.22/173.19 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_not__square__less__zero,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring(T_a) % 173.22/173.19 => ~ 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_add__scale__eq__noteq,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 173.22/173.19 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 173.22/173.19 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 => ( ( V_a = V_b % 173.22/173.19 & V_c != V_d ) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sum__squares__eq__zero__iff,axiom, % 173.22/173.19 ! [V_y_2,V_x_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_less__1__mult,axiom, % 173.22/173.19 ! [V_n,V_m,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_eq__add__iff1,axiom, % 173.22/173.19 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oring(T_a) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> 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 ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_eq__add__iff2,axiom, % 173.22/173.19 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oring(T_a) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 173.22/173.19 ! [V_m,V_a,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 173.22/173.19 ! [V_a,V_m,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 173.22/173.19 ! [V_m,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_square__eq__1__iff,axiom, % 173.22/173.19 ! [V_x_2,T_a] : % 173.22/173.19 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 173.22/173.19 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 173.22/173.19 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 173.22/173.19 ! [V_x,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__ring__1(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__eq__1__iff,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( 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)) % 173.22/173.19 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.22/173.19 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__0__less__mult__iff,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__cancel2,axiom, % 173.22/173.19 ! [V_n_2,V_k_2,V_m_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.22/173.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__mono1,axiom, % 173.22/173.19 ! [V_k,V_j,V_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__mono2,axiom, % 173.22/173.19 ! [V_k,V_j,V_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Suc__mult__less__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__Suc__right,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__Suc,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Suc__mult__le__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__eq__self__implies__10,axiom, % 173.22/173.19 ! [V_n,V_m] : % 173.22/173.19 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 173.22/173.19 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.22/173.19 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_Ints__mult,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oring__1(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__cancel__left__pos,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__cancel__left__neg,axiom, % 173.22/173.19 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__strict__mono,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__strict__mono_H,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__le__imp__less,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__less__imp__less,axiom, % 173.22/173.19 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => 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))) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__right__less__imp__less,axiom, % 173.22/173.19 ! [V_b,V_c,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__imp__less__right,axiom, % 173.22/173.19 ! [V_b,V_c,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__left__less__imp__less,axiom, % 173.22/173.19 ! [V_b,V_a,V_c,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__less__imp__less__left,axiom, % 173.22/173.19 ! [V_b,V_a,V_c,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__right__le__imp__le,axiom, % 173.22/173.19 ! [V_b,V_c,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__left__le__imp__le,axiom, % 173.22/173.19 ! [V_b,V_a,V_c,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sum__squares__ge__zero,axiom, % 173.22/173.19 ! [V_y,V_x,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring(T_a) % 173.22/173.19 => 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)))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sum__squares__le__zero__iff,axiom, % 173.22/173.19 ! [V_y_2,V_x_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_not__sum__squares__lt__zero,axiom, % 173.22/173.19 ! [V_y,V_x,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring(T_a) % 173.22/173.19 => ~ 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sum__squares__gt__zero__iff,axiom, % 173.22/173.19 ! [V_y_2,V_x_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__ring__strict(T_a) % 173.22/173.19 => ( 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)))) % 173.22/173.19 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__left__le__one__le,axiom, % 173.22/173.19 ! [V_y,V_x,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 173.22/173.19 => 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)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__right__le__one__le,axiom, % 173.22/173.19 ! [V_y,V_x,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 173.22/173.19 => 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)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_le__add__iff1,axiom, % 173.22/173.19 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_le__add__iff2,axiom, % 173.22/173.19 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_less__add__iff2,axiom, % 173.22/173.19 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_less__add__iff1,axiom, % 173.22/173.19 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Oordered__ring(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_n__less__m__mult__n,axiom, % 173.22/173.19 ! [V_m,V_n] : % 173.22/173.19 ( 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)) % 173.22/173.19 => ( 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)) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_n__less__n__mult__m,axiom, % 173.22/173.19 ! [V_m,V_n] : % 173.22/173.19 ( 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)) % 173.22/173.19 => ( 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)) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_one__less__mult,axiom, % 173.22/173.19 ! [V_m,V_n] : % 173.22/173.19 ( 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)) % 173.22/173.19 => ( 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)) % 173.22/173.19 => 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_one__le__mult__iff,axiom, % 173.22/173.19 ! [V_n_2,V_m_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( 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)) % 173.22/173.19 & 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__le__cancel2,axiom, % 173.22/173.19 ! [V_n_2,V_k_2,V_m_2] : % 173.22/173.19 ( 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))) % 173.22/173.19 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.22/173.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_fold__image__distrib,axiom, % 173.22/173.19 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_convex__bound__le,axiom, % 173.22/173.19 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__1(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 173.22/173.19 => 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)) ) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_fold__image__insert,axiom, % 173.22/173.19 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Oab__semigroup__mult(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_mult__eq__if,axiom, % 173.22/173.19 ! [V_n,V_m] : % 173.22/173.19 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.19 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 => 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_convex__bound__lt,axiom, % 173.22/173.19 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 173.22/173.19 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 173.22/173.19 => 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)) ) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_fold__image__Un__Int,axiom, % 173.22/173.19 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.19 => 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))) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_fold__image__reindex,axiom, % 173.22/173.19 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 173.22/173.19 ( class_Groups_Oab__semigroup__mult(T_c) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.19 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 173.22/173.19 => 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) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__less__add__iff2,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__less__add__iff1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__le__add__iff1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__diff__add__eq1,axiom, % 173.22/173.19 ! [V_n,V_m,V_u,V_i,V_j] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__eq__add__iff1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> 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 ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__le__add__iff2,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> 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))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__assoc,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__commute,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__eq__cancel__disj,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( 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) % 173.22/173.19 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.19 | V_m_2 = V_n_2 ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_left__add__mult__distrib,axiom, % 173.22/173.19 ! [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) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__eq__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> V_m_2 = V_n_2 ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__less__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__mult__le__cancel1,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_k_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__eq__add__iff2,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.22/173.19 => ( 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) % 173.22/173.19 <=> 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) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_nat__diff__add__eq2,axiom, % 173.22/173.19 ! [V_n,V_m,V_u,V_j,V_i] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__multicount,axiom, % 173.22/173.19 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 173.22/173.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 173.22/173.19 => 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 ) % 173.22/173.19 => 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)) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_fold__image__Un__one,axiom, % 173.22/173.19 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 173.22/173.19 => ( ! [B_x] : % 173.22/173.19 ( 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))) % 173.22/173.19 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 173.22/173.19 => 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)) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_arith__series__nat,axiom, % 173.22/173.19 ! [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)))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__if,axiom, % 173.22/173.19 ! [V_x,T_a] : % 173.22/173.19 ( class_Groups_Osgn__if(T_a) % 173.22/173.19 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 173.22/173.19 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.19 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 173.22/173.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.19 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__neg,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.19 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__1__neg,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( 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)) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_finite__lessThan,axiom, % 173.22/173.19 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_lessThan__eq__iff,axiom, % 173.22/173.19 ! [V_y_2,V_x_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 173.22/173.19 <=> V_x_2 = V_y_2 ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__sgn,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_lessThan__0,axiom, % 173.22/173.19 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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_lessThan__Suc,axiom, % 173.22/173.19 ! [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)) ). % 173.22/173.19 % 173.22/173.19 fof(fact_card__lessThan,axiom, % 173.22/173.19 ! [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 ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__0__0,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.19 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn0,axiom, % 173.22/173.19 ! [T_a] : % 173.22/173.19 ( class_Groups_Osgn__if(T_a) % 173.22/173.19 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__times,axiom, % 173.22/173.19 ! [V_b,V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 173.22/173.19 ! [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))) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__lessThan__Suc,axiom, % 173.22/173.19 ! [V_n_2,V_f_2,T_a] : % 173.22/173.19 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_lessThan__iff,axiom, % 173.22/173.19 ! [V_k_2,V_i_2,T_a] : % 173.22/173.19 ( class_Orderings_Oord(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_lessThan__subset__iff,axiom, % 173.22/173.19 ! [V_y_2,V_x_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__less,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__greater,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_lessThan__strict__subset__iff,axiom, % 173.22/173.19 ! [V_n_2,V_m_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => ( 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))) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_single__Diff__lessThan,axiom, % 173.22/173.19 ! [V_k_2,T_a] : % 173.22/173.19 ( class_Orderings_Oorder(T_a) % 173.22/173.19 => 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))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__pos,axiom, % 173.22/173.19 ! [V_a,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.19 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sgn__1__pos,axiom, % 173.22/173.19 ! [V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.19 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 173.22/173.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_arith__series__general,axiom, % 173.22/173.19 ! [V_n_2,V_d_2,V_a_2,T_a] : % 173.22/173.19 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.19 => 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)))) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_sum__diff__distrib,axiom, % 173.22/173.19 ! [V_n_2,V_P_2,V_Q_2] : % 173.22/173.19 ( ! [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))) % 173.22/173.19 => 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)) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_setsum__natinterval__difff,axiom, % 173.22/173.19 ! [V_f_2,V_n_2,V_m_2,T_a] : % 173.22/173.19 ( class_Groups_Oab__group__add(T_a) % 173.22/173.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.19 => 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)))) ) % 173.22/173.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.19 => 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) ) ) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_ivl__disj__un_I2_J,axiom, % 173.22/173.19 ! [V_u_2,T_a] : % 173.22/173.19 ( class_Orderings_Olinorder(T_a) % 173.22/173.19 => 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) ) ). % 173.22/173.19 % 173.22/173.19 fof(fact_fold__graph__permute__diff,axiom, % 173.22/173.19 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 173.22/173.20 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Oremove,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 173.22/173.20 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => 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)))))) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_negative__zless,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__atMost,axiom, % 173.22/173.20 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__atLeastAtMost,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeast0AtMost,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Oidem,axiom, % 173.22/173.20 ! [V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__eq__iff,axiom, % 173.22/173.20 ! [V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Nat_Osemiring__char__0(T_a) % 173.22/173.20 => ( 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) % 173.22/173.20 <=> V_m_2 = V_n_2 ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf_Oidem,axiom, % 173.22/173.20 ! [V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf_Ocommute,axiom, % 173.22/173.20 ! [V_b,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__commute,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 173.22/173.20 ! [V_b,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__left__idem,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 173.22/173.20 ! [V_c,V_a,V_b,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__left__commute,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf_Oassoc,axiom, % 173.22/173.20 ! [V_c,V_b,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__assoc,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atMost__eq__iff,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 173.22/173.20 <=> V_x_2 = V_y_2 ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Int__atLeastAtMostL1,axiom, % 173.22/173.20 ! [V_d_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Int__atLeastAtMostR1,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__le__iff__disj,axiom, % 173.22/173.20 ! [V_z_2,V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 173.22/173.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__le1,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__le2,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__iff__inf,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.20 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__inf__iff,axiom, % 173.22/173.20 ! [V_z_2,V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__infI1,axiom, % 173.22/173.20 ! [V_b,V_x,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__infI2,axiom, % 173.22/173.20 ! [V_a,V_x,V_b,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__absorb1,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__absorb2,axiom, % 173.22/173.20 ! [V_x,V_y,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__infI,axiom, % 173.22/173.20 ! [V_b,V_a,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__greatest,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__mono,axiom, % 173.22/173.20 ! [V_d,V_b,V_c,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__infE,axiom, % 173.22/173.20 ! [V_b,V_a,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.22/173.20 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__less__iff__conj,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,V_z_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__less__iff__disj,axiom, % 173.22/173.20 ! [V_z_2,V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 173.22/173.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oless__infI1,axiom, % 173.22/173.20 ! [V_b,V_x,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oless__infI2,axiom, % 173.22/173.20 ! [V_a,V_x,V_b,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__add__distrib__left,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__diff__distrib__left,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_inf__min,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.20 & class_Orderings_Olinorder(T_a) ) % 173.22/173.20 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__0L,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__0R,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__Suc__Suc,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__le__0__conv,axiom, % 173.22/173.20 ! [V_n_2] : % 173.22/173.20 ( 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))) % 173.22/173.20 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__zle__neg,axiom, % 173.22/173.20 ! [V_m_2,V_n_2] : % 173.22/173.20 ( 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)))) % 173.22/173.20 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.20 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__eq__0__conv,axiom, % 173.22/173.20 ! [V_n_2] : % 173.22/173.20 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.20 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__0,axiom, % 173.22/173.20 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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_negative__eq__positive,axiom, % 173.22/173.20 ! [V_m_2,V_n_2] : % 173.22/173.20 ( 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) % 173.22/173.20 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.20 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__Suc,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_not__zle__0__negative,axiom, % 173.22/173.20 ! [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))))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_negative__zless__0,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zless__iff__Suc__zadd,axiom, % 173.22/173.20 ! [V_z_2,V_w_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 173.22/173.20 <=> ? [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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zless__int,axiom, % 173.22/173.20 ! [V_n_2,V_m_2] : % 173.22/173.20 ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__int__left,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__int,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__Suc__atLeastAtMost,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__int,axiom, % 173.22/173.20 ! [V_n_2,V_m_2] : % 173.22/173.20 ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__diff,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__int,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__mult,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__1,axiom, % 173.22/173.20 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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_inj__int,axiom, % 173.22/173.20 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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_empty__fold__graphE,axiom, % 173.22/173.20 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.20 ( 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)) % 173.22/173.20 => V_x_2 = V_z_2 ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold__graph_OemptyI,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold__graph_Oequations_I1_J,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold__graph__imp__finite,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.20 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 173.22/173.20 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atMost__0,axiom, % 173.22/173.20 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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atMost__Suc,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__add__atLeastAtMost,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__setsum,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I10_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__Suc0__eq__1,axiom, % 173.22/173.20 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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zero__less__int__conv,axiom, % 173.22/173.20 ! [V_n_2] : % 173.22/173.20 ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__zless__mono2__lemma,axiom, % 173.22/173.20 ! [V_k,V_j,V_i] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__0__le__iff,axiom, % 173.22/173.20 ! [V_n,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zero__le__imp__of__nat,axiom, % 173.22/173.20 ! [V_m,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastAtMostSuc__conv,axiom, % 173.22/173.20 ! [V_n_2,V_m_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zdiff__int,axiom, % 173.22/173.20 ! [V_m,V_n] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__less__0__iff,axiom, % 173.22/173.20 ! [V_m,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => ~ 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__0,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__less__iff,axiom, % 173.22/173.20 ! [V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_less__imp__of__nat__less,axiom, % 173.22/173.20 ! [V_n,V_m,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__less__imp__less,axiom, % 173.22/173.20 ! [V_n,V_m,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__le__iff,axiom, % 173.22/173.20 ! [V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__add,axiom, % 173.22/173.20 ! [V_n,V_m,T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__mult,axiom, % 173.22/173.20 ! [V_n,V_m,T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__1,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Ints__of__nat,axiom, % 173.22/173.20 ! [V_n_2,T_a] : % 173.22/173.20 ( class_Rings_Oring__1(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastatMost__empty__iff2,axiom, % 173.22/173.20 ! [V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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) % 173.22/173.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastatMost__empty__iff,axiom, % 173.22/173.20 ! [V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastatMost__empty,axiom, % 173.22/173.20 ! [V_a_2,V_b_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastatMost__subset__iff,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 173.22/173.20 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastAtMost__singleton,axiom, % 173.22/173.20 ! [V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastAtMost__singleton__iff,axiom, % 173.22/173.20 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> ( V_a_2 = V_b_2 % 173.22/173.20 & V_b_2 = V_ca_2 ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastAtMost__singleton_H,axiom, % 173.22/173.20 ! [V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( V_a_2 = V_b_2 % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold__graph_OinsertI,axiom, % 173.22/173.20 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 173.22/173.20 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__uminus__atLeastAtMost,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 173.22/173.20 ! [V_n_2,V_m_2,V_f_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 173.22/173.20 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_gauss__sum,axiom, % 173.22/173.20 ! [V_n_2,T_a] : % 173.22/173.20 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__setsum,axiom, % 173.22/173.20 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_inj__of__nat,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( class_Nat_Osemiring__char__0(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_lessThan__Suc__atMost,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_card__atMost,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atMost__iff,axiom, % 173.22/173.20 ! [V_k_2,V_i_2,T_a] : % 173.22/173.20 ( class_Orderings_Oord(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atMost__subset__iff,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Oin__idem,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__Suc,axiom, % 173.22/173.20 ! [V_m,T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__diff,axiom, % 173.22/173.20 ! [V_m,V_n,T_a] : % 173.22/173.20 ( class_Rings_Oring__1(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_card__atLeastAtMost,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 173.22/173.20 ! [V_k_2,V_f_2] : % 173.22/173.20 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold__graph__insert__swap,axiom, % 173.22/173.20 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 173.22/173.20 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__constant,axiom, % 173.22/173.20 ! [V_A_2,V_y_2,T_b,T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastatMost__psubset__iff,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 173.22/173.20 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 173.22/173.20 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 173.22/173.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I4_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__Suc2,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__Suc1,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min__insert,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Osubset__idem,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.20 => 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) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min__Un,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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)) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_of__nat__0__less__iff,axiom, % 173.22/173.20 ! [V_n_2,T_a] : % 173.22/173.20 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__head__Suc,axiom, % 173.22/173.20 ! [V_f_2,V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__atMost__Suc,axiom, % 173.22/173.20 ! [V_n_2,V_f_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Diff1__fold__graph,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.20 ( 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)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Oinsert,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Oinsert__remove,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 173.22/173.20 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => 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)))))) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Ounion__inter,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Ounion__disjoint,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => 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)) ) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__cl__ivl__Suc,axiom, % 173.22/173.20 ! [V_f_2,V_m_2,V_n_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 173.22/173.20 => 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) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__ub__add__nat,axiom, % 173.22/173.20 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( 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)))) % 173.22/173.20 => 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)))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 173.22/173.20 ! [V_n_2,T_a] : % 173.22/173.20 ( class_Rings_Osemiring__1(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ex__nat__less,axiom, % 173.22/173.20 ! [V_P_2,V_n_2] : % 173.22/173.20 ( ? [B_m] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 173.22/173.20 & hBOOL(hAPP(V_P_2,B_m)) ) % 173.22/173.20 <=> ? [B_x] : % 173.22/173.20 ( 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))) % 173.22/173.20 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_all__nat__less,axiom, % 173.22/173.20 ! [V_P_2,V_n_2] : % 173.22/173.20 ( ! [B_m] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 173.22/173.20 => hBOOL(hAPP(V_P_2,B_m)) ) % 173.22/173.20 <=> ! [B_x] : % 173.22/173.20 ( 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))) % 173.22/173.20 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zdiff__int__split,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,V_P_2] : % 173.22/173.20 ( 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)))) % 173.22/173.20 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 173.22/173.20 => 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)))) ) % 173.22/173.20 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 173.22/173.20 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_dual__max,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__ord__min,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( class_Orderings_Oord(T_a) % 173.22/173.20 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold1Set_Ointros,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 173.22/173.20 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 173.22/173.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_negative__zle,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_simp__from__to,axiom, % 173.22/173.20 ! [V_i_2,V_j_2] : % 173.22/173.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 173.22/173.20 => 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)) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_inf__nat__def,axiom, % 173.22/173.20 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__iff__zadd,axiom, % 173.22/173.20 ! [V_z_2,V_w_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 173.22/173.20 <=> ? [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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_not__int__zless__negative,axiom, % 173.22/173.20 ! [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)))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__int__eq,axiom, % 173.22/173.20 ! [V_n_2,V_m_2] : % 173.22/173.20 ( 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) % 173.22/173.20 <=> V_m_2 = V_n_2 ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__less__0__conv,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_negative__zle__0,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zero__zle__int,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__1__right,axiom, % 173.22/173.20 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__1,axiom, % 173.22/173.20 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 173.22/173.20 % 173.22/173.20 fof(fact_pos__zmult__eq__1__iff,axiom, % 173.22/173.20 ! [V_n_2,V_m_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 173.22/173.20 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.22/173.20 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.22/173.20 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__zless__mono2,axiom, % 173.22/173.20 ! [V_k,V_j,V_i] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zdiff__zmult__distrib2,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zdiff__zmult__distrib,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__assoc,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__commute,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zmult__zminus,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__zmult__distrib,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__zmult__distrib2,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__add1__eq__le,axiom, % 173.22/173.20 ! [V_z_2,V_w_2] : % 173.22/173.20 ( 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)))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_add1__zle__eq,axiom, % 173.22/173.20 ! [V_z_2,V_w_2] : % 173.22/173.20 ( 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)) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_le__imp__0__less,axiom, % 173.22/173.20 ! [V_z] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zless__imp__add1__zle,axiom, % 173.22/173.20 ! [V_z,V_w] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_odd__less__0,axiom, % 173.22/173.20 ! [V_z_2] : % 173.22/173.20 ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zless__add1__eq,axiom, % 173.22/173.20 ! [V_z_2,V_w_2] : % 173.22/173.20 ( 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)))) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 173.22/173.20 | V_w_2 = V_z_2 ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__zminus__inverse2,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_odd__nonzero,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__0,axiom, % 173.22/173.20 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__0__right,axiom, % 173.22/173.20 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__0__neq__1,axiom, % 173.22/173.20 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zminus__0,axiom, % 173.22/173.20 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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__0__less__1,axiom, % 173.22/173.20 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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__diff1__eq,axiom, % 173.22/173.20 ! [V_z_2,V_w_2] : % 173.22/173.20 ( 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)))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_less__bin__lemma,axiom, % 173.22/173.20 ! [V_l_2,V_k_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 173.22/173.20 <=> 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_int__one__le__iff__zero__less,axiom, % 173.22/173.20 ! [V_z_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__refl,axiom, % 173.22/173.20 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__linear,axiom, % 173.22/173.20 ! [V_w,V_z] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 173.22/173.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__trans,axiom, % 173.22/173.20 ! [V_k,V_j,V_i] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zle__antisym,axiom, % 173.22/173.20 ! [V_w,V_z] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 173.22/173.20 => V_z = V_w ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zminus__zminus,axiom, % 173.22/173.20 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 173.22/173.20 % 173.22/173.20 fof(fact_zless__linear,axiom, % 173.22/173.20 ! [V_y,V_x] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 173.22/173.20 | V_x = V_y % 173.22/173.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zless__le,axiom, % 173.22/173.20 ! [V_w_2,V_z_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 173.22/173.20 & V_z_2 != V_w_2 ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_diff__int__def,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_diff__int__def__symmetric,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__left__mono,axiom, % 173.22/173.20 ! [V_k,V_j,V_i] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__assoc,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__left__commute,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__commute,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zminus__zadd__distrib,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__strict__right__mono,axiom, % 173.22/173.20 ! [V_k,V_j,V_i] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zadd__zless__mono,axiom, % 173.22/173.20 ! [V_z,V_z_H,V_w,V_w_H] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zsgn__def,axiom, % 173.22/173.20 ! [V_i] : % 173.22/173.20 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.20 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.22/173.20 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 173.22/173.20 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold1Set__nonempty,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,V_f_2,T_a] : % 173.22/173.20 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 173.22/173.20 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_empty__fold1SetE,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_fold1Set__sing,axiom, % 173.22/173.20 ! [V_b_2,V_a_2,V_f_2,T_a] : % 173.22/173.20 ( 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)) % 173.22/173.20 <=> V_a_2 = V_b_2 ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_self__quotient__aux1,axiom, % 173.22/173.20 ! [V_q,V_r,V_a] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_self__quotient__aux2,axiom, % 173.22/173.20 ! [V_q,V_r,V_a] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zdiv__mono2__neg__lemma,axiom, % 173.22/173.20 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 173.22/173.20 ( 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) % 173.22/173.20 => ( 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))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_unique__quotient__lemma__neg,axiom, % 173.22/173.20 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_zdiv__mono2__lemma,axiom, % 173.22/173.20 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 173.22/173.20 ( 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) % 173.22/173.20 => ( 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))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_unique__quotient__lemma,axiom, % 173.22/173.20 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__atLeastAtMost__int,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_q__pos__lemma,axiom, % 173.22/173.20 ! [V_r_H,V_q_H,V_b_H] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_q__neg__lemma,axiom, % 173.22/173.20 ! [V_r_H,V_q_H,V_b_H] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 173.22/173.20 ! [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)))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 173.22/173.20 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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 173.22/173.20 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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_infinite__UNIV__int,axiom, % 173.22/173.20 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 173.22/173.20 ! [V_y_2,V_x_2] : % 173.22/173.20 ( 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) % 173.22/173.20 <=> V_x_2 = V_y_2 ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 173.22/173.20 ! [V_B_2,V_A_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.20 <=> 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 173.22/173.20 ! [V_B_2,V_A_2] : % 173.22/173.20 ( V_A_2 = V_B_2 % 173.22/173.20 <=> 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 173.22/173.20 ! [V_B_2,V_A_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.20 <=> 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 173.22/173.20 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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 173.22/173.20 ! [V_A_2,V_x_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 173.22/173.20 <=> 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 173.22/173.20 ! [V_A_2] : % 173.22/173.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 173.22/173.20 <=> 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 173.22/173.20 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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 173.22/173.20 ! [V_y,V_x] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 173.22/173.20 ! [V_P_2] : % 173.22/173.20 ( ? [B_x] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.22/173.20 & hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.20 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 173.22/173.20 ! [V_P_2] : % 173.22/173.20 ( ! [B_x] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.22/173.20 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.20 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 173.22/173.20 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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 173.22/173.20 ! [V_y,V_x] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 173.22/173.20 ! [V_y_2,V_x_2] : % 173.22/173.20 ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 173.22/173.20 ! [V_y_2,V_x_2] : % 173.22/173.20 ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_bset_I8_J,axiom, % 173.22/173.20 ! [V_B_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 173.22/173.20 => 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))) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_aset_I6_J,axiom, % 173.22/173.20 ! [V_A_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_aset_I8_J,axiom, % 173.22/173.20 ! [V_t_2,V_A_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_bset_I6_J,axiom, % 173.22/173.20 ! [V_t_2,V_B_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_periodic__finite__ex,axiom, % 173.22/173.20 ! [V_P_2,V_d_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 173.22/173.20 => ( ! [B_x,B_k] : % 173.22/173.20 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.20 <=> 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)))) ) % 173.22/173.20 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.20 <=> ? [B_x] : % 173.22/173.20 ( 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))) % 173.22/173.20 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_bset_I3_J,axiom, % 173.22/173.20 ! [V_B_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ( ! [B_x] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xa] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 173.22/173.20 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 173.22/173.20 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_aset_I3_J,axiom, % 173.22/173.20 ! [V_A_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ( ! [B_x] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xa] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 173.22/173.20 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 173.22/173.20 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_aset_I5_J,axiom, % 173.22/173.20 ! [V_A_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_bset_I7_J,axiom, % 173.22/173.20 ! [V_B_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 173.22/173.20 => 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))) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_bset_I4_J,axiom, % 173.22/173.20 ! [V_B_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( B_x != V_t_2 % 173.22/173.20 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_aset_I4_J,axiom, % 173.22/173.20 ! [V_A_2,V_t_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( B_x != V_t_2 % 173.22/173.20 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_aset_I7_J,axiom, % 173.22/173.20 ! [V_t_2,V_A_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_bset_I5_J,axiom, % 173.22/173.20 ! [V_t_2,V_B_2,V_D_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.22/173.20 => ! [B_x] : % 173.22/173.20 ( ! [B_xa] : % 173.22/173.20 ( 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))) % 173.22/173.20 => ! [B_xb] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.22/173.20 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Min_Oclosed,axiom, % 173.22/173.20 ! [V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( ! [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)))))) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__bounded,axiom, % 173.22/173.20 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 173.22/173.20 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 173.22/173.20 & class_Rings_Osemiring__1(T_b) ) % 173.22/173.20 => ( ! [B_i] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 173.22/173.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_tsub__def,axiom, % 173.22/173.20 ! [V_x,V_y] : % 173.22/173.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 173.22/173.20 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 173.22/173.20 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 173.22/173.20 ! [V_x_2,V_y_2,V_ca_2] : % 173.22/173.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 173.22/173.20 => 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)) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 173.22/173.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 173.22/173.20 => 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))) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I5_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Oremove,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 173.22/173.20 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => 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)))))) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThan__0,axiom, % 173.22/173.20 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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__greaterThanAtMost,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__greaterThanAtMost__int,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__atLeastLessThan,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThan__eq__iff,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 173.22/173.20 <=> V_x_2 = V_y_2 ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__uminus__greaterThanAtMost,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__uminus__atLeastLessThan,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 173.22/173.20 => V_b_2 = V_d_2 ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 173.22/173.20 => V_a_2 = V_ca_2 ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__eq__iff,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 173.22/173.20 => ( 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) % 173.22/173.20 <=> ( V_a_2 = V_ca_2 % 173.22/173.20 & V_b_2 = V_d_2 ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I11_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I5_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_all__nat__less__eq,axiom, % 173.22/173.20 ! [V_P_2,V_n_2] : % 173.22/173.20 ( ! [B_m] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 173.22/173.20 => hBOOL(hAPP(V_P_2,B_m)) ) % 173.22/173.20 <=> ! [B_x] : % 173.22/173.20 ( 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))) % 173.22/173.20 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ex__nat__less__eq,axiom, % 173.22/173.20 ! [V_P_2,V_n_2] : % 173.22/173.20 ( ? [B_m] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 173.22/173.20 & hBOOL(hAPP(V_P_2,B_m)) ) % 173.22/173.20 <=> ? [B_x] : % 173.22/173.20 ( 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))) % 173.22/173.20 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__add__Un,axiom, % 173.22/173.20 ! [V_k_2,V_j_2,V_i_2] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan0,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeast0LessThan,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_card__atLeastLessThan,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__Suc__atLeastLessThan,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__empty,axiom, % 173.22/173.20 ! [V_a_2,V_b_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__empty__iff2,axiom, % 173.22/173.20 ! [V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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) % 173.22/173.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__empty__iff,axiom, % 173.22/173.20 ! [V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__subset__iff,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 173.22/173.20 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 173.22/173.20 ! [V_n_2,V_m_2,V_f_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I17_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 173.22/173.20 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__diff,axiom, % 173.22/173.20 ! [V_m_2,V_n_2,V_i_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I11_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThanAtMost__empty,axiom, % 173.22/173.20 ! [V_k_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 173.22/173.20 ! [V_l_2,V_k_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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) % 173.22/173.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThanAtMost__empty__iff,axiom, % 173.22/173.20 ! [V_l_2,V_k_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__add__atLeastLessThan,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I20_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I14_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__add__nat__ivl,axiom, % 173.22/173.20 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__diff__nat__ivl,axiom, % 173.22/173.20 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Groups_Oab__group__add(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_card__greaterThanAtMost,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThan__iff,axiom, % 173.22/173.20 ! [V_k_2,V_i_2,T_a] : % 173.22/173.20 ( class_Orderings_Oord(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThan__subset__iff,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThan__singleton,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 173.22/173.20 ! [V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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 ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I21_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Compl__greaterThan,axiom, % 173.22/173.20 ! [V_k_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Compl__atMost,axiom, % 173.22/173.20 ! [V_k_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I15_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I8_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_subset__card__intvl__is__intvl,axiom, % 173.22/173.20 ! [V_k_2,V_A_2] : % 173.22/173.20 ( 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))))) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I2_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 173.22/173.20 ! [V_k_2,V_f_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__head__upt__Suc,axiom, % 173.22/173.20 ! [V_f_2,V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I22_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I16_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThanSuc,axiom, % 173.22/173.20 ! [V_n_2,V_m_2] : % 173.22/173.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.20 => 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)) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I9_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I3_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.20 => 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) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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)) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__op__ivl__Suc,axiom, % 173.22/173.20 ! [V_f_2,V_m_2,V_n_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.22/173.20 => 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) ) % 173.22/173.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__int_I7_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 173.22/173.20 ! [V_y,V_x] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__uminus__greaterThan,axiom, % 173.22/173.20 ! [V_x_2,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__uminus__lessThan,axiom, % 173.22/173.20 ! [V_x_2,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThan__Suc,axiom, % 173.22/173.20 ! [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)))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_tsub__eq,axiom, % 173.22/173.20 ! [V_x,V_y] : % 173.22/173.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 173.22/173.20 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => 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 ) % 173.22/173.20 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.20 => 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)))))) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => 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)) ) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.20 => ( 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)) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I6_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_setsum__head,axiom, % 173.22/173.20 ! [V_P_2,V_n_2,V_m_2,T_a] : % 173.22/173.20 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 173.22/173.20 ! [V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( ! [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)))))) % 173.22/173.20 => 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)) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I19_J,axiom, % 173.22/173.20 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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))))))) ) ) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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))))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_ivl__disj__un_I4_J,axiom, % 173.22/173.20 ! [V_u_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 173.22/173.20 => 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) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__greaterThanLessThan,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__atLeastLessThan__int,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__greaterThanLessThan__int,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_sup__max,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.20 & class_Orderings_Olinorder(T_a) ) % 173.22/173.20 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__0R,axiom, % 173.22/173.20 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__0L,axiom, % 173.22/173.20 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 173.22/173.20 % 173.22/173.20 fof(fact_Max_Oidem,axiom, % 173.22/173.20 ! [V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup_Oidem,axiom, % 173.22/173.20 ! [V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup_Ocommute,axiom, % 173.22/173.20 ! [V_b,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__commute,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup_Oleft__idem,axiom, % 173.22/173.20 ! [V_b,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__left__idem,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup_Oleft__commute,axiom, % 173.22/173.20 ! [V_c,V_a,V_b,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__left__commute,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup_Oassoc,axiom, % 173.22/173.20 ! [V_c,V_b,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__assoc,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__add__distrib__left,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__diff__distrib__left,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_le__max__iff__disj,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,V_z_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 173.22/173.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_le__maxI1,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_le__maxI2,axiom, % 173.22/173.20 ! [V_x,V_y,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__iff__sup,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.20 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__sup__iff,axiom, % 173.22/173.20 ! [V_z_2,V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__supI1,axiom, % 173.22/173.20 ! [V_b,V_a,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__supI2,axiom, % 173.22/173.20 ! [V_a,V_b,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__absorb2,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__absorb1,axiom, % 173.22/173.20 ! [V_x,V_y,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.20 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__supI,axiom, % 173.22/173.20 ! [V_b,V_x,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__least,axiom, % 173.22/173.20 ! [V_z,V_x,V_y,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__mono,axiom, % 173.22/173.20 ! [V_d,V_b,V_c,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.22/173.20 => 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))) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Ole__supE,axiom, % 173.22/173.20 ! [V_x,V_b,V_a,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.22/173.20 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_less__max__iff__disj,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,V_z_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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))) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 173.22/173.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__less__iff__conj,axiom, % 173.22/173.20 ! [V_z_2,V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( 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)) % 173.22/173.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 173.22/173.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oless__supI1,axiom, % 173.22/173.20 ! [V_b,V_a,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oless__supI2,axiom, % 173.22/173.20 ! [V_a,V_b,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 173.22/173.20 => 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))) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__Suc__Suc,axiom, % 173.22/173.20 ! [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)) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__inf__absorb,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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 ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__sup__absorb,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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 ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__inf__distrib1,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Osup__inf__distrib2,axiom, % 173.22/173.20 ! [V_x,V_z,V_y,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 173.22/173.20 ! [V_x,V_z,V_y,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Int__greaterThanLessThan,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Odistrib__inf__le,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_min__max_Odistrib__sup__le,axiom, % 173.22/173.20 ! [V_z,V_y,V_x,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)))) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_minus__min__eq__max,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_minus__max__eq__min,axiom, % 173.22/173.20 ! [V_y,V_x,T_a] : % 173.22/173.20 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_nat__minus__add__max,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 173.22/173.20 ! [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))) ). % 173.22/173.20 % 173.22/173.20 fof(fact_greaterThanLessThan__empty,axiom, % 173.22/173.20 ! [V_k_2,V_l_2,T_a] : % 173.22/173.20 ( class_Orderings_Oorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 173.22/173.20 => 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)) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__Suc2,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__Suc1,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__uminus__greaterThanLessThan,axiom, % 173.22/173.20 ! [V_y_2,V_x_2,T_a] : % 173.22/173.20 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_max__ord__max,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( class_Orderings_Oord(T_a) % 173.22/173.20 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Max_Oin__idem,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.20 => 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) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Int__atLeastAtMost,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Int__atLeastLessThan,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Int__greaterThanAtMost,axiom, % 173.22/173.20 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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)) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_dual__min,axiom, % 173.22/173.20 ! [T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => 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) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_image__add__int__atLeastLessThan,axiom, % 173.22/173.20 ! [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) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Max__insert,axiom, % 173.22/173.20 ! [V_x_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => 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)) ) ) ) ). % 173.22/173.20 % 173.22/173.20 fof(fact_Max_Osubset__idem,axiom, % 173.22/173.20 ! [V_B_2,V_A_2,T_a] : % 173.22/173.20 ( class_Orderings_Olinorder(T_a) % 173.22/173.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.20 => 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) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Osup__Inf__absorb,axiom, % 173.22/173.21 ! [V_a_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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 ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max__Un,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__int_I12_J,axiom, % 173.22/173.21 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__int_I13_J,axiom, % 173.22/173.21 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__int_I9_J,axiom, % 173.22/173.21 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_card__greaterThanLessThan,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__int_I1_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__int_I10_J,axiom, % 173.22/173.21 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_Oinsert,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_Oinsert__remove,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 173.22/173.21 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => 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)))))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_Ounion__inter,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( 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)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_Ounion__disjoint,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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)) % 173.22/173.21 => 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)) ) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I15_J,axiom, % 173.22/173.21 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I16_J,axiom, % 173.22/173.21 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_Oremove,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 173.22/173.21 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => 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)))))) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I7_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I3_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I18_J,axiom, % 173.22/173.21 ! [V_u_2,V_m_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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))))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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))))))) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_Oclosed,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( ! [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)))))) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_atLeast__Suc,axiom, % 173.22/173.21 ! [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)))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OInf__le__Sup,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_sup__nat__def,axiom, % 173.22/173.21 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 173.22/173.21 % 173.22/173.21 fof(fact_atLeast__eq__iff,axiom, % 173.22/173.21 ! [V_y_2,V_x_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 173.22/173.21 <=> V_x_2 = V_y_2 ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_atLeast__iff,axiom, % 173.22/173.21 ! [V_k_2,V_i_2,T_a] : % 173.22/173.21 ( class_Orderings_Oord(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_atLeast__subset__iff,axiom, % 173.22/173.21 ! [V_y_2,V_x_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_atLeast__0,axiom, % 173.22/173.21 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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 173.22/173.21 ! [V_x_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => 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 ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Compl__lessThan,axiom, % 173.22/173.21 ! [V_k_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Compl__atLeast,axiom, % 173.22/173.21 ! [V_k_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_atLeast__Suc__greaterThan,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.21 => 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) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 173.22/173.21 ! [V_a_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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 ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I14_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__int_I8_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Int__atLeastAtMostR2,axiom, % 173.22/173.21 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Int__atLeastAtMostL2,axiom, % 173.22/173.21 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__int_I6_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_image__uminus__atLeast,axiom, % 173.22/173.21 ! [V_x_2,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_image__uminus__atMost,axiom, % 173.22/173.21 ! [V_x_2,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => 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 ) % 173.22/173.21 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => 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)))))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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)) % 173.22/173.21 => 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)) ) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( 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)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_atMost__Int__atLeast,axiom, % 173.22/173.21 ! [V_n_2,T_a] : % 173.22/173.21 ( class_Orderings_Oorder(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I1_J,axiom, % 173.22/173.21 ! [V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I13_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ivl__disj__un_I12_J,axiom, % 173.22/173.21 ! [V_u_2,V_l_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Oremove,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 173.22/173.21 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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)) % 173.22/173.21 => 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)))))) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( ! [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)))))) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_image__atLeastZeroLessThan__int,axiom, % 173.22/173.21 ! [V_u_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 173.22/173.21 ! [V_N_2,V_h_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( ! [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)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.21 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 173.22/173.21 ! [V_N_2,V_h_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( ! [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)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.21 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_Ohom__commute,axiom, % 173.22/173.21 ! [V_N_2,V_h_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( ! [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)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.21 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__int,axiom, % 173.22/173.21 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__0,axiom, % 173.22/173.21 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 173.22/173.21 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_eq__nat__nat__iff,axiom, % 173.22/173.21 ! [V_z_H_2,V_z_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 173.22/173.21 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 173.22/173.21 <=> V_z_2 = V_z_H_2 ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ex__nat,axiom, % 173.22/173.21 ! [V_P_2] : % 173.22/173.21 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.22/173.21 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_all__nat,axiom, % 173.22/173.21 ! [V_P_2] : % 173.22/173.21 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.22/173.21 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 173.22/173.21 ! [V_y_2,V_x_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 173.22/173.21 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 173.22/173.21 <=> V_x_2 = V_y_2 ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 173.22/173.21 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__set__return__embed,axiom, % 173.22/173.21 ! [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 ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 173.22/173.21 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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__0__iff,axiom, % 173.22/173.21 ! [V_i_2] : % 173.22/173.21 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__le__0,axiom, % 173.22/173.21 ! [V_z] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zless__nat__conj,axiom, % 173.22/173.21 ! [V_z_2,V_w_2] : % 173.22/173.21 ( 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))) % 173.22/173.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__mono__iff,axiom, % 173.22/173.21 ! [V_w_2,V_z_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 173.22/173.21 ! [V_y_2,V_x_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__1,axiom, % 173.22/173.21 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_int__nat__eq,axiom, % 173.22/173.21 ! [V_z] : % 173.22/173.21 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_int__eq__iff,axiom, % 173.22/173.21 ! [V_z_2,V_m_2] : % 173.22/173.21 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 173.22/173.21 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__0__le,axiom, % 173.22/173.21 ! [V_z] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zless__nat__eq__int__zless,axiom, % 173.22/173.21 ! [V_z_2,V_m_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 173.22/173.21 <=> 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__zminus__int,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_a] : % 173.22/173.21 ( ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.21 & class_Groups_Ocomm__monoid__mult(T_a) ) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_card__atLeastZeroLessThan__int,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_card__atLeastLessThan__int,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__less__nat__eq,axiom, % 173.22/173.21 ! [V_z_2] : % 173.22/173.21 ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__less__eq__zless,axiom, % 173.22/173.21 ! [V_z_2,V_w_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 173.22/173.21 ! [V_y_2,V_x_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__eq__iff,axiom, % 173.22/173.21 ! [V_m_2,V_w_2] : % 173.22/173.21 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 173.22/173.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.22/173.21 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.22/173.21 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__eq__iff2,axiom, % 173.22/173.21 ! [V_w_2,V_m_2] : % 173.22/173.21 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 173.22/173.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.22/173.21 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.22/173.21 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__le__eq__zle,axiom, % 173.22/173.21 ! [V_z_2,V_w_2] : % 173.22/173.21 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.22/173.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_split__nat,axiom, % 173.22/173.21 ! [V_i_2,V_P_2] : % 173.22/173.21 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 173.22/173.21 <=> ( ! [B_n] : % 173.22/173.21 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 173.22/173.21 => hBOOL(hAPP(V_P_2,B_n)) ) % 173.22/173.21 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__add__distrib,axiom, % 173.22/173.21 ! [V_z_H,V_z] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 173.22/173.21 ! [V_y,V_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__mult__distrib,axiom, % 173.22/173.21 ! [V_z_H,V_z] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 173.22/173.21 ! [V_y,V_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__diff__distrib,axiom, % 173.22/173.21 ! [V_z,V_z_H] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_card__greaterThanAtMost__int,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 173.22/173.21 ! [V_y,V_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_one__less__nat__eq,axiom, % 173.22/173.21 ! [V_z_2] : % 173.22/173.21 ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__less__iff,axiom, % 173.22/173.21 ! [V_m_2,V_w_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 173.22/173.21 <=> 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 173.22/173.21 ! [V_z] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__mult__distrib__neg,axiom, % 173.22/173.21 ! [V_z_H,V_z] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 173.22/173.21 ! [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)))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_card__atLeastAtMost__int,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_card__greaterThanLessThan__int,axiom, % 173.22/173.21 ! [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)))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__aux__def,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__morphism__nat__int,axiom, % 173.22/173.21 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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 173.22/173.21 ! [V_n_2,V_m_2] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_m_2) % 173.22/173.21 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__of__nat,axiom, % 173.22/173.21 ! [V_k,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => 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)))) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 173.22/173.21 ! [V_x_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 173.22/173.21 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 173.22/173.21 ! [V_y_2,V_x_2] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_x_2) % 173.22/173.21 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__eq__iff,axiom, % 173.22/173.21 ! [V_z_2,V_w_2,T_a] : % 173.22/173.21 ( class_Int_Oring__char__0(T_a) % 173.22/173.21 => ( 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) % 173.22/173.21 <=> V_w_2 = V_z_2 ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__int__eq,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => ( V_A_2 = V_B_2 % 173.22/173.21 <=> 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 173.22/173.21 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 173.22/173.21 ! [V_y,V_x] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_x) % 173.22/173.21 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.22/173.21 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 173.22/173.21 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 173.22/173.21 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 173.22/173.21 ! [V_y,V_x] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_x) % 173.22/173.21 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.22/173.21 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 173.22/173.21 ! [V_y,V_x] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_x) % 173.22/173.21 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.22/173.21 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 173.22/173.21 ! [V_A_2,V_x_2] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_x_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 173.22/173.21 <=> 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__0,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__0__eq__iff,axiom, % 173.22/173.21 ! [V_z_2,T_a] : % 173.22/173.21 ( class_Int_Oring__char__0(T_a) % 173.22/173.21 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 173.22/173.21 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__eq__0__iff,axiom, % 173.22/173.21 ! [V_z_2,T_a] : % 173.22/173.21 ( class_Int_Oring__char__0(T_a) % 173.22/173.21 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 173.22/173.21 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__le__iff,axiom, % 173.22/173.21 ! [V_z_2,V_w_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__less__iff,axiom, % 173.22/173.21 ! [V_z_2,V_w_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__add,axiom, % 173.22/173.21 ! [V_z,V_w,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__mult,axiom, % 173.22/173.21 ! [V_z,V_w,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__1,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__diff,axiom, % 173.22/173.21 ! [V_z,V_w,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__of__nat__eq,axiom, % 173.22/173.21 ! [V_n,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__minus,axiom, % 173.22/173.21 ! [V_z,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Ints__of__int,axiom, % 173.22/173.21 ! [V_z_2,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__set__def,axiom, % 173.22/173.21 ! [V_S_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_S_2) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_is__nat__def,axiom, % 173.22/173.21 ! [V_x_2] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_x_2) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__setsum,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 173.22/173.21 ! [V_y_2,V_x_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.22/173.21 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__set__return__embed,axiom, % 173.22/173.21 ! [V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => 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 ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 173.22/173.21 ! [V_x_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__le__0__iff,axiom, % 173.22/173.21 ! [V_z_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__0__le__iff,axiom, % 173.22/173.21 ! [V_z_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__less__0__iff,axiom, % 173.22/173.21 ! [V_z_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__0__less__iff,axiom, % 173.22/173.21 ! [V_z_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__nat__nat,axiom, % 173.22/173.21 ! [V_z,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 173.22/173.21 ! [V_f_2,V_A_2,T_a] : % 173.22/173.21 ( ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.21 & class_Groups_Ocomm__monoid__mult(T_a) ) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 173.22/173.21 ! [V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 173.22/173.21 <=> 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 173.22/173.21 ! [V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.21 <=> 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2] : % 173.22/173.21 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.21 <=> 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 173.22/173.21 ! [V_f_2,V_A_2,T_a] : % 173.22/173.21 ( ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Min_Ohom__commute,axiom, % 173.22/173.21 ! [V_N_2,V_h_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( ! [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)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.21 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_decr__mult__lemma,axiom, % 173.22/173.21 ! [V_k_2,V_P_2,V_d_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 173.22/173.21 => ( ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.21 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.22/173.21 => ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.21 => 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)))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_negD,axiom, % 173.22/173.21 ! [V_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => ? [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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_incr__mult__lemma,axiom, % 173.22/173.21 ! [V_k_2,V_P_2,V_d_2] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 173.22/173.21 => ( ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.21 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.22/173.21 => ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.21 => 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)))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__eq__id,axiom, % 173.22/173.21 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__less__imp__eq__int,axiom, % 173.22/173.21 ! [V_k] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.22/173.21 => ? [B_n] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 173.22/173.21 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_incr__lemma,axiom, % 173.22/173.21 ! [V_x,V_z,V_d] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 173.22/173.21 => 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)))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_decr__lemma,axiom, % 173.22/173.21 ! [V_z,V_x,V_d] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 173.22/173.21 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 173.22/173.21 ( ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.21 & class_Groups_Ocomm__monoid__mult(T_a) ) % 173.22/173.21 => ( V_A_2 = V_B_2 % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.21 => ( ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.22/173.21 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 173.22/173.21 => 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) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1Set_Oequations,axiom, % 173.22/173.21 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 173.22/173.21 ( 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)) % 173.22/173.21 <=> ? [B_a,B_A] : % 173.22/173.21 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 173.22/173.21 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 173.22/173.21 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setsum__abs,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setsum__abs__ge__zero,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__minus__commute,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__int__eq,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__le__D1,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__ge__self,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__of__nat,axiom, % 173.22/173.21 ! [V_n,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__one,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__minus__cancel,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__idempotent,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__mult,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__mult__self,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__add__abs,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__zero,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__eq__0,axiom, % 173.22/173.21 ! [V_a_2,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__setsum__abs,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__of__nonneg,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__le__zero__iff,axiom, % 173.22/173.21 ! [V_a_2,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__ge__zero,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__of__pos,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__less__abs__iff,axiom, % 173.22/173.21 ! [V_a_2,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__not__less__zero,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ~ 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__triangle__ineq,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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)))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__mult__less,axiom, % 173.22/173.21 ! [V_d,V_b,V_c,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__triangle__ineq3,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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)))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__triangle__ineq2,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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)))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__triangle__ineq2__sym,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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)))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__ge__minus__self,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__le__iff,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( 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)) % 173.22/173.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 173.22/173.21 & 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__leI,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__le__D2,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__less__iff,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 173.22/173.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__zmult__eq__1,axiom, % 173.22/173.21 ! [V_n,V_m] : % 173.22/173.21 ( 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) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_mult__sgn__abs,axiom, % 173.22/173.21 ! [V_x,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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 ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__sgn,axiom, % 173.22/173.21 ! [V_k,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__mult__pos,axiom, % 173.22/173.21 ! [V_y,V_x,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__eq__mult,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Oordered__ring__abs(T_a) % 173.22/173.21 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 173.22/173.21 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__triangle__ineq4,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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)))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__diff__triangle__ineq,axiom, % 173.22/173.21 ! [V_d,V_c,V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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))))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__minus__le__zero,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__of__nonpos,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__of__neg,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__if,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Oabs__if(T_a) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zabs__less__one__iff,axiom, % 173.22/173.21 ! [V_z_2] : % 173.22/173.21 ( 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))) % 173.22/173.21 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zabs__def,axiom, % 173.22/173.21 ! [V_i] : % 173.22/173.21 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.21 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__abs__mult__distrib,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nitpick_Oint__lcm__def,axiom, % 173.22/173.21 ! [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)))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_insert__fold1SetE,axiom, % 173.22/173.21 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 173.22/173.21 ( 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)) % 173.22/173.21 => ~ ! [B_a,B_A] : % 173.22/173.21 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat0__intermed__int__val,axiom, % 173.22/173.21 ! [V_k_2,V_f_2,V_n_2] : % 173.22/173.21 ( ! [B_i] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 173.22/173.21 => 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))) ) % 173.22/173.21 => ( 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)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 173.22/173.21 => ? [B_i] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 173.22/173.21 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_int__val__lemma,axiom, % 173.22/173.21 ! [V_k_2,V_f_2,V_n_2] : % 173.22/173.21 ( ! [B_i] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 173.22/173.21 => 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))) ) % 173.22/173.21 => ( 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)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 173.22/173.21 => ? [B_i] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 173.22/173.21 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__Un,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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)) % 173.22/173.21 => 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)) ) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__singleton,axiom, % 173.22/173.21 ! [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 ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__singleton__def,axiom, % 173.22/173.21 ! [V_a_2,V_f_2,T_a,V_g_2] : % 173.22/173.21 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 173.22/173.21 => 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 ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_folding__one_Oeq__fold,axiom, % 173.22/173.21 ! [V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.21 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__def,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Sup__fin_OF__eq,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Lattices_Olattice(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Inf__fin_OF__eq,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Lattices_Olattice(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Min_OF__eq,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Max_OF__eq,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__belowI,axiom, % 173.22/173.21 ! [V_a_2,V_A_2,T_a] : % 173.22/173.21 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_below__fold1__iff,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Ofold1__belowI,axiom, % 173.22/173.21 ! [V_a_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__insert__idem,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__below__iff,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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)) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Obelow__fold1__iff,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__Un2,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_strict__below__fold1__iff,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__strict__below__iff,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( 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)) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__insert,axiom, % 173.22/173.21 ! [V_x_2,V_A_2,T_a] : % 173.22/173.21 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__antimono,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => 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))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_semilattice__big_OF__eq,axiom, % 173.22/173.21 ! [V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.21 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fold1__in,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => ( ! [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)))))) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_hom__fold1__commute,axiom, % 173.22/173.21 ! [V_N_2,V_h_2,T_a] : % 173.22/173.21 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.21 => ( ! [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)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 173.22/173.21 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.21 => ( ! [B_x] : % 173.22/173.21 ( 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))) % 173.22/173.21 => hAPP(V_g_2,B_x) = V_z_2 ) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem__remove,axiom, % 173.22/173.21 ! [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))))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 173.22/173.21 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 173.22/173.21 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 173.22/173.21 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem__insert,axiom, % 173.22/173.21 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.21 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem__sup,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.21 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem__inf,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.21 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 173.22/173.21 ! [V_x_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 173.22/173.21 ! [T_a] : % 173.22/173.21 ( class_Orderings_Olinorder(T_a) % 173.22/173.21 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_pigeonhole__infinite,axiom, % 173.22/173.21 ! [V_f_2,T_b,V_A_2,T_a] : % 173.22/173.21 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 173.22/173.21 => ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & ~ 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)))))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__le__eq__Un0,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ex__bij__betw__nat__finite__1,axiom, % 173.22/173.21 ! [V_M_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_M_2)) % 173.22/173.21 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_a,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_M_2)),V_M_2) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_diff__nat__eq__if,axiom, % 173.22/173.21 ! [V_z_2,V_z_H_2] : % 173.22/173.21 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 173.22/173.21 => 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) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP1__I,axiom, % 173.22/173.21 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__o,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_finite__UN,axiom, % 173.22/173.21 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP1__iff,axiom, % 173.22/173.21 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.21 ( 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)) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_not__neg__0,axiom, % 173.22/173.21 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_not__neg__int,axiom, % 173.22/173.21 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_not__neg__1,axiom, % 173.22/173.21 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP__UN__eq,axiom, % 173.22/173.21 ! [V_x_2,V_r_2,T_b,T_a] : % 173.22/173.21 ( 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)) % 173.22/173.21 <=> 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_not__neg__eq__ge__0,axiom, % 173.22/173.21 ! [V_x_2] : % 173.22/173.21 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_neg__def,axiom, % 173.22/173.21 ! [V_Z_2] : % 173.22/173.21 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_neg__nat,axiom, % 173.22/173.21 ! [V_z] : % 173.22/173.21 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 173.22/173.21 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_not__neg__nat,axiom, % 173.22/173.21 ! [V_z] : % 173.22/173.21 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 173.22/173.21 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__lessThan__UNIV,axiom, % 173.22/173.21 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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__atMost__UNIV,axiom, % 173.22/173.21 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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__atLeast__UNIV,axiom, % 173.22/173.21 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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__UN__finite__eq,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__le__add__shift,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_neg__zminus__int,axiom, % 173.22/173.21 ! [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))))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__I,axiom, % 173.22/173.21 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_vimage__eq__UN,axiom, % 173.22/173.21 ! [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))))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_image__eq__UN,axiom, % 173.22/173.21 ! [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)))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__Pow__subset,axiom, % 173.22/173.21 ! [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)))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ball__UN,axiom, % 173.22/173.21 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.21 ( ! [B_x] : % 173.22/173.21 ( 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))) % 173.22/173.21 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.21 => ! [B_xa] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 173.22/173.21 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP__commute,axiom, % 173.22/173.21 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 173.22/173.21 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__UN__flatten,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I9_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I9_J,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP__le__iff,axiom, % 173.22/173.21 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 173.22/173.21 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.21 => ( 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)) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_less__SUP__iff,axiom, % 173.22/173.21 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 173.22/173.21 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.21 & class_Orderings_Olinorder(T_a) ) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__iff,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 173.22/173.21 ( 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))) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP__const,axiom, % 173.22/173.21 ! [V_M_2,T_a,V_A_2,T_b] : % 173.22/173.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.21 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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 ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UNION__empty__conv_I1_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.21 ( 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) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.21 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__empty2,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__constant,axiom, % 173.22/173.21 ! [V_ca_2,T_b,T_a,V_A_2] : % 173.22/173.21 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) % 173.22/173.21 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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 ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UNION__empty__conv_I2_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( 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)) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.21 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__subset__iff,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 173.22/173.21 ( 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)) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I10_J,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_image__UN,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I10_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__Un,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__Un__distrib,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I5_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I4_J,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I5_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Int__UN__distrib,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I4_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Int__UN__distrib2,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUPR__apply,axiom, % 173.22/173.21 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 173.22/173.21 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I6_J,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I6_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_vimage__UN,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP__subset,axiom, % 173.22/173.21 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_le__SUPI,axiom, % 173.22/173.21 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 173.22/173.21 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__insert__distrib,axiom, % 173.22/173.21 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__upper,axiom, % 173.22/173.21 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__absorb,axiom, % 173.22/173.21 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I1_J,axiom, % 173.22/173.21 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 173.22/173.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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))) ) % 173.22/173.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__singleton,axiom, % 173.22/173.21 ! [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 ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I1_J,axiom, % 173.22/173.21 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 173.22/173.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) % 173.22/173.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I2_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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 ) % 173.22/173.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__extend__simps_I3_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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 ) % 173.22/173.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I2_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) % 173.22/173.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__simps_I3_J,axiom, % 173.22/173.21 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.21 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) % 173.22/173.21 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__insert,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__finite2__subset,axiom, % 173.22/173.21 ! [V_B_2,V_k_2,V_A_2,T_a] : % 173.22/173.21 ( ! [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))) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ex__bij__betw__nat__finite,axiom, % 173.22/173.21 ! [V_M_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_M_2)) % 173.22/173.21 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_a,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_M_2)),V_M_2) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__finite2__eq,axiom, % 173.22/173.21 ! [V_B_2,V_k_2,V_A_2,T_a] : % 173.22/173.21 ( ! [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) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_UN__finite__subset,axiom, % 173.22/173.21 ! [V_C_2,V_A_2,T_a] : % 173.22/173.21 ( ! [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)) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP2__I,axiom, % 173.22/173.21 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_finite__UN__I,axiom, % 173.22/173.21 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ! [B_a] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 173.22/173.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setsum__SucD,axiom, % 173.22/173.21 ! [V_n_2,V_A_2,V_f_2,T_a] : % 173.22/173.21 ( 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) % 173.22/173.21 => ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Oremove,axiom, % 173.22/173.21 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => 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)))))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_ex__bij__betw__finite__nat,axiom, % 173.22/173.21 ! [V_M_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_M_2)) % 173.22/173.21 => ? [B_h] : c_Fun_Obij__betw(T_a,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_M_2))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_SUP2__iff,axiom, % 173.22/173.21 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 173.22/173.21 ( 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)) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__setprod,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.21 & class_Rings_Oring__1(T_a) ) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__nat__setprod,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.21 & class_Rings_Osemiring__1(T_a) ) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_int__setprod,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__timesf,axiom, % 173.22/173.21 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__1,axiom, % 173.22/173.21 ! [V_A_2,T_b,T_a] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__setprod,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 173.22/173.21 ! [V_A_2,V_f_2,T_a] : % 173.22/173.21 ( ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.21 & class_Groups_Ocomm__monoid__mult(T_a) ) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__zero__iff,axiom, % 173.22/173.21 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( ( class_Rings_Ocomm__semiring__1(T_b) % 173.22/173.21 & class_Rings_Ono__zero__divisors(T_b) ) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( 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) % 173.22/173.21 <=> ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__zero,axiom, % 173.22/173.21 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ? [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.21 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Oempty,axiom, % 173.22/173.21 ! [V_g_2,T_b,T_a] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__empty,axiom, % 173.22/173.21 ! [V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__infinite,axiom, % 173.22/173.21 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Oinfinite,axiom, % 173.22/173.21 ! [V_g_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__eq__1__iff,axiom, % 173.22/173.21 ! [V_f_2,V_F_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.21 => ( 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) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 173.22/173.21 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 173.22/173.21 ! [V_f_2,V_A_2,T_a] : % 173.22/173.21 ( ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.21 & class_Groups_Ocomm__monoid__mult(T_a) ) % 173.22/173.21 => ( c_Nat__Transfer_Onat__set(V_A_2) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Odistrib,axiom, % 173.22/173.21 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__pos__nat__iff,axiom, % 173.22/173.21 ! [V_f_2,V_S_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ! [B_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__reindex,axiom, % 173.22/173.21 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.22/173.21 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__reindex__cong,axiom, % 173.22/173.21 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.22/173.21 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.21 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 173.22/173.21 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 173.22/173.21 => 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) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__reindex__id,axiom, % 173.22/173.21 ! [V_B_2,V_f_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__delta_H,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.21 => 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) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.21 => 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) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__delta,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.21 => 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) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.21 => 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) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Oinsert,axiom, % 173.22/173.21 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__insert,axiom, % 173.22/173.21 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Ounion__inter,axiom, % 173.22/173.21 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__Un__Int,axiom, % 173.22/173.21 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Oreindex,axiom, % 173.22/173.21 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Oeq__fold,axiom, % 173.22/173.21 ! [V_g_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_OF__eq,axiom, % 173.22/173.21 ! [V_g_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Oinsert__remove,axiom, % 173.22/173.21 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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)))))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Ounion__disjoint,axiom, % 173.22/173.21 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( 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)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__Un__disjoint,axiom, % 173.22/173.21 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( 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)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod_Ounion__inter__neutral,axiom, % 173.22/173.21 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.21 => ( ! [B_x] : % 173.22/173.21 ( 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))) % 173.22/173.21 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__Un__one,axiom, % 173.22/173.21 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 173.22/173.21 => ( ! [B_x] : % 173.22/173.21 ( 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))) % 173.22/173.21 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__gen__delta,axiom, % 173.22/173.21 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.21 => 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)))) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 173.22/173.21 => 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)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__diff1,axiom, % 173.22/173.21 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Fields_Ofield(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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)) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.21 => 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) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zpower__zpower,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 173.22/173.21 ! [V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_minus__divide__left,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 173.22/173.21 ! [V_q,V_y,V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_int__power,axiom, % 173.22/173.21 ! [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) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zpower__int,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_times__divide__eq__right,axiom, % 173.22/173.21 ! [V_c,V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_add__divide__distrib,axiom, % 173.22/173.21 ! [V_c,V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__zero,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__zero__left,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__1,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 173.22/173.21 ! [V_q,V_p,V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_diff__divide__distrib,axiom, % 173.22/173.21 ! [V_c,V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__int__power,axiom, % 173.22/173.21 ! [V_n,V_z,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 173.22/173.21 ! [V_n,V_x] : % 173.22/173.21 ( c_Nat__Transfer_Ois__nat(V_x) % 173.22/173.21 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__power__eq,axiom, % 173.22/173.21 ! [V_n,V_z] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 173.22/173.21 ! [V_n,V_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setsum__divide__distrib,axiom, % 173.22/173.21 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.21 ( class_Fields_Ofield(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_eq__divide__imp,axiom, % 173.22/173.21 ! [V_b,V_a,V_c,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 173.22/173.21 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__eq__imp,axiom, % 173.22/173.21 ! [V_a,V_b,V_c,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 173.22/173.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nonzero__divide__eq__eq,axiom, % 173.22/173.21 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 173.22/173.21 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nonzero__eq__divide__eq,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 173.22/173.21 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_right__inverse__eq,axiom, % 173.22/173.21 ! [V_a_2,V_b_2,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 173.22/173.21 <=> V_a_2 = V_b_2 ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__self,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__self__if,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 173.22/173.21 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 173.22/173.21 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nonzero__minus__divide__divide,axiom, % 173.22/173.21 ! [V_a,V_b,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => 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) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nonzero__minus__divide__right,axiom, % 173.22/173.21 ! [V_a,V_b,T_a] : % 173.22/173.21 ( class_Rings_Odivision__ring(T_a) % 173.22/173.21 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 173.22/173.21 ! [V_q,V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 173.22/173.21 ! [V_q,V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 173.22/173.21 ! [V_q,V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 173.22/173.21 ! [V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 173.22/173.21 ! [V_q,V_p,V_x,T_a] : % 173.22/173.21 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 173.22/173.21 ! [V_n,V_x] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zpower__zadd__distrib,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_Ints__power,axiom, % 173.22/173.21 ! [V_n_2,V_a_2,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__dividef,axiom, % 173.22/173.21 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Fields_Ofield__inverse__zero(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_geometric__sum,axiom, % 173.22/173.21 ! [V_n_2,V_x_2,T_a] : % 173.22/173.21 ( class_Fields_Ofield(T_a) % 173.22/173.21 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__le__zpower__abs,axiom, % 173.22/173.21 ! [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))) ). % 173.22/173.21 % 173.22/173.21 fof(fact_setprod__constant,axiom, % 173.22/173.21 ! [V_y_2,V_A_2,T_a,T_b] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__eq__if,axiom, % 173.22/173.21 ! [V_p,V_m] : % 173.22/173.21 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.21 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 173.22/173.21 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.21 => 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)))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__less__zpower__abs__iff,axiom, % 173.22/173.21 ! [V_n_2,V_x_2] : % 173.22/173.21 ( 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))) % 173.22/173.21 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.21 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_card__Pow,axiom, % 173.22/173.21 ! [V_A_2,T_a] : % 173.22/173.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__strict__mono,axiom, % 173.22/173.21 ! [V_n,V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.21 => 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))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__diff,axiom, % 173.22/173.21 ! [V_m,V_n,V_a,T_a] : % 173.22/173.21 ( class_Fields_Ofield(T_a) % 173.22/173.21 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.21 => 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_one__less__power,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__increasing__iff,axiom, % 173.22/173.21 ! [V_y_2,V_x_2,V_b_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_field__power__not__zero,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 173.22/173.21 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__Suc__0,axiom, % 173.22/173.21 ! [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)) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 173.22/173.21 ! [V_m_2,V_x_2] : % 173.22/173.21 ( 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)) % 173.22/173.21 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.21 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__zero__less__power__iff,axiom, % 173.22/173.21 ! [V_n_2,V_x_2] : % 173.22/173.21 ( 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))) % 173.22/173.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 173.22/173.21 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__power__less__imp__less,axiom, % 173.22/173.21 ! [V_n,V_m,V_i] : % 173.22/173.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 173.22/173.21 => ( 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))) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__mult__distrib,axiom, % 173.22/173.21 ! [V_n,V_b,V_a,T_a] : % 173.22/173.21 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__commutes,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__one,axiom, % 173.22/173.21 ! [V_n,T_a] : % 173.22/173.21 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_of__nat__power,axiom, % 173.22/173.21 ! [V_n,V_m,T_a] : % 173.22/173.21 ( class_Rings_Osemiring__1(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__mult,axiom, % 173.22/173.21 ! [V_n,V_m,V_a,T_a] : % 173.22/173.21 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__divide,axiom, % 173.22/173.21 ! [V_n,V_b,V_a,T_a] : % 173.22/173.21 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__abs,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__one__right,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.21 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__le__power,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__mono,axiom, % 173.22/173.21 ! [V_n,V_b,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__less__power,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__eq__0__iff,axiom, % 173.22/173.21 ! [V_n_2,V_a_2,T_a] : % 173.22/173.21 ( ( class_Power_Opower(T_a) % 173.22/173.21 & class_Rings_Omult__zero(T_a) % 173.22/173.21 & class_Rings_Ono__zero__divisors(T_a) % 173.22/173.21 & class_Rings_Ozero__neq__one(T_a) ) % 173.22/173.21 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_one__le__power,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => 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))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__0__Suc,axiom, % 173.22/173.21 ! [V_n,T_a] : % 173.22/173.21 ( ( class_Power_Opower(T_a) % 173.22/173.21 & class_Rings_Osemiring__0(T_a) ) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__inject__exp,axiom, % 173.22/173.21 ! [V_n_2,V_m_2,V_a_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 173.22/173.21 => ( 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) % 173.22/173.21 <=> V_m_2 = V_n_2 ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__Suc,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Power_Opower(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__Suc2,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nat__one__le__power,axiom, % 173.22/173.21 ! [V_n,V_i] : % 173.22/173.21 ( 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)) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__0,axiom, % 173.22/173.21 ! [V_a,T_a] : % 173.22/173.21 ( class_Power_Opower(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__add,axiom, % 173.22/173.21 ! [V_n,V_m,V_a,T_a] : % 173.22/173.21 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_nonzero__power__divide,axiom, % 173.22/173.21 ! [V_n,V_a,V_b,T_a] : % 173.22/173.21 ( class_Fields_Ofield(T_a) % 173.22/173.21 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.21 => 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)) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__one__over,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__power__minus,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__less__imp__less__base,axiom, % 173.22/173.21 ! [V_b,V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__le__imp__le__base,axiom, % 173.22/173.21 ! [V_b,V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( 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)))) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__inject__base,axiom, % 173.22/173.21 ! [V_b,V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( 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)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.21 => V_a = V_b ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__less__power__Suc,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => 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)))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__gt1__lemma,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => 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)))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__0__left,axiom, % 173.22/173.21 ! [V_n,T_a] : % 173.22/173.21 ( ( class_Power_Opower(T_a) % 173.22/173.21 & class_Rings_Osemiring__0(T_a) ) % 173.22/173.21 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.21 => 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) ) % 173.22/173.21 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.21 => 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) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__gt1,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => 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)))) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__strict__increasing,axiom, % 173.22/173.21 ! [V_a,V_N,V_n,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__less__imp__less__exp,axiom, % 173.22/173.21 ! [V_n,V_m,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => ( 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))) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__strict__increasing__iff,axiom, % 173.22/173.21 ! [V_y_2,V_x_2,V_b_2,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__le__power__abs,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.21 => 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))) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__increasing,axiom, % 173.22/173.21 ! [V_a,V_N,V_n,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__minus,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Oring__1(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__Suc__less,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__eq__imp__eq__base,axiom, % 173.22/173.21 ! [V_b,V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( 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) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.21 => V_a = V_b ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__Suc__less__one,axiom, % 173.22/173.21 ! [V_n,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__strict__decreasing,axiom, % 173.22/173.21 ! [V_a,V_N,V_n,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.22/173.21 => 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))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__decreasing,axiom, % 173.22/173.21 ! [V_a,V_N,V_n,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.22/173.21 => 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))) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_power__le__imp__le__exp,axiom, % 173.22/173.21 ! [V_n,V_m,V_a,T_a] : % 173.22/173.21 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.22/173.21 => ( 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))) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_le__divide__eq,axiom, % 173.22/173.21 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.21 => 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)) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => 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))) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__le__eq,axiom, % 173.22/173.21 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.21 => ( 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)) % 173.22/173.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.21 => 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))) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => 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)) ) % 173.22/173.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_pos__le__divide__eq,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> 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)) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_pos__divide__le__eq,axiom, % 173.22/173.21 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.21 => ( 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)) % 173.22/173.21 <=> 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_times__divide__times__eq,axiom, % 173.22/173.21 ! [V_w,V_z,V_y,V_x,T_a] : % 173.22/173.21 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_minus__divide__divide,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.21 => 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) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_minus__divide__right,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_abs__divide,axiom, % 173.22/173.21 ! [V_b,V_a,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.21 => 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)) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__right__mono__neg,axiom, % 173.22/173.21 ! [V_c,V_b,V_a,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__right__mono,axiom, % 173.22/173.21 ! [V_c,V_b,V_a,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.21 => 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))) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_divide__le__0__iff,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 173.22/173.21 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 173.22/173.21 % 173.22/173.21 fof(fact_zero__le__divide__iff,axiom, % 173.22/173.21 ! [V_b_2,V_a_2,T_a] : % 173.22/173.21 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.21 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 173.22/173.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__strict__right__mono__neg,axiom, % 173.22/173.22 ! [V_c,V_a,V_b,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__strict__right__mono,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__neg__neg,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__neg__pos,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__pos__neg,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__pos__pos,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__less__0__iff,axiom, % 173.22/173.22 ! [V_b_2,V_a_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 173.22/173.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zero__less__divide__iff,axiom, % 173.22/173.22 ! [V_b_2,V_a_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 173.22/173.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__divide__eq,axiom, % 173.22/173.22 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.22 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 173.22/173.22 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 173.22/173.22 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__eq__eq,axiom, % 173.22/173.22 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 173.22/173.22 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 173.22/173.22 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 173.22/173.22 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__divide__mult__cancel__right,axiom, % 173.22/173.22 ! [V_b,V_a,V_c,T_a] : % 173.22/173.22 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__divide__mult__cancel__left,axiom, % 173.22/173.22 ! [V_b,V_a,V_c,T_a] : % 173.22/173.22 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_frac__eq__eq,axiom, % 173.22/173.22 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 173.22/173.22 ( class_Fields_Ofield(T_a) % 173.22/173.22 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => ( 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) % 173.22/173.22 <=> 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) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nonzero__abs__divide,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__nonpos__neg,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__nonpos__pos,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_frac__le,axiom, % 173.22/173.22 ! [V_z,V_w,V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 173.22/173.22 => 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))) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_frac__less,axiom, % 173.22/173.22 ! [V_z,V_w,V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 173.22/173.22 => 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))) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_frac__less2,axiom, % 173.22/173.22 ! [V_z,V_w,V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 173.22/173.22 => 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))) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__nonneg__neg,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__nonneg__pos,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__divide__eq,axiom, % 173.22/173.22 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__less__eq,axiom, % 173.22/173.22 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 => ( 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)) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__less__divide__eq,axiom, % 173.22/173.22 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__divide__less__eq,axiom, % 173.22/173.22 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( 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)) % 173.22/173.22 <=> 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__imp__div__pos__less,axiom, % 173.22/173.22 ! [V_z,V_x,V_y,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => ( 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))) % 173.22/173.22 => 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__imp__less__div__pos,axiom, % 173.22/173.22 ! [V_x,V_z,V_y,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => ( 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)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__less__divide__eq,axiom, % 173.22/173.22 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__divide__less__eq,axiom, % 173.22/173.22 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( 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)) % 173.22/173.22 <=> 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__strict__left__mono,axiom, % 173.22/173.22 ! [V_c,V_a,V_b,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.22 => ( 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))) % 173.22/173.22 => 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))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__strict__left__mono__neg,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( 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))) % 173.22/173.22 => 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))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__num__frac,axiom, % 173.22/173.22 ! [V_x,V_z,V_y,T_a] : % 173.22/173.22 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__divide__eq__iff,axiom, % 173.22/173.22 ! [V_y,V_x,V_z,T_a] : % 173.22/173.22 ( class_Fields_Ofield(T_a) % 173.22/173.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__frac__num,axiom, % 173.22/173.22 ! [V_z,V_x,V_y,T_a] : % 173.22/173.22 ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__add__eq__iff,axiom, % 173.22/173.22 ! [V_y,V_x,V_z,T_a] : % 173.22/173.22 ( class_Fields_Ofield(T_a) % 173.22/173.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__frac__eq,axiom, % 173.22/173.22 ! [V_w,V_x,V_z,V_y,T_a] : % 173.22/173.22 ( class_Fields_Ofield(T_a) % 173.22/173.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__divide__eq__iff,axiom, % 173.22/173.22 ! [V_y,V_x,V_z,T_a] : % 173.22/173.22 ( class_Fields_Ofield(T_a) % 173.22/173.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__diff__eq__iff,axiom, % 173.22/173.22 ! [V_y,V_x,V_z,T_a] : % 173.22/173.22 ( class_Fields_Ofield(T_a) % 173.22/173.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__frac__eq,axiom, % 173.22/173.22 ! [V_w,V_x,V_z,V_y,T_a] : % 173.22/173.22 ( class_Fields_Ofield(T_a) % 173.22/173.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_gt__half__sum,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__half__sum,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.22/173.22 => 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))))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_abs__div__pos,axiom, % 173.22/173.22 ! [V_x,V_y,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__left__mono__neg,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( 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))) % 173.22/173.22 => 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))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__left__mono,axiom, % 173.22/173.22 ! [V_c,V_a,V_b,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.22/173.22 => ( 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))) % 173.22/173.22 => 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))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__divide__le__eq,axiom, % 173.22/173.22 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( 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)) % 173.22/173.22 <=> 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__le__divide__eq,axiom, % 173.22/173.22 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__imp__le__div__pos,axiom, % 173.22/173.22 ! [V_x,V_z,V_y,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => ( 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)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__imp__div__pos__le,axiom, % 173.22/173.22 ! [V_z,V_x,V_y,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field(T_a) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => ( 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))) % 173.22/173.22 => 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 173.22/173.22 ! [V_f_2,V_A_2,T_a] : % 173.22/173.22 ( ! [B_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.22 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_setprod__Un,axiom, % 173.22/173.22 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.22 ( class_Fields_Ofield(T_b) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( 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))) % 173.22/173.22 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 173.22/173.22 => 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))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__power__power,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Power_Opower(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_int__power__div__base,axiom, % 173.22/173.22 ! [V_k,V_m] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.22/173.22 => 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)))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__by__1,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zero,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zminus2,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zminus__zminus,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__0,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__by__0,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( c_Nat__Transfer_Ois__nat(V_x) % 173.22/173.22 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.22/173.22 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__neg__pos__less0,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 173.22/173.22 ! [V_a_2,V_b_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 173.22/173.22 ! [V_a_2,V_b_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__self,axiom, % 173.22/173.22 ! [V_a] : % 173.22/173.22 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__mult1__if,axiom, % 173.22/173.22 ! [V_b,V_a,V_c,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__self2__is__id,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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 ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__self1__is__id,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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 ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__mult2,axiom, % 173.22/173.22 ! [V_b,V_a,V_c,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__mult1,axiom, % 173.22/173.22 ! [V_b,V_a,V_c,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__self,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__eq__0__iff,axiom, % 173.22/173.22 ! [V_k_2,V_i_2] : % 173.22/173.22 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 173.22/173.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 173.22/173.22 ! [V_a_2,V_b_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 173.22/173.22 ! [V_i_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 173.22/173.22 ! [V_b_2,V_a_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__mono2,axiom, % 173.22/173.22 ! [V_b,V_b_H,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__nonneg__neg__le0,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__pos__pos__trivial,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 173.22/173.22 ! [V_a_2,V_b_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__nonpos__pos__le0,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__mono2__neg,axiom, % 173.22/173.22 ! [V_b,V_b_H,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__neg__neg__trivial,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__mono1,axiom, % 173.22/173.22 ! [V_b,V_a_H,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__mono1__neg,axiom, % 173.22/173.22 ! [V_b,V_a_H,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_int__div__less__self,axiom, % 173.22/173.22 ! [V_k,V_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zmult2__eq,axiom, % 173.22/173.22 ! [V_b,V_a,V_c] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power_Opower_Opower__0,axiom, % 173.22/173.22 ! [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 ). % 173.22/173.22 % 173.22/173.22 fof(fact_power_Opower_Opower__Suc,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__self1,axiom, % 173.22/173.22 ! [V_c,V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__self2,axiom, % 173.22/173.22 ! [V_c,V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__add__self1,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__add__self2,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divmod__int__rel__div__eq,axiom, % 173.22/173.22 ! [V_r_1,V_y,V_b_1,V_a_1] : % 173.22/173.22 ( 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) % 173.22/173.22 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 173.22/173.22 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__zdiv,axiom, % 173.22/173.22 ! [V_k_2,V_n_2,V_P_2] : % 173.22/173.22 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 173.22/173.22 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.22 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.22/173.22 => ! [B_i] : % 173.22/173.22 ( ? [B_j] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 173.22/173.22 & 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) ) % 173.22/173.22 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 173.22/173.22 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ! [B_i] : % 173.22/173.22 ( ? [B_j] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 & 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) ) % 173.22/173.22 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_z3div__def,axiom, % 173.22/173.22 ! [V_k,V_l] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.22/173.22 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_strong__setprod__reindex__cong,axiom, % 173.22/173.22 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 173.22/173.22 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.22/173.22 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.22 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.22 => 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) ) % 173.22/173.22 => 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) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_setprod__mono__one__left,axiom, % 173.22/173.22 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 173.22/173.22 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( 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))) % 173.22/173.22 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 173.22/173.22 => 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) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_setprod__mono__one__right,axiom, % 173.22/173.22 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 173.22/173.22 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( 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))) % 173.22/173.22 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 173.22/173.22 => 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) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult2__eq,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__le__mono,axiom, % 173.22/173.22 ! [V_k,V_n,V_m] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__le__dividend,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__1,axiom, % 173.22/173.22 ! [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 ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__less,axiom, % 173.22/173.22 ! [V_n,V_m] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__mult__div__cancel__disj,axiom, % 173.22/173.22 ! [V_n,V_m,V_k] : % 173.22/173.22 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__int,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__le__mono2,axiom, % 173.22/173.22 ! [V_k,V_n,V_m] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__self__is__m,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult__self1__is__m,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__mult__div__cancel1,axiom, % 173.22/173.22 ! [V_n,V_m,V_k] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__less__dividend,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__if,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__geq,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.22 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__div,axiom, % 173.22/173.22 ! [V_k_2,V_n_2,V_P_2] : % 173.22/173.22 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 173.22/173.22 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.22/173.22 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => ! [B_i,B_j] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 173.22/173.22 => ( 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) % 173.22/173.22 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__div__distrib,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__div__geq,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__div_H,axiom, % 173.22/173.22 ! [V_n_2,V_m_2,V_P_2] : % 173.22/173.22 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 173.22/173.22 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.22/173.22 | ? [B_q] : % 173.22/173.22 ( 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)) % 173.22/173.22 & 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)))) % 173.22/173.22 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__div__lemma,axiom, % 173.22/173.22 ! [V_m_2,V_q_2,V_n_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.22/173.22 => ( ( 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)) % 173.22/173.22 & 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)))) ) % 173.22/173.22 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Nitpick_Onat__lcm__def,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_field__le__mult__one__interval,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 => ( ! [B_z] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 173.22/173.22 => 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)) ) ) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 173.22/173.22 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 173.22/173.22 ( ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.22 & class_Groups_Ocomm__monoid__mult(T_a) ) % 173.22/173.22 => ( V_A_2 = V_B_2 % 173.22/173.22 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.22/173.22 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 173.22/173.22 => 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) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__pos__lemma,axiom, % 173.22/173.22 ! [V_n_2,V_P_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ! [B_i,B_j] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 173.22/173.22 & 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) ) % 173.22/173.22 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( c_Nat__Transfer_Ois__nat(V_x) % 173.22/173.22 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.22/173.22 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__diff__cong,axiom, % 173.22/173.22 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 173.22/173.22 ( class_Divides_Oring__div(T_a) % 173.22/173.22 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 173.22/173.22 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__diff__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Oring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__diff__left__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Oring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__diff__right__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Oring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zero,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__self,axiom, % 173.22/173.22 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__right__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__left__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__mult1,axiom, % 173.22/173.22 ! [V_b,V_a,V_c,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__mult2,axiom, % 173.22/173.22 ! [V_b,V_c,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__simps_I4_J,axiom, % 173.22/173.22 ! [V_b,V_c,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__cong,axiom, % 173.22/173.22 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 173.22/173.22 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__add__self2,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__add__self1,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__add__right__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__add__left__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__add__eq,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__simps_I2_J,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__simps_I1_J,axiom, % 173.22/173.22 ! [V_b,V_c,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__add__cong,axiom, % 173.22/173.22 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 173.22/173.22 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__minus__cong,axiom, % 173.22/173.22 ! [V_a_H,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Oring__div(T_a) % 173.22/173.22 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__minus__eq,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Oring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__0,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__by__0,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__self,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mod__trivial,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zminus2,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zminus__zminus,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zminus__zmod,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiff__zmod__left,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiff__zmod__right,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zmult1__eq,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__simps_I3_J,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zpower__zmod,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__self2__is__0,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__self1__is__0,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__self2,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__self1,axiom, % 173.22/173.22 ! [V_b,V_c,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__by__1,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__div__trivial,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__le__nonneg__dividend,axiom, % 173.22/173.22 ! [V_k,V_m] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__mod__bound,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__mod__bound,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__eq__0__iff,axiom, % 173.22/173.22 ! [V_d_2,V_m_2] : % 173.22/173.22 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zminus2__not__zero,axiom, % 173.22/173.22 ! [V_l,V_k] : % 173.22/173.22 ( 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) % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zminus1__not__zero,axiom, % 173.22/173.22 ! [V_l,V_k] : % 173.22/173.22 ( 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) % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_DIVISION__BY__ZERO,axiom, % 173.22/173.22 ! [V_a] : % 173.22/173.22 ( 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) % 173.22/173.22 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zdiv__trivial,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zadd1__eq,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__div__equality2,axiom, % 173.22/173.22 ! [V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__div__equality,axiom, % 173.22/173.22 ! [V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mod__equality2,axiom, % 173.22/173.22 ! [V_c,V_a,V_b,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mod__equality,axiom, % 173.22/173.22 ! [V_c,V_b,V_a,T_a] : % 173.22/173.22 ( class_Divides_Osemiring__div(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__mod__sign,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pos__mod__conj,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.22 => ( 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))) % 173.22/173.22 & 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__pos__pos__trivial,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__mod__sign,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__mod__conj,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( 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))) % 173.22/173.22 & 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__neg__neg__trivial,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zminus1__eq__if,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zminus2__eq__if,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zdiv__equality,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zmult1__eq,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zmod__equality,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zmod__equality2,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zdiv__equality_H,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmult__div__cancel,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__pos__neg__trivial,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.22 => ( 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))) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divmod__int__rel__mod__eq,axiom, % 173.22/173.22 ! [V_y,V_q_1,V_b_1,V_a_1] : % 173.22/173.22 ( 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) % 173.22/173.22 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 173.22/173.22 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmult2__lemma__aux2,axiom, % 173.22/173.22 ! [V_q,V_r,V_b,V_c] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmult2__lemma__aux1,axiom, % 173.22/173.22 ! [V_q,V_r,V_b,V_c] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmult2__lemma__aux4,axiom, % 173.22/173.22 ! [V_q,V_b,V_r,V_c] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmult2__lemma__aux3,axiom, % 173.22/173.22 ! [V_q,V_b,V_r,V_c] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.22/173.22 => 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))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__zmod,axiom, % 173.22/173.22 ! [V_k_2,V_n_2,V_P_2] : % 173.22/173.22 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 173.22/173.22 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 173.22/173.22 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.22/173.22 => ! [B_i,B_j] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 173.22/173.22 & 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) ) % 173.22/173.22 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 173.22/173.22 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ! [B_i,B_j] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 & 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) ) % 173.22/173.22 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__zmult2__eq,axiom, % 173.22/173.22 ! [V_b,V_a,V_c] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zminus1__eq__if,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__zminus2__eq__if,axiom, % 173.22/173.22 ! [V_a,V_b] : % 173.22/173.22 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.22 => 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)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__neg__lemma,axiom, % 173.22/173.22 ! [V_n_2,V_P_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ! [B_i,B_j] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 & 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) ) % 173.22/173.22 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_z3mod__def,axiom, % 173.22/173.22 ! [V_k,V_l] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.22/173.22 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Nitpick_Oint__gcd__def,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_setprod__pos__nat,axiom, % 173.22/173.22 ! [V_f_2,V_S_2,T_a] : % 173.22/173.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 173.22/173.22 => 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))) ) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_card__quotient__disjoint,axiom, % 173.22/173.22 ! [V_r_2,V_A_2,T_a] : % 173.22/173.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.22 => ( 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) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__less,axiom, % 173.22/173.22 ! [V_n,V_m] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__less__eq__dividend,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__distrib2,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__distrib,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotient__empty,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotient__is__empty2,axiom, % 173.22/173.22 ! [V_r_2,V_A_2,T_a] : % 173.22/173.22 ( 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) % 173.22/173.22 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotient__is__empty,axiom, % 173.22/173.22 ! [V_r_2,V_A_2,T_a] : % 173.22/173.22 ( 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)) % 173.22/173.22 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__1,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__Suc,axiom, % 173.22/173.22 ! [V_n,V_m] : % 173.22/173.22 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.22 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__less__divisor,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__eq__0__iff,axiom, % 173.22/173.22 ! [V_d_2,V_m_2] : % 173.22/173.22 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__if,axiom, % 173.22/173.22 ! [V_n,V_m] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__geq,axiom, % 173.22/173.22 ! [V_n,V_m] : % 173.22/173.22 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__self3,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__mod__geq,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__int,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__add1__eq,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__gcd_Osimps,axiom, % 173.22/173.22 ! [V_x,V_y] : % 173.22/173.22 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 173.22/173.22 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__le__divisor,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult__self4,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__mult2__eq,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mult1__eq,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Omod__div__equality_H,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__div__cancel,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__mod__equality_H,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotient__diff1,axiom, % 173.22/173.22 ! [V_a_2,V_A_2,V_r_2,T_a] : % 173.22/173.22 ( 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) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__lemma,axiom, % 173.22/173.22 ! [V_q,V_b,V_r,V_c] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_split__mod,axiom, % 173.22/173.22 ! [V_k_2,V_n_2,V_P_2] : % 173.22/173.22 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 173.22/173.22 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 173.22/173.22 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 => ! [B_i,B_j] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 173.22/173.22 => ( 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) % 173.22/173.22 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__times__mod__eq,axiom, % 173.22/173.22 ! [V_m,V_k] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__mod__distrib,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 173.22/173.22 ! [V_y,V_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotient__def,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_singleton__quotient,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotientI,axiom, % 173.22/173.22 ! [V_r_2,V_A_2,V_x_2,T_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_fold__image__1,axiom, % 173.22/173.22 ! [V_f_2,V_S_2,T_a,T_b] : % 173.22/173.22 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 173.22/173.22 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Image__eq__UN,axiom, % 173.22/173.22 ! [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))))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Image__Int__subset,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Image__UN,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotientE,axiom, % 173.22/173.22 ! [V_r_2,V_A_2,V_X_2,T_a] : % 173.22/173.22 ( 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))) % 173.22/173.22 => ~ ! [B_x] : % 173.22/173.22 ( 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)))) % 173.22/173.22 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Image__empty,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Image__mono,axiom, % 173.22/173.22 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 173.22/173.22 ( 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)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Un__Image,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Image__Un,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__mod__eq__lemma,axiom, % 173.22/173.22 ! [V_y,V_n,V_x] : % 173.22/173.22 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 173.22/173.22 => ? [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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_card_Oneutral,axiom, % 173.22/173.22 ! [V_A_2,T_a] : % 173.22/173.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.22 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.22 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.22 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__induct__0,axiom, % 173.22/173.22 ! [V_i_2,V_P_2,V_p_2] : % 173.22/173.22 ( ! [B_i] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 173.22/173.22 => ( hBOOL(hAPP(V_P_2,B_i)) % 173.22/173.22 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 173.22/173.22 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 173.22/173.22 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_fold__image__cong,axiom, % 173.22/173.22 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 173.22/173.22 ( class_Groups_Oab__semigroup__mult(T_b) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.22 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__by__empty,axiom, % 173.22/173.22 ! [V_B_2,T_a,V_A_2] : % 173.22/173.22 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Min__eqI,axiom, % 173.22/173.22 ! [V_x_2,V_A_2,T_a] : % 173.22/173.22 ( class_Orderings_Olinorder(T_a) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.22 => ( ! [B_y] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.22 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Max__eqI,axiom, % 173.22/173.22 ! [V_x_2,V_A_2,T_a] : % 173.22/173.22 ( class_Orderings_Olinorder(T_a) % 173.22/173.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.22 => ( ! [B_y] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.22 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_expand__Suc,axiom, % 173.22/173.22 ! [V_v] : % 173.22/173.22 ( 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))) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_quotient__disj,axiom, % 173.22/173.22 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.22 => ( 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))) % 173.22/173.22 => ( 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))) % 173.22/173.22 => ( V_X_2 = V_Y_2 % 173.22/173.22 | 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)) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_of__nat__number__of__lemma,axiom, % 173.22/173.22 ! [V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__reorient,axiom, % 173.22/173.22 ! [V_x_2,V_w_2,T_a] : % 173.22/173.22 ( class_Int_Onumber(T_a) % 173.22/173.22 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 173.22/173.22 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__number__of,axiom, % 173.22/173.22 ! [V_y_2,V_x_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Int_Oring__char__0(T_a) ) % 173.22/173.22 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 173.22/173.22 <=> V_x_2 = V_y_2 ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__eq,axiom, % 173.22/173.22 ! [V_k,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_of__int__number__of__eq,axiom, % 173.22/173.22 ! [V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_of__nat__number__of__eq,axiom, % 173.22/173.22 ! [V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__number__of__eq__not__less,axiom, % 173.22/173.22 ! [V_w_2,V_v_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber(T_a) % 173.22/173.22 & class_Orderings_Olinorder(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ~ 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_right__distrib__number__of,axiom, % 173.22/173.22 ! [V_c,V_b,V_v,T_b] : % 173.22/173.22 ( ( class_Int_Onumber(T_b) % 173.22/173.22 & class_Rings_Osemiring(T_b) ) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_left__distrib__number__of,axiom, % 173.22/173.22 ! [V_v,V_b,V_a,T_b] : % 173.22/173.22 ( ( class_Int_Onumber(T_b) % 173.22/173.22 & class_Rings_Osemiring(T_b) ) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_left__diff__distrib__number__of,axiom, % 173.22/173.22 ! [V_v,V_b,V_a,T_b] : % 173.22/173.22 ( ( class_Int_Onumber(T_b) % 173.22/173.22 & class_Rings_Oring(T_b) ) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_right__diff__distrib__number__of,axiom, % 173.22/173.22 ! [V_c,V_b,V_v,T_b] : % 173.22/173.22 ( ( class_Int_Onumber(T_b) % 173.22/173.22 & class_Rings_Oring(T_b) ) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__number__of,axiom, % 173.22/173.22 ! [V_y_2,V_x_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__number__of,axiom, % 173.22/173.22 ! [V_y_2,V_x_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_min__number__of,axiom, % 173.22/173.22 ! [V_v,V_u,T_b] : % 173.22/173.22 ( ( class_Int_Onumber(T_b) % 173.22/173.22 & class_Orderings_Oord(T_b) ) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_max__number__of,axiom, % 173.22/173.22 ! [V_v,V_u,T_b] : % 173.22/173.22 ( ( class_Int_Onumber(T_b) % 173.22/173.22 & class_Orderings_Oord(T_b) ) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__number__of__left,axiom, % 173.22/173.22 ! [V_z,V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__number__of__eq,axiom, % 173.22/173.22 ! [V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__add,axiom, % 173.22/173.22 ! [V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__mult,axiom, % 173.22/173.22 ! [V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_arith__simps_I32_J,axiom, % 173.22/173.22 ! [V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__number__of__left,axiom, % 173.22/173.22 ! [V_z,V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__diff,axiom, % 173.22/173.22 ! [V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_arith__simps_I30_J,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__minus,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Ints__number__of,axiom, % 173.22/173.22 ! [V_w_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__divide__eq__number__of1,axiom, % 173.22/173.22 ! [V_w_2,V_b_2,V_a_2,T_a] : % 173.22/173.22 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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)) % 173.22/173.22 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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 ) % 173.22/173.22 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__divide__eq__number__of,axiom, % 173.22/173.22 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 173.22/173.22 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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) % 173.22/173.22 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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 ) % 173.22/173.22 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__eq__eq__number__of,axiom, % 173.22/173.22 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 173.22/173.22 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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) % 173.22/173.22 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__eq__eq__number__of1,axiom, % 173.22/173.22 ! [V_a_2,V_w_2,V_b_2,T_a] : % 173.22/173.22 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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 % 173.22/173.22 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__number__of__diff1,axiom, % 173.22/173.22 ! [V_c,V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_minus__number__of__mult,axiom, % 173.22/173.22 ! [V_z,V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__number__of__eq,axiom, % 173.22/173.22 ! [V_w,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__divide__eq__number__of1,axiom, % 173.22/173.22 ! [V_w_2,V_b_2,V_a_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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)))) % 173.22/173.22 <=> ( ( 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))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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)))) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__divide__eq__number__of,axiom, % 173.22/173.22 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__less__eq__number__of,axiom, % 173.22/173.22 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__less__eq__number__of1,axiom, % 173.22/173.22 ! [V_a_2,V_w_2,V_b_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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)) % 173.22/173.22 <=> ( ( 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))) % 173.22/173.22 => 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)))) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_abs__number__of,axiom, % 173.22/173.22 ! [V_x,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__number__of__diff2,axiom, % 173.22/173.22 ! [V_w,V_c,V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__divide__eq__number__of1,axiom, % 173.22/173.22 ! [V_w_2,V_b_2,V_a_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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)))) % 173.22/173.22 <=> ( ( 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))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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)))) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__divide__eq__number__of,axiom, % 173.22/173.22 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__le__eq__number__of,axiom, % 173.22/173.22 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.22 => 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))) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__le__eq__number__of1,axiom, % 173.22/173.22 ! [V_a_2,V_w_2,V_b_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber(T_a) ) % 173.22/173.22 => ( 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)) % 173.22/173.22 <=> ( ( 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))) % 173.22/173.22 => 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)))) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_equiv__class__self,axiom, % 173.22/173.22 ! [V_a_2,V_r_2,V_A_2,T_a] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.22 => 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)))))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_UN__equiv__class,axiom, % 173.22/173.22 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.22 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_UN__equiv__class2,axiom, % 173.22/173.22 ! [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] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 173.22/173.22 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 173.22/173.22 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 173.22/173.22 => 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) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_one__mod__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_one__div__nat__number__of,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__eq__number__of__int__code,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_minus__numeral__code_I5_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__number__of__int__code,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_plus__numeral__code_I9_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__is__id,axiom, % 173.22/173.22 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 173.22/173.22 % 173.22/173.22 fof(fact_times__numeral__code_I5_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_int__number__of__def,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__def,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_congruent2__implies__congruent,axiom, % 173.22/173.22 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 173.22/173.22 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.22 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_minus__numeral__code_I6_J,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__imp__number__of__eq__0,axiom, % 173.22/173.22 ! [V_v] : % 173.22/173.22 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_int__eq__iff__number__of,axiom, % 173.22/173.22 ! [V_v_2,V_m_2] : % 173.22/173.22 ( 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) % 173.22/173.22 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 173.22/173.22 & 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H_2,V_v_2] : % 173.22/173.22 ( 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) % 173.22/173.22 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 173.22/173.22 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 173.22/173.22 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__add__left,axiom, % 173.22/173.22 ! [V_k,V_v_H,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.22/173.22 => 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) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_int__nat__number__of,axiom, % 173.22/173.22 ! [V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.22/173.22 => 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))) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_congruent2__implies__congruent__UN,axiom, % 173.22/173.22 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 173.22/173.22 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 173.22/173.22 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 173.22/173.22 => 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)) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__nat__number__of,axiom, % 173.22/173.22 ! [V_n,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__nat__number__of__number__of,axiom, % 173.22/173.22 ! [V_w,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__nat__number__of__add,axiom, % 173.22/173.22 ! [V_n,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__nat__number__of,axiom, % 173.22/173.22 ! [V_v_2,V_v_H_2] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_min__number__of__Suc,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_min__Suc__number__of,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I19_J,axiom, % 173.22/173.22 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__bin__simps_I1_J,axiom, % 173.22/173.22 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__Pls__right,axiom, % 173.22/173.22 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__Pls,axiom, % 173.22/173.22 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 173.22/173.22 % 173.22/173.22 fof(fact_Pls__def,axiom, % 173.22/173.22 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 173.22/173.22 % 173.22/173.22 fof(fact_succ__pred,axiom, % 173.22/173.22 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I2_J,axiom, % 173.22/173.22 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_minus__Pls,axiom, % 173.22/173.22 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__Pls,axiom, % 173.22/173.22 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__Pls,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_semiring__norm_I112_J,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__numeral__0,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__numeral__0__right,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_bin__less__0__simps_I1_J,axiom, % 173.22/173.22 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__Pls,axiom, % 173.22/173.22 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.22 % 173.22/173.22 fof(fact_semiring__norm_I113_J,axiom, % 173.22/173.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zero__is__num__zero,axiom, % 173.22/173.22 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__diff__number__of,axiom, % 173.22/173.22 ! [V_m,V_v] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_not__neg__number__of__Pls,axiom, % 173.22/173.22 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__add__1,axiom, % 173.22/173.22 ! [V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__1__add__number__of,axiom, % 173.22/173.22 ! [V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__iff__pred__less,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pred__def,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__diff__1,axiom, % 173.22/173.22 ! [V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__Numeral0,axiom, % 173.22/173.22 ! [V_x,T_a] : % 173.22/173.22 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber__ring(T_a) ) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__0__number__of,axiom, % 173.22/173.22 ! [V_v_2] : % 173.22/173.22 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__number__of__0,axiom, % 173.22/173.22 ! [V_v_2] : % 173.22/173.22 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of2,axiom, % 173.22/173.22 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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H_2,V_v_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 173.22/173.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H_2,V_v_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_succ__def,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__special_I3_J,axiom, % 173.22/173.22 ! [V_x_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__special_I1_J,axiom, % 173.22/173.22 ! [V_y_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__special_I1_J,axiom, % 173.22/173.22 ! [V_y_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__special_I3_J,axiom, % 173.22/173.22 ! [V_x_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__0__number__of,axiom, % 173.22/173.22 ! [V_v_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 173.22/173.22 => 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)) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__succ,axiom, % 173.22/173.22 ! [V_k,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__pred,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__nat__number__of,axiom, % 173.22/173.22 ! [V_v_H,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__mult__left,axiom, % 173.22/173.22 ! [V_k,V_v_H,V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__number__of__pred__iff__0,axiom, % 173.22/173.22 ! [V_v_2] : % 173.22/173.22 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 173.22/173.22 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__eq__number__of,axiom, % 173.22/173.22 ! [V_v_2,V_n_2] : % 173.22/173.22 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 173.22/173.22 <=> 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))))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__number__of__Suc,axiom, % 173.22/173.22 ! [V_n_2,V_v_2] : % 173.22/173.22 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 173.22/173.22 <=> 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))))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__case__number__of,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__number__of__Suc,axiom, % 173.22/173.22 ! [V_n_2,V_v_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__Suc__number__of,axiom, % 173.22/173.22 ! [V_v_2,V_n_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> 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))))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__Suc__number__of,axiom, % 173.22/173.22 ! [V_v_2,V_n_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> 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))))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__number__of__Suc,axiom, % 173.22/173.22 ! [V_n_2,V_v_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__nat__number__of,axiom, % 173.22/173.22 ! [V_v] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_max__Suc__number__of,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_max__number__of__Suc,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__case__add__eq__if,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__rec__add__eq__if,axiom, % 173.22/173.22 ! [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))))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__rec__number__of,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_UN__equiv__class__type2,axiom, % 173.22/173.22 ! [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] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 173.22/173.22 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 173.22/173.22 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 173.22/173.22 => ( 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))) % 173.22/173.22 => ( 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))) % 173.22/173.22 => ( ! [B_x1] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 173.22/173.22 => ! [B_x2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 173.22/173.22 => 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)) ) ) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_UN__equiv__class__type,axiom, % 173.22/173.22 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 173.22/173.22 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.22 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 173.22/173.22 => ( 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))) % 173.22/173.22 => ( ! [B_x] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.22 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 173.22/173.22 => 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)) ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__rec__0,axiom, % 173.22/173.22 ! [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 ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__rec__Suc,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__special_I3_J,axiom, % 173.22/173.22 ! [V_x_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.22 <=> 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)))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__special_I1_J,axiom, % 173.22/173.22 ! [V_y_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 173.22/173.22 <=> 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)))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__number__of__odd__number__of,axiom, % 173.22/173.22 ! [V_v_2,V_w_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_iszero__number__of__Bit1,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Int_Oring__char__0(T_a) ) % 173.22/173.22 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__eq__int__code_I16_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I34_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I51_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 173.22/173.22 <=> V_k_2 = V_l_2 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I17_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__int__code_I16_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I46_J,axiom, % 173.22/173.22 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I39_J,axiom, % 173.22/173.22 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 173.22/173.22 % 173.22/173.22 fof(fact_not__iszero__Numeral1,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_iszero__def,axiom, % 173.22/173.22 ! [V_z_2,T_a] : % 173.22/173.22 ( class_Rings_Osemiring__1(T_a) % 173.22/173.22 => ( c_Int_Oiszero(T_a,V_z_2) % 173.22/173.22 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_iszero__0,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Rings_Osemiring__1(T_a) % 173.22/173.22 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_not__iszero__1,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Rings_Osemiring__1(T_a) % 173.22/173.22 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_bin__less__0__simps_I4_J,axiom, % 173.22/173.22 ! [V_w_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I22_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I12_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Bit1__def,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__number__of__Bit1,axiom, % 173.22/173.22 ! [V_w_2] : % 173.22/173.22 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 173.22/173.22 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_minus__Bit1,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_succ__Pls,axiom, % 173.22/173.22 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__Bit1,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__numeral__1,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__numeral__1__right,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_numeral__1__eq__1,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_semiring__norm_I110_J,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I29_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I5_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__Numeral1,axiom, % 173.22/173.22 ! [V_x,T_a] : % 173.22/173.22 ( ( class_Fields_Ofield(T_a) % 173.22/173.22 & class_Int_Onumber__ring(T_a) ) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_divide__numeral__1,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( ( class_Fields_Ofield(T_a) % 173.22/173.22 & class_Int_Onumber__ring(T_a) ) % 173.22/173.22 => 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 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__special_I2_J,axiom, % 173.22/173.22 ! [V_y_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 173.22/173.22 <=> 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)))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__special_I4_J,axiom, % 173.22/173.22 ! [V_x_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 173.22/173.22 <=> 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))))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_one__is__num__one,axiom, % 173.22/173.22 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__numeral__1__eq__1,axiom, % 173.22/173.22 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Numeral1__eq1__nat,axiom, % 173.22/173.22 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 173.22/173.22 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_iszero__Numeral0,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_numeral__1__eq__Suc__0,axiom, % 173.22/173.22 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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_numeral__3__eq__3,axiom, % 173.22/173.22 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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power3__eq__cube,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 173.22/173.22 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))))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc3__eq__add__3,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 173.22/173.22 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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 173.22/173.22 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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__special_I2_J,axiom, % 173.22/173.22 ! [V_y_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_le__special_I4_J,axiom, % 173.22/173.22 ! [V_x_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__special_I4_J,axiom, % 173.22/173.22 ! [V_x_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__special_I2_J,axiom, % 173.22/173.22 ! [V_y_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.22 => ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__special_I2_J,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__special_I3_J,axiom, % 173.22/173.22 ! [V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__diff__eq__diff__pred,axiom, % 173.22/173.22 ! [V_m,V_n] : % 173.22/173.22 ( 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)) % 173.22/173.22 => 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__mod__eq__add3__mod,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod__Suc__eq__mod__add3,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Suc__div__eq__add3__div,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div__Suc__eq__div__add3,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_eq__number__of__eq,axiom, % 173.22/173.22 ! [V_y_2,V_x_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 173.22/173.22 <=> 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)))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__special_I1_J,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__special_I2_J,axiom, % 173.22/173.22 ! [V_v,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__Bit1,axiom, % 173.22/173.22 ! [V_w_2] : % 173.22/173.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 173.22/173.22 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 173.22/173.22 => 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)))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__number__of__odd,axiom, % 173.22/173.22 ! [V_z_2,V_w_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => ( ( 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))) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zpower__number__of__odd,axiom, % 173.22/173.22 ! [V_z_2,V_w_2] : % 173.22/173.22 ( ( 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))) % 173.22/173.22 => 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))) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__zmod__mult__2,axiom, % 173.22/173.22 ! [V_b,V_a] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__number__of__Bit1,axiom, % 173.22/173.22 ! [V_v,V_w] : % 173.22/173.22 ( ( 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))) % 173.22/173.22 => 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)) ) % 173.22/173.22 & ( ~ 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))) % 173.22/173.22 => 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)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_arith__series__int,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I49_J,axiom, % 173.22/173.22 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I50_J,axiom, % 173.22/173.22 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Bit0__Pls,axiom, % 173.22/173.22 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I38_J,axiom, % 173.22/173.22 ! [V_l_2] : % 173.22/173.22 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 173.22/173.22 <=> c_Int_OPls = V_l_2 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I44_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 173.22/173.22 <=> V_k_2 = c_Int_OPls ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__int__code_I13_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I14_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Bit0__def,axiom, % 173.22/173.22 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__Bit0__Bit0,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I48_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 173.22/173.22 <=> V_k_2 = V_l_2 ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_minus__Bit0,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__Bit0,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__bin__simps_I7_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I31_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__eq__int__code_I13_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_bin__less__0__simps_I3_J,axiom, % 173.22/173.22 ! [V_w_2] : % 173.22/173.22 ( 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))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I27_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I21_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__eq__int__code_I14_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I32_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I4_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I10_J,axiom, % 173.22/173.22 ! [V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I16_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__int__code_I15_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__Bit0__Bit1,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__Bit1__Bit0,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__bin__simps_I3_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__bin__simps_I10_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__bin__simps_I9_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zdiv__number__of__Bit0,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_neg__number__of__Bit0,axiom, % 173.22/173.22 ! [V_w_2] : % 173.22/173.22 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 173.22/173.22 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pred__Bit1,axiom, % 173.22/173.22 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 173.22/173.22 % 173.22/173.22 fof(fact_pred__Bit0,axiom, % 173.22/173.22 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_iszero__number__of__Bit0,axiom, % 173.22/173.22 ! [V_w_2,T_a] : % 173.22/173.22 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.22 & class_Int_Oring__char__0(T_a) ) % 173.22/173.22 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 173.22/173.22 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_succ__Bit0,axiom, % 173.22/173.22 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 173.22/173.22 % 173.22/173.22 fof(fact_succ__Bit1,axiom, % 173.22/173.22 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__number__of__Bit0,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of__Bit0,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I15_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__int__code_I14_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_rel__simps_I33_J,axiom, % 173.22/173.22 ! [V_l_2,V_k_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_less__eq__int__code_I15_J,axiom, % 173.22/173.22 ! [V_k2_2,V_k1_2] : % 173.22/173.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_card__UNIV__bool,axiom, % 173.22/173.22 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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__Bit1,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_diff__bin__simps_I8_J,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__Bit1__Bit1,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__number__of__even,axiom, % 173.22/173.22 ! [V_w_2,V_z_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zpower__number__of__even,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_double__number__of__Bit0,axiom, % 173.22/173.22 ! [V_w,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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)) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_number__of1,axiom, % 173.22/173.22 ! [V_n] : % 173.22/173.22 ( 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))) % 173.22/173.22 => ( 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)))) % 173.22/173.22 & 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)))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 173.22/173.22 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__number__of__even__number__of,axiom, % 173.22/173.22 ! [V_w_2,V_v_2,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__2__right,axiom, % 173.22/173.22 ! [V_z,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mult__2,axiom, % 173.22/173.22 ! [V_z,T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_one__add__one__is__two,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Int_Onumber__ring(T_a) % 173.22/173.22 => 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))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zero__power2,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Rings_Osemiring__1(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zero__eq__power2,axiom, % 173.22/173.22 ! [V_a_2,T_a] : % 173.22/173.22 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 173.22/173.22 => ( 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) % 173.22/173.22 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_numeral__2__eq__2,axiom, % 173.22/173.22 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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_semiring__norm_I115_J,axiom, % 173.22/173.22 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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power2__eq__square,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 173.22/173.22 ! [V_x,T_a] : % 173.22/173.22 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.22 => 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 173.22/173.22 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))))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__2__eq__Suc,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__2__eq__Suc_H,axiom, % 173.22/173.22 ! [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)) ). % 173.22/173.22 % 173.22/173.22 fof(fact_one__power2,axiom, % 173.22/173.22 ! [T_a] : % 173.22/173.22 ( class_Rings_Osemiring__1(T_a) % 173.22/173.22 => 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) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power2__minus,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Rings_Oring__1(T_a) % 173.22/173.22 => 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__mult__2__right,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__mult__2,axiom, % 173.22/173.22 ! [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) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power__even__eq,axiom, % 173.22/173.22 ! [V_n,V_a,T_a] : % 173.22/173.22 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.22 => 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 173.22/173.22 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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 173.22/173.22 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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power2__abs,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.22 => 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_abs__power2,axiom, % 173.22/173.22 ! [V_a,T_a] : % 173.22/173.22 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.22 => 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)))) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_nat__1__add__1,axiom, % 173.22/173.22 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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_mod2__Suc__Suc,axiom, % 173.22/173.22 ! [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)))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_div2__Suc__Suc,axiom, % 173.22/173.22 ! [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))))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_zmod__number__of__Bit0,axiom, % 173.22/173.22 ! [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))) ). % 173.22/173.22 % 173.22/173.22 fof(fact_add__self__div__2,axiom, % 173.22/173.22 ! [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 ). % 173.22/173.22 % 173.22/173.22 fof(fact_half__gt__zero,axiom, % 173.22/173.22 ! [V_r,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber__ring(T_a) ) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 173.22/173.22 => 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)))))) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_half__gt__zero__iff,axiom, % 173.22/173.22 ! [V_r_2,T_a] : % 173.22/173.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.22/173.22 & class_Int_Onumber__ring(T_a) ) % 173.22/173.22 => ( 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)))))) % 173.22/173.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power2__eq__imp__eq,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.22 => ( 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)))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.22 => V_x = V_y ) ) ) ) ). % 173.22/173.22 % 173.22/173.22 fof(fact_power2__le__imp__le,axiom, % 173.22/173.22 ! [V_y,V_x,T_a] : % 173.22/173.22 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.22 => ( 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)))))) % 173.22/173.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zero__le__power2,axiom, % 173.22/173.23 ! [V_a,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => 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)))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power2__less__0,axiom, % 173.22/173.23 ! [V_a,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ~ 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zero__less__power2,axiom, % 173.22/173.23 ! [V_a_2,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ( 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)))))) % 173.22/173.23 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sum__power2__eq__zero__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ( 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) % 173.22/173.23 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.23 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power2__eq__square__number__of,axiom, % 173.22/173.23 ! [V_w,T_b] : % 173.22/173.23 ( ( class_Groups_Omonoid__mult(T_b) % 173.22/173.23 & class_Int_Onumber(T_b) ) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_less__2__cases,axiom, % 173.22/173.23 ! [V_n] : % 173.22/173.23 ( 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))))) % 173.22/173.23 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat__2,axiom, % 173.22/173.23 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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power2__eq__1__iff,axiom, % 173.22/173.23 ! [V_a_2,T_a] : % 173.22/173.23 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 173.22/173.23 => ( 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) % 173.22/173.23 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 173.22/173.23 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 173.22/173.23 ! [V_n,V_x,T_a] : % 173.22/173.23 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power__minus__even,axiom, % 173.22/173.23 ! [V_n,V_a,T_a] : % 173.22/173.23 ( class_Rings_Oring__1(T_a) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power2__less__imp__less,axiom, % 173.22/173.23 ! [V_y,V_x,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__semidom(T_a) % 173.22/173.23 => ( 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)))))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sum__power2__ge__zero,axiom, % 173.22/173.23 ! [V_y,V_x,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => 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))))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sum__power2__le__zero__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ( 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))) % 173.22/173.23 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.23 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sum__power2__gt__zero__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ( 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))))))) % 173.22/173.23 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 173.22/173.23 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_not__sum__power2__lt__zero,axiom, % 173.22/173.23 ! [V_y,V_x,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ~ 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power2__sum,axiom, % 173.22/173.23 ! [V_y,V_x,T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zero__le__even__power_H,axiom, % 173.22/173.23 ! [V_n,V_a,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power__odd__eq,axiom, % 173.22/173.23 ! [V_n,V_a,T_a] : % 173.22/173.23 ( class_Groups_Omonoid__mult(T_a) % 173.22/173.23 => 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))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 173.22/173.23 ! [V_n,V_x,T_a] : % 173.22/173.23 ( class_Rings_Ocomm__semiring__1(T_a) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power__minus1__even,axiom, % 173.22/173.23 ! [V_n,T_a] : % 173.22/173.23 ( class_Rings_Oring__1(T_a) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zdiv__number__of__Bit1,axiom, % 173.22/173.23 ! [V_v,V_w] : % 173.22/173.23 ( ( 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))) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ 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))) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod2__gr__0,axiom, % 173.22/173.23 ! [V_m_2] : % 173.22/173.23 ( 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)))))) % 173.22/173.23 <=> 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__2__gt__zero,axiom, % 173.22/173.23 ! [V_n] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 173.22/173.23 => 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)))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power2__diff,axiom, % 173.22/173.23 ! [V_y,V_x,T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_odd__0__le__power__imp__0__le,axiom, % 173.22/173.23 ! [V_n,V_a,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ( 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))))) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_odd__power__less__zero,axiom, % 173.22/173.23 ! [V_n,V_a,T_a] : % 173.22/173.23 ( class_Rings_Olinordered__idom(T_a) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power__minus1__odd,axiom, % 173.22/173.23 ! [V_n,T_a] : % 173.22/173.23 ( class_Rings_Oring__1(T_a) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Suc__n__div__2__gt__zero,axiom, % 173.22/173.23 ! [V_n] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.23 => 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)))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_of__nat__double,axiom, % 173.22/173.23 ! [V_x,T_a] : % 173.22/173.23 ( class_Rings_Osemiring__1(T_a) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pos__zmod__mult__2,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pos__zdiv__mult__2,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_neg__zdiv__mult__2,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_int__of__code,axiom, % 173.22/173.23 ! [V_k] : % 173.22/173.23 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.23 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.22/173.23 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.23 => ( ( 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) % 173.22/173.23 => 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)))))) ) % 173.22/173.23 & ( 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) % 173.22/173.23 => 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)) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_of__int__num,axiom, % 173.22/173.23 ! [V_k_2,T_a] : % 173.22/173.23 ( class_Rings_Oring__1(T_a) % 173.22/173.23 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 173.22/173.23 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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))) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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))))) ) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power__m1__odd,axiom, % 173.22/173.23 ! [V_n,T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I45_J,axiom, % 173.22/173.23 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I42_J,axiom, % 173.22/173.23 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I24_J,axiom, % 173.22/173.23 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral__zero__minus__one,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I7_J,axiom, % 173.22/173.23 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I37_J,axiom, % 173.22/173.23 c_Int_OPls != c_Int_OMin ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I40_J,axiom, % 173.22/173.23 c_Int_OMin != c_Int_OPls ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I47_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 173.22/173.23 <=> V_k_2 = c_Int_OMin ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I43_J,axiom, % 173.22/173.23 ! [V_l_2] : % 173.22/173.23 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 173.22/173.23 <=> c_Int_OMin = V_l_2 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Bit1__Min,axiom, % 173.22/173.23 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 173.22/173.23 % 173.22/173.23 fof(fact_bin__less__0__simps_I2_J,axiom, % 173.22/173.23 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I23_J,axiom, % 173.22/173.23 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I20_J,axiom, % 173.22/173.23 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I26_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I30_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I3_J,axiom, % 173.22/173.23 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I6_J,axiom, % 173.22/173.23 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I13_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I9_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I28_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I8_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_eq__number__of__Pls__Min,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Int_OMin__def,axiom, % 173.22/173.23 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mult__Min,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_neg__number__of__Min,axiom, % 173.22/173.23 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__Pls,axiom, % 173.22/173.23 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 173.22/173.23 % 173.22/173.23 fof(fact_add__Min__right,axiom, % 173.22/173.23 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 173.22/173.23 % 173.22/173.23 fof(fact_add__Min,axiom, % 173.22/173.23 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__Min,axiom, % 173.22/173.23 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nonzero__number__of__Min,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_succ__Min,axiom, % 173.22/173.23 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 173.22/173.23 % 173.22/173.23 fof(fact_diff__bin__simps_I2_J,axiom, % 173.22/173.23 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mult__minus1__right,axiom, % 173.22/173.23 ! [V_z,T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mult__minus1,axiom, % 173.22/173.23 ! [V_z,T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_number__of__Min,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_arith__simps_I31_J,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_abs__minus__one,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.23 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divide__minus1,axiom, % 173.22/173.23 ! [V_x,T_a] : % 173.22/173.23 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.23 & class_Int_Onumber__ring(T_a) ) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I11_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__simps_I25_J,axiom, % 173.22/173.23 ! [V_k_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zmod__minus1__right,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_diff__bin__simps_I4_J,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_minus__Min,axiom, % 173.22/173.23 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zmult__eq__1__iff,axiom, % 173.22/173.23 ! [V_n_2,V_m_2] : % 173.22/173.23 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.22/173.23 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.22/173.23 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 173.22/173.23 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 173.22/173.23 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 173.22/173.23 ! [V_n,V_m] : % 173.22/173.23 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.22/173.23 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.22/173.23 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_diff__bin__simps_I6_J,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_diff__bin__simps_I5_J,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_of__int__m1,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zdiv__minus1__right,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zero__code__numeral__code,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_minus1__divide,axiom, % 173.22/173.23 ! [V_x,T_a] : % 173.22/173.23 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.22/173.23 & class_Int_Onumber__ring(T_a) ) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_abs__power__minus__one,axiom, % 173.22/173.23 ! [V_n,T_a] : % 173.22/173.23 ( ( class_Int_Onumber__ring(T_a) % 173.22/173.23 & class_Rings_Olinordered__idom(T_a) ) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__eq__minus1,axiom, % 173.22/173.23 ! [V_b] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__pos__neg__trivial,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( 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))) % 173.22/173.23 => 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) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zmod__minus1,axiom, % 173.22/173.23 ! [V_b] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_one__code__numeral__code,axiom, % 173.22/173.23 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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_power__m1__even,axiom, % 173.22/173.23 ! [V_n,T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_OFrac__def,axiom, % 173.22/173.23 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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_int__ge__less__than2__def,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_int__ge__less__than__def,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_congruent__def,axiom, % 173.22/173.23 ! [V_f_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 173.22/173.23 <=> ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_inj__graph,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_Oprod__def,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat__of__aux__code,axiom, % 173.22/173.23 ! [V_n,V_i] : % 173.22/173.23 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.23 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 173.22/173.23 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__rel__def,axiom, % 173.22/173.23 ! [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))))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__correct,axiom, % 173.22/173.23 ! [V_a,V_b] : % 173.22/173.23 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zmult2__lemma,axiom, % 173.22/173.23 ! [V_c,V_r,V_q,V_b,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osize_I1_J,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nats__number__of,axiom, % 173.22/173.23 ! [V_w_2,T_a] : % 173.22/173.23 ( class_Int_Onumber__ring(T_a) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_enum__all__prod__def,axiom, % 173.22/173.23 ! [V_P_2,T_a,T_b] : % 173.22/173.23 ( ( class_Enum_Oenum(T_b) % 173.22/173.23 & class_Enum_Oenum(T_a) ) % 173.22/173.23 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 173.22/173.23 <=> 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))))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_enum__ex__prod__def,axiom, % 173.22/173.23 ! [V_P_2,T_a,T_b] : % 173.22/173.23 ( ( class_Enum_Oenum(T_b) % 173.22/173.23 & class_Enum_Oenum(T_a) ) % 173.22/173.23 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 173.22/173.23 <=> 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))))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_congruent2D,axiom, % 173.22/173.23 ! [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] : % 173.22/173.23 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_congruentD,axiom, % 173.22/173.23 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_bot__empty__eq2,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__equals__eq2,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,T_b,T_a] : % 173.22/173.23 ( 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) % 173.22/173.23 <=> V_R_2 = V_S_2 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_inf__Int__eq2,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__subset__eq2,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sup__Un__eq2,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rev__ImageI,axiom, % 173.22/173.23 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Image__iff,axiom, % 173.22/173.23 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 173.22/173.23 <=> ? [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.23 & 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_unique__remainder,axiom, % 173.22/173.23 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => V_r = V_r_H ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_unique__quotient,axiom, % 173.22/173.23 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => V_q = V_q_H ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_self__remainder,axiom, % 173.22/173.23 ! [V_r,V_q,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__rel__0,axiom, % 173.22/173.23 ! [V_b] : % 173.22/173.23 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_SUP__UN__eq2,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_self__quotient,axiom, % 173.22/173.23 ! [V_r,V_q,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__rel__mod,axiom, % 173.22/173.23 ! [V_r,V_q,V_b,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__rel__div,axiom, % 173.22/173.23 ! [V_r,V_q,V_b,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nats__0,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( class_Rings_Osemiring__1(T_a) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__mod__div,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nats__add,axiom, % 173.22/173.23 ! [V_b_2,V_a_2,T_a] : % 173.22/173.23 ( class_Rings_Osemiring__1(T_a) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 173.22/173.23 => 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))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nats__mult,axiom, % 173.22/173.23 ! [V_b_2,V_a_2,T_a] : % 173.22/173.23 ( class_Rings_Osemiring__1(T_a) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 173.22/173.23 => 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))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nats__1,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( class_Rings_Osemiring__1(T_a) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_of__nat__in__Nats,axiom, % 173.22/173.23 ! [V_n_2,T_a] : % 173.22/173.23 ( class_Rings_Osemiring__1(T_a) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Image__singleton__iff,axiom, % 173.22/173.23 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 173.22/173.23 ( 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)))))) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equiv__class__eq,axiom, % 173.22/173.23 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_quotient__eq__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 173.22/173.23 => ( V_X_2 = V_Y_2 % 173.22/173.23 <=> hBOOL(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)) ) ) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_quotient__eqI,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 173.22/173.23 => ( hBOOL(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)) % 173.22/173.23 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__rel__div__mod,axiom, % 173.22/173.23 ! [V_a,V_b] : % 173.22/173.23 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Image__singleton,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equiv__class__eq__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( hBOOL(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)) % 173.22/173.23 <=> ( 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)))) % 173.22/173.23 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.23 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_eq__equiv__class__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 173.22/173.23 => ( 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)))) % 173.22/173.23 <=> hBOOL(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)) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_eq__equiv__class,axiom, % 173.22/173.23 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 173.22/173.23 ( 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)))) % 173.22/173.23 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equiv__class__subset,axiom, % 173.22/173.23 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)))))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_eq__equiv__class__iff2,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 173.22/173.23 => ( 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) % 173.22/173.23 <=> hBOOL(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)) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zadd1__lemma,axiom, % 173.22/173.23 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zminus1__lemma,axiom, % 173.22/173.23 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => 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))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_subset__equiv__class,axiom, % 173.22/173.23 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( 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)))))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equiv__class__nondisjoint,axiom, % 173.22/173.23 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( 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))))))) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__relI,axiom, % 173.22/173.23 ! [V_r,V_q,V_b,V_a] : % 173.22/173.23 ( 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) % 173.22/173.23 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.22/173.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.22/173.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_zmult1__lemma,axiom, % 173.22/173.23 ! [V_a,V_r,V_q,V_c,V_b] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__imageI,axiom, % 173.22/173.23 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_norm__frac_Osimps,axiom, % 173.22/173.23 ! [V_a_2,V_b_2] : % 173.22/173.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.22/173.23 => 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))) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_adjust__eq,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sup2E,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sup2CI,axiom, % 173.22/173.23 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 173.22/173.23 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_inf2E,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.22/173.23 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_inf2I,axiom, % 173.22/173.23 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mem__splitI,axiom, % 173.22/173.23 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 173.22/173.23 => 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_splitI,axiom, % 173.22/173.23 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_prod__caseI,axiom, % 173.22/173.23 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_bot2E,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__Pair,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_splitD_H,axiom, % 173.22/173.23 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_swap__inj__on,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_predicate2D,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rev__predicate2D,axiom, % 173.22/173.23 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sup2I1,axiom, % 173.22/173.23 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_sup2I2,axiom, % 173.22/173.23 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_inf2D2,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_inf2D1,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Pair__inject,axiom, % 173.22/173.23 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 173.22/173.23 ( 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) % 173.22/173.23 => ~ ( V_a = V_a_H % 173.22/173.23 => V_b != V_b_H ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Pair__eq,axiom, % 173.22/173.23 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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) % 173.22/173.23 <=> ( V_a_2 = V_a_H_2 % 173.22/173.23 & V_b_2 = V_b_H_2 ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__paired__All,axiom, % 173.22/173.23 ! [T_b,T_a,V_P_2] : % 173.22/173.23 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.23 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__weak__cong,axiom, % 173.22/173.23 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 173.22/173.23 ( V_p_2 = V_q_2 % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__twice,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__conv,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_prod_Osimps_I2_J,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_splitD,axiom, % 173.22/173.23 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__eta,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__paired__The,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_The__split__eq,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_adjust__def,axiom, % 173.22/173.23 ! [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))))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_in__rel__def,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__mod__code__numeral__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 173.22/173.23 ! [V_w] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( 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)))) % 173.22/173.23 => 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))) ) % 173.22/173.23 & ( ~ 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)))) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg__correct,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg__div__mod,axiom, % 173.22/173.23 ! [V_l,V_k] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg__minus1,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg_Osimps,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( ( ( 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))) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ ( 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))) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg__eqn,axiom, % 173.22/173.23 ! [V_a,V_b] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => ( ( 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))) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ 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))) % 173.22/173.23 => 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))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg__eqn__number__of,axiom, % 173.22/173.23 ! [V_w,V_v] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( 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)))) % 173.22/173.23 => 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))) ) % 173.22/173.23 & ( ~ 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)))) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_Orefl_H__def,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 173.22/173.23 <=> ! [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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 173.22/173.23 ! [V_w] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( 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))) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ 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))) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg_Osimps,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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) ) % 173.22/173.23 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg__0,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg__correct,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg__div__mod,axiom, % 173.22/173.23 ! [V_l,V_k] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg__eqn,axiom, % 173.22/173.23 ! [V_a,V_b] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.22/173.23 => 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) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.22/173.23 => 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))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg__eqn__number__of,axiom, % 173.22/173.23 ! [V_w,V_v] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( 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))) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ 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))) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__def,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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))) ) ) ) ) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => 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))) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__step,axiom, % 173.22/173.23 ! [V_m,V_n] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__pdivmod,axiom, % 173.22/173.23 ! [V_l_2,V_k_2] : % 173.22/173.23 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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) ) % 173.22/173.23 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)))) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apsnd__compose,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negateSnd__def,axiom, % 173.22/173.23 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apsnd__conv,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__zero,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__base,axiom, % 173.22/173.23 ! [V_n,V_m] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.22/173.23 => 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apsnd__id,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negateSnd__eq,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__div__mod,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__rel__neg,axiom, % 173.22/173.23 ! [V_qr,V_b,V_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__if,axiom, % 173.22/173.23 ! [V_m_2,V_n_2] : % 173.22/173.23 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 173.22/173.23 => 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) ) % 173.22/173.23 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pdivmod__def,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pdivmod__posDivAlg,axiom, % 173.22/173.23 ! [V_k,V_l] : % 173.22/173.23 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__int__code,axiom, % 173.22/173.23 ! [V_l_2,V_k_2] : % 173.22/173.23 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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) ) % 173.22/173.23 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 => 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)))) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_UN__equiv__class__inject,axiom, % 173.22/173.23 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 173.22/173.23 => ( 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) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => ! [B_y] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 173.22/173.23 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 173.22/173.23 => 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)) ) ) ) % 173.22/173.23 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 173.22/173.23 ! [V_c,V_r,V_q,V_b,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 173.22/173.23 ! [V_a,V_r,V_q,V_c,V_b] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__rel__unique,axiom, % 173.22/173.23 ! [V_qr_H,V_qr,V_n,V_m] : % 173.22/173.23 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 173.22/173.23 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 173.22/173.23 => V_qr = V_qr_H ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 173.22/173.23 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__eq,axiom, % 173.22/173.23 ! [V_qr,V_n,V_m] : % 173.22/173.23 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 173.22/173.23 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__eq,axiom, % 173.22/173.23 ! [V_r,V_q,V_n,V_m] : % 173.22/173.23 ( 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))) % 173.22/173.23 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__eq,axiom, % 173.22/173.23 ! [V_r,V_q,V_n,V_m] : % 173.22/173.23 ( 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))) % 173.22/173.23 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__rel,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__rel__add1__eq,axiom, % 173.22/173.23 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.22/173.23 => 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__Suc__I,axiom, % 173.22/173.23 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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))) % 173.22/173.23 => ( 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)) % 173.22/173.23 => hBOOL(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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__Suc__I2,axiom, % 173.22/173.23 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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)) % 173.22/173.23 => ( 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))) % 173.22/173.23 => hBOOL(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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__0__E,axiom, % 173.22/173.23 ! [V_R_2,V_y_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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))) % 173.22/173.23 => V_x_2 = V_y_2 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__1,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__0__I,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg_Opsimps,axiom, % 173.22/173.23 ! [V_b_2,V_a_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( ( 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))) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ ( 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))) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg_Opsimps,axiom, % 173.22/173.23 ! [V_b_2,V_a_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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) ) % 173.22/173.23 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__pos__neg__1__number__of,axiom, % 173.22/173.23 ! [V_w] : % 173.22/173.23 ( 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))) % 173.22/173.23 => 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))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__eqD,axiom, % 173.22/173.23 ! [V_a,V_y,V_x,T_a,T_b] : % 173.22/173.23 ( 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 % 173.22/173.23 => V_y = V_a ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__conv,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__def,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__apsnd,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apsnd__eq__conv,axiom, % 173.22/173.23 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 173.22/173.23 ( 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) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__int__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__neg__pos,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__pos__pos,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__pos__pos__1__number__of,axiom, % 173.22/173.23 ! [V_w] : % 173.22/173.23 ( 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))) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__pos__neg,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__neg__neg,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_norm__frac_Opsimps,axiom, % 173.22/173.23 ! [V_b_2,V_a_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.22/173.23 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.22/173.23 => 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))) ) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_negDivAlg_Opinduct,axiom, % 173.22/173.23 ! [V_P_2,V_a1_2,V_a0_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ! [B_a,B_b] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( ~ ( 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))) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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))) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_posDivAlg_Opinduct,axiom, % 173.22/173.23 ! [V_P_2,V_a1_2,V_a0_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ! [B_a,B_b] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 173.22/173.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.22/173.23 => 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))) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mod__nat__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_accp__subset,axiom, % 173.22/173.23 ! [V_R2_2,V_R1_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_irrefl__def,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Relation_Oirrefl(T_a,V_r_2) % 173.22/173.23 <=> ! [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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_norm__frac_Opinduct,axiom, % 173.22/173.23 ! [V_P_2,V_a1_2,V_a0_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ! [B_a,B_b] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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))) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_accp__downward,axiom, % 173.22/173.23 ! [V_a_2,V_b_2,V_r_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 173.22/173.23 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_accp_Oequations,axiom, % 173.22/173.23 ! [V_a_2,V_r_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 173.22/173.23 <=> ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 173.22/173.23 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_accp_Osimps,axiom, % 173.22/173.23 ! [V_a_2,V_r_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 173.22/173.23 <=> ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 173.22/173.23 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat__gcd_Opsimps,axiom, % 173.22/173.23 ! [V_y_2,V_x_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 173.22/173.23 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat_Osize_I2_J,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_in__measure,axiom, % 173.22/173.23 ! [V_f_2,V_y_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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))) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat_Osize_I1_J,axiom, % 173.22/173.23 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__pos__neg__1__number__of,axiom, % 173.22/173.23 ! [V_w] : % 173.22/173.23 ( 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))) % 173.22/173.23 => 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))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat__def,axiom, % 173.22/173.23 ! [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)))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat__gcd_Opinduct,axiom, % 173.22/173.23 ! [V_P_2,V_a1_2,V_a0_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ! [B_x,B_y] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__eqD,axiom, % 173.22/173.23 ! [V_a,V_y,V_x,T_b,T_a] : % 173.22/173.23 ( 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 % 173.22/173.23 => V_x = V_a ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__conv,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_Rep__Integ__inject,axiom, % 173.22/173.23 ! [V_y_2,V_x_2] : % 173.22/173.23 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 173.22/173.23 <=> V_x_2 = V_y_2 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__def,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__apsnd,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_prod__eqI,axiom, % 173.22/173.23 ! [V_q,V_p,T_b,T_a] : % 173.22/173.23 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 173.22/173.23 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 173.22/173.23 => V_p = V_q ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Pair__fst__snd__eq,axiom, % 173.22/173.23 ! [T_b,T_a,V_t_2,V_s_2] : % 173.22/173.23 ( V_s_2 = V_t_2 % 173.22/173.23 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 173.22/173.23 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__collapse,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_surjective__pairing,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_prod__case__beta,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__int__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__comp__eq,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__beta,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_split__comp,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_The__split,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__neg__pos,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__pos__pos,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__pos__pos__1__number__of,axiom, % 173.22/173.23 ! [V_w] : % 173.22/173.23 ( 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))) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__pos__neg,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__neg__neg,axiom, % 173.22/173.23 ! [V_b,V_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_prod__size__simp,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_conjI__realizer,axiom, % 173.22/173.23 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 173.22/173.23 ( hBOOL(hAPP(V_P_2,V_p_2)) % 173.22/173.23 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 173.22/173.23 => ( 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)))) % 173.22/173.23 & 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)))) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_exI__realizer,axiom, % 173.22/173.23 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 173.22/173.23 => 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_div__nat__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_divmod__nat__rel__def,axiom, % 173.22/173.23 ! [V_qr_2,V_n_2,V_m_2] : % 173.22/173.23 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 173.22/173.23 <=> ( 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)) % 173.22/173.23 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.23 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.22/173.23 => ( 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))) % 173.22/173.23 & 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)) ) ) % 173.22/173.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.22/173.23 => ( 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))) % 173.22/173.23 & 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))) ) ) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_inv__image__def,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_setsum__mult__setsum__if__inj,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 173.22/173.23 ( class_Rings_Osemiring__0(T_c) % 173.22/173.23 => ( 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))) % 173.22/173.23 => 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))))))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mlex__leq,axiom, % 173.22/173.23 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( hBOOL(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)) % 173.22/173.23 => hBOOL(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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_SigmaI,axiom, % 173.22/173.23 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__empty1,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Times__eq__cancel2,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 173.22/173.23 => ( 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)) % 173.22/173.23 <=> V_A_2 = V_B_2 ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__Diff__distrib2,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Times__Diff__distrib1,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__Diff__distrib1,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_UN__Times__distrib,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_card__cartesian__product,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_setsum__cartesian__product,axiom, % 173.22/173.23 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 173.22/173.23 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__empty2,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Times__empty,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Compl__Times__UNIV2,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Compl__Times__UNIV1,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_setprod__cartesian__product,axiom, % 173.22/173.23 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 173.22/173.23 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__Un__distrib1,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Times__Un__distrib1,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__Un__distrib2,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_swap__product,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__cartesian__product,axiom, % 173.22/173.23 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equiv__type,axiom, % 173.22/173.23 ! [V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.23 => 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__Int__distrib1,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Times__Int__distrib1,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__Int__distrib2,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_UNIV__Times__UNIV,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mem__Sigma__iff,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.23 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_SigmaD1,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_SigmaD2,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_SigmaE2,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.23 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_card__cartesian__product__singleton,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Times__subset__cancel2,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 173.22/173.23 => ( 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)))) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_insert__times__insert,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Image__subset,axiom, % 173.22/173.23 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( 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)))) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__cartesian__productD2,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.23 ( 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)))) % 173.22/173.23 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__cartesian__productD1,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.23 ( 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)))) % 173.22/173.23 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Sigma__def,axiom, % 173.22/173.23 ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_SetCompr__Sigma__eq,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Collect__split,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__image__times,axiom, % 173.22/173.23 ! [V_A_2,T_b,T_a,V_B_2] : % 173.22/173.23 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 => 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 ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__image__times,axiom, % 173.22/173.23 ! [V_B_2,T_b,T_a,V_A_2] : % 173.22/173.23 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 => 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 ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_in__inv__image,axiom, % 173.22/173.23 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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))) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__equiv__class,axiom, % 173.22/173.23 ! [V_X_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( 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)))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_vimage__Times,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__quotient,axiom, % 173.22/173.23 ! [V_r_2,V_A_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( 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)))) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_image__split__eq__Sigma,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mlex__less,axiom, % 173.22/173.23 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 173.22/173.23 ( 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))) % 173.22/173.23 => hBOOL(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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rp__inv__image__def,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fold__image__Sigma,axiom, % 173.22/173.23 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 173.22/173.23 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.22/173.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osize_I2_J,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Oinject,axiom, % 173.22/173.23 ! [V_code__numeral_H_2,V_code__numeral_2] : % 173.22/173.23 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 173.22/173.23 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osimps_I3_J,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osimps_I2_J,axiom, % 173.22/173.23 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Suc__code__numeral__minus__one,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osize_I4_J,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_in__finite__psubset,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.23 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 173.22/173.23 ! [V_A_2,V_I_2,T_b,T_a] : % 173.22/173.23 ? [B_f] : % 173.22/173.23 ( 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)) % 173.22/173.23 & 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osize_I3_J,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__psubset__def,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_setprod__Sigma,axiom, % 173.22/173.23 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 173.22/173.23 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.22/173.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_setsum__Sigma,axiom, % 173.22/173.23 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 173.22/173.23 ( class_Groups_Ocomm__monoid__add(T_c) % 173.22/173.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_card__SigmaI,axiom, % 173.22/173.23 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 173.22/173.23 => 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) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Field__insert,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat_Osize_I4_J,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_prod_Orecs,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat__size,axiom, % 173.22/173.23 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat_Osize_I3_J,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Field__empty,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mono__Field,axiom, % 173.22/173.23 ! [V_s_2,V_r_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Field__Un,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__Field,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__SigmaI,axiom, % 173.22/173.23 ! [V_B_2,T_b,V_A_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.23 => ( ! [B_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__on__def,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__on__def_H,axiom, % 173.22/173.23 ! [V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.23 <=> ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 173.22/173.23 => 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)) ) % 173.22/173.23 & ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__on__Id__on,axiom, % 173.22/173.23 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__on__def_H,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__on__empty,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__on__Un,axiom, % 173.22/173.23 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__on__Int,axiom, % 173.22/173.23 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__on__empty,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Image__Id__on,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__onD2,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( hBOOL(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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__onD1,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( hBOOL(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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__onD,axiom, % 173.22/173.23 ! [V_a_2,V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__on__subset__Times,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__on__eqI,axiom, % 173.22/173.23 ! [V_A_2,T_a,V_b_2,V_a_2] : % 173.22/173.23 ( V_a_2 = V_b_2 % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__on__iff,axiom, % 173.22/173.23 ! [V_A_2,V_y_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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))) % 173.22/173.23 <=> ( V_x_2 = V_y_2 % 173.22/173.23 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__on__def,axiom, % 173.22/173.23 ! [V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.23 <=> ( 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)))) % 173.22/173.23 & ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_reflp__def,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Predicate_Oreflp(T_a,V_r_2) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__onI,axiom, % 173.22/173.23 ! [V_A_2,V_r_2,T_a] : % 173.22/173.23 ( 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)))) % 173.22/173.23 => ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => 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)) ) % 173.22/173.23 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_in__lex__prod,axiom, % 173.22/173.23 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 <=> ( 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)) % 173.22/173.23 | ( V_a_2 = V_a_H_2 % 173.22/173.23 & 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_reflpE,axiom, % 173.22/173.23 ! [V_x_2,V_r_2,T_a] : % 173.22/173.23 ( c_Predicate_Oreflp(T_a,V_r_2) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_same__fstI,axiom, % 173.22/173.23 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 173.22/173.23 ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.23 => ( 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))) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equivp__equiv,axiom, % 173.22/173.23 ! [V_A_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__onE,axiom, % 173.22/173.23 ! [V_A_2,V_ca_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 173.22/173.23 => ~ ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equivp__transp,axiom, % 173.22/173.23 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equivp__symp,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_R_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equivp__reflp,axiom, % 173.22/173.23 ! [V_x_2,V_R_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 173.22/173.23 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equivp__def,axiom, % 173.22/173.23 ! [V_R_2,T_a] : % 173.22/173.23 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 173.22/173.23 <=> ! [B_x,B_y] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 173.22/173.23 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_identity__equivp,axiom, % 173.22/173.23 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apsnd__apfst,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apfst__apsnd,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__lessI2,axiom, % 173.22/173.23 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apfst__compose,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__apfst,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apfst__eq__conv,axiom, % 173.22/173.23 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 173.22/173.23 ( 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) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__apfst,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apfst__conv,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apsnd__apfst__commute,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apfst__id,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__lessI1,axiom, % 173.22/173.23 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__leqI2,axiom, % 173.22/173.23 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_smax__insertI,axiom, % 173.22/173.23 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_smin__insertI,axiom, % 173.22/173.23 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_smin__emptyI,axiom, % 173.22/173.23 ! [V_X_2] : % 173.22/173.23 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_smax__emptyI,axiom, % 173.22/173.23 ! [V_Y_2] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 173.22/173.23 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__leqI1,axiom, % 173.22/173.23 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wmin__insertI,axiom, % 173.22/173.23 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wmax__insertI,axiom, % 173.22/173.23 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wmin__emptyI,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wmax__emptyI,axiom, % 173.22/173.23 ! [V_X_2] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_min__weak__def,axiom, % 173.22/173.23 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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__weak__def,axiom, % 173.22/173.23 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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_min__rpair__set,axiom, % 173.22/173.23 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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__strict__def,axiom, % 173.22/173.23 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rp__inv__image__rp,axiom, % 173.22/173.23 ! [V_f_2,T_b,V_P_2,T_a] : % 173.22/173.23 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 173.22/173.23 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__ext__additive,axiom, % 173.22/173.23 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_min__strict__def,axiom, % 173.22/173.23 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__rpair__set,axiom, % 173.22/173.23 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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__extp__max__ext__eq,axiom, % 173.22/173.23 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 173.22/173.23 ( 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) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equiv__intrel__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2] : % 173.22/173.23 ( 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)))) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_less__than__iff,axiom, % 173.22/173.23 ! [V_y_2,V_x_2] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_equiv__intrel,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__less__def,axiom, % 173.22/173.23 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 173.22/173.23 % 173.22/173.23 fof(fact_measure__def,axiom, % 173.22/173.23 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mlex__prod__def,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_intrel__iff,axiom, % 173.22/173.23 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> 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) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_of__int,axiom, % 173.22/173.23 ! [V_j_2,V_i_2,T_a] : % 173.22/173.23 ( class_Rings_Oring__1(T_a) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_One__int__def,axiom, % 173.22/173.23 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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mult,axiom, % 173.22/173.23 ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Rep__Integ__inverse,axiom, % 173.22/173.23 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 173.22/173.23 % 173.22/173.23 fof(fact_minus,axiom, % 173.22/173.23 ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Zero__int__def,axiom, % 173.22/173.23 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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_int__def,axiom, % 173.22/173.23 ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_add,axiom, % 173.22/173.23 ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_nat,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_minus__int__def,axiom, % 173.22/173.23 ! [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))))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_less,axiom, % 173.22/173.23 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 173.22/173.23 ( 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))))))) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_le,axiom, % 173.22/173.23 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 173.22/173.23 ( 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))))))) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_eq__Abs__Integ,axiom, % 173.22/173.23 ! [V_z_2] : % 173.22/173.23 ~ ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Integ__def,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__E2,axiom, % 173.22/173.23 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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))) % 173.22/173.23 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 => V_x_2 != V_z_2 ) % 173.22/173.23 => ~ ! [B_y,B_m] : % 173.22/173.23 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ~ 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))) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Rep__Integ,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition__Integ,axiom, % 173.22/173.23 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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__E,axiom, % 173.22/173.23 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 173.22/173.23 ( hBOOL(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))) % 173.22/173.23 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.23 => V_x_2 != V_z_2 ) % 173.22/173.23 => ~ ! [B_y,B_m] : % 173.22/173.23 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ~ 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)) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_ImageE,axiom, % 173.22/173.23 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 173.22/173.23 => ~ ! [B_x] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition_OAbs__image,axiom, % 173.22/173.23 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 173.22/173.23 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition_ORep__range,axiom, % 173.22/173.23 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 173.22/173.23 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 173.22/173.23 => 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 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition_OAbs__inject,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 173.22/173.23 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.22/173.23 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 173.22/173.23 <=> V_x_2 = V_y_2 ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition_ORep__inject,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 173.22/173.23 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 173.22/173.23 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 173.22/173.23 <=> V_x_2 = V_y_2 ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition_ORep__inverse,axiom, % 173.22/173.23 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 173.22/173.23 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 173.22/173.23 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition_ORep,axiom, % 173.22/173.23 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 173.22/173.23 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_type__definition_OAbs__inverse,axiom, % 173.22/173.23 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 173.22/173.23 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.22/173.23 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_SigmaE,axiom, % 173.22/173.23 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ~ ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => ! [B_y] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 173.22/173.23 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__surj,axiom, % 173.22/173.23 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_reflcl__set__eq,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_r_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> hBOOL(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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_IdI,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__imageI,axiom, % 173.22/173.23 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Image__Id,axiom, % 173.22/173.23 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__map__pair,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__prod__fun,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__ident,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__comp__map__pair,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair_Ocompositionality,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__compose,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair_Ocomp,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__comp__map__pair,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__simp,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair_Oidentity,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__in__Id__conv,axiom, % 173.22/173.23 ! [V_b_2,V_a_2,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 <=> V_a_2 = V_b_2 ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_relpow_Osimps_I1_J,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__Id,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apsnd__def,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_apfst__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair_Oid,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pair__leq__def,axiom, % 173.22/173.23 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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_refl__reflcl,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__def,axiom, % 173.22/173.23 ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_irrefl__diff__Id,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__surj__on,axiom, % 173.22/173.23 ! [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] : % 173.22/173.23 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 173.22/173.23 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_map__pair__inj__on,axiom, % 173.22/173.23 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.23 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 173.22/173.23 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_prod__fun__imageE,axiom, % 173.22/173.23 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ~ ! [B_x,B_y] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ~ 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_total__on__diff__Id,axiom, % 173.22/173.23 ! [V_r_2,V_A_2,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osimps_I5_J,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_total__on__empty,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_total__on__def,axiom, % 173.22/173.23 ! [V_r_2,V_A_2,T_a] : % 173.22/173.23 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 173.22/173.23 <=> ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.23 => ! [B_xa] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 173.22/173.23 => ( B_x != B_xa % 173.22/173.23 => ( 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)) % 173.22/173.23 | 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)) ) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_code__numeral_Osimps_I4_J,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_accp__acc__eq,axiom, % 173.22/173.23 ! [V_x_2,V_r_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__def,axiom, % 173.22/173.23 ! [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))))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__extp_Oequations,axiom, % 173.22/173.23 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 173.22/173.23 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 173.22/173.23 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 173.22/173.23 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 & ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 173.22/173.23 => ? [B_xa] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 173.22/173.23 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__compI,axiom, % 173.22/173.23 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_R__O__Id,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_Id__O__R,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__distrib2,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__distrib,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__UNION__distrib,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__UNION__distrib2,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__mono,axiom, % 173.22/173.23 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_O__assoc,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__commute,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__empty2,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__empty1,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_relpow_Osimps_I2_J,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__pow__add,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_union__comp__emptyL,axiom, % 173.22/173.23 ! [V_B_2,V_C_2,V_A_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_union__comp__emptyR,axiom, % 173.22/173.23 ! [V_C_2,V_B_2,V_A_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_rel__comp__subset__Sigma,axiom, % 173.22/173.23 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( 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)))) % 173.22/173.23 => ( 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)))) % 173.22/173.23 => 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)))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_acc__subset,axiom, % 173.22/173.23 ! [V_R2_2,V_R1_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_acc__downward,axiom, % 173.22/173.23 ! [V_a_2,V_r_2,V_b_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 173.22/173.23 => ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_acc_Osimps,axiom, % 173.22/173.23 ! [V_r_2,V_a_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 173.22/173.23 <=> ! [B_x] : % 173.22/173.23 ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__ext__compat,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_min__ext__compat,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__comp__rel__comp__eq,axiom, % 173.22/173.23 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_reduction__pairI,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_R_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__ext_Ointros,axiom, % 173.22/173.23 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 173.22/173.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 173.22/173.23 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 => ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 173.22/173.23 => ? [B_xa] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 173.22/173.23 & 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)) ) ) % 173.22/173.23 => 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))) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__less__than,axiom, % 173.22/173.23 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__comp_Ointros,axiom, % 173.22/173.23 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 173.22/173.23 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__empty,axiom, % 173.22/173.23 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__inv__image,axiom, % 173.22/173.23 ! [V_f_2,T_b,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__lex__prod,axiom, % 173.22/173.23 ! [V_rb_2,T_b,V_ra_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_ra_2) % 173.22/173.23 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 173.22/173.23 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__measure,axiom, % 173.22/173.23 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__comp__self,axiom, % 173.22/173.23 ! [V_R_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_R_2) % 173.22/173.23 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__not__refl,axiom, % 173.22/173.23 ! [V_a_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => ~ 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__not__sym,axiom, % 173.22/173.23 ! [V_x_2,V_a_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ~ hBOOL(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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__asym,axiom, % 173.22/173.23 ! [V_x_2,V_a_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => ~ hBOOL(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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__irrefl,axiom, % 173.22/173.23 ! [V_a_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => ~ 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_min__ext__wf,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__comp_Oequations,axiom, % 173.22/173.23 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> ? [B_b] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 173.22/173.23 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__subset,axiom, % 173.22/173.23 ! [V_p_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__Int1,axiom, % 173.22/173.23 ! [V_r_H_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__Int2,axiom, % 173.22/173.23 ! [V_r_H_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__exp,axiom, % 173.22/173.23 ! [V_R_2,V_n_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__mlex,axiom, % 173.22/173.23 ! [V_f_2,V_R_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_R_2) % 173.22/173.23 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__finite__psubset,axiom, % 173.22/173.23 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__pair__less,axiom, % 173.22/173.23 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 173.22/173.23 % 173.22/173.23 fof(fact_max__ext__wf,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__less,axiom, % 173.22/173.23 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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__int__ge__less__than,axiom, % 173.22/173.23 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__int__ge__less__than2,axiom, % 173.22/173.23 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__acc__iff,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_acc__wfD,axiom, % 173.22/173.23 ! [V_x_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__no__loop,axiom, % 173.22/173.23 ! [V_R_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__union__merge,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> 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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 <=> ~ ? [B_f] : % 173.22/173.23 ! [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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfE__pf,axiom, % 173.22/173.23 ! [V_A_2,V_R_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_R_2) % 173.22/173.23 => ( 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))) % 173.22/173.23 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__union__compatible,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_R_2) % 173.22/173.23 => ( c_Wellfounded_Owf(T_a,V_S_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf,axiom, % 173.22/173.23 ! [T_a] : % 173.22/173.23 ( class_Orderings_Owellorder(T_a) % 173.22/173.23 => 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)))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_reduction__pair__def,axiom, % 173.22/173.23 ! [V_P_2,T_a] : % 173.22/173.23 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 173.22/173.23 <=> ( 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)) % 173.22/173.23 & 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))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_reduction__pair__lemma,axiom, % 173.22/173.23 ! [V_S_2,V_R_2,V_P_2,T_a] : % 173.22/173.23 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( 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))) % 173.22/173.23 => ( c_Wellfounded_Owf(T_a,V_S_2) % 173.22/173.23 => 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)) ) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__map__pair__image,axiom, % 173.22/173.23 ! [V_f_2,T_b,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__lenlex,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__if__measure,axiom, % 173.22/173.23 ! [T_a,V_g_2,V_f_2,V_P_2] : % 173.22/173.23 ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.23 => 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))) ) % 173.22/173.23 => 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))))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_Ozero__frac__def,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_Oone__frac__def,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_pred__nat__def,axiom, % 173.22/173.23 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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__pred__nat,axiom, % 173.22/173.23 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_Ofrac__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__lex,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__lexn,axiom, % 173.22/173.23 ! [V_n_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_lex__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_lexn_Osimps_I1_J,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__same__fst,axiom, % 173.22/173.23 ! [T_a,V_R_2,T_b,V_P_2] : % 173.22/173.23 ( ! [B_x] : % 173.22/173.23 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.23 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 173.22/173.23 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__Collect__split,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfP__def,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_OwfP(T_a,V_r_2) % 173.22/173.23 <=> 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfP__empty,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_RangeI,axiom, % 173.22/173.23 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__Id__on,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfP__accp__iff,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_OwfP(T_a,V_r_2) % 173.22/173.23 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_accp__wfPD,axiom, % 173.22/173.23 ! [V_x_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_OwfP(T_a,V_r_2) % 173.22/173.23 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfP__subset,axiom, % 173.22/173.23 ! [V_p_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_OwfP(T_a,V_r_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__empty,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__empty__iff,axiom, % 173.22/173.23 ! [V_r_2,T_a,T_b] : % 173.22/173.23 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__Un__eq,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__Id,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__Range,axiom, % 173.22/173.23 ! [V_r_2,T_b,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_snd__eq__Range,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__iff,axiom, % 173.22/173.23 ! [V_r_2,T_b,V_a_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 173.22/173.23 <=> ? [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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__insert,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__Int__subset,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Range__Diff__subset,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__in__rel,axiom, % 173.22/173.23 ! [V_R_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_R_2) % 173.22/173.23 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfP__wf__eq,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_RangeP__Range__eq,axiom, % 173.22/173.23 ! [V_x_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_RangeE,axiom, % 173.22/173.23 ! [V_r_2,T_b,V_b_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 173.22/173.23 => ~ ! [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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfP__acyclicP,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_OwfP(T_a,V_r_2) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_RangeP_Ointros,axiom, % 173.22/173.23 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 173.22/173.23 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_acyclic__subset,axiom, % 173.22/173.23 ! [V_r_2,V_s_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_RangeP_Oequations,axiom, % 173.22/173.23 ! [V_a2_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 173.22/173.23 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__acyclic,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__iff__acyclic__if__finite,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 173.22/173.23 => ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__acyclic__wf,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 173.22/173.23 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 173.22/173.23 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Nitpick_Owf_H__def,axiom, % 173.22/173.23 ! [V_r_2,T_a] : % 173.22/173.23 ( c_Nitpick_Owf_H(T_a,V_r_2) % 173.22/173.23 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 173.22/173.23 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 173.22/173.23 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wf__Un,axiom, % 173.22/173.23 ! [V_s_2,V_r_2,T_a] : % 173.22/173.23 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.23 => ( c_Wellfounded_Owf(T_a,V_s_2) % 173.22/173.23 => ( 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)) % 173.22/173.23 => 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)) ) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Rep__Integ__cases,axiom, % 173.22/173.23 ! [V_y_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 173.22/173.23 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_DomainI,axiom, % 173.22/173.23 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__Id__on,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__empty,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__empty__iff,axiom, % 173.22/173.23 ! [V_r_2,T_b,T_a] : % 173.22/173.23 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.23 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__mono,axiom, % 173.22/173.23 ! [V_s_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__Un__eq,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__Id,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_finite__Domain,axiom, % 173.22/173.23 ! [V_r_2,T_b,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 173.22/173.23 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_fst__eq__Domain,axiom, % 173.22/173.23 ! [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) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__iff,axiom, % 173.22/173.23 ! [V_r_2,T_b,V_a_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 173.22/173.23 <=> ? [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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__insert,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__Int__subset,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__Diff__subset,axiom, % 173.22/173.23 ! [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)))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Field__def,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Domain__Collect__split,axiom, % 173.22/173.23 ! [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)) ). % 173.22/173.23 % 173.22/173.23 fof(fact_DomainP__Domain__eq,axiom, % 173.22/173.23 ! [V_x_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( 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)) % 173.22/173.23 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_DomainE,axiom, % 173.22/173.23 ! [V_r_2,T_b,V_a_2,T_a] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 173.22/173.23 => ~ ! [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)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Rep__Integ__induct,axiom, % 173.22/173.23 ! [V_P_2,V_y_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 173.22/173.23 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 173.22/173.23 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_DomainP_Ointros,axiom, % 173.22/173.23 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 173.22/173.23 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_DomainP_Oequations,axiom, % 173.22/173.23 ! [V_a1_2,V_r_2,T_b,T_a] : % 173.22/173.23 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 173.22/173.23 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Abs__Integ__induct,axiom, % 173.22/173.23 ! [V_x_2,V_P_2] : % 173.22/173.23 ( ! [B_y] : % 173.22/173.23 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 173.22/173.23 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 173.22/173.23 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Abs__Integ__cases,axiom, % 173.22/173.23 ! [V_x_2] : % 173.22/173.23 ~ ! [B_y] : % 173.22/173.23 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 173.22/173.23 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_wfP__SUP,axiom, % 173.22/173.23 ! [T_a,V_r_2,T_b] : % 173.22/173.23 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 173.22/173.23 => ( ! [B_i,B_j] : % 173.22/173.23 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 173.22/173.23 => 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)) ) % 173.22/173.23 => 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)) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mem__splitE,axiom, % 173.22/173.23 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 173.22/173.23 ( 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))) % 173.22/173.23 => ~ ! [B_x,B_y] : % 173.22/173.23 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 173.22/173.23 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_mem__splitI2,axiom, % 173.22/173.23 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 173.22/173.23 ( ! [B_a,B_b] : % 173.22/173.23 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 173.22/173.23 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 173.22/173.23 => 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))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_Eps__split,axiom, % 173.22/173.23 ! [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))) ). % 173.22/173.23 % 173.22/173.23 fof(fact_some__sym__eq__trivial,axiom, % 173.22/173.23 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 173.22/173.23 % 173.22/173.23 fof(fact_some__eq__trivial,axiom, % 173.22/173.23 ! [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 ). % 173.22/173.23 % 173.22/173.23 fof(fact_some__eq__ex,axiom, % 173.22/173.23 ! [T_a,V_P_2] : % 173.22/173.23 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 173.22/173.23 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_someI__ex,axiom, % 173.22/173.23 ! [T_a,V_P_2] : % 173.22/173.23 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.23 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_someI,axiom, % 173.22/173.23 ! [T_a,V_x_2,V_P_2] : % 173.22/173.23 ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.23 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 173.22/173.23 % 173.22/173.23 fof(fact_tfl__some,axiom, % 173.22/173.24 ! [T_a,B_P] : % 173.22/173.24 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 173.22/173.24 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_exE__some,axiom, % 173.22/173.24 ! [T_a,V_ca_2,V_P_2] : % 173.22/173.24 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 173.22/173.24 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 173.22/173.24 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Eps__split__eq,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_split__paired__Eps,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inv__into__def,axiom, % 173.22/173.24 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inv__def,axiom, % 173.22/173.24 ! [V_y_2,V_f_2,T_b,T_a] : hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(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_y_2)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_LeastM__def,axiom, % 173.22/173.24 ! [V_P_2,V_m_2,T_a,T_b] : % 173.22/173.24 ( class_Orderings_Oord(T_b) % 173.22/173.24 => c_Hilbert__Choice_OLeastM(T_a,T_b,V_m_2,V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_GreatestM__def,axiom, % 173.22/173.24 ! [V_P_2,V_m_2,T_a,T_b] : % 173.22/173.24 ( class_Orderings_Oord(T_b) % 173.22/173.24 => hAPP(c_Hilbert__Choice_OGreatestM(T_a,T_b,V_m_2),V_P_2) = c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2))),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_m_2))),V_m_2))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_wfI__pf,axiom, % 173.22/173.24 ! [V_R_2,T_a] : % 173.22/173.24 ( ! [B_A] : % 173.22/173.24 ( 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))) % 173.22/173.24 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 173.22/173.24 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_LeastM__nat__le,axiom, % 173.22/173.24 ! [T_a,V_m_2,V_x_2,V_P_2] : % 173.22/173.24 ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,V_x_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_LeastM__nat__lemma,axiom, % 173.22/173.24 ! [V_m_2,T_a,V_k_2,V_P_2] : % 173.22/173.24 ( hBOOL(hAPP(V_P_2,V_k_2)) % 173.22/173.24 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 173.22/173.24 & ! [B_y] : % 173.22/173.24 ( hBOOL(hAPP(V_P_2,B_y)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_m_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))),hAPP(V_m_2,B_y))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Greatest__def,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Orderings_Oord(T_a) % 173.22/173.24 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 173.22/173.24 ! [V_R_2,V_p_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_r__into__rtrancl,axiom, % 173.22/173.24 ! [V_r_2,V_p_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl_Ortrancl__refl,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_LeastM__natI,axiom, % 173.22/173.24 ! [V_m_2,T_a,V_k_2,V_P_2] : % 173.22/173.24 ( hBOOL(hAPP(V_P_2,V_k_2)) % 173.22/173.24 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Domain__rtrancl,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Range__rtrancl,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__idemp__self__comp,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_r__comp__rtrancl__eq,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__subset__rtrancl,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__subset,axiom, % 173.22/173.24 ! [V_S_2,V_R_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( 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))) % 173.22/173.24 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__mono,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Image__closed__trancl,axiom, % 173.22/173.24 ! [V_X_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__Un__rtrancl,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__rtrancl__UnI,axiom, % 173.22/173.24 ! [V_S_2,V_R_2,V_x_2,T_a] : % 173.22/173.24 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 173.22/173.24 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_refl__rtrancl,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rel__pow__imp__rtrancl,axiom, % 173.22/173.24 ! [V_R_2,V_n_2,V_p_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__power,axiom, % 173.22/173.24 ! [V_R_2,V_p_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 173.22/173.24 <=> ? [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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__idemp,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__trans,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( 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))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__Un__subset,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__empty,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__reflcl,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__reflcl__absorb,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__r__diff__Id,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__unfold,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Not__Domain__rtrancl,axiom, % 173.22/173.24 ! [V_y_2,V_R_2,V_x_2,T_a] : % 173.22/173.24 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 173.22/173.24 => ( hBOOL(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))) % 173.22/173.24 <=> V_x_2 = V_y_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_acc__downwards__aux,axiom, % 173.22/173.24 ! [V_r_2,V_a_2,V_b_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_acc__downwards,axiom, % 173.22/173.24 ! [V_b_2,V_r_2,V_a_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_wf__insert,axiom, % 173.22/173.24 ! [V_r_2,V_x_2,V_y_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.24 & ~ hBOOL(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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_acyclic__insert,axiom, % 173.22/173.24 ! [V_r_2,V_x_2,V_y_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 173.22/173.24 & ~ hBOOL(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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__Int__subset,axiom, % 173.22/173.24 ! [V_r_2,V_s_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( 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)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_pred__nat__trancl__eq__le,axiom, % 173.22/173.24 ! [V_n_2,V_m_2] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__subset__Sigma__aux,axiom, % 173.22/173.24 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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)))) % 173.22/173.24 => ( V_a_2 = V_b_2 % 173.22/173.24 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__insert,axiom, % 173.22/173.24 ! [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)))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sequence__trans,axiom, % 173.22/173.24 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 173.22/173.24 ( ! [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))) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl_Or__into__trancl,axiom, % 173.22/173.24 ! [V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__into__rtrancl,axiom, % 173.22/173.24 ! [V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__rtrancl__absorb,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__trancl__absorb,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_wf__trancl,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.24 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__mono,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,V_p_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 173.22/173.24 => ( 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)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_r__into__trancl_H,axiom, % 173.22/173.24 ! [V_r_2,V_p_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__trans,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__into__trancl2,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( 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))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_r__r__into__trancl,axiom, % 173.22/173.24 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( 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)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__trancl,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 173.22/173.24 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__empty,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__range,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__domain,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__unfold__left,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__unfold__right,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__unfold,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__subset__Sigma,axiom, % 173.22/173.24 ! [V_A_2,V_r_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_less__than__def,axiom, % 173.22/173.24 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__eq__or__trancl,axiom, % 173.22/173.24 ! [V_R_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 <=> ( V_x_2 = V_y_2 % 173.22/173.24 | ( V_x_2 != V_y_2 % 173.22/173.24 & hBOOL(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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__into__trancl2,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( 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))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtranclD,axiom, % 173.22/173.24 ! [V_R_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( V_a_2 = V_b_2 % 173.22/173.24 | ( V_a_2 != V_b_2 % 173.22/173.24 & 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__into__trancl1,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__rtrancl__trancl,axiom, % 173.22/173.24 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__trancl__trancl,axiom, % 173.22/173.24 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => hBOOL(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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_acyclic__def,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 173.22/173.24 <=> ! [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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__reflcl,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_reflcl__trancl,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__Int__subset,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( 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)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__subset__Field2,axiom, % 173.22/173.24 ! [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))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__power,axiom, % 173.22/173.24 ! [V_R_2,V_p_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 173.22/173.24 <=> ? [B_n] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 173.22/173.24 & 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_less__eq,axiom, % 173.22/173.24 ! [V_n_2,V_m_2] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_irrefl__tranclI,axiom, % 173.22/173.24 ! [V_x_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ~ hBOOL(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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_acyclicI,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( ! [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))) % 173.22/173.24 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__converse,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__converse,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__rel__comp,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__Un,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converseD,axiom, % 173.22/173.24 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converseI,axiom, % 173.22/173.24 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__iff,axiom, % 173.22/173.24 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__Id,axiom, % 173.22/173.24 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 173.22/173.24 % 173.22/173.24 fof(fact_total__on__converse,axiom, % 173.22/173.24 ! [V_r_2,V_A_2,T_a] : % 173.22/173.24 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 173.22/173.24 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__converse,axiom, % 173.22/173.24 ! [V_r_2,T_b,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 173.22/173.24 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Field__converse,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__Int,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__converse,axiom, % 173.22/173.24 ! [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 ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__Id__on,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_refl__on__converse,axiom, % 173.22/173.24 ! [V_r_2,V_A_2,T_a] : % 173.22/173.24 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 173.22/173.24 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__inv__image,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_acyclic__converse,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 173.22/173.24 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__UNION,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_wf__converse__trancl,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 173.22/173.24 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_equiv__comp__eq,axiom, % 173.22/173.24 ! [V_r_2,V_A_2,T_a] : % 173.22/173.24 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.24 => 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 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Range__converse,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Domain__converse,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Range__def,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__converseD,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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)))) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__converseI,axiom, % 173.22/173.24 ! [V_r_2,V_x_2,V_y_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => hBOOL(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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__converseD,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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)))) % 173.22/173.24 => hBOOL(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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_trancl__converseI,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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)))) % 173.22/173.24 => hBOOL(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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Image__subset__eq,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> 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))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_refl__on__comp__subset,axiom, % 173.22/173.24 ! [V_r_2,V_A_2,T_a] : % 173.22/173.24 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_comp__equivI,axiom, % 173.22/173.24 ! [V_A_2,V_r_2,T_a] : % 173.22/173.24 ( 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 % 173.22/173.24 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 173.22/173.24 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__acyclic__wf__converse,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 173.22/173.24 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 173.22/173.24 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__def,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Image__Int__eq,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 173.22/173.24 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__Un__separator__converseE,axiom, % 173.22/173.24 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ! [B_y] : % 173.22/173.24 ( 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)) % 173.22/173.24 => B_y = B_x ) ) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valued__rel__comp,axiom, % 173.22/173.24 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 173.22/173.24 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 173.22/173.24 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valued__subset,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 173.22/173.24 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valued__rel__pow,axiom, % 173.22/173.24 ! [V_n_2,V_R_2,T_a] : % 173.22/173.24 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valued__Id,axiom, % 173.22/173.24 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valued__Id__on,axiom, % 173.22/173.24 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valued__def,axiom, % 173.22/173.24 ! [V_r_2,T_b,T_a] : % 173.22/173.24 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 173.22/173.24 <=> ! [B_x,B_y] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ! [B_z] : % 173.22/173.24 ( 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)) % 173.22/173.24 => B_y = B_z ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valuedD,axiom, % 173.22/173.24 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 173.22/173.24 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 173.22/173.24 => ( 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)) % 173.22/173.24 => ( 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)) % 173.22/173.24 => V_y_2 = V_z_2 ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_single__valued__confluent,axiom, % 173.22/173.24 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 173.22/173.24 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 173.22/173.24 => ( hBOOL(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))) % 173.22/173.24 => ( hBOOL(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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 | 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))) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__Un__separatorE,axiom, % 173.22/173.24 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ! [B_y] : % 173.22/173.24 ( 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)) % 173.22/173.24 => B_x = B_y ) ) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rel__pow__Suc__E,axiom, % 173.22/173.24 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 => ~ ! [B_y] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ~ 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rel__pow__Suc__D2,axiom, % 173.22/173.24 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 => ? [B_y] : % 173.22/173.24 ( 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)) % 173.22/173.24 & 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rel__pow__Suc__E2,axiom, % 173.22/173.24 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 => ~ ! [B_y] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ~ 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sigma__mono,axiom, % 173.22/173.24 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => 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))) ) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_tranclD2,axiom, % 173.22/173.24 ! [V_R_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 => ? [B_z] : % 173.22/173.24 ( 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))) % 173.22/173.24 & 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_tranclD,axiom, % 173.22/173.24 ! [V_R_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 => ? [B_z] : % 173.22/173.24 ( 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)) % 173.22/173.24 & 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_not__acc__down,axiom, % 173.22/173.24 ! [V_R_2,V_x_2,T_a] : % 173.22/173.24 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 173.22/173.24 => ~ ! [B_z] : % 173.22/173.24 ( 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)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_acc_OaccI,axiom, % 173.22/173.24 ! [V_r_2,V_x_2,T_a] : % 173.22/173.24 ( ! [B_y] : % 173.22/173.24 ( 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)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_max__ext_Osimps,axiom, % 173.22/173.24 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 173.22/173.24 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 173.22/173.24 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 & ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 173.22/173.24 => ? [B_xa] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 173.22/173.24 & 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)) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_wf__no__infinite__down__chainE,axiom, % 173.22/173.24 ! [V_f_2,V_r_2,T_a] : % 173.22/173.24 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.24 => ~ ! [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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_scomp__unfold,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_scomp__apply,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_scomp__Pair,axiom, % 173.22/173.24 ! [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 ). % 173.22/173.24 % 173.22/173.24 fof(fact_Pair__scomp,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_scomp__scomp,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_scomp__def,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_iterate_Osimps,axiom, % 173.22/173.24 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 173.22/173.24 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_IdE,axiom, % 173.22/173.24 ! [V_p_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 173.22/173.24 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_log_Osimps,axiom, % 173.22/173.24 ! [V_i,V_b] : % 173.22/173.24 ( ( ( 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))) % 173.22/173.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 173.22/173.24 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 173.22/173.24 & ( ~ ( 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))) % 173.22/173.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_minus__shift__def,axiom, % 173.22/173.24 ! [V_r,V_l,V_k] : % 173.22/173.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inc__shift__def,axiom, % 173.22/173.24 ! [V_k,V_v] : % 173.22/173.24 ( ( V_v = V_k % 173.22/173.24 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 173.22/173.24 & ( V_v != V_k % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_range,axiom, % 173.22/173.24 ! [V_s,V_k] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_setsum__ivl__cong,axiom, % 173.22/173.24 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 173.22/173.24 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.24 & class_Orderings_Oord(T_a) ) % 173.22/173.24 => ( V_a_2 = V_ca_2 % 173.22/173.24 => ( V_b_2 = V_d_2 % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 173.22/173.24 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 173.22/173.24 => 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)) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nat__intermed__int__val,axiom, % 173.22/173.24 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 173.22/173.24 ( ! [B_i] : % 173.22/173.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 173.22/173.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 173.22/173.24 => 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))) ) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 173.22/173.24 => ? [B_i] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 173.22/173.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 173.22/173.24 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_mod__div__decomp,axiom, % 173.22/173.24 ! [V_b,V_a,T_a] : % 173.22/173.24 ( class_Divides_Osemiring__div(T_a) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold__empty,axiom, % 173.22/173.24 ! [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 ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold__image__def,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding_Oeq__fold,axiom, % 173.22/173.24 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold__def,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_union__fold__insert,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold__sup__insert,axiom, % 173.22/173.24 ! [V_a_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold__inf__insert,axiom, % 173.22/173.24 ! [V_a_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_Ofold__inf__insert,axiom, % 173.22/173.24 ! [V_a_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_Ofold__sup__insert,axiom, % 173.22/173.24 ! [V_a_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 173.22/173.24 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 173.22/173.24 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sup__SUPR__fold__sup,axiom, % 173.22/173.24 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sup__le__fold__sup,axiom, % 173.22/173.24 ! [V_b_2,V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold__inf__le__inf,axiom, % 173.22/173.24 ! [V_b_2,V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 173.22/173.24 ! [V_b_2,V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_Osup__le__fold__sup,axiom, % 173.22/173.24 ! [V_b_2,V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold1__eq__fold__idem,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Olattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Olattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Min_Oeq__fold__idem_H,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Max_Oeq__fold__idem_H,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_minus__fold__remove,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding__one_Oeq__fold_H,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_SUPR__fold__sup,axiom, % 173.22/173.24 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold1__eq__fold,axiom, % 173.22/173.24 ! [V_a_2,V_A_2,T_a] : % 173.22/173.24 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Olattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Olattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Min_Oeq__fold_H,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Max_Oeq__fold_H,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__rec,axiom, % 173.22/173.24 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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)))))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 173.22/173.24 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)))))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 173.22/173.24 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 173.22/173.24 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Groups_Oab__semigroup__mult(T_a) % 173.22/173.24 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 173.22/173.24 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 173.22/173.24 => V_y_2 = V_x_2 ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 173.22/173.24 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 173.22/173.24 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__equality,axiom, % 173.22/173.24 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 173.22/173.24 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 173.22/173.24 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 173.22/173.24 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__insert,axiom, % 173.22/173.24 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 173.22/173.24 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => ? [B_y_H] : % 173.22/173.24 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 173.22/173.24 & 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)) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INFI__fold__inf,axiom, % 173.22/173.24 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF1__D,axiom, % 173.22/173.24 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF1__E,axiom, % 173.22/173.24 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__D,axiom, % 173.22/173.24 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__E,axiom, % 173.22/173.24 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF2__E,axiom, % 173.22/173.24 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF2__D,axiom, % 173.22/173.24 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__INT,axiom, % 173.22/173.24 ! [V_A_2,T_b,V_I_2,T_a] : % 173.22/173.24 ( ? [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 173.22/173.24 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__lower,axiom, % 173.22/173.24 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF__less__iff,axiom, % 173.22/173.24 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 173.22/173.24 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 & class_Orderings_Olinorder(T_a) ) % 173.22/173.24 => ( 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)) % 173.22/173.24 <=> ? [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__subset__iff,axiom, % 173.22/173.24 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_le__INF__iff,axiom, % 173.22/173.24 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( 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))) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Image__INT__subset,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Compl__UN,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Compl__INT,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I2_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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 ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I1_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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 ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF__const,axiom, % 173.22/173.24 ! [V_M_2,T_a,V_A_2,T_b] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__constant,axiom, % 173.22/173.24 ! [V_ca_2,T_b,T_a,V_A_2] : % 173.22/173.24 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__empty,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I5_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I5_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Un__INT__distrib2,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I6_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Un__INT__distrib,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I7_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I6_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I7_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__insert__distrib,axiom, % 173.22/173.24 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__Int__distrib,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INFI__bool__eq,axiom, % 173.22/173.24 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF__commute,axiom, % 173.22/173.24 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INFI__apply,axiom, % 173.22/173.24 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Pow__INT__eq,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_vimage__INT,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I10_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I10_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.24 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.24 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF__INT__eq2,axiom, % 173.22/173.24 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__iff,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__absorb,axiom, % 173.22/173.24 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF__INT__eq,axiom, % 173.22/173.24 ! [V_x_2,V_r_2,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Collect__ball__eq,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__insert,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__Un,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_UN__extend__simps_I7_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_UN__simps_I7_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I9_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I9_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converse__INTER,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF__subset,axiom, % 173.22/173.24 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INTER__def,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I2_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I1_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Collect__all__eq,axiom, % 173.22/173.24 ! [V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),V_P_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I3_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I3_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I4_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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 ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_bij__image__INT,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Fun_Obij__betw(T_a,T_b,V_f_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))) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF__leI,axiom, % 173.22/173.24 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__greaterThan__UNIV,axiom, % 173.22/173.24 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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I4_J,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 173.22/173.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Image__INT__eq,axiom, % 173.22/173.24 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 173.22/173.24 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 173.22/173.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inf__INFI__fold__inf,axiom, % 173.22/173.24 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__fold__inf,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__fold__sup,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__Inter,axiom, % 173.22/173.24 ! [V_M_2,T_a] : % 173.22/173.24 ( ? [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 173.22/173.24 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 173.22/173.24 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_UnionI,axiom, % 173.22/173.24 ! [V_A_2,V_C_2,V_X_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_InterE,axiom, % 173.22/173.24 ! [V_X_2,V_C_2,V_A_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_InterD,axiom, % 173.22/173.24 ! [V_X_2,V_C_2,V_A_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Un__Inter,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF2__iff,axiom, % 173.22/173.24 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INF1__iff,axiom, % 173.22/173.24 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__extend__simps_I8_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INT__simps_I8_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__image__eq,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_INTER__eq__Inter__image,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__empty,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Domain__Union,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_vimage__Union,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_image__Union,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Int__Union2,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Int__Union,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_UN__extend__simps_I8_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_UN__simps_I8_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Range__Union,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sigma__Union,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__Pow__eq,axiom, % 173.22/173.24 ! [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 ). % 173.22/173.24 % 173.22/173.24 fof(fact_Field__Union,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__disjoint,axiom, % 173.22/173.24 ! [V_A_2,V_C_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__Sup,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__Inf,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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)))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__lower,axiom, % 173.22/173.24 ! [V_A_2,V_B_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__le__iff,axiom, % 173.22/173.24 ! [V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( 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)) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_le__Inf__iff,axiom, % 173.22/173.24 ! [V_A_2,V_b_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( 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))) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__upper,axiom, % 173.22/173.24 ! [V_A_2,V_B_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__less__iff,axiom, % 173.22/173.24 ! [V_a_2,V_S_2,T_a] : % 173.22/173.24 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 & class_Orderings_Olinorder(T_a) ) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 173.22/173.24 <=> ? [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 173.22/173.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_less__Sup__iff,axiom, % 173.22/173.24 ! [V_S_2,V_a_2,T_a] : % 173.22/173.24 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 & class_Orderings_Olinorder(T_a) ) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 173.22/173.24 <=> ? [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 173.22/173.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__mono,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__quotient,axiom, % 173.22/173.24 ! [V_r_2,V_A_2,T_a] : % 173.22/173.24 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.24 => 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 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__insert,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__UnionD,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 173.22/173.24 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_subset__Pow__Union,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__anti__mono,axiom, % 173.22/173.24 ! [V_A_2,V_B_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__empty,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__eq,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__UNIV,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__Un__distrib,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__insert,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__image__eq,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_UNION__eq__Union__image,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__upper,axiom, % 173.22/173.24 ! [V_A_2,V_x_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__UNIV,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__lower,axiom, % 173.22/173.24 ! [V_A_2,V_x_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__Un__distrib,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__empty,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__singleton,axiom, % 173.22/173.24 ! [V_a_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__insert,axiom, % 173.22/173.24 ! [V_A_2,V_a_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Int__Inter__image,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__singleton,axiom, % 173.22/173.24 ! [V_a_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__UNIV,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__empty,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__UNIV,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__insert,axiom, % 173.22/173.24 ! [V_A_2,V_a_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Un__eq__Union,axiom, % 173.22/173.24 ! [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))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Un__Union__image,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__Int__subset,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Int__eq__Inter,axiom, % 173.22/173.24 ! [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))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__Un__subset,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__binary,axiom, % 173.22/173.24 ! [V_b_2,V_a_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__binary,axiom, % 173.22/173.24 ! [V_b_2,V_a_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sup__Sup__fold__sup,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Sup__fin__Sup,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inf__Inf__fold__inf,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inf__fin__Inf,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_image__INT,axiom, % 173.22/173.24 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.22/173.24 => 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)) ) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 173.22/173.24 => 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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_card__partition,axiom, % 173.22/173.24 ! [V_k_2,V_C_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 173.22/173.24 => ( ! [B_c] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 173.22/173.24 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 173.22/173.24 => ( ! [B_c1] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 173.22/173.24 => ! [B_c2] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 173.22/173.24 => ( B_c1 != B_c2 % 173.22/173.24 => 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)) ) ) ) % 173.22/173.24 => 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)) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__def,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Union__def,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__Union,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 173.22/173.24 => ( ! [B_M] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 173.22/173.24 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_insert__partition,axiom, % 173.22/173.24 ! [V_F_2,V_x_2,T_a] : % 173.22/173.24 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ! [B_xa] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( B_x != B_xa % 173.22/173.24 => 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)) ) ) ) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inj__on__Inter,axiom, % 173.22/173.24 ! [V_f_2,T_b,T_a,V_S_2] : % 173.22/173.24 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 173.22/173.24 => ( ! [B_A] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 173.22/173.24 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Inter__subset,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a] : % 173.22/173.24 ( ! [B_X] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 173.22/173.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inj__on__INTER,axiom, % 173.22/173.24 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 173.22/173.24 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 => ( ! [B_i] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 173.22/173.24 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 173.22/173.24 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.24 => ( 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)) % 173.22/173.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => ~ ! [B_y] : % 173.22/173.24 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 173.22/173.24 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 173.22/173.24 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 173.22/173.24 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_InterI,axiom, % 173.22/173.24 ! [V_A_2,V_C_2,T_a] : % 173.22/173.24 ( ! [B_X] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_inf__le__fold__inf,axiom, % 173.22/173.24 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Osemilattice__inf(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_fold__sup__le__sup,axiom, % 173.22/173.24 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 173.22/173.24 ( class_Lattices_Osemilattice__sup(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 173.22/173.24 => 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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_wf__eq__minimal,axiom, % 173.22/173.24 ! [V_r_2,T_a] : % 173.22/173.24 ( c_Wellfounded_Owf(T_a,V_r_2) % 173.22/173.24 <=> ! [B_Q] : % 173.22/173.24 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 173.22/173.24 => ? [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 173.22/173.24 & ! [B_y] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.22/173.24 => 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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_transfer__nat__int__set__cong,axiom, % 173.22/173.24 ! [V_P_H_2,V_P_2] : % 173.22/173.24 ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.22/173.24 => ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.24 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding__image__simple__idem_Oidem,axiom, % 173.22/173.24 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.24 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 173.22/173.24 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_UnionE,axiom, % 173.22/173.24 ! [V_C_2,V_A_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ~ ! [B_X] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rel__compE,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ~ ! [B_x,B_y,B_z] : % 173.22/173.24 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 173.22/173.24 => ( 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)) % 173.22/173.24 => ~ 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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_converseE,axiom, % 173.22/173.24 ! [V_r_2,V_yx_2,T_b,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ~ ! [B_x,B_y] : % 173.22/173.24 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 173.22/173.24 => ~ 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Oplus__frac__def,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Otimes__frac__def,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Oof__frac__def,axiom, % 173.22/173.24 ! [V_q,T_a,T_b] : % 173.22/173.24 ( ( class_Rings_Oinverse(T_b) % 173.22/173.24 & class_Rings_Oring__1(T_b) ) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Oless__frac__def,axiom, % 173.22/173.24 ! [V_r_2,V_q_2,T_a] : % 173.22/173.24 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 173.22/173.24 <=> 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 173.22/173.24 ! [V_r_2,V_q_2,T_a] : % 173.22/173.24 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 173.22/173.24 <=> 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Odenom__def,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Onum__def,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_setprod__pos,axiom, % 173.22/173.24 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( class_Rings_Olinordered__semidom(T_b) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_internal__split__def,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_internal__split__conv,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_setprod__nonneg,axiom, % 173.22/173.24 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.24 ( class_Rings_Olinordered__semidom(T_b) % 173.22/173.24 => ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_bool_Osize_I1_J,axiom, % 173.22/173.24 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.24 % 173.22/173.24 fof(fact_bool_Osize_I2_J,axiom, % 173.22/173.24 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__less__ub,axiom, % 173.22/173.24 ! [V_u_2,V_f_2] : % 173.22/173.24 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lenlex__def,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_neq__if__length__neq,axiom, % 173.22/173.24 ! [V_ys,V_xs,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 => V_xs != V_ys ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexn__length,axiom, % 173.22/173.24 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 173.22/173.24 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lenlex__conv,axiom, % 173.22/173.24 ! [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)))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__sublists,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__sublist,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexn_Osimps_I2_J,axiom, % 173.22/173.24 ! [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)))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexord__lex,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 & 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_impossible__Cons,axiom, % 173.22/173.24 ! [V_x,V_ys,V_xs,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexord__cons__cons,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( 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)) % 173.22/173.24 | ( V_a_2 = V_b_2 % 173.22/173.24 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Oinject,axiom, % 173.22/173.24 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> ( V_a_2 = V_a_H_2 % 173.22/173.24 & V_list_2 = V_list_H_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_not__Cons__self2,axiom, % 173.22/173.24 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 173.22/173.24 % 173.22/173.24 fof(fact_not__Cons__self,axiom, % 173.22/173.24 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osize_I4_J,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Cons__in__lex,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( ( hBOOL(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)) % 173.22/173.24 & 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) ) % 173.22/173.24 | ( V_x_2 = V_y_2 % 173.22/173.24 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__Cons__def,axiom, % 173.22/173.24 ! [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)))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_pick_Osimps,axiom, % 173.22/173.24 ! [V_xs,V_x,T_a,V_i] : % 173.22/173.24 ( ( 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))) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( ~ 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))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_select__weight__cons__zero,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 173.22/173.24 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Cons__acc__listrel1I,axiom, % 173.22/173.24 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 173.22/173.24 => ( 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)))) % 173.22/173.24 => 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)))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1__mono,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1__converse,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 173.22/173.24 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1I2,axiom, % 173.22/173.24 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1__eq__len,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__listrel1__eq__len,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__listrel1__converse,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 173.22/173.24 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1I1,axiom, % 173.22/173.24 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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)) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Cons__listrel1__Cons,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( ( hBOOL(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)) % 173.22/173.24 & V_xs_2 = V_ys_2 ) % 173.22/173.24 | ( V_x_2 = V_y_2 % 173.22/173.24 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osize_I2_J,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__Cons,axiom, % 173.22/173.24 ! [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))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__rtrancl__refl,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__mono,axiom, % 173.22/173.24 ! [V_s_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__eq__len,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__rtrancl__trans,axiom, % 173.22/173.24 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__reflcl__if__listrel1,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1__subset__listrel,axiom, % 173.22/173.24 ! [V_r_H_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel_OCons,axiom, % 173.22/173.24 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(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)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrelp__listrel__eq,axiom, % 173.22/173.24 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__Cons2,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => ~ ! [B_x,B_xs] : % 173.22/173.24 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 173.22/173.24 => ( 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)) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrelp_OCons,axiom, % 173.22/173.24 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 173.22/173.24 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrelp_Oequations_I2_J,axiom, % 173.22/173.24 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 173.22/173.24 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__Cons1,axiom, % 173.22/173.24 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => ~ ! [B_y,B_ys] : % 173.22/173.24 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 173.22/173.24 => ( 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)) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__subset,axiom, % 173.22/173.24 ! [V_A_2,V_r_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => 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))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lists__UNIV,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lists__mono,axiom, % 173.22/173.24 ! [V_B_2,V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_equiv__listrel,axiom, % 173.22/173.24 ! [V_r_2,V_A_2,T_a] : % 173.22/173.24 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__refl__on,axiom, % 173.22/173.24 ! [V_r_2,V_A_2,T_a] : % 173.22/173.24 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Cons__in__lists__iff,axiom, % 173.22/173.24 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lists__accI,axiom, % 173.22/173.24 ! [V_r_2,V_xs_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lists__accD,axiom, % 173.22/173.24 ! [V_r_2,V_xs_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__iff__nth,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( 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) % 173.22/173.24 & ! [B_n] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexord__irreflexive,axiom, % 173.22/173.24 ! [V_y_2,V_r_2,T_a] : % 173.22/173.24 ( ! [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)) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__Cons__0,axiom, % 173.22/173.24 ! [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 ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth_Osimps,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__Cons__Suc,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__eq__iff__nth__eq,axiom, % 173.22/173.24 ! [T_a,V_ys_2,V_xs_2] : % 173.22/173.24 ( V_xs_2 = V_ys_2 % 173.22/173.24 <=> ( 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) % 173.22/173.24 & ! [B_i] : % 173.22/173.24 ( 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))) % 173.22/173.24 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_infinite__UNIV__listI,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__Cons_H,axiom, % 173.22/173.24 ! [V_xs,V_x,T_a,V_n] : % 173.22/173.24 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 173.22/173.24 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__Cons__number__of,axiom, % 173.22/173.24 ! [V_xs,V_x,T_a,V_v] : % 173.22/173.24 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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 ) % 173.22/173.24 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexord__take__index__conv,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( ( 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))) % 173.22/173.24 & 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 ) % 173.22/173.24 | ? [B_i] : % 173.22/173.24 ( 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)))) % 173.22/173.24 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 173.22/173.24 & 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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexord__linear,axiom, % 173.22/173.24 ! [V_y_2,V_x_2,V_r_2,T_a] : % 173.22/173.24 ( ! [B_a,B_b] : % 173.22/173.24 ( 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)) % 173.22/173.24 | B_a = B_b % 173.22/173.24 | 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)) ) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 | V_x_2 = V_y_2 % 173.22/173.24 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__all,axiom, % 173.22/173.24 ! [V_n,V_xs,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__take,axiom, % 173.22/173.24 ! [V_xs,T_a,V_n,V_i] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__take,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sublist__upt__eq__take,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__take,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__Suc__Cons,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__lists__length__le,axiom, % 173.22/173.24 ! [V_n_2,V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__sublist,axiom, % 173.22/173.24 ! [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))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__set,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__take__subset,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__set__takeD,axiom, % 173.22/173.24 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_List_Oset_Osimps_I2_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__ConsD,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => ( V_y_2 = V_x_2 % 173.22/173.24 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__set__sublistD,axiom, % 173.22/173.24 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_notin__set__sublistI,axiom, % 173.22/173.24 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => ~ 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sublists__powset,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__subset__Cons,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__sublist__subset,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_card__length,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_all__set__conv__all__nth,axiom, % 173.22/173.24 ! [V_P_2,V_xs_2,T_a] : % 173.22/173.24 ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.24 <=> ! [B_i] : % 173.22/173.24 ( 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))) % 173.22/173.24 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__take__subset__set__take,axiom, % 173.22/173.24 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__size__estimation,axiom, % 173.22/173.24 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__size__estimation_H,axiom, % 173.22/173.24 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 173.22/173.24 => 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))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__lists__conv__set,axiom, % 173.22/173.24 ! [V_A_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__pos__if__in__set,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__mem,axiom, % 173.22/173.24 ! [V_xs_2,T_a,V_n_2] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__set__conv__nth,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 <=> ? [B_i] : % 173.22/173.24 ( 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))) % 173.22/173.24 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lists__eq__set,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__conv__nth,axiom, % 173.22/173.24 ! [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))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_finite__lists__length__eq,axiom, % 173.22/173.24 ! [V_n_2,V_A_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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))))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__iff__zip,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( 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) % 173.22/173.24 & ! [B_x] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => 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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__n__lists,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__zip,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__zip,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip__Cons__Cons,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__eq__iff__zip__eq,axiom, % 173.22/173.24 ! [T_a,V_ys_2,V_xs_2] : % 173.22/173.24 ( V_xs_2 = V_ys_2 % 173.22/173.24 <=> ( 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) % 173.22/173.24 & ! [B_x] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip__same,axiom, % 173.22/173.24 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 & V_a_2 = V_b_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__zip__leftD,axiom, % 173.22/173.24 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__zip__rightD,axiom, % 173.22/173.24 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__set__zipE,axiom, % 173.22/173.24 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__zip,axiom, % 173.22/173.24 ! [V_ys,T_b,V_xs,T_a,V_i] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__n__lists__elem,axiom, % 173.22/173.24 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 173.22/173.24 ( 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)))) % 173.22/173.24 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__n__lists,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__zip,axiom, % 173.22/173.24 ! [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)))))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_product__list__set,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_greaterThanLessThan__upto,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_atLeastAtMost__upto,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__upto,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_atLeastLessThan__upto,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_greaterThanAtMost__upto,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nat__list__def,axiom, % 173.22/173.24 ! [V_l_2] : % 173.22/173.24 ( c_List_Onat__list(V_l_2) % 173.22/173.24 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listsum__setsum__nth,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 173.22/173.24 ! [V_ns_2] : % 173.22/173.24 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 <=> ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 173.22/173.24 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listsum__simps_I2_J,axiom, % 173.22/173.24 ! [V_xs,V_x,T_a] : % 173.22/173.24 ( class_Groups_Omonoid__add(T_a) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_elem__le__listsum__nat,axiom, % 173.22/173.24 ! [V_ns,V_k] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__size__pointwise,axiom, % 173.22/173.24 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 173.22/173.24 ( ! [B_x] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_butlast__take,axiom, % 173.22/173.24 ! [V_xs,T_a,V_n] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__set__butlastD,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 173.22/173.24 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__butlast,axiom, % 173.22/173.24 ! [V_xs,T_a,V_n] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__butlast,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_butlast__conv__take,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listsum__update__nat,axiom, % 173.22/173.24 ! [V_n,V_ns,V_k] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__take__lemma,axiom, % 173.22/173.24 ! [V_ys,V_xs,T_a,V_k] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => ( ! [B_i] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 173.22/173.24 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 173.22/173.24 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__beyond,axiom, % 173.22/173.24 ! [V_x,V_i,V_xs,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__list__update__neq,axiom, % 173.22/173.24 ! [V_x,V_xs,T_a,V_j,V_i] : % 173.22/173.24 ( V_i != V_j % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__id,axiom, % 173.22/173.24 ! [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 ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__list__update,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__code_I2_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update_Osimps_I2_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__code_I3_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__overwrite,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__swap,axiom, % 173.22/173.24 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 173.22/173.24 ( V_i != V_i_H % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_update__zip,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip__update,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__update__subsetI,axiom, % 173.22/173.24 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 173.22/173.24 ( 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)) % 173.22/173.24 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__update__subset__insert,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__list__update,axiom, % 173.22/173.24 ! [V_x,V_j,V_xs,T_a,V_i] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( ( V_i = V_j % 173.22/173.24 => 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 ) % 173.22/173.24 & ( V_i != V_j % 173.22/173.24 => 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) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__same__conv,axiom, % 173.22/173.24 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 173.22/173.24 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__list__update__eq,axiom, % 173.22/173.24 ! [V_x,V_xs,T_a,V_i] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__update__memI,axiom, % 173.22/173.24 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 173.22/173.24 ( 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))) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_butlast__list__update,axiom, % 173.22/173.24 ! [V_x,V_xs,T_a,V_k] : % 173.22/173.24 ( ( 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)) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( 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)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel1__iff__update,axiom, % 173.22/173.24 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ? [B_y,B_n] : % 173.22/173.24 ( 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)) % 173.22/173.24 & 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))) % 173.22/173.24 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__list__update,axiom, % 173.22/173.24 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.24 => ( ~ 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)))))) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__zipI1,axiom, % 173.22/173.24 ! [V_ys,T_b,V_xs,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__zipI2,axiom, % 173.22/173.24 ! [V_xs,T_b,V_ys,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__n__lists,axiom, % 173.22/173.24 ! [V_n,V_xs,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__sublistI,axiom, % 173.22/173.24 ! [V_I_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__upto,axiom, % 173.22/173.24 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__product,axiom, % 173.22/173.24 ! [V_ys,T_b,V_xs,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.24 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__take,axiom, % 173.22/173.24 ! [V_i,V_xs,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct_Osimps_I2_J,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 173.22/173.24 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_card__distinct,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__card,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__conv__nth,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.24 <=> ! [B_i] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ! [B_j] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( B_i != B_j % 173.22/173.24 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_nth__eq__iff__index__eq,axiom, % 173.22/173.24 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.24 => ( 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))) % 173.22/173.24 => ( 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))) % 173.22/173.24 => ( 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) % 173.22/173.24 <=> V_i_2 = V_j_2 ) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__listsum__conv__Setsum,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nitpick_Ocard_H__def,axiom, % 173.22/173.24 ! [V_A_2,T_a] : % 173.22/173.24 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)))) ) % 173.22/173.24 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__remove1__eq,axiom, % 173.22/173.24 ! [V_x_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.24 => 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__remove1,axiom, % 173.22/173.24 ! [V_x,V_xs,T_a] : % 173.22/173.24 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__remove1__subset,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_in__set__remove1,axiom, % 173.22/173.24 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 173.22/173.24 ( V_a_2 != V_b_2 % 173.22/173.24 => ( 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)))) % 173.22/173.24 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_notin__set__remove1,axiom, % 173.22/173.24 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => ~ 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)))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_remove1__idem,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_remove1_Osimps_I2_J,axiom, % 173.22/173.24 ! [V_xs,T_a,V_y,V_x] : % 173.22/173.24 ( ( V_x = V_y % 173.22/173.24 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 173.22/173.24 & ( V_x != V_y % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_remove1__commute,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__remove1,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sorted__list__of__set__remove,axiom, % 173.22/173.24 ! [V_x_2,V_A_2,T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__Cons__number__of,axiom, % 173.22/173.24 ! [V_xs,V_x,T_a,V_v] : % 173.22/173.24 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lists_ONil,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__Nil2,axiom, % 173.22/173.24 ! [V_r_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__Nil1,axiom, % 173.22/173.24 ! [V_r_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct_Osimps_I1_J,axiom, % 173.22/173.24 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_distinct__butlast,axiom, % 173.22/173.24 ! [T_a,V_xs] : % 173.22/173.24 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.24 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.24 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_remove1_Osimps_I1_J,axiom, % 173.22/173.24 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip__Nil,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip_Osimps_I1_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sublist__empty,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osize_I1_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sorted__list__of__set__empty,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Orderings_Olinorder(T_a) % 173.22/173.24 => 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) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sublist__nil,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrelp_Oequations_I1_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrelp_ONil,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_product_Osimps_I1_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_upto__empty,axiom, % 173.22/173.24 ! [V_i,V_j] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 173.22/173.24 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osimps_I2_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osimps_I3_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sublists_Osimps_I1_J,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__0,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__eq__Nil,axiom, % 173.22/173.24 ! [V_xs_2,V_n_2,T_a] : % 173.22/173.24 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.24 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__Nil,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_n__lists__Nil,axiom, % 173.22/173.24 ! [T_a,V_n] : % 173.22/173.24 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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))) ) % 173.22/173.24 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_n__lists_Osimps_I1_J,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_List_Oset_Osimps_I1_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__empty2,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 173.22/173.24 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__empty,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.22/173.24 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_butlast_Osimps_I2_J,axiom, % 173.22/173.24 ! [V_x,T_a,V_xs] : % 173.22/173.24 ( ( V_xs = c_List_Olist_ONil(T_a) % 173.22/173.24 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 173.22/173.24 & ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osize_I3_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__0__conv,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_butlast_Osimps_I1_J,axiom, % 173.22/173.24 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listsum__simps_I1_J,axiom, % 173.22/173.24 ! [T_a] : % 173.22/173.24 ( class_Groups_Omonoid__add(T_a) % 173.22/173.24 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__code_I1_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update_Osimps_I1_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list__update__nonempty,axiom, % 173.22/173.24 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 173.22/173.24 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 173.22/173.24 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__greater__0__conv,axiom, % 173.22/173.24 ! [V_xs_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__1__Cons,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_not__Nil__listrel1,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_not__listrel1__Nil,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel_ONil,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lexord__Nil__right,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nil2__notin__lex,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Nil__notin__lex,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__Cons,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_upto_Osimps,axiom, % 173.22/173.24 ! [V_j,V_i] : % 173.22/173.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 173.22/173.24 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sublist__singleton,axiom, % 173.22/173.24 ! [V_x_2,T_a,V_A_2] : % 173.22/173.24 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_lists__empty,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_take__Cons_H,axiom, % 173.22/173.24 ! [V_xs,V_x,T_a,V_n] : % 173.22/173.24 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_upto__rec__number__of,axiom, % 173.22/173.24 ! [V_n,V_m] : % 173.22/173.24 ( ( 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))) % 173.22/173.24 => 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))) ) % 173.22/173.24 & ( ~ 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))) % 173.22/173.24 => 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) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listrel__Nil,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__Cons__sing__Nil,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_upto_Opsimps,axiom, % 173.22/173.24 ! [V_j_2,V_i_2] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 173.22/173.24 => 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)) ) % 173.22/173.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 173.22/173.24 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_select,axiom, % 173.22/173.24 ! [V_s_2,T_a,V_xs_2] : % 173.22/173.24 ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.24 => 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))) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listset_Osimps_I1_J,axiom, % 173.22/173.24 ! [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))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip__Cons1,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osimps_I5_J,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_list_Osimps_I4_J,axiom, % 173.22/173.24 ! [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 ). % 173.22/173.24 % 173.22/173.24 fof(fact_listset_Osimps_I2_J,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip__Cons,axiom, % 173.22/173.24 ! [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) ). % 173.22/173.24 % 173.22/173.24 fof(fact_upto_Opinduct,axiom, % 173.22/173.24 ! [V_P_2,V_a1_2,V_a0_2] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( ! [B_i,B_j] : % 173.22/173.24 ( 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))) % 173.22/173.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 173.22/173.24 => 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)) ) % 173.22/173.24 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 173.22/173.24 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_anamorph_Osimps,axiom, % 173.22/173.24 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 173.22/173.24 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.24 => 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) ) % 173.22/173.24 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.24 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_sublist__Cons,axiom, % 173.22/173.24 ! [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)))) ). % 173.22/173.24 % 173.22/173.24 fof(fact_snoc__listrel1__snoc__iff,axiom, % 173.22/173.24 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 173.22/173.24 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.24 & V_x_2 = V_y_2 ) % 173.22/173.24 | ( V_xs_2 = V_ys_2 % 173.22/173.24 & hBOOL(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)) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append__eq__Cons__conv,axiom, % 173.22/173.24 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 173.22/173.24 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 173.22/173.24 | ? [B_ys_H] : % 173.22/173.24 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 173.22/173.24 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Cons__eq__append__conv,axiom, % 173.22/173.24 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 173.22/173.24 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 173.22/173.24 | ? [B_ys_H] : % 173.22/173.24 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 173.22/173.24 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append1__eq__conv,axiom, % 173.22/173.24 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> ( V_xs_2 = V_ys_2 % 173.22/173.24 & V_x_2 = V_y_2 ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append__Cons,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_Cons__eq__appendI,axiom, % 173.22/173.24 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 173.22/173.24 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 173.22/173.24 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 173.22/173.24 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append__in__lists__conv,axiom, % 173.22/173.24 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( 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))) % 173.22/173.24 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 173.22/173.24 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append__eq__appendI,axiom, % 173.22/173.24 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 173.22/173.24 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 173.22/173.24 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 173.22/173.24 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append__same__eq,axiom, % 173.22/173.24 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> V_ys_2 = V_zs_2 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_same__append__eq,axiom, % 173.22/173.24 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> V_ys_2 = V_zs_2 ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append__eq__append__conv2,axiom, % 173.22/173.24 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 <=> ? [B_us] : % 173.22/173.24 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 173.22/173.24 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 173.22/173.24 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 173.22/173.24 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_append__assoc,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_set__append,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_zip__append,axiom, % 173.22/173.24 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 173.22/173.24 ( 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) % 173.22/173.24 => ( 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) % 173.22/173.24 => 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)) ) ) ). % 173.22/173.24 % 173.22/173.24 fof(fact_length__append,axiom, % 173.22/173.24 ! [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)) ). % 173.22/173.24 % 173.22/173.24 fof(fact_listsum__append,axiom, % 173.22/173.24 ! [V_ys,V_xs,T_a] : % 173.22/173.24 ( class_Groups_Omonoid__add(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_butlast__append,axiom, % 173.22/173.25 ! [V_xs,T_a,V_ys] : % 173.22/173.25 ( ( V_ys = c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 173.22/173.25 & ( V_ys != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__Nil,axiom, % 173.22/173.25 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 173.22/173.25 % 173.22/173.25 fof(fact_Nil__is__append__conv,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 173.22/173.25 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 173.22/173.25 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__Nil2,axiom, % 173.22/173.25 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 173.22/173.25 % 173.22/173.25 fof(fact_self__append__conv,axiom, % 173.22/173.25 ! [V_ys_2,T_a,V_xs_2] : % 173.22/173.25 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 173.22/173.25 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_self__append__conv2,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_ys_2] : % 173.22/173.25 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__is__Nil__conv,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 173.22/173.25 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__self__conv,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 173.22/173.25 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__self__conv2,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_eq__Nil__appendI,axiom, % 173.22/173.25 ! [T_a,V_ys,V_xs] : % 173.22/173.25 ( V_xs = V_ys % 173.22/173.25 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__append__length,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__append__length__plus,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__update__append1,axiom, % 173.22/173.25 ! [V_x,V_ys,V_xs,T_a,V_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__update__length,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remove1__append,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__set__butlast__appendI,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 173.22/173.25 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 173.22/173.25 => 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))))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_butlast__snoc,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__listrel1I,axiom, % 173.22/173.25 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.25 & V_us_2 = V_vs_2 ) % 173.22/173.25 | ( V_xs_2 = V_ys_2 % 173.22/173.25 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lexord__append__leftI,axiom, % 173.22/173.25 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__append,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 173.22/173.25 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 173.22/173.25 & 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__append,axiom, % 173.22/173.25 ! [V_ys,V_xs,T_a,V_n] : % 173.22/173.25 ( ( 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))) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( ~ 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))) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__update__append,axiom, % 173.22/173.25 ! [V_x,V_ys,V_xs,T_a,V_n] : % 173.22/173.25 ( ( 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))) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( ~ 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))) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sublist__append,axiom, % 173.22/173.25 ! [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)))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listrel1I,axiom, % 173.22/173.25 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(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)) % 173.22/173.25 => ( 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)) % 173.22/173.25 => ( 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)) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lexord__append__left__rightI,axiom, % 173.22/173.25 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__Suc__conv__app__nth,axiom, % 173.22/173.25 ! [V_xs,T_a,V_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listrel1E,axiom, % 173.22/173.25 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.25 => ~ ! [B_x,B_y] : % 173.22/173.25 ( 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)) % 173.22/173.25 => ! [B_us,B_vs] : % 173.22/173.25 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 173.22/173.25 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lexord__append__leftD,axiom, % 173.22/173.25 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.25 => ( ! [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)) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate1__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upd__conv__take__nth__drop,axiom, % 173.22/173.25 ! [V_a,V_xs,T_a,V_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__take__drop__id,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__1__Cons,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__Suc__Cons,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__via__drop,axiom, % 173.22/173.25 ! [V_ys,V_y,V_xs,V_n,T_a] : % 173.22/173.25 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 173.22/173.25 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__drop,axiom, % 173.22/173.25 ! [V_i,V_xs,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct1__rotate,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 173.22/173.25 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__zip,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__drop,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__0,axiom, % 173.22/173.25 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__drop,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__take,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__set__dropD,axiom, % 173.22/173.25 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__rotate1,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__drop__subset,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__rotate1,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__drop,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_butlast__drop,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__butlast,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__Nil,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate1__is__Nil__conv,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__drop__subset__set__drop,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 173.22/173.25 => 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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__all,axiom, % 173.22/173.25 ! [V_n,V_xs,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__eq__Nil,axiom, % 173.22/173.25 ! [V_xs_2,V_n_2,T_a] : % 173.22/173.25 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__eq__conv__conj,axiom, % 173.22/173.25 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 173.22/173.25 <=> ( 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) % 173.22/173.25 & 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__Cons,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__Cons_H,axiom, % 173.22/173.25 ! [V_xs,V_x,T_a,V_n] : % 173.22/173.25 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__drop,axiom, % 173.22/173.25 ! [V_xs,T_a,V_i,V_n] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__eq__append__conv__if,axiom, % 173.22/173.25 ! [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] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> ( ( 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))) % 173.22/173.25 => ( 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) % 173.22/173.25 & 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) ) ) % 173.22/173.25 & ( ~ 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))) % 173.22/173.25 => ( 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 % 173.22/173.25 & 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 ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__drop_H,axiom, % 173.22/173.25 ! [V_xs,T_a,V_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__simps,axiom, % 173.22/173.25 ! [V_xs,V_x,T_b,T_a] : % 173.22/173.25 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 173.22/173.25 & 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__Cons__number__of,axiom, % 173.22/173.25 ! [V_xs,V_x,T_a,V_v] : % 173.22/173.25 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__add,axiom, % 173.22/173.25 ! [V_xs,T_a,V_j,V_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate1__length01,axiom, % 173.22/173.25 ! [V_xs,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__append1,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__append2,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_id__take__nth__drop,axiom, % 173.22/173.25 ! [V_xs,T_a,V_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__hd__drop,axiom, % 173.22/173.25 ! [V_xs,T_a,V_n] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__drop__conv__nth,axiom, % 173.22/173.25 ! [V_n,T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd_Osimps,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__append2,axiom, % 173.22/173.25 ! [V_ys,T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__append,axiom, % 173.22/173.25 ! [V_ys,T_a,V_xs] : % 173.22/173.25 ( ( V_xs = c_List_Olist_ONil(T_a) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__in__set,axiom, % 173.22/173.25 ! [T_a,V_xs_2] : % 173.22/173.25 ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__conv__nth,axiom, % 173.22/173.25 ! [T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate1__hd__tl,axiom, % 173.22/173.25 ! [T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__rotate__conv__nth,axiom, % 173.22/173.25 ! [V_n,T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__tl,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_tl__drop,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_tl__append2,axiom, % 173.22/173.25 ! [V_ys,T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_tl_Osimps_I2_J,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__tl,axiom, % 173.22/173.25 ! [V_xs,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__rotate,axiom, % 173.22/173.25 ! [V_xs_2,V_n_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 173.22/173.25 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__add,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__rotate,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate0,axiom, % 173.22/173.25 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__rotate,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__rotate,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_tl_Osimps_I1_J,axiom, % 173.22/173.25 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__is__Nil__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_n_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate1__rotate__swap,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__tl,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__conv__mod,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__Suc,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__Suc,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_tl__append,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__id,axiom, % 173.22/173.25 ! [V_xs,T_a,V_n] : % 173.22/173.25 ( 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) % 173.22/173.25 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__length01,axiom, % 173.22/173.25 ! [V_n,V_xs,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__tl,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_tl__take,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__Suc,axiom, % 173.22/173.25 ! [V_n,T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__drop__take,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_fold1__set,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.22/173.25 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lexord__append__rightI,axiom, % 173.22/173.25 ! [V_r_2,V_x_2,T_a,V_y_2] : % 173.22/173.25 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__Nil,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_start__le__sum,axiom, % 173.22/173.25 ! [V_ns_2,V_n_2,V_m_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__absorb0,axiom, % 173.22/173.25 ! [V_zs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Groups_Omonoid__add(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__assoc,axiom, % 173.22/173.25 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 173.22/173.25 ( class_Groups_Osemigroup__add(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__Cons,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__append,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__foldl,axiom, % 173.22/173.25 ! [T_a] : % 173.22/173.25 ( class_Groups_Omonoid__add(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sum__eq__0__conv,axiom, % 173.22/173.25 ! [V_ns_2,V_m_2] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 & ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 173.22/173.25 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 173.22/173.25 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Sup__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Inf__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Sup__fin__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Lattices_Olattice(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Inf__fin__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Lattices_Olattice(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Min__fin__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Max__fin__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_min__max_OInf__fin__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_min__max_OSup__fin__set__fold,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_SUPR__set__fold,axiom, % 173.22/173.25 ! [V_f_2,V_xs_2,T_b,T_a] : % 173.22/173.25 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_INFI__set__fold,axiom, % 173.22/173.25 ! [V_f_2,V_xs_2,T_b,T_a] : % 173.22/173.25 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_elem__le__sum,axiom, % 173.22/173.25 ! [V_ns_2,V_n_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__list__of__set__insert,axiom, % 173.22/173.25 ! [V_x_2,V_A_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.25 => 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)))))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lexord__Nil__left,axiom, % 173.22/173.25 ! [V_r_2,V_y_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.25 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__key_Osimps_I1_J,axiom, % 173.22/173.25 ! [V_x_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__key_Osimps_I2_J,axiom, % 173.22/173.25 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( ( 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))) % 173.22/173.25 => 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)) ) % 173.22/173.25 & ( ~ 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))) % 173.22/173.25 => 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)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remove1__insort,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_fun__left__comm__insort,axiom, % 173.22/173.25 ! [T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__left__comm,axiom, % 173.22/173.25 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__key__left__comm,axiom, % 173.22/173.25 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__insort,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__insort,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__not__Nil,axiom, % 173.22/173.25 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__insort,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => ( 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))) % 173.22/173.25 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__insert__insort__key,axiom, % 173.22/173.25 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( ~ 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)))) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__insert__insort,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__insort__insert,axiom, % 173.22/173.25 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__insert__triv,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__insort__insert,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__insert__key__triv,axiom, % 173.22/173.25 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( 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)))) % 173.22/173.25 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__list__update,axiom, % 173.22/173.25 ! [V_x,V_k,T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => ( ( 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)) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 173.22/173.25 & ( 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)) % 173.22/173.25 => 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) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__conv__nth,axiom, % 173.22/173.25 ! [T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__appendL,axiom, % 173.22/173.25 ! [V_xs,T_a,V_ys] : % 173.22/173.25 ( V_ys = c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__appendR,axiom, % 173.22/173.25 ! [V_xs,T_a,V_ys] : % 173.22/173.25 ( V_ys != c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__append,axiom, % 173.22/173.25 ! [V_xs,T_a,V_ys] : % 173.22/173.25 ( ( V_ys = c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 173.22/173.25 & ( V_ys != c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last_Osimps,axiom, % 173.22/173.25 ! [V_x,T_a,V_xs] : % 173.22/173.25 ( ( V_xs = c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 173.22/173.25 & ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__ConsR,axiom, % 173.22/173.25 ! [V_x,T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__ConsL,axiom, % 173.22/173.25 ! [V_x,T_a,V_xs] : % 173.22/173.25 ( V_xs = c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__in__set,axiom, % 173.22/173.25 ! [T_a,V_as_2] : % 173.22/173.25 ( V_as_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__snoc,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__drop,axiom, % 173.22/173.25 ! [V_xs,T_a,V_n] : % 173.22/173.25 ( 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))) % 173.22/173.25 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__butlast__last__id,axiom, % 173.22/173.25 ! [T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_snoc__eq__iff__butlast,axiom, % 173.22/173.25 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 173.22/173.25 ( 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 % 173.22/173.25 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 173.22/173.25 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lists_Osimps,axiom, % 173.22/173.25 ! [V_A_2,V_a_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 173.22/173.25 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 173.22/173.25 | ? [B_a,B_l] : % 173.22/173.25 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 173.22/173.25 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 173.22/173.25 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_select__weigth__select,axiom, % 173.22/173.25 ! [T_a,V_xs_2] : % 173.22/173.25 ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_inj__mapI,axiom, % 173.22/173.25 ! [V_f_2,T_b,T_a] : % 173.22/173.25 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__map,axiom, % 173.22/173.25 ! [V_f_2,T_b,T_a,V_xs_2] : % 173.22/173.25 ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__map,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_uminus__listsum__map,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Groups_Oab__group__add(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__tl,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__inj__on,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( 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) % 173.22/173.25 => ( 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))) % 173.22/173.25 => V_xs_2 = V_ys_2 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_inj__on__map__eq__map,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( 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) % 173.22/173.25 <=> V_xs_2 = V_ys_2 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__is__Nil__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map_Osimps_I1_J,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Nil__is__map__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__update,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__subtractf,axiom, % 173.22/173.25 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Groups_Oab__group__add(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__mult__const,axiom, % 173.22/173.25 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Rings_Osemiring__0(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__const__mult,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 173.22/173.25 ( class_Rings_Osemiring__0(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__0,axiom, % 173.22/173.25 ! [V_xs_2,T_b,T_a] : % 173.22/173.25 ( class_Groups_Omonoid__add(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__addf,axiom, % 173.22/173.25 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__butlast,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__map,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__eq__imp__length__eq,axiom, % 173.22/173.25 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( 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) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__eq__conv,axiom, % 173.22/173.25 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 173.22/173.25 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_inj__map__eq__map,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.25 => ( 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) % 173.22/173.25 <=> V_xs_2 = V_ys_2 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__injective,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( 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) % 173.22/173.25 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.22/173.25 => V_xs_2 = V_ys_2 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__ident,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map_Osimps_I2_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__same__conv__map,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__map2,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__zip__map2,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__zip__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__map1,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__map__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__fun__upd,axiom, % 173.22/173.25 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 173.22/173.25 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hAPP(hAPP(c_List_Omap(T_a,T_b),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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__map,axiom, % 173.22/173.25 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__map,axiom, % 173.22/173.25 ! [V_f_2,T_b,T_a,V_xs_2] : % 173.22/173.25 ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__abs,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.22/173.25 => 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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__map,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 173.22/173.25 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 173.22/173.25 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__size__map,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_List_Omap_Ocomp,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__comp__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_List_Omap_Ocompositionality,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__map,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_List_Omap_Oid,axiom, % 173.22/173.25 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_List_Omap_Oidentity,axiom, % 173.22/173.25 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_inj__mapD,axiom, % 173.22/173.25 ! [V_f_2,T_b,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_inj__map,axiom, % 173.22/173.25 ! [V_f_2,T_b,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 173.22/173.25 ! [V_f_2,V_xs_2,T_a,T_b] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__triv,axiom, % 173.22/173.25 ! [V_xs_2,V_r_2,T_b,T_a] : % 173.22/173.25 ( class_Rings_Osemiring__1(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_product_Osimps_I2_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__map__remove1,axiom, % 173.22/173.25 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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)))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_inj__on__mapI,axiom, % 173.22/173.25 ! [V_A_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Nitpick_Osetsum_H__def,axiom, % 173.22/173.25 ! [V_f_2,V_A_2,T_a,T_b] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.25 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.25 => 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))))) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.25 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pick__same,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_l_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sublists_Osimps_I2_J,axiom, % 173.22/173.25 ! [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))))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__fst__zip,axiom, % 173.22/173.25 ! [V_ys_2,T_b,V_xs_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => 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 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_code__numeral_Oof__nat__inject,axiom, % 173.22/173.25 ! [V_y_2,V_x_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 173.22/173.25 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 173.22/173.25 <=> V_x_2 = V_y_2 ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_one__code__numeral__def,axiom, % 173.22/173.25 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_less__code__numeral__code,axiom, % 173.22/173.25 ! [V_m_2,V_n_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zero__code__numeral__def,axiom, % 173.22/173.25 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 173.22/173.25 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 173.22/173.25 % 173.22/173.25 fof(fact_times__code__numeral__code,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 173.22/173.25 ! [V_m_2,V_n_2] : % 173.22/173.25 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 173.22/173.25 <=> V_n_2 = V_m_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__snd__zip,axiom, % 173.22/173.25 ! [V_ys_2,T_b,V_xs_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => 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 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_number__of__code__numeral__def,axiom, % 173.22/173.25 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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__map__fst__snd,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_plus__code__numeral__code,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_less__eq__code__numeral__code,axiom, % 173.22/173.25 ! [V_m_2,V_n_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__set__sublists,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => 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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pick__member,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_i_2] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => 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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__eq__conv,axiom, % 173.22/173.25 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 173.22/173.25 <=> ( 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 % 173.22/173.25 & 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 ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__size__conv__listsum,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_code__numeral__not__eq__zero,axiom, % 173.22/173.25 ! [V_i_2] : % 173.22/173.25 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.22/173.25 <=> 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 173.22/173.25 ! [V_j_2,V_i_2,V_f_2,T_a] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 173.22/173.25 ! [V_l_2,V_k_2,V_f_2,T_a] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_select__weight__member,axiom, % 173.22/173.25 ! [V_s_2,V_xs_2,T_a] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => 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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_select__weight__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_select__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_subtract__code__numeral__code,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_times__code__numeral__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nat__of__inverse,axiom, % 173.22/173.25 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 173.22/173.25 % 173.22/173.25 fof(fact_of__nat__nat__of,axiom, % 173.22/173.25 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 173.22/173.25 % 173.22/173.25 fof(fact_nat__of__of__nat,axiom, % 173.22/173.25 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 173.22/173.25 % 173.22/173.25 fof(fact_type__definition__code__numeral,axiom, % 173.22/173.25 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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_less__code__numeral__def,axiom, % 173.22/173.25 ! [V_m_2,V_n_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 173.22/173.25 <=> 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nat__of,axiom, % 173.22/173.25 ! [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)))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 173.22/173.25 ! [V_l_2,V_k_2] : % 173.22/173.25 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 173.22/173.25 <=> V_k_2 = V_l_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_code__numeral_Onat__of__inject,axiom, % 173.22/173.25 ! [V_y_2,V_x_2] : % 173.22/173.25 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 173.22/173.25 <=> V_x_2 = V_y_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nat__of__number,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_int__of__def,axiom, % 173.22/173.25 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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_less__eq__code__numeral__def,axiom, % 173.22/173.25 ! [V_m_2,V_n_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 173.22/173.25 <=> 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nat__of__code,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nat__of__aux__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Suc__code__numeral__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_minus__code__numeral__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_of__nat__inverse,axiom, % 173.22/173.25 ! [V_y_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 173.22/173.25 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_plus__code__numeral__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_div__code__numeral__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_subtract__code__numeral__def,axiom, % 173.22/173.25 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 173.22/173.25 % 173.22/173.25 fof(fact_minus__code__numeral__code,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_mod__code__numeral__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_code__numeral__decr,axiom, % 173.22/173.25 ! [V_k] : % 173.22/173.25 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__mono,axiom, % 173.22/173.25 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 173.22/173.25 ( ( class_Groups_Omonoid__add(T_b) % 173.22/173.25 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 173.22/173.25 => ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 173.22/173.25 => 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)))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_partition__set,axiom, % 173.22/173.25 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lists__Int__eq,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp_ONil,axiom, % 173.22/173.25 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp_Oequations_I1_J,axiom, % 173.22/173.25 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__listsp__conv__set,axiom, % 173.22/173.25 ! [V_xs_2,V_A_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp__infI,axiom, % 173.22/173.25 ! [V_B_2,V_l_2,V_A_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp__inf__eq,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp__conj__eq,axiom, % 173.22/173.25 ! [V_x_2,V_B_2,V_A_2,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 173.22/173.25 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp_Oequations_I2_J,axiom, % 173.22/173.25 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 173.22/173.25 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 173.22/173.25 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__in__listsp__conv,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 173.22/173.25 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 173.22/173.25 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp__mono,axiom, % 173.22/173.25 ! [V_B_2,V_A_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_partition__P,axiom, % 173.22/173.25 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 & ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 173.22/173.25 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_partition_Osimps_I1_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsp__lists__eq,axiom, % 173.22/173.25 ! [V_x_2,V_A_2,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_partition_Osimps_I2_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_lists__IntI,axiom, % 173.22/173.25 ! [V_B_2,V_A_2,V_l_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__def,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 <=> ( 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) % 173.22/173.25 & ! [B_x] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_all__nth__imp__all__set,axiom, % 173.22/173.25 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( ! [B_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__map1,axiom, % 173.22/173.25 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__map2,axiom, % 173.22/173.25 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__append,axiom, % 173.22/173.25 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => ( 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)) % 173.22/173.25 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__appendI,axiom, % 173.22/173.25 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 173.22/173.25 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__dropI,axiom, % 173.22/173.25 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__Cons,axiom, % 173.22/173.25 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 173.22/173.25 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__eq,axiom, % 173.22/173.25 ! [T_a,V_ys_2,V_xs_2] : % 173.22/173.25 ( V_xs_2 = V_ys_2 % 173.22/173.25 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__takeI,axiom, % 173.22/173.25 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__lengthD,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__Nil,axiom, % 173.22/173.25 ! [V_ys_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 173.22/173.25 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__Nil2,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__conv__all__nth,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 <=> ( 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) % 173.22/173.25 & ! [B_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__nthD,axiom, % 173.22/173.25 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__nthD2,axiom, % 173.22/173.25 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__update__cong,axiom, % 173.22/173.25 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 173.22/173.25 => 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)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__update__cong2,axiom, % 173.22/173.25 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2I,axiom, % 173.22/173.25 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 173.22/173.25 => ( 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) % 173.22/173.25 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 173.22/173.25 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__remdups,axiom, % 173.22/173.25 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__remdups__leq,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups__eq__nil__iff,axiom, % 173.22/173.25 ! [V_x_2,T_a] : % 173.22/173.25 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups__eq__nil__right__iff,axiom, % 173.22/173.25 ! [V_x_2,T_a] : % 173.22/173.25 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 173.22/173.25 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups_Osimps_I1_J,axiom, % 173.22/173.25 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__remdups__eq,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__remdups,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups__remdups,axiom, % 173.22/173.25 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__remdups__id,axiom, % 173.22/173.25 ! [V_xs,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.25 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups__id__iff__distinct,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 173.22/173.25 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remove1__remdups,axiom, % 173.22/173.25 ! [V_x,V_xs,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups__map__remdups,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups_Osimps_I2_J,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__remdups__card__conv,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__remdups__concat,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__conv__foldl,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__conv__concat,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__sort,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 173.22/173.25 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat_Osimps_I2_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__sort,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__sort,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sort__key__simps_I1_J,axiom, % 173.22/173.25 ! [V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat_Osimps_I1_J,axiom, % 173.22/173.25 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__concat,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Nil__eq__concat__conv,axiom, % 173.22/173.25 ! [V_xss_2,T_a] : % 173.22/173.25 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 173.22/173.25 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__eq__Nil__conv,axiom, % 173.22/173.25 ! [V_xss_2,T_a] : % 173.22/173.25 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 173.22/173.25 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__concat,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__concat,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sort__key__simps_I2_J,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sort__foldl__insort,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__injective,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 173.22/173.25 => ( 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) % 173.22/173.25 => ( ! [B_x] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => 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)) ) % 173.22/173.25 => V_xs_2 = V_ys_2 ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__eq__concat__iff,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => 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)) ) % 173.22/173.25 => ( 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) % 173.22/173.25 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 173.22/173.25 <=> V_xs_2 = V_ys_2 ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__map__singleton,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_n__lists_Osimps_I2_J,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose_Osimps_I3_J,axiom, % 173.22/173.25 ! [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))))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__aux__filter__head,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__concat,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__sort,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__insort__triv,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter_Osimps_I1_J,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose_Osimps_I1_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__empty__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__filter__le,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sum__length__filter__compl,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__is__subset,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__id__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__filter,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remove1__filter__not,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 173.22/173.25 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__remove1,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter_Osimps_I2_J,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 173.22/173.25 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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)) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__filter,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_partition__filter1,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_partition__filter2,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_remdups__filter,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose_Osimps_I2_J,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__transpose,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_i_2] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__map__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__filter,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__filter__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__filter__less,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_partition__filter__conv,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__minus__filter__out,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__in__sublist,axiom, % 173.22/173.25 ! [V_s_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__empty,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 173.22/173.25 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__filter__conv__card,axiom, % 173.22/173.25 ! [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))))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__aux__filter__tail,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose_Opsimps_I3_J,axiom, % 173.22/173.25 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose_Opsimps_I2_J,axiom, % 173.22/173.25 ! [V_xss_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sublist__shift__lemma__Suc,axiom, % 173.22/173.25 ! [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)))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_select__weigth__drop__zero,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pick__drop__zero,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose_Opsimps_I1_J,axiom, % 173.22/173.25 ! [T_a] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__max__length,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__aux__max,axiom, % 173.22/173.25 ! [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)))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldr_Osimps_I1_J,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldr_Osimps_I2_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldr__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldr__conv__foldl,axiom, % 173.22/173.25 ! [V_a_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Groups_Oab__semigroup__add(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldr__map,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__foldr1,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Groups_Omonoid__add(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__foldr1__lemma,axiom, % 173.22/173.25 ! [V_xs_2,V_a_2,T_a] : % 173.22/173.25 ( class_Groups_Omonoid__add(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__transpose,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sublist__def,axiom, % 173.22/173.25 ! [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))))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sublist__shift__lemma,axiom, % 173.22/173.25 ! [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))))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_atLeastLessThan__upt,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__upt,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__upt,axiom, % 173.22/173.25 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__add__eq__append,axiom, % 173.22/173.25 ! [V_k,V_j,V_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__Suc,axiom, % 173.22/173.25 ! [V_j,V_i] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => 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))) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__Suc__append,axiom, % 173.22/173.25 ! [V_j,V_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__upt,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__upt,axiom, % 173.22/173.25 ! [V_j,V_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__rec,axiom, % 173.22/173.25 ! [V_j,V_i] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => 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)) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__conv__Cons,axiom, % 173.22/173.25 ! [V_j,V_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__upt,axiom, % 173.22/173.25 ! [V_n,V_m,V_i] : % 173.22/173.25 ( 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)) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__list__of__set__range,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__eq__Nil__conv,axiom, % 173.22/173.25 ! [V_j_2,V_i_2] : % 173.22/173.25 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 173.22/173.25 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__conv__Nil,axiom, % 173.22/173.25 ! [V_i,V_j] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 173.22/173.25 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__0,axiom, % 173.22/173.25 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__upt,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__rec__number__of,axiom, % 173.22/173.25 ! [V_n,V_m] : % 173.22/173.25 ( ( 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))) % 173.22/173.25 => 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))) ) % 173.22/173.25 & ( ~ 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))) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_upt__eq__Cons__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 173.22/173.25 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 173.22/173.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 173.22/173.25 & V_i_2 = V_x_2 % 173.22/173.25 & 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 ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__upt,axiom, % 173.22/173.25 ! [V_j,V_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__Suc__upt,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_atLeastAtMost__upt,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_atLeast__upt,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__upt,axiom, % 173.22/173.25 ! [V_j,V_k,V_i] : % 173.22/173.25 ( 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)) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_greaterThanAtMost__upt,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_greaterThanLessThan__upt,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_atMost__upto,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__nth,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 173.22/173.25 ! [V_n_2,V_m_2,V_f_2,T_a] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 173.22/173.25 ! [V_n_2,V_m_2,V_f_2,T_a] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__map__upt,axiom, % 173.22/173.25 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__rectangle,axiom, % 173.22/173.25 ! [V_n_2,T_a,V_xs_2] : % 173.22/173.25 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 173.22/173.25 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.22/173.25 => ( ! [B_i] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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 ) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__key__remove1,axiom, % 173.22/173.25 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 173.22/173.25 => ( 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 % 173.22/173.25 => 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 ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted_ONil,axiom, % 173.22/173.25 ! [T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__single,axiom, % 173.22/173.25 ! [V_x,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__upt,axiom, % 173.22/173.25 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__sort,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__insort,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( 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)) % 173.22/173.25 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__tl,axiom, % 173.22/173.25 ! [V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted_Oequations_I1_J,axiom, % 173.22/173.25 ! [T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__butlast,axiom, % 173.22/173.25 ! [V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__take,axiom, % 173.22/173.25 ! [V_n,V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__upto,axiom, % 173.22/173.25 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__remove1,axiom, % 173.22/173.25 ! [V_a,V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__many,axiom, % 173.22/173.25 ! [V_zs,V_y,V_x,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 173.22/173.25 => 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))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__many__eq,axiom, % 173.22/173.25 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( 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))) % 173.22/173.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 173.22/173.25 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__drop,axiom, % 173.22/173.25 ! [V_n,V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__insort__insert,axiom, % 173.22/173.25 ! [V_x_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__remdups,axiom, % 173.22/173.25 ! [V_l,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__distinct__set__unique,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 173.22/173.25 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 173.22/173.25 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__sort__key,axiom, % 173.22/173.25 ! [V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__insort__insert__key,axiom, % 173.22/173.25 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__map__remove1,axiom, % 173.22/173.25 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__insort__key,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( 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))) % 173.22/173.25 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__filter,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__map__same,axiom, % 173.22/173.25 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__same,axiom, % 173.22/173.25 ! [V_xs_2,V_g_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__Cons,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 173.22/173.25 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 & ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__append,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 173.22/173.25 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 173.22/173.25 & ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ! [B_xa] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__insort,axiom, % 173.22/173.25 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 173.22/173.25 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted_Oequations_I2_J,axiom, % 173.22/173.25 ! [V_a1_2,V_a2_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 173.22/173.25 <=> ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 173.22/173.25 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__list__of__set,axiom, % 173.22/173.25 ! [V_A_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.25 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 173.22/173.25 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 173.22/173.25 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__remove1,axiom, % 173.22/173.25 ! [V_xs_2,V_a_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 => 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 ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__equals__nth__mono,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 <=> ! [B_j] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ! [B_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 173.22/173.25 => 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))) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__nth__mono,axiom, % 173.22/173.25 ! [V_j,V_i,V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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))) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__sorted__distinct__set__unique,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => ( 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))) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 173.22/173.25 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 173.22/173.25 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__column,axiom, % 173.22/173.25 ! [V_i_2,V_xs_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__nth__transpose__sorted,axiom, % 173.22/173.25 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( 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)))) % 173.22/173.25 => ( 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)))) % 173.22/173.25 => 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) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_inj__on__rev,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__is__Nil__conv,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Nil__is__rev__conv,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 173.22/173.25 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev_Osimps_I1_J,axiom, % 173.22/173.25 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 173.22/173.25 % 173.22/173.25 fof(fact_singleton__rev__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__singleton__conv,axiom, % 173.22/173.25 ! [V_x_2,V_xs_2,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__rev,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 173.22/173.25 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__concat,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__filter,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__rev,axiom, % 173.22/173.25 ! [V_ys,T_b,V_xs,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__rev,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__rev,axiom, % 173.22/173.25 ! [V_xs,T_a] : % 173.22/173.25 ( class_Groups_Ocomm__monoid__add(T_a) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__is__rev__conv,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 173.22/173.25 <=> V_xs_2 = V_ys_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__swap,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 173.22/173.25 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__rev__ident,axiom, % 173.22/173.25 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__rev,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__rev1,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 173.22/173.25 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__rev,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__foldr,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldr__foldl,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev_Osimps_I2_J,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__eq__Cons__iff,axiom, % 173.22/173.25 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 173.22/173.25 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 173.22/173.25 <=> 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__rev,axiom, % 173.22/173.25 ! [T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__rev,axiom, % 173.22/173.25 ! [T_a,V_xs] : % 173.22/173.25 ( V_xs != c_List_Olist_ONil(T_a) % 173.22/173.25 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__transpose,axiom, % 173.22/173.25 ! [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)))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__foldl__cons,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__take,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__drop,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rotate__rev,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__nth,axiom, % 173.22/173.25 ! [V_xs,T_a,V_n] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__update,axiom, % 173.22/173.25 ! [V_y,V_xs,T_a,V_k] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__rev__nth__mono,axiom, % 173.22/173.25 ! [V_j,V_i,V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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))) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldr__max__sorted,axiom, % 173.22/173.25 ! [V_y_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 173.22/173.25 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 173.22/173.25 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 173.22/173.25 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => 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) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__transpose__sorted,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 173.22/173.25 => 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))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__column__length,axiom, % 173.22/173.25 ! [V_i_2,V_xs_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transpose__transpose,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 173.22/173.25 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__takeWhile,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__takeWhile__le,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__takeWhileD,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__eq__all__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__takeWhile__fst,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__takeWhile__snd,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__takeWhile,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__tail,axiom, % 173.22/173.25 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 173.22/173.25 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile_Osimps_I2_J,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 173.22/173.25 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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)) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__eq__take,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile_Osimps_I1_J,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_return__list__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__append1,axiom, % 173.22/173.25 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__length__takeWhile,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ~ 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))))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__nth,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__not__last,axiom, % 173.22/173.25 ! [T_a,V_xs_2] : % 173.22/173.25 ( V_xs_2 != c_List_Olist_ONil(T_a) % 173.22/173.25 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 173.22/173.25 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transfer__nat__int__list__return__embed,axiom, % 173.22/173.25 ! [V_l] : % 173.22/173.25 ( c_List_Onat__list(V_l) % 173.22/173.25 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_embed__list__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__neq__rev,axiom, % 173.22/173.25 ! [V_x_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__neq__rev,axiom, % 173.22/173.25 ! [V_x_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__dropWhile__id,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__map,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__dropWhile,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__dropWhile__le,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__eq__Nil__conv,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__dropWhile,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 173.22/173.25 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__dropWhile,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile_Osimps_I2_J,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 173.22/173.25 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile_Osimps_I1_J,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__append1,axiom, % 173.22/173.25 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__eq__Cons__conv,axiom, % 173.22/173.25 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> ( 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)) % 173.22/173.25 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__eq__drop,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__nth,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => 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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_listsum__map__filter,axiom, % 173.22/173.25 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 173.22/173.25 ( class_Groups_Omonoid__add(T_b) % 173.22/173.25 => ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.25 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted__nth__monoI,axiom, % 173.22/173.25 ! [V_xs,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( ! [B_i,B_j] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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))) ) ) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__eq__filter,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__eq__take__P__nth,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 173.22/173.25 ( ! [B_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 173.22/173.25 => ( 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))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 173.22/173.25 => ( ( 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))) % 173.22/173.25 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 173.22/173.25 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__takeWhile__less__P__nth,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 173.22/173.25 ( ! [B_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 173.22/173.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 173.22/173.25 => ( 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))) % 173.22/173.25 => 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)))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted_Osimps,axiom, % 173.22/173.25 ! [V_a_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 173.22/173.25 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 173.22/173.25 | ? [B_xs,B_x] : % 173.22/173.25 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 173.22/173.25 & ! [B_xa] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 173.22/173.25 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__removeAll__inj__on,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_List_Oinsert__def,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 173.22/173.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_removeAll__append,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_removeAll__id,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insert__remdups,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_removeAll__filter__not__eq,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_removeAll__filter__not,axiom, % 173.22/173.25 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 173.22/173.25 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__insert,axiom, % 173.22/173.25 ! [V_x,V_xs,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__removeAll,axiom, % 173.22/173.25 ! [V_x,V_xs,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_removeAll_Osimps_I2_J,axiom, % 173.22/173.25 ! [V_xs,T_a,V_y,V_x] : % 173.22/173.25 ( ( V_x = V_y % 173.22/173.25 => 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) ) % 173.22/173.25 & ( V_x != V_y % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_removeAll_Osimps_I1_J,axiom, % 173.22/173.25 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__remove1__removeAll,axiom, % 173.22/173.25 ! [V_x,V_xs,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 173.22/173.25 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__set__insert,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_List_Oset__insert,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insert__Nil,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__removeAll__inj,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 173.22/173.25 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_set__removeAll,axiom, % 173.22/173.25 ! [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)))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_not__in__set__insert,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_maps__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__map__maps,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_maps__simps_I2_J,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_maps__simps_I1_J,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_distinct__concat,axiom, % 173.22/173.25 ! [V_xs_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 173.22/173.25 => ( ! [B_ys] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 173.22/173.25 => ( ! [B_ys] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 173.22/173.25 => ! [B_zs] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 173.22/173.25 => ( B_ys != B_zs % 173.22/173.25 => 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)) ) ) ) % 173.22/173.25 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_measures__lesseq,axiom, % 173.22/173.25 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( hBOOL(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))) % 173.22/173.25 => hBOOL(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)))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_wf__measures,axiom, % 173.22/173.25 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__measures_I1_J,axiom, % 173.22/173.25 ! [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))))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_measures__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__measures_I2_J,axiom, % 173.22/173.25 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(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)))) % 173.22/173.25 <=> ( 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))) % 173.22/173.25 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.22/173.25 & hBOOL(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))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_measures__less,axiom, % 173.22/173.25 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => hBOOL(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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_foldl__apply,axiom, % 173.22/173.25 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => 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)) ) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__obtain__same__length,axiom, % 173.22/173.25 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 173.22/173.25 ( ( 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)) % 173.22/173.25 => 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)))) ) % 173.22/173.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pos__not__random__dseq__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_dropWhile__append2,axiom, % 173.22/173.25 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all2__all__nthI,axiom, % 173.22/173.25 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 => ( ! [B_n] : % 173.22/173.25 ( 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))) % 173.22/173.25 => 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))) ) % 173.22/173.25 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_finite__sorted__distinct__unique,axiom, % 173.22/173.25 ! [V_A_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.22/173.25 => ? [B_x] : % 173.22/173.25 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 173.22/173.25 & c_List_Olinorder__class_Osorted(T_a,B_x) % 173.22/173.25 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 173.22/173.25 & ! [B_y] : % 173.22/173.25 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 173.22/173.25 & c_List_Olinorder__class_Osorted(T_a,B_y) % 173.22/173.25 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 173.22/173.25 => B_y = B_x ) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_takeWhile__append2,axiom, % 173.22/173.25 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_insort__is__Cons,axiom, % 173.22/173.25 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 173.22/173.25 ( class_Orderings_Olinorder(T_b) % 173.22/173.25 => ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Cons__eq__filter__iff,axiom, % 173.22/173.25 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> ? [B_us,B_vs] : % 173.22/173.25 ( 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)) % 173.22/173.25 & ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 173.22/173.25 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 & hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__eq__Cons__iff,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 173.22/173.25 ( 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) % 173.22/173.25 <=> ? [B_us,B_vs] : % 173.22/173.25 ( 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)) % 173.22/173.25 & ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 173.22/173.25 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 & hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ball__nth,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_sorted_OCons,axiom, % 173.22/173.25 ! [V_x_2,V_xs_2,T_a] : % 173.22/173.25 ( class_Orderings_Olinorder(T_a) % 173.22/173.25 => ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 173.22/173.25 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 173.22/173.25 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex__length,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 173.22/173.25 <=> ? [B_n] : % 173.22/173.25 ( 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))) % 173.22/173.25 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__set__conv__decomp__first,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 <=> ? [B_ys] : % 173.22/173.25 ( ? [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)) % 173.22/173.25 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex__simps_I1_J,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 173.22/173.25 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex__rev,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 173.22/173.25 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex__iff,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 173.22/173.25 <=> ? [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex__append,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 173.22/173.25 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 173.22/173.25 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex__simps_I2_J,axiom, % 173.22/173.25 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__set__conv__decomp,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 <=> ? [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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__set__conv__decomp__last,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 <=> ? [B_ys,B_zs] : % 173.22/173.25 ( 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)) % 173.22/173.25 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all__length,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 173.22/173.25 <=> ! [B_n] : % 173.22/173.25 ( 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))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_finite__induct,axiom, % 173.22/173.25 ! [V_P_2,V_F_2,T_a] : % 173.22/173.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 173.22/173.25 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.25 => ( ! [B_x,B_F] : % 173.22/173.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 173.22/173.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 173.22/173.25 => ( hBOOL(hAPP(V_P_2,B_F)) % 173.22/173.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 173.22/173.25 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all__simps_I1_J,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 173.22/173.25 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all__rev,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 173.22/173.25 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all__iff,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all__append,axiom, % 173.22/173.25 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 173.22/173.25 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 173.22/173.25 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all__simps_I2_J,axiom, % 173.22/173.25 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Ball__set__list__all,axiom, % 173.22/173.25 ! [V_P_2,V_xs_2,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__all__iff__raw,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 173.22/173.25 <=> ! [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex1__simps_I2_J,axiom, % 173.22/173.25 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 173.22/173.25 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_measure__function__int,axiom, % 173.22/173.25 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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex1__simps_I1_J,axiom, % 173.22/173.25 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_is__measure_Ointros,axiom, % 173.22/173.25 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 173.22/173.25 % 173.22/173.25 fof(fact_is__measure_Oequations,axiom, % 173.22/173.25 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 173.22/173.25 % 173.22/173.25 fof(fact_is__measure_Osimps,axiom, % 173.22/173.25 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 173.22/173.25 % 173.22/173.25 fof(fact_measure__size,axiom, % 173.22/173.25 ! [T_a] : % 173.22/173.25 ( class_Nat_Osize(T_a) % 173.22/173.25 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_measure__snd,axiom, % 173.22/173.25 ! [T_b,V_f_2,T_a] : % 173.22/173.25 ( c_FunDef_Ois__measure(T_a,V_f_2) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_measure__fst,axiom, % 173.22/173.25 ! [T_b,V_f_2,T_a] : % 173.22/173.25 ( c_FunDef_Ois__measure(T_a,V_f_2) % 173.22/173.25 => 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_list__ex1__iff,axiom, % 173.22/173.25 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.25 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 173.22/173.25 <=> ? [B_x] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 & hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.25 & ! [B_y] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.25 & hBOOL(hAPP(V_P_2,B_y)) ) % 173.22/173.25 => B_y = B_x ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_transfer__morphism__int__nat,axiom, % 173.22/173.25 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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 173.22/173.25 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 173.22/173.25 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_bool_Osize_I3_J,axiom, % 173.22/173.25 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.25 % 173.22/173.25 fof(fact_bool_Osize_I4_J,axiom, % 173.22/173.25 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Opos__empty__def,axiom, % 173.22/173.25 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pos__empty__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Opos__bind__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pos__bind__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 173.22/173.25 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 173.22/173.25 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.22/173.25 => 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)) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_neg__bind__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pos__map__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pos__single__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_neg__map__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Opos__single__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_neg__single__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Oneg__single__def,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_,axiom, % 173.22/173.25 ! [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)))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_small__lazy__list_Osimps,axiom, % 173.22/173.25 ! [V_d_2,T_a] : % 173.22/173.25 ( class_Lazy__Sequence_Osmall__lazy(T_a) % 173.22/173.25 => 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)))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__splice,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_small__lazy__prod__def,axiom, % 173.22/173.25 ! [V_d,T_b,T_a] : % 173.22/173.25 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 173.22/173.25 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 173.22/173.25 => 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)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_splice_Osimps_I1_J,axiom, % 173.22/173.25 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 173.22/173.25 % 173.22/173.25 fof(fact_splice__Nil2,axiom, % 173.22/173.25 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 173.22/173.25 % 173.22/173.25 fof(fact_splice_Osimps_I3_J,axiom, % 173.22/173.25 ! [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))) ). % 173.22/173.25 % 173.22/173.25 fof(fact_splice_Osimps_I2_J,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_New__DSequence_Opos__union__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_acyclicP__converse,axiom, % 173.22/173.25 ! [V_r_2,T_a] : % 173.22/173.25 ( 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)))) % 173.22/173.25 <=> 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_converse__meet,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_converse__pred__comp,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_converse__join,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversepD,axiom, % 173.22/173.25 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 173.22/173.25 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversep_Ointros,axiom, % 173.22/173.25 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 173.22/173.25 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversep_Oequations,axiom, % 173.22/173.25 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 173.22/173.25 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversep__iff,axiom, % 173.22/173.25 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 173.22/173.25 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversep__conversep,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversep__eq,axiom, % 173.22/173.25 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversep__noteq,axiom, % 173.22/173.25 ! [V_y_2,V_x_2,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> V_x_2 != V_y_2 ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_conversep__converse__eq,axiom, % 173.22/173.25 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 173.22/173.25 ( 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)) % 173.22/173.25 <=> 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))) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_pos__union__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_small__lazy_H_Osimps,axiom, % 173.22/173.25 ! [V_i,V_d] : % 173.22/173.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 173.22/173.25 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 173.22/173.25 => 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)))) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_small__lazy__int__def,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_small__lazy_H_Opsimps,axiom, % 173.22/173.25 ! [V_i_2,V_d_2] : % 173.22/173.25 ( 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))) % 173.22/173.25 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 173.22/173.25 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 173.22/173.25 => 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)))) ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_tl__replicate,axiom, % 173.22/173.25 ! [V_x,T_a,V_n] : % 173.22/173.25 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => 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) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_replicate__length__filter,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_length__replicate,axiom, % 173.22/173.25 ! [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 ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__replicate__const,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_in__set__replicate,axiom, % 173.22/173.25 ! [V_y_2,V_n_2,V_x_2,T_a] : % 173.22/173.25 ( 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)))) % 173.22/173.25 <=> ( V_x_2 = V_y_2 % 173.22/173.25 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_replicate__app__Cons__same,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_replicate__Suc,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_rev__replicate,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_last__replicate,axiom, % 173.22/173.25 ! [V_x,T_a,V_n] : % 173.22/173.25 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_take__replicate,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_hd__replicate,axiom, % 173.22/173.25 ! [V_x,T_a,V_n] : % 173.22/173.25 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_drop__replicate,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_zip__replicate,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Ball__set__replicate,axiom, % 173.22/173.25 ! [V_P_2,V_a_2,V_n_2,T_a] : % 173.22/173.25 ( ! [B_x] : % 173.22/173.25 ( 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)))) % 173.22/173.25 => hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 173.22/173.25 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_Bex__set__replicate,axiom, % 173.22/173.25 ! [V_P_2,V_a_2,V_n_2,T_a] : % 173.22/173.25 ( ? [B_x] : % 173.22/173.25 ( 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)))) % 173.22/173.25 & hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.25 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 173.22/173.25 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_replicate__eq__replicate,axiom, % 173.22/173.25 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] : % 173.22/173.25 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2) % 173.22/173.25 <=> ( V_m_2 = V_n_2 % 173.22/173.25 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.25 => V_x_2 = V_y_2 ) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_nth__replicate,axiom, % 173.22/173.25 ! [V_x,T_a,V_n,V_i] : % 173.22/173.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 173.22/173.25 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_append__replicate__commute,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_replicate__add,axiom, % 173.22/173.25 ! [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)) ). % 173.22/173.25 % 173.22/173.25 fof(fact_filter__replicate,axiom, % 173.22/173.25 ! [V_n_2,T_a,V_x_2,V_P_2] : % 173.22/173.25 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) % 173.22/173.25 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 173.22/173.25 => 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) ) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_concat__replicate__trivial,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_replicate__empty,axiom, % 173.22/173.25 ! [V_x_2,V_n_2,T_a] : % 173.22/173.25 ( c_List_Oreplicate(T_a,V_n_2,V_x_2) = c_List_Olist_ONil(T_a) % 173.22/173.25 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_empty__replicate,axiom, % 173.22/173.25 ! [V_x_2,V_n_2,T_a] : % 173.22/173.25 ( c_List_Olist_ONil(T_a) = c_List_Oreplicate(T_a,V_n_2,V_x_2) % 173.22/173.25 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.22/173.25 % 173.22/173.25 fof(fact_replicate__0,axiom, % 173.22/173.25 ! [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) ). % 173.22/173.25 % 173.22/173.25 fof(fact_map__replicate,axiom, % 173.22/173.26 ! [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)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_replicate__append__same,axiom, % 173.22/173.26 ! [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)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_map__replicate__trivial,axiom, % 173.22/173.26 ! [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) ). % 173.22/173.26 % 173.22/173.26 fof(fact_set__replicate__conv__if,axiom, % 173.22/173.26 ! [V_x_2,T_a,V_n_2] : % 173.22/173.26 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.26 => 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)) ) % 173.22/173.26 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.26 => 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))) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_set__replicate,axiom, % 173.22/173.26 ! [V_x_2,T_a,V_n_2] : % 173.22/173.26 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.22/173.26 => 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))) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_set__replicate__Suc,axiom, % 173.22/173.26 ! [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))) ). % 173.22/173.26 % 173.22/173.26 fof(fact_small__lazy_H_Opinduct,axiom, % 173.22/173.26 ! [V_P_2,V_a1_2,V_a0_2] : % 173.22/173.26 ( 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))) % 173.22/173.26 => ( ! [B_d,B_i] : % 173.22/173.26 ( 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))) % 173.22/173.26 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 173.22/173.26 => 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)))) ) % 173.22/173.26 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) ) % 173.22/173.26 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_eq__comp__r,axiom, % 173.22/173.26 ! [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 ). % 173.22/173.26 % 173.22/173.26 fof(fact_field__le__epsilon,axiom, % 173.22/173.26 ! [V_y,V_x,T_a] : % 173.22/173.26 ( class_Fields_Olinordered__field(T_a) % 173.22/173.26 => ( ! [B_e] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 173.22/173.26 => 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))) ) % 173.22/173.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 173.22/173.26 ! [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))) ). % 173.22/173.26 % 173.22/173.26 fof(fact__01,axiom, % 173.22/173.26 ! [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)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Oinject,axiom, % 173.22/173.26 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 173.22/173.26 ( 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) % 173.22/173.26 <=> ( V_a_2 = V_a_H_2 % 173.22/173.26 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 173.22/173.26 ! [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))) ). % 173.22/173.26 % 173.22/173.26 fof(fact_size__code,axiom, % 173.22/173.26 ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = 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)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence__size__code,axiom, % 173.22/173.26 ! [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) = 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)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_seq__case,axiom, % 173.22/173.26 ! [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) = 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)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_yieldn__def,axiom, % 173.22/173.26 ! [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)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 173.22/173.26 ! [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) ). % 173.22/173.26 % 173.22/173.26 fof(fact_refl__on__INTER,axiom, % 173.22/173.26 ! [V_r_2,V_A_2,T_b,V_S_2,T_a] : % 173.22/173.26 ( ! [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 173.22/173.26 => c_Relation_Orefl__on(T_b,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 173.22/173.26 => 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)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_in__set__member,axiom, % 173.22/173.26 ! [V_xs_2,V_x_2,T_a] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.26 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_a),V_xs_2),V_x_2)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_member__rec_I2_J,axiom, % 173.22/173.26 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_member__set,axiom, % 173.22/173.26 ! [T_a] : c_List_Omember(T_a) = c_List_Oset(T_a) ). % 173.22/173.26 % 173.22/173.26 fof(fact_member__rec_I1_J,axiom, % 173.22/173.26 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_List_Omember(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_y_2)) % 173.22/173.26 <=> ( V_x_2 = V_y_2 % 173.22/173.26 | hBOOL(hAPP(hAPP(c_List_Omember(T_a),V_xs_2),V_y_2)) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_List_Omember__def,axiom, % 173.22/173.26 ! [V_x_2,V_xs_2,T_a] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_List_Omember(T_a),V_xs_2),V_x_2)) % 173.22/173.26 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_pair__box_Osize_I1_J,axiom, % 173.22/173.26 ! [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))) ). % 173.22/173.26 % 173.22/173.26 fof(fact_list__ex1__iff__raw,axiom, % 173.22/173.26 ! [V_xs_2,V_P_2,T_a] : % 173.22/173.26 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 173.22/173.26 <=> ? [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.26 & hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.26 & ! [B_y] : % 173.22/173.26 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.22/173.26 & hBOOL(hAPP(V_P_2,B_y)) ) % 173.22/173.26 => B_y = B_x ) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_pair__box_Oinject,axiom, % 173.22/173.26 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 173.22/173.26 ( 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) % 173.22/173.26 <=> ( V_a_2 = V_a_H_2 % 173.22/173.26 & V_b_2 = V_b_H_2 ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_pair__box_Osize_I2_J,axiom, % 173.22/173.26 ! [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) ). % 173.22/173.26 % 173.22/173.26 fof(fact_pair__box_Osimps_I2_J,axiom, % 173.22/173.26 ! [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) ). % 173.22/173.26 % 173.22/173.26 fof(fact_pair__box_Orecs,axiom, % 173.22/173.26 ! [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) ). % 173.22/173.26 % 173.22/173.26 fof(fact_THE__default__def,axiom, % 173.22/173.26 ! [V_d_2,T_a,V_P_2] : % 173.22/173.26 ( ( ? [B_x] : % 173.22/173.26 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.26 & ! [B_y] : % 173.22/173.26 ( hBOOL(hAPP(V_P_2,B_y)) % 173.22/173.26 => B_y = B_x ) ) % 173.22/173.26 => c_FunDef_OTHE__default(T_a,V_d_2,V_P_2) = c_HOL_OThe(T_a,V_P_2) ) % 173.22/173.26 & ( ~ ? [B_x] : % 173.22/173.26 ( hBOOL(hAPP(V_P_2,B_x)) % 173.22/173.26 & ! [B_y] : % 173.22/173.26 ( hBOOL(hAPP(V_P_2,B_y)) % 173.22/173.26 => B_y = B_x ) ) % 173.22/173.26 => c_FunDef_OTHE__default(T_a,V_d_2,V_P_2) = V_d_2 ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_setsum__UNION__zero,axiom, % 173.22/173.26 ! [V_f_2,V_S_2,T_a,T_b] : % 173.22/173.26 ( class_Groups_Ocomm__monoid__add(T_b) % 173.22/173.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_S_2)) % 173.22/173.26 => ( ! [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_S_2)) % 173.22/173.26 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 173.22/173.26 => ( ! [B_T1] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_T1),V_S_2)) % 173.22/173.26 => ! [B_T2] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_T2),V_S_2)) % 173.22/173.26 => ( B_T1 != B_T2 % 173.22/173.26 => ! [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_T1)) % 173.22/173.26 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_T2)) % 173.22/173.26 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) % 173.22/173.26 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2)),V_S_2) ) ) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_SUP2__E,axiom, % 173.22/173.26 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 173.22/173.26 ( 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)) % 173.22/173.26 => ~ ! [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.26 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_INF2__I,axiom, % 173.22/173.26 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,T_a] : % 173.22/173.26 ( ! [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.22/173.26 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) % 173.22/173.26 => 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)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_finite__maxlen,axiom, % 173.22/173.26 ! [V_M_2,T_a] : % 173.22/173.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),V_M_2)) % 173.22/173.26 => ? [B_n] : % 173.22/173.26 ! [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),V_M_2)) % 173.22/173.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),B_x)),B_n)) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osize_I1_J,axiom, % 173.22/173.26 ! [V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.26 % 173.22/173.26 fof(fact__02,axiom, % 173.22/173.26 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osimps_I2_J,axiom, % 173.22/173.26 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osimps_I3_J,axiom, % 173.22/173.26 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osimps_I4_J,axiom, % 173.22/173.26 ! [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_OEmpty(T_b)) = V_f1_2 ). % 173.22/173.26 % 173.22/173.26 fof(fact_lazy__sequence_Osize_I3_J,axiom, % 173.22/173.26 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.22/173.26 % 173.22/173.26 fof(fact_list__all__iff__all__interval__int,axiom, % 173.22/173.26 ! [V_j_2,V_i_2,V_P_2] : % 173.22/173.26 ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2)) % 173.22/173.26 <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_list__ex__iff__not__all__inverval__int,axiom, % 173.22/173.26 ! [V_j_2,V_i_2,V_P_2] : % 173.22/173.26 ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2)) % 173.22/173.26 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_P_2),V_i_2,V_j_2) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_all__interval__int__def,axiom, % 173.22/173.26 ! [V_j_2,V_i_2,V_P_2] : % 173.22/173.26 ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) % 173.22/173.26 <=> ! [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) % 173.22/173.26 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_code__numeral_Orecs_I2_J,axiom, % 173.22/173.26 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_a,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_a,V_f1_2,V_f2_2,V_code__numeral_2)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_Random_Osimps,axiom, % 173.22/173.26 ! [V_size_2,V_g_2,T_a,V_nrandom_2] : % 173.22/173.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) % 173.22/173.26 => c_Random__Sequence_ORandom(T_a,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_a)) ) % 173.22/173.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) % 173.22/173.26 => c_Random__Sequence_ORandom(T_a,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_a,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_a,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_a,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a))))),tc_prod(T_a,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(T_a,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_a)),c_Product__Type_Ofst(T_a,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_code__numeral_Orecs_I1_J,axiom, % 173.22/173.26 ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 173.22/173.26 % 173.22/173.26 fof(fact_Random__Sequence_Oempty__def,axiom, % 173.22/173.26 ! [V_size_2,V_nrandom_2,T_a] : c_Random__Sequence_Oempty(T_a,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_a)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_Random__Sequence_Osingle__def,axiom, % 173.22/173.26 ! [V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_a),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_a),V_x_2)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_Random__Sequence_Omap__def,axiom, % 173.22/173.26 ! [V_P_2,V_f_2,T_a,T_b] : c_Random__Sequence_Omap(T_b,T_a,V_f_2,V_P_2) = c_Random__Sequence_Obind(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_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_a)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_b,c_Random__Sequence_Osingle(T_a)),V_f_2)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_exE__realizer,axiom, % 173.22/173.26 ! [T_c,V_f_2,V_Q_2,V_p_2,T_a,T_b,V_P_2] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2)),hAPP(c_Product__Type_Ofst(T_b,T_a),V_p_2))) % 173.22/173.26 => ( ! [B_x,B_y] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x)) % 173.22/173.26 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 173.22/173.26 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_c),V_f_2),V_p_2))) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_Image__Collect__split,axiom, % 173.22/173.26 ! [V_A_2,V_P_2,T_a,T_b] : hAPP(c_Relation_OImage(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))),V_A_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_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_A_2)))),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2)))) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lexord__trans,axiom, % 173.22/173.26 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) % 173.22/173.26 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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_z_2)),c_List_Olexord(T_a,V_r_2))) % 173.22/173.26 => ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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_z_2)),c_List_Olexord(T_a,V_r_2))) ) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__less__than,axiom, % 173.22/173.26 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__lex__prod,axiom, % 173.22/173.26 ! [V_R2_2,T_b,V_R1_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_R1_2) % 173.22/173.26 => ( c_Relation_Otrans(T_b,V_R2_2) % 173.22/173.26 => c_Relation_Otrans(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_R1_2,V_R2_2)) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_transD,axiom, % 173.22/173.26 ! [V_ca_2,V_b_2,V_a_2,V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 => ( 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)) % 173.22/173.26 => ( 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)) % 173.22/173.26 => 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)),V_r_2)) ) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__def,axiom, % 173.22/173.26 ! [V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 <=> ! [B_x,B_y] : % 173.22/173.26 ( 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)) % 173.22/173.26 => ! [B_z] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_z)),V_r_2)) % 173.22/173.26 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_z)),V_r_2)) ) ) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_INT__eq,axiom, % 173.22/173.26 ! [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_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),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)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_B_2))))) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__inv__image,axiom, % 173.22/173.26 ! [V_f_2,T_b,V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__reflclI,axiom, % 173.22/173.26 ! [V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 => c_Relation_Otrans(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))) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_SUPR__bool__eq,axiom, % 173.22/173.26 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_HOL_Obool) = c_Set_OBex(T_a) ). % 173.22/173.26 % 173.22/173.26 fof(fact_bex__UNIV,axiom, % 173.22/173.26 ! [V_P_2,T_a] : % 173.22/173.26 ( ? [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.26 & hBOOL(hAPP(V_P_2,B_x)) ) % 173.22/173.26 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__rtrancl,axiom, % 173.22/173.26 ! [V_r_2,T_a] : c_Relation_Otrans(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_lexord__transI,axiom, % 173.22/173.26 ! [V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 => c_Relation_Otrans(tc_List_Olist(T_a),c_List_Olexord(T_a,V_r_2)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__finite__psubset,axiom, % 173.22/173.26 ! [T_a] : c_Relation_Otrans(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__trancl,axiom, % 173.22/173.26 ! [V_r_2,T_a] : c_Relation_Otrans(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trancl__id,axiom, % 173.22/173.26 ! [V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 => c_Transitive__Closure_Otrancl(T_a,V_r_2) = V_r_2 ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__Id__on,axiom, % 173.22/173.26 ! [V_A_2,T_a] : c_Relation_Otrans(T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__Id,axiom, % 173.22/173.26 ! [T_a] : c_Relation_Otrans(T_a,c_Relation_OId(T_a)) ). % 173.22/173.26 % 173.22/173.26 fof(fact_bex__empty,axiom, % 173.22/173.26 ! [V_P_2,T_a] : % 173.22/173.26 ~ ? [B_x] : % 173.22/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 173.22/173.26 & hBOOL(hAPP(V_P_2,B_x)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_listrel__trans,axiom, % 173.22/173.26 ! [V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.22/173.26 => c_Relation_Otrans(tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_trans__converse,axiom, % 173.22/173.26 ! [V_r_2,T_a] : % 173.22/173.26 ( c_Relation_Otrans(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 173.22/173.26 <=> c_Relation_Otrans(T_a,V_r_2) ) ). % 173.22/173.26 % 173.22/173.26 fof(fact_finite__Collect__bex,axiom, % 173.22/173.26 ! [V_Q_2,T_b,V_A_2,T_a] : % 173.22/173.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 173.51/173.26 => ( 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),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),V_Q_2))))) % 173.51/173.26 <=> ! [B_x] : % 173.51/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 173.51/173.26 => 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_x)))) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_trans__O__subset,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.51/173.26 => 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_r_2)),V_r_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_trans__Int,axiom, % 173.51/173.26 ! [V_s_2,V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.51/173.26 => ( c_Relation_Otrans(T_a,V_s_2) % 173.51/173.26 => c_Relation_Otrans(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_s_2)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_Union__eq,axiom, % 173.51/173.26 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(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_OEx(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_fconj),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)))) ). % 173.51/173.26 % 173.51/173.26 fof(fact_UN__eq,axiom, % 173.51/173.26 ! [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_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),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)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_B_2))))) ). % 173.51/173.26 % 173.51/173.26 fof(fact_list__ex__iff__raw,axiom, % 173.51/173.26 ! [V_xs_2,V_P_2,T_a] : % 173.51/173.26 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 173.51/173.26 <=> ? [B_x] : % 173.51/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.51/173.26 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_Bex__set__list__ex,axiom, % 173.51/173.26 ! [V_P_2,V_xs_2,T_a] : % 173.51/173.26 ( ? [B_x] : % 173.51/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 173.51/173.26 & hBOOL(hAPP(V_P_2,B_x)) ) % 173.51/173.26 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_Sup__apply,axiom, % 173.51/173.26 ! [V_x_2,V_A_2,T_b,T_a] : % 173.51/173.26 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.51/173.26 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_fun(T_b,T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_b,T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,T_a))),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_fun(T_b,T_a))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),T_b,T_a),c_COMBI(tc_fun(T_b,T_a))),V_x_2)))))) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_Sup__fun__def,axiom, % 173.51/173.26 ! [V_x_2,V_A_2,T_b,T_a] : % 173.51/173.26 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.51/173.26 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_fun(T_b,T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_b,T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,T_a))),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_fun(T_b,T_a))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),T_b,T_a),c_COMBI(tc_fun(T_b,T_a))),V_x_2)))))) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_Inf__apply,axiom, % 173.51/173.26 ! [V_x_2,V_A_2,T_b,T_a] : % 173.51/173.26 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.51/173.26 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_fun(T_b,T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_b,T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,T_a))),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_fun(T_b,T_a))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),T_b,T_a),c_COMBI(tc_fun(T_b,T_a))),V_x_2)))))) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_Inf__fun__def,axiom, % 173.51/173.26 ! [V_x_2,V_A_2,T_b,T_a] : % 173.51/173.26 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 173.51/173.26 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_fun(T_b,T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_b,T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,T_a))),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,T_a),T_a),tc_fun(tc_fun(T_b,T_a),tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_fun(T_b,T_a))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_b,T_a),T_b,T_a),c_COMBI(tc_fun(T_b,T_a))),V_x_2)))))) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_max__extp_Ointros,axiom, % 173.51/173.26 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 173.51/173.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 173.51/173.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 173.51/173.26 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.51/173.26 => ( ! [B_x] : % 173.51/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 173.51/173.26 => ? [B_xa] : % 173.51/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 173.51/173.26 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) % 173.51/173.26 => c_Wellfounded_Omax__extp(T_a,V_R_2,V_X_2,V_Y_2) ) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_transp__def,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Predicate_Otransp(T_a,V_r_2) % 173.51/173.26 <=> c_Relation_Otrans(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))) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_transpE,axiom, % 173.51/173.26 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 173.51/173.26 ( c_Predicate_Otransp(T_a,V_r_2) % 173.51/173.26 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 173.51/173.26 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2)) % 173.51/173.26 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_equivpE,axiom, % 173.51/173.26 ! [V_R_2,T_a] : % 173.51/173.26 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 173.51/173.26 => ~ ( c_Predicate_Oreflp(T_a,V_R_2) % 173.51/173.26 => ( c_Predicate_Osymp(T_a,V_R_2) % 173.51/173.26 => ~ c_Predicate_Otransp(T_a,V_R_2) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_equivpI,axiom, % 173.51/173.26 ! [V_R_2,T_a] : % 173.51/173.26 ( c_Predicate_Oreflp(T_a,V_R_2) % 173.51/173.26 => ( c_Predicate_Osymp(T_a,V_R_2) % 173.51/173.26 => ( c_Predicate_Otransp(T_a,V_R_2) % 173.51/173.26 => c_Equiv__Relations_Oequivp(T_a,V_R_2) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sympE,axiom, % 173.51/173.26 ! [V_y_2,V_x_2,V_r_2,T_a] : % 173.51/173.26 ( c_Predicate_Osymp(T_a,V_r_2) % 173.51/173.26 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 173.51/173.26 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_equivp__reflp__symp__transp,axiom, % 173.51/173.26 ! [V_R_2,T_a] : % 173.51/173.26 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 173.51/173.26 <=> ( c_Predicate_Oreflp(T_a,V_R_2) % 173.51/173.26 & c_Predicate_Osymp(T_a,V_R_2) % 173.51/173.26 & c_Predicate_Otransp(T_a,V_R_2) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_max__extp_Osimps,axiom, % 173.51/173.26 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 173.51/173.26 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 173.51/173.26 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 173.51/173.26 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 173.51/173.26 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 173.51/173.26 & ! [B_x] : % 173.51/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 173.51/173.26 => ? [B_xa] : % 173.51/173.26 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 173.51/173.26 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_trans__diff__Id,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Otrans(T_a,V_r_2) % 173.51/173.26 => ( c_Relation_Oantisym(T_a,V_r_2) % 173.51/173.26 => c_Relation_Otrans(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))) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisym__def,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Oantisym(T_a,V_r_2) % 173.51/173.26 <=> ! [B_x,B_y] : % 173.51/173.26 ( 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)) % 173.51/173.26 => ( 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)) % 173.51/173.26 => B_x = B_y ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisymD,axiom, % 173.51/173.26 ! [V_b_2,V_a_2,V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Oantisym(T_a,V_r_2) % 173.51/173.26 => ( 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)) % 173.51/173.26 => ( 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)),V_r_2)) % 173.51/173.26 => V_a_2 = V_b_2 ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisym__converse,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Oantisym(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 173.51/173.26 <=> c_Relation_Oantisym(T_a,V_r_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisym__empty,axiom, % 173.51/173.26 ! [T_a] : c_Relation_Oantisym(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisym__Id__on,axiom, % 173.51/173.26 ! [V_A_2,T_a] : c_Relation_Oantisym(T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisym__Id,axiom, % 173.51/173.26 ! [T_a] : c_Relation_Oantisym(T_a,c_Relation_OId(T_a)) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisym__subset,axiom, % 173.51/173.26 ! [V_s_2,V_r_2,T_a] : % 173.51/173.26 ( 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)) % 173.51/173.26 => ( c_Relation_Oantisym(T_a,V_s_2) % 173.51/173.26 => c_Relation_Oantisym(T_a,V_r_2) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_antisym__reflcl,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Oantisym(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))) % 173.51/173.26 <=> c_Relation_Oantisym(T_a,V_r_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_acyclic__impl__antisym__rtrancl,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 173.51/173.26 => c_Relation_Oantisym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_fun__lub__def,axiom, % 173.51/173.26 ! [V_x_2,V_A_2,V_L_2,T_c,T_a,T_b] : c_Partial__Function_Ofun__lub(T_b,T_a,T_c,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__trans__comp__subset,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => ( c_Relation_Otrans(T_a,V_r_2) % 173.51/173.26 => 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_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2)),V_r_2)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_symD,axiom, % 173.51/173.26 ! [V_b_2,V_a_2,V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => ( 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)) % 173.51/173.26 => 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)),V_r_2)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__def,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 <=> ! [B_x,B_y] : % 173.51/173.26 ( 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)) % 173.51/173.26 => 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)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__inv__image,axiom, % 173.51/173.26 ! [V_f_2,T_b,V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => c_Relation_Osym(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__Int__converse,axiom, % 173.51/173.26 ! [V_r_2,T_a] : c_Relation_Osym(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__Un__converse,axiom, % 173.51/173.26 ! [V_r_2,T_a] : c_Relation_Osym(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__rtrancl,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => c_Relation_Osym(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__trancl,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => c_Relation_Osym(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__Id__on,axiom, % 173.51/173.26 ! [V_A_2,T_a] : c_Relation_Osym(T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__Id,axiom, % 173.51/173.26 ! [T_a] : c_Relation_Osym(T_a,c_Relation_OId(T_a)) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__Un,axiom, % 173.51/173.26 ! [V_s_2,V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => ( c_Relation_Osym(T_a,V_s_2) % 173.51/173.26 => c_Relation_Osym(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)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_listrel__sym,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => c_Relation_Osym(tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__conv__converse__eq,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 <=> hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2) = V_r_2 ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__converse,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 173.51/173.26 <=> c_Relation_Osym(T_a,V_r_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_sym__Int,axiom, % 173.51/173.26 ! [V_s_2,V_r_2,T_a] : % 173.51/173.26 ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => ( c_Relation_Osym(T_a,V_s_2) % 173.51/173.26 => c_Relation_Osym(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_s_2)) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_equiv__def,axiom, % 173.51/173.26 ! [V_r_2,V_A_2,T_a] : % 173.51/173.26 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.51/173.26 <=> ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.51/173.26 & c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 & c_Relation_Otrans(T_a,V_r_2) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_equivI,axiom, % 173.51/173.26 ! [V_r_2,V_A_2,T_a] : % 173.51/173.26 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.51/173.26 => ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => ( c_Relation_Otrans(T_a,V_r_2) % 173.51/173.26 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_equivE,axiom, % 173.51/173.26 ! [V_r_2,V_A_2,T_a] : % 173.51/173.26 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 173.51/173.26 => ~ ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 173.51/173.26 => ( c_Relation_Osym(T_a,V_r_2) % 173.51/173.26 => ~ c_Relation_Otrans(T_a,V_r_2) ) ) ) ). % 173.51/173.26 % 173.51/173.26 fof(fact_symp__def,axiom, % 173.51/173.26 ! [V_r_2,T_a] : % 173.51/173.26 ( c_Predicate_Osymp(T_a,V_r_2) % 173.51/173.26 <=> c_Relation_Osym(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))) ) ). % 173.51/173.26 % 173.51/173.26 %----Arity declarations (219) % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 173.51/173.26 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Obounded__lattice(T_1) % 173.51/173.26 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 173.51/173.26 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Obounded__lattice(T_1) % 173.51/173.26 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Obounded__lattice(T_1) % 173.51/173.26 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Olattice(T_1) % 173.51/173.26 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Olattice(T_1) % 173.51/173.26 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Odistrib__lattice(T_1) % 173.51/173.26 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Oboolean__algebra(T_1) % 173.51/173.26 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Orderings_Opreorder,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Orderings_Opreorder(T_1) % 173.51/173.26 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Finite__Set_Ofinite,axiom, % 173.51/173.26 ! [T_1,T_2] : % 173.51/173.26 ( ( class_Finite__Set_Ofinite(T_2) % 173.51/173.26 & class_Finite__Set_Ofinite(T_1) ) % 173.51/173.26 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Lattices_Olattice,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Lattices_Olattice(T_1) % 173.51/173.26 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Orderings_Oorder,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Orderings_Oorder(T_1) % 173.51/173.26 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Orderings_Otop,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Orderings_Otop(T_1) % 173.51/173.26 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Orderings_Oord,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Orderings_Oord(T_1) % 173.51/173.26 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Orderings_Obot,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Orderings_Obot(T_1) % 173.51/173.26 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Groups_Ouminus,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Groups_Ouminus(T_1) % 173.51/173.26 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Groups_Ominus,axiom, % 173.51/173.26 ! [T_2,T_1] : % 173.51/173.26 ( class_Groups_Ominus(T_1) % 173.51/173.26 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_fun__Enum_Oenum,axiom, % 173.51/173.26 ! [T_1,T_2] : % 173.51/173.26 ( ( class_Enum_Oenum(T_2) % 173.51/173.26 & class_Enum_Oenum(T_1) ) % 173.51/173.26 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Com__Ocom__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_Com_Ocom) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 173.51/173.26 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 173.51/173.26 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 173.51/173.26 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 173.51/173.26 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 173.51/173.26 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 173.51/173.26 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 173.51/173.26 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 173.51/173.26 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 173.51/173.26 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 173.51/173.26 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 173.51/173.26 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 173.51/173.26 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 173.51/173.26 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 173.51/173.26 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 173.51/173.26 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 173.51/173.26 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 173.51/173.26 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 173.51/173.26 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 173.51/173.26 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 173.51/173.26 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 173.51/173.26 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 173.51/173.26 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 173.51/173.26 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 173.51/173.26 class_Divides_Osemiring__div(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 173.51/173.26 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 173.51/173.26 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 173.51/173.26 class_Groups_Oab__group__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 173.51/173.26 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 173.51/173.26 class_Rings_Oordered__ring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 173.51/173.26 class_Orderings_Opreorder(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 173.51/173.26 class_Orderings_Olinorder(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 173.51/173.26 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 173.51/173.26 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 173.51/173.26 class_Groups_Omonoid__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 173.51/173.26 class_Rings_Osemiring__1(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 173.51/173.26 class_Rings_Osemiring__0(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 173.51/173.26 class_Lattices_Olattice(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 173.51/173.26 class_Groups_Ogroup__add(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 173.51/173.26 class_Divides_Oring__div(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 173.51/173.26 class_Rings_Omult__zero(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 173.51/173.26 class_Orderings_Oorder(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 173.51/173.26 class_Int_Oring__char__0(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 173.51/173.26 class_Int_Onumber__ring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 173.51/173.26 class_Rings_Osemiring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Orderings_Oord,axiom, % 173.51/173.26 class_Orderings_Oord(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 173.51/173.26 class_Groups_Ouminus(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 173.51/173.26 class_Groups_Osgn__if(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 173.51/173.26 class_Groups_Oabs__if(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 173.51/173.26 class_Rings_Oring__1(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ominus,axiom, % 173.51/173.26 class_Groups_Ominus(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Power_Opower,axiom, % 173.51/173.26 class_Power_Opower(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Ozero,axiom, % 173.51/173.26 class_Groups_Ozero(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oring,axiom, % 173.51/173.26 class_Rings_Oring(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Rings_Oidom,axiom, % 173.51/173.26 class_Rings_Oidom(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Int_Onumber,axiom, % 173.51/173.26 class_Int_Onumber(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Int__Oint__Groups_Oone,axiom, % 173.51/173.26 class_Groups_Oone(tc_Int_Oint) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 173.51/173.26 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 173.51/173.26 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 173.51/173.26 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 173.51/173.26 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 173.51/173.26 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 173.51/173.26 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 173.51/173.26 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 173.51/173.26 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 173.51/173.26 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 173.51/173.26 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 173.51/173.26 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 173.51/173.26 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 173.51/173.26 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 173.51/173.26 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 173.51/173.26 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 173.51/173.26 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 173.51/173.26 class_Orderings_Owellorder(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 173.51/173.26 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 173.51/173.26 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 173.51/173.26 class_Orderings_Opreorder(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 173.51/173.26 class_Orderings_Olinorder(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 173.51/173.26 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 173.51/173.26 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 173.51/173.26 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 173.51/173.26 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 173.51/173.26 class_Lattices_Olattice(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 173.51/173.26 class_Rings_Omult__zero(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 173.51/173.26 class_Orderings_Oorder(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 173.51/173.26 class_Rings_Osemiring(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 173.51/173.26 class_Orderings_Oord(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 173.51/173.26 class_Orderings_Obot(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 173.51/173.26 class_Groups_Ominus(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Power_Opower,axiom, % 173.51/173.26 class_Power_Opower(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 173.51/173.26 class_Groups_Ozero(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Int_Onumber,axiom, % 173.51/173.26 class_Int_Onumber(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Groups_Oone,axiom, % 173.51/173.26 class_Groups_Oone(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nat__Onat__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_Nat_Onat) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 173.51/173.26 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 173.51/173.26 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 173.51/173.26 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 173.51/173.26 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 173.51/173.26 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 173.51/173.26 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 173.51/173.26 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 173.51/173.26 class_Orderings_Opreorder(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 173.51/173.26 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 173.51/173.26 class_Lattices_Olattice(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 173.51/173.26 class_Orderings_Oorder(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 173.51/173.26 class_Orderings_Otop(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 173.51/173.26 class_Orderings_Oord(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 173.51/173.26 class_Orderings_Obot(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 173.51/173.26 class_Groups_Ouminus(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 173.51/173.26 class_Groups_Ominus(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 173.51/173.26 class_Enum_Oenum(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_HOL__Obool__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_HOL_Obool) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Com__Ostate__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_Com_Ostate) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Com__Ovname__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_Com_Ovname) ). % 173.51/173.26 % 173.51/173.26 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 173.51/173.26 ! [T_1] : % 173.51/173.26 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 173.51/173.26 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_List__Olist__Nat_Osize,axiom, % 173.51/173.26 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 173.51/173.26 % 173.51/173.26 fof(arity_sum__Finite__Set_Ofinite,axiom, % 173.51/173.26 ! [T_1,T_2] : % 173.51/173.26 ( ( class_Finite__Set_Ofinite(T_2) % 173.51/173.26 & class_Finite__Set_Ofinite(T_1) ) % 173.51/173.26 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_sum__Enum_Oenum,axiom, % 173.51/173.26 ! [T_1,T_2] : % 173.51/173.26 ( ( class_Enum_Oenum(T_2) % 173.51/173.26 & class_Enum_Oenum(T_1) ) % 173.51/173.26 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_sum__Nat_Osize,axiom, % 173.51/173.26 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 173.51/173.26 ! [T_1] : % 173.51/173.26 ( class_Finite__Set_Ofinite(T_1) % 173.51/173.26 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 173.51/173.26 ! [T_1] : % 173.51/173.26 ( class_Enum_Oenum(T_1) % 173.51/173.26 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Option__Ooption__Nat_Osize,axiom, % 173.51/173.26 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 173.51/173.26 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 173.51/173.26 % 173.51/173.26 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 173.51/173.26 ! [T_1,T_2] : % 173.51/173.26 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 173.51/173.26 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 173.51/173.26 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_prod__Finite__Set_Ofinite,axiom, % 173.51/173.26 ! [T_1,T_2] : % 173.51/173.26 ( ( class_Finite__Set_Ofinite(T_2) % 173.51/173.26 & class_Finite__Set_Ofinite(T_1) ) % 173.51/173.26 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_prod__Enum_Oenum,axiom, % 173.51/173.26 ! [T_1,T_2] : % 173.51/173.26 ( ( class_Enum_Oenum(T_2) % 173.51/173.26 & class_Enum_Oenum(T_1) ) % 173.51/173.26 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 173.51/173.26 % 173.51/173.26 fof(arity_prod__Nat_Osize,axiom, % 173.51/173.26 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 173.51/173.26 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 173.51/173.26 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 173.51/173.26 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_Product__Type_Ounit) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 173.51/173.26 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 173.51/173.26 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 173.51/173.26 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 173.51/173.26 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 173.51/173.26 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 173.51/173.26 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 173.51/173.26 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 173.51/173.26 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 173.51/173.26 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 173.51/173.26 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 173.51/173.26 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 173.51/173.26 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 173.51/173.26 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 173.51/173.26 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 173.51/173.26 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 173.51/173.26 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 173.51/173.26 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 173.51/173.26 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 173.51/173.26 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 173.51/173.26 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 173.51/173.26 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 173.51/173.26 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 173.51/173.26 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 173.51/173.26 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 173.51/173.26 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 173.51/173.26 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 173.51/173.26 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 173.51/173.26 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 173.51/173.26 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 173.51/173.26 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 173.51/173.26 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 173.51/173.26 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 173.51/173.26 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 173.51/173.26 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 173.51/173.26 % 173.51/173.26 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 173.51/173.26 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 173.51/173.26 % 173.51/173.26 %----Helper facts (20) % 173.51/173.26 fof(help_c__COMBI__1,axiom, % 173.51/173.26 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 173.51/173.26 % 173.51/173.26 fof(help_c__COMBK__1,axiom, % 173.51/173.26 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 173.51/173.26 % 173.51/173.26 fof(help_c__COMBB__1,axiom, % 173.51/173.26 ! [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)) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__COMBC__1,axiom, % 173.51/173.26 ! [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) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__COMBS__1,axiom, % 173.51/173.26 ! [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)) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fequal__1,axiom, % 173.51/173.26 ! [V_y_2,V_x_2] : % 173.51/173.26 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 173.51/173.26 | V_x_2 = V_y_2 ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fequal__2,axiom, % 173.51/173.26 ! [V_y_2,V_x_2] : % 173.51/173.26 ( V_x_2 != V_y_2 % 173.51/173.26 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fFalse__1,axiom, % 173.51/173.26 ~ hBOOL(c_fFalse) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fTrue__1,axiom, % 173.51/173.26 hBOOL(c_fTrue) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fNot__1,axiom, % 173.51/173.26 ! [V_P_2] : % 173.51/173.26 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 173.51/173.26 | ~ hBOOL(V_P_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fNot__2,axiom, % 173.51/173.26 ! [V_P_2] : % 173.51/173.26 ( ~ ~ hBOOL(V_P_2) % 173.51/173.26 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fconj__1,axiom, % 173.51/173.26 ! [V_Q_2,V_P_2] : % 173.51/173.26 ( ~ hBOOL(V_P_2) % 173.51/173.26 | ~ hBOOL(V_Q_2) % 173.51/173.26 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fconj__2,axiom, % 173.51/173.26 ! [V_Q_2,V_P_2] : % 173.51/173.26 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 173.51/173.26 | hBOOL(V_P_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fconj__3,axiom, % 173.51/173.26 ! [V_Q_2,V_P_2] : % 173.51/173.26 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 173.51/173.26 | hBOOL(V_Q_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fdisj__1,axiom, % 173.51/173.26 ! [V_Q_2,V_P_2] : % 173.51/173.26 ( ~ hBOOL(V_P_2) % 173.51/173.26 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fdisj__2,axiom, % 173.51/173.26 ! [V_P_2,V_Q_2] : % 173.51/173.26 ( ~ hBOOL(V_Q_2) % 173.51/173.26 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fdisj__3,axiom, % 173.51/173.26 ! [V_Q_2,V_P_2] : % 173.51/173.26 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 173.51/173.26 | hBOOL(V_P_2) % 173.51/173.26 | hBOOL(V_Q_2) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fimplies__1,axiom, % 173.51/173.26 ! [V_Q_2,V_P_2] : % 173.51/173.26 ( hBOOL(V_P_2) % 173.51/173.26 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fimplies__2,axiom, % 173.51/173.26 ! [V_P_2,V_Q_2] : % 173.51/173.26 ( ~ hBOOL(V_Q_2) % 173.51/173.26 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 173.51/173.26 % 173.51/173.26 fof(help_c__fimplies__3,axiom, % 173.51/173.26 ! [V_Q_2,V_P_2] : % 173.51/173.26 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 173.51/173.26 | ~ hBOOL(V_P_2) % 173.51/173.26 | hBOOL(V_Q_2) ) ). % 173.51/173.26 % 173.51/173.26 %----Conjectures (2) % 173.51/173.26 fof(conj_0,hypothesis, % 173.51/173.26 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),v_c),c_Natural_Oevalc(v_c))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 173.51/173.26 % 173.51/173.26 fof(conj_1,conjecture, % 173.51/173.26 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(v_c))))),c_fequal))),v_c),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 173.51/173.26 % 173.51/173.26 %------------------------------------------------------------------------------ % 173.51/173.26 %------------------------------------------- % 173.51/173.26 % Proof found % 173.51/173.26 % SZS status Theorem for theBenchmark % 173.51/173.26 % SZS output start Proof % 173.51/173.26 %ClaNum:10408(EqnAxiom:3056) % 173.51/173.26 %VarNum:70602(SingletonVarNum:20598) % 173.51/173.26 %MaxLitNum:8 % 173.51/173.26 %MaxfuncDepth:15 % 173.51/173.26 %SharedTerms:1053 % 173.51/173.26 %goalClause: 4717 % 173.51/173.26 %singleGoalClaCount:1 % 173.51/173.26 [3060]P1(a905) % 173.51/173.26 [3061]P1(a910) % 173.51/173.26 [3062]P106(a195) % 173.51/173.26 [3063]P2(a905) % 173.51/173.26 [3064]P2(a910) % 173.51/173.26 [3065]P2(a1) % 173.51/173.26 [3066]P3(a905) % 173.51/173.26 [3067]P101(a905) % 173.51/173.26 [3068]P101(a910) % 173.51/173.26 [3069]P101(a1) % 173.51/173.26 [3070]P102(a905) % 173.51/173.26 [3071]P102(a910) % 173.51/173.26 [3072]P102(a1) % 173.51/173.26 [3073]P99(a905) % 173.51/173.26 [3074]P99(a910) % 173.51/173.26 [3075]P99(a1) % 173.51/173.26 [3076]P107(a910) % 173.51/173.26 [3077]P107(a1) % 173.51/173.26 [3078]P107(a110) % 173.51/173.26 [3079]P108(a905) % 173.51/173.26 [3080]P100(a905) % 173.51/173.26 [3081]P109(a905) % 173.51/173.26 [3082]P109(a910) % 173.51/173.26 [3083]P109(a1) % 173.51/173.26 [3084]P109(a110) % 173.51/173.26 [3085]P4(a1) % 173.51/173.26 [3086]P84(a905) % 173.51/173.26 [3087]P85(a905) % 173.51/173.26 [3088]P85(a1) % 173.51/173.26 [3089]P5(a905) % 173.51/173.26 [3090]P5(a910) % 173.51/173.26 [3091]P5(a1) % 173.51/173.26 [3092]P5(a110) % 173.51/173.26 [3093]P110(a910) % 173.51/173.26 [3094]P110(a1) % 173.51/173.26 [3095]P110(a110) % 173.51/173.26 [3096]P111(a905) % 173.51/173.26 [3097]P111(a910) % 173.51/173.26 [3098]P111(a1) % 173.51/173.26 [3099]P111(a110) % 173.51/173.26 [3100]P112(a905) % 173.51/173.26 [3101]P112(a910) % 173.51/173.26 [3102]P112(a1) % 173.51/173.26 [3103]P112(a110) % 173.51/173.26 [3104]P6(a1) % 173.51/173.26 [3105]P7(a905) % 173.51/173.26 [3106]P7(a913) % 173.51/173.26 [3107]P71(a1) % 173.51/173.26 [3108]P72(a910) % 173.51/173.26 [3109]P72(a1) % 173.51/173.26 [3110]P72(a110) % 173.51/173.26 [3111]P113(a1) % 173.51/173.26 [3112]P86(a910) % 173.51/173.26 [3113]P86(a1) % 173.51/173.26 [3114]P86(a110) % 173.51/173.26 [3115]P66(a905) % 173.51/173.26 [3116]P66(a913) % 173.51/173.26 [3117]P88(a910) % 173.51/173.26 [3118]P88(a1) % 173.51/173.26 [3119]P88(a110) % 173.51/173.26 [3120]P73(a910) % 173.51/173.26 [3121]P73(a1) % 173.51/173.26 [3122]P73(a110) % 173.51/173.26 [3123]P74(a910) % 173.51/173.26 [3124]P74(a1) % 173.51/173.26 [3125]P74(a110) % 173.51/173.26 [3126]P75(a910) % 173.51/173.26 [3127]P75(a1) % 173.51/173.26 [3128]P75(a110) % 173.51/173.26 [3129]P89(a910) % 173.51/173.26 [3130]P89(a1) % 173.51/173.26 [3131]P89(a110) % 173.51/173.26 [3132]P114(a1) % 173.51/173.26 [3133]P79(a910) % 173.51/173.26 [3134]P79(a1) % 173.51/173.26 [3135]P79(a110) % 173.51/173.26 [3136]P117(a910) % 173.51/173.26 [3137]P117(a1) % 173.51/173.26 [3138]P117(a110) % 173.51/173.26 [3139]P144(a910) % 173.51/173.26 [3140]P144(a1) % 173.51/173.26 [3141]P81(a910) % 173.51/173.26 [3142]P81(a1) % 173.51/173.26 [3143]P81(a110) % 173.51/173.26 [3144]P93(a910) % 173.51/173.26 [3145]P93(a1) % 173.51/173.26 [3146]P93(a110) % 173.51/173.26 [3147]P82(a910) % 173.51/173.26 [3148]P82(a1) % 173.51/173.26 [3149]P82(a110) % 173.51/173.26 [3150]P80(a1) % 173.51/173.26 [3151]P90(a910) % 173.51/173.26 [3152]P90(a1) % 173.51/173.26 [3153]P90(a110) % 173.51/173.26 [3154]P119(a910) % 173.51/173.26 [3155]P119(a1) % 173.51/173.26 [3156]P119(a110) % 173.51/173.26 [3157]P120(a1) % 173.51/173.26 [3158]P145(a910) % 173.51/173.26 [3159]P145(a1) % 173.51/173.26 [3160]P145(a110) % 173.51/173.26 [3161]P139(a1) % 173.51/173.26 [3162]P94(a1) % 173.51/173.26 [3163]P78(a910) % 173.51/173.26 [3164]P78(a1) % 173.51/173.26 [3165]P78(a110) % 173.51/173.26 [3166]P76(a910) % 173.51/173.26 [3167]P76(a1) % 173.51/173.26 [3168]P76(a110) % 173.51/173.26 [3169]P128(a910) % 173.51/173.26 [3170]P128(a1) % 173.51/173.26 [3171]P128(a110) % 173.51/173.26 [3172]P140(a1) % 173.51/173.26 [3173]P129(a910) % 173.51/173.26 [3174]P129(a1) % 173.51/173.26 [3175]P129(a110) % 173.51/173.26 [3176]P118(a910) % 173.51/173.26 [3177]P118(a1) % 173.51/173.26 [3178]P118(a110) % 173.51/173.26 [3179]P142(a910) % 173.51/173.26 [3180]P142(a1) % 173.51/173.26 [3181]P142(a110) % 173.51/173.26 [3182]P83(a910) % 173.51/173.26 [3183]P83(a1) % 173.51/173.26 [3184]P83(a110) % 173.51/173.26 [3185]P121(a1) % 173.51/173.26 [3186]P143(a910) % 173.51/173.26 [3187]P143(a1) % 173.51/173.26 [3188]P143(a110) % 173.51/173.26 [3189]P134(a910) % 173.51/173.26 [3190]P134(a1) % 173.51/173.26 [3191]P134(a110) % 173.51/173.26 [3192]P135(a1) % 173.51/173.26 [3193]P137(a910) % 173.51/173.26 [3194]P137(a1) % 173.51/173.26 [3195]P137(a110) % 173.51/173.26 [3196]P136(a910) % 173.51/173.26 [3197]P136(a1) % 173.51/173.26 [3198]P136(a110) % 173.51/173.26 [3199]P126(a1) % 173.51/173.26 [3200]P127(a1) % 173.51/173.26 [3201]P124(a910) % 173.51/173.26 [3202]P124(a1) % 173.51/173.26 [3203]P124(a110) % 173.51/173.26 [3204]P130(a910) % 173.51/173.26 [3205]P130(a1) % 173.51/173.26 [3206]P130(a110) % 173.51/173.26 [3207]P141(a1) % 173.51/173.26 [3208]P131(a910) % 173.51/173.26 [3209]P131(a1) % 173.51/173.26 [3210]P131(a110) % 173.51/173.26 [3211]P132(a1) % 173.51/173.26 [3212]P133(a1) % 173.51/173.26 [3213]P91(a1) % 173.51/173.26 [3214]P103(a910) % 173.51/173.26 [3215]P103(a1) % 173.51/173.26 [3216]P103(a110) % 173.51/173.26 [3217]P87(a1) % 173.51/173.26 [3218]P138(a1) % 173.51/173.26 [3219]P77(a1) % 173.51/173.26 [3220]P8(a905) % 173.51/173.26 [3221]P115(a910) % 173.51/173.26 [3222]P115(a1) % 173.51/173.26 [3223]P115(a110) % 173.51/173.26 [3224]P64(a910) % 173.51/173.26 [3225]P64(a1) % 173.51/173.26 [3226]P64(a110) % 173.51/173.26 [3227]P65(a1) % 173.51/173.26 [3228]P95(a1) % 173.51/173.26 [3229]P96(a910) % 173.51/173.26 [3230]P96(a1) % 173.51/173.26 [3231]P96(a110) % 173.51/173.26 [3232]P116(a910) % 173.51/173.26 [3233]P92(a910) % 173.51/173.26 [3234]P92(a1) % 173.51/173.26 [3235]P92(a110) % 173.51/173.26 [3236]P105(a905) % 173.51/173.26 [3237]P105(a906) % 173.51/173.26 [3238]P105(a910) % 173.51/173.26 [3239]P105(a908) % 173.51/173.26 [3240]P105(a907) % 173.51/173.26 [3241]P105(a913) % 173.51/173.26 [3242]P105(a110) % 173.51/173.26 [3243]P105(a329) % 173.51/173.26 [3244]P104(a913) % 173.51/173.26 [3245]P104(a1) % 173.51/173.26 [3246]P98(a905) % 173.51/173.26 [3262]P40(a910,a251) % 173.51/173.26 [3263]P40(a910,a323) % 173.51/173.26 [3264]P41(a910,a251) % 173.51/173.26 [4616]~E(a108,a90) % 173.51/173.26 [4617]~P106(a250) % 173.51/173.26 [3057]E(f2(a1),a90) % 173.51/173.26 [3058]E(f111(a110),a3) % 173.51/173.26 [3059]E(f23(a110),a24) % 173.51/173.26 [3247]E(f196(a910),f2(a910)) % 173.51/173.26 [3248]E(f29(a25),f2(a910)) % 173.51/173.26 [3249]E(f112(a910),f244(a910)) % 173.51/173.26 [3250]E(f121(a910),f245(a910)) % 173.51/173.26 [3251]E(f113(a1),f33(a1)) % 173.51/173.26 [3252]E(f91(a250),f2(a910)) % 173.51/173.26 [3253]E(f91(a195),f2(a910)) % 173.51/173.26 [3254]P9(f2(a1)) % 173.51/173.26 [3255]P9(f85(a1)) % 173.51/173.26 [3314]P40(f916(a910,a910),a39) % 173.51/173.26 [3657]E(f325(a910,a910,a251,a251),a39) % 173.51/173.26 [4618]~E(f85(a1),f2(a1)) % 173.51/173.26 [3256]E(f4(f2(a110)),f2(a910)) % 173.51/173.26 [3257]E(f122(f2(a910)),f2(a910)) % 173.51/173.26 [3268]E(f333(f86(a1),a90),a90) % 173.51/173.26 [3272]E(f333(a3,f2(a910)),f2(a110)) % 173.51/173.26 [3273]E(f333(a123,f2(a910)),f85(a910)) % 173.51/173.26 [3274]E(f333(a115,f85(a1)),f85(a910)) % 173.51/173.26 [3275]E(f333(a3,f85(a910)),f85(a110)) % 173.51/173.26 [3277]E(f333(f114(a1),a90),f2(a1)) % 173.51/173.26 [3278]E(f333(f114(a110),a90),f2(a110)) % 173.51/173.26 [3279]E(f333(a115,f2(a1)),f2(a910)) % 173.51/173.26 [3280]E(f333(f197(a905),a250),f2(a910)) % 173.51/173.26 [3281]E(f333(f197(a905),a195),f2(a910)) % 173.51/173.26 [3282]E(f333(f197(a907),a25),f2(a910)) % 173.51/173.26 [3283]E(f333(f114(a910),a90),f2(a910)) % 173.51/173.26 [3287]E(f333(f86(a1),f85(a1)),a108) % 173.51/173.26 [3294]E(f333(f86(a1),f2(a1)),f2(a1)) % 173.51/173.26 [3296]E(f333(f197(a110),f2(a110)),f2(a910)) % 173.51/173.26 [3297]E(f333(f111(a1),f2(a910)),f2(a1)) % 173.51/173.26 [3298]E(f333(f111(a1),f85(a910)),f85(a1)) % 173.51/173.26 [3310]E(f333(a115,f85(a1)),f333(a123,f2(a910))) % 173.51/173.26 [3312]E(f324(f916(a910,a910),a39),a40) % 173.51/173.26 [3313]E(f326(f916(a910,a910),a39),a75) % 173.51/173.26 [3339]E(f333(f289(a910),f2(a910)),f196(f917(a910,a905))) % 173.51/173.26 [3340]E(f333(f290(a910),f2(a910)),f254(f917(a910,a905))) % 173.51/173.26 [3349]P43(f196(f917(a1,a905))) % 173.51/173.26 [3383]E(f333(f333(f23(a110),f2(a110)),f85(a110)),f2(a110)) % 173.51/173.26 [3459]P106(f333(f333(f247(a1),a108),f2(a1))) % 173.51/173.26 [3484]P106(f333(f333(f246(a1),f2(a1)),f85(a1))) % 173.51/173.26 [3485]P106(f333(f333(f247(a1),f2(a1)),f85(a1))) % 173.51/173.26 [3688]E(f333(f333(f295(a910,a910,a910),a323),f313(a910,a323)),a251) % 173.51/173.26 [3730]P44(a1,a910,a115,f333(f246(a1),f2(a1))) % 173.51/173.26 [3734]E(f333(f333(f45(a910,f917(a910,a905)),f254(f917(a910,a905))),f289(a910)),f254(f917(a910,a905))) % 173.51/173.26 [3735]E(f333(f333(f45(a910,f917(a910,a905)),f254(f917(a910,a905))),f307(a910)),f254(f917(a910,a905))) % 173.51/173.26 [3736]E(f333(f333(f45(a910,f917(a910,a905)),f254(f917(a910,a905))),f290(a910)),f254(f917(a910,a905))) % 173.51/173.26 [3737]E(f333(f333(f46(a910,f917(a910,a905)),f254(f917(a910,a905))),f310(a910)),f196(f917(a910,a905))) % 173.51/173.26 [3753]P27(a910,a1,f111(a1),f254(f917(a910,a905))) % 173.51/173.26 [3767]P44(a910,a1,f111(a1),f333(f16(a905,a910),a195)) % 173.51/173.26 [3904]E(f333(f79(a910,a110,a1,a3),a115),f114(a110)) % 173.51/173.26 [4126]P60(a110,a910,a20,a3,f254(f917(a910,a905))) % 173.51/173.26 [4133]P60(a1,f917(f916(a910,a910),a905),a118,a96,a109) % 173.51/173.26 [4387]E(f270(a1,a1,a1,a1,f33(a1),f86(a1)),a57) % 173.51/173.26 [4641]~E(f333(f114(a1),a108),f333(f114(a1),a90)) % 173.51/173.26 [4642]~P106(f333(a201,f2(a1))) % 173.51/173.26 [4643]~P106(f333(a201,f85(a1))) % 173.51/173.26 [4684]~P106(f333(f333(f247(a1),a90),f2(a1))) % 173.51/173.26 [3331]E(f333(f333(f23(a1),a108),a108),a90) % 173.51/173.26 [3347]E(f333(f111(a1),f333(a123,f2(a910))),f85(a1)) % 173.51/173.26 [3412]E(f333(f41(a913),f254(f917(a913,a905))),f85(a910)) % 173.51/173.26 [3432]P106(f333(a201,f333(f114(a1),a108))) % 173.51/173.26 [3434]P106(f333(f333(f246(a1),a108),a90)) % 173.51/173.26 [3436]P106(f333(f333(f247(a1),a108),a90)) % 173.51/173.26 [3494]E(f333(f333(f315(a910),f2(a910)),f196(f917(a910,a905))),f333(f307(a910),f2(a910))) % 173.51/173.26 [3549]P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),a90))) % 173.51/173.26 [3561]E(f333(f316(a910,a910,a123),f254(f917(a910,a905))),f333(f310(a910),f2(a910))) % 173.51/173.26 [3598]P11(f916(a910,a910),f254(f917(f916(a910,a910),a905)),a119) % 173.51/173.26 [3911]E(f333(f79(a910,a1,a110,f111(a1)),a20),a22) % 173.51/173.26 [3972]P40(a910,f333(f252(f916(a910,a910)),f333(f269(a910,a910,a905),f247(a910)))) % 173.51/173.26 [4675]~P106(f333(a201,f333(f114(a1),a90))) % 173.51/173.26 [4676]~P106(f333(f333(f246(a1),a90),a108)) % 173.51/173.26 [4677]~P106(f333(f333(f247(a1),a90),a90)) % 173.51/173.26 [4678]~P106(f333(f333(f247(a1),a90),a108)) % 173.51/173.26 [4679]~P106(f333(f333(f247(a1),a108),a108)) % 173.51/173.26 [4690]~P106(f333(f67(a910),f254(f917(a910,a905)))) % 173.51/173.26 [4691]~P106(f333(f67(a1),f254(f917(a1,a905)))) % 173.51/173.26 [4092]P26(a906,a919,f333(f333(f315(f909(a906)),f333(f333(f333(f98(a906),a330),a920),f202(a920))),f196(f917(f909(a906),a905)))) % 173.51/173.26 [4553]E(f333(f269(a1,a1,a905),f333(f333(f8(f917(a1,a905),f917(a1,a905),a1),f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f247(a1),f2(a1))))),f333(f333(f7(a1,a1,f917(a1,a905)),f333(f333(f8(f917(a1,f917(a1,a905)),f917(a1,f917(a1,a905)),a1),f7(a1,a1,a905)),f333(f333(f8(f917(a1,a1),f917(a1,f917(a1,a905)),a1),f333(f8(a1,f917(a1,a905),a1),a330)),a229))),f85(a1)))),a225) % 173.51/173.26 [4717]~P26(a906,a919,f333(f333(f315(f909(a906)),f333(f333(f333(f98(a906),f333(f333(f8(f917(a906,f917(a906,a905)),f917(a906,a905),a906),f333(f8(f917(a906,a905),a905,a906),f95(a906))),f333(f333(f8(f917(a906,a905),f917(a906,f917(a906,a905)),a906),f333(f7(a906,f917(a906,a905),f917(a906,a905)),f333(f333(f8(f917(a906,f917(a905,a905)),f917(f917(a906,a905),f917(a906,a905)),a906),f18(a906,a905,a905)),f333(f333(f8(f917(a906,a905),f917(a906,f917(a905,a905)),a906),f333(f8(a905,f917(a905,a905),a906),a336)),f202(a920))))),a330))),a920),a330)),f196(f917(f909(a906),a905)))) % 173.51/173.26 [3632]E(f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108),f333(f86(a1),a108)) % 173.51/173.26 [3670]E(f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108),f333(f333(f23(a1),a90),a108)) % 173.51/173.26 [3838]E(f333(f333(f66(f916(a910,a910)),f254(f917(f916(a910,a910),a905))),a119),a109) % 173.51/173.26 [3867]E(f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f85(a1)) % 173.51/173.26 [3868]E(f333(f114(a110),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f85(a110)) % 173.51/173.26 [3869]E(f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f85(a910)) % 173.51/173.26 [3873]E(f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(a123,f2(a910))) % 173.51/173.26 [4255]E(f333(f333(f121(f917(f916(f916(a910,a910),f916(a910,a910)),a905)),a39),f313(f916(a910,a910),f196(f917(f916(f916(a910,a910),f916(a910,a910)),a905)))),a77) % 173.51/173.26 [4322]E(f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),f2(a910)),f2(a910))),f196(f917(f916(a910,a910),a905))))),f2(a1)) % 173.51/173.26 [4323]E(f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),f85(a910)),f2(a910))),f196(f917(f916(a910,a910),a905))))),f85(a1)) % 173.51/173.26 [4336]E(f333(f252(f916(a910,a910)),f333(f269(a910,a910,a905),f333(f333(f8(a910,f917(a910,a905),a910),f333(f7(a910,a910,a905),a330)),a123))),a323) % 173.51/173.26 [4308]E(f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),f333(a123,f333(a123,f2(a910)))) % 173.51/173.26 [4311]E(f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),f333(f333(f87(a910),f85(a910)),f85(a910))) % 173.51/173.26 [4312]E(f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),f333(f41(a905),f254(f917(a905,a905)))) % 173.51/173.26 [4374]P9(f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))) % 173.51/173.26 [4443]P29(f917(f916(a910,a910),a905),f333(f333(f265(f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905),f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905)),a40),a76)) % 173.51/173.26 [4444]P29(f917(f916(a910,a910),a905),f333(f333(f265(f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905),f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905)),a75),a78)) % 173.51/173.26 [4484]E(f333(f333(f121(f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905)),f326(f916(a910,a910),a77)),f333(f333(f315(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),f196(f917(f916(a910,a910),a905))),f196(f917(f916(a910,a910),a905)))),f196(f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905)))),a78) % 173.51/173.26 [4485]E(f333(f333(f121(f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905)),f324(f916(a910,a910),a77)),f333(f333(f315(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),f196(f917(f916(a910,a910),a905))),f196(f917(f916(a910,a910),a905)))),f196(f917(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a905)))),a76) % 173.51/173.26 [4376]E(f333(a115,f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(a123,f333(a123,f2(a910)))) % 173.51/173.26 [4421]E(f333(f111(a1),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))) % 173.51/173.26 [4454]P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.26 [4455]E(f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108)),f333(a123,f333(a123,f333(a123,f2(a910))))) % 173.51/173.26 [4499]P9(f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))) % 173.51/173.26 [4525]E(f333(f111(a1),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))) % 173.51/173.26 [4538]P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108)))) % 173.51/173.26 [3265]P10(x32651,a330) % 173.51/173.26 [3658]P27(a910,a910,a123,x36581) % 173.51/173.26 [3258]P105(f909(x32581)) % 173.51/173.26 [3259]P105(f914(x32591)) % 173.51/173.26 [3260]P105(f911(x32601)) % 173.51/173.26 [3261]P105(f912(x32611)) % 173.51/173.26 [3284]P40(a1,f116(x32841)) % 173.51/173.26 [3285]P40(a1,f117(x32851)) % 173.51/173.26 [3335]P40(f917(x33351,a905),f320(x33351)) % 173.51/173.26 [3336]P41(f917(x33361,a905),f320(x33361)) % 173.51/173.26 [3361]E(f255(x33611,x33611,a330),a330) % 173.51/173.26 [3376]E(f51(a1,x33761,x33761),f2(a1)) % 173.51/173.26 [3429]P17(x34291,f917(x34291,a905),f315(x34291)) % 173.51/173.26 [4622]~E(f333(a123,x46221),x46221) % 173.51/173.26 [4634]~E(f333(a123,x46341),f2(a910)) % 173.51/173.26 [3266]E(f36(f34(x32661)),f2(a910)) % 173.51/173.26 [3267]E(f36(f35(x32671)),f2(a910)) % 173.51/173.26 [3269]E(f333(f197(a910),x32691),x32691) % 173.51/173.26 [3270]E(f333(f114(a1),x32701),x32701) % 173.51/173.26 [3286]E(f333(a96,f334(x32861)),x32861) % 173.51/173.26 [3299]E(f125(x32991,f124(x32991)),f124(x32991)) % 173.51/173.26 [3300]E(f160(x33001,f124(x33001)),f124(x33001)) % 173.51/173.26 [3302]E(f333(f197(a908),f34(x33021)),f2(a910)) % 173.51/173.26 [3303]E(f333(f197(a908),f35(x33031)),f2(a910)) % 173.51/173.26 [3307]E(f333(f175(x33071),f124(x33071)),f124(x33071)) % 173.51/173.26 [3308]E(f333(f179(x33081),f124(x33081)),f124(x33081)) % 173.51/173.26 [3309]E(f333(f176(x33091),f124(x33091)),f124(x33091)) % 173.51/173.26 [3315]E(f333(f114(a1),x33151),f333(f113(a1),x33151)) % 173.51/173.26 [3316]E(f333(a96,f333(a118,x33161)),x33161) % 173.51/173.26 [3318]E(f333(a3,f333(a20,x33181)),x33181) % 173.51/173.26 [3319]E(f333(a20,f333(a3,x33191)),x33191) % 173.51/173.26 [3320]P9(f333(f111(a1),x33201)) % 173.51/173.26 [3329]E(f333(f197(f911(x33291)),f124(x33291)),f2(a910)) % 173.51/173.26 [3330]E(f333(f197(f912(x33301)),f130(x33301)),f2(a910)) % 173.51/173.26 [3352]E(f333(f333(f23(a910),x33521),f2(a910)),x33521) % 173.51/173.26 [3353]E(f333(f333(f87(a910),x33531),f2(a910)),x33531) % 173.51/173.26 [3354]E(f333(f333(f87(a1),x33541),f2(a1)),x33541) % 173.51/173.26 [3355]E(f333(f333(f88(a910),x33551),f85(a910)),x33551) % 173.51/173.26 [3356]E(f333(f333(f88(a1),x33561),f85(a1)),x33561) % 173.51/173.26 [3357]E(f333(f333(f245(a910),x33571),f2(a910)),x33571) % 173.51/173.26 [3358]E(f333(f333(f88(a910),x33581),f2(a910)),f2(a910)) % 173.51/173.26 [3359]E(f333(f333(f244(a910),x33591),f2(a910)),f2(a910)) % 173.51/173.26 [3360]E(f333(f333(f42(a1),x33601),f2(a1)),f2(a1)) % 173.51/173.26 [3367]E(f333(f180(x33671),f124(x33671)),f196(f917(x33671,a905))) % 173.51/173.26 [3371]P106(f333(f145(x33711),f124(x33711))) % 173.51/173.26 [3377]E(f333(f162(x33771,x33771),f5(x33771)),f33(f911(x33771))) % 173.51/173.26 [3378]E(f333(f162(x33781,x33781),f33(x33781)),f33(f911(x33781))) % 173.51/173.26 [3379]E(f51(a1,x33791,f2(a1)),x33791) % 173.51/173.26 [3380]E(f333(f246(a910),f333(a123,x33801)),f333(f247(a910),x33801)) % 173.51/173.26 [3381]E(f333(f289(a910),f333(a123,x33811)),f333(f307(a910),x33811)) % 173.51/173.26 [3382]E(f333(f290(a910),f333(a123,x33821)),f333(f310(a910),x33821)) % 173.51/173.26 [3384]E(f51(a1,f2(a1),x33841),f2(a1)) % 173.51/173.26 [3397]E(f333(f333(f87(a910),x33971),f85(a910)),f333(a123,x33971)) % 173.51/173.26 [3406]E(f333(f308(a910,x34061),f2(a910)),f196(f917(a910,a905))) % 173.51/173.26 [3418]E(f309(a910,f2(a910),x34181),f333(f307(a910),x34181)) % 173.51/173.26 [3462]E(f333(f333(f23(a910),f333(a123,x34621)),f85(a910)),x34621) % 173.51/173.26 [3474]E(f53(f2(a1),x34741),f333(f333(f265(a1,a1),f2(a1)),f2(a1))) % 173.51/173.26 [3524]P106(f333(f333(f247(a910),x35241),f333(a123,x35241))) % 173.51/173.26 [3536]P106(f333(f333(f247(a910),f2(a910)),f333(a123,x35361))) % 173.51/173.26 [3766]E(f99(x37661,x37661,f254(f917(x37661,a905)),f33(x37661)),f33(x37661)) % 173.51/173.26 [3825]E(f333(f333(f23(a110),f333(a3,f333(a123,f333(a20,x38251)))),f85(a110)),x38251) % 173.51/173.26 [3896]P106(f333(f333(f246(a1),f333(f86(a1),f333(f111(a1),x38961))),f2(a1))) % 173.51/173.26 [4042]P106(f333(f333(f247(a1),f333(f86(a1),f333(f111(a1),f333(a123,x40421)))),f2(a1))) % 173.51/173.26 [4648]~E(f254(f917(x46481,a905)),f196(f917(x46481,a905))) % 173.51/173.26 [4687]~P106(f333(f333(f247(a910),x46871),f2(a910))) % 173.51/173.26 [4700]~P106(f333(f333(f247(a1),f333(f111(a1),x47001)),f2(a1))) % 173.51/173.26 [3334]E(f187(x33341,f124(f911(x33341))),f124(f911(x33341))) % 173.51/173.26 [3337]E(f333(f333(f88(a1),a90),x33371),a90) % 173.51/173.26 [3338]E(f333(f333(f87(a1),a90),x33381),x33381) % 173.51/173.26 [3341]E(f333(a115,f333(f111(a1),x33411)),x33411) % 173.51/173.26 [3342]E(f333(f333(f23(a1),x33421),a90),x33421) % 173.51/173.26 [3343]E(f333(f333(f87(a1),x33431),a90),x33431) % 173.51/173.26 [3346]E(f333(f333(f23(a910),x33461),x33461),f2(a910)) % 173.51/173.26 [3350]E(f333(f86(a1),f333(f86(a1),x33501)),x33501) % 173.51/173.26 [3351]E(f333(f41(a910),f333(f289(a910),x33511)),x33511) % 173.51/173.26 [3362]E(f333(f333(f87(a910),f2(a910)),x33621),x33621) % 173.51/173.26 [3363]E(f333(f333(f87(a1),f2(a1)),x33631),x33631) % 173.51/173.26 [3364]E(f333(f333(f88(a910),f85(a910)),x33641),x33641) % 173.51/173.26 [3365]E(f333(f333(f88(a1),f85(a1)),x33651),x33651) % 173.51/173.26 [3366]E(f333(f333(f245(a910),f2(a910)),x33661),x33661) % 173.51/173.26 [3372]E(f333(f333(f23(a910),f2(a910)),x33721),f2(a910)) % 173.51/173.26 [3373]E(f333(f333(f88(a910),f2(a910)),x33731),f2(a910)) % 173.51/173.26 [3374]E(f333(f333(f244(a910),f2(a910)),x33741),f2(a910)) % 173.51/173.26 [3375]E(f333(f333(f42(a1),f2(a1)),x33751),f2(a1)) % 173.51/173.26 [3385]E(f137(x33851,f333(f86(a1),x33851)),f140(a1,x33851)) % 173.51/173.26 [3390]E(f333(f308(a910,f2(a910)),x33901),f333(f289(a910),x33901)) % 173.51/173.26 [3391]E(f333(f333(f88(a1),a108),x33911),f333(f86(a1),x33911)) % 173.51/173.26 [3399]E(f333(a115,f333(f114(a1),x33991)),f333(f114(a910),x33991)) % 173.51/173.26 [3400]E(f333(a20,f333(f114(a110),x34001)),f333(f114(a910),x34001)) % 173.51/173.26 [3401]E(f333(f41(a910),f333(f307(a910),x34011)),f333(a123,x34011)) % 173.51/173.26 [3410]E(f333(f333(f87(a910),f85(a910)),x34101),f333(a123,x34101)) % 173.51/173.26 [3414]E(f333(f113(a1),f333(f111(a1),x34141)),f333(f111(a1),x34141)) % 173.51/173.26 [3415]E(f333(f82(a1),f333(f111(a1),x34151)),f333(f111(a1),x34151)) % 173.51/173.26 [3419]E(f333(f41(x34191),f196(f917(x34191,a905))),f2(a910)) % 173.51/173.26 [3421]E(f333(f333(f42(a910),x34211),f333(a123,f2(a910))),x34211) % 173.51/173.26 [3430]E(f51(a910,x34301,f333(a123,f2(a910))),f2(a910)) % 173.51/173.26 [3431]E(f51(a1,x34311,f333(f114(a1),a108)),f2(a1)) % 173.51/173.26 [3445]E(f333(f333(f42(a1),x34451),f333(f114(a1),a108)),f333(f86(a1),x34451)) % 173.51/173.26 [3449]E(f147(a910,f333(f308(a910,x34491),f2(a910))),f124(a910)) % 173.51/173.26 [3450]E(f333(f333(f87(a1),x34501),f85(a1)),f333(f333(f23(a1),x34501),a108)) % 173.51/173.26 [3451]E(f333(f333(f23(a1),x34511),f85(a1)),f333(f333(f87(a1),x34511),a108)) % 173.51/173.26 [3456]P106(f333(f333(f202(a25),x34561),x34561)) % 173.51/173.26 [3457]P106(f333(f333(f246(a910),x34571),x34571)) % 173.51/173.26 [3458]P106(f333(f333(f246(a1),x34581),x34581)) % 173.51/173.26 [3463]E(f333(f86(a1),f333(f114(a1),x34631)),f333(f114(a1),f333(f86(a1),x34631))) % 173.51/173.26 [3464]P106(f333(f67(a910),f333(f289(a910),x34641))) % 173.51/173.26 [3465]P106(f333(f67(a910),f333(f307(a910),x34651))) % 173.51/173.26 [3472]E(f169(x34721,f254(f917(x34721,a905))),f254(f917(f911(x34721),a905))) % 173.51/173.26 [3477]P106(f333(f333(f246(a910),f2(a910)),x34771)) % 173.51/173.26 [3487]E(f333(f333(f87(a910),f122(x34871)),f333(a123,f2(a910))),f122(f333(a123,x34871))) % 173.51/173.26 [3488]E(f333(f252(x34881),f333(f16(a905,x34881),a250)),f196(f917(x34881,a905))) % 173.51/173.26 [3489]E(f333(f252(x34891),f333(f16(a905,x34891),a195)),f254(f917(x34891,a905))) % 173.51/173.26 [3493]E(f333(f333(f315(a910),x34931),f333(f289(a910),x34931)),f333(f289(a910),f333(a123,x34931))) % 173.51/173.26 [3505]E(f333(f333(f87(a1),f85(a1)),f333(f111(a1),x35051)),f333(f111(a1),f333(a123,x35051))) % 173.51/173.26 [3507]E(f333(f333(f159(f911(x35071)),f124(x35071)),f124(f911(x35071))),f60(x35071,f124(x35071))) % 173.51/173.26 [3527]E(f196(f917(f916(x35271,x35271),a905)),f253(x35271,f196(f917(x35271,a905)))) % 173.51/173.26 [3528]E(f333(f314(x35281),f254(f917(x35281,a905))),f254(f917(f917(x35281,a905),a905))) % 173.51/173.26 [3529]E(f333(f86(f917(x35291,a905)),f196(f917(x35291,a905))),f254(f917(x35291,a905))) % 173.51/173.26 [3530]E(f333(f86(f917(x35301,a905)),f254(f917(x35301,a905))),f196(f917(x35301,a905))) % 173.51/173.26 [3532]P106(f333(f67(x35321),f196(f917(x35321,a905)))) % 173.51/173.26 [3534]E(f333(f308(a910,x35341),f333(a123,x35341)),f333(f333(f315(a910),x35341),f196(f917(a910,a905)))) % 173.51/173.26 [3535]E(f92(f916(a910,a910),f54(x35351,f2(a910))),f333(f333(f265(a910,a910),f2(a910)),x35351)) % 173.51/173.26 [3548]E(f333(f333(f315(a910),f333(a123,x35481)),f333(f307(a910),x35481)),f333(f307(a910),f333(a123,x35481))) % 173.51/173.26 [3552]P40(x35521,f196(f917(f916(x35521,x35521),a905))) % 173.51/173.26 [3553]P42(x35531,f196(f917(f916(x35531,x35531),a905))) % 173.51/173.26 [3556]P106(f333(f333(f246(a1),f2(a1)),f333(f111(a1),x35561))) % 173.51/173.26 [3563]E(f333(f333(f87(a910),f333(f197(a910),x35631)),f333(a123,f2(a910))),f333(f197(a910),f333(a123,x35631))) % 173.51/173.26 [3665]P43(f333(f316(a910,a1,f111(a1)),x36651)) % 173.51/173.26 [3702]P56(x37021,f196(f917(x37021,a905)),f196(f917(f916(x37021,x37021),a905))) % 173.51/173.26 [3726]E(f333(f333(f265(a1,a1),f333(f114(a1),a108)),f333(f333(f23(a1),x37261),f85(a1))),f56(f333(f114(a1),a108),x37261)) % 173.51/173.26 [3779]P63(x37791,f333(f16(f917(x37791,a905),x37791),f333(f16(a905,x37791),a250))) % 173.51/173.26 [3983]P106(f333(f333(f335(f917(f916(a910,a910),a905)),f334(x39831)),a109)) % 173.51/173.26 [4008]P106(f333(f333(f335(f917(f916(a910,a910),a905)),f333(a118,x40081)),a109)) % 173.51/173.26 [4142]P27(x41421,f917(x41421,a905),f333(f333(f7(x41421,f917(x41421,a905),f917(x41421,a905)),f315(x41421)),f196(f917(x41421,a905))),f254(f917(x41421,a905))) % 173.51/173.26 [4645]~E(f333(f333(f87(a1),x46451),x46451),a108) % 173.51/173.26 [4674]~E(f333(a3,f333(a123,f333(a20,x46741))),f2(a110)) % 173.51/173.26 [4680]~P106(f333(a201,f333(f111(a1),x46801))) % 173.51/173.26 [4683]~P106(f333(f333(f247(a910),x46831),x46831)) % 173.51/173.26 [4693]~P106(f333(f333(f246(a910),f333(a123,x46931)),x46931)) % 173.51/173.26 [3479]E(f333(a115,f333(f86(a1),f333(f111(a1),x34791))),f2(a910)) % 173.51/173.26 [3482]E(f333(f333(f87(a1),f333(f86(a1),x34821)),x34821),f2(a1)) % 173.51/173.26 [3486]E(f333(f41(a1),f333(f308(a1,f2(a1)),x34861)),f333(a115,x34861)) % 173.51/173.26 [3498]E(f333(f333(f256(a910),f333(a123,f2(a910))),x34981),f333(a123,f2(a910))) % 173.51/173.26 [3595]E(f333(f288(x35951),f196(f917(f916(x35951,x35951),a905))),f196(f917(x35951,a905))) % 173.51/173.26 [3603]E(f44(f917(x36031,a905),f196(f917(f917(x36031,a905),a905))),f254(f917(x36031,a905))) % 173.51/173.26 [3604]E(f44(f917(x36041,a905),f254(f917(f917(x36041,a905),a905))),f196(f917(x36041,a905))) % 173.51/173.26 [3605]E(f43(f917(x36051,a905),f196(f917(f917(x36051,a905),a905))),f196(f917(x36051,a905))) % 173.51/173.26 [3606]E(f43(f917(x36061,a905),f254(f917(f917(x36061,a905),a905))),f254(f917(x36061,a905))) % 173.51/173.26 [3648]E(f333(f333(f315(f911(x36481)),f124(x36481)),f196(f917(f911(x36481),a905))),f169(x36481,f196(f917(x36481,a905)))) % 173.51/173.26 [3649]E(f333(f333(f315(f911(x36491)),f124(x36491)),f196(f917(f911(x36491),a905))),f170(x36491,f124(f917(x36491,a905)))) % 173.51/173.26 [3687]E(f333(f333(f87(a910),f4(x36871)),f333(a123,f2(a910))),f4(f333(a3,f333(a123,f333(a20,x36871))))) % 173.51/173.26 [3717]E(f333(f41(a1),f333(f316(a910,a1,f111(a1)),x37171)),f333(f41(a910),x37171)) % 173.51/173.26 [3720]P106(f333(f333(f246(a910),x37201),f333(f333(f88(a910),x37201),x37201))) % 173.51/173.26 [3757]E(f333(f316(a1,a910,a115),f309(a1,f2(a1),f333(f111(a1),x37571))),f333(f307(a910),x37571)) % 173.51/173.26 [3774]E(f333(f333(f42(a910),f333(a123,f2(a910))),f333(f114(a910),x37741)),f333(a115,f333(f333(f42(a1),f85(a1)),f333(f114(a1),x37741)))) % 173.51/173.26 [3776]E(f333(f180(a910),f147(a910,f333(f308(a910,f2(a910)),f333(a123,x37761)))),f333(f307(a910),x37761)) % 173.51/173.26 [3777]E(f333(f333(f87(a910),f333(f197(a110),x37771)),f333(a123,f2(a910))),f333(f197(a110),f333(a3,f333(a123,f333(a20,x37771))))) % 173.51/173.26 [3798]P42(x37981,f313(x37981,f196(f917(f916(x37981,x37981),a905)))) % 173.51/173.26 [3799]P55(x37991,f313(x37991,f196(f917(f916(x37991,x37991),a905)))) % 173.51/173.26 [3800]E(f333(f316(a1,a910,a115),f333(f316(a910,a1,f111(a1)),x38001)),x38001) % 173.51/173.26 [3831]E(f333(f333(f315(a910),f2(a910)),f333(f316(a910,a910,a123),f333(f289(a910),x38311))),f333(f289(a910),f333(a123,x38311))) % 173.51/173.26 [3837]P58(x38371,x38371,f313(x38371,f196(f917(f916(x38371,x38371),a905)))) % 173.51/173.26 [3843]P106(f333(a201,f333(f86(a1),f333(f111(a1),f333(a123,x38431))))) % 173.51/173.26 [3853]E(f333(f333(f23(f917(a910,a905)),f333(f290(a910),x38531)),f333(f333(f315(a910),x38531),f196(f917(a910,a905)))),f333(f290(a910),f333(a123,x38531))) % 173.51/173.26 [3870]E(f333(f333(f87(a1),f333(f333(f23(a1),a90),x38701)),f333(f333(f23(a1),a90),x38701)),f333(f333(f23(a1),a90),f333(f333(f87(a1),x38701),x38701))) % 173.51/173.26 [3885]E(f333(f333(f315(f917(x38851,a905)),f196(f917(x38851,a905))),f196(f917(f917(x38851,a905),a905))),f333(f314(x38851),f196(f917(x38851,a905)))) % 173.51/173.26 [3912]E(f333(f333(f23(f917(a910,a905)),f333(f310(a910),x39121)),f333(f333(f315(a910),f333(a123,x39121)),f196(f917(a910,a905)))),f333(f310(a910),f333(a123,x39121))) % 173.51/173.26 [4020]E(f333(f114(a910),f333(f333(f87(a1),x40201),x40201)),f333(f333(f93(a910,a910),f333(f114(a910),x40201)),f333(f333(f18(a910,a910,a910),f87(a910)),f5(a910)))) % 173.51/173.26 [4396]P17(x43961,f917(x43961,a905),f333(f333(f8(f917(x43961,a905),f917(f917(x43961,a905),f917(x43961,a905)),x43961),f333(f7(f917(x43961,a905),f917(x43961,a905),f917(x43961,a905)),f23(f917(x43961,a905)))),f333(f333(f7(x43961,f917(x43961,a905),f917(x43961,a905)),f315(x43961)),f196(f917(x43961,a905))))) % 173.51/173.26 [4483]E(f333(f252(f916(a1,a1)),f333(f269(a1,a1,a905),f333(f333(f8(f917(a1,a905),f917(a1,a905),a1),f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),x44831)))),f247(a1)))),f116(x44831)) % 173.51/173.26 [4516]E(f333(f252(f916(a1,a1)),f333(f269(a1,a1,a905),f333(f333(f18(a1,f917(a1,a905),f917(a1,a905)),f333(f333(f8(f917(a905,a905),f917(f917(a1,a905),f917(a1,a905)),a1),f8(a905,a905,a1)),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),x45161)))),f247(a1)))),f117(x45161)) % 173.51/173.26 [4569]E(f333(f252(f916(f917(x45691,a905),f917(x45691,a905))),f333(f269(f917(x45691,a905),f917(x45691,a905),a905),f333(f333(f7(f917(x45691,a905),f917(f917(x45691,a905),a905),f917(f917(x45691,a905),a905)),f333(f333(f8(f917(f917(x45691,a905),f917(a905,a905)),f917(f917(f917(x45691,a905),a905),f917(f917(x45691,a905),a905)),f917(x45691,a905)),f18(f917(x45691,a905),a905,a905)),f333(f333(f8(f917(f917(x45691,a905),a905),f917(f917(x45691,a905),f917(a905,a905)),f917(x45691,a905)),f333(f8(a905,f917(a905,a905),f917(x45691,a905)),a331)),f247(f917(x45691,a905))))),f67(x45691)))),f320(x45691)) % 173.51/173.26 [4697]~P106(f333(f67(f911(x46971)),f254(f917(f911(x46971),a905)))) % 173.51/173.26 [4709]~P106(f333(f333(f246(a1),f2(a1)),f333(f86(a1),f333(f111(a1),f333(a123,x47091))))) % 173.51/173.26 [3627]E(f333(f333(f23(a1),f333(f333(f87(a1),x36271),a108)),a108),x36271) % 173.51/173.26 [3641]E(f333(f180(a910),f147(a910,f333(f308(a910,f2(a910)),x36411))),f333(f289(a910),x36411)) % 173.51/173.26 [3892]E(f333(f333(f87(a1),f333(f333(f87(a1),f85(a1)),x38921)),x38921),f333(f333(f23(a1),f333(f333(f87(a1),x38921),x38921)),a108)) % 173.51/173.26 [3939]E(f333(f293(x39391,x39391),f313(x39391,f196(f917(f916(x39391,x39391),a905)))),f313(x39391,f196(f917(f916(x39391,x39391),a905)))) % 173.51/173.26 [3986]P106(f333(f333(f246(a910),x39861),f333(f333(f88(a910),x39861),f333(f333(f88(a910),x39861),x39861)))) % 173.51/173.26 [4259]P106(f333(f67(a910),f333(f252(a910),f333(f333(f7(a910,a910,a905),f246(a910)),x42591)))) % 173.51/173.26 [4260]P106(f333(f67(a910),f333(f252(a910),f333(f333(f7(a910,a910,a905),f247(a910)),x42601)))) % 173.51/173.26 [4532]E(f333(f252(f916(x45321,x45321)),f333(f333(f8(f917(x45321,a905),a905,f916(x45321,x45321)),f94(x45321)),f333(f333(f7(f916(x45321,x45321),f917(x45321,f916(x45321,x45321)),f917(x45321,a905)),f333(f333(f8(f917(f916(x45321,x45321),a905),f917(f917(x45321,f916(x45321,x45321)),f917(x45321,a905)),f916(x45321,x45321)),f8(f916(x45321,x45321),a905,x45321)),a330)),f333(f333(f18(x45321,x45321,f916(x45321,x45321)),f265(x45321,x45321)),f5(x45321))))),f313(x45321,f196(f917(f916(x45321,x45321),a905)))) % 173.51/173.26 [4699]~E(f333(f333(f23(a1),f333(f333(f87(a1),x46991),x46991)),a108),a90) % 173.51/173.26 [4701]~E(f333(f333(f87(a1),f333(f333(f87(a1),f85(a1)),x47011)),x47011),f2(a1)) % 173.51/173.26 [4033]E(f333(f333(f87(a1),f333(f333(f23(a1),a108),x40331)),f333(f333(f23(a1),a108),x40331)),f333(f333(f23(a1),a108),f333(f333(f23(a1),f333(f333(f87(a1),x40331),x40331)),a108))) % 173.51/173.26 [4150]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),a108),x41501)),f333(f333(f23(a1),a108),x41501))),a108),f333(f333(f23(a1),a108),f333(f333(f87(a1),x41501),x41501))) % 173.51/173.26 [4182]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f87(a1),x41821),a108)),f333(f333(f87(a1),x41821),a108))),a108),f333(f333(f87(a1),f333(f333(f87(a1),x41821),x41821)),a108)) % 173.51/173.26 [4220]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),a108),x42201)),f333(f333(f23(a1),a108),x42201))),a108),f333(f333(f23(a1),a90),f333(f333(f23(a1),f333(f333(f87(a1),x42201),x42201)),a108))) % 173.51/173.26 [4318]E(f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x43181),f2(a910))),f196(f917(f916(a910,a910),a905))))),f333(f111(a1),x43181)) % 173.51/173.26 [4328]E(f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),f555(x43281)),f569(x43281))),f196(f917(f916(a910,a910),a905))))),x43281) % 173.51/173.26 [4360]E(f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x43601)),f333(f316(a910,a1,f111(a1)),f333(f252(a910),f333(f333(f8(a1,a905,a910),x43601),f111(a1))))) % 173.51/173.26 [4404]P43(f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x44041))) % 173.51/173.26 [4424]P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x44241),f196(f917(f916(a910,a910),a905)))),a78)) % 173.51/173.26 [4429]E(f333(f316(a1,a910,a115),f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),f333(f333(f8(a910,a905,a1),x44291),a115)))),f333(f252(a910),x44291)) % 173.51/173.26 [4584]E(f318(a910,f333(f333(f45(f916(a910,a910),f917(a910,a905)),f333(a118,x45841)),f333(f269(a910,a910,f917(a910,a905)),f333(f333(f7(a910,f917(a910,a905),f917(a910,f917(a910,a905))),f333(f333(f8(f917(a910,f917(f917(a910,a905),f917(a910,a905))),f917(f917(a910,a905),f917(a910,f917(a910,a905))),a910),f7(a910,f917(a910,a905),f917(a910,a905))),f333(f333(f8(f917(a910,a910),f917(a910,f917(f917(a910,a905),f917(a910,a905))),a910),f333(f8(a910,f917(f917(a910,a905),f917(a910,a905)),a910),f315(a910))),f23(a910)))),f196(f917(a910,a905)))))),f333(a115,x45841)) % 173.51/173.26 [4077]E(f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),x40771),x40771)),a108)),a108),f333(f333(f87(a1),x40771),x40771)) % 173.51/173.26 [4127]E(f333(f333(f23(a1),f333(f333(f23(a1),f333(f333(f87(a1),x41271),x41271)),a108)),a108),f333(f333(f87(a1),f333(f333(f23(a1),x41271),a108)),f333(f333(f23(a1),x41271),a108))) % 173.51/173.26 [4334]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f87(a1),f333(f86(a1),x43341)),a108)),f333(f333(f87(a1),f333(f86(a1),x43341)),a108))),a108),f333(f86(a1),f333(f333(f23(a1),f333(f333(f87(a1),x43341),x43341)),a108))) % 173.51/173.26 [4377]E(f333(f333(f87(a910),x43771),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(a123,f333(a123,x43771))) % 173.51/173.26 [4378]E(f333(f333(f88(a910),x43781),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f87(a910),x43781),x43781)) % 173.51/173.26 [4379]E(f333(f333(f42(a910),f333(f333(f87(a910),x43791),x43791)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x43791) % 173.51/173.26 [4457]E(f51(a910,f333(a123,f333(a123,x44571)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f51(a910,x44571,f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.26 [4601]E(f333(a96,f333(f333(f45(f916(a910,a910),f917(f916(a910,a910),a905)),f333(a118,x46011)),f333(f269(a910,a910,f917(f916(a910,a910),a905)),f333(f333(f8(f917(a910,f917(f916(a910,a910),a905)),f917(a910,f917(f916(a910,a910),a905)),a910),f333(f8(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905),a910),f292(f916(a910,a910),f916(a910,a910),a119))),f333(f333(f7(a910,f917(f916(a910,a910),a905),f917(a910,f917(f916(a910,a910),a905))),f333(f333(f8(f917(a910,f917(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f917(f917(f916(a910,a910),a905),f917(a910,f917(f916(a910,a910),a905))),a910),f7(a910,f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f8(f917(a910,f916(a910,a910)),f917(a910,f917(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),a910),f333(f8(f916(a910,a910),f917(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),a910),f315(f916(a910,a910)))),f333(f7(a910,a910,f916(a910,a910)),f265(a910,a910))))),f196(f917(f916(a910,a910),a905))))))),f333(f86(a1),x46011)) % 173.51/173.26 [4452]E(f333(f333(f87(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x44521),f333(a123,f333(a123,x44521))) % 173.51/173.26 [4453]E(f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x44531),f333(f333(f87(a910),x44531),x44531)) % 173.51/173.26 [4489]E(f333(f333(f42(a910),f333(a123,f333(a123,x44891))),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(a123,f333(f333(f42(a910),x44891),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.26 [4539]E(f333(f333(f87(a910),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),x45391),f333(a123,f333(a123,f333(a123,x45391)))) % 173.51/173.26 [4614]E(f333(f269(a1,a1,f916(a1,a1)),f333(f333(f18(a1,f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),f333(f333(f8(f917(a1,f917(f916(a1,a1),f916(a1,a1))),f917(f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),a1),f18(a1,f916(a1,a1),f916(a1,a1))),f333(f333(f8(f917(a1,f916(a1,a1)),f917(a1,f917(f916(a1,a1),f916(a1,a1))),a1),f333(f18(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f333(f333(f8(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f107(f916(a1,a1))),f333(f333(f8(a1,a905,a1),f333(f246(a1),f2(a1))),f333(f333(f7(a1,a1,a1),f23(a1)),x46141))))),f333(f333(f7(a1,f917(a1,a1),f917(a1,f916(a1,a1))),f333(f333(f8(f917(a1,f916(a1,a1)),f917(f917(a1,a1),f917(a1,f916(a1,a1))),a1),f8(a1,f916(a1,a1),a1)),f333(f333(f8(a1,f917(a1,f916(a1,a1)),a1),f265(a1,a1)),f333(f333(f7(a1,a1,a1),f333(f333(f8(a1,f917(a1,a1),a1),f87(a1)),f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f85(a1))))),f333(f333(f7(a1,a1,a1),f23(a1)),x46141))))),f333(f333(f8(a1,f917(a1,f916(a1,a1)),a1),f265(a1,a1)),f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))))),f49(x46141)) % 173.51/173.26 [3304]P105(f916(x33041,x33042)) % 173.51/173.26 [3305]P105(f918(x33051,x33052)) % 173.51/173.26 [3306]P105(f915(x33061,x33062)) % 173.51/173.26 [3323]P16(a1,f186(x33231,x33232)) % 173.51/173.26 [3324]P40(x33241,f161(x33241,x33242)) % 173.51/173.26 [3325]P41(x33251,f253(x33251,x33252)) % 173.51/173.26 [3326]P41(x33261,f313(x33261,x33262)) % 173.51/173.26 [3327]P42(x33271,f253(x33271,x33272)) % 173.51/173.26 [3328]P55(x33281,f253(x33281,x33282)) % 173.51/173.26 [3392]P34(x33921,x33922,f124(x33921)) % 173.51/173.26 [3425]P56(x34251,x34252,f253(x34251,x34252)) % 173.51/173.26 [3426]P58(x34261,x34261,f253(x34261,x34262)) % 173.51/173.26 [3690]P27(x36901,x36901,f5(x36901),x36902) % 173.51/173.26 [3691]P27(x36911,x36911,f33(x36911),x36912) % 173.51/173.26 [3698]P35(x36981,x36982,f124(x36981),f124(x36981)) % 173.51/173.26 [3707]P27(f911(x37071),f911(x37071),f176(x37071),x37072) % 173.51/173.26 [4118]P28(x41181,x41181,f33(x41181),x41182,x41182) % 173.51/173.26 [4620]~E(f35(x46201),f34(x46202)) % 173.51/173.26 [4626]~E(f31(x46261,x46262),a25) % 173.51/173.26 [4627]~E(f30(x46271,x46272),a25) % 173.51/173.26 [4628]~E(f26(x46281,x46282),a25) % 173.51/173.26 [4657]~P36(x46571,x46572,f124(x46571)) % 173.51/173.26 [4658]~P38(x46581,x46582,f124(x46581)) % 173.51/173.26 [3288]E(f333(f252(x32881),x32882),x32882) % 173.51/173.26 [3289]E(f333(f5(x32891),x32892),x32892) % 173.51/173.26 [3291]E(f333(f33(x32911),x32912),x32912) % 173.51/173.26 [3301]E(f333(f199(x33011),x33012),f126(x33011)) % 173.51/173.26 [3311]E(f29(f26(x33111,x33112)),f2(a910)) % 173.51/173.26 [3321]E(f92(x33211,f333(a330,x33212)),x33212) % 173.51/173.26 [3322]E(f97(x33221,f333(a330,x33222)),x33222) % 173.51/173.26 [3344]E(f333(f197(a907),f26(x33441,x33442)),f2(a910)) % 173.51/173.26 [3345]E(f333(f135(x33451,x33452),f130(x33451)),f2(a910)) % 173.51/173.26 [3348]E(f333(f144(x33481,x33482),f124(x33481)),f124(x33481)) % 173.51/173.26 [3368]E(f313(x33681,f313(x33681,x33682)),f313(x33681,x33682)) % 173.51/173.26 [3369]E(f160(x33691,f160(x33691,x33692)),f160(x33691,x33692)) % 173.51/173.26 [3387]E(f333(f333(f142(x33871),x33872),f124(x33871)),x33872) % 173.51/173.26 [3393]E(f181(x33931,x33932,f124(x33931)),x33932) % 173.51/173.26 [3394]E(f127(x33941,f130(x33941),x33942),x33942) % 173.51/173.26 [3395]E(f181(x33951,f124(x33951),x33952),x33952) % 173.51/173.26 [3396]E(f177(x33961,f2(a910),x33962),f124(x33961)) % 173.51/173.26 [3402]E(f333(f333(f183(x34021),x34022),f124(x34021)),f124(x34021)) % 173.51/173.26 [3403]E(f333(f333(f146(x34031),x34032),f124(x34031)),f124(x34031)) % 173.51/173.26 [3405]E(f163(x34051,x34052,f124(x34051)),f2(a910)) % 173.51/173.26 [3407]E(f178(x34071,x34072,f124(x34071)),f124(x34071)) % 173.51/173.26 [3408]E(f185(x34081,x34082,f124(x34081)),f124(x34081)) % 173.51/173.27 [3409]E(f184(x34091,f124(x34091),x34092),f124(x34091)) % 173.51/173.27 [3413]E(f333(f180(x34131),f160(x34131,x34132)),f333(f180(x34131),x34132)) % 173.51/173.27 [3416]E(f333(f291(x34161,x34161),f253(x34161,x34162)),x34162) % 173.51/173.27 [3417]E(f333(f263(x34171,x34171),f253(x34171,x34172)),x34172) % 173.51/173.27 [3424]E(f333(f293(x34241,x34241),f253(x34241,x34242)),f253(x34241,x34242)) % 173.51/173.27 [3437]E(f313(f911(x34371),f165(x34371,x34372)),f166(x34371,f313(x34371,x34372))) % 173.51/173.27 [3439]P106(f333(f145(a1),f186(x34391,x34392))) % 173.51/173.27 [3447]E(f333(f291(x34471,x34471),f313(x34471,x34472)),f254(f917(x34471,a905))) % 173.51/173.27 [3448]E(f333(f263(x34481,x34481),f313(x34481,x34482)),f254(f917(x34481,a905))) % 173.51/173.27 [3452]P106(f333(f145(x34521),f160(x34521,x34522))) % 173.51/173.27 [3454]P106(f333(f168(x34541,x34542),f124(x34541))) % 173.51/173.27 [3461]E(f333(f180(a1),f186(x34611,x34612)),f309(a1,x34611,x34612)) % 173.51/173.27 [3475]P59(x34751,f196(f917(x34751,a905)),x34752) % 173.51/173.27 [3480]E(f333(f268(a1,a1),f52(x34801,x34802)),f51(a1,x34801,x34802)) % 173.51/173.27 [3481]E(f333(f308(a910,x34811),f333(a123,x34812)),f309(a910,x34811,x34812)) % 173.51/173.27 [3497]E(f333(f333(f159(x34971),x34972),f124(x34971)),f148(x34971,x34972,f124(x34971))) % 173.51/173.27 [3509]E(f309(a910,f333(a123,x35091),x35092),f311(a910,x35091,x35092)) % 173.51/173.27 [3512]P56(x35121,f254(f917(x35121,a905)),f313(x35121,x35122)) % 173.51/173.27 [3575]E(f333(f333(f23(a910),x35751),f333(a123,x35752)),f333(f41(a910),f312(a910,x35752,x35751))) % 173.51/173.27 [3628]E(f174(x36281,x36282,f124(x36281)),f333(f333(f265(f911(x36281),f911(x36281)),f124(x36281)),f124(x36281))) % 173.51/173.27 [3646]E(f333(f269(x36461,x36462,f916(x36461,x36462)),f265(x36461,x36462)),f33(f916(x36461,x36462))) % 173.51/173.27 [3650]P106(f333(f333(f335(f911(x36501)),f124(x36501)),f169(x36501,x36502))) % 173.51/173.27 [3651]E(f333(f197(f911(x36511)),f125(x36511,x36512)),f333(f333(f23(a910),f333(f197(f911(x36511)),x36512)),f85(a910))) % 173.51/173.27 [3659]P106(f333(f67(a910),f309(a910,x36591,x36592))) % 173.51/173.27 [3660]P106(f333(f67(a910),f311(a910,x36601,x36602))) % 173.51/173.27 [3661]P106(f333(f67(a910),f312(a910,x36611,x36612))) % 173.51/173.27 [3662]P106(f333(f67(a1),f309(a1,x36621,x36622))) % 173.51/173.27 [3663]P106(f333(f67(a1),f311(a1,x36631,x36632))) % 173.51/173.27 [3664]P106(f333(f67(a1),f312(a1,x36641,x36642))) % 173.51/173.27 [3773]E(f333(f316(a910,a910,a123),f309(a910,x37731,x37732)),f309(a910,f333(a123,x37731),f333(a123,x37732))) % 173.51/173.27 [3794]E(f333(f333(f295(x37941,x37941,x37941),f313(x37941,x37942)),f313(x37941,x37942)),f313(x37941,x37942)) % 173.51/173.27 [3829]E(f333(f333(f265(a1,a1),f333(f333(f42(a1),x38291),x38292)),f51(a1,x38291,x38292)),f52(x38291,x38292)) % 173.51/173.27 [3830]E(f333(f333(f265(a110,a110),f333(f333(f42(a110),x38301),x38302)),f51(a110,x38301,x38302)),f21(x38301,x38302)) % 173.51/173.27 [3857]E(f333(f333(f265(a910,a910),f333(f333(f42(a910),x38571),x38572)),f51(a910,x38571,x38572)),f92(f916(a910,a910),f54(x38571,x38572))) % 173.51/173.27 [3908]P106(f333(f333(f247(a910),f333(f333(f23(a910),x39081),x39082)),f333(a123,x39081))) % 173.51/173.27 [3958]P41(x39581,f333(f333(f295(x39581,x39581,x39581),x39582),f313(x39581,x39582))) % 173.51/173.27 [4007]E(f333(f333(f87(a1),f333(f333(f88(a1),x40071),f333(f333(f42(a1),x40072),x40071))),f51(a1,x40072,x40071)),x40072) % 173.51/173.27 [4011]E(f333(f333(f45(a910,f917(f916(f911(x40111),f911(x40111)),a905)),f254(f917(a910,a905))),f151(x40111,x40112)),f153(x40111,x40112)) % 173.51/173.27 [4236]P106(f333(f333(f335(f916(f911(x42361),f911(x42361))),f333(f333(f265(f911(x42361),f911(x42361)),f124(x42361)),f124(x42361))),f166(x42361,x42362))) % 173.51/173.27 [4346]E(f266(x43461,x43461,x43461,a330,f266(x43461,x43461,x43461,x43462,a330)),x43462) % 173.51/173.27 [4389]E(f270(x43891,x43891,x43892,x43892,f5(x43891),f5(x43892)),f33(f916(x43891,x43892))) % 173.51/173.27 [4391]E(f270(x43911,x43911,x43912,x43912,f33(x43911),f33(x43912)),f33(f916(x43911,x43912))) % 173.51/173.27 [3386]E(f333(f176(x33861),f333(f176(x33861),x33862)),x33862) % 173.51/173.27 [3388]E(f333(f333(f146(x33881),f2(a910)),x33882),x33882) % 173.51/173.27 [3404]E(f333(f333(f183(x34041),f2(a910)),x34042),f124(x34041)) % 173.51/173.27 [3411]E(f333(f333(f142(x34111),f124(x34111)),x34112),x34112) % 173.51/173.27 [3420]E(f43(f917(x34201,a905),f333(f314(x34201),x34202)),x34202) % 173.51/173.27 [3422]E(f333(f180(x34221),f333(f175(x34221),x34222)),f333(f180(x34221),x34222)) % 173.51/173.27 [3423]E(f333(f180(x34231),f333(f176(x34231),x34232)),f333(f180(x34231),x34232)) % 173.51/173.27 [3428]E(f333(f333(f23(a110),x34281),x34282),f333(f333(a24,x34281),x34282)) % 173.51/173.27 [3441]E(f333(f333(f87(a910),x34411),x34412),f333(f333(f87(a910),x34412),x34411)) % 173.51/173.27 [3442]E(f333(f333(f87(a1),x34421),x34422),f333(f333(f87(a1),x34422),x34421)) % 173.51/173.27 [3443]E(f333(f333(f88(a910),x34431),x34432),f333(f333(f88(a910),x34432),x34431)) % 173.51/173.27 [3444]E(f333(f333(f88(a1),x34441),x34442),f333(f333(f88(a1),x34442),x34441)) % 173.51/173.27 [3467]E(f333(f333(f191(x34671,x34671),f2(a910)),x34672),f33(x34671)) % 173.51/173.27 [3468]E(f333(f197(f911(x34681)),f333(f175(x34681),x34682)),f333(f197(f911(x34681)),x34682)) % 173.51/173.27 [3469]E(f333(f197(f911(x34691)),f333(f176(x34691),x34692)),f333(f197(f911(x34691)),x34692)) % 173.51/173.27 [3470]E(f184(x34701,x34702,f196(f917(a910,a905))),f124(x34701)) % 173.51/173.27 [3471]E(f333(f333(f162(x34711,x34711),f5(x34711)),x34712),x34712) % 173.51/173.27 [3473]E(f333(f264(a1,a1),f52(x34731,x34732)),f333(f333(f42(a1),x34731),x34732)) % 173.51/173.27 [3490]E(f333(f197(f911(x34901)),f160(x34901,x34902)),f333(f41(x34901),f333(f180(x34901),x34902))) % 173.51/173.27 [3491]E(f29(f30(x34911,x34912)),f333(f333(f87(a910),f29(x34912)),f333(a123,f2(a910)))) % 173.51/173.27 [3492]E(f333(f288(x34921),f333(f293(x34921,x34921),x34922)),f333(f288(x34921),x34922)) % 173.51/173.27 [3496]P106(f333(f67(x34961),f333(f180(x34961),x34962))) % 173.51/173.27 [3504]E(f333(f333(f87(a1),x35041),f333(f86(a1),x35042)),f333(f333(f23(a1),x35041),x35042)) % 173.51/173.27 [3511]P26(x35111,x35112,f196(f917(f909(x35111),a905))) % 173.51/173.27 [3513]E(f333(f316(x35131,x35131,f5(x35131)),x35132),x35132) % 173.51/173.27 [3514]E(f333(f316(x35141,x35141,f33(x35141)),x35142),x35142) % 173.51/173.27 [3515]E(f333(f317(x35151,x35151,f5(x35151)),x35152),x35152) % 173.51/173.27 [3516]E(f333(f317(x35161,x35161,f33(x35161)),x35162),x35162) % 173.51/173.27 [3517]P106(f333(f254(f917(x35171,a905)),x35172)) % 173.51/173.27 [3519]E(f333(f41(a910),f333(f308(a910,x35191),x35192)),f333(f333(f23(a910),x35192),x35191)) % 173.51/173.27 [3520]E(f333(f308(a910,f333(a123,x35201)),x35202),f312(a910,x35201,x35202)) % 173.51/173.27 [3533]E(f333(f333(f315(x35331),x35332),f196(f917(x35331,a905))),f333(f252(x35331),f333(a330,x35332))) % 173.51/173.27 [3538]E(f313(x35381,f333(f293(x35381,x35381),x35382)),f333(f293(x35381,x35381),f313(x35381,x35382))) % 173.51/173.27 [3543]E(f333(f333(f87(a910),f333(a123,x35431)),x35432),f333(f333(f87(a910),x35431),f333(a123,x35432))) % 173.51/173.27 [3544]E(f333(f333(f23(a910),f333(a123,x35441)),f333(a123,x35442)),f333(f333(f23(a910),x35441),x35442)) % 173.51/173.27 [3550]E(f61(x35501,f2(a910),x35502),f333(f333(f159(f911(x35501)),f124(x35501)),f124(f911(x35501)))) % 173.51/173.27 [3551]E(f333(f41(a910),f311(a910,x35511,x35512)),f333(f333(f23(a910),x35512),x35511)) % 173.51/173.27 [3560]P40(x35601,f333(f333(f294(a910,x35601),a251),x35602)) % 173.51/173.27 [3562]P16(a910,f147(a910,f333(f308(a910,x35621),x35622))) % 173.51/173.27 [3564]P106(f333(f67(a910),f333(f308(a910,x35641),x35642))) % 173.51/173.27 [3565]P106(f333(f67(a1),f333(f308(a1,x35651),x35652))) % 173.51/173.27 [3568]E(f333(f293(f911(x35681),f911(x35681)),f165(x35681,x35682)),f165(x35681,f333(f293(x35681,x35681),x35682))) % 173.51/173.27 [3569]E(f333(f197(a907),f30(x35691,x35692)),f333(f333(f87(a910),f333(f197(a907),x35692)),f333(a123,f2(a910)))) % 173.51/173.27 [3571]E(f333(f308(a1,x35711),f333(f333(f87(a1),x35712),f85(a1))),f309(a1,x35711,x35712)) % 173.51/173.27 [3574]E(f333(f333(f42(a1),f333(f86(a1),x35741)),f333(f86(a1),x35742)),f333(f333(f42(a1),x35741),x35742)) % 173.51/173.27 [3582]E(f333(f333(f191(f916(x35821,x35821),a905),f85(a910)),x35822),x35822) % 173.51/173.27 [3584]E(f333(f333(f121(f917(x35841,a905)),x35842),f196(f917(x35841,a905))),x35842) % 173.51/173.27 [3585]E(f333(f333(f112(f917(x35851,a905)),x35852),f254(f917(x35851,a905))),x35852) % 173.51/173.27 [3586]E(f333(f333(f23(f917(x35861,a905)),x35862),f196(f917(x35861,a905))),x35862) % 173.51/173.27 [3587]E(f333(f264(a910,a910),f92(f916(a910,a910),f54(x35871,x35872))),f333(f333(f42(a910),x35871),x35872)) % 173.51/173.27 [3594]E(f309(a1,f333(f333(f87(a1),x35941),f85(a1)),x35942),f311(a1,x35941,x35942)) % 173.51/173.27 [3599]E(f333(f268(a910,a910),f92(f916(a910,a910),f54(x35991,x35992))),f51(a910,x35991,x35992)) % 173.51/173.27 [3609]P106(f333(f333(f335(x36091),x36092),f254(f917(x36091,a905)))) % 173.51/173.27 [3612]E(f333(f333(f23(a910),f333(a123,x36121)),x36122),f333(f41(a910),f309(a910,x36122,x36121))) % 173.51/173.27 [3637]E(f333(f333(f121(f917(x36371,a905)),x36372),f254(f917(x36371,a905))),f254(f917(x36371,a905))) % 173.51/173.27 [3638]E(f333(f333(f112(f917(x36381,a905)),x36382),f196(f917(x36381,a905))),f196(f917(x36381,a905))) % 173.51/173.27 [3639]E(f333(f333(f23(f917(x36391,a905)),x36392),f254(f917(x36391,a905))),f196(f917(x36391,a905))) % 173.51/173.27 [3654]E(f51(a1,f333(f86(a1),x36541),f333(f86(a1),x36542)),f333(f86(a1),f51(a1,x36541,x36542))) % 173.51/173.27 [3655]E(f51(a1,f333(f111(a1),x36551),f333(f111(a1),x36552)),f333(f111(a1),f51(a910,x36551,x36552))) % 173.51/173.27 [3666]E(f333(f197(f911(x36661)),f333(f179(x36661),x36662)),f333(f333(f23(a910),f333(f197(f911(x36661)),x36662)),f85(a910))) % 173.51/173.27 [3692]E(f333(f333(f42(a1),f51(a1,x36921,x36922)),x36922),f2(a1)) % 173.51/173.27 [3700]E(f333(a3,f51(a910,f333(a20,x37001),f333(a20,x37002))),f51(a110,x37001,x37002)) % 173.51/173.27 [3739]E(f333(a3,f333(f333(f23(a910),f333(a20,x37391)),f333(a20,x37392))),f333(f333(f23(a110),x37391),x37392)) % 173.51/173.27 [3740]E(f333(a3,f333(f333(f87(a910),f333(a20,x37401)),f333(a20,x37402))),f333(f333(f87(a110),x37401),x37402)) % 173.51/173.27 [3741]E(f333(a3,f333(f333(f88(a910),f333(a20,x37411)),f333(a20,x37412))),f333(f333(f88(a110),x37411),x37412)) % 173.51/173.27 [3742]E(f333(a3,f333(f333(f42(a910),f333(a20,x37421)),f333(a20,x37422))),f333(f333(f42(a110),x37421),x37422)) % 173.51/173.27 [3751]E(f333(f316(a910,a910,a123),f333(f308(a910,x37511),x37512)),f333(f308(a910,f333(a123,x37511)),f333(a123,x37512))) % 173.51/173.27 [3778]P106(f333(f54(x37781,x37782),f92(f916(a910,a910),f54(x37781,x37782)))) % 173.51/173.27 [3803]E(f333(f333(f87(a910),f333(f333(f87(a910),f29(x38031)),f29(x38032))),f333(a123,f2(a910))),f29(f31(x38031,x38032))) % 173.51/173.27 [3804]E(f51(a910,f333(a123,f51(a910,x38041,x38042)),x38042),f51(a910,f333(a123,x38041),x38042)) % 173.51/173.27 [3816]E(f333(f333(f46(f917(x38161,a905),f917(x38161,a905)),x38162),f5(f917(x38161,a905))),f44(f917(x38161,a905),x38162)) % 173.51/173.27 [3817]E(f333(f333(f45(f917(x38171,a905),f917(x38171,a905)),x38172),f5(f917(x38171,a905))),f43(f917(x38171,a905),x38172)) % 173.51/173.27 [3818]E(f333(f316(f911(x38181),f917(x38181,a905),f180(x38181)),f333(f180(f911(x38181)),f60(x38181,x38182))),f333(f314(x38181),f333(f180(x38181),x38182))) % 173.51/173.27 [3822]P106(f333(f333(f335(f917(x38221,a905)),x38222),f333(f314(x38221),x38222))) % 173.51/173.27 [3828]E(f51(a1,f333(f86(a1),f51(a1,x38281,x38282)),x38282),f51(a1,f333(f86(a1),x38281),x38282)) % 173.51/173.27 [3839]P106(f333(f333(f246(f917(x38391,a905)),x38392),f254(f917(x38391,a905)))) % 173.51/173.27 [3841]E(f333(f333(f295(x38411,x38411,x38411),f313(x38411,x38412)),f313(x38411,f313(x38411,x38412))),f313(x38411,x38412)) % 173.51/173.27 [3842]E(f333(f333(f121(f917(x38421,a905)),f333(f263(x38421,x38421),x38422)),f333(f291(x38421,x38421),x38422)),f333(f288(x38421),x38422)) % 173.51/173.27 [3863]E(f319(x38631,x38632,f254(f917(x38631,a905)),f254(f917(x38632,a905))),f254(f917(f918(x38631,x38632),a905))) % 173.51/173.27 [3913]P106(f333(f333(f246(a910),f51(a910,x39131,x39132)),x39131)) % 173.51/173.27 [3937]P106(f333(f333(f246(a1),f333(f86(a1),f333(f111(a1),x39371))),f333(f111(a1),x39372))) % 173.51/173.27 [3963]P106(f333(f333(f335(f917(x39631,a905)),f196(f917(x39631,a905))),f333(f314(x39631),x39632))) % 173.51/173.27 [3968]E(f313(x39681,f333(f333(f295(x39681,x39681,x39681),x39682),f313(x39681,x39682))),f313(x39681,x39682)) % 173.51/173.27 [3971]E(f333(f333(f295(x39711,x39711,x39711),f313(x39711,x39712)),x39712),f333(f333(f295(x39711,x39711,x39711),x39712),f313(x39711,x39712))) % 173.51/173.27 [3973]E(f333(a115,f333(f333(f87(a1),f333(f333(f23(a1),x39731),x39732)),f85(a1))),f333(f41(a1),f309(a1,x39732,x39731))) % 173.51/173.27 [3987]E(f333(f291(x39871,x39871),f333(f333(f295(x39871,x39871,x39871),x39872),f313(x39871,x39872))),f333(f291(x39871,x39871),x39872)) % 173.51/173.27 [3988]E(f333(f263(x39881,x39881),f333(f333(f295(x39881,x39881,x39881),x39882),f313(x39881,x39882))),f333(f263(x39881,x39881),x39882)) % 173.51/173.27 [4003]E(f333(f333(f87(a910),f333(f333(f87(a910),f333(f197(a907),x40031)),f333(f197(a907),x40032))),f333(a123,f2(a910))),f333(f197(a907),f31(x40031,x40032))) % 173.51/173.27 [4006]E(f333(f150(f911(x40061),f911(x40061),f142(x40061),f124(x40061)),f177(f911(x40061),x40062,f124(x40061))),f124(x40061)) % 173.51/173.27 [4015]P27(a910,a910,f333(f333(f7(a910,a910,a910),f87(a910)),x40151),x40152) % 173.51/173.27 [4017]P16(a910,f333(f176(a910),f333(f333(f162(f911(x40171),a910),f197(f911(x40171))),f187(x40171,x40172)))) % 173.51/173.27 [4050]P55(x40501,f333(f333(f121(f917(f916(x40501,x40501),a905)),x40502),f333(f293(x40501,x40501),x40502))) % 173.51/173.27 [4051]P55(x40511,f333(f333(f112(f917(f916(x40511,x40511),a905)),x40512),f333(f293(x40511,x40511),x40512))) % 173.51/173.27 [4062]P106(f333(f333(f247(a1),f333(f86(a1),f333(f111(a1),f333(a123,x40621)))),f333(f111(a1),x40622))) % 173.51/173.27 [4107]E(f333(f150(f911(x41071),x41071,f333(f7(x41071,f911(x41071),f911(x41071)),f159(x41071)),f124(x41071)),x41072),f333(f176(x41071),x41072)) % 173.51/173.27 [4157]P106(f333(f333(f246(f917(f916(f911(x41571),f911(x41571)),a905)),f166(x41571,x41572)),f313(f911(x41571),f165(x41571,x41572)))) % 173.51/173.27 [4186]P106(f333(f54(x41861,x41862),f333(f333(f265(a910,a910),f333(f333(f42(a910),x41861),x41862)),f51(a910,x41861,x41862)))) % 173.51/173.27 [4198]P106(f333(f333(f246(f917(f916(f911(x41981),f911(x41981)),a905)),f165(x41981,f313(x41981,x41982))),f313(f911(x41981),f165(x41981,x41982)))) % 173.51/173.27 [4414]E(f333(f333(f271(f916(a110,a110),a110,f916(a110,a110),f916(x44141,f916(a110,a110))),f276(f333(f173(a110),f333(f333(f162(f916(a110,x44141),a110),f264(a110,x44141)),x44142)))),f333(f333(f8(x44141,f917(f916(a110,a110),f916(x44141,f916(a110,a110))),a110),f265(x44141,f916(a110,a110))),f277(x44141,x44142))),f275(x44141,x44142)) % 173.51/173.27 [4491]E(f235(a910,f916(x44911,f912(x44911)),f2(a910),f333(f269(x44911,f912(x44911),a910),f333(f16(f917(f912(x44911),a910),x44911),f333(f333(f7(f912(x44911),a910,a910),f333(f333(f8(a910,f917(a910,a910),f912(x44911)),f87(a910)),f197(f912(x44911)))),f85(a910)))),f333(f143(x44911),x44912)),f333(f197(f912(x44911)),x44912)) % 173.51/173.27 [4600]E(f333(f269(f917(f916(x46001,x46001),a905),f917(f916(x46001,x46001),a905),f917(f917(x46002,x46001),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905)))),f333(f333(f7(f917(f916(x46001,x46001),a905),f917(f917(f916(x46001,x46001),a905),f917(f917(x46002,x46001),f917(f916(x46002,x46002),a905))),f917(f917(f916(x46001,x46001),a905),f917(f917(x46002,x46001),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905))))),f333(f333(f8(f917(f917(f917(x46002,x46001),f917(f916(x46002,x46002),a905)),f917(f917(x46002,x46001),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905)))),f917(f917(f917(f916(x46001,x46001),a905),f917(f917(x46002,x46001),f917(f916(x46002,x46002),a905))),f917(f917(f916(x46001,x46001),a905),f917(f917(x46002,x46001),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905))))),f917(f916(x46001,x46001),a905)),f8(f917(f917(x46002,x46001),f917(f916(x46002,x46002),a905)),f917(f917(x46002,x46001),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905))),f917(f916(x46001,x46001),a905))),f333(f333(f8(f917(f917(x46002,x46001),f917(f917(f916(x46002,x46002),a905),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905)))),f917(f917(f917(x46002,x46001),f917(f916(x46002,x46002),a905)),f917(f917(x46002,x46001),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905)))),f917(f916(x46001,x46001),a905)),f18(f917(x46002,x46001),f917(f916(x46002,x46002),a905),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905)))),f333(f333(f8(f917(f917(x46002,x46001),f917(f916(x46002,x46002),a905)),f917(f917(x46002,x46001),f917(f917(f916(x46002,x46002),a905),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905)))),f917(f916(x46001,x46001),a905)),f333(f8(f917(f916(x46002,x46002),a905),f917(f917(f916(x46002,x46002),a905),f916(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905))),f917(x46002,x46001)),f265(f917(f916(x46002,x46002),a905),f917(f916(x46002,x46002),a905)))),f294(x46001,x46002))))),f294(x46001,x46002))),f80(x46001,x46002)) % 173.51/173.27 [4681]~E(f333(f314(x46811),x46812),f196(f917(f917(x46811,a905),a905))) % 173.51/173.27 [4692]~P106(f333(f333(f180(x46921),f124(x46921)),x46922)) % 173.51/173.27 [4696]~P106(f333(f333(f335(x46961),x46962),f196(f917(x46961,a905)))) % 173.51/173.27 [4704]~P106(f333(f333(f247(f917(x47041,a905)),x47042),f196(f917(x47041,a905)))) % 173.51/173.27 [3522]E(f333(f333(f23(a910),x35221),f333(f333(f87(a910),x35221),x35222)),f2(a910)) % 173.51/173.27 [3525]E(f333(f333(f121(f917(x35251,a905)),x35252),x35252),x35252) % 173.51/173.27 [3526]E(f333(f333(f112(f917(x35261,a905)),x35262),x35262),x35262) % 173.51/173.27 [3554]E(f333(f333(f23(f917(x35541,a905)),x35542),x35542),f196(f917(x35541,a905))) % 173.51/173.27 [3557]E(f333(f151(x35571,x35572),f2(a910)),f196(f917(f916(f911(x35571),f911(x35571)),a905))) % 173.51/173.27 [3558]E(f333(f333(f87(a910),x35581),f333(a123,x35582)),f333(a123,f333(f333(f87(a910),x35581),x35582))) % 173.51/173.27 [3570]E(f203(f333(f111(a1),x35701),f333(f111(a1),x35702)),f333(f111(a1),f333(f333(f23(a910),x35701),x35702))) % 173.51/173.27 [3573]E(f333(f333(f42(a1),f333(f86(a1),x35731)),x35732),f333(f333(f42(a1),x35731),f333(f86(a1),x35732))) % 173.51/173.27 [3577]E(f333(f41(a1),f333(f308(a1,x35771),x35772)),f333(a115,f333(f333(f23(a1),x35772),x35771))) % 173.51/173.27 [3580]E(f333(f333(f87(a910),f333(a123,x35801)),x35802),f333(a123,f333(f333(f87(a910),x35801),x35802))) % 173.51/173.27 [3583]E(f333(f86(f917(x35831,a905)),f333(f86(f917(x35831,a905)),x35832)),x35832) % 173.51/173.27 [3596]E(f187(x35961,f333(f333(f159(f911(x35961)),f124(x35961)),x35962)),f187(x35961,x35962)) % 173.51/173.27 [3600]E(f333(f333(f87(a910),x36001),f333(f333(f88(a910),x36001),x36002)),f333(f333(f88(a910),x36001),f333(a123,x36002))) % 173.51/173.27 [3607]E(f333(f333(a24,f333(a3,x36071)),f333(a3,x36072)),f333(a3,f333(f333(f23(a910),x36071),x36072))) % 173.51/173.27 [3619]E(f333(f333(f88(a1),f333(f86(a1),x36191)),x36192),f333(f86(a1),f333(f333(f88(a1),x36191),x36192))) % 173.51/173.27 [3621]E(f333(f333(f256(a1),f333(f111(a1),x36211)),x36212),f333(f111(a1),f333(f333(f256(a910),x36211),x36212))) % 173.51/173.27 [3622]E(f333(f333(f87(a110),f333(a3,x36221)),f333(a3,x36222)),f333(a3,f333(f333(f87(a910),x36221),x36222))) % 173.51/173.27 [3623]E(f333(f333(f88(a110),f333(a3,x36231)),f333(a3,x36232)),f333(a3,f333(f333(f88(a910),x36231),x36232))) % 173.51/173.27 [3624]E(f333(f333(f244(a910),f333(a123,x36241)),f333(a123,x36242)),f333(a123,f333(f333(f244(a910),x36241),x36242))) % 173.51/173.27 [3625]E(f333(f333(f245(a910),f333(a123,x36251)),f333(a123,x36252)),f333(a123,f333(f333(f245(a910),x36251),x36252))) % 173.51/173.27 [3630]E(f333(f180(a910),f147(a910,f333(f308(a910,x36301),x36302))),f333(f308(a910,x36301),x36302)) % 173.51/173.27 [3631]E(f318(x36311,f333(f333(f315(x36311),x36312),f196(f917(x36311,a905)))),x36312) % 173.51/173.27 [3635]E(f333(f291(x36351,x36352),f196(f917(f916(x36351,x36352),a905))),f196(f917(x36352,a905))) % 173.51/173.27 [3636]E(f333(f263(x36361,x36362),f196(f917(f916(x36361,x36362),a905))),f196(f917(x36361,a905))) % 173.51/173.27 [3640]E(f333(a115,f333(f333(f23(a1),x36401),x36402)),f333(f41(a1),f311(a1,x36402,x36401))) % 173.51/173.27 [3645]E(f333(f333(f87(a910),x36451),f333(f333(f88(a910),x36452),x36451)),f333(f333(f88(a910),f333(a123,x36452)),x36451)) % 173.51/173.27 [3647]E(f333(f333(f66(x36471),f196(f917(x36471,a905))),x36472),f196(f917(f917(x36471,a905),a905))) % 173.51/173.27 [3656]E(f333(f197(f911(a910)),f147(a910,f333(f308(a910,x36561),x36562))),f333(f333(f23(a910),x36562),x36561)) % 173.51/173.27 [3671]E(f333(f333(f121(f917(x36711,a905)),f196(f917(x36711,a905))),x36712),x36712) % 173.51/173.27 [3672]E(f333(f333(f112(f917(x36721,a905)),f254(f917(x36721,a905))),x36722),x36722) % 173.51/173.27 [3673]E(f333(f333(f87(a1),f333(f86(a1),x36731)),f333(f86(a1),x36732)),f333(f86(a1),f333(f333(f87(a1),x36731),x36732))) % 173.51/173.27 [3678]E(f333(f333(f87(a1),f333(f111(a1),x36781)),f333(f111(a1),x36782)),f333(f111(a1),f333(f333(f87(a910),x36781),x36782))) % 173.51/173.27 [3679]E(f333(f333(f87(a1),f333(f114(a1),x36791)),f333(f114(a1),x36792)),f333(f114(a1),f333(f333(f87(a1),x36791),x36792))) % 173.51/173.27 [3681]E(f333(f333(f88(a1),f333(f111(a1),x36811)),f333(f111(a1),x36812)),f333(f111(a1),f333(f333(f88(a910),x36811),x36812))) % 173.51/173.27 [3682]E(f333(f333(f88(a1),f333(f114(a1),x36821)),f333(f114(a1),x36822)),f333(f114(a1),f333(f333(f88(a1),x36821),x36822))) % 173.51/173.27 [3683]E(f333(f333(f42(a1),f333(f111(a1),x36831)),f333(f111(a1),x36832)),f333(f111(a1),f333(f333(f42(a910),x36831),x36832))) % 173.51/173.27 [3701]E(f333(f333(f6(x37011,a910),f333(f16(a910,x37011),f85(a910))),x37012),f333(f41(x37011),x37012)) % 173.51/173.27 [3712]E(f333(f86(a1),f51(a1,f333(f86(a1),x37121),x37122)),f51(a1,x37121,f333(f86(a1),x37122))) % 173.51/173.27 [3714]E(f333(f180(a1),f186(x37141,f333(f333(f23(a1),x37142),f85(a1)))),f333(f308(a1,x37141),x37142)) % 173.51/173.27 [3718]P106(f333(f333(f246(a910),x37181),f333(f333(f87(a910),x37182),x37181))) % 173.51/173.27 [3719]P106(f333(f333(f246(a910),x37191),f333(f333(f87(a910),x37191),x37192))) % 173.51/173.27 [3722]E(f333(f333(f121(f917(x37221,a905)),f254(f917(x37221,a905))),x37222),f254(f917(x37221,a905))) % 173.51/173.27 [3723]E(f333(f333(f112(f917(x37231,a905)),f196(f917(x37231,a905))),x37232),f196(f917(x37231,a905))) % 173.51/173.27 [3724]E(f333(f333(f23(f917(x37241,a905)),f196(f917(x37241,a905))),x37242),f196(f917(x37241,a905))) % 173.51/173.27 [3731]E(f333(f333(f265(a1,a1),x37311),f333(f86(a1),x37312)),f333(a57,f333(f333(f265(a1,a1),x37311),x37312))) % 173.51/173.27 [3732]E(f333(f308(a1,f333(f333(f87(a1),x37321),f85(a1))),x37322),f312(a1,x37321,x37322)) % 173.51/173.27 [3743]E(f333(f333(f88(a910),x37431),f333(f333(f42(a910),x37432),x37431)),f333(f333(f23(a910),x37432),f51(a910,x37432,x37431))) % 173.51/173.27 [3744]E(f333(f333(f88(a1),x37441),f333(f333(f42(a1),x37442),x37441)),f333(f333(f23(a1),x37442),f51(a1,x37442,x37441))) % 173.51/173.27 [3748]E(f333(f180(a1),f186(f333(f333(f87(a1),x37481),f85(a1)),x37482)),f311(a1,x37481,x37482)) % 173.51/173.27 [3752]P106(f333(f333(f246(f917(x37521,a905)),x37522),x37522)) % 173.51/173.27 [3755]E(f333(f333(f121(f917(x37551,a905)),x37552),f333(f86(f917(x37551,a905)),x37552)),f254(f917(x37551,a905))) % 173.51/173.27 [3756]E(f333(f333(f112(f917(x37561,a905)),x37562),f333(f86(f917(x37561,a905)),x37562)),f196(f917(x37561,a905))) % 173.51/173.27 [3764]E(f333(f333(f23(a910),f333(f333(f23(a910),x37641),f85(a910))),x37642),f333(f333(f23(a910),x37641),f333(a123,x37642))) % 173.51/173.27 [3770]E(f333(f333(f23(f917(x37701,a905)),f254(f917(x37701,a905))),x37702),f333(f86(f917(x37701,a905)),x37702)) % 173.51/173.27 [3771]E(f333(f333(f23(a1),f333(f114(a1),x37711)),f333(f114(a1),x37712)),f333(f114(a1),f333(f333(f87(a1),x37711),f333(f86(a1),x37712)))) % 173.51/173.27 [3784]E(f333(f180(a910),f147(a910,f333(f308(a910,x37841),f333(a123,x37842)))),f309(a910,x37841,x37842)) % 173.51/173.27 [3792]P106(f333(f333(f333(f333(a204,a25),x37921),x37922),x37921)) % 173.51/173.27 [3801]E(f333(f197(f911(f911(x38011))),f60(x38011,x38012)),f333(f333(f256(a910),f333(a123,f333(a123,f2(a910)))),f333(f197(f911(x38011)),x38012))) % 173.51/173.27 [3820]E(f333(f333(f191(f916(x38201,x38201),a905),f2(a910)),x38202),f313(x38201,f196(f917(f916(x38201,x38201),a905)))) % 173.51/173.27 [3824]P106(f333(f145(a910),f147(a910,f333(f308(a910,x38241),x38242)))) % 173.51/173.27 [3840]E(f333(f316(a1,a910,a115),f309(a1,f333(f111(a1),x38401),f333(f111(a1),x38402))),f309(a910,x38401,x38402)) % 173.51/173.27 [3849]E(f193(a910,f2(a910),f5(a910),f333(f333(f23(a910),x38491),x38492)),f333(f333(f23(a910),x38491),f333(a123,x38492))) % 173.51/173.27 [3850]E(f333(a115,f333(f333(f23(a1),x38501),f333(f333(f87(a1),x38502),f85(a1)))),f333(f41(a1),f312(a1,x38502,x38501))) % 173.51/173.27 [3886]E(f333(f333(f162(a910,a910),a123),f147(a910,f333(f308(a910,x38861),x38862))),f147(a910,f333(f308(a910,f333(a123,x38861)),f333(a123,x38862)))) % 173.51/173.27 [3894]E(f333(f180(a1),f186(f333(f333(f87(a1),x38941),f85(a1)),f333(f333(f23(a1),x38942),f85(a1)))),f312(a1,x38941,x38942)) % 173.51/173.27 [3905]P106(f333(f333(f246(f917(x39051,a905)),f196(f917(x39051,a905))),x39052)) % 173.51/173.27 [3909]E(f92(x39091,f333(f333(f7(x39091,x39091,a905),a330),x39092)),x39092) % 173.51/173.27 [3910]E(f97(x39101,f333(f333(f7(x39101,x39101,a905),a330),x39102)),x39102) % 173.51/173.27 [3914]E(f333(f180(a910),f147(a910,f333(f308(a910,f333(a123,x39141)),f333(a123,x39142)))),f311(a910,x39141,x39142)) % 173.51/173.27 [3940]E(f333(f333(f267(x39401,x39402),f254(f917(x39401,a905))),f333(f16(f917(x39402,a905),x39401),f254(f917(x39402,a905)))),f254(f917(f916(x39401,x39402),a905))) % 173.51/173.27 [3975]E(f333(f252(x39751),f333(f333(f8(a905,a905,x39751),a328),x39752)),f333(f86(f917(x39751,a905)),f333(f252(x39751),x39752))) % 173.51/173.27 [3978]E(f333(f252(x39781),f333(f333(f7(x39781,x39781,a905),a330),x39782)),f333(f333(f315(x39781),x39782),f196(f917(x39781,a905)))) % 173.51/173.27 [3984]E(f333(f333(f87(a1),f333(f333(f23(a1),x39841),x39842)),f333(f333(f23(a1),x39841),x39842)),f333(f333(f23(a1),f333(f333(f87(a1),x39841),x39841)),f333(f333(f87(a1),x39842),x39842))) % 173.51/173.27 [3985]E(f333(f333(f87(a1),f333(f333(f87(a1),x39851),x39851)),f333(f333(f87(a1),x39852),x39852)),f333(f333(f87(a1),f333(f333(f87(a1),x39851),x39852)),f333(f333(f87(a1),x39851),x39852))) % 173.51/173.27 [4000]P106(f333(f333(f246(a910),f333(f41(x40001),f333(f180(x40001),x40002))),f333(f197(f911(x40001)),x40002))) % 173.51/173.27 [4001]P106(f333(f333(f246(a910),f333(f197(f911(x40011)),f160(x40011,x40012))),f333(f197(f911(x40011)),x40012))) % 173.51/173.27 [4012]E(f333(f252(x40121),f333(f333(f7(x40121,f917(x40121,a905),a905),f335(x40121)),x40122)),x40122) % 173.51/173.27 [4028]E(f333(f333(f183(x40281),f333(f333(f23(a910),f333(f197(f911(x40281)),x40282)),f85(a910))),x40282),f125(x40281,x40282)) % 173.51/173.27 [4049]E(f193(a910,f2(a910),f333(f333(f8(a910,a910,a910),a123),f333(f244(a910),x40491)),x40492),f333(f333(f244(a910),f333(a123,x40491)),x40492)) % 173.51/173.27 [4054]E(f43(f917(x40541,a905),f333(f316(f917(f916(x40541,x40541),a905),f917(x40541,a905),f288(x40541)),x40542)),f333(f288(x40541),f43(f917(f916(x40541,x40541),a905),x40542))) % 173.51/173.27 [4055]E(f193(a910,f333(a123,x40551),f333(f333(f8(a910,a910,a910),a123),f333(f245(a910),x40551)),x40552),f333(f333(f245(a910),f333(a123,x40551)),x40552)) % 173.51/173.27 [4057]E(f333(f333(f265(a1,a1),f333(f333(f42(a1),f333(f82(a1),x40571)),f333(f82(a1),x40572))),f51(a1,f333(f82(a1),x40571),f333(f82(a1),x40572))),f59(x40571,x40572)) % 173.51/173.27 [4079]P106(f333(f333(f246(f917(f917(x40791,a905),a905)),x40792),f333(f314(x40791),f43(f917(x40791,a905),x40792)))) % 173.51/173.27 [4112]E(f333(f333(f45(x41121,f917(x41121,a905)),x41122),f333(f333(f7(x41121,f917(x41121,a905),f917(x41121,a905)),f315(x41121)),f196(f917(x41121,a905)))),x41122) % 173.51/173.27 [4113]E(f333(f333(f295(x41131,x41131,x41131),f333(f293(x41131,x41131),x41132)),f313(x41131,f333(f293(x41131,x41131),x41132))),f333(f293(x41131,x41131),f333(f333(f295(x41131,x41131,x41131),x41132),f313(x41131,x41132)))) % 173.51/173.27 [4178]E(f333(f180(x41781),f333(f150(f911(x41781),f911(x41781),f142(x41781),f124(x41781)),x41782)),f333(f333(f45(f911(x41781),f917(x41781,a905)),f333(f180(f911(x41781)),x41782)),f180(x41781))) % 173.51/173.27 [4209]E(f333(f333(f121(f917(f916(x42091,x42091),a905)),f313(x42091,f196(f917(f916(x42091,x42091),a905)))),f333(f333(f295(x42091,x42091,x42091),f313(x42091,x42092)),x42092)),f313(x42091,x42092)) % 173.51/173.27 [4245]E(f333(f333(f189(x42451,x42451),x42452),x42452),f333(f333(f162(x42451,f916(x42451,x42451)),f333(f333(f18(x42451,x42451,f916(x42451,x42451)),f265(x42451,x42451)),f5(x42451))),x42452)) % 173.51/173.27 [4356]E(f333(f150(a910,f911(x43561),f333(f7(f911(x43561),a910,a910),f333(f333(f8(a910,f917(a910,a910),f911(x43561)),f245(a910)),f197(f911(x43561)))),f2(a910)),f333(f176(f911(x43561)),x43562)),f333(f197(f911(f911(x43561))),f187(x43561,x43562))) % 173.51/173.27 [4428]E(f333(f333(f294(f916(a910,f911(x44281)),f911(x44281)),f325(a910,f911(x44281),a251,f153(x44281,x44282))),f333(f333(f18(f911(x44281),f911(x44281),f916(a910,f911(x44281))),f333(f333(f8(a910,f917(f911(x44281),f916(a910,f911(x44281))),f911(x44281)),f265(a910,f911(x44281))),f197(f911(x44281)))),f5(f911(x44281)))),f154(x44281,x44282)) % 173.51/173.27 [4555]E(f333(f252(x45551),f333(f333(f8(f917(f917(x45551,a905),a905),a905,x45551),f95(f917(x45551,a905))),f333(f333(f8(f917(f917(x45551,a905),a905),f917(f917(x45551,a905),a905),x45551),f333(f18(f917(x45551,a905),a905,a905),f333(f333(f8(a905,f917(a905,a905),f917(x45551,a905)),a336),f333(f333(f7(f917(x45551,a905),f917(f917(x45551,a905),a905),a905),f335(f917(x45551,a905))),x45552)))),f335(x45551)))),f44(f917(x45551,a905),x45552)) % 173.51/173.27 [4556]E(f333(f252(x45561),f333(f333(f8(f917(f917(x45561,a905),a905),a905,x45561),f94(f917(x45561,a905))),f333(f333(f8(f917(f917(x45561,a905),a905),f917(f917(x45561,a905),a905),x45561),f333(f18(f917(x45561,a905),a905,a905),f333(f333(f8(a905,f917(a905,a905),f917(x45561,a905)),a331),f333(f333(f7(f917(x45561,a905),f917(f917(x45561,a905),a905),a905),f335(f917(x45561,a905))),x45562)))),f335(x45561)))),f43(f917(x45561,a905),x45562)) % 173.51/173.27 [4705]~P106(f333(f333(f247(a1),f333(f111(a1),x47051)),f333(f86(a1),f333(f111(a1),x47052)))) % 173.51/173.27 [3643]E(f333(f333(f23(a910),f333(f333(f87(a910),x36431),x36432)),x36432),x36431) % 173.51/173.27 [3644]E(f333(f333(f23(a910),f333(f333(f87(a910),x36441),x36442)),x36441),x36442) % 173.51/173.27 [3713]E(f333(f333(f87(a910),f333(f333(f23(a910),x37131),x37132)),x37132),f333(f333(f245(a910),x37131),x37132)) % 173.51/173.27 [3827]E(f333(f333(f88(a910),f333(f333(f42(a910),x38271),x38272)),x38272),f333(f333(f23(a910),x38271),f51(a910,x38271,x38272))) % 173.51/173.27 [3854]E(f333(f180(a910),f147(a910,f333(f308(a910,f333(a123,x38541)),x38542))),f312(a910,x38541,x38542)) % 173.51/173.27 [3862]E(f333(f111(a1),f228(f333(a115,f333(f82(a1),x38621)),f333(a115,f333(f82(a1),x38622)))),f333(f333(a229,x38621),x38622)) % 173.51/173.27 [3864]E(f333(f333(f121(f917(x38641,a905)),f333(f86(f917(x38641,a905)),x38642)),x38642),f254(f917(x38641,a905))) % 173.51/173.27 [3865]E(f333(f333(f112(f917(x38651,a905)),f333(f86(f917(x38651,a905)),x38652)),x38652),f196(f917(x38651,a905))) % 173.51/173.27 [3882]P106(f333(f333(f246(a910),f333(f333(f23(a910),x38821),x38822)),x38821)) % 173.51/173.27 [3883]P106(f333(f333(f246(a910),f333(f333(f42(a910),x38831),x38832)),x38831)) % 173.51/173.27 [3906]P106(f333(f333(f247(a910),x39061),f333(a123,f333(f333(f87(a910),x39062),x39061)))) % 173.51/173.27 [3907]P106(f333(f333(f247(a910),x39071),f333(a123,f333(f333(f87(a910),x39071),x39072)))) % 173.51/173.27 [3924]E(f333(f333(f88(a910),f333(a115,f333(f82(a1),x39241))),f333(a115,f333(f82(a1),x39242))),f333(a115,f333(f82(a1),f333(f333(f88(a1),x39241),x39242)))) % 173.51/173.27 [3936]P106(f333(f333(f246(a1),f2(a1)),f333(f333(f256(a1),f333(f82(a1),x39361)),x39362))) % 173.51/173.27 [4005]E(f333(f292(f911(x40051),f911(x40051),f166(x40051,x40052)),f333(f333(f315(f911(x40051)),f124(x40051)),f196(f917(f911(x40051),a905)))),f333(f333(f315(f911(x40051)),f124(x40051)),f196(f917(f911(x40051),a905)))) % 173.51/173.27 [4024]E(f333(f333(f121(f917(f916(x40241,x40241),a905)),f313(x40241,x40242)),f313(x40241,f196(f917(f916(x40241,x40241),a905)))),f313(x40241,x40242)) % 173.51/173.27 [4039]E(f333(f333(f42(a1),f333(f114(a1),f333(f333(f87(a1),x40391),x40391))),f333(f114(a1),f333(f333(f87(a1),x40392),x40392))),f333(f333(f42(a1),f333(f114(a1),x40391)),f333(f114(a1),x40392))) % 173.51/173.27 [4102]E(f333(f333(f256(a1),x41021),f333(f114(a910),f333(f333(f87(a1),x41022),x41022))),f333(f333(f93(a1,a1),f333(f333(f256(a1),x41021),f333(f114(a910),x41022))),f333(f333(f18(a1,a1,a1),f88(a1)),f5(a1)))) % 173.51/173.27 [4108]E(f333(f252(f917(x41081,a905)),f333(f333(f7(f917(x41081,a905),f917(x41081,a905),a905),f246(f917(x41081,a905))),x41082)),f333(f314(x41081),x41082)) % 173.51/173.27 [4123]E(f333(f333(f162(a1,a910),a115),f333(f333(f142(a1),f333(f333(f162(a910,a1),f111(a1)),x41231)),f333(f333(f162(a910,a1),f111(a1)),x41232))),f333(f333(f142(a910),x41231),x41232)) % 173.51/173.27 [4156]E(f333(f316(a1,a1,f333(f333(f7(a1,a1,a1),f87(a1)),x41561)),f333(f308(a1,f2(a1)),f333(f333(f23(a1),x41562),x41561))),f333(f308(a1,x41561),x41562)) % 173.51/173.27 [4158]P57(x41581,f333(f333(f23(f917(f916(x41581,x41581),a905)),x41582),f313(x41581,f196(f917(f916(x41581,x41581),a905))))) % 173.51/173.27 [4176]E(f333(f197(f911(x41761)),f333(f150(f911(x41761),f911(x41761),f142(x41761),f124(x41761)),x41762)),f333(f173(a910),f333(f333(f162(f911(x41761),a910),f197(f911(x41761))),x41762))) % 173.51/173.27 [4180]P56(x41801,f254(f917(x41801,a905)),f333(f333(f121(f917(f916(x41801,x41801),a905)),x41802),f313(x41801,f196(f917(f916(x41801,x41801),a905))))) % 173.51/173.27 [4225]E(f193(a910,f2(a910),f333(f333(f8(a910,a910,a910),a123),f333(f333(f7(a910,a910,a910),f244(a910)),x42251)),x42252),f333(f333(f244(a910),x42252),f333(a123,x42251))) % 173.51/173.27 [4228]E(f193(a910,f333(a123,x42281),f333(f333(f8(a910,a910,a910),a123),f333(f333(f7(a910,a910,a910),f245(a910)),x42281)),x42282),f333(f333(f245(a910),x42282),f333(a123,x42281))) % 173.51/173.27 [4231]E(f333(f316(x42311,f911(x42311),f333(f333(f7(x42311,f911(x42311),f911(x42311)),f159(x42311)),f124(x42311))),x42312),f182(x42311,x42312,f333(f333(f315(f911(x42311)),f124(x42311)),f196(f917(f911(x42311),a905))))) % 173.51/173.27 [4233]E(f333(f333(f121(f917(f916(x42331,x42331),a905)),f333(f333(f295(x42331,x42331,x42331),x42332),f313(x42331,x42332))),f313(x42331,f196(f917(f916(x42331,x42331),a905)))),f313(x42331,x42332)) % 173.51/173.27 [4240]P106(f333(f333(f246(f917(f916(x42401,x42401),a905)),f253(x42401,x42402)),f333(f333(f267(x42401,x42401),x42402),f333(f16(f917(x42401,a905),x42401),x42402)))) % 173.51/173.27 [4243]E(f333(f316(a1,a910,a115),f333(f333(f121(f917(a1,a905)),f333(f316(a910,a1,f111(a1)),x42431)),f333(f316(a910,a1,f111(a1)),x42432))),f333(f333(f121(f917(a910,a905)),x42431),x42432)) % 173.51/173.27 [4244]E(f333(f316(a1,a910,a115),f333(f333(f112(f917(a1,a905)),f333(f316(a910,a1,f111(a1)),x42441)),f333(f316(a910,a1,f111(a1)),x42442))),f333(f333(f112(f917(a910,a905)),x42441),x42442)) % 173.51/173.27 [4247]E(f333(f252(x42471),f333(f333(f8(a905,a905,x42471),a328),f333(f333(f7(x42471,f917(x42471,a905),a905),f335(x42471)),x42472))),f333(f86(f917(x42471,a905)),x42472)) % 173.51/173.27 [4274]E(f333(f150(f911(x42741),f911(x42741),f142(x42741),f124(x42741)),f333(f333(f162(f911(x42741),f911(x42741)),f176(x42741)),f333(f176(f911(x42741)),x42742))),f333(f176(x42741),f333(f150(f911(x42741),f911(x42741),f142(x42741),f124(x42741)),x42742))) % 173.51/173.27 [4301]E(f333(f333(f45(a910,f917(f916(x43011,x43011),a905)),f254(f917(a910,a905))),f333(f333(f7(a910,f917(f916(x43011,x43011),a905),f917(f916(x43011,x43011),a905)),f191(f916(x43011,x43011),a905)),x43012)),f313(x43011,x43012)) % 173.51/173.27 [4319]E(f92(x43191,f333(f333(f8(f917(x43191,a905),a905,x43191),f333(a330,x43192)),f333(f333(f7(x43191,f917(x43191,a905),f917(x43191,a905)),f315(x43191)),f196(f917(x43191,a905))))),f318(x43191,x43192)) % 173.51/173.27 [4327]E(f333(f197(f911(x43271)),f160(x43271,f333(f150(f911(x43271),f911(x43271),f142(x43271),f124(x43271)),x43272))),f333(f41(x43271),f333(f333(f45(f911(x43271),f917(x43271,a905)),f333(f180(f911(x43271)),x43272)),f180(x43271)))) % 173.51/173.27 [4341]E(f333(f333(f121(f917(f916(x43411,x43411),a905)),x43412),f333(f333(f295(x43411,x43411,x43411),f333(f333(f295(x43411,x43411,x43411),x43412),f313(x43411,x43412))),x43412)),f333(f333(f295(x43411,x43411,x43411),x43412),f313(x43411,x43412))) % 173.51/173.27 [4364]P106(f333(f333(f246(f917(f916(x43641,x43641),a905)),f333(f333(f295(x43641,x43641,x43641),x43642),f313(x43641,x43642))),f333(f333(f267(x43641,x43641),f333(f288(x43641),x43642)),f333(f16(f917(x43641,a905),x43641),f333(f288(x43641),x43642))))) % 173.51/173.27 [4405]E(f333(f252(f911(x44051)),f333(f333(f7(f911(x44051),f917(x44051,a905),a905),f333(f333(f8(f917(x44051,a905),f917(f917(x44051,a905),a905),f911(x44051)),f246(f917(x44051,a905))),f180(x44051))),x44052)),f169(x44051,x44052)) % 173.51/173.27 [4416]E(f333(f164(f911(x44161),x44161,f124(x44161),f333(f333(f8(f911(x44161),f917(f911(x44161),f911(x44161)),x44161),f333(f7(f911(x44161),f911(x44161),f911(x44161)),f142(x44161))),f333(f333(f7(x44161,f911(x44161),f911(x44161)),f159(x44161)),f124(x44161)))),x44162),f333(f175(x44161),x44162)) % 173.51/173.27 [4456]P27(f917(x44561,x44562),f917(f916(x44561,x44562),a905),f333(f333(f8(f917(f916(x44561,x44562),a905),f917(f916(x44561,x44562),a905),f917(x44561,x44562)),f252(f916(x44561,x44562))),f333(f333(f8(f917(x44561,f917(x44562,a905)),f917(f916(x44561,x44562),a905),f917(x44561,x44562)),f269(x44561,x44562,a905)),f333(f8(x44562,f917(x44562,a905),x44561),f333(f7(x44562,x44562,a905),a330)))),f254(f917(f917(x44561,x44562),a905))) % 173.51/173.27 [4461]E(f51(a1,f333(f114(a1),f333(f333(f87(a1),x44611),x44611)),f333(f114(a1),f333(f333(f87(a1),x44612),x44612))),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f51(a1,f333(f114(a1),x44611),f333(f114(a1),x44612)))) % 173.51/173.27 [4505]E(f333(f333(f45(x45051,f917(f916(x45051,x45051),a905)),x45052),f333(f333(f7(x45051,f917(f916(x45051,x45051),a905),f917(f916(x45051,x45051),a905)),f333(f333(f8(f916(x45051,x45051),f917(f917(f916(x45051,x45051),a905),f917(f916(x45051,x45051),a905)),x45051),f315(f916(x45051,x45051))),f333(f333(f18(x45051,x45051,f916(x45051,x45051)),f265(x45051,x45051)),f5(x45051)))),f196(f917(f916(x45051,x45051),a905)))),f253(x45051,x45052)) % 173.51/173.27 [4513]E(f214(x45131,f333(f333(f265(a1,a1),f333(f86(a1),f333(f333(f79(f916(a1,a1),a1,x45131,f264(a1,a1)),f224(x45131)),x45132))),f333(f333(f79(f916(a1,a1),a1,x45131,f268(a1,a1)),f224(x45131)),x45132))),f239(x45131,x45132)) % 173.51/173.27 [4596]E(f333(f252(f917(x45961,a905)),f333(f333(f8(f917(f917(x45961,a905),a905),a905,f917(x45961,a905)),f94(f917(x45961,a905))),f333(f333(f7(f917(x45961,a905),f917(f917(x45961,a905),a905),f917(f917(x45961,a905),a905)),f333(f333(f8(f917(f917(x45961,a905),f917(a905,a905)),f917(f917(f917(x45961,a905),a905),f917(f917(x45961,a905),a905)),f917(x45961,a905)),f18(f917(x45961,a905),a905,a905)),f333(f333(f8(f917(f917(x45961,a905),a905),f917(f917(x45961,a905),f917(a905,a905)),f917(x45961,a905)),f333(f8(a905,f917(a905,a905),f917(x45961,a905)),a331)),f333(f333(f7(f917(x45961,a905),f917(f917(x45961,a905),f917(x45961,a905)),f917(f917(x45961,a905),a905)),f333(f333(f8(f917(f917(x45961,a905),a905),f917(f917(f917(x45961,a905),f917(x45961,a905)),f917(f917(x45961,a905),a905)),f917(x45961,a905)),f8(f917(x45961,a905),a905,f917(x45961,a905))),a330)),f86(f917(x45961,a905)))))),f333(f333(f8(f917(f917(x45961,a905),a905),a905,f917(x45961,a905)),f333(f335(f917(x45961,a905)),x45962)),f314(x45961))))),f333(f314(x45961),f333(f86(f917(x45961,a905)),x45962))) % 173.51/173.27 [4703]~E(f333(f333(f87(a1),x47031),x47031),f333(f333(f23(a1),f333(f333(f87(a1),x47032),x47032)),a108)) % 173.51/173.27 [4707]~P106(f333(f333(f247(a910),f333(f333(f87(a910),x47071),x47072)),x47072)) % 173.51/173.27 [4708]~P106(f333(f333(f247(a910),f333(f333(f87(a910),x47081),x47082)),x47081)) % 173.51/173.27 [3941]E(f333(f333(f23(a910),x39411),f333(f333(f88(a910),f333(f333(f42(a910),x39411),x39412)),x39412)),f51(a910,x39411,x39412)) % 173.51/173.27 [3942]E(f333(f333(f23(a1),x39421),f333(f333(f88(a1),f333(f333(f42(a1),x39421),x39422)),x39422)),f51(a1,x39421,x39422)) % 173.51/173.27 [3976]E(f333(f333(f162(a910,x39761),f333(f172(x39761),x39762)),f147(a910,f333(f308(a910,f2(a910)),f333(f197(f911(x39761)),x39762)))),x39762) % 173.51/173.27 [4035]E(f333(f292(x40351,x40351,f313(x40351,f196(f917(f916(x40351,x40351),a905)))),x40352),x40352) % 173.51/173.27 [4161]E(f313(x41611,f333(f333(f121(f917(f916(x41611,x41611),a905)),x41612),f313(x41611,f196(f917(f916(x41611,x41611),a905))))),f313(x41611,x41612)) % 173.51/173.27 [4162]E(f313(x41621,f333(f333(f23(f917(f916(x41621,x41621),a905)),x41622),f313(x41621,f196(f917(f916(x41621,x41621),a905))))),f313(x41621,x41622)) % 173.51/173.27 [4212]E(f333(f333(f23(a1),f333(f333(f23(a1),f333(f333(f87(a1),x42121),x42121)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),x42122),x42122)),a108)),f333(f333(f87(a1),f333(f333(f23(a1),x42121),x42122)),f333(f333(f23(a1),x42121),x42122))) % 173.51/173.27 [4252]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f87(a1),x42521),x42522)),f333(f333(f87(a1),x42521),x42522))),a108),f333(f333(f87(a1),f333(f333(f87(a1),x42521),x42521)),f333(f333(f23(a1),f333(f333(f87(a1),x42522),x42522)),a108))) % 173.51/173.27 [4277]E(f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),x42771),x42771)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),x42772),x42772)),a108)),f333(f333(f87(a1),f333(f333(f87(a1),x42771),f333(f333(f23(a1),x42772),a108))),f333(f333(f87(a1),x42771),f333(f333(f23(a1),x42772),a108)))) % 173.51/173.27 [4288]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),x42881),x42882)),f333(f333(f23(a1),x42881),x42882))),a108),f333(f333(f23(a1),f333(f333(f23(a1),f333(f333(f87(a1),x42881),x42881)),a108)),f333(f333(f87(a1),x42882),x42882))) % 173.51/173.27 [4289]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f87(a1),x42891),x42892)),f333(f333(f87(a1),x42891),x42892))),a108),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),x42891),x42891)),a108)),f333(f333(f87(a1),x42892),x42892))) % 173.51/173.27 [4338]E(f333(f111(a1),f333(f333(f42(a910),f333(f333(f88(a910),f333(a115,f333(f82(a1),x43381))),f333(a115,f333(f82(a1),x43382)))),f228(f333(a115,f333(f82(a1),x43381)),f333(a115,f333(f82(a1),x43382))))),f230(x43381,x43382)) % 173.51/173.27 [4382]E(f333(f333(f271(f916(a110,a110),a110,f916(a110,a110),f916(x43821,f916(a110,a110))),f276(f333(a3,f333(f197(f911(x43821)),x43822)))),f333(f333(f8(x43821,f917(f916(a110,a110),f916(x43821,f916(a110,a110))),a110),f265(x43821,f916(a110,a110))),f333(f333(f8(a910,x43821,a110),f333(f172(x43821),x43822)),a20))),f282(x43821,x43822)) % 173.51/173.27 [4462]E(f333(f150(a910,f911(x44621),f333(f7(f911(x44621),a910,a910),f333(f333(f8(a910,f917(a910,a910),f911(x44621)),f245(a910)),f197(f911(x44621)))),f2(a910)),f333(f176(f911(x44621)),f187(x44621,x44622))),f333(f197(f911(f911(x44621))),f333(f144(f911(x44621),f333(f333(f8(a905,a905,f911(x44621)),a328),f333(f333(f7(f911(x44621),f911(x44621),a905),a330),f124(x44621)))),x44622))) % 173.51/173.27 [4468]E(f333(f333(f45(a910,f917(x44681,a905)),f254(f917(a910,a905))),f333(f333(f7(a910,f917(a910,f917(x44681,a905)),f917(x44681,a905)),f333(f333(f8(f917(a910,a905),f917(f917(a910,f917(x44681,a905)),f917(x44681,a905)),a910),f45(a910,f917(x44681,a905))),f308(a910,f2(a910)))),x44682)),f333(f333(f45(a910,f917(x44681,a905)),f254(f917(a910,a905))),x44682)) % 173.51/173.27 [4490]P106(f333(f67(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),x44901)),f333(f333(f7(a910,a910,a905),f247(a910)),x44902))))) % 173.51/173.27 [4605]E(f333(f252(f916(f911(x46051),f911(x46051))),f333(f269(f911(x46051),f911(x46051),a905),f333(f333(f18(f911(x46051),f917(f911(x46051),a905),f917(f911(x46051),a905)),f333(f333(f8(f917(f911(x46051),f917(a905,a905)),f917(f917(f911(x46051),a905),f917(f911(x46051),a905)),f911(x46051)),f18(f911(x46051),a905,a905)),f333(f333(f8(f917(f911(x46051),a905),f917(f911(x46051),f917(a905,a905)),f911(x46051)),f333(f8(a905,f917(a905,a905),f911(x46051)),a332)),f333(f333(f7(f911(x46051),f917(f911(x46051),a910),f917(f911(x46051),a905)),f333(f333(f8(f917(a910,a905),f917(f917(f911(x46051),a910),f917(f911(x46051),a905)),f911(x46051)),f8(a910,a905,f911(x46051))),f333(f333(f8(a910,f917(a910,a905),f911(x46051)),f247(a910)),f197(f911(x46051))))),f197(f911(x46051)))))),f333(f333(f18(f911(x46051),f917(f911(x46051),a905),f917(f911(x46051),a905)),f333(f333(f8(f917(f911(x46051),f917(a905,a905)),f917(f917(f911(x46051),a905),f917(f911(x46051),a905)),f911(x46051)),f18(f911(x46051),a905,a905)),f333(f333(f8(f917(f911(x46051),a905),f917(f911(x46051),f917(a905,a905)),f911(x46051)),f333(f8(a905,f917(a905,a905),f911(x46051)),a331)),f333(f333(f7(f911(x46051),f917(f911(x46051),a910),f917(f911(x46051),a905)),f333(f333(f8(f917(a910,a905),f917(f917(f911(x46051),a910),f917(f911(x46051),a905)),f911(x46051)),f8(a910,a905,f911(x46051))),f333(f333(f8(a910,f917(a910,a905),f911(x46051)),a330),f197(f911(x46051))))),f197(f911(x46051)))))),f333(f333(f7(f911(x46051),f917(f916(f911(x46051),f911(x46051)),a905),f917(f911(x46051),a905)),f333(f333(f8(f917(f911(x46051),f917(f917(f916(f911(x46051),f911(x46051)),a905),a905)),f917(f917(f916(f911(x46051),f911(x46051)),a905),f917(f911(x46051),a905)),f911(x46051)),f7(f911(x46051),f917(f916(f911(x46051),f911(x46051)),a905),a905)),f333(f333(f8(f917(f911(x46051),f916(f911(x46051),f911(x46051))),f917(f911(x46051),f917(f917(f916(f911(x46051),f911(x46051)),a905),a905)),f911(x46051)),f333(f8(f916(f911(x46051),f911(x46051)),f917(f917(f916(f911(x46051),f911(x46051)),a905),a905),f911(x46051)),f335(f916(f911(x46051),f911(x46051))))),f265(f911(x46051),f911(x46051))))),f153(x46051,x46052)))))),f154(x46051,x46052)) % 173.51/173.27 [4280]E(f333(f333(f87(a1),f333(f333(f87(a1),f333(f333(f88(a1),x42801),x42802)),f333(f333(f88(a1),x42801),x42802))),x42802),f333(f333(f88(a1),f333(f333(f23(a1),f333(f333(f87(a1),x42801),x42801)),a108)),x42802)) % 173.51/173.27 [4381]E(f333(a115,f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x43811),x43812)),f196(f917(f916(a910,a910),a905)))))),f333(f333(f23(a910),x43811),x43812)) % 173.51/173.27 [4385]E(f333(f333(f295(x43851,x43851,x43851),f333(f333(f121(f917(f916(x43851,x43851),a905)),x43852),f313(x43851,f196(f917(f916(x43851,x43851),a905))))),f313(x43851,f333(f333(f121(f917(f916(x43851,x43851),a905)),x43852),f313(x43851,f196(f917(f916(x43851,x43851),a905)))))),f313(x43851,x43852)) % 173.51/173.27 [4422]E(f277(x44221,f333(f144(f916(a110,x44221),f333(f269(a110,x44221,a905),f333(f333(f8(a905,f917(x44221,a905),a110),f16(a905,x44221)),f333(f247(a110),f2(a110))))),x44222)),f277(x44221,x44222)) % 173.51/173.27 [4423]E(f275(x44231,f333(f144(f916(a110,x44231),f333(f269(a110,x44231,a905),f333(f333(f8(a905,f917(x44231,a905),a110),f16(a905,x44231)),f333(f247(a110),f2(a110))))),x44232)),f275(x44231,x44232)) % 173.51/173.27 [4425]E(f333(f86(a1),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x44251),x44252)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x44252),x44251)),f196(f917(f916(a910,a910),a905)))))) % 173.51/173.27 [4481]E(f333(f333(f294(f911(a910),x44811),f153(a910,a251)),f333(f333(f7(x44811,f911(f917(x44811,a910)),f911(a910)),f333(f333(f8(f917(f917(x44811,a910),a910),f917(f911(f917(x44811,a910)),f911(a910)),x44811),f162(f917(x44811,a910),a910)),f333(f7(f917(x44811,a910),x44811,a910),f5(f917(x44811,a910))))),x44812)),f161(x44811,x44812)) % 173.51/173.27 [4502]E(f333(f333(f93(a1,a910),f333(f114(a1),f333(f333(f87(a1),x45021),a108))),f333(f333(f18(a1,a910,a910),f333(f333(f7(a1,a910,f917(a910,a910)),f333(f333(f8(a905,f917(a910,f917(a910,a910)),a1),f107(a910)),a201)),f2(a910))),f333(f333(f8(a910,a910,a1),a123),f333(f333(f8(a910,a910,a1),f333(f244(a910),x45022)),a115)))),f333(f333(f244(a910),f333(a123,x45022)),f333(f114(a910),x45021))) % 173.51/173.27 [4503]E(f333(f333(f93(a1,a910),f333(f114(a1),f333(f333(f87(a1),x45031),a108))),f333(f333(f18(a1,a910,a910),f333(f333(f7(a1,a910,f917(a910,a910)),f333(f333(f8(a905,f917(a910,f917(a910,a910)),a1),f107(a910)),a201)),f333(a123,x45032))),f333(f333(f8(a910,a910,a1),a123),f333(f333(f8(a910,a910,a1),f333(f245(a910),x45032)),a115)))),f333(f333(f245(a910),f333(a123,x45032)),f333(f114(a910),x45031))) % 173.51/173.27 [4523]E(f333(f150(f911(x45231),f911(x45231),f142(x45231),f124(x45231)),f333(f333(f162(f911(x45231),f911(x45231)),f164(f911(x45231),x45231,f124(x45231),f333(f333(f8(f911(x45231),f917(f911(x45231),f911(x45231)),x45231),f16(f911(x45231),f911(x45231))),f333(f333(f7(x45231,f911(x45231),f911(x45231)),f159(x45231)),f124(x45231))))),x45232)),f333(f333(f162(f911(x45231),x45231),f149(x45231)),f333(f144(f911(x45231),f333(f333(f8(a905,a905,f911(x45231)),a328),f333(f333(f7(f911(x45231),f911(x45231),a905),a330),f124(x45231)))),x45232))) % 173.51/173.27 [4585]E(f333(f269(a1,a1,a905),f333(f333(f7(a1,f917(a1,a905),f917(a1,a905)),f333(f333(f8(f917(a1,f917(a905,a905)),f917(f917(a1,a905),f917(a1,a905)),a1),f18(a1,a905,a905)),f333(f333(f8(f917(a1,a905),f917(a1,f917(a905,a905)),a1),f333(f8(a905,f917(a905,a905),a1),a331)),f333(f333(f8(f917(a1,a1),f917(a1,a905),a1),f333(f8(a1,a905,a1),f333(a330,x45851))),f333(f333(f8(a1,f917(a1,a1),a1),f87(a1)),f333(f88(a1),x45852)))))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),f333(a336,f333(f333(f247(a1),f2(a1)),x45852))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),f333(f333(f7(a1,a1,a905),f247(a1)),x45852))))),f333(f333(f8(a905,a905,a1),f333(a336,f333(a328,f333(f333(f247(a1),f2(a1)),x45852)))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f247(a1),x45852))),f333(f333(f7(a1,a1,a905),f246(a1)),f2(a1))))))),f55(x45851,x45852)) % 173.51/173.27 [4588]E(f333(f252(x45881),f333(f333(f8(f917(a910,a905),a905,x45881),f94(a910)),f333(f333(f7(x45881,f917(a910,a905),f917(a910,a905)),f333(f333(f8(f917(a910,f917(a905,a905)),f917(f917(a910,a905),f917(a910,a905)),x45881),f18(a910,a905,a905)),f333(f333(f8(f917(a910,a905),f917(a910,f917(a905,a905)),x45881),f333(f8(a905,f917(a905,a905),a910),a331)),f333(f333(f7(x45881,f917(a910,x45881),f917(a910,a905)),f333(f333(f8(f917(x45881,a905),f917(f917(a910,x45881),f917(a910,a905)),x45881),f8(x45881,a905,a910)),a330)),f333(f172(x45881),x45882))))),f333(f333(f7(a910,a910,a905),f247(a910)),f333(f197(f911(x45881)),x45882))))),f333(f180(x45881),x45882)) % 173.51/173.27 [4395]E(f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),x43951),a108)),x43952)),f333(f333(f23(a1),f333(f333(f87(a1),x43951),a108)),x43952))),a108),f333(f333(f23(a1),f333(f333(f87(a1),x43951),x43951)),f333(f333(f23(a1),f333(f333(f87(a1),x43952),x43952)),a108))) % 173.51/173.27 [4518]E(f333(f150(f911(f911(x45181)),f911(f911(x45181)),f142(f911(x45181)),f124(f911(x45181))),f333(f333(f162(f911(x45181),f911(f911(x45181))),f164(f911(f911(x45181)),x45181,f124(f911(x45181)),f333(f16(f917(f911(x45181),f911(f911(x45181))),x45181),f333(f333(f7(f911(x45181),f911(f911(x45181)),f911(f911(x45181))),f159(f911(x45181))),f124(f911(x45181)))))),x45182)),f333(f333(f162(f911(x45181),f911(x45181)),f179(x45181)),f333(f144(f911(x45181),f333(f333(f8(a905,a905,f911(x45181)),a328),f333(f333(f7(f911(x45181),f911(x45181),a905),a330),f124(x45181)))),x45182))) % 173.51/173.27 [4528]E(f333(f333(f93(a1,a910),f333(f114(a1),f333(f333(f87(a1),x45281),a108))),f333(f333(f18(a1,a910,a910),f333(f333(f7(a1,a910,f917(a910,a910)),f333(f333(f8(a905,f917(a910,f917(a910,a910)),a1),f107(a910)),a201)),f2(a910))),f333(f333(f8(a910,a910,a1),a123),f333(f333(f7(a1,a910,a910),f333(f333(f8(a910,f917(a910,a910),a1),f244(a910)),a115)),x45282)))),f333(f333(f244(a910),f333(f114(a910),x45281)),f333(a123,x45282))) % 173.51/173.27 [4529]E(f333(f333(f93(a1,a910),f333(f114(a1),f333(f333(f87(a1),x45291),a108))),f333(f333(f18(a1,a910,a910),f333(f333(f7(a1,a910,f917(a910,a910)),f333(f333(f8(a905,f917(a910,f917(a910,a910)),a1),f107(a910)),a201)),f333(a123,x45292))),f333(f333(f8(a910,a910,a1),a123),f333(f333(f7(a1,a910,a910),f333(f333(f8(a910,f917(a910,a910),a1),f245(a910)),a115)),x45292)))),f333(f333(f245(a910),f333(f114(a910),x45291)),f333(a123,x45292))) % 173.51/173.27 [4517]E(f333(f269(x45171,x45171,a905),f333(f333(f18(x45171,a905,f917(x45171,a905)),f333(f333(f8(f917(x45171,f917(a905,a905)),f917(a905,f917(x45171,a905)),x45171),f7(x45171,a905,a905)),f333(f333(f8(f917(x45171,a905),f917(x45171,f917(a905,a905)),x45171),f333(f8(a905,f917(a905,a905),x45171),a331)),a330))),x45172)),f253(x45171,x45172)) % 173.51/173.27 [4562]E(f333(f333(f42(a910),x45621),f333(f333(f87(a910),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),x45622)),f333(f333(f42(a910),x45621),f333(a123,f333(a123,f333(a123,x45622))))) % 173.51/173.27 [4563]E(f51(a910,x45631,f333(f333(f87(a910),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),x45632)),f51(a910,x45631,f333(a123,f333(a123,f333(a123,x45632))))) % 173.51/173.27 [4564]E(f51(a910,f333(f333(f87(a910),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),x45641),x45642),f51(a910,f333(a123,f333(a123,f333(a123,x45641))),x45642)) % 173.51/173.27 [4576]E(f133(f333(x45761,f333(f333(f88(a110),f333(f114(a110),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),x45762))),f333(f212(x45761),x45762)) % 173.51/173.27 [4577]E(f333(f333(f42(a910),f333(f333(f87(a910),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),x45771)),x45772),f333(f333(f42(a910),f333(a123,f333(a123,f333(a123,x45771)))),x45772)) % 173.51/173.27 [4651]~E(f28(x46511,x46512,x46513),a25) % 173.51/173.27 [4652]~E(f27(x46521,x46522,x46523),a25) % 173.51/173.27 [4656]~E(f136(x46561,x46562,x46563),f130(x46561)) % 173.51/173.27 [3370]E(f333(f200(x33701,x33702),x33703),f131(x33701,x33702)) % 173.51/173.27 [3389]E(f333(f211(x33891,x33892),x33893),f333(f138(x33891),x33892)) % 173.51/173.27 [3466]E(f333(f333(f162(x34661,x34662),x34663),f124(x34661)),f124(x34662)) % 173.51/173.27 [3506]E(f333(f192(x35061,x35062,x35063),f2(a910)),x35062) % 173.51/173.27 [3508]E(f333(f333(f189(x35081,x35082),x35083),f124(x35082)),f124(f916(x35081,x35082))) % 173.51/173.27 [3523]E(f333(f197(f911(x35231)),f177(x35231,x35232,x35233)),x35232) % 173.51/173.27 [3542]E(f92(x35421,f68(x35421,x35422,x35423)),f333(f69(x35421,x35422),x35423)) % 173.51/173.27 [3546]E(f255(x35461,x35462,f255(x35462,x35461,x35463)),x35463) % 173.51/173.27 [3566]E(f333(f176(x35661),f177(x35661,x35662,x35663)),f177(x35661,x35662,x35663)) % 173.51/173.27 [3593]E(f148(x35931,x35932,f160(x35931,x35933)),f160(x35931,f148(x35931,x35932,x35933))) % 173.51/173.27 [3610]E(f333(f264(f911(x36101),f911(x36101)),f174(x36101,x36102,x36103)),f333(f144(x36101,x36102),x36103)) % 173.51/173.27 [3652]E(f333(f333(f159(x36521),x36522),f177(x36521,x36523,x36522)),f177(x36521,f333(a123,x36523),x36522)) % 173.51/173.27 [3684]E(f193(x36841,x36842,x36843,f2(a910)),x36842) % 173.51/173.27 [3685]E(f17(x36851,x36852,x36853,f2(a110)),x36852) % 173.51/173.27 [3686]E(f19(x36861,x36862,x36863,f2(a110)),x36862) % 173.51/173.27 [3693]E(f171(x36931,x36932,x36933,f124(x36931)),f124(x36932)) % 173.51/173.27 [3699]E(f333(f333(f172(x36991),f333(f333(f159(x36991),x36992),x36993)),f2(a910)),x36992) % 173.51/173.27 [3733]E(f65(x37331,x37332,f124(x37331),x37333),f124(f916(x37331,x37332))) % 173.51/173.27 [3754]P27(x37541,x37542,x37543,f196(f917(x37541,a905))) % 173.51/173.27 [3858]E(f274(x38581,x38582,x38583),f333(f265(f917(a110,f917(a905,f914(f912(x38581)))),f916(a110,a110)),f47(x38581))) % 173.51/173.27 [3915]E(f333(f79(x39151,x39152,x39151,x39153),f33(x39151)),x39153) % 173.51/173.27 [4094]P106(f333(f333(f335(f916(x40941,x40941)),f333(f333(f265(x40941,x40941),x40942),x40942)),f313(x40941,x40943))) % 173.51/173.27 [4712]~P106(f333(f333(f335(f916(f911(x47121),f911(x47121))),f333(f333(f265(f911(x47121),f911(x47121)),x47122),f124(x47121))),f153(x47121,x47123))) % 173.51/173.27 [4713]~P106(f333(f333(f335(f916(f911(x47131),f911(x47131))),f333(f333(f265(f911(x47131),f911(x47131)),x47132),f124(x47131))),f155(x47131,x47133))) % 173.51/173.27 [4714]~P106(f333(f333(f335(f916(f911(x47141),f911(x47141))),f333(f333(f265(f911(x47141),f911(x47141)),x47142),f124(x47141))),f165(x47141,x47143))) % 173.51/173.27 [4715]~P106(f333(f333(f335(f916(f911(x47151),f911(x47151))),f333(f333(f265(f911(x47151),f911(x47151)),f124(x47151)),x47152)),f153(x47151,x47153))) % 173.51/173.27 [4716]~P106(f333(f333(f335(f916(f911(x47161),f911(x47161))),f333(f333(f265(f911(x47161),f911(x47161)),f124(x47161)),x47162)),f165(x47161,x47163))) % 173.51/173.27 [3440]E(f333(f333(f213(x34401),x34402),x34403),f214(x34401,f227(x34402,x34403))) % 173.51/173.27 [3495]E(f333(f293(x34951,x34952),f333(f293(x34952,x34951),x34953)),x34953) % 173.51/173.27 [3518]E(f333(f333(f189(x35181,x35182),f124(x35181)),x35183),f124(f916(x35181,x35182))) % 173.51/173.27 [3521]E(f184(x35211,x35212,f333(f289(a910),x35213)),f333(f333(f183(x35211),x35213),x35212)) % 173.51/173.27 [3539]E(f160(x35391,f333(f144(x35391,x35392),x35393)),f333(f144(x35391,x35392),f160(x35391,x35393))) % 173.51/173.27 [3540]E(f333(f291(x35401,x35402),f333(f293(x35402,x35401),x35403)),f333(f263(x35402,x35401),x35403)) % 173.51/173.27 [3541]E(f333(f263(x35411,x35412),f333(f293(x35412,x35411),x35413)),f333(f291(x35412,x35411),x35413)) % 173.51/173.27 [3559]E(f333(f144(x35591,x35592),f333(f176(x35591),x35593)),f333(f176(x35591),f333(f144(x35591,x35592),x35593))) % 173.51/173.27 [3572]E(f333(f333(f146(x35721),x35722),f333(f179(x35721),x35723)),f333(f333(f146(x35721),f333(a123,x35722)),x35723)) % 173.51/173.27 [3588]E(f29(f27(x35881,x35882,x35883)),f333(f333(f87(a910),f29(x35883)),f333(a123,f2(a910)))) % 173.51/173.27 [3589]E(f333(f316(x35891,x35892,x35893),f196(f917(x35891,a905))),f196(f917(x35892,a905))) % 173.51/173.27 [3590]E(f333(f317(x35901,x35902,x35903),f196(f917(x35902,a905))),f196(f917(x35901,a905))) % 173.51/173.27 [3591]E(f333(f317(x35911,x35912,x35913),f254(f917(x35912,a905))),f254(f917(x35911,a905))) % 173.51/173.27 [3592]E(f333(f292(x35921,x35922,x35923),f196(f917(x35921,a905))),f196(f917(x35922,a905))) % 173.51/173.27 [3617]E(f333(f333(f315(x36171),x36172),f333(f180(x36171),x36173)),f333(f180(x36171),f148(x36171,x36172,x36173))) % 173.51/173.27 [3703]E(f333(f197(a907),f27(x37031,x37032,x37033)),f333(f333(f87(a910),f333(f197(a907),x37033)),f333(a123,f2(a910)))) % 173.51/173.27 [3704]E(f333(f316(f916(x37041,x37042),x37042,f268(x37041,x37042)),x37043),f333(f291(x37041,x37042),x37043)) % 173.51/173.27 [3705]E(f333(f316(f916(x37051,x37052),x37051,f264(x37051,x37052)),x37053),f333(f263(x37051,x37052),x37053)) % 173.51/173.27 [3725]E(f333(f180(x37251),f177(x37251,f333(a123,x37252),x37253)),f333(f333(f315(x37251),x37253),f196(f917(x37251,a905)))) % 173.51/173.27 [3783]E(f333(f333(f265(x37831,x37832),f333(f264(x37831,x37832),x37833)),f333(f268(x37831,x37832),x37833)),x37833) % 173.51/173.27 [3790]E(f333(f197(f912(x37901)),f136(x37901,x37902,x37903)),f333(f333(f87(a910),f333(f197(f912(x37901)),x37903)),f333(a123,f2(a910)))) % 173.51/173.27 [3793]E(f333(f333(f269(x37931,x37932,x37931),f16(x37931,x37932)),x37933),f333(f264(x37931,x37932),x37933)) % 173.51/173.27 [3871]E(f29(f28(x38711,x38712,x38713)),f333(f333(f87(a910),f333(f333(f87(a910),f29(x38712)),f29(x38713))),f333(a123,f2(a910)))) % 173.51/173.27 [3920]E(f333(f79(x39201,x39201,x39202,f33(x39201)),x39203),x39203) % 173.51/173.27 [3927]E(f333(f333(f142(x39271),f177(x39271,x39272,x39273)),f333(f333(f159(x39271),x39273),f124(x39271))),f333(f333(f159(x39271),x39273),f177(x39271,x39272,x39273))) % 173.51/173.27 [4027]P106(f333(f333(f202(f26(x40271,x40272)),x40273),f333(f333(f333(a205,x40273),x40271),f333(x40272,x40273)))) % 173.51/173.27 [4029]E(f333(f197(a907),f28(x40291,x40292,x40293)),f333(f333(f87(a910),f333(f333(f87(a910),f333(f197(a907),x40292)),f333(f197(a907),x40293))),f333(a123,f2(a910)))) % 173.51/173.27 [4103]P106(f333(f333(f246(f917(x41031,a905)),f333(f180(x41031),f333(f144(x41031,x41032),x41033))),f333(f180(x41031),x41033))) % 173.51/173.27 [4147]P106(f333(f333(f246(f917(x41471,a905)),f333(f180(x41471),f333(f333(f183(x41471),x41472),x41473))),f333(f180(x41471),x41473))) % 173.51/173.27 [4148]P106(f333(f333(f246(f917(x41481,a905)),f333(f180(x41481),f333(f333(f146(x41481),x41482),x41483))),f333(f180(x41481),x41483))) % 173.51/173.27 [4152]P106(f333(f333(f246(f917(x41521,a905)),f333(f180(x41521),f184(x41521,x41522,x41523))),f333(f180(x41521),x41522))) % 173.51/173.27 [4153]P106(f333(f333(f246(f917(x41531,a905)),f333(f180(x41531),f178(x41531,x41532,x41533))),f333(f180(x41531),x41533))) % 173.51/173.27 [4174]P27(f916(x41741,x41742),f916(x41742,x41741),f333(f269(x41741,x41742,f916(x41742,x41741)),f333(f7(x41742,x41741,f916(x41742,x41741)),f265(x41742,x41741))),x41743) % 173.51/173.27 [4185]E(f333(f333(f333(f191(f911(x41851),f911(x41851)),f51(a910,x41852,f333(f197(f911(x41851)),x41853))),f175(x41851)),x41853),f333(f333(f333(f191(f911(x41851),f911(x41851)),x41852),f175(x41851)),x41853)) % 173.51/173.27 [4229]P106(f333(f333(f335(f916(f911(x42291),f911(x42291))),f333(f333(f265(f911(x42291),f911(x42291)),x42292),x42292)),f166(x42291,f313(x42291,x42293)))) % 173.51/173.27 [4368]E(f92(f916(x43681,x43682),f333(f333(f18(f916(x43681,x43682),x43682,a905),f333(f333(f8(x43681,f917(x43682,a905),f916(x43681,x43682)),x43683),f264(x43681,x43682))),f268(x43681,x43682))),f92(f916(x43681,x43682),f333(f269(x43681,x43682,a905),x43683))) % 173.51/173.27 [4369]E(f97(f916(x43691,x43692),f333(f333(f18(f916(x43691,x43692),x43692,a905),f333(f333(f8(x43691,f917(x43692,a905),f916(x43691,x43692)),x43693),f264(x43691,x43692))),f268(x43691,x43692))),f97(f916(x43691,x43692),f333(f269(x43691,x43692,a905),x43693))) % 173.51/173.27 [4402]E(f333(f333(f294(f916(a910,x44021),x44021),f325(a910,x44021,a251,x44022)),f333(f333(f18(x44021,x44021,f916(a910,x44021)),f333(f333(f8(a910,f917(x44021,f916(a910,x44021)),x44021),f265(a910,x44021)),x44023)),f5(x44021))),f327(x44021,x44023,x44022)) % 173.51/173.27 [4464]E(f333(f270(x44641,x44641,x44642,x44642,f5(x44641),f5(x44642)),x44643),x44643) % 173.51/173.27 [4537]E(f333(f150(f911(f911(x45371)),f911(f911(x45371)),f142(f911(x45371)),f124(f911(x45371))),f333(f333(f162(f911(x45371),f911(f911(x45371))),f333(f333(f7(f911(x45371),f911(x45371),f911(f911(x45371))),f333(f333(f8(f917(x45371,f911(x45371)),f917(f911(x45371),f911(f911(x45371))),f911(x45371)),f162(x45371,f911(x45371))),f333(f7(x45371,f911(x45371),f911(x45371)),f159(x45371)))),x45372)),f61(x45371,x45373,x45372))),f61(x45371,f333(a123,x45373),x45372)) % 173.51/173.27 [4595]E(f235(a910,f916(x45951,f912(x45951)),f2(a910),f333(f269(x45951,f912(x45951),a910),f333(f333(f7(x45951,a910,f917(f912(x45951),a910)),f333(f333(f8(f917(f912(x45951),f917(a910,a910)),f917(a910,f917(f912(x45951),a910)),x45951),f7(f912(x45951),a910,a910)),f333(f333(f8(f917(f912(x45951),a910),f917(f912(x45951),f917(a910,a910)),x45951),f333(f8(a910,f917(a910,a910),f912(x45951)),f87(a910))),f333(f333(f7(x45951,f917(f912(x45951),a910),f917(f912(x45951),a910)),f333(f333(f8(f917(a910,a910),f917(f917(f912(x45951),a910),f917(f912(x45951),a910)),x45951),f8(a910,a910,f912(x45951))),f333(f333(f8(a910,f917(a910,a910),x45951),f87(a910)),x45952))),f135(x45951,x45952))))),f85(a910))),f333(f143(x45951),x45953)),f333(f135(x45951,x45952),x45953)) % 173.51/173.27 [4604]E(f333(f333(f93(a1,x46041),f230(f333(f333(f79(f916(a1,a1),a1,x46041,f268(a1,a1)),f224(x46041)),x46042),f333(f333(f79(f916(a1,a1),a1,x46041,f268(a1,a1)),f224(x46041)),x46043))),f333(f333(f18(a1,a1,x46041),f333(f333(f8(a1,f917(a1,x46041),a1),f213(x46041)),f333(f333(f18(a1,a1,a1),f333(f333(f8(a1,f917(a1,a1),a1),f87(a1)),f333(f333(f8(a1,a1,a1),f333(f88(a1),f333(f333(f79(f916(a1,a1),a1,x46041,f264(a1,a1)),f224(x46041)),x46042))),f333(f333(f7(a1,a1,a1),f42(a1)),f333(f333(f79(f916(a1,a1),a1,x46041,f268(a1,a1)),f224(x46041)),x46042))))),f333(f333(f8(a1,a1,a1),f333(f88(a1),f333(f333(f79(f916(a1,a1),a1,x46041,f264(a1,a1)),f224(x46041)),x46043))),f333(f333(f7(a1,a1,a1),f42(a1)),f333(f333(f79(f916(a1,a1),a1,x46041,f268(a1,a1)),f224(x46041)),x46043)))))),f5(a1))),f242(x46041,x46042,x46043)) % 173.51/173.27 [4647]~E(f333(f333(f159(x46471),x46472),x46473),x46473) % 173.51/173.27 [4654]~E(f333(f333(f159(x46541),x46542),x46543),f124(x46541)) % 173.51/173.27 [4672]~E(f333(f333(f315(x46721),x46722),x46723),f196(f917(x46721,a905))) % 173.51/173.27 [4694]~E(f333(f316(x46941,f917(x46941,a905),x46942),x46943),f333(f314(x46941),x46943)) % 173.51/173.27 [3500]E(f333(f333(f167(x35001,f124(x35001)),x35002),x35003),f124(x35001)) % 173.51/173.27 [3501]E(f333(f149(x35011),f333(f333(f159(x35011),x35012),x35013)),x35012) % 173.51/173.27 [3502]E(f333(f179(x35021),f333(f333(f159(x35021),x35022),x35023)),x35023) % 173.51/173.27 [3545]E(f333(f333(f146(x35451),f85(a910)),f333(f333(f159(x35451),x35452),x35453)),x35453) % 173.51/173.27 [3579]E(f125(x35791,f333(f333(f146(x35791),x35792),x35793)),f333(f333(f146(x35791),x35792),f125(x35791,x35793))) % 173.51/173.27 [3581]E(f333(f333(f167(x35811,x35812),x35813),f333(f333(f172(x35811),x35812),x35813)),x35812) % 173.51/173.27 [3602]E(f333(f333(f315(x36021),x36022),f333(f333(f315(x36021),x36022),x36023)),f333(f333(f315(x36021),x36022),x36023)) % 173.51/173.27 [3613]E(f333(f333(f315(x36131),x36132),f333(f180(x36131),x36133)),f333(f180(x36131),f333(f333(f159(x36131),x36132),x36133))) % 173.51/173.27 [3615]E(f333(f333(f146(x36151),x36152),f333(f179(x36151),x36153)),f333(f179(x36151),f333(f333(f146(x36151),x36152),x36153))) % 173.51/173.27 [3626]E(f333(f333(f183(x36261),f85(a910)),f333(f333(f159(x36261),x36262),x36263)),f333(f333(f159(x36261),x36262),f124(x36261))) % 173.51/173.27 [3669]E(f333(f69(x36691,x36692),f333(f333(f315(x36691),x36693),f196(f917(x36691,a905)))),x36693) % 173.51/173.27 [3715]E(f333(f333(f87(a910),x37151),f333(f333(f87(a910),x37152),x37153)),f333(f333(f87(a910),x37152),f333(f333(f87(a910),x37151),x37153))) % 173.51/173.27 [3716]E(f333(f333(f87(a1),x37161),f333(f333(f87(a1),x37162),x37163)),f333(f333(f87(a1),x37162),f333(f333(f87(a1),x37161),x37163))) % 173.51/173.27 [3721]E(f333(f333(f267(x37211,x37212),f196(f917(x37211,a905))),x37213),f196(f917(f916(x37211,x37212),a905))) % 173.51/173.27 [3746]E(f333(f333(f121(f917(x37461,a905)),x37462),x37463),f333(f333(f121(f917(x37461,a905)),x37463),x37462)) % 173.51/173.27 [3747]E(f333(f333(f112(f917(x37471,a905)),x37472),x37473),f333(f333(f112(f917(x37471,a905)),x37473),x37472)) % 173.51/173.27 [3749]E(f333(f333(f142(x37491),x37492),f333(f333(f159(x37491),x37493),f124(x37491))),f333(f175(x37491),f333(f333(f159(x37491),x37493),x37492))) % 173.51/173.27 [3750]E(f333(f333(f142(x37501),f333(f176(x37501),x37502)),f333(f176(x37501),x37503)),f333(f176(x37501),f333(f333(f142(x37501),x37503),x37502))) % 173.51/173.27 [3760]E(f333(f179(x37601),f333(f333(f183(x37601),f333(a123,x37602)),x37603)),f333(f333(f183(x37601),x37602),f333(f179(x37601),x37603))) % 173.51/173.27 [3768]P106(f333(f333(f335(x37681),x37682),f333(f333(f315(x37681),x37682),x37683))) % 173.51/173.27 [3772]E(f333(f333(f46(x37721,f917(x37722,a905)),f196(f917(x37721,a905))),x37723),f254(f917(x37722,a905))) % 173.51/173.27 [3775]E(f333(f292(x37751,x37751,f253(x37751,x37752)),x37753),f333(f333(f112(f917(x37751,a905)),x37752),x37753)) % 173.51/173.27 [3789]E(f333(f197(f911(x37891)),f333(f333(f159(x37891),x37892),x37893)),f333(f333(f87(a910),f333(f197(f911(x37891)),x37893)),f333(a123,f2(a910)))) % 173.51/173.27 [3795]E(f125(x37951,f333(f333(f142(x37951),x37952),f333(f333(f159(x37951),x37953),f124(x37951)))),x37952) % 173.51/173.27 [3796]E(f152(x37961,f333(f333(f142(x37961),x37962),f333(f333(f159(x37961),x37963),f124(x37961)))),x37963) % 173.51/173.27 [3805]E(f333(f333(f142(x38051),f333(f333(f183(x38051),x38052),x38053)),f333(f333(f146(x38051),x38052),x38053)),x38053) % 173.51/173.27 [3814]E(f333(f333(f23(a910),f333(f333(f87(a910),x38141),x38142)),f333(f333(f87(a910),x38143),x38142)),f333(f333(f23(a910),x38141),x38143)) % 173.51/173.27 [3815]E(f333(f333(f23(a910),f333(f333(f87(a910),x38151),x38152)),f333(f333(f87(a910),x38151),x38153)),f333(f333(f23(a910),x38152),x38153)) % 173.51/173.27 [3821]E(f333(f333(f142(x38211),f333(f176(x38211),x38212)),f333(f333(f159(x38211),x38213),f124(x38211))),f333(f176(x38211),f333(f333(f159(x38211),x38213),x38212))) % 173.51/173.27 [3823]E(f333(f333(f87(a910),f333(f197(f911(x38231)),x38232)),f333(f197(f911(x38231)),x38233)),f333(f197(f911(x38231)),f333(f333(f142(x38231),x38232),x38233))) % 173.51/173.27 [3826]E(f333(f333(f87(a910),f333(f197(f911(x38261)),x38262)),f333(f197(f911(x38261)),x38263)),f333(f197(f911(x38261)),f181(x38261,x38262,x38263))) % 173.51/173.27 [3833]E(f333(f333(f121(f917(x38331,a905)),f333(f180(x38331),x38332)),f333(f180(x38331),x38333)),f333(f180(x38331),f333(f333(f142(x38331),x38332),x38333))) % 173.51/173.27 [3834]E(f51(a910,f333(f333(f88(a910),x38341),x38342),f333(f333(f88(a910),x38341),x38343)),f333(f333(f88(a910),x38341),f51(a910,x38342,x38343))) % 173.51/173.27 [3846]E(f333(f333(f183(x38461),f333(f333(f23(a910),x38462),f85(a910))),f333(f179(x38461),x38463)),f333(f179(x38461),f333(f333(f183(x38461),x38462),x38463))) % 173.51/173.27 [3851]E(f333(f333(f112(f917(x38511,a905)),x38512),f333(f86(f917(x38511,a905)),x38513)),f333(f333(f23(f917(x38511,a905)),x38512),x38513)) % 173.51/173.27 [3852]E(f333(f333(f23(f917(x38521,a905)),x38522),f333(f86(f917(x38521,a905)),x38523)),f333(f333(f112(f917(x38521,a905)),x38522),x38523)) % 173.51/173.27 [3875]E(f333(f333(f267(x38751,x38752),x38753),f333(f16(f917(x38752,a905),x38751),f196(f917(x38752,a905)))),f196(f917(f916(x38751,x38752),a905))) % 173.51/173.27 [3877]E(f333(f333(f23(a910),f333(f333(f88(a910),x38771),x38772)),f333(f333(f88(a910),x38771),x38773)),f333(f333(f88(a910),x38771),f333(f333(f23(a910),x38772),x38773))) % 173.51/173.27 [3878]E(f333(f333(f87(a910),f333(f333(f88(a910),x38781),x38782)),f333(f333(f88(a910),x38781),x38783)),f333(f333(f88(a910),x38781),f333(f333(f87(a910),x38782),x38783))) % 173.51/173.27 [3879]E(f333(f333(f23(a1),f333(f333(f88(a1),x38791),x38792)),f333(f333(f88(a1),x38791),x38793)),f333(f333(f88(a1),x38791),f333(f333(f23(a1),x38792),x38793))) % 173.51/173.27 [3880]E(f333(f333(f87(a1),f333(f333(f88(a1),x38801),x38802)),f333(f333(f88(a1),x38801),x38803)),f333(f333(f88(a1),x38801),f333(f333(f87(a1),x38802),x38803))) % 173.51/173.27 [3881]E(f333(f333(f88(a1),f333(f333(f256(a1),x38811),x38812)),f333(f333(f256(a1),x38811),x38813)),f333(f333(f256(a1),x38811),f333(f333(f87(a910),x38812),x38813))) % 173.51/173.27 [3895]E(f333(f333(f45(x38951,f917(x38952,a905)),x38953),f333(f16(f917(x38952,a905),x38951),f196(f917(x38952,a905)))),f196(f917(x38952,a905))) % 173.51/173.27 [3897]E(f51(a910,f333(f333(f88(a910),x38971),x38972),f333(f333(f88(a910),x38973),x38972)),f333(f333(f88(a910),f51(a910,x38971,x38973)),x38972)) % 173.51/173.27 [3901]E(f51(a1,f333(f333(f23(a1),x39011),f51(a1,x39012,x39013)),x39013),f51(a1,f333(f333(f23(a1),x39011),x39012),x39013)) % 173.51/173.27 [3902]E(f51(a1,f333(f333(f88(a1),x39021),f51(a1,x39022,x39023)),x39023),f51(a1,f333(f333(f88(a1),x39021),x39022),x39023)) % 173.51/173.27 [3903]P106(f333(f333(f246(f917(x39031,a905)),x39032),f333(f333(f315(x39031),x39033),x39032))) % 173.51/173.27 [3979]E(f333(f333(f46(f917(x39791,a905),f917(x39791,a905)),x39792),f333(f121(f917(x39791,a905)),x39793)),f333(f333(f121(f917(x39791,a905)),x39793),f44(f917(x39791,a905),x39792))) % 173.51/173.27 [3980]E(f333(f333(f45(f917(x39801,a905),f917(x39801,a905)),x39802),f333(f112(f917(x39801,a905)),x39803)),f333(f333(f112(f917(x39801,a905)),x39803),f43(f917(x39801,a905),x39802))) % 173.51/173.27 [3991]E(f333(f180(x39911),f333(f333(f333(f191(f911(x39911),f911(x39911)),x39912),f175(x39911)),x39913)),f333(f180(x39911),x39913)) % 173.51/173.27 [3995]E(f333(f333(f183(x39951),f333(f197(f911(x39951)),f185(x39951,x39952,x39953))),x39953),f185(x39951,x39952,x39953)) % 173.51/173.27 [3999]E(f333(f197(f911(x39991)),f333(f333(f333(f191(f911(x39991),f911(x39991)),x39992),f175(x39991)),x39993)),f333(f197(f911(x39991)),x39993)) % 173.51/173.27 [4002]E(f333(f333(f269(x40021,x40022,x40022),f333(f16(f917(x40022,x40022),x40021),f5(x40022))),x40023),f333(f268(x40021,x40022),x40023)) % 173.51/173.27 [4009]E(f51(a1,f333(f333(f23(a1),f51(a1,x40091,x40092)),x40093),x40092),f51(a1,f333(f333(f23(a1),x40091),x40093),x40092)) % 173.51/173.27 [4010]E(f51(a1,f333(f333(f256(a1),f51(a1,x40101,x40102)),x40103),x40102),f51(a1,f333(f333(f256(a1),x40101),x40103),x40102)) % 173.51/173.27 [4013]E(f333(f333(f45(f917(f916(x40131,x40132),a905),f917(x40132,a905)),x40133),f291(x40131,x40132)),f333(f291(x40131,x40132),f43(f917(f916(x40131,x40132),a905),x40133))) % 173.51/173.27 [4014]E(f333(f333(f45(f917(f916(x40141,x40142),a905),f917(x40141,a905)),x40143),f263(x40141,x40142)),f333(f263(x40141,x40142),f43(f917(f916(x40141,x40142),a905),x40143))) % 173.51/173.27 [4040]E(f333(f79(x40401,x40401,x40401,x40402),f333(f333(f191(x40401,x40401),x40403),x40402)),f333(f333(f191(x40401,x40401),f333(a123,x40403)),x40402)) % 173.51/173.27 [4058]E(f333(f333(f146(x40581),f333(f333(f23(a910),f333(f197(f911(x40581)),x40582)),x40583)),f333(f176(x40581),x40582)),f333(f176(x40581),f333(f333(f183(x40581),x40583),x40582))) % 173.51/173.27 [4059]E(f333(f333(f183(x40591),f333(f333(f23(a910),f333(f197(f911(x40591)),x40592)),x40593)),f333(f176(x40591),x40592)),f333(f176(x40591),f333(f333(f146(x40591),x40593),x40592))) % 173.51/173.27 [4061]E(f333(f333(f87(a910),f333(f173(a910),f333(f333(f162(x40611,a910),x40612),x40613))),f333(f197(f911(x40611)),x40613)),f163(x40611,x40612,x40613)) % 173.51/173.27 [4080]E(f333(f175(x40801),f333(f333(f333(f191(f911(x40801),f911(x40801)),x40802),f175(x40801)),x40803)),f333(f333(f333(f191(f911(x40801),f911(x40801)),f333(a123,x40802)),f175(x40801)),x40803)) % 173.51/173.27 [4095]P106(f333(f333(f246(a910),f333(f197(f911(x40951)),f333(f144(x40951,x40952),x40953))),f333(f197(f911(x40951)),x40953))) % 173.51/173.27 [4111]E(f333(f333(f121(f917(f917(x41111,a905),a905)),f333(f314(x41111),x41112)),f333(f316(f917(x41111,a905),f917(x41111,a905),f333(f315(x41111),x41113)),f333(f314(x41111),x41112))),f333(f314(x41111),f333(f333(f315(x41111),x41113),x41112))) % 173.51/173.27 [4129]P26(x41291,x41292,f333(f333(f315(f909(x41291)),f333(f333(f333(f98(x41291),x41293),a25),x41293)),f196(f917(f909(x41291),a905)))) % 173.51/173.27 [4144]P106(f333(f333(f246(a910),f333(f197(f911(x41441)),f185(x41441,x41442,x41443))),f333(f197(f911(x41441)),x41443))) % 173.51/173.27 [4151]E(f333(f263(x41511,x41512),f333(f252(f916(x41511,x41512)),f333(f269(x41511,x41512,a905),x41513))),f333(f252(x41511),f333(f333(f8(f917(x41512,a905),a905,x41511),f94(x41512)),x41513))) % 173.51/173.27 [4163]E(f333(f316(a910,a910,f333(f333(f7(a910,a910,a910),f87(a910)),x41631)),f309(a910,x41632,x41633)),f309(a910,f333(f333(f87(a910),x41632),x41631),f333(f333(f87(a910),x41633),x41631))) % 173.51/173.27 [4177]E(f333(f316(a910,a910,f333(f333(f7(a910,a910,a910),f87(a910)),x41771)),f333(f308(a910,x41772),x41773)),f333(f308(a910,f333(f333(f87(a910),x41772),x41771)),f333(f333(f87(a910),x41773),x41771))) % 173.51/173.27 [4195]E(f333(f333(f189(x41951,x41952),f333(f333(f162(f916(x41951,x41952),x41951),f264(x41951,x41952)),x41953)),f333(f333(f162(f916(x41951,x41952),x41952),f268(x41951,x41952)),x41953)),x41953) % 173.51/173.27 [4200]E(f333(f333(f87(a910),f333(f333(f88(a910),x42001),f51(a910,f333(f333(f42(a910),x42002),x42001),x42003))),f51(a910,x42002,x42001)),f51(a910,x42002,f333(f333(f88(a910),x42001),x42003))) % 173.51/173.27 [4213]E(f333(f333(f142(x42131),x42132),f333(f150(f911(x42131),f911(x42131),f142(x42131),f124(x42131)),x42133)),f333(f150(f911(x42131),f911(x42131),f142(x42131),x42132),x42133)) % 173.51/173.27 [4234]P106(f333(f333(f335(f916(x42341,x42341)),f333(f333(f265(x42341,x42341),x42342),x42342)),f333(f333(f191(f916(x42341,x42341),a905),f2(a910)),x42343))) % 173.51/173.27 [4239]E(f333(f252(x42391),f333(f333(f8(f917(x42392,a905),a905,x42391),f94(x42392)),f333(f7(x42392,x42391,a905),x42393))),f333(f291(x42392,x42391),f333(f252(f916(x42392,x42391)),f333(f269(x42392,x42391,a905),x42393)))) % 173.51/173.27 [4256]E(f333(f333(f121(f917(x42561,a905)),f333(f333(f45(a910,f917(x42561,a905)),f309(a910,f85(a910),x42562)),x42563)),f333(x42563,f2(a910))),f333(f333(f45(a910,f917(x42561,a905)),f333(f307(a910),x42562)),x42563)) % 173.51/173.27 [4271]E(f333(f150(f911(x42711),f911(x42711),f142(x42711),f124(x42711)),f333(f333(f162(f911(x42711),f911(x42711)),f144(x42711,x42712)),x42713)),f333(f144(x42711,x42712),f333(f150(f911(x42711),f911(x42711),f142(x42711),f124(x42711)),x42713))) % 173.51/173.27 [4275]E(f333(f268(f911(x42751),f911(x42751)),f174(x42751,x42752,x42753)),f333(f144(x42751,f333(f79(a905,a905,x42751,a328),x42752)),x42753)) % 173.51/173.27 [4293]E(f333(f333(f46(x42931,f917(x42932,a905)),f254(f917(x42931,a905))),f333(f333(f8(f917(x42932,a905),f917(x42932,a905),x42931),f252(x42932)),f333(f7(x42932,x42931,a905),x42933))),f333(f252(x42932),f333(f333(f8(f917(x42931,a905),a905,x42932),f95(x42931)),x42933))) % 173.51/173.27 [4321]E(f333(f333(f87(a1),f333(f333(f87(a1),f333(f333(f88(a1),x43211),f333(f333(f42(a1),x43212),x43211))),f51(a1,x43212,x43211))),x43213),f333(f333(f87(a1),x43212),x43213)) % 173.51/173.27 [4357]E(f333(f333(f87(a1),f333(f333(f87(a1),f333(f333(f88(a1),f333(f333(f42(a1),x43571),x43572)),x43572)),f51(a1,x43571,x43572))),x43573),f333(f333(f87(a1),x43571),x43573)) % 173.51/173.27 [4383]E(f92(f916(x43831,x43832),f333(f269(x43831,x43832,a905),f333(f333(f8(f917(x43832,f916(x43831,x43832)),f917(x43832,a905),x43831),f333(f8(f916(x43831,x43832),a905,x43832),x43833)),f265(x43831,x43832)))),f92(f916(x43831,x43832),x43833)) % 173.51/173.27 [4384]E(f97(f916(x43841,x43842),f333(f269(x43841,x43842,a905),f333(f333(f8(f917(x43842,f916(x43841,x43842)),f917(x43842,a905),x43841),f333(f8(f916(x43841,x43842),a905,x43842),x43843)),f265(x43841,x43842)))),f97(f916(x43841,x43842),x43843)) % 173.51/173.27 [4411]P106(f333(f333(f246(f917(x44111,a905)),f43(f917(x44111,a905),f333(f333(f112(f917(f917(x44111,a905),a905)),x44112),x44113))),f333(f333(f112(f917(x44111,a905)),f43(f917(x44111,a905),x44112)),f43(f917(x44111,a905),x44113)))) % 173.51/173.27 [4412]E(f333(f176(x44121),f333(f333(f333(f191(f911(x44121),f911(x44121)),f333(f333(f23(a910),f333(f197(f911(x44121)),x44122)),f51(a910,x44123,f333(f197(f911(x44121)),x44122)))),f175(x44121)),x44122)),f333(f333(f333(f191(f911(x44121),f911(x44121)),x44123),f175(x44121)),f333(f176(x44121),x44122))) % 173.51/173.27 [4449]P106(f333(f333(f246(a910),f333(f197(f911(x44491)),f333(f333(f146(x44491),f333(f197(f911(x44491)),f185(x44491,x44492,x44493))),x44493))),f333(f197(f911(x44491)),x44493))) % 173.51/173.27 [4706]~P106(f333(f68(x47061,x47062,f196(f917(x47061,a905))),x47063)) % 173.51/173.27 [4711]~P106(f333(f333(f335(f916(x47111,x47111)),f333(f333(f265(x47111,x47111),x47112),x47113)),f161(x47111,f124(f917(x47111,a910))))) % 173.51/173.27 [3761]E(f333(f197(f911(x37611)),f333(f333(f183(x37611),x37612),x37613)),f333(f333(f244(a910),f333(f197(f911(x37611)),x37613)),x37612)) % 173.51/173.27 [3762]E(f333(f197(f911(x37621)),f333(f333(f146(x37621),x37622),x37623)),f333(f333(f23(a910),f333(f197(f911(x37621)),x37623)),x37622)) % 173.51/173.27 [3788]E(f333(f197(f911(f911(x37881))),f61(x37881,x37882,x37883)),f333(f333(f256(a910),f333(f197(f911(x37881)),x37883)),x37882)) % 173.51/173.27 [3807]E(f333(f333(f42(a910),f333(f333(f42(a910),x38071),x38072)),x38073),f333(f333(f42(a910),x38071),f333(f333(f88(a910),x38072),x38073))) % 173.51/173.27 [3808]E(f333(f333(f23(a910),f333(f333(f23(a910),x38081),x38082)),x38083),f333(f333(f23(a910),x38081),f333(f333(f87(a910),x38082),x38083))) % 173.51/173.27 [3809]E(f333(f333(f87(a910),f333(f333(f87(a910),x38091),x38092)),x38093),f333(f333(f87(a910),x38091),f333(f333(f87(a910),x38092),x38093))) % 173.51/173.27 [3810]E(f333(f333(f87(a1),f333(f333(f87(a1),x38101),x38102)),x38103),f333(f333(f87(a1),x38101),f333(f333(f87(a1),x38102),x38103))) % 173.51/173.27 [3811]E(f333(f333(f88(a910),f333(f333(f88(a910),x38111),x38112)),x38113),f333(f333(f88(a910),x38111),f333(f333(f88(a910),x38112),x38113))) % 173.51/173.27 [3812]E(f333(f333(f88(a1),f333(f333(f88(a1),x38121),x38122)),x38123),f333(f333(f88(a1),x38121),f333(f333(f88(a1),x38122),x38123))) % 173.51/173.27 [3813]E(f333(f333(f256(a1),f333(f333(f256(a1),x38131),x38132)),x38133),f333(f333(f256(a1),x38131),f333(f333(f88(a910),x38132),x38133))) % 173.51/173.27 [3832]E(f170(x38321,f333(f333(f159(f917(x38321,a905)),x38322),x38323)),f182(x38321,x38322,f170(x38321,x38323))) % 173.51/173.27 [3876]E(f333(f333(f23(a910),f333(f333(f23(a910),x38761),x38762)),x38763),f333(f333(f23(a910),f333(f333(f23(a910),x38761),x38763)),x38762)) % 173.51/173.27 [3884]E(f333(f333(f112(f917(x38841,a905)),x38842),f333(f333(f23(f917(x38841,a905)),x38843),x38842)),f196(f917(x38841,a905))) % 173.51/173.27 [3888]E(f333(f333(f162(a910,x38881),f333(f16(x38881,a910),x38882)),f147(a910,f333(f308(a910,f2(a910)),x38883))),f177(x38881,x38883,x38882)) % 173.51/173.27 [3925]E(f44(f917(x39251,a905),f333(f333(f315(f917(x39251,a905)),x39252),x39253)),f333(f333(f112(f917(x39251,a905)),x39252),f44(f917(x39251,a905),x39253))) % 173.51/173.27 [3926]E(f43(f917(x39261,a905),f333(f333(f315(f917(x39261,a905)),x39262),x39263)),f333(f333(f121(f917(x39261,a905)),x39262),f43(f917(x39261,a905),x39263))) % 173.51/173.27 [3928]E(f177(x39281,f333(f197(f911(x39281)),f333(f144(x39281,f333(a330,x39282)),x39283)),x39282),f333(f144(x39281,f333(a330,x39282)),x39283)) % 173.51/173.27 [3930]E(f333(f333(f23(a910),f333(f333(f88(a910),x39301),x39302)),f333(f333(f88(a910),x39303),x39302)),f333(f333(f88(a910),f333(f333(f23(a910),x39301),x39303)),x39302)) % 173.51/173.27 [3931]E(f333(f333(f87(a910),f333(f333(f88(a910),x39311),x39312)),f333(f333(f88(a910),x39313),x39312)),f333(f333(f88(a910),f333(f333(f87(a910),x39311),x39313)),x39312)) % 173.51/173.27 [3932]E(f333(f333(f23(a1),f333(f333(f88(a1),x39321),x39322)),f333(f333(f88(a1),x39323),x39322)),f333(f333(f88(a1),f333(f333(f23(a1),x39321),x39323)),x39322)) % 173.51/173.27 [3933]E(f333(f333(f87(a1),f333(f333(f88(a1),x39331),x39332)),f333(f333(f88(a1),x39333),x39332)),f333(f333(f88(a1),f333(f333(f87(a1),x39331),x39333)),x39332)) % 173.51/173.27 [3935]E(f333(f333(f244(a910),f333(f333(f23(a910),x39351),x39352)),f333(f333(f23(a910),x39353),x39352)),f333(f333(f23(a910),f333(f333(f244(a910),x39351),x39353)),x39352)) % 173.51/173.27 [3957]E(f333(f333(f112(f917(f911(x39571),a905)),f168(x39571,x39572)),f168(x39571,x39573)),f168(x39571,f333(f333(f112(f917(x39571,a905)),x39572),x39573))) % 173.51/173.27 [3960]E(f333(f333(f121(f917(x39601,a905)),x39602),f333(f333(f121(f917(x39601,a905)),x39602),x39603)),f333(f333(f121(f917(x39601,a905)),x39602),x39603)) % 173.51/173.27 [3961]E(f333(f333(f121(f917(x39611,a905)),x39612),f333(f333(f23(f917(x39611,a905)),x39613),x39612)),f333(f333(f121(f917(x39611,a905)),x39612),x39613)) % 173.51/173.27 [3962]E(f333(f333(f112(f917(x39621,a905)),x39622),f333(f333(f112(f917(x39621,a905)),x39622),x39623)),f333(f333(f112(f917(x39621,a905)),x39622),x39623)) % 173.51/173.27 [3974]E(f333(f333(f295(x39741,x39742,x39742),x39743),f313(x39742,f196(f917(f916(x39742,x39742),a905)))),x39743) % 173.51/173.27 [3977]E(f333(f333(f121(f917(x39771,a905)),f333(f333(f315(x39771),x39772),f196(f917(x39771,a905)))),x39773),f333(f333(f315(x39771),x39772),x39773)) % 173.51/173.27 [3994]E(f333(f333(f23(a910),f333(f333(f23(a910),f333(a123,x39941)),x39942)),f333(a123,x39943)),f333(f333(f23(a910),f333(f333(f23(a910),x39941),x39942)),x39943)) % 173.51/173.27 [4022]E(f333(f333(f112(f917(f917(x40221,a905),a905)),f333(f314(x40221),x40222)),f333(f314(x40221),x40223)),f333(f314(x40221),f333(f333(f112(f917(x40221,a905)),x40222),x40223))) % 173.51/173.27 [4025]E(f333(f333(f121(f917(x40251,a905)),f333(f86(f917(x40251,a905)),x40252)),x40253),f333(f86(f917(x40251,a905)),f333(f333(f23(f917(x40251,a905)),x40252),x40253))) % 173.51/173.27 [4037]E(f333(f333(f315(x40371),x40372),f333(f333(f23(f917(x40371,a905)),x40373),f333(f333(f315(x40371),x40372),f196(f917(x40371,a905))))),f333(f333(f315(x40371),x40372),x40373)) % 173.51/173.27 [4047]P106(f333(f333(f246(f917(x40471,a905)),x40472),f333(f333(f121(f917(x40471,a905)),x40473),x40472))) % 173.51/173.27 [4048]P106(f333(f333(f246(f917(x40481,a905)),x40482),f333(f333(f121(f917(x40481,a905)),x40482),x40483))) % 173.51/173.27 [4052]E(f333(f333(f112(f917(x40521,a905)),f333(f86(f917(x40521,a905)),x40522)),f333(f86(f917(x40521,a905)),x40523)),f333(f86(f917(x40521,a905)),f333(f333(f121(f917(x40521,a905)),x40522),x40523))) % 173.51/173.27 [4053]E(f333(f333(f121(f917(x40531,a905)),f333(f86(f917(x40531,a905)),x40532)),f333(f86(f917(x40531,a905)),x40533)),f333(f86(f917(x40531,a905)),f333(f333(f112(f917(x40531,a905)),x40532),x40533))) % 173.51/173.27 [4066]P106(f333(f333(f246(f917(x40661,a905)),f333(f180(x40661),x40662)),f333(f180(x40661),f333(f333(f159(x40661),x40663),x40662)))) % 173.51/173.27 [4078]E(f333(f333(f121(f917(x40781,a905)),f333(f333(f23(f917(x40781,a905)),x40782),x40783)),f333(f333(f112(f917(x40781,a905)),x40782),x40783)),x40782) % 173.51/173.27 [4131]E(f333(f333(f6(x41311,a1),f333(f333(f8(a910,a1,x41311),f111(a1)),x41312)),x41313),f333(f111(a1),f333(f333(f6(x41311,a910),x41312),x41313))) % 173.51/173.27 [4132]E(f333(f333(f9(x41321,a1),f333(f333(f8(a910,a1,x41321),f111(a1)),x41322)),x41323),f333(f111(a1),f333(f333(f9(x41321,a910),x41322),x41323))) % 173.51/173.27 [4179]E(f333(f333(f142(x41791),f185(x41791,x41792,x41793)),f333(f333(f146(x41791),f333(f197(f911(x41791)),f185(x41791,x41792,x41793))),x41793)),x41793) % 173.51/173.27 [4183]E(f333(f86(f917(f916(x41831,x41832),a905)),f333(f333(f267(x41831,x41832),x41833),f333(f16(f917(x41832,a905),x41831),f254(f917(x41832,a905))))),f333(f333(f267(x41831,x41832),f333(f86(f917(x41831,a905)),x41833)),f333(f16(f917(x41832,a905),x41831),f254(f917(x41832,a905))))) % 173.51/173.27 [4184]E(f333(f86(f917(f916(x41841,x41842),a905)),f333(f333(f267(x41841,x41842),f254(f917(x41841,a905))),f333(f16(f917(x41842,a905),x41841),x41843))),f333(f333(f267(x41841,x41842),f254(f917(x41841,a905))),f333(f16(f917(x41842,a905),x41841),f333(f86(f917(x41842,a905)),x41843)))) % 173.51/173.27 [4235]E(f333(f333(f45(f917(x42351,a905),f917(x42351,a905)),x42352),f333(f333(f7(f917(x42351,a905),f917(x42351,a905),f917(x42351,a905)),f112(f917(x42351,a905))),x42353)),f333(f333(f112(f917(x42351,a905)),f43(f917(x42351,a905),x42352)),x42353)) % 173.51/173.27 [4241]E(f333(f150(f911(x42411),f911(x42411),f142(x42411),f124(x42411)),f333(f333(f159(f911(x42411)),x42412),x42413)),f333(f333(f142(x42411),x42412),f333(f150(f911(x42411),f911(x42411),f142(x42411),f124(x42411)),x42413))) % 173.51/173.27 [4262]E(f333(f333(f315(f917(x42621,a905)),f333(f292(x42621,x42621,x42622),f333(f333(f315(x42621),x42623),f196(f917(x42621,a905))))),f196(f917(f917(x42621,a905),a905))),f333(f333(f66(x42621),f333(f333(f315(x42621),x42623),f196(f917(x42621,a905)))),x42622)) % 173.51/173.27 [4272]E(f333(f333(f87(a910),f333(f333(f88(a910),x42721),f333(f333(f42(a910),x42722),x42723))),f333(f333(f42(a910),f333(f333(f88(a910),x42721),f51(a910,x42722,x42723))),x42723)),f333(f333(f42(a910),f333(f333(f88(a910),x42721),x42722)),x42723)) % 173.51/173.27 [4273]E(f333(f333(f87(a1),f333(f333(f88(a1),x42731),f333(f333(f42(a1),x42732),x42733))),f333(f333(f42(a1),f333(f333(f88(a1),x42731),f51(a1,x42732,x42733))),x42733)),f333(f333(f42(a1),f333(f333(f88(a1),x42731),x42732)),x42733)) % 173.51/173.27 [4306]E(f333(f333(f23(f917(x43061,a905)),f333(f180(x43061),x43062)),f333(f333(f315(x43061),x43063),f196(f917(x43061,a905)))),f333(f180(x43061),f333(f144(x43061,f333(f333(f8(a905,a905,x43061),a328),f333(a330,x43063))),x43062))) % 173.51/173.27 [4355]E(f333(f333(f142(x43551),f333(f150(f911(x43551),f911(x43551),f142(x43551),f124(x43551)),x43552)),f333(f150(f911(x43551),f911(x43551),f142(x43551),f124(x43551)),x43553)),f333(f150(f911(x43551),f911(x43551),f142(x43551),f124(x43551)),f333(f333(f142(f911(x43551)),x43552),x43553))) % 173.51/173.27 [4358]E(f333(f333(f265(f911(x43581),f911(x43581)),f333(f144(x43581,x43582),x43583)),f333(f144(x43581,f333(f79(a905,a905,x43581,a328),x43582)),x43583)),f174(x43581,x43582,x43583)) % 173.51/173.27 [4361]E(f333(f333(f87(a910),f333(f333(f87(a910),f333(f333(f42(a910),x43611),x43612)),f333(f333(f42(a910),x43613),x43612))),f333(f333(f42(a910),f333(f333(f87(a910),f51(a910,x43611,x43612)),f51(a910,x43613,x43612))),x43612)),f333(f333(f42(a910),f333(f333(f87(a910),x43611),x43613)),x43612)) % 173.51/173.27 [4362]E(f333(f333(f87(a1),f333(f333(f87(a1),f333(f333(f42(a1),x43621),x43622)),f333(f333(f42(a1),x43623),x43622))),f333(f333(f42(a1),f333(f333(f87(a1),f51(a1,x43621,x43622)),f51(a1,x43623,x43622))),x43622)),f333(f333(f42(a1),f333(f333(f87(a1),x43621),x43623)),x43622)) % 173.51/173.27 [4415]E(f333(f333(f112(f917(f911(x44151),a905)),f333(f333(f7(f911(x44151),f917(f911(x44151),a905),a905),f335(f911(x44151))),f169(x44151,x44152))),f333(f333(f7(f911(x44151),f917(f911(x44151),a905),a905),f335(f911(x44151))),f169(x44151,x44153))),f168(x44151,f333(f333(f112(f917(x44151,a905)),f333(f333(f7(x44151,f917(x44151,a905),a905),f335(x44151)),x44152)),f333(f333(f7(x44151,f917(x44151,a905),a905),f335(x44151)),x44153)))) % 173.51/173.27 [4427]E(f333(f252(x44271),f333(f333(f18(x44271,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44271),a332),f333(f333(f7(x44271,x44271,a905),a330),x44272))),f333(f333(f7(x44271,f917(x44271,a905),a905),f335(x44271)),x44273))),f333(f333(f315(x44271),x44272),x44273)) % 173.51/173.27 [4447]E(f333(f333(f93(f911(f911(x44471)),f911(f911(x44471))),f60(x44471,x44472)),f333(f333(f18(f911(f911(x44471)),f911(f911(x44471)),f911(f911(x44471))),f333(f333(f8(f911(f911(x44471)),f917(f911(f911(x44471)),f911(f911(x44471))),f911(f911(x44471))),f142(f911(x44471))),f333(f162(f911(x44471),f911(x44471)),f333(f159(x44471),x44473)))),f5(f911(f911(x44471))))),f60(x44471,f333(f333(f159(x44471),x44473),x44472))) % 173.51/173.27 [4450]E(f333(f252(x44501),f333(f333(f18(x44501,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44501),a332),f333(f333(f7(x44501,f917(x44501,a905),a905),f335(x44501)),x44502))),f333(f333(f7(x44501,f917(x44501,a905),a905),f335(x44501)),x44503))),f333(f333(f121(f917(x44501,a905)),x44502),x44503)) % 173.51/173.27 [4451]E(f333(f252(x44511),f333(f333(f18(x44511,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44511),a331),f333(f333(f7(x44511,f917(x44511,a905),a905),f335(x44511)),x44512))),f333(f333(f7(x44511,f917(x44511,a905),a905),f335(x44511)),x44513))),f333(f333(f112(f917(x44511,a905)),x44512),x44513)) % 173.51/173.27 [4540]E(f333(f333(f45(x45401,f917(f917(x45401,a905),a905)),x45402),f333(f333(f7(x45401,f917(f917(x45401,a905),a905),f917(f917(x45401,a905),a905)),f333(f333(f8(f917(x45401,a905),f917(f917(f917(x45401,a905),a905),f917(f917(x45401,a905),a905)),x45401),f315(f917(x45401,a905))),f333(f333(f8(f917(x45401,a905),f917(x45401,a905),x45401),f292(x45401,x45401,x45403)),f333(f333(f7(x45401,f917(x45401,a905),f917(x45401,a905)),f315(x45401)),f196(f917(x45401,a905)))))),f196(f917(f917(x45401,a905),a905)))),f333(f333(f66(x45401),x45402),x45403)) % 173.51/173.27 [4542]E(f333(f333(f213(x45421),f333(f333(f88(a1),f333(f333(f79(f916(a1,a1),a1,x45421,f264(a1,a1)),f224(x45421)),x45422)),f333(f333(f79(f916(a1,a1),a1,x45421,f264(a1,a1)),f224(x45421)),x45423))),f333(f333(f88(a1),f333(f333(f79(f916(a1,a1),a1,x45421,f268(a1,a1)),f224(x45421)),x45422)),f333(f333(f79(f916(a1,a1),a1,x45421,f268(a1,a1)),f224(x45421)),x45423))),f240(x45421,x45422,x45423)) % 173.51/173.27 [4545]E(f333(f252(f911(x45451)),f333(f333(f18(f911(x45451),a905,a905),f333(f333(f8(a905,f917(a905,a905),f911(x45451)),a331),f333(f333(f7(f911(x45451),a910,a905),f333(f333(f8(a910,f917(a910,a905),f911(x45451)),a330),f197(f911(x45451)))),x45452))),f333(f333(f7(f911(x45451),f917(x45451,a905),a905),f333(f333(f8(f917(x45451,a905),f917(f917(x45451,a905),a905),f911(x45451)),f246(f917(x45451,a905))),f180(x45451))),f333(f180(x45451),x45453)))),f333(f180(f911(x45451)),f61(x45451,x45452,x45453))) % 173.51/173.27 [3948]E(f51(a910,f333(f333(f87(a910),f333(f333(f88(a910),x39481),x39482)),x39483),x39482),f51(a910,x39483,x39482)) % 173.51/173.27 [3993]E(f147(a910,f333(f308(a910,f333(f333(f87(a910),x39931),x39932)),x39933)),f333(f333(f146(a910),x39932),f147(a910,f333(f308(a910,x39931),x39933)))) % 173.51/173.27 [4036]E(f333(f333(f87(a1),f333(f111(a1),x40361)),f333(f333(f87(a1),f333(f111(a1),x40362)),x40363)),f333(f333(f87(a1),f333(f111(a1),f333(f333(f87(a910),x40361),x40362))),x40363)) % 173.51/173.27 [4043]E(f333(f333(f121(f917(x40431,a905)),f333(f333(f23(f917(x40431,a905)),x40432),x40433)),x40433),f333(f333(f121(f917(x40431,a905)),x40432),x40433)) % 173.51/173.27 [4044]E(f333(f333(f23(f917(x40441,a905)),f333(f333(f23(f917(x40441,a905)),x40442),x40443)),x40443),f333(f333(f23(f917(x40441,a905)),x40442),x40443)) % 173.51/173.27 [4067]E(f333(f333(f295(x40671,x40671,x40672),f313(x40671,f196(f917(f916(x40671,x40671),a905)))),x40673),x40673) % 173.51/173.27 [4075]E(f333(f333(f121(f917(x40751,a905)),f333(f288(x40751),x40752)),f333(f288(x40751),x40753)),f333(f288(x40751),f333(f333(f121(f917(f916(x40751,x40751),a905)),x40752),x40753))) % 173.51/173.27 [4085]E(f275(x40851,f333(f333(f159(f916(a110,x40851)),f333(f333(f265(a110,x40851),f2(a110)),x40852)),x40853)),f275(x40851,x40853)) % 173.51/173.27 [4087]E(f333(f333(f112(f917(x40871,a905)),f44(f917(x40871,a905),x40872)),f44(f917(x40871,a905),x40873)),f44(f917(x40871,a905),f333(f333(f121(f917(f917(x40871,a905),a905)),x40872),x40873))) % 173.51/173.27 [4088]E(f333(f333(f121(f917(x40881,a905)),f43(f917(x40881,a905),x40882)),f43(f917(x40881,a905),x40883)),f43(f917(x40881,a905),f333(f333(f121(f917(f917(x40881,a905),a905)),x40882),x40883))) % 173.51/173.27 [4125]E(f333(f333(f295(x41251,x41251,x41251),f333(f333(f191(f916(x41251,x41251),a905),x41252),x41253)),x41253),f333(f333(f191(f916(x41251,x41251),a905),f333(a123,x41252)),x41253)) % 173.51/173.27 [4171]P106(f333(f333(f246(f917(x41711,a905)),f333(f333(f112(f917(x41711,a905)),x41712),x41713)),x41713)) % 173.51/173.27 [4172]P106(f333(f333(f246(f917(x41721,a905)),f333(f333(f112(f917(x41721,a905)),x41722),x41723)),x41722)) % 173.51/173.27 [4173]P106(f333(f333(f246(f917(x41731,a905)),f333(f333(f23(f917(x41731,a905)),x41732),x41733)),x41732)) % 173.51/173.27 [4197]E(f313(x41971,f333(f333(f121(f917(f916(x41971,x41971),a905)),f313(x41971,x41972)),f313(x41971,x41973))),f313(x41971,f333(f333(f121(f917(f916(x41971,x41971),a905)),x41972),x41973))) % 173.51/173.27 [4201]E(f43(f917(x42011,a905),f333(f333(f315(f917(x42011,a905)),x42012),f333(f333(f315(f917(x42011,a905)),x42013),f196(f917(f917(x42011,a905),a905))))),f333(f333(f121(f917(x42011,a905)),x42012),x42013)) % 173.51/173.27 [4202]E(f44(f917(x42021,a905),f333(f333(f315(f917(x42021,a905)),x42022),f333(f333(f315(f917(x42021,a905)),x42023),f196(f917(f917(x42021,a905),a905))))),f333(f333(f112(f917(x42021,a905)),x42022),x42023)) % 173.51/173.27 [4207]E(f333(f333(f295(x42071,x42071,x42071),f333(f333(f191(f916(x42071,x42071),a905),x42072),x42073)),x42073),f333(f333(f295(x42071,x42071,x42071),x42073),f333(f333(f191(f916(x42071,x42071),a905),x42072),x42073))) % 173.51/173.27 [4276]E(f333(f333(f121(f917(x42761,a905)),f333(f252(x42761),f333(f333(f7(x42761,x42761,a905),a330),x42762))),x42763),f333(f333(f315(x42761),x42762),x42763)) % 173.51/173.27 [4278]E(f333(a115,f333(f333(f6(x42781,a1),f333(f333(f8(a910,a1,x42781),f111(a1)),x42782)),x42783)),f333(f333(f6(x42781,a910),x42782),x42783)) % 173.51/173.27 [4279]E(f333(a115,f333(f333(f9(x42791,a1),f333(f333(f8(a910,a1,x42791),f111(a1)),x42792)),x42793)),f333(f333(f9(x42791,a910),x42792),x42793)) % 173.51/173.27 [4352]E(f333(f164(f911(x43521),x43521,f333(f179(x43521),x43522),f333(f16(f917(f911(x43521),f911(x43521)),x43521),f333(f333(f7(f911(x43521),f911(x43521),f911(x43521)),f142(x43521)),x43522))),x43523),f333(f179(x43521),f333(f333(f142(x43521),x43523),x43522))) % 173.51/173.27 [4380]P106(f333(f333(f246(f917(f917(x43801,a905),a905)),f333(f333(f121(f917(f917(x43801,a905),a905)),f333(f314(x43801),x43802)),f333(f314(x43801),x43803))),f333(f314(x43801),f333(f333(f121(f917(x43801,a905)),x43802),x43803)))) % 173.51/173.27 [4469]E(f333(f252(x44691),f333(f333(f18(x44691,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44691),a331),f333(f333(f7(x44691,f917(x44691,a905),a905),f335(x44691)),x44692))),f333(f333(f8(a905,a905,x44691),a328),f333(f333(f7(x44691,f917(x44691,a905),a905),f335(x44691)),x44693)))),f333(f333(f23(f917(x44691,a905)),x44692),x44693)) % 173.51/173.27 [4493]E(f333(f41(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,a910,a905),f247(a910)),f333(f197(f911(x44931)),x44932)))),f333(f333(f8(x44931,a905,a910),x44933),f333(f172(x44931),x44932))))),f333(f197(f911(x44931)),f333(f144(x44931,x44933),x44932))) % 173.51/173.27 [4495]E(f333(f197(f911(x44951)),f184(x44951,x44952,x44953)),f333(f41(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,a910,a905),f247(a910)),f333(f197(f911(x44951)),x44952)))),f333(f333(f7(a910,f917(a910,a905),a905),f335(a910)),x44953))))) % 173.51/173.27 [4591]E(f333(f333(f112(f917(f916(f911(x45911),f911(x45911)),a905)),f333(f316(f916(f916(x45911,f911(x45911)),f916(x45911,f911(x45911))),f916(f911(x45911),f911(x45911)),f270(f916(x45911,f911(x45911)),f911(x45911),f916(x45911,f911(x45911)),f911(x45911),f333(f269(x45911,f911(x45911),f911(x45911)),f159(x45911)),f333(f269(x45911,f911(x45911),f911(x45911)),f159(x45911)))),f325(x45911,f911(x45911),x45912,f333(f151(x45911,x45912),x45913)))),f333(f252(f916(f911(x45911),f911(x45911))),f333(f269(f911(x45911),f911(x45911),a905),f333(f333(f7(f911(x45911),f917(f911(x45911),a905),f917(f911(x45911),a905)),f333(f333(f8(f917(a905,a905),f917(f917(f911(x45911),a905),f917(f911(x45911),a905)),f911(x45911)),f8(a905,a905,f911(x45911))),f333(f333(f8(a905,f917(a905,a905),f911(x45911)),a331),f333(f333(f7(f911(x45911),a910,a905),f333(f333(f8(a910,f917(a910,a905),f911(x45911)),a330),f197(f911(x45911)))),f333(a123,x45913))))),f333(f333(f7(f911(x45911),a910,a905),f333(f333(f8(a910,f917(a910,a905),f911(x45911)),a330),f197(f911(x45911)))),f333(a123,x45913)))))),f333(f151(x45911,x45912),f333(a123,x45913))) % 173.51/173.27 [4089]E(f51(a910,f333(a123,f333(f333(f87(a910),f333(f333(f88(a910),x40891),x40892)),x40893)),x40892),f51(a910,f333(a123,x40893),x40892)) % 173.51/173.27 [4339]E(f333(f252(x43391),f333(f333(f18(x43391,a905,a905),f333(f333(f8(a905,f917(a905,a905),x43391),a331),x43392)),x43393)),f333(f333(f112(f917(x43391,a905)),f333(f252(x43391),x43392)),f333(f252(x43391),x43393))) % 173.51/173.27 [4340]E(f333(f252(x43401),f333(f333(f18(x43401,a905,a905),f333(f333(f8(a905,f917(a905,a905),x43401),a332),x43402)),x43403)),f333(f333(f121(f917(x43401,a905)),f333(f252(x43401),x43402)),f333(f252(x43401),x43403))) % 173.51/173.27 [4342]E(f333(f333(f142(x43421),f333(f333(f146(x43421),f51(a910,x43422,f333(f197(f911(x43421)),x43423))),x43423)),f333(f333(f183(x43421),f51(a910,x43422,f333(f197(f911(x43421)),x43423))),x43423)),f333(f333(f333(f191(f911(x43421),f911(x43421)),x43422),f175(x43421)),x43423)) % 173.51/173.27 [4348]E(f333(f252(x43481),f333(f333(f18(x43481,a905,a905),f333(f333(f8(a905,f917(a905,a905),x43481),a336),x43482)),x43483)),f333(f333(f121(f917(x43481,a905)),f333(f86(f917(x43481,a905)),f333(f252(x43481),x43482))),f333(f252(x43481),x43483))) % 173.51/173.27 [4363]E(f333(f333(f87(a910),f333(f197(f911(x43631)),f333(f144(x43631,x43632),x43633))),f333(f197(f911(x43631)),f333(f144(x43631,f333(f333(f8(a905,a905,x43631),a328),x43632)),x43633))),f333(f197(f911(x43631)),x43633)) % 173.51/173.27 [4386]P106(f333(f333(f246(f917(x43861,a905)),f333(f333(f121(f917(x43861,a905)),f44(f917(x43861,a905),x43862)),f44(f917(x43861,a905),x43863))),f44(f917(x43861,a905),f333(f333(f112(f917(f917(x43861,a905),a905)),x43862),x43863)))) % 173.51/173.27 [4400]E(f333(f180(x44001),f333(f144(x44001,f333(f333(f8(a905,a905,x44001),a328),f333(f333(f7(x44001,x44001,a905),a330),x44002))),x44003)),f333(f333(f23(f917(x44001,a905)),f333(f180(x44001),x44003)),f333(f333(f315(x44001),x44002),f196(f917(x44001,a905))))) % 173.51/173.27 [4409]P106(f333(f333(f246(f917(f916(x44091,x44091),a905)),f333(f333(f121(f917(f916(x44091,x44091),a905)),f313(x44091,x44092)),f313(x44091,x44093))),f313(x44091,f333(f333(f121(f917(f916(x44091,x44091),a905)),x44092),x44093)))) % 173.51/173.27 [4432]E(f333(f333(f88(a910),f333(a123,f333(a123,f2(a910)))),f333(f333(f6(a910,a910),f333(f333(f8(a910,a910,a910),f333(f87(a910),x44321)),f333(f333(f7(a910,a910,a910),f88(a910)),x44322))),f333(f289(a910),x44323))),f333(f333(f88(a910),x44323),f333(f333(f87(a910),x44321),f333(f333(f87(a910),x44321),f333(f333(f88(a910),f333(f333(f23(a910),x44323),f85(a910))),x44322))))) % 173.51/173.27 [4442]E(f333(f252(x44421),f333(f333(f18(x44421,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44421),a331),f333(f333(f7(x44421,f917(x44421,a905),a905),f335(x44421)),f333(f180(x44421),x44422)))),x44423)),f333(f180(x44421),f333(f144(x44421,x44423),x44422))) % 173.51/173.27 [4590]E(f333(f252(x45901),f333(f333(f8(f917(a910,a905),a905,x45901),f94(a910)),f333(f333(f7(x45901,f917(a910,a905),f917(a910,a905)),f333(f333(f8(f917(a910,f917(a905,a905)),f917(f917(a910,a905),f917(a910,a905)),x45901),f18(a910,a905,a905)),f333(f333(f8(f917(a910,a905),f917(a910,f917(a905,a905)),x45901),f333(f8(a905,f917(a905,a905),a910),a331)),f333(f333(f7(x45901,f917(a910,x45901),f917(a910,a905)),f333(f333(f8(f917(x45901,a905),f917(f917(a910,x45901),f917(a910,a905)),x45901),f8(x45901,a905,a910)),a330)),f333(f172(x45901),x45902))))),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,a910,a905),f247(a910)),f333(f197(f911(x45901)),x45902)))),f333(f333(f7(a910,f917(a910,a905),a905),f335(a910)),x45903))))),f333(f180(x45901),f184(x45901,x45902,x45903))) % 173.51/173.27 [4482]E(f333(f252(x44821),f333(f333(f18(x44821,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44821),a336),f333(f333(f8(a905,a905,x44821),a328),f333(f333(f7(x44821,x44821,a905),a330),x44822)))),x44823)),f333(f333(f315(x44821),x44822),f333(f252(x44821),x44823))) % 173.51/173.27 [4514]E(f333(f333(f162(f916(x45141,a910),x45141),f264(x45141,a910)),f333(f144(f916(x45141,a910),f333(f333(f7(f916(x45141,a910),f917(a910,a905),a905),f333(f333(f8(a910,f917(f917(a910,a905),a905),f916(x45141,a910)),f335(a910)),f268(x45141,a910))),x45142)),f333(f333(f189(x45141,a910),x45143),f147(a910,f333(f308(a910,f2(a910)),f333(f197(f911(x45141)),x45143)))))),f184(x45141,x45143,x45142)) % 173.51/173.27 [4541]E(f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f6(a910,a1),f333(f333(f8(a1,a1,a910),f333(f87(a1),x45411)),f333(f333(f7(a910,a1,a1),f333(f333(f8(a1,f917(a1,a1),a910),f88(a1)),f111(a1))),x45412))),f333(f289(a910),x45413))),f333(f333(f88(a1),f333(f111(a1),x45413)),f333(f333(f87(a1),x45411),f333(f333(f87(a1),x45411),f333(f333(f88(a1),f333(f111(a1),f333(f333(f23(a910),x45413),f85(a910)))),x45412))))) % 173.51/173.27 [4583]E(f333(f252(f916(x45831,x45832)),f333(f269(x45831,x45832,a905),f333(f333(f7(x45831,f917(f916(x45832,x45831),a905),f917(x45832,a905)),f333(f333(f8(f917(x45832,f917(f917(f916(x45832,x45831),a905),a905)),f917(f917(f916(x45832,x45831),a905),f917(x45832,a905)),x45831),f7(x45832,f917(f916(x45832,x45831),a905),a905)),f333(f333(f8(f917(x45832,f916(x45832,x45831)),f917(x45832,f917(f917(f916(x45832,x45831),a905),a905)),x45831),f333(f8(f916(x45832,x45831),f917(f917(f916(x45832,x45831),a905),a905),x45832),f335(f916(x45832,x45831)))),f333(f7(x45832,x45831,f916(x45832,x45831)),f265(x45832,x45831))))),x45833))),f333(f293(x45832,x45831),x45833)) % 173.51/173.27 [4612]E(f333(f252(f911(x46121)),f333(f333(f8(f917(x46121,a905),a905,f911(x46121)),f94(x46121)),f333(f333(f8(f917(x46121,f917(f911(x46121),a905)),f917(x46121,a905),f911(x46121)),f333(f8(f917(f911(x46121),a905),a905,x46121),f94(f911(x46121)))),f333(f333(f7(f911(x46121),f917(x46121,f917(f911(x46121),a905)),f917(x46121,f917(f911(x46121),a905))),f333(f333(f8(f917(x46121,f917(f917(f911(x46121),a905),f917(f911(x46121),a905))),f917(f917(x46121,f917(f911(x46121),a905)),f917(x46121,f917(f911(x46121),a905))),f911(x46121)),f18(x46121,f917(f911(x46121),a905),f917(f911(x46121),a905))),f333(f333(f8(f917(x46121,f917(f911(x46121),f917(a905,a905))),f917(x46121,f917(f917(f911(x46121),a905),f917(f911(x46121),a905))),f911(x46121)),f333(f8(f917(f911(x46121),f917(a905,a905)),f917(f917(f911(x46121),a905),f917(f911(x46121),a905)),x46121),f18(f911(x46121),a905,a905))),f333(f333(f8(f917(x46121,f917(f911(x46121),a905)),f917(x46121,f917(f911(x46121),f917(a905,a905))),f911(x46121)),f333(f8(f917(f911(x46121),a905),f917(f911(x46121),f917(a905,a905)),x46121),f333(f8(a905,f917(a905,a905),f911(x46121)),a331))),f333(f333(f7(f911(x46121),f917(x46121,f917(f911(x46121),f911(x46121))),f917(x46121,f917(f911(x46121),a905))),f333(f333(f8(f917(f917(f911(x46121),f911(x46121)),f917(f911(x46121),a905)),f917(f917(x46121,f917(f911(x46121),f911(x46121))),f917(x46121,f917(f911(x46121),a905))),f911(x46121)),f8(f917(f911(x46121),f911(x46121)),f917(f911(x46121),a905),x46121)),f333(f333(f8(f917(f911(x46121),a905),f917(f917(f911(x46121),f911(x46121)),f917(f911(x46121),a905)),f911(x46121)),f8(f911(x46121),a905,f911(x46121))),a330))),f159(x46121)))))),f333(f333(f7(x46121,f917(f911(x46121),a905),f917(f911(x46121),a905)),f333(f333(f8(f917(a905,a905),f917(f917(f911(x46121),a905),f917(f911(x46121),a905)),x46121),f8(a905,a905,f911(x46121))),f333(f333(f8(a905,f917(a905,a905),x46121),a331),f333(f333(f7(x46121,f917(x46121,a905),a905),f335(x46121)),x46122)))),f333(f333(f7(f911(x46121),f917(f911(x46121),a905),a905),f335(f911(x46121))),x46123)))))),f182(x46121,x46122,x46123)) % 173.51/173.27 [4603]E(f333(f333(f93(a1,f916(a1,a1)),f333(f333(f23(a1),x46031),x46032)),f333(f333(f7(a1,f916(a1,a1),f916(a1,a1)),f333(f333(f18(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f333(f333(f8(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f107(f916(a1,a1))),f333(f246(a1),f2(a1)))),f333(f265(a1,a1),f333(f333(f87(a1),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x46033)),f85(a1))))),f333(f333(f265(a1,a1),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x46033)),x46031))),f333(f49(x46032),f333(f333(f265(a1,a1),x46033),x46031))) % 173.51/173.27 [4636]~E(f30(x46361,x46362),f31(x46363,x46364)) % 173.51/173.27 [4639]~E(f26(x46391,x46392),f31(x46393,x46394)) % 173.51/173.27 [4640]~E(f26(x46401,x46402),f30(x46403,x46404)) % 173.51/173.27 [3642]E(f127(x36421,f333(x36422,x36423),f333(x36424,x36423)),f333(f215(x36421,x36422,x36424),x36423)) % 173.51/173.27 [3694]E(f333(f333(f257(x36941,x36942,x36943),x36944),f2(a910)),x36942) % 173.51/173.27 [3708]E(f37(x37081,x37082,x37083,f34(x37084)),f333(x37083,x37084)) % 173.51/173.27 [3709]E(f37(x37091,x37092,x37093,f35(x37094)),f333(x37092,x37094)) % 173.51/173.27 [3710]E(f38(x37101,x37102,x37103,f34(x37104)),f333(x37103,x37104)) % 173.51/173.27 [3711]E(f38(x37111,x37112,x37113,f35(x37114)),f333(x37112,x37114)) % 173.51/173.27 [3738]E(f193(x37381,x37382,x37383,f333(a123,x37384)),f333(x37383,x37384)) % 173.51/173.27 [3780]E(f178(x37801,x37802,f178(x37801,x37803,x37804)),f178(x37801,x37803,f178(x37801,x37802,x37804))) % 173.51/173.27 [3781]E(f136(x37811,x37812,f127(x37811,x37813,x37814)),f127(x37811,f136(x37811,x37812,x37813),x37814)) % 173.51/173.27 [3916]E(f333(f164(x39161,x39162,x39163,x39164),f124(x39162)),x39163) % 173.51/173.27 [3917]E(f333(f150(x39171,x39172,x39173,x39174),f124(x39172)),x39174) % 173.51/173.27 [3954]E(f333(f197(f915(x39541,x39542)),f232(x39541,x39542,x39543,x39544)),f2(a910)) % 173.51/173.27 [4021]E(f333(f333(f142(x40211),f177(x40211,x40212,x40213)),f177(x40211,x40214,x40213)),f333(f333(f142(x40211),f177(x40211,x40214,x40213)),f177(x40211,x40212,x40213))) % 173.51/173.27 [4109]E(f333(f333(f271(x41091,x41092,x41093,f916(x41092,x41093)),x41094),f265(x41092,x41093)),x41094) % 173.51/173.27 [4124]E(f81(x41241,x41242,x41243,x41244,f333(x41243,x41244)),x41243) % 173.51/173.27 [4393]P45(x43931,x43932,x43933,x43934,f196(f917(x43931,a905)),x43934) % 173.51/173.27 [3446]E(f333(f333(f16(x34461,x34462),x34463),x34464),x34463) % 173.51/173.27 [3728]E(f178(x37281,x37282,f333(f144(x37281,x37283),x37284)),f333(f144(x37281,x37283),f178(x37281,x37282,x37284))) % 173.51/173.27 [3763]E(f333(f333(f70(x37631,x37632,x37633),x37634),f196(f917(x37631,a905))),x37634) % 173.51/173.27 [3787]E(f333(f333(f172(x37871),f333(f333(f159(x37871),x37872),x37873)),f333(a123,x37874)),f333(f333(f172(x37871),x37873),x37874)) % 173.51/173.27 [3856]E(f333(f333(x38561,x38562),f333(f192(x38563,x38564,x38561),x38562)),f333(f192(x38563,x38564,x38561),f333(a123,x38562))) % 173.51/173.27 [3952]E(f333(f333(f167(x39521,f333(f333(f159(x39521),x39522),x39523)),f2(a910)),x39524),f333(f333(f159(x39521),x39524),x39523)) % 173.51/173.27 [3964]E(f333(f333(f45(f917(x39641,a905),f917(x39642,a905)),x39643),f316(x39641,x39642,x39644)),f333(f316(x39641,x39642,x39644),f43(f917(x39641,a905),x39643))) % 173.51/173.27 [3965]E(f333(f333(f45(f917(x39651,a905),f917(x39652,a905)),x39653),f317(x39652,x39651,x39654)),f333(f317(x39652,x39651,x39654),f43(f917(x39651,a905),x39653))) % 173.51/173.27 [4064]E(f333(f135(x40641,x40642),f136(x40641,x40643,x40644)),f333(f333(f87(a910),f333(f333(f87(a910),f333(x40642,x40643)),f333(f135(x40641,x40642),x40644))),f333(a123,f2(a910)))) % 173.51/173.27 [4084]E(f333(f150(x40841,x40842,f333(f7(x40842,x40841,x40841),x40843),x40844),f333(f176(x40842),f124(x40842))),x40844) % 173.51/173.27 [4122]P106(f333(f333(f333(f333(a204,f26(x41221,x41222)),x41223),x41224),f333(f333(f333(a205,x41223),x41221),f333(x41222,x41223)))) % 173.51/173.27 [4130]E(f83(x41301,x41302,x41303,x41304,f196(f917(x41301,a905))),x41303) % 173.51/173.27 [4191]E(f235(x41911,f916(x41912,f912(x41912)),x41913,f333(f269(x41912,f912(x41912),x41911),x41914),f333(f143(x41912),f130(x41912))),x41913) % 173.51/173.27 [4324]E(f333(f269(x43241,x43242,x43243),f333(f333(f8(f917(x43242,f916(x43241,x43242)),f917(x43242,x43243),x43241),f333(f8(f916(x43241,x43242),x43243,x43242),x43244)),f265(x43241,x43242))),x43244) % 173.51/173.27 [3633]E(f333(f268(x36331,x36332),f333(f333(f265(x36331,x36332),x36333),x36334)),x36334) % 173.51/173.27 [3634]E(f333(f264(x36341,x36342),f333(f333(f265(x36341,x36342),x36343),x36344)),x36343) % 173.51/173.27 [3667]E(f333(f197(f911(x36671)),f333(f333(f167(x36671,x36672),x36673),x36674)),f333(f197(f911(x36671)),x36672)) % 173.51/173.27 [3668]E(f333(f197(f911(x36681)),f333(f333(f162(x36682,x36681),x36683),x36684)),f333(f197(f911(x36682)),x36684)) % 173.51/173.27 [3689]E(f333(f333(f146(x36891),f333(a123,x36892)),f333(f333(f159(x36891),x36893),x36894)),f333(f333(f146(x36891),x36892),x36894)) % 173.51/173.27 [3758]E(f333(f333(f183(x37581),x37582),f177(x37581,x37583,x37584)),f177(x37581,f333(f333(f244(a910),x37582),x37583),x37584)) % 173.51/173.27 [3759]E(f333(f333(f146(x37591),x37592),f177(x37591,x37593,x37594)),f177(x37591,f333(f333(f23(a910),x37593),x37592),x37594)) % 173.51/173.27 [3765]E(f333(f333(f315(x37651),x37652),f333(f333(f315(x37651),x37653),x37654)),f333(f333(f315(x37651),x37653),f333(f333(f315(x37651),x37652),x37654))) % 173.51/173.27 [3769]E(f333(f333(f162(x37691,x37692),x37693),f125(x37691,x37694)),f125(x37692,f333(f333(f162(x37691,x37692),x37693),x37694))) % 173.51/173.27 [3785]E(f333(f176(x37851),f333(f333(f162(x37852,x37851),x37853),x37854)),f333(f333(f162(x37852,x37851),x37853),f333(f176(x37852),x37854))) % 173.51/173.27 [3786]E(f333(f333(f162(x37861,x37862),x37863),f333(f179(x37861),x37864)),f333(f179(x37862),f333(f333(f162(x37861,x37862),x37863),x37864))) % 173.51/173.27 [3802]E(f333(f333(f183(x38021),f333(a123,x38022)),f333(f333(f159(x38021),x38023),x38024)),f333(f333(f159(x38021),x38023),f333(f333(f183(x38021),x38022),x38024))) % 173.51/173.27 [3806]E(f333(f180(x38061),f333(f333(f162(x38062,x38061),x38063),x38064)),f333(f316(x38062,x38061,x38063),f333(f180(x38062),x38064))) % 173.51/173.27 [3819]E(f333(f333(f162(x38191,x38192),f333(f16(x38192,x38191),x38193)),x38194),f177(x38192,f333(f197(f911(x38191)),x38194),x38193)) % 173.51/173.27 [3855]E(f17(x38551,x38552,x38553,f333(a3,f333(a123,f333(a20,x38554)))),f333(x38553,x38554)) % 173.51/173.27 [3859]E(f333(f333(f142(x38591),f333(f144(x38591,x38592),x38593)),f333(f144(x38591,x38592),x38594)),f333(f144(x38591,x38592),f333(f333(f142(x38591),x38593),x38594))) % 173.51/173.27 [3872]E(f160(x38721,f333(f333(f162(x38722,x38721),x38723),f160(x38722,x38724))),f160(x38721,f333(f333(f162(x38722,x38721),x38723),x38724))) % 173.51/173.27 [3887]E(f333(f293(x38871,x38871),f333(f333(f294(x38872,x38871),x38873),x38874)),f333(f333(f294(x38872,x38871),f333(f293(x38872,x38872),x38873)),x38874)) % 173.51/173.27 [3898]E(f333(f333(f295(x38981,x38982,x38983),x38984),f196(f917(f916(x38982,x38983),a905))),f196(f917(f916(x38981,x38983),a905))) % 173.51/173.27 [3899]E(f333(f333(f183(x38991),f333(f333(f23(a910),x38992),x38993)),f333(f333(f146(x38991),x38993),x38994)),f333(f333(f146(x38991),x38993),f333(f333(f183(x38991),x38992),x38994))) % 173.51/173.27 [3918]E(f333(f333(f142(x39181),f177(x39181,x39182,x39183)),f177(x39181,x39184,x39183)),f177(x39181,f333(f333(f87(a910),x39182),x39184),x39183)) % 173.51/173.27 [3919]E(f333(f333(f333(f285(x39191),x39192),x39193),x39194),f333(f265(f917(a110,f917(a905,f914(f912(x39191)))),f916(a110,a110)),f333(f48(x39191),x39192))) % 173.51/173.27 [3945]E(f44(f917(x39451,a905),f333(f316(x39452,f917(x39451,a905),x39453),x39454)),f333(f333(f46(x39452,f917(x39451,a905)),x39454),x39453)) % 173.51/173.27 [3946]E(f43(f917(x39461,a905),f333(f316(x39462,f917(x39461,a905),x39463),x39464)),f333(f333(f45(x39462,f917(x39461,a905)),x39464),x39463)) % 173.51/173.27 [3947]E(f333(f197(f911(f916(x39471,x39472))),f333(f333(f189(x39471,x39472),x39473),x39474)),f333(f333(f244(a910),f333(f197(f911(x39471)),x39473)),f333(f197(f911(x39472)),x39474))) % 173.51/173.27 [3949]E(f333(f317(x39491,x39492,x39493),f333(f86(f917(x39492,a905)),x39494)),f333(f86(f917(x39491,a905)),f333(f317(x39491,x39492,x39493),x39494))) % 173.51/173.27 [3998]E(f333(f317(x39981,x39982,x39983),f333(f252(x39982),x39984)),f333(f252(x39981),f333(f333(f8(x39982,a905,x39981),x39984),x39983))) % 173.51/173.27 [4016]E(f333(f333(f172(x40161),f333(f333(f142(x40161),x40162),f333(f333(f159(x40161),x40163),x40164))),f333(f197(f911(x40161)),x40162)),x40163) % 173.51/173.27 [4041]E(f333(f316(x40411,x40412,x40413),f333(f317(x40411,x40412,x40413),x40414)),f333(f333(f112(f917(x40412,a905)),x40414),f333(f316(x40411,x40412,x40413),f254(f917(x40411,a905))))) % 173.51/173.27 [4060]P106(f333(f333(f335(x40601),f333(x40602,x40603)),f333(f316(x40604,x40601,x40602),f254(f917(x40604,a905))))) % 173.51/173.27 [4068]E(f19(x40681,x40682,x40683,f333(a3,f333(a123,f333(a20,x40684)))),f333(f333(x40683,x40684),f19(x40681,x40682,x40683,x40684))) % 173.51/173.27 [4072]E(f333(f333(f142(x40721),f177(x40721,x40722,x40723)),f333(f333(f159(x40721),x40723),x40724)),f333(f333(f159(x40721),x40723),f333(f333(f142(x40721),f177(x40721,x40722,x40723)),x40724))) % 173.51/173.27 [4074]E(f333(f333(f267(x40741,x40742),f333(f180(x40741),x40743)),f333(f16(f917(x40742,a905),x40741),f333(f180(x40742),x40744))),f333(f180(f916(x40741,x40742)),f65(x40741,x40742,x40743,x40744))) % 173.51/173.27 [4086]E(f163(x40861,x40862,f333(f333(f159(x40861),x40863),x40864)),f333(f333(f87(a910),f333(f333(f87(a910),f333(x40862,x40863)),f163(x40861,x40862,x40864))),f333(a123,f2(a910)))) % 173.51/173.27 [4100]E(f193(f911(x41001),f333(f333(f159(x41001),x41002),x41003),f333(f333(f7(a910,f911(x41001),f911(x41001)),f146(x41001)),x41003),x41004),f333(f333(f146(x41001),x41004),f333(f333(f159(x41001),x41002),x41003))) % 173.51/173.27 [4101]P27(x41011,f916(x41012,x41011),f337(x41013,x41014,x41012,x41011),f333(f333(f45(x41012,f917(x41011,a905)),x41014),x41013)) % 173.51/173.27 [4110]E(f333(f333(f23(f917(x41101,a905)),f333(f333(f23(f917(x41101,a905)),x41102),x41103)),f333(f333(f315(x41101),x41104),f196(f917(x41101,a905)))),f333(f333(f23(f917(x41101,a905)),x41102),f333(f333(f315(x41101),x41104),x41103))) % 173.51/173.27 [4120]E(f333(f333(f191(f917(x41201,x41202),f917(x41201,x41202)),x41203),f79(x41202,x41202,x41201,x41204)),f79(x41202,x41202,x41201,f333(f333(f191(x41202,x41202),x41203),x41204))) % 173.51/173.27 [4196]E(f333(f333(f333(f191(f911(x41961),f911(x41961)),x41962),f175(x41961)),f333(f333(f333(f191(f911(x41961),f911(x41961)),x41963),f175(x41961)),x41964)),f333(f333(f333(f191(f911(x41961),f911(x41961)),f333(f333(f87(a910),x41962),x41963)),f175(x41961)),x41964)) % 173.51/173.27 [4281]P106(f333(f333(f246(f917(x42811,a905)),f333(f180(x42811),f333(f333(f167(x42811,x42812),x42813),x42814))),f333(f333(f315(x42811),x42814),f333(f180(x42811),x42812)))) % 173.51/173.27 [4314]E(f333(f333(f45(f917(x43141,a905),f917(f916(x43141,x43142),a905)),x43143),f333(f333(f7(f917(x43141,a905),f917(x43141,f917(x43142,a905)),f917(f916(x43141,x43142),a905)),f267(x43141,x43142)),x43144)),f333(f333(f267(x43141,x43142),f43(f917(x43141,a905),x43143)),x43144)) % 173.51/173.27 [4351]E(f221(x43511,x43512,x43513,f333(f79(x43512,f917(a110,f917(a110,f917(f916(a110,a110),f917(a110,f912(x43512))))),x43511,f216(x43512)),x43514)),f222(x43511,x43512,x43514,x43513)) % 173.51/173.27 [4366]E(f218(x43661,x43662,x43663,f333(f79(x43662,f917(a110,f917(a110,f917(f916(a110,a110),f917(a110,f912(f914(x43662)))))),x43661,f217(x43662)),x43664)),f219(x43661,x43662,x43664,x43663)) % 173.51/173.27 [4371]P106(f333(f72(x43711,x43712,x43713,x43714,f196(f917(x43711,a905))),x43714)) % 173.51/173.27 [4410]E(f333(f333(f45(x44101,f917(x44102,a905)),x44103),f333(f333(f7(x44101,f917(x44102,a905),f917(x44102,a905)),f333(f333(f8(x44102,f917(f917(x44102,a905),f917(x44102,a905)),x44101),f315(x44102)),x44104)),f196(f917(x44102,a905)))),f333(f316(x44101,x44102,x44104),x44103)) % 173.51/173.27 [4417]P106(f333(f333(f246(f917(x44171,a905)),f333(f291(x44172,x44171),f333(f333(f112(f917(f916(x44172,x44171),a905)),x44173),x44174))),f333(f333(f112(f917(x44171,a905)),f333(f291(x44172,x44171),x44173)),f333(f291(x44172,x44171),x44174)))) % 173.51/173.27 [4418]P106(f333(f333(f246(f917(x44181,a905)),f333(f263(x44181,x44182),f333(f333(f112(f917(f916(x44181,x44182),a905)),x44183),x44184))),f333(f333(f112(f917(x44181,a905)),f333(f263(x44181,x44182),x44183)),f333(f263(x44181,x44182),x44184)))) % 173.51/173.27 [4478]P106(f333(f333(f246(f917(f916(x44781,x44782),a905)),f333(f316(x44782,f916(x44781,x44782),f337(x44783,x44784,x44781,x44782)),f333(f333(f45(x44781,f917(x44782,a905)),x44784),x44783))),f333(f333(f267(x44781,x44782),x44784),x44783))) % 173.51/173.27 [4479]E(f333(f129(x44791,f916(x44791,x44792),x44793),f333(f333(f8(f917(x44792,f912(f916(x44791,x44792))),f912(f916(x44791,x44792)),x44791),f129(x44792,f916(x44791,x44792),x44794)),f333(f333(f8(f917(x44792,f916(x44791,x44792)),f917(x44792,f912(f916(x44791,x44792))),x44791),f333(f8(f916(x44791,x44792),f912(f916(x44791,x44792)),x44792),f138(f916(x44791,x44792)))),f265(x44791,x44792)))),f139(x44791,x44792,x44793,x44794)) % 173.51/173.27 [4480]E(f283(x44801,x44802,x44803,f333(f79(x44802,f917(a110,f917(a110,f917(f916(a110,a110),f916(f917(a110,f917(a905,f914(f912(x44802)))),f916(a110,a110))))),x44801,f285(x44802)),x44804)),f286(x44801,x44802,x44804,x44803)) % 173.51/173.27 [4520]E(f92(f916(x45201,x45202),f333(f269(x45201,x45202,a905),f333(f333(f7(x45201,f917(x45202,a905),f917(x45202,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x45202,a905),f917(x45202,a905)),x45201),f8(a905,a905,x45202)),f333(f333(f8(a905,f917(a905,a905),x45201),a331),f333(a330,x45203)))),f333(a330,x45204)))),f333(f333(f265(x45201,x45202),x45203),x45204)) % 173.51/173.27 [4521]E(f97(f916(x45211,x45212),f333(f269(x45211,x45212,a905),f333(f333(f7(x45211,f917(x45212,a905),f917(x45212,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x45212,a905),f917(x45212,a905)),x45211),f8(a905,a905,x45212)),f333(f333(f8(a905,f917(a905,a905),x45211),a331),f333(a330,x45213)))),f333(a330,x45214)))),f333(f333(f265(x45211,x45212),x45213),x45214)) % 173.51/173.27 [4594]E(f333(f333(f269(f911(x45941),f911(x45941),f916(f911(x45941),f911(x45941))),f333(f333(f18(f911(x45941),f917(f911(x45941),f916(f911(x45941),f911(x45941))),f917(f911(x45941),f916(f911(x45941),f911(x45941)))),f333(f333(f8(f917(f911(x45941),f917(f916(f911(x45941),f911(x45941)),f916(f911(x45941),f911(x45941)))),f917(f917(f911(x45941),f916(f911(x45941),f911(x45941))),f917(f911(x45941),f916(f911(x45941),f911(x45941)))),f911(x45941)),f18(f911(x45941),f916(f911(x45941),f911(x45941)),f916(f911(x45941),f911(x45941)))),f333(f333(f8(f917(f911(x45941),f916(f911(x45941),f911(x45941))),f917(f911(x45941),f917(f916(f911(x45941),f911(x45941)),f916(f911(x45941),f911(x45941)))),f911(x45941)),f333(f8(f916(f911(x45941),f911(x45941)),f917(f916(f911(x45941),f911(x45941)),f916(f911(x45941),f911(x45941))),f911(x45941)),f333(f107(f916(f911(x45941),f911(x45941))),f333(x45942,x45943)))),f333(f333(f8(f911(x45941),f917(f911(x45941),f916(f911(x45941),f911(x45941))),f911(x45941)),f265(f911(x45941),f911(x45941))),f333(f159(x45941),x45943))))),f333(f333(f7(f911(x45941),f917(f911(x45941),f911(x45941)),f917(f911(x45941),f916(f911(x45941),f911(x45941)))),f333(f333(f8(f917(f911(x45941),f916(f911(x45941),f911(x45941))),f917(f917(f911(x45941),f911(x45941)),f917(f911(x45941),f916(f911(x45941),f911(x45941)))),f911(x45941)),f8(f911(x45941),f916(f911(x45941),f911(x45941)),f911(x45941))),f265(f911(x45941),f911(x45941)))),f333(f159(x45941),x45943)))),f174(x45941,x45942,x45944)),f174(x45941,x45942,f333(f333(f159(x45941),x45943),x45944))) % 173.51/173.27 [3706]E(f333(f197(f909(x37061)),f333(f333(f333(f98(x37061),x37062),x37063),x37064)),f2(a910)) % 173.51/173.27 [3835]E(f333(f333(f183(x38351),x38352),f333(f333(f183(x38351),x38353),x38354)),f333(f333(f183(x38351),f333(f333(f244(a910),x38352),x38353)),x38354)) % 173.51/173.27 [3836]E(f333(f333(f146(x38361),x38362),f333(f333(f146(x38361),x38363),x38364)),f333(f333(f146(x38361),f333(f333(f87(a910),x38362),x38363)),x38364)) % 173.51/173.27 [3847]E(f333(f333(f142(x38471),f333(f333(f159(x38471),x38472),x38473)),x38474),f333(f333(f159(x38471),x38472),f333(f333(f142(x38471),x38473),x38474))) % 173.51/173.27 [3848]E(f333(f333(f142(x38481),f333(f333(f142(x38481),x38482),x38483)),x38484),f333(f333(f142(x38481),x38482),f333(f333(f142(x38481),x38483),x38484))) % 173.51/173.27 [3929]E(f333(f333(f172(x39291),f333(f333(f159(x39291),x39292),x39293)),x39294),f193(x39291,x39292,f333(f172(x39291),x39293),x39294)) % 173.51/173.27 [3938]E(f333(f333(f191(x39381,x39381),x39382),f333(f333(f191(x39381,x39381),x39383),x39384)),f333(f333(f191(x39381,x39381),f333(f333(f88(a910),x39383),x39382)),x39384)) % 173.51/173.27 [3967]E(f333(f333(f121(f917(x39671,a905)),x39672),f333(f333(f315(x39671),x39673),x39674)),f333(f333(f315(x39671),x39673),f333(f333(f121(f917(x39671,a905)),x39672),x39674))) % 173.51/173.27 [3981]E(f333(f333(f333(f191(x39811,x39811),x39812),x39813),f333(x39813,x39814)),f333(x39813,f333(f333(f333(f191(x39811,x39811),x39812),x39813),x39814))) % 173.51/173.27 [3989]E(f333(f333(f295(x39891,x39892,x39893),f196(f917(f916(x39891,x39892),a905))),x39894),f196(f917(f916(x39891,x39893),a905))) % 173.51/173.27 [4004]E(f333(f333(f121(f917(x40041,a905)),f333(f333(f315(x40041),x40042),x40043)),x40044),f333(f333(f315(x40041),x40042),f333(f333(f121(f917(x40041,a905)),x40043),x40044))) % 173.51/173.27 [4023]E(f333(f41(f916(x40231,x40232)),f333(f333(f267(x40231,x40232),x40233),f333(f16(f917(x40232,a905),x40231),x40234))),f333(f333(f88(a910),f333(f41(x40231),x40233)),f333(f41(x40232),x40234))) % 173.51/173.27 [4032]E(f333(f333(f112(f917(x40321,a905)),f333(f333(f315(x40321),x40322),x40323)),f333(f333(f315(x40321),x40322),x40324)),f333(f333(f315(x40321),x40322),f333(f333(f112(f917(x40321,a905)),x40323),x40324))) % 173.51/173.27 [4045]E(f333(f333(f121(f917(x40451,a905)),x40452),f333(f333(f121(f917(x40451,a905)),x40453),x40454)),f333(f333(f121(f917(x40451,a905)),x40453),f333(f333(f121(f917(x40451,a905)),x40452),x40454))) % 173.51/173.27 [4046]E(f333(f333(f112(f917(x40461,a905)),x40462),f333(f333(f112(f917(x40461,a905)),x40463),x40464)),f333(f333(f112(f917(x40461,a905)),x40463),f333(f333(f112(f917(x40461,a905)),x40462),x40464))) % 173.51/173.27 [4056]E(f70(x40561,x40562,f333(f333(f8(x40562,f917(x40562,x40562),x40561),x40563),x40564)),f333(f71(x40562,x40561,x40563),x40564)) % 173.51/173.27 [4065]E(f187(x40651,f333(f333(f162(f911(x40652),f911(x40651)),f333(f162(x40652,x40651),x40653)),x40654)),f333(f333(f162(f911(x40652),f911(x40651)),f333(f162(x40652,x40651),x40653)),f187(x40652,x40654))) % 173.51/173.27 [4083]E(f333(f150(f911(x40831),f911(x40831),f142(x40831),f124(x40831)),f333(f333(f162(x40832,f911(x40831)),x40833),x40834)),f171(x40832,x40831,x40833,x40834)) % 173.51/173.27 [4143]E(f333(f79(x41431,x41431,x41431,f333(f333(f191(x41431,x41431),x41432),x41433)),f333(f333(f191(x41431,x41431),x41434),x41433)),f333(f333(f191(x41431,x41431),f333(f333(f87(a910),x41432),x41434)),x41433)) % 173.51/173.27 [4166]E(f333(f333(f112(f917(x41661,a905)),f333(f333(f121(f917(x41661,a905)),x41662),x41663)),f333(f333(f121(f917(x41661,a905)),x41662),x41664)),f333(f333(f121(f917(x41661,a905)),x41662),f333(f333(f112(f917(x41661,a905)),x41663),x41664))) % 173.51/173.27 [4167]E(f333(f333(f121(f917(x41671,a905)),f333(f333(f112(f917(x41671,a905)),x41672),x41673)),f333(f333(f112(f917(x41671,a905)),x41672),x41674)),f333(f333(f112(f917(x41671,a905)),x41672),f333(f333(f121(f917(x41671,a905)),x41673),x41674))) % 173.51/173.27 [4168]E(f333(f333(f23(f917(x41681,a905)),f333(f333(f112(f917(x41681,a905)),x41682),x41683)),f333(f333(f112(f917(x41681,a905)),x41682),x41684)),f333(f333(f112(f917(x41681,a905)),x41682),f333(f333(f23(f917(x41681,a905)),x41683),x41684))) % 173.51/173.27 [4169]E(f333(f333(f112(f917(x41691,a905)),f333(f333(f23(f917(x41691,a905)),x41692),x41693)),f333(f333(f23(f917(x41691,a905)),x41692),x41694)),f333(f333(f23(f917(x41691,a905)),x41692),f333(f333(f121(f917(x41691,a905)),x41693),x41694))) % 173.51/173.27 [4170]E(f333(f333(f121(f917(x41701,a905)),f333(f333(f23(f917(x41701,a905)),x41702),x41703)),f333(f333(f23(f917(x41701,a905)),x41702),x41704)),f333(f333(f23(f917(x41701,a905)),x41702),f333(f333(f112(f917(x41701,a905)),x41703),x41704))) % 173.51/173.27 [4175]E(f333(f41(f916(x41751,x41752)),f333(f333(f267(x41751,x41752),f333(f333(f315(x41751),x41753),f196(f917(x41751,a905)))),f333(f16(f917(x41752,a905),x41751),x41754))),f333(f41(x41752),x41754)) % 173.51/173.27 [4210]E(f333(f333(f46(x42101,f917(x42102,a905)),x42103),f333(f333(f8(f917(x42102,a905),f917(x42102,a905),x42101),f86(f917(x42102,a905))),x42104)),f333(f86(f917(x42102,a905)),f333(f333(f45(x42101,f917(x42102,a905)),x42103),x42104))) % 173.51/173.27 [4211]E(f333(f333(f45(x42111,f917(x42112,a905)),x42113),f333(f333(f8(f917(x42112,a905),f917(x42112,a905),x42111),f86(f917(x42112,a905))),x42114)),f333(f86(f917(x42112,a905)),f333(f333(f46(x42111,f917(x42112,a905)),x42113),x42114))) % 173.51/173.27 [4227]E(f333(f333(f295(x42271,x42271,x42271),f333(f333(f191(f916(x42271,x42271),a905),x42272),x42273)),f333(f333(f191(f916(x42271,x42271),a905),x42274),x42273)),f333(f333(f191(f916(x42271,x42271),a905),f333(f333(f87(a910),x42272),x42274)),x42273)) % 173.51/173.27 [4257]E(f333(f333(f46(x42571,f917(f917(x42572,a905),a905)),x42573),f333(f333(f8(f917(x42572,a905),f917(f917(x42572,a905),a905),x42571),f314(x42572)),x42574)),f333(f314(x42572),f333(f333(f46(x42571,f917(x42572,a905)),x42573),x42574))) % 173.51/173.27 [4286]E(f333(f333(f45(f917(x42861,a905),f917(x42862,a905)),x42863),f333(f333(f7(f917(x42861,a905),f917(x42861,f917(x42862,a905)),f917(x42862,a905)),f45(x42861,f917(x42862,a905))),x42864)),f333(f333(f45(x42861,f917(x42862,a905)),f43(f917(x42861,a905),x42863)),x42864)) % 173.51/173.27 [4287]E(f333(f333(f46(f917(x42871,a905),f917(x42872,a905)),x42873),f333(f333(f7(f917(x42871,a905),f917(x42871,f917(x42872,a905)),f917(x42872,a905)),f46(x42871,f917(x42872,a905))),x42874)),f333(f333(f46(x42871,f917(x42872,a905)),f43(f917(x42871,a905),x42873)),x42874)) % 173.51/173.27 [4292]E(f333(f333(f162(x42921,x42922),x42923),f333(f150(f911(x42921),f911(x42921),f142(x42921),f124(x42921)),x42924)),f333(f150(f911(x42922),f911(x42922),f142(x42922),f124(x42922)),f333(f333(f162(f911(x42921),f911(x42922)),f333(f162(x42921,x42922),x42923)),x42924))) % 173.51/173.27 [4295]E(f193(f911(x42951),f124(x42951),f333(f333(f8(f911(x42951),f911(x42951),a910),f333(f159(x42951),x42952)),f333(f333(f7(a910,f911(x42951),f911(x42951)),f183(x42951)),x42953)),x42954),f333(f333(f183(x42951),x42954),f333(f333(f159(x42951),x42952),x42953))) % 173.51/173.27 [4333]P106(f333(f333(f246(f917(x43331,a905)),f333(f316(x43332,x43331,x43333),f333(f317(x43332,x43331,x43333),x43334))),x43334)) % 173.51/173.27 [4335]E(f333(f316(f916(x43351,x43352),f916(x43352,x43351),f333(f269(x43351,x43352,f916(x43352,x43351)),f333(f7(x43352,x43351,f916(x43352,x43351)),f265(x43352,x43351)))),f333(f333(f267(x43351,x43352),x43353),f333(f16(f917(x43352,a905),x43351),x43354))),f333(f333(f267(x43352,x43351),x43354),f333(f16(f917(x43351,a905),x43352),x43353))) % 173.51/173.27 [4344]E(f333(f333(f45(x43441,f917(x43442,a905)),x43443),f333(f333(f8(f917(x43441,a905),f917(x43442,a905),x43441),f317(x43442,x43441,x43444)),f333(f333(f7(x43441,f917(x43441,a905),f917(x43441,a905)),f315(x43441)),f196(f917(x43441,a905))))),f333(f317(x43442,x43441,x43444),x43443)) % 173.51/173.27 [4345]E(f333(f333(f45(x43451,f917(x43452,a905)),x43453),f333(f333(f8(f917(x43451,a905),f917(x43452,a905),x43451),f292(x43451,x43452,x43454)),f333(f333(f7(x43451,f917(x43451,a905),f917(x43451,a905)),f315(x43451)),f196(f917(x43451,a905))))),f333(f292(x43451,x43452,x43454),x43453)) % 173.51/173.27 [4431]E(f333(f333(f121(f917(x44311,a905)),f333(f333(f121(f917(x44311,a905)),f333(f333(f112(f917(x44311,a905)),x44312),x44313)),f333(f333(f112(f917(x44311,a905)),x44313),x44314))),f333(f333(f112(f917(x44311,a905)),x44314),x44312)),f333(f333(f112(f917(x44311,a905)),f333(f333(f112(f917(x44311,a905)),f333(f333(f121(f917(x44311,a905)),x44312),x44313)),f333(f333(f121(f917(x44311,a905)),x44313),x44314))),f333(f333(f121(f917(x44311,a905)),x44314),x44312))) % 173.51/173.27 [4494]E(f333(f150(f911(x44941),f911(x44941),f142(x44941),f124(x44941)),f333(f333(f162(x44942,f911(x44941)),f333(f333(f7(x44942,f911(x44941),f911(x44941)),f333(f333(f8(x44941,f917(f911(x44941),f911(x44941)),x44942),f159(x44941)),x44943)),f124(x44941))),x44944)),f333(f333(f162(x44942,x44941),x44943),x44944)) % 173.51/173.27 [4504]E(f333(f333(f93(a1,x45041),f333(f114(a1),f333(f333(f87(a1),x45042),a108))),f333(f333(f18(a1,x45041,x45041),f333(f333(f7(a1,x45041,f917(x45041,x45041)),f333(f333(f8(a905,f917(x45041,f917(x45041,x45041)),a1),f107(x45041)),a201)),x45043)),f333(f333(f8(a910,x45041,a1),x45044),a115))),f193(x45041,x45043,x45044,f333(f114(a910),x45042))) % 173.51/173.27 [4535]E(f333(f252(x45351),f333(f333(f8(f917(x45352,a905),a905,x45351),f94(x45352)),f333(f333(f8(f917(x45352,a905),f917(x45352,a905),x45351),f333(f18(x45352,a905,a905),f333(f333(f8(a905,f917(a905,a905),x45352),a331),f333(f333(f7(x45352,f917(x45352,a905),a905),f335(x45352)),x45353)))),f333(f7(x45352,x45351,a905),x45354)))),f333(f292(x45352,x45351,f333(f252(f916(x45352,x45351)),f333(f269(x45352,x45351,a905),x45354))),x45353)) % 173.51/173.27 [4710]~P106(f333(f333(f196(f917(x47101,f917(x47102,a905))),x47103),x47104)) % 173.51/173.27 [3992]E(f333(f333(f172(x39921),f333(f333(f142(x39921),x39922),x39923)),f333(f333(f87(a910),f333(f197(f911(x39921)),x39922)),x39924)),f333(f333(f172(x39921),x39923),x39924)) % 173.51/173.27 [3997]E(f333(f333(f146(x39971),x39972),f333(f333(f183(x39971),f333(f333(f87(a910),x39973),x39972)),x39974)),f333(f333(f183(x39971),x39973),f333(f333(f146(x39971),x39972),x39974))) % 173.51/173.27 [4098]E(f333(f333(f121(f917(x40981,a905)),f333(f291(x40982,x40981),x40983)),f333(f291(x40982,x40981),x40984)),f333(f291(x40982,x40981),f333(f333(f121(f917(f916(x40982,x40981),a905)),x40983),x40984))) % 173.51/173.27 [4099]E(f333(f333(f121(f917(x40991,a905)),f333(f263(x40991,x40992),x40993)),f333(f263(x40991,x40992),x40994)),f333(f263(x40991,x40992),f333(f333(f121(f917(f916(x40991,x40992),a905)),x40993),x40994))) % 173.51/173.27 [4104]E(f333(f333(f121(f917(x41041,a905)),f333(f333(f121(f917(x41041,a905)),x41042),x41043)),x41044),f333(f333(f121(f917(x41041,a905)),x41042),f333(f333(f121(f917(x41041,a905)),x41043),x41044))) % 173.51/173.27 [4105]E(f333(f333(f112(f917(x41051,a905)),f333(f333(f112(f917(x41051,a905)),x41052),x41053)),x41054),f333(f333(f112(f917(x41051,a905)),x41052),f333(f333(f112(f917(x41051,a905)),x41053),x41054))) % 173.51/173.27 [4106]E(f333(f333(f23(f917(x41061,a905)),f333(f333(f112(f917(x41061,a905)),x41062),x41063)),x41064),f333(f333(f112(f917(x41061,a905)),x41062),f333(f333(f23(f917(x41061,a905)),x41063),x41064))) % 173.51/173.27 [4145]E(f333(f333(f121(f917(f916(x41451,x41452),a905)),f333(f293(x41452,x41451),x41453)),f333(f293(x41452,x41451),x41454)),f333(f293(x41452,x41451),f333(f333(f121(f917(f916(x41452,x41451),a905)),x41453),x41454))) % 173.51/173.27 [4146]E(f333(f333(f112(f917(f916(x41461,x41462),a905)),f333(f293(x41462,x41461),x41463)),f333(f293(x41462,x41461),x41464)),f333(f293(x41462,x41461),f333(f333(f112(f917(f916(x41462,x41461),a905)),x41463),x41464))) % 173.51/173.27 [4159]E(f333(f333(f121(f917(x41591,f917(x41592,a905))),f255(x41592,x41591,x41593)),f255(x41592,x41591,x41594)),f255(x41592,x41591,f333(f333(f121(f917(x41592,f917(x41591,a905))),x41593),x41594))) % 173.51/173.27 [4160]E(f333(f333(f112(f917(x41601,f917(x41602,a905))),f255(x41602,x41601,x41603)),f255(x41602,x41601,x41604)),f255(x41602,x41601,f333(f333(f112(f917(x41602,f917(x41601,a905))),x41603),x41604))) % 173.51/173.27 [4214]E(f333(f333(f112(f917(x42141,a905)),f333(f333(f121(f917(x42141,a905)),x42142),x42143)),f333(f333(f121(f917(x42141,a905)),x42144),x42143)),f333(f333(f121(f917(x42141,a905)),f333(f333(f112(f917(x42141,a905)),x42142),x42144)),x42143)) % 173.51/173.27 [4215]E(f333(f333(f121(f917(x42151,a905)),f333(f333(f112(f917(x42151,a905)),x42152),x42153)),f333(f333(f112(f917(x42151,a905)),x42154),x42153)),f333(f333(f112(f917(x42151,a905)),f333(f333(f121(f917(x42151,a905)),x42152),x42154)),x42153)) % 173.51/173.27 [4216]E(f333(f333(f23(f917(x42161,a905)),f333(f333(f112(f917(x42161,a905)),x42162),x42163)),f333(f333(f112(f917(x42161,a905)),x42164),x42163)),f333(f333(f112(f917(x42161,a905)),f333(f333(f23(f917(x42161,a905)),x42162),x42164)),x42163)) % 173.51/173.27 [4217]E(f333(f333(f121(f917(x42171,a905)),f333(f333(f23(f917(x42171,a905)),x42172),x42173)),f333(f333(f23(f917(x42171,a905)),x42174),x42173)),f333(f333(f23(f917(x42171,a905)),f333(f333(f121(f917(x42171,a905)),x42172),x42174)),x42173)) % 173.51/173.27 [4218]E(f333(f333(f23(f917(x42181,a905)),f333(f333(f112(f917(x42181,a905)),x42182),x42183)),f333(f333(f112(f917(x42181,a905)),x42184),x42183)),f333(f333(f23(f917(x42181,a905)),f333(f333(f112(f917(x42181,a905)),x42182),x42183)),x42184)) % 173.51/173.27 [4230]E(f333(f333(f23(f917(x42301,a905)),f333(f333(f23(f917(x42301,a905)),x42302),f333(f333(f315(x42301),x42303),f196(f917(x42301,a905))))),x42304),f333(f333(f23(f917(x42301,a905)),x42302),f333(f333(f315(x42301),x42303),x42304))) % 173.51/173.27 [4283]E(f333(f333(f121(f917(x42831,a905)),f333(f333(f315(x42831),x42832),f333(f333(f315(x42831),x42833),f196(f917(x42831,a905))))),f333(f288(x42831),x42834)),f333(f288(x42831),f333(f333(f315(f916(x42831,x42831)),f333(f333(f265(x42831,x42831),x42832),x42833)),x42834))) % 173.51/173.27 [4309]E(f333(f333(f45(a910,f917(x43091,a905)),f333(f307(a910),x43092)),f333(f333(f8(a910,f917(x43091,a905),a910),x43093),f333(f333(f7(a910,a910,a910),f87(a910)),x43094))),f333(f333(f45(a910,f917(x43091,a905)),f309(a910,x43094,f333(f333(f87(a910),x43092),x43094))),x43093)) % 173.51/173.27 [4310]E(f182(x43101,f333(f292(x43101,x43101,x43102),f333(f333(f315(x43101),x43103),f196(f917(x43101,a905)))),f333(f292(f911(x43101),f911(x43101),f166(x43101,x43102)),f333(f333(f315(f911(x43101)),x43104),f196(f917(f911(x43101),a905))))),f333(f292(f911(x43101),f911(x43101),f166(x43101,x43102)),f333(f333(f315(f911(x43101)),f333(f333(f159(x43101),x43103),x43104)),f196(f917(f911(x43101),a905))))) % 173.51/173.27 [4373]E(f333(f252(x43731),f333(f333(f7(x43731,f917(x43732,a905),a905),f333(f333(f8(x43732,f917(f917(x43732,a905),a905),x43731),f335(x43732)),x43733)),x43734)),f333(f317(x43731,x43732,x43733),x43734)) % 173.51/173.27 [4463]E(f333(f252(x44631),f333(f333(f7(x44631,f917(f916(x44632,x44631),a905),a905),f333(f333(f8(f916(x44632,x44631),f917(f917(f916(x44632,x44631),a905),a905),x44631),f335(f916(x44632,x44631))),f333(f265(x44632,x44631),x44633))),x44634)),f333(f292(x44632,x44631,x44634),f333(f333(f315(x44632),x44633),f196(f917(x44632,a905))))) % 173.51/173.27 [4477]E(f333(f333(f162(f916(x44771,a910),x44771),f264(x44771,a910)),f333(f144(f916(x44771,a910),f333(f333(f8(a910,a905,f916(x44771,a910)),x44772),f333(f333(f8(a910,a910,f916(x44771,a910)),a123),f268(x44771,a910)))),f333(f333(f189(x44771,a910),x44773),x44774))),f333(f333(f162(f916(x44771,a910),x44771),f264(x44771,a910)),f333(f144(f916(x44771,a910),f333(f333(f8(a910,a905,f916(x44771,a910)),x44772),f268(x44771,a910))),f333(f333(f189(x44771,a910),x44773),f333(f333(f162(a910,a910),a123),x44774))))) % 173.51/173.27 [4486]P106(f333(f333(f246(f917(f917(x44861,a905),a905)),f333(f333(f45(x44862,f917(f917(x44861,a905),a905)),x44863),f333(f333(f8(f917(x44861,a905),f917(f917(x44861,a905),a905),x44862),f314(x44861)),x44864))),f333(f314(x44861),f333(f333(f45(x44862,f917(x44861,a905)),x44863),x44864)))) % 173.51/173.27 [4527]E(f333(f333(f93(a1,x45271),f333(f114(a1),f333(f333(f87(a1),x45272),a108))),f333(f333(f18(a1,x45271,x45271),f333(f333(f7(a1,x45271,f917(x45271,x45271)),f333(f333(f8(a905,f917(x45271,f917(x45271,x45271)),a1),f107(x45271)),a201)),x45273)),f333(f333(f18(a1,x45271,x45271),f333(f333(f8(a910,f917(x45271,x45271),a1),x45274),a115)),f333(f333(f8(a910,x45271,a1),f192(x45271,x45273,x45274)),a115)))),f333(f192(x45271,x45273,x45274),f333(f114(a910),x45272))) % 173.51/173.27 [4551]E(f333(f252(f916(x45511,x45512)),f333(f269(x45511,x45512,a905),f333(f333(f7(x45511,f917(x45512,a905),f917(x45512,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x45512,a905),f917(x45512,a905)),x45511),f8(a905,a905,x45512)),f333(f333(f8(a905,f917(a905,a905),x45511),a331),f333(f333(f7(x45511,f917(x45511,a905),a905),f335(x45511)),x45513)))),f333(f333(f7(x45512,f917(x45512,a905),a905),f335(x45512)),x45514)))),f241(x45511,x45512,x45513,x45514)) % 173.51/173.27 [4587]E(f333(f333(f45(x45871,f917(f916(x45871,x45872),a905)),x45873),f333(f333(f18(x45871,f917(x45872,f917(f916(x45871,x45872),a905)),f917(f916(x45871,x45872),a905)),f333(f333(f8(f917(x45872,a905),f917(f917(x45872,f917(f916(x45871,x45872),a905)),f917(f916(x45871,x45872),a905)),x45871),f45(x45872,f917(f916(x45871,x45872),a905))),x45874)),f333(f333(f7(x45871,f917(f916(x45871,x45872),a905),f917(x45872,f917(f916(x45871,x45872),a905))),f333(f333(f8(f917(x45872,f917(f917(f916(x45871,x45872),a905),f917(f916(x45871,x45872),a905))),f917(f917(f916(x45871,x45872),a905),f917(x45872,f917(f916(x45871,x45872),a905))),x45871),f7(x45872,f917(f916(x45871,x45872),a905),f917(f916(x45871,x45872),a905))),f333(f333(f8(f917(x45872,f916(x45871,x45872)),f917(x45872,f917(f917(f916(x45871,x45872),a905),f917(f916(x45871,x45872),a905))),x45871),f333(f8(f916(x45871,x45872),f917(f917(f916(x45871,x45872),a905),f917(f916(x45871,x45872),a905)),x45872),f315(f916(x45871,x45872)))),f265(x45871,x45872)))),f196(f917(f916(x45871,x45872),a905))))),f333(f333(f267(x45871,x45872),x45873),x45874)) % 173.51/173.27 [4154]E(f333(f333(f142(x41541),f333(f333(f183(x41541),x41542),x41543)),f333(f333(f183(x41541),f333(f333(f23(a910),x41542),f333(f197(f911(x41541)),x41543))),x41544)),f333(f333(f183(x41541),x41542),f333(f333(f142(x41541),x41543),x41544))) % 173.51/173.27 [4155]E(f333(f333(f142(x41551),f333(f333(f146(x41551),x41552),x41553)),f333(f333(f146(x41551),f333(f333(f23(a910),x41552),f333(f197(f911(x41551)),x41553))),x41554)),f333(f333(f146(x41551),x41552),f333(f333(f142(x41551),x41553),x41554))) % 173.51/173.27 [4204]E(f333(f333(f87(a910),f333(f333(f88(a910),x42041),x42042)),f333(f333(f87(a910),f333(f333(f88(a910),x42043),x42042)),x42044)),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f87(a910),x42041),x42043)),x42042)),x42044)) % 173.51/173.27 [4349]E(f97(x43491,f333(f333(f7(x43491,x43492,a905),f333(f333(f8(x43492,f917(x43492,a905),x43491),a330),x43493)),x43494)),f333(f99(x43491,x43492,f254(f917(x43491,a905)),x43493),x43494)) % 173.51/173.27 [4397]P106(f333(f333(f246(f917(x43971,a905)),f333(f333(f23(f917(x43971,a905)),f333(f291(x43972,x43971),x43973)),f333(f291(x43972,x43971),x43974))),f333(f291(x43972,x43971),f333(f333(f23(f917(f916(x43972,x43971),a905)),x43973),x43974)))) % 173.51/173.27 [4398]P106(f333(f333(f246(f917(x43981,a905)),f333(f333(f23(f917(x43981,a905)),f333(f263(x43981,x43982),x43983)),f333(f263(x43981,x43982),x43984))),f333(f263(x43981,x43982),f333(f333(f23(f917(f916(x43981,x43982),a905)),x43983),x43984)))) % 173.51/173.27 [4506]E(f333(f333(f87(a1),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x45061),x45062)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x45063),x45064)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),f333(f333(f87(a910),x45061),x45063)),f333(f333(f87(a910),x45062),x45064))),f196(f917(f916(a910,a910),a905)))))) % 173.51/173.27 [4546]E(f333(f333(f88(a1),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x45461),x45462)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x45463),x45464)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),f333(f333(f87(a910),f333(f333(f88(a910),x45461),x45463)),f333(f333(f88(a910),x45462),x45464))),f333(f333(f87(a910),f333(f333(f88(a910),x45461),x45464)),f333(f333(f88(a910),x45462),x45463)))),f196(f917(f916(a910,a910),a905)))))) % 173.51/173.27 [4567]E(f333(f252(x45671),f333(f333(f8(f917(x45672,a905),a905,x45671),f95(x45672)),f333(f333(f8(f917(x45672,a905),f917(x45672,a905),x45671),f333(f18(x45672,a905,a905),f333(f333(f8(a905,f917(a905,a905),x45672),a336),f333(f333(f7(x45672,f917(x45672,a905),a905),f335(x45672)),x45673)))),f333(f333(f7(x45671,f917(x45672,f917(x45671,a905)),f917(x45672,a905)),f333(f333(f8(f917(f917(x45671,a905),a905),f917(f917(x45672,f917(x45671,a905)),f917(x45672,a905)),x45671),f8(f917(x45671,a905),a905,x45672)),f335(x45671))),x45674)))),f333(f333(f46(x45672,f917(x45671,a905)),x45673),x45674)) % 173.51/173.27 [4602]E(f333(f333(f295(x46021,x46021,x46021),f333(f333(f315(f916(x46021,x46021)),f333(f333(f265(x46021,x46021),x46022),x46023)),x46024)),f313(x46021,f333(f333(f315(f916(x46021,x46021)),f333(f333(f265(x46021,x46021),x46022),x46023)),x46024))),f333(f333(f121(f917(f916(x46021,x46021),a905)),f333(f333(f295(x46021,x46021,x46021),x46024),f313(x46021,x46024))),f333(f252(f916(x46021,x46021)),f333(f269(x46021,x46021,a905),f333(f333(f7(x46021,f917(x46021,a905),f917(x46021,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x46021,a905),f917(x46021,a905)),x46021),f8(a905,a905,x46021)),f333(f333(f8(a905,f917(a905,a905),x46021),a331),f333(f333(f7(x46021,f917(f916(x46021,x46021),a905),a905),f333(f333(f8(f916(x46021,x46021),f917(f917(f916(x46021,x46021),a905),a905),x46021),f335(f916(x46021,x46021))),f333(f333(f7(x46021,x46021,f916(x46021,x46021)),f265(x46021,x46021)),x46022))),f313(x46021,x46024))))),f333(f333(f7(x46021,f917(f916(x46021,x46021),a905),a905),f333(f333(f8(f916(x46021,x46021),f917(f917(f916(x46021,x46021),a905),a905),x46021),f335(f916(x46021,x46021))),f333(f265(x46021,x46021),x46023))),f313(x46021,x46024))))))) % 173.51/173.27 [4399]E(f333(f144(x43991,f333(f333(f18(x43991,a905,a905),f333(f333(f8(a905,f917(a905,a905),x43991),a331),x43992)),x43993)),x43994),f333(f144(x43991,x43993),f333(f144(x43991,x43992),x43994))) % 173.51/173.27 [4500]E(f333(f333(f142(x45001),f333(f333(f333(f107(f911(x45001)),f333(f333(f335(a910),f2(a910)),x45002)),f333(f333(f159(x45001),x45003),f124(x45001))),f124(x45001))),f184(x45001,x45004,f333(f252(a910),f333(f333(f7(a910,f917(a910,a905),a905),f333(f333(f8(a910,f917(f917(a910,a905),a905),a910),f335(a910)),a123)),x45002)))),f184(x45001,f333(f333(f159(x45001),x45003),x45004),x45002)) % 173.51/173.27 [4598]E(f333(f252(f916(x45981,x45982)),f333(f333(f8(f917(a910,a905),a905,f916(x45981,x45982)),f94(a910)),f333(f333(f7(f916(x45981,x45982),f917(a910,a905),f917(a910,a905)),f333(f333(f8(f917(a910,f917(a905,a905)),f917(f917(a910,a905),f917(a910,a905)),f916(x45981,x45982)),f18(a910,a905,a905)),f333(f333(f8(f917(a910,a905),f917(a910,f917(a905,a905)),f916(x45981,x45982)),f333(f8(a905,f917(a905,a905),a910),a331)),f333(f333(f7(f916(x45981,x45982),f917(a910,f916(x45981,x45982)),f917(a910,a905)),f333(f333(f8(f917(f916(x45981,x45982),a905),f917(f917(a910,f916(x45981,x45982)),f917(a910,a905)),f916(x45981,x45982)),f8(f916(x45981,x45982),a905,a910)),a330)),f333(f333(f18(a910,x45982,f916(x45981,x45982)),f333(f333(f8(x45981,f917(x45982,f916(x45981,x45982)),a910),f265(x45981,x45982)),f333(f172(x45981),x45983))),f333(f172(x45982),x45984)))))),f333(f333(f7(a910,a910,a905),f247(a910)),f333(f333(f244(a910),f333(f197(f911(x45981)),x45983)),f333(f197(f911(x45982)),x45984)))))),f333(f180(f916(x45981,x45982)),f333(f333(f189(x45981,x45982),x45983),x45984))) % 173.51/173.27 [4519]E(f333(f252(f916(x45191,x45192)),f333(f269(x45191,x45192,a905),f333(f333(f7(x45191,f917(x45192,a905),f917(x45192,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x45192,a905),f917(x45192,a905)),x45191),f8(a905,a905,x45192)),f333(f333(f8(a905,f917(a905,a905),x45191),a331),x45193))),x45194))),f333(f333(f267(x45191,x45192),f333(f252(x45191),x45193)),f333(f16(f917(x45192,a905),x45191),f333(f252(x45192),x45194)))) % 173.51/173.27 [4522]E(f333(f252(f916(x45221,x45222)),f333(f269(x45221,x45222,a905),f333(f333(f18(x45221,f917(x45222,a905),f917(x45222,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x45222,a905),f917(x45222,a905)),x45221),f8(a905,a905,x45222)),f333(f333(f8(a905,f917(a905,a905),x45221),a331),x45223))),x45224))),f333(f333(f267(x45221,x45222),f333(f252(x45221),x45223)),f333(f333(f8(f917(x45222,a905),f917(x45222,a905),x45221),f252(x45222)),x45224))) % 173.51/173.27 [4534]E(f333(f252(x45341),f333(f333(f8(f917(x45342,a905),a905,x45341),f95(x45342)),f333(f333(f8(f917(x45342,a905),f917(x45342,a905),x45341),f333(f18(x45342,a905,a905),f333(f333(f8(a905,f917(a905,a905),x45342),a336),f333(f333(f7(x45342,f917(x45342,a905),a905),f335(x45342)),x45343)))),x45344))),f333(f333(f46(x45342,f917(x45341,a905)),x45343),f333(f333(f8(f917(x45341,a905),f917(x45341,a905),x45342),f252(x45341)),f333(f7(x45341,x45342,a905),x45344)))) % 173.51/173.27 [4579]E(f333(f333(f162(f916(x45791,a910),x45791),f264(x45791,a910)),f333(f144(f916(x45791,a910),f333(f333(f7(f916(x45791,a910),f917(a910,a905),a905),f333(f333(f8(a910,f917(f917(a910,a905),a905),f916(x45791,a910)),f335(a910)),f268(x45791,a910))),x45792)),f333(f333(f189(x45791,a910),x45793),f147(a910,f333(f308(a910,x45794),f333(f333(f87(a910),x45794),f333(f197(f911(x45791)),x45793))))))),f333(f333(f162(f916(x45791,a910),x45791),f264(x45791,a910)),f333(f144(f916(x45791,a910),f333(f333(f7(f916(x45791,a910),f917(a910,a905),a905),f333(f333(f8(a910,f917(f917(a910,a905),a905),f916(x45791,a910)),f335(a910)),f333(f333(f7(f916(x45791,a910),a910,a910),f333(f333(f8(a910,f917(a910,a910),f916(x45791,a910)),f87(a910)),f268(x45791,a910))),x45794))),x45792)),f333(f333(f189(x45791,a910),x45793),f147(a910,f333(f308(a910,f2(a910)),f333(f197(f911(x45791)),x45793))))))) % 173.51/173.27 [4580]E(f333(a123,f333(f333(f245(a910),f333(f197(f911(x45801)),x45802)),f333(f150(a910,f911(x45803),f333(f7(f911(x45803),a910,a910),f333(f333(f8(a910,f917(a910,a910),f911(x45803)),f245(a910)),f333(f333(f7(f911(x45803),a910,a910),f333(f333(f8(a910,f917(a910,a910),f911(x45803)),f23(a910)),f197(f911(x45803)))),f333(a123,f2(a910))))),f2(a910)),f333(f176(f911(x45803)),f333(f144(f911(x45803),f333(f333(f8(a905,a905,f911(x45803)),a328),f333(f333(f7(f911(x45803),f911(x45803),a905),a330),f124(x45803)))),x45804))))),f333(f333(f245(a910),f333(a123,f333(f197(f911(x45801)),x45802))),f333(f150(a910,f911(x45803),f333(f7(f911(x45803),a910,a910),f333(f333(f8(a910,f917(a910,a910),f911(x45803)),f245(a910)),f197(f911(x45803)))),f2(a910)),f333(f176(f911(x45803)),x45804)))) % 173.51/173.27 [4533]E(f333(f333(f142(x45331),f184(x45331,x45332,x45333)),f184(x45331,x45334,f333(f252(a910),f333(f333(f7(a910,f917(a910,a905),a905),f333(f333(f8(a910,f917(f917(a910,a905),a905),a910),f335(a910)),f333(f333(f7(a910,a910,a910),f87(a910)),f333(f197(f911(x45331)),x45332)))),x45333)))),f184(x45331,f333(f333(f142(x45331),x45332),x45334),x45333)) % 173.51/173.27 [4581]E(f43(f917(x45811,a905),f333(f252(f917(x45811,a905)),f333(f333(f8(f917(x45812,a905),a905,f917(x45811,a905)),f94(x45812)),f333(f333(f8(f917(x45812,a905),f917(x45812,a905),f917(x45811,a905)),f333(f18(x45812,a905,a905),f333(f333(f8(a905,f917(a905,a905),x45812),a331),f333(f333(f7(x45812,f917(x45812,a905),a905),f335(x45812)),x45813)))),f333(f333(f7(f917(x45811,a905),f917(x45812,f917(x45811,a905)),f917(x45812,a905)),f333(f333(f8(f917(f917(x45811,a905),a905),f917(f917(x45812,f917(x45811,a905)),f917(x45812,a905)),f917(x45811,a905)),f8(f917(x45811,a905),a905,x45812)),a330)),x45814))))),f333(f333(f45(x45812,f917(x45811,a905)),x45813),x45814)) % 173.51/173.27 [4582]E(f44(f917(x45821,a905),f333(f252(f917(x45821,a905)),f333(f333(f8(f917(x45822,a905),a905,f917(x45821,a905)),f94(x45822)),f333(f333(f8(f917(x45822,a905),f917(x45822,a905),f917(x45821,a905)),f333(f18(x45822,a905,a905),f333(f333(f8(a905,f917(a905,a905),x45822),a331),f333(f333(f7(x45822,f917(x45822,a905),a905),f335(x45822)),x45823)))),f333(f333(f7(f917(x45821,a905),f917(x45822,f917(x45821,a905)),f917(x45822,a905)),f333(f333(f8(f917(f917(x45821,a905),a905),f917(f917(x45822,f917(x45821,a905)),f917(x45822,a905)),f917(x45821,a905)),f8(f917(x45821,a905),a905,x45822)),a330)),x45824))))),f333(f333(f46(x45822,f917(x45821,a905)),x45823),x45824)) % 173.51/173.27 [4589]E(f333(f333(f159(f911(x45891)),f333(f333(f159(x45891),x45892),f333(f150(f911(x45891),f911(x45891),f142(x45891),f124(x45891)),f333(f333(f162(f911(x45891),f911(x45891)),f164(f911(x45891),x45891,f124(x45891),f333(f333(f8(f911(x45891),f917(f911(x45891),f911(x45891)),x45891),f16(f911(x45891),f911(x45891))),f333(f333(f7(x45891,f911(x45891),f911(x45891)),f159(x45891)),f124(x45891))))),x45893)))),f187(x45891,f333(f333(f159(f911(x45891)),x45894),f333(f150(f911(f911(x45891)),f911(f911(x45891)),f142(f911(x45891)),f124(f911(x45891))),f333(f333(f162(f911(x45891),f911(f911(x45891))),f164(f911(f911(x45891)),x45891,f124(f911(x45891)),f333(f16(f917(f911(x45891),f911(f911(x45891))),x45891),f333(f333(f7(f911(x45891),f911(f911(x45891)),f911(f911(x45891))),f159(f911(x45891))),f124(f911(x45891)))))),x45893))))),f187(x45891,f333(f333(f159(f911(x45891)),f333(f333(f159(x45891),x45892),x45894)),x45893))) % 173.51/173.27 [4599]E(f333(f252(f916(x45991,x45991)),f333(f269(x45991,x45991,a905),f333(f333(f7(x45991,f917(f916(x45992,x45992),a905),f917(x45991,a905)),f333(f333(f8(f917(x45991,f917(f917(f916(x45992,x45992),a905),a905)),f917(f917(f916(x45992,x45992),a905),f917(x45991,a905)),x45991),f7(x45991,f917(f916(x45992,x45992),a905),a905)),f333(f333(f8(f917(x45991,f916(x45992,x45992)),f917(x45991,f917(f917(f916(x45992,x45992),a905),a905)),x45991),f333(f8(f916(x45992,x45992),f917(f917(f916(x45992,x45992),a905),a905),x45991),f335(f916(x45992,x45992)))),f333(f333(f7(x45991,f917(x45991,x45992),f917(x45991,f916(x45992,x45992))),f333(f333(f8(f917(x45992,f916(x45992,x45992)),f917(f917(x45991,x45992),f917(x45991,f916(x45992,x45992))),x45991),f8(x45992,f916(x45992,x45992),x45991)),f333(f333(f8(x45992,f917(x45992,f916(x45992,x45992)),x45991),f265(x45992,x45992)),x45993))),x45993)))),x45994))),f333(f333(f294(x45992,x45991),x45994),x45993)) % 173.51/173.27 [4659]~E(f31(x46591,x46592),f28(x46593,x46594,x46595)) % 173.51/173.27 [4660]~E(f31(x46601,x46602),f27(x46603,x46604,x46605)) % 173.51/173.27 [4661]~E(f30(x46611,x46612),f28(x46613,x46614,x46615)) % 173.51/173.27 [4662]~E(f30(x46621,x46622),f27(x46623,x46624,x46625)) % 173.51/173.27 [4663]~E(f26(x46631,x46632),f28(x46633,x46634,x46635)) % 173.51/173.27 [4664]~E(f26(x46641,x46642),f27(x46643,x46644,x46645)) % 173.51/173.27 [4665]~E(f28(x46651,x46652,x46653),f31(x46654,x46655)) % 173.51/173.27 [4666]~E(f28(x46661,x46662,x46663),f30(x46664,x46665)) % 173.51/173.27 [4667]~E(f28(x46671,x46672,x46673),f26(x46674,x46675)) % 173.51/173.27 [4668]~E(f27(x46681,x46682,x46683),f31(x46684,x46685)) % 173.51/173.27 [4669]~E(f27(x46691,x46692,x46693),f30(x46694,x46695)) % 173.51/173.27 [4670]~E(f27(x46701,x46702,x46703),f26(x46704,x46705)) % 173.51/173.27 [3729]E(f333(f333(f162(x37291,x37292),x37293),f177(x37291,x37294,x37295)),f177(x37292,x37294,f333(x37293,x37295))) % 173.51/173.27 [4299]E(f333(f81(x42991,x42992,x42993,x42994,x42995),x42994),x42995) % 173.51/173.27 [4350]E(f266(x43501,x43502,x43503,f255(x43502,x43501,x43504),f255(x43503,x43502,x43505)),f255(x43503,x43501,f266(x43503,x43502,x43501,x43505,x43504))) % 173.51/173.27 [3923]E(f333(f333(f269(x39231,x39232,x39233),x39234),x39235),f333(f333(x39234,f333(f264(x39231,x39232),x39235)),f333(f268(x39231,x39232),x39235))) % 173.51/173.27 [3959]E(f333(f333(f333(f71(x39591,x39592,x39593),x39594),x39595),f196(f917(x39592,a905))),x39595) % 173.51/173.27 [4238]E(f333(f79(f911(x42381),f911(x42382),f911(x42383),f333(f162(x42381,x42382),x42384)),f333(f162(x42383,x42381),x42385)),f333(f162(x42383,x42382),f333(f79(x42381,x42382,x42383,x42384),x42385))) % 173.51/173.27 [4313]E(f92(x43131,f72(x43132,x43131,x43133,x43134,x43135)),f333(f333(f70(x43132,x43131,x43133),x43134),x43135)) % 173.51/173.27 [4347]E(f333(f333(f87(a910),f333(f333(f87(a910),f333(x43471,f333(f264(x43472,x43473),x43474))),f333(x43475,f333(f268(x43472,x43473),x43474)))),f333(a123,f2(a910))),f273(x43472,x43473,x43471,x43475,x43474)) % 173.51/173.27 [3860]E(f333(f333(f183(x38601),x38602),f333(f333(f162(x38603,x38601),x38604),x38605)),f333(f333(f162(x38603,x38601),x38604),f333(f333(f183(x38603),x38602),x38605))) % 173.51/173.27 [3861]E(f333(f333(f146(x38611),x38612),f333(f333(f162(x38613,x38611),x38614),x38615)),f333(f333(f162(x38613,x38611),x38614),f333(f333(f146(x38613),x38612),x38615))) % 173.51/173.27 [3893]E(f333(f333(f162(x38931,x38932),x38933),f333(f333(f159(x38931),x38934),x38935)),f333(f333(f159(x38932),f333(x38933,x38934)),f333(f333(f162(x38931,x38932),x38933),x38935))) % 173.51/173.27 [3953]E(f333(f316(x39531,x39532,x39533),f333(f333(f315(x39531),x39534),x39535)),f333(f333(f315(x39532),f333(x39533,x39534)),f333(f316(x39531,x39532,x39533),x39535))) % 173.51/173.27 [3982]E(f181(x39821,f333(f333(f159(x39821),x39822),x39823),f333(f333(f159(x39821),x39824),x39825)),f333(f333(f159(x39821),x39822),f333(f333(f159(x39821),x39824),f181(x39821,x39823,x39825)))) % 173.51/173.27 [4018]E(f333(f333(f189(x40181,x40182),f333(f333(f183(x40181),x40183),x40184)),f333(f333(f183(x40182),x40183),x40185)),f333(f333(f183(f916(x40181,x40182)),x40183),f333(f333(f189(x40181,x40182),x40184),x40185))) % 173.51/173.27 [4019]E(f333(f333(f189(x40191,x40192),f333(f333(f146(x40191),x40193),x40194)),f333(f333(f146(x40192),x40193),x40195)),f333(f333(f146(f916(x40191,x40192)),x40193),f333(f333(f189(x40191,x40192),x40194),x40195))) % 173.51/173.27 [4031]E(f333(f333(f167(x40311,f333(f333(f159(x40311),x40312),x40313)),f333(a123,x40314)),x40315),f333(f333(f159(x40311),x40312),f333(f333(f167(x40311,x40313),x40314),x40315))) % 173.51/173.27 [4034]E(f333(f333(f142(x40341),f333(f333(f162(x40342,x40341),x40343),x40344)),f333(f333(f162(x40342,x40341),x40343),x40345)),f333(f333(f162(x40342,x40341),x40343),f333(f333(f142(x40342),x40344),x40345))) % 173.51/173.27 [4038]E(f333(f333(x40381,x40382),f333(f333(f257(x40383,x40384,x40381),x40382),x40385)),f333(f333(f257(x40383,x40384,x40381),x40382),f333(a123,x40385))) % 173.51/173.27 [4069]E(f171(x40691,x40692,x40693,f333(f333(f159(x40691),x40694),x40695)),f333(f333(f142(x40692),f333(x40693,x40694)),f171(x40691,x40692,x40693,x40695))) % 173.51/173.27 [4081]E(f333(f333(f295(x40811,x40812,x40813),f333(f293(x40812,x40811),x40814)),f333(f293(x40813,x40812),x40815)),f333(f293(x40813,x40811),f333(f333(f295(x40813,x40812,x40811),x40815),x40814))) % 173.51/173.27 [4114]E(f333(f333(f333(f191(f911(x41141),f911(x41141)),x41142),f175(x41141)),f333(f333(f162(x41143,x41141),x41144),x41145)),f333(f333(f162(x41143,x41141),x41144),f333(f333(f333(f191(f911(x41143),f911(x41143)),x41142),f175(x41143)),x41145))) % 173.51/173.27 [4115]E(f333(f333(f271(x41151,x41152,x41151,x41153),f333(f265(x41152,x41151),x41154)),x41155),f333(x41155,x41154)) % 173.51/173.27 [4140]E(f163(x41401,x41402,f333(f333(f162(x41403,x41401),x41404),x41405)),f163(x41403,f333(f79(x41401,a910,x41403,x41402),x41404),x41405)) % 173.51/173.27 [4203]E(f185(f916(x42031,x42032),f333(f79(x42032,a905,f916(x42031,x42032),x42033),f268(x42031,x42032)),f333(f333(f189(x42031,x42032),x42034),x42035)),f333(f333(f189(x42031,x42032),x42034),f185(x42032,x42033,x42035))) % 173.51/173.27 [4208]E(f333(f316(x42081,x42082,f333(f333(f8(x42083,x42082,x42081),x42084),x42085)),f254(f917(x42081,a905))),f333(f316(x42083,x42082,x42084),f333(f316(x42081,x42083,x42085),f254(f917(x42081,a905))))) % 173.51/173.27 [4221]E(f185(f916(x42211,x42212),f333(f79(x42211,a905,f916(x42211,x42212),x42213),f264(x42211,x42212)),f333(f333(f189(x42211,x42212),x42214),x42215)),f333(f333(f189(x42211,x42212),f185(x42211,x42213,x42214)),x42215)) % 173.51/173.27 [4242]E(f333(f333(f121(f917(x42421,a905)),f333(f317(x42421,x42422,x42423),f333(f333(f315(x42422),x42424),f196(f917(x42422,a905))))),f333(f317(x42421,x42422,x42423),x42425)),f333(f317(x42421,x42422,x42423),f333(f333(f315(x42422),x42424),x42425))) % 173.51/173.27 [4298]E(f333(f333(f142(f916(x42981,x42982)),f333(f333(f162(x42982,f916(x42981,x42982)),f333(f265(x42981,x42982),x42983)),x42984)),f65(x42981,x42982,x42985,x42984)),f65(x42981,x42982,f333(f333(f159(x42981),x42983),x42985),x42984)) % 173.51/173.27 [4300]E(f333(f333(f162(x43001,x43002),x43003),f185(x43001,f333(f79(x43002,a905,x43001,x43004),x43003),x43005)),f185(x43002,x43004,f333(f333(f162(x43001,x43002),x43003),x43005))) % 173.51/173.27 [4305]E(f333(f150(x43051,x43052,f333(f7(x43052,x43051,x43051),f333(f7(x43051,x43052,x43051),x43053)),x43054),f333(f176(x43052),f333(f176(x43052),x43055))),f333(f150(x43051,x43052,x43053,x43054),x43055)) % 173.51/173.27 [4407]P106(f333(f333(f246(f917(x44071,a905)),f333(f316(x44072,x44071,x44073),f333(f333(f112(f917(x44072,a905)),x44074),x44075))),f333(f333(f112(f917(x44071,a905)),f333(f316(x44072,x44071,x44073),x44074)),f333(f316(x44072,x44071,x44073),x44075)))) % 173.51/173.27 [4408]P106(f333(f333(f246(f917(x44081,a905)),f333(f292(x44082,x44081,x44083),f333(f333(f112(f917(x44082,a905)),x44084),x44085))),f333(f333(f112(f917(x44081,a905)),f333(f292(x44082,x44081,x44083),x44084)),f333(f292(x44082,x44081,x44083),x44085)))) % 173.51/173.27 [4507]E(f333(f268(x45071,x45072),f333(f270(x45073,x45071,x45072,x45072,x45074,f33(x45072)),x45075)),f333(f268(x45073,x45072),x45075)) % 173.51/173.27 [4508]E(f333(f264(x45081,x45082),f333(f270(x45081,x45081,x45083,x45082,f33(x45081),x45084),x45085)),f333(f264(x45081,x45083),x45085)) % 173.51/173.27 [4593]P26(x45931,x45932,f333(f333(f315(f909(x45931)),f333(f333(f333(f98(x45931),f333(f333(f7(x45931,f917(a906,a906),f917(a906,a905)),f333(f333(f8(f917(a906,a905),f917(f917(a906,a906),f917(a906,a905)),x45931),f8(a906,a905,a906)),x45933)),f333(f333(f18(a906,a910,a906),f333(f333(f7(a906,a908,f917(a910,a906)),a205),x45934)),x45935))),f26(x45934,x45935)),x45933)),f196(f917(f909(x45931),a905)))) % 173.51/173.27 [4597]P26(x45971,x45972,f333(f333(f315(f909(x45971)),f333(f333(f333(f98(x45971),f333(f333(f7(x45971,f917(a906,a905),f917(a906,a905)),f333(f333(f8(f917(a906,f917(a905,a905)),f917(f917(a906,a905),f917(a906,a905)),x45971),f18(a906,a905,a905)),f333(f333(f8(f917(a906,a905),f917(a906,f917(a905,a905)),x45971),f333(f8(a905,f917(a905,a905),a906),a331)),x45973))),f333(f333(f8(a905,a905,a906),a328),x45974))),f30(x45974,x45975)),x45973)),f196(f917(f909(x45971),a905)))) % 173.51/173.27 [3695]E(f333(f333(f333(f333(f216(x36951),x36952),x36953),x36954),x36955),f211(x36951,x36952)) % 173.51/173.27 [3696]E(f333(f333(f333(f333(f217(x36961),x36962),x36963),x36964),x36965),f200(x36961,x36962)) % 173.51/173.27 [3745]E(f104(x37451,x37452,f333(f333(f333(f98(x37451),x37453),x37454),x37455)),f2(a910)) % 173.51/173.27 [4070]E(f333(f333(f45(x40701,f917(x40702,a905)),f333(f333(f315(x40701),x40703),x40704)),x40705),f333(f333(f121(f917(x40702,a905)),f333(x40705,x40703)),f333(f333(f45(x40701,f917(x40702,a905)),x40704),x40705))) % 173.51/173.27 [4071]E(f333(f333(f46(x40711,f917(x40712,a905)),f333(f333(f315(x40711),x40713),x40714)),x40715),f333(f333(f112(f917(x40712,a905)),f333(x40715,x40713)),f333(f333(f46(x40711,f917(x40712,a905)),x40714),x40715))) % 173.51/173.27 [4119]E(f333(f129(x41191,x41192,f333(x41193,x41194)),f333(f333(f7(x41191,a110,f912(x41192)),x41195),x41194)),f333(f209(x41191,x41192,x41193,x41195),x41194)) % 173.51/173.27 [4134]E(f333(f333(f121(f917(x41341,a905)),f333(f316(x41342,x41341,x41343),x41344)),f333(f316(x41342,x41341,x41343),x41345)),f333(f316(x41342,x41341,x41343),f333(f333(f121(f917(x41342,a905)),x41344),x41345))) % 173.51/173.27 [4135]E(f333(f333(f121(f917(x41351,a905)),f333(f317(x41351,x41352,x41353),x41354)),f333(f317(x41351,x41352,x41353),x41355)),f333(f317(x41351,x41352,x41353),f333(f333(f121(f917(x41352,a905)),x41354),x41355))) % 173.51/173.27 [4136]E(f333(f333(f112(f917(x41361,a905)),f333(f317(x41361,x41362,x41363),x41364)),f333(f317(x41361,x41362,x41363),x41365)),f333(f317(x41361,x41362,x41363),f333(f333(f112(f917(x41362,a905)),x41364),x41365))) % 173.51/173.27 [4137]E(f333(f333(f23(f917(x41371,a905)),f333(f317(x41371,x41372,x41373),x41374)),f333(f317(x41371,x41372,x41373),x41375)),f333(f317(x41371,x41372,x41373),f333(f333(f23(f917(x41372,a905)),x41374),x41375))) % 173.51/173.27 [4138]E(f333(f333(f121(f917(x41381,a905)),f333(f292(x41382,x41381,x41383),x41384)),f333(f292(x41382,x41381,x41383),x41385)),f333(f292(x41382,x41381,x41383),f333(f333(f121(f917(x41382,a905)),x41384),x41385))) % 173.51/173.27 [4199]E(f333(f333(f167(x41991,f333(f333(f142(x41991),x41992),f333(f333(f159(x41991),x41993),x41994))),f333(f197(f911(x41991)),x41992)),x41995),f333(f333(f142(x41991),x41992),f333(f333(f159(x41991),x41995),x41994))) % 173.51/173.27 [4206]E(f333(f333(f46(x42061,f917(x42062,a905)),x42063),f333(f333(f8(f917(x42062,a905),f917(x42062,a905),x42061),f333(f315(x42062),x42064)),x42065)),f333(f333(f315(x42062),x42064),f333(f333(f46(x42061,f917(x42062,a905)),x42063),x42065))) % 173.51/173.27 [4359]E(f333(f333(f162(x43591,x43592),x43593),f333(f144(x43591,f333(f79(x43592,a905,x43591,x43594),x43593)),x43595)),f333(f144(x43592,x43594),f333(f333(f162(x43591,x43592),x43593),x43595))) % 173.51/173.27 [4365]E(f333(f197(f911(x43651)),f333(f144(x43651,x43652),f333(f333(f162(x43653,x43651),x43654),x43655))),f333(f197(f911(x43653)),f333(f144(x43653,f333(f79(x43651,a905,x43653,x43652),x43654)),x43655))) % 173.51/173.27 [4572]E(f333(f164(f911(f916(x45721,x45722)),x45722,f124(f916(x45721,x45722)),f333(f333(f7(x45722,f917(f911(x45722),f911(f916(x45721,x45722))),f917(f911(x45722),f911(f916(x45721,x45722)))),f333(f333(f8(f917(f911(f916(x45721,x45722)),f911(f916(x45721,x45722))),f917(f917(f911(x45722),f911(f916(x45721,x45722))),f917(f911(x45722),f911(f916(x45721,x45722)))),x45722),f8(f911(f916(x45721,x45722)),f911(f916(x45721,x45722)),f911(x45722))),f333(f333(f8(f916(x45721,x45722),f917(f911(f916(x45721,x45722)),f911(f916(x45721,x45722))),x45722),f159(f916(x45721,x45722))),f333(f265(x45721,x45722),x45723)))),f333(f189(x45721,x45722),x45724))),x45725),f333(f333(f189(x45721,x45722),f333(f333(f159(x45721),x45723),x45724)),x45725)) % 173.51/173.27 [4063]E(f333(f333(f167(x40631,f333(f333(f167(x40631,x40632),x40633),x40634)),x40633),x40635),f333(f333(f167(x40631,x40632),x40633),x40635)) % 173.51/173.27 [4116]E(f333(f291(x41161,x41162),f333(f333(f315(f916(x41161,x41162)),f333(f333(f265(x41161,x41162),x41163),x41164)),x41165)),f333(f333(f315(x41162),x41164),f333(f291(x41161,x41162),x41165))) % 173.51/173.27 [4117]E(f333(f263(x41171,x41172),f333(f333(f315(f916(x41171,x41172)),f333(f333(f265(x41171,x41172),x41173),x41174)),x41175)),f333(f333(f315(x41171),x41173),f333(f263(x41171,x41172),x41175))) % 173.51/173.27 [4164]E(f132(x41641,x41642,f333(x41643,x41644),f333(f333(f7(x41641,a110,f912(f914(x41642))),x41645),x41644)),f333(f207(x41641,x41642,x41643,x41645),x41644)) % 173.51/173.27 [4192]E(f333(f333(f121(f917(f916(x41921,x41922),a905)),f333(f333(f267(x41921,x41922),x41923),x41924)),f333(f333(f267(x41921,x41922),x41925),x41924)),f333(f333(f267(x41921,x41922),f333(f333(f121(f917(x41921,a905)),x41923),x41925)),x41924)) % 173.51/173.27 [4193]E(f333(f333(f112(f917(f916(x41931,x41932),a905)),f333(f333(f267(x41931,x41932),x41933),x41934)),f333(f333(f267(x41931,x41932),x41935),x41934)),f333(f333(f267(x41931,x41932),f333(f333(f112(f917(x41931,a905)),x41933),x41935)),x41934)) % 173.51/173.27 [4194]E(f333(f333(f23(f917(f916(x41941,x41942),a905)),f333(f333(f267(x41941,x41942),x41943),x41944)),f333(f333(f267(x41941,x41942),x41945),x41944)),f333(f333(f267(x41941,x41942),f333(f333(f23(f917(x41941,a905)),x41943),x41945)),x41944)) % 173.51/173.27 [4253]E(f333(f333(f121(f917(x42531,a905)),f333(f333(f45(x42532,f917(x42531,a905)),x42533),x42534)),f333(f333(f45(x42532,f917(x42531,a905)),x42535),x42534)),f333(f333(f45(x42532,f917(x42531,a905)),f333(f333(f121(f917(x42532,a905)),x42533),x42535)),x42534)) % 173.51/173.27 [4254]E(f333(f333(f112(f917(x42541,a905)),f333(f333(f46(x42542,f917(x42541,a905)),x42543),x42544)),f333(f333(f46(x42542,f917(x42541,a905)),x42545),x42544)),f333(f333(f46(x42542,f917(x42541,a905)),f333(f333(f121(f917(x42542,a905)),x42543),x42545)),x42544)) % 173.51/173.27 [4268]E(f333(f333(f45(x42681,f917(x42682,a905)),x42683),f333(f333(f8(f917(x42682,a905),f917(x42682,a905),x42681),f333(f112(f917(x42682,a905)),x42684)),x42685)),f333(f333(f112(f917(x42682,a905)),x42684),f333(f333(f45(x42681,f917(x42682,a905)),x42683),x42685))) % 173.51/173.27 [4269]E(f333(f333(f45(x42691,f917(x42692,a905)),x42693),f333(f333(f8(f917(x42692,a905),f917(x42692,a905),x42691),f333(f23(f917(x42692,a905)),x42694)),x42695)),f333(f333(f23(f917(x42692,a905)),x42694),f333(f333(f46(x42691,f917(x42692,a905)),x42693),x42695))) % 173.51/173.27 [4270]E(f333(f333(f46(x42701,f917(x42702,a905)),x42703),f333(f333(f8(f917(x42702,a905),f917(x42702,a905),x42701),f333(f121(f917(x42702,a905)),x42704)),x42705)),f333(f333(f121(f917(x42702,a905)),x42704),f333(f333(f46(x42701,f917(x42702,a905)),x42703),x42705))) % 173.51/173.27 [4325]E(f193(f911(x43251),f333(f333(f159(x43251),x43252),x43253),f333(f333(f8(f911(x43251),f911(x43251),a910),f333(f159(x43251),x43254)),f333(f333(f7(a910,x43251,f911(x43251)),f167(x43251,x43253)),x43252)),x43255),f333(f333(f167(x43251,f333(f333(f159(x43251),x43254),x43253)),x43255),x43252)) % 173.51/173.27 [4329]E(f333(f333(f45(x43291,f917(f916(x43292,x43293),a905)),x43294),f333(f333(f8(f917(f916(x43293,x43292),a905),f917(f916(x43292,x43293),a905),x43291),f293(x43293,x43292)),x43295)),f333(f293(x43293,x43292),f333(f333(f45(x43291,f917(f916(x43293,x43292),a905)),x43294),x43295))) % 173.51/173.27 [4330]E(f333(f333(f46(x43301,f917(f916(x43302,x43303),a905)),x43304),f333(f333(f8(f917(f916(x43303,x43302),a905),f917(f916(x43302,x43303),a905),x43301),f293(x43303,x43302)),x43305)),f333(f293(x43303,x43302),f333(f333(f46(x43301,f917(f916(x43303,x43302),a905)),x43304),x43305))) % 173.51/173.27 [4430]P106(f333(f333(f246(f917(x44301,a905)),f333(f333(f23(f917(x44301,a905)),f333(f316(x44302,x44301,x44303),x44304)),f333(f316(x44302,x44301,x44303),x44305))),f333(f316(x44302,x44301,x44303),f333(f333(f23(f917(x44302,a905)),x44304),x44305)))) % 173.51/173.27 [4575]E(f333(f164(f911(f916(x45751,x45752)),x45751,f124(f916(x45751,x45752)),f333(f333(f7(x45751,f917(f911(x45751),f911(f916(x45751,x45752))),f917(f911(x45751),f911(f916(x45751,x45752)))),f333(f333(f8(f917(f911(f916(x45751,x45752)),f911(f916(x45751,x45752))),f917(f917(f911(x45751),f911(f916(x45751,x45752))),f917(f911(x45751),f911(f916(x45751,x45752)))),x45751),f8(f911(f916(x45751,x45752)),f911(f916(x45751,x45752)),f911(x45751))),f333(f333(f8(f916(x45751,x45752),f917(f911(f916(x45751,x45752)),f911(f916(x45751,x45752))),x45751),f159(f916(x45751,x45752))),f333(f333(f7(x45751,x45752,f916(x45751,x45752)),f265(x45751,x45752)),x45753)))),f333(f333(f7(f911(x45751),f911(x45752),f911(f916(x45751,x45752))),f189(x45751,x45752)),x45754))),x45755),f333(f333(f189(x45751,x45752),x45755),f333(f333(f159(x45752),x45753),x45754))) % 173.51/173.27 [4294]E(f333(f333(f121(f917(x42941,a905)),f333(f292(x42942,x42941,x42943),x42944)),f333(f292(x42942,x42941,x42945),x42944)),f333(f292(x42942,x42941,f333(f333(f121(f917(f916(x42942,x42941),a905)),x42943),x42945)),x42944)) % 173.51/173.27 [4331]E(f333(f333(f142(f916(x43311,x43312)),f333(f333(f189(x43311,x43312),x43313),f333(f333(f183(x43312),f333(f197(f911(x43311)),x43313)),x43314))),f333(f333(f189(x43311,x43312),x43315),f333(f333(f146(x43312),f333(f197(f911(x43311)),x43313)),x43314))),f333(f333(f189(x43311,x43312),f333(f333(f142(x43311),x43313),x43315)),x43314)) % 173.51/173.27 [4433]E(f333(f333(f267(x44331,x44332),x44333),f333(f333(f18(x44331,f917(x44332,a905),f917(x44332,a905)),f333(f333(f8(f917(x44332,a905),f917(f917(x44332,a905),f917(x44332,a905)),x44331),f121(f917(x44332,a905))),x44334)),x44335)),f333(f333(f121(f917(f916(x44331,x44332),a905)),f333(f333(f267(x44331,x44332),x44333),x44334)),f333(f333(f267(x44331,x44332),x44333),x44335))) % 173.51/173.27 [4434]E(f333(f333(f267(x44341,x44342),x44343),f333(f333(f18(x44341,f917(x44342,a905),f917(x44342,a905)),f333(f333(f8(f917(x44342,a905),f917(f917(x44342,a905),f917(x44342,a905)),x44341),f112(f917(x44342,a905))),x44344)),x44345)),f333(f333(f112(f917(f916(x44341,x44342),a905)),f333(f333(f267(x44341,x44342),x44343),x44344)),f333(f333(f267(x44341,x44342),x44343),x44345))) % 173.51/173.27 [4435]E(f333(f333(f267(x44351,x44352),x44353),f333(f333(f18(x44351,f917(x44352,a905),f917(x44352,a905)),f333(f333(f8(f917(x44352,a905),f917(f917(x44352,a905),f917(x44352,a905)),x44351),f23(f917(x44352,a905))),x44354)),x44355)),f333(f333(f23(f917(f916(x44351,x44352),a905)),f333(f333(f267(x44351,x44352),x44353),x44354)),f333(f333(f267(x44351,x44352),x44353),x44355))) % 173.51/173.27 [4439]E(f333(f333(f45(x44391,f917(x44392,a905)),x44393),f333(f333(f7(x44391,f917(x44392,a905),f917(x44392,a905)),f333(f333(f8(f917(x44392,a905),f917(f917(x44392,a905),f917(x44392,a905)),x44391),f112(f917(x44392,a905))),x44394)),x44395)),f333(f333(f112(f917(x44392,a905)),f333(f333(f45(x44391,f917(x44392,a905)),x44393),x44394)),x44395)) % 173.51/173.27 [4440]E(f333(f333(f45(x44401,f917(x44402,a905)),x44403),f333(f333(f7(x44401,f917(x44402,a905),f917(x44402,a905)),f333(f333(f8(f917(x44402,a905),f917(f917(x44402,a905),f917(x44402,a905)),x44401),f23(f917(x44402,a905))),x44404)),x44405)),f333(f333(f23(f917(x44402,a905)),f333(f333(f45(x44401,f917(x44402,a905)),x44403),x44404)),x44405)) % 173.51/173.27 [4441]E(f333(f333(f46(x44411,f917(x44412,a905)),x44413),f333(f333(f7(x44411,f917(x44412,a905),f917(x44412,a905)),f333(f333(f8(f917(x44412,a905),f917(f917(x44412,a905),f917(x44412,a905)),x44411),f121(f917(x44412,a905))),x44414)),x44415)),f333(f333(f121(f917(x44412,a905)),f333(f333(f46(x44411,f917(x44412,a905)),x44413),x44414)),x44415)) % 173.51/173.27 [4445]E(f333(f333(f45(x44451,f917(x44452,a905)),x44453),f333(f333(f18(x44451,f917(x44452,a905),f917(x44452,a905)),f333(f333(f8(f917(x44452,a905),f917(f917(x44452,a905),f917(x44452,a905)),x44451),f121(f917(x44452,a905))),x44454)),x44455)),f333(f333(f121(f917(x44452,a905)),f333(f333(f45(x44451,f917(x44452,a905)),x44453),x44454)),f333(f333(f45(x44451,f917(x44452,a905)),x44453),x44455))) % 173.51/173.27 [4446]E(f333(f333(f46(x44461,f917(x44462,a905)),x44463),f333(f333(f18(x44461,f917(x44462,a905),f917(x44462,a905)),f333(f333(f8(f917(x44462,a905),f917(f917(x44462,a905),f917(x44462,a905)),x44461),f112(f917(x44462,a905))),x44464)),x44465)),f333(f333(f112(f917(x44462,a905)),f333(f333(f46(x44461,f917(x44462,a905)),x44463),x44464)),f333(f333(f46(x44461,f917(x44462,a905)),x44463),x44465))) % 173.51/173.27 [4459]E(f333(f333(f45(x44591,f917(x44592,a905)),x44593),f333(f333(f18(x44591,f917(x44592,a905),f917(x44592,a905)),f333(f333(f8(f917(x44592,a905),f917(f917(x44592,a905),f917(x44592,a905)),x44591),f121(f917(x44592,a905))),x44594)),x44595)),f333(f333(f121(f917(x44592,a905)),f43(f917(x44592,a905),f333(f316(x44591,f917(x44592,a905),x44594),x44593))),f43(f917(x44592,a905),f333(f316(x44591,f917(x44592,a905),x44595),x44593)))) % 173.51/173.27 [4460]E(f333(f333(f46(x44601,f917(x44602,a905)),x44603),f333(f333(f18(x44601,f917(x44602,a905),f917(x44602,a905)),f333(f333(f8(f917(x44602,a905),f917(f917(x44602,a905),f917(x44602,a905)),x44601),f112(f917(x44602,a905))),x44604)),x44605)),f333(f333(f112(f917(x44602,a905)),f44(f917(x44602,a905),f333(f316(x44601,f917(x44602,a905),x44604),x44603))),f44(f917(x44602,a905),f333(f316(x44601,f917(x44602,a905),x44605),x44603)))) % 173.51/173.27 [4496]E(f333(f333(f146(x44961),f333(f197(f911(x44961)),f185(x44961,x44962,f333(f333(f162(x44963,x44961),x44964),x44965)))),f333(f333(f162(x44963,x44961),x44964),x44965)),f333(f333(f162(x44963,x44961),x44964),f333(f333(f146(x44963),f333(f197(f911(x44963)),f185(x44963,f333(f79(x44961,a905,x44963,x44962),x44964),x44965))),x44965))) % 173.51/173.27 [4372]E(f333(f333(f142(f916(x43721,x43722)),f333(f333(f189(x43721,x43722),f333(f333(f183(x43721),f333(f197(f911(x43722)),x43723)),x43724)),x43723)),f333(f333(f189(x43721,x43722),f333(f333(f146(x43721),f333(f197(f911(x43722)),x43723)),x43724)),x43725)),f333(f333(f189(x43721,x43722),x43724),f333(f333(f142(x43722),x43723),x43725))) % 173.51/173.27 [4487]E(f92(x44871,f333(f333(f18(x44871,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44871),a331),f333(f333(f7(x44871,f917(x44871,a905),a905),f335(x44871)),x44872))),f333(f333(f7(x44871,x44873,a905),f333(f333(f8(x44873,f917(x44873,a905),x44871),a330),x44874)),x44875))),f333(f84(x44871,x44873,x44872,x44874),x44875)) % 173.51/173.27 [4488]E(f97(x44881,f333(f333(f18(x44881,a905,a905),f333(f333(f8(a905,f917(a905,a905),x44881),a331),f333(f333(f7(x44881,f917(x44881,a905),a905),f335(x44881)),x44882))),f333(f333(f7(x44881,x44883,a905),f333(f333(f8(x44883,f917(x44883,a905),x44881),a330),x44884)),x44885))),f333(f99(x44881,x44883,x44882,x44884),x44885)) % 173.51/173.27 [4536]E(f333(f333(f93(a1,x45361),f333(f114(a1),f333(f333(f87(a1),x45362),a108))),f333(f333(f18(a1,x45361,x45361),f333(f333(f7(a1,x45361,f917(x45361,x45361)),f333(f333(f8(a905,f917(x45361,f917(x45361,x45361)),a1),f107(x45361)),a201)),f193(x45361,x45363,x45364,x45365))),f333(f333(f8(a910,x45361,a1),x45364),f333(f333(f7(a1,a910,a910),f333(f333(f8(a910,f917(a910,a910),a1),f87(a910)),a115)),x45365)))),f193(x45361,x45363,x45364,f333(f333(f87(a910),f333(f114(a910),x45362)),x45365))) % 173.51/173.27 [4571]E(f333(f333(f93(a1,x45711),f333(f114(a1),f333(f333(f87(a1),x45712),a108))),f333(f333(f18(a1,x45711,x45711),f333(f333(f7(a1,x45711,f917(x45711,x45711)),f333(f333(f8(a905,f917(x45711,f917(x45711,x45711)),a1),f107(x45711)),a201)),f333(f192(x45711,x45713,x45714),x45715))),f333(f333(f18(a1,x45711,x45711),f333(f333(f8(a910,f917(x45711,x45711),a1),x45714),f333(f333(f7(a1,a910,a910),f333(f333(f8(a910,f917(a910,a910),a1),f87(a910)),a115)),x45715))),f333(f333(f8(a910,x45711,a1),f192(x45711,x45713,x45714)),f333(f333(f7(a1,a910,a910),f333(f333(f8(a910,f917(a910,a910),a1),f87(a910)),a115)),x45715))))),f333(f192(x45711,x45713,x45714),f333(f333(f87(a910),f333(f114(a910),x45712)),x45715))) % 173.51/173.27 [4613]E(f333(f252(f916(x46131,x46132)),f333(f269(x46131,x46132,a905),f333(f333(f8(f917(x46132,f917(x46133,a905)),f917(x46132,a905),x46131),f333(f8(f917(x46133,a905),a905,x46132),f94(x46133))),f333(f333(f7(x46131,f917(x46132,f917(x46133,a905)),f917(x46132,f917(x46133,a905))),f333(f333(f8(f917(f917(x46133,a905),f917(x46133,a905)),f917(f917(x46132,f917(x46133,a905)),f917(x46132,f917(x46133,a905))),x46131),f8(f917(x46133,a905),f917(x46133,a905),x46132)),f333(f333(f8(f917(x46133,f917(a905,a905)),f917(f917(x46133,a905),f917(x46133,a905)),x46131),f18(x46133,a905,a905)),f333(f333(f8(f917(x46133,a905),f917(x46133,f917(a905,a905)),x46131),f333(f8(a905,f917(a905,a905),x46133),a331)),f333(f333(f7(x46131,f917(f916(x46131,x46133),a905),f917(x46133,a905)),f333(f333(f8(f917(x46133,f917(f917(f916(x46131,x46133),a905),a905)),f917(f917(f916(x46131,x46133),a905),f917(x46133,a905)),x46131),f7(x46133,f917(f916(x46131,x46133),a905),a905)),f333(f333(f8(f917(x46133,f916(x46131,x46133)),f917(x46133,f917(f917(f916(x46131,x46133),a905),a905)),x46131),f333(f8(f916(x46131,x46133),f917(f917(f916(x46131,x46133),a905),a905),x46133),f335(f916(x46131,x46133)))),f265(x46131,x46133)))),x46134))))),f333(f333(f7(x46132,f917(f916(x46133,x46132),a905),f917(x46133,a905)),f333(f333(f8(f917(x46133,f917(f917(f916(x46133,x46132),a905),a905)),f917(f917(f916(x46133,x46132),a905),f917(x46133,a905)),x46132),f7(x46133,f917(f916(x46133,x46132),a905),a905)),f333(f333(f8(f917(x46133,f916(x46133,x46132)),f917(x46133,f917(f917(f916(x46133,x46132),a905),a905)),x46132),f333(f8(f916(x46133,x46132),f917(f917(f916(x46133,x46132),a905),a905),x46133),f335(f916(x46133,x46132)))),f333(f7(x46133,x46132,f916(x46133,x46132)),f265(x46133,x46132))))),x46135))))),f333(f333(f295(x46131,x46133,x46132),x46134),x46135)) % 173.51/173.27 [4689]~E(f27(x46891,x46892,x46893),f28(x46894,x46895,x46896)) % 173.51/173.27 [4222]E(f236(x42221,x42222,x42223,x42224,f232(x42221,x42222,x42225,x42226)),f333(f333(x42224,x42225),x42226)) % 173.51/173.27 [4223]E(f237(x42231,x42232,x42233,x42234,f232(x42231,x42232,x42235,x42236)),f333(f333(x42234,x42235),x42236)) % 173.51/173.27 [4367]E(f81(x43671,x43672,f81(x43671,x43672,x43673,x43674,x43675),x43674,x43676),f81(x43671,x43672,x43673,x43674,x43676)) % 173.51/173.27 [4475]E(f333(f79(f916(x44751,x44752),x44752,f916(x44753,x44754),f268(x44751,x44752)),f270(x44753,x44751,x44754,x44752,x44755,x44756)),f333(f79(x44754,x44752,f916(x44753,x44754),x44756),f268(x44753,x44754))) % 173.51/173.27 [4476]E(f333(f79(f916(x44761,x44762),x44761,f916(x44763,x44764),f264(x44761,x44762)),f270(x44763,x44761,x44764,x44762,x44765,x44766)),f333(f79(x44763,x44761,f916(x44763,x44764),x44765),f264(x44763,x44764))) % 173.51/173.27 [4091]E(f333(f333(f79(x40911,x40912,x40913,x40914),x40915),x40916),f333(x40914,f333(x40915,x40916))) % 173.51/173.27 [4232]E(f235(x42321,f916(x42322,f912(x42322)),x42323,f333(f269(x42322,f912(x42322),x42321),x42324),f333(f143(x42322),f136(x42322,x42325,x42326))),f333(f333(x42324,x42325),x42326)) % 173.51/173.27 [4282]E(f238(x42821,x42822,x42823,x42824,f232(x42821,x42822,x42825,x42826)),f333(f333(f87(a910),f333(f333(f87(a910),f333(x42823,x42825)),f333(x42824,x42826))),f333(a123,f2(a910)))) % 173.51/173.27 [3891]E(f333(f333(f269(x38911,x38912,x38913),x38914),f333(f333(f265(x38911,x38912),x38915),x38916)),f333(f333(x38914,x38915),x38916)) % 173.51/173.27 [3950]E(f333(f333(f333(f8(x39501,x39502,x39503),x39504),x39505),x39506),f333(x39504,f333(x39505,x39506))) % 173.51/173.27 [3951]E(f333(f333(f333(f7(x39511,x39512,x39513),x39514),x39515),x39516),f333(f333(x39514,x39516),x39515)) % 173.51/173.27 [3969]E(f333(f333(f333(f18(x39691,x39692,x39693),x39694),x39695),x39696),f333(f333(x39694,x39696),f333(x39695,x39696))) % 173.51/173.27 [3990]E(f333(f164(x39901,x39902,x39903,x39904),f333(f333(f159(x39902),x39905),x39906)),f333(f333(x39904,x39905),x39906)) % 173.51/173.27 [4030]E(f177(f916(x40301,x40302),f333(f333(f244(a910),x40303),x40304),f333(f333(f265(x40301,x40302),x40305),x40306)),f333(f333(f189(x40301,x40302),f177(x40301,x40303,x40305)),f177(x40302,x40304,x40306))) % 173.51/173.27 [4096]E(f333(f333(f159(f916(x40961,x40962)),f333(f333(f265(x40961,x40962),x40963),x40964)),f333(f333(f189(x40961,x40962),x40965),x40966)),f333(f333(f189(x40961,x40962),f333(f333(f159(x40961),x40963),x40965)),f333(f333(f159(x40962),x40964),x40966))) % 173.51/173.27 [4097]E(f333(f333(f162(x40971,x40972),x40973),f333(f333(f167(x40971,x40974),x40975),x40976)),f333(f333(f167(x40972,f333(f333(f162(x40971,x40972),x40973),x40974)),x40975),f333(x40973,x40976))) % 173.51/173.27 [4139]E(f333(f150(x41391,x41392,x41393,x41394),f333(f333(f159(x41392),x41395),x41396)),f333(f150(x41391,x41392,x41393,f333(f333(x41393,x41394),x41395)),x41396)) % 173.51/173.27 [4165]E(f272(x41651,x41652,x41653,x41654,f333(f333(f265(x41651,x41652),x41655),x41656)),f333(f333(x41654,x41655),x41656)) % 173.51/173.27 [4246]E(f333(f333(f45(x42461,f917(x42462,a905)),x42463),f333(f79(x42464,f917(x42462,a905),x42461,x42465),x42466)),f333(f333(f45(x42464,f917(x42462,a905)),f333(f316(x42461,x42464,x42466),x42463)),x42465)) % 173.51/173.27 [4297]E(f333(f333(f162(x42971,x42972),x42973),f333(f333(f162(x42974,x42971),x42975),x42976)),f333(f333(f162(x42974,x42972),f333(f79(x42971,x42972,x42974,x42973),x42975)),x42976)) % 173.51/173.27 [4303]E(f333(f316(x43031,x43032,f333(f79(x43033,x43032,x43031,x43034),x43035)),x43036),f333(f316(x43033,x43032,x43034),f333(f316(x43031,x43033,x43035),x43036))) % 173.51/173.27 [4304]E(f333(f317(x43041,x43042,f333(f79(x43043,x43042,x43041,x43044),x43045)),x43046),f333(f317(x43041,x43043,x43045),f333(f317(x43043,x43042,x43044),x43046))) % 173.51/173.27 [4332]E(f333(f150(x43321,x43322,x43323,f333(f150(x43321,x43322,x43323,x43324),x43325)),x43326),f333(f150(x43321,x43322,x43323,x43324),f333(f333(f142(x43322),x43325),x43326))) % 173.51/173.27 [4465]E(f333(f270(x44651,x44651,x44652,x44653,f33(x44651),x44654),f333(f333(f265(x44651,x44652),x44655),x44656)),f333(f333(f265(x44651,x44653),x44655),f333(x44654,x44656))) % 173.51/173.27 [4466]E(f333(f270(x44661,x44662,x44663,x44663,x44664,f33(x44663)),f333(f333(f265(x44661,x44663),x44665),x44666)),f333(f333(f265(x44662,x44663),f333(x44664,x44665)),x44666)) % 173.51/173.27 [4554]E(f333(f333(f162(f916(x45541,x45542),f916(x45541,x45543)),f333(f269(x45541,x45542,f916(x45541,x45543)),f333(f333(f7(x45541,f917(x45542,x45543),f917(x45542,f916(x45541,x45543))),f333(f333(f8(f917(x45543,f916(x45541,x45543)),f917(f917(x45542,x45543),f917(x45542,f916(x45541,x45543))),x45541),f8(x45543,f916(x45541,x45543),x45542)),f265(x45541,x45543))),x45544))),f333(f333(f189(x45541,x45542),x45545),x45546)),f333(f333(f189(x45541,x45543),x45545),f333(f333(f162(x45542,x45543),x45544),x45546))) % 173.51/173.27 [3955]E(f105(x39551,x39552,x39553,f333(f333(f333(f98(x39551),x39554),x39555),x39556)),f333(f333(f333(x39553,x39554),x39555),x39556)) % 173.51/173.27 [3956]E(f106(x39561,x39562,x39563,f333(f333(f333(f98(x39561),x39564),x39565),x39566)),f333(f333(f333(x39563,x39564),x39565),x39566)) % 173.51/173.27 [4149]E(f333(f333(f79(x41491,x41492,x41493,f333(f16(x41492,x41491),x41494)),x41495),x41496),x41494) % 173.51/173.27 [4181]E(f333(f316(x41811,x41812,x41813),f333(f316(x41814,x41811,x41815),x41816)),f333(f316(x41814,x41812,f333(f333(f8(x41811,x41812,x41814),x41813),x41815)),x41816)) % 173.51/173.27 [4187]E(f333(f333(f45(x41871,f917(x41872,a905)),f333(f316(x41873,x41871,x41874),x41875)),x41876),f333(f333(f45(x41873,f917(x41872,a905)),x41875),f333(f333(f8(x41871,f917(x41872,a905),x41873),x41876),x41874))) % 173.51/173.27 [4188]E(f333(f333(f46(x41881,f917(x41882,a905)),f333(f316(x41883,x41881,x41884),x41885)),x41886),f333(f333(f46(x41883,f917(x41882,a905)),x41885),f333(f333(f8(x41881,f917(x41882,a905),x41883),x41886),x41884))) % 173.51/173.27 [4189]E(f333(f333(f45(x41891,f917(x41892,a905)),x41893),f333(f333(f8(x41894,f917(x41892,a905),x41891),x41895),x41896)),f333(f333(f45(x41894,f917(x41892,a905)),f333(f316(x41891,x41894,x41896),x41893)),x41895)) % 173.51/173.27 [4190]E(f333(f333(f46(x41901,f917(x41902,a905)),x41903),f333(f333(f8(x41904,f917(x41902,a905),x41901),x41905),x41906)),f333(f333(f46(x41904,f917(x41902,a905)),f333(f316(x41901,x41904,x41906),x41903)),x41905)) % 173.51/173.27 [4248]E(f333(f333(f45(x42481,f917(x42482,a905)),x42483),f333(f333(f8(f917(x42484,a905),f917(x42482,a905),x42481),f316(x42484,x42482,x42485)),x42486)),f333(f316(x42484,x42482,x42485),f333(f333(f45(x42481,f917(x42484,a905)),x42483),x42486))) % 173.51/173.27 [4249]E(f333(f333(f45(x42491,f917(x42492,a905)),x42493),f333(f333(f8(f917(x42494,a905),f917(x42492,a905),x42491),f317(x42492,x42494,x42495)),x42496)),f333(f317(x42492,x42494,x42495),f333(f333(f45(x42491,f917(x42494,a905)),x42493),x42496))) % 173.51/173.27 [4250]E(f333(f333(f46(x42501,f917(x42502,a905)),x42503),f333(f333(f8(f917(x42504,a905),f917(x42502,a905),x42501),f317(x42502,x42504,x42505)),x42506)),f333(f317(x42502,x42504,x42505),f333(f333(f46(x42501,f917(x42504,a905)),x42503),x42506))) % 173.51/173.27 [4251]E(f333(f333(f45(x42511,f917(x42512,a905)),x42513),f333(f333(f8(f917(x42514,a905),f917(x42512,a905),x42511),f292(x42514,x42512,x42515)),x42516)),f333(f292(x42514,x42512,x42515),f333(f333(f45(x42511,f917(x42514,a905)),x42513),x42516))) % 173.51/173.27 [4337]E(f333(f150(x43371,x43372,f333(f7(x43372,x43371,x43371),x43373),x43374),f333(f176(x43372),f333(f333(f159(x43372),x43375),x43376))),f333(f333(x43373,x43375),f333(f150(x43371,x43372,f333(f7(x43372,x43371,x43371),x43373),x43374),f333(f176(x43372),x43376)))) % 173.51/173.27 [4394]E(f333(f333(f18(f916(x43941,x43942),x43942,x43943),f333(f333(f8(x43944,f917(x43942,x43943),f916(x43941,x43942)),x43945),f333(f333(f8(x43941,x43944,f916(x43941,x43942)),x43946),f264(x43941,x43942)))),f268(x43941,x43942)),f333(f269(x43941,x43942,x43943),f333(f333(f8(x43944,f917(x43942,x43943),x43941),x43945),x43946))) % 173.51/173.27 [4401]E(f333(f150(x44011,x44012,f333(f7(x44012,x44011,x44011),x44013),f333(f150(x44011,x44012,f333(f7(x44012,x44011,x44011),x44013),x44014),f333(f176(x44012),x44015))),f333(f176(x44012),x44016)),f333(f150(x44011,x44012,f333(f7(x44012,x44011,x44011),x44013),x44014),f333(f176(x44012),f333(f333(f142(x44012),x44016),x44015)))) % 173.51/173.27 [4403]E(f333(f333(f162(f916(x44031,x44032),f916(x44033,x44032)),f333(f269(x44031,x44032,f916(x44033,x44032)),f333(f333(f8(x44033,f917(x44032,f916(x44033,x44032)),x44031),f265(x44033,x44032)),x44034))),f333(f333(f189(x44031,x44032),x44035),x44036)),f333(f333(f189(x44033,x44032),f333(f333(f162(x44031,x44033),x44034),x44035)),x44036)) % 173.51/173.27 [4448]P106(f333(f333(f246(f917(x44481,a905)),f333(f292(x44482,x44481,x44483),f333(f333(f46(x44484,f917(x44482,a905)),x44485),x44486))),f333(f333(f46(x44484,f917(x44481,a905)),x44485),f333(f333(f8(f917(x44482,a905),f917(x44481,a905),x44484),f292(x44482,x44481,x44483)),x44486)))) % 173.51/173.27 [4261]E(f333(f333(f189(x42611,x42612),f333(f333(f167(x42611,x42613),x42614),f333(f264(x42611,x42612),x42615))),f333(f333(f167(x42612,x42616),x42614),f333(f268(x42611,x42612),x42615))),f333(f333(f167(f916(x42611,x42612),f333(f333(f189(x42611,x42612),x42613),x42616)),x42614),x42615)) % 173.51/173.27 [4320]E(f333(f333(f121(f917(f916(x43201,x43202),a905)),f333(f333(f295(x43201,x43203,x43202),x43204),x43205)),f333(f333(f295(x43201,x43203,x43202),x43204),x43206)),f333(f333(f295(x43201,x43203,x43202),x43204),f333(f333(f121(f917(f916(x43203,x43202),a905)),x43205),x43206))) % 173.51/173.27 [4413]E(f333(f333(f315(f916(x44131,x44132)),f333(f333(f265(x44131,x44132),x44133),x44134)),f333(f333(f121(f917(f916(x44131,x44132),a905)),f333(f333(f267(x44131,x44132),x44135),f333(f16(f917(x44132,a905),x44131),f333(f333(f315(x44132),x44134),x44136)))),f333(f333(f267(x44131,x44132),f333(f333(f315(x44131),x44133),x44135)),f333(f16(f917(x44132,a905),x44131),x44136)))),f333(f333(f267(x44131,x44132),f333(f333(f315(x44131),x44133),x44135)),f333(f16(f917(x44132,a905),x44131),f333(f333(f315(x44132),x44134),x44136)))) % 173.51/173.27 [4492]E(f333(f333(f112(f917(x44921,a905)),f333(f317(x44921,x44922,f333(f79(f916(x44922,x44923),x44922,x44921,f264(x44922,x44923)),x44924)),x44925)),f333(f317(x44921,x44923,f333(f79(f916(x44922,x44923),x44923,x44921,f268(x44922,x44923)),x44924)),x44926)),f333(f317(x44921,f916(x44922,x44923),x44924),f333(f333(f267(x44922,x44923),x44925),f333(f16(f917(x44923,a905),x44922),x44926)))) % 173.51/173.27 [4343]E(f333(f333(f121(f917(f916(x43431,x43432),a905)),f333(f333(f295(x43431,x43433,x43432),x43434),x43435)),f333(f333(f295(x43431,x43433,x43432),x43436),x43435)),f333(f333(f295(x43431,x43433,x43432),f333(f333(f121(f917(f916(x43431,x43433),a905)),x43434),x43436)),x43435)) % 173.51/173.27 [4473]E(f333(f333(f45(x44731,f917(x44732,a905)),x44733),f333(f333(f7(x44731,f917(x44734,f917(x44732,a905)),f917(x44732,a905)),f333(f333(f8(f917(x44734,a905),f917(f917(x44734,f917(x44732,a905)),f917(x44732,a905)),x44731),f45(x44734,f917(x44732,a905))),x44735)),x44736)),f333(f333(f45(x44734,f917(x44732,a905)),f333(f333(f45(x44731,f917(x44734,a905)),x44733),x44735)),x44736)) % 173.51/173.27 [4474]E(f333(f333(f46(x44741,f917(x44742,a905)),x44743),f333(f333(f7(x44741,f917(x44744,f917(x44742,a905)),f917(x44742,a905)),f333(f333(f8(f917(x44744,a905),f917(f917(x44744,f917(x44742,a905)),f917(x44742,a905)),x44741),f46(x44744,f917(x44742,a905))),x44745)),x44746)),f333(f333(f46(x44744,f917(x44742,a905)),f333(f333(f45(x44741,f917(x44744,a905)),x44743),x44745)),x44746)) % 173.51/173.27 [4526]E(f333(f269(x45261,x45262,f916(x45263,x45264)),f333(f333(f7(x45261,f917(x45262,x45264),f917(x45262,f916(x45263,x45264))),f333(f333(f8(f917(x45264,f916(x45263,x45264)),f917(f917(x45262,x45264),f917(x45262,f916(x45263,x45264))),x45261),f8(x45264,f916(x45263,x45264),x45262)),f333(f333(f8(x45263,f917(x45264,f916(x45263,x45264)),x45261),f265(x45263,x45264)),x45265))),x45266)),f270(x45261,x45263,x45262,x45264,x45265,x45266)) % 173.51/173.27 [4549]E(f333(f316(x45491,x45492,f333(f333(f18(x45491,x45492,x45492),f333(f333(f18(x45491,x45492,f917(x45492,x45492)),f333(f333(f8(a905,f917(x45492,f917(x45492,x45492)),x45491),f107(x45492)),x45493)),x45494)),x45495)),x45496),f333(f333(f121(f917(x45492,a905)),f333(f316(x45491,x45492,x45494),f333(f333(f112(f917(x45491,a905)),x45496),f333(f252(x45491),x45493)))),f333(f316(x45491,x45492,x45495),f333(f333(f112(f917(x45491,a905)),x45496),f333(f252(x45491),f333(f333(f8(a905,a905,x45491),a328),x45493)))))) % 173.51/173.27 [4561]E(f333(f316(x45611,f916(x45612,x45613),f333(f333(f18(x45611,x45613,f916(x45612,x45613)),f333(f333(f8(x45612,f917(x45613,f916(x45612,x45613)),x45611),f265(x45612,x45613)),x45614)),x45615)),x45616),f333(f333(f267(x45612,x45613),f333(f316(x45611,x45612,x45614),x45616)),f333(f333(f8(f917(x45611,a905),f917(x45613,a905),x45612),f316(x45611,x45613,x45615)),f333(f333(f7(x45612,f917(x45611,a905),f917(x45611,a905)),f333(f333(f8(f917(x45611,a905),f917(f917(x45611,a905),f917(x45611,a905)),x45612),f112(f917(x45611,a905))),f333(f333(f8(f917(x45612,a905),f917(x45611,a905),x45612),f317(x45611,x45612,x45614)),f333(f333(f7(x45612,f917(x45612,a905),f917(x45612,a905)),f315(x45612)),f196(f917(x45612,a905)))))),x45616)))) % 173.51/173.27 [4586]E(f258(x45861,x45862,x45863,x45864,x45865,x45866),f333(x45864,f333(f252(x45861),f333(f333(f8(f917(f917(x45863,x45861),a905),a905,x45861),f94(f917(x45863,x45861))),f333(f333(f8(f917(f917(x45863,x45861),a905),f917(f917(x45863,x45861),a905),x45861),f333(f18(f917(x45863,x45861),a905,a905),f333(f333(f8(a905,f917(a905,a905),f917(x45863,x45861)),a331),f333(f333(f7(f917(x45863,x45861),f917(f917(x45863,x45861),a905),a905),f335(f917(x45863,x45861))),x45865)))),f333(f333(f7(x45861,f917(f917(x45863,x45861),x45861),f917(f917(x45863,x45861),a905)),f333(f333(f8(f917(x45861,a905),f917(f917(f917(x45863,x45861),x45861),f917(f917(x45863,x45861),a905)),x45861),f8(x45861,a905,f917(x45863,x45861))),a330)),f333(f333(f7(f917(x45863,x45861),x45863,x45861),f5(f917(x45863,x45861))),x45866))))))) % 173.51/173.27 [4375]E(f333(f79(x43751,x43752,x43753,x43754),f81(x43753,x43751,x43755,x43756,x43757)),f81(x43753,x43752,f333(f79(x43751,x43752,x43753,x43754),x43755),x43756,f333(x43754,x43757))) % 173.51/173.27 [4509]E(f333(f268(x45091,x45092),f333(f270(x45093,x45091,x45094,x45092,x45095,x45096),x45097)),f333(x45096,f333(f268(x45093,x45094),x45097))) % 173.51/173.27 [4510]E(f333(f264(x45101,x45102),f333(f270(x45103,x45101,x45104,x45102,x45105,x45106),x45107)),f333(x45105,f333(f264(x45103,x45104),x45107))) % 173.51/173.27 [4224]E(f333(f333(f189(x42241,x42242),f333(f333(f167(x42241,x42243),x42244),x42245)),f333(f333(f167(x42242,x42246),x42244),x42247)),f333(f333(f167(f916(x42241,x42242),f333(f333(f189(x42241,x42242),x42243),x42246)),x42244),f333(f333(f265(x42241,x42242),x42245),x42247))) % 173.51/173.27 [4291]E(f333(f333(f333(f271(x42911,x42912,x42913,x42914),x42915),x42916),x42917),f333(f333(f269(x42912,x42913,x42914),x42916),f333(x42915,x42917))) % 173.51/173.27 [4302]E(f333(f333(f333(f271(x43021,x43022,x43023,x43024),x43025),x43026),x43027),f333(f333(x43026,f333(f264(x43022,x43023),f333(x43025,x43027))),f333(f268(x43022,x43023),f333(x43025,x43027)))) % 173.51/173.27 [4353]E(f333(f79(x43531,x43532,x43533,x43534),f333(f79(x43535,x43531,x43533,x43536),x43537)),f333(f79(x43535,x43532,x43533,f333(f79(x43531,x43532,x43535,x43534),x43536)),x43537)) % 173.51/173.27 [4530]E(f333(f270(x45301,x45302,x45303,x45303,x45304,f33(x45303)),f333(f270(x45301,x45301,x45305,x45303,f33(x45301),x45306),x45307)),f333(f333(f265(x45302,x45303),f333(x45304,f333(f264(x45301,x45305),x45307))),f333(x45306,f333(f268(x45301,x45305),x45307)))) % 173.51/173.27 [4531]E(f333(f270(x45311,x45311,x45312,x45313,f33(x45311),x45314),f333(f270(x45315,x45311,x45312,x45312,x45316,f33(x45312)),x45317)),f333(f333(f265(x45311,x45313),f333(x45316,f333(f264(x45315,x45312),x45317))),f333(x45314,f333(f268(x45315,x45312),x45317)))) % 173.51/173.27 [4547]E(f333(f270(x45471,x45472,x45473,x45473,x45474,f33(x45473)),f333(f270(x45475,x45471,x45473,x45473,x45476,f33(x45473)),x45477)),f333(f270(x45475,x45472,x45473,x45473,f333(f79(x45471,x45472,x45475,x45474),x45476),f33(x45473)),x45477)) % 173.51/173.27 [4548]E(f333(f270(x45481,x45481,x45482,x45483,f33(x45481),x45484),f333(f270(x45481,x45481,x45485,x45482,f33(x45481),x45486),x45487)),f333(f270(x45481,x45481,x45485,x45483,f33(x45481),f333(f79(x45482,x45483,x45485,x45484),x45486)),x45487)) % 173.51/173.27 [4558]E(f333(f270(x45581,x45582,x45583,x45583,x45584,f33(x45583)),f333(f270(x45581,x45581,x45585,x45583,f33(x45581),x45586),x45587)),f333(f270(x45582,x45582,x45585,x45583,f33(x45582),x45586),f333(f270(x45581,x45582,x45585,x45585,x45584,f33(x45585)),x45587))) % 173.51/173.27 [4258]E(f333(f333(f295(x42581,x42582,x42583),f333(f333(f295(x42581,x42584,x42582),x42585),x42586)),x42587),f333(f333(f295(x42581,x42584,x42583),x42585),f333(f333(f295(x42584,x42582,x42583),x42586),x42587))) % 173.51/173.27 [4326]E(f333(f333(f269(x43261,x43262,x43263),f333(f79(x43264,f917(x43262,x43263),x43261,x43265),x43266)),x43267),f333(f333(x43265,f333(x43266,f333(f264(x43261,x43262),x43267))),f333(f268(x43261,x43262),x43267))) % 173.51/173.27 [4406]E(f333(f150(x44061,x44062,f333(f7(x44062,x44061,x44061),x44063),x44064),f333(f176(x44062),f333(f333(f162(x44065,x44062),x44066),x44067))),f333(f150(x44061,x44065,f333(f7(x44065,x44061,x44061),f333(f79(x44062,f917(x44061,x44061),x44065,x44063),x44066)),x44064),f333(f176(x44065),x44067))) % 173.51/173.27 [4354]E(f333(f333(f45(x43541,f917(f916(x43542,x43543),a905)),x43544),f333(f333(f8(f917(f916(x43545,x43543),a905),f917(f916(x43542,x43543),a905),x43541),f333(f295(x43542,x43545,x43543),x43546)),x43547)),f333(f333(f295(x43542,x43545,x43543),x43546),f333(f333(f45(x43541,f917(f916(x43545,x43543),a905)),x43544),x43547))) % 173.51/173.27 [4497]E(f333(f333(f45(x44971,f917(f916(x44972,x44973),a905)),x44974),f333(f333(f7(x44971,f917(f916(x44975,x44973),a905),f917(f916(x44972,x44973),a905)),f333(f333(f8(f917(f916(x44972,x44975),a905),f917(f917(f916(x44975,x44973),a905),f917(f916(x44972,x44973),a905)),x44971),f295(x44972,x44975,x44973)),x44976)),x44977)),f333(f333(f295(x44972,x44975,x44973),f333(f333(f45(x44971,f917(f916(x44972,x44975),a905)),x44974),x44976)),x44977)) % 173.51/173.27 [4498]E(f333(f150(x44981,x44982,f333(f333(f7(x44981,f917(x44982,x44983),f917(x44982,x44981)),f333(f333(f8(f917(x44983,x44981),f917(f917(x44982,x44983),f917(x44982,x44981)),x44981),f8(x44983,x44981,x44982)),x44984)),x44985),x44986),x44987),f333(f150(x44981,x44983,x44984,x44986),f333(f333(f162(x44982,x44983),x44985),x44987))) % 173.51/173.27 [4559]E(f333(f333(f46(x45591,f917(x45592,a905)),x45593),f333(f333(f8(f917(x45594,f917(x45592,a905)),f917(x45592,a905),x45591),f333(f46(x45594,f917(x45592,a905)),x45595)),f333(f333(f7(x45591,f917(x45594,f917(x45592,a905)),f917(x45594,f917(x45592,a905))),f333(f333(f8(f917(f917(x45592,a905),f917(x45592,a905)),f917(f917(x45594,f917(x45592,a905)),f917(x45594,f917(x45592,a905))),x45591),f8(f917(x45592,a905),f917(x45592,a905),x45594)),f333(f333(f8(f917(x45592,a905),f917(f917(x45592,a905),f917(x45592,a905)),x45591),f121(f917(x45592,a905))),x45596))),x45597))),f333(f333(f121(f917(x45592,a905)),f333(f333(f46(x45591,f917(x45592,a905)),x45593),x45596)),f333(f333(f46(x45594,f917(x45592,a905)),x45595),x45597))) % 173.51/173.27 [4560]E(f333(f333(f45(x45601,f917(x45602,a905)),x45603),f333(f333(f8(f917(x45604,f917(x45602,a905)),f917(x45602,a905),x45601),f333(f45(x45604,f917(x45602,a905)),x45605)),f333(f333(f7(x45601,f917(x45604,f917(x45602,a905)),f917(x45604,f917(x45602,a905))),f333(f333(f8(f917(f917(x45602,a905),f917(x45602,a905)),f917(f917(x45604,f917(x45602,a905)),f917(x45604,f917(x45602,a905))),x45601),f8(f917(x45602,a905),f917(x45602,a905),x45604)),f333(f333(f8(f917(x45602,a905),f917(f917(x45602,a905),f917(x45602,a905)),x45601),f112(f917(x45602,a905))),x45606))),x45607))),f333(f333(f112(f917(x45602,a905)),f333(f333(f45(x45601,f917(x45602,a905)),x45603),x45606)),f333(f333(f45(x45604,f917(x45602,a905)),x45605),x45607))) % 173.51/173.27 [4552]E(f209(x45521,x45522,f333(f333(f333(x45523,x45524),x45525),x45526),f333(f333(f7(x45521,f916(a110,a110),f917(a110,f912(x45522))),f333(f333(f7(x45521,a110,f917(f916(a110,a110),f917(a110,f912(x45522)))),f333(f333(f7(x45521,a110,f917(a110,f917(f916(a110,a110),f917(a110,f912(x45522))))),x45527),x45524)),x45525)),x45526)),f333(f333(f333(f221(x45521,x45522,x45523,x45527),x45524),x45525),x45526)) % 173.51/173.27 [4566]E(f210(x45661,x45662,f333(f333(f333(x45663,x45664),x45665),x45666),f333(f333(f7(x45661,f916(a110,a110),f917(a110,f912(x45662))),f333(f333(f7(x45661,a110,f917(f916(a110,a110),f917(a110,f912(x45662)))),f333(f333(f7(x45661,a110,f917(a110,f917(f916(a110,a110),f917(a110,f912(x45662))))),x45667),x45664)),x45665)),x45666)),f223(x45661,x45662,x45663,x45667,x45664,x45665,x45666)) % 173.51/173.27 [4557]E(f207(x45571,x45572,f333(f333(f333(x45573,x45574),x45575),x45576),f333(f333(f7(x45571,f916(a110,a110),f917(a110,f912(f914(x45572)))),f333(f333(f7(x45571,a110,f917(f916(a110,a110),f917(a110,f912(f914(x45572))))),f333(f333(f7(x45571,a110,f917(a110,f917(f916(a110,a110),f917(a110,f912(f914(x45572)))))),x45577),x45574)),x45575)),x45576)),f333(f333(f333(f218(x45571,x45572,x45573,x45577),x45574),x45575),x45576)) % 173.51/173.27 [4568]E(f208(x45681,x45682,f333(f333(f333(x45683,x45684),x45685),x45686),f333(f333(f7(x45681,f916(a110,a110),f917(a110,f912(f914(x45682)))),f333(f333(f7(x45681,a110,f917(f916(a110,a110),f917(a110,f912(f914(x45682))))),f333(f333(f7(x45681,a110,f917(a110,f917(f916(a110,a110),f917(a110,f912(f914(x45682)))))),x45687),x45684)),x45685)),x45686)),f220(x45681,x45682,x45683,x45687,x45684,x45685,x45686)) % 173.51/173.27 [4467]E(f333(f270(x44671,x44672,x44673,x44674,x44675,x44676),f333(f333(f265(x44671,x44673),x44677),x44678)),f333(f333(f265(x44672,x44674),f333(x44675,x44677)),f333(x44676,x44678))) % 173.51/173.27 [4570]E(f333(f333(f162(f916(x45701,x45702),f916(x45703,x45704)),f333(f269(x45701,x45702,f916(x45703,x45704)),f333(f333(f7(x45701,f917(x45702,x45704),f917(x45702,f916(x45703,x45704))),f333(f333(f8(f917(x45704,f916(x45703,x45704)),f917(f917(x45702,x45704),f917(x45702,f916(x45703,x45704))),x45701),f8(x45704,f916(x45703,x45704),x45702)),f333(f333(f8(x45703,f917(x45704,f916(x45703,x45704)),x45701),f265(x45703,x45704)),x45705))),x45706))),f333(f333(f189(x45701,x45702),x45707),x45708)),f333(f333(f189(x45703,x45704),f333(f333(f162(x45701,x45703),x45705),x45707)),f333(f333(f162(x45702,x45704),x45706),x45708))) % 173.51/173.27 [4573]E(f333(f333(f162(f916(x45731,x45732),x45733),f333(f269(x45731,x45732,x45733),f333(f333(f8(f917(x45732,f916(x45731,x45734)),f917(x45732,x45733),x45731),f333(f8(f916(x45731,x45734),x45733,x45732),x45735)),f333(f333(f7(x45731,f917(x45732,x45734),f917(x45732,f916(x45731,x45734))),f333(f333(f8(f917(x45734,f916(x45731,x45734)),f917(f917(x45732,x45734),f917(x45732,f916(x45731,x45734))),x45731),f8(x45734,f916(x45731,x45734),x45732)),f265(x45731,x45734))),x45736)))),f333(f333(f189(x45731,x45732),x45737),x45738)),f333(f333(f162(f916(x45731,x45734),x45733),x45735),f333(f333(f189(x45731,x45734),x45737),f333(f333(f162(x45732,x45734),x45736),x45738)))) % 173.51/173.27 [4501]E(f333(f333(f162(f916(x45011,x45012),x45013),f333(f269(x45011,x45012,x45013),f333(f333(f8(f917(x45012,f916(x45014,x45012)),f917(x45012,x45013),x45011),f333(f8(f916(x45014,x45012),x45013,x45012),x45015)),f333(f333(f8(x45014,f917(x45012,f916(x45014,x45012)),x45011),f265(x45014,x45012)),x45016)))),f333(f333(f189(x45011,x45012),x45017),x45018)),f333(f333(f162(f916(x45014,x45012),x45013),x45015),f333(f333(f189(x45014,x45012),f333(f333(f162(x45011,x45014),x45016),x45017)),x45018))) % 173.51/173.27 [4458]E(f333(f333(f269(x44581,x44582,x44583),f333(f333(f8(f917(x44582,f916(x44584,x44585)),f917(x44582,x44583),x44581),f333(f8(f916(x44584,x44585),x44583,x44582),f333(f269(x44584,x44585,x44583),x44586))),x44587)),x44588),f333(f333(f269(x44584,x44585,x44583),x44586),f333(f333(f269(x44581,x44582,f916(x44584,x44585)),x44587),x44588))) % 173.51/173.27 [4574]E(f333(f333(f45(f916(x45741,x45742),f917(f916(x45743,x45744),a905)),f333(f333(f267(x45741,x45742),x45745),f333(f16(f917(x45742,a905),x45741),x45746))),f333(f269(x45741,x45742,f917(f916(x45743,x45744),a905)),f333(f333(f7(x45741,f917(x45742,f917(x45743,f917(x45744,a905))),f917(x45742,f917(f916(x45743,x45744),a905))),f333(f333(f8(f917(f917(x45743,f917(x45744,a905)),f917(f916(x45743,x45744),a905)),f917(f917(x45742,f917(x45743,f917(x45744,a905))),f917(x45742,f917(f916(x45743,x45744),a905))),x45741),f8(f917(x45743,f917(x45744,a905)),f917(f916(x45743,x45744),a905),x45742)),f333(f333(f8(f917(x45743,a905),f917(f917(x45743,f917(x45744,a905)),f917(f916(x45743,x45744),a905)),x45741),f267(x45743,x45744)),x45747))),f333(f333(f8(f917(x45744,a905),f917(x45743,f917(x45744,a905)),x45742),f16(f917(x45744,a905),x45743)),x45748)))),f333(f333(f267(x45743,x45744),f333(f333(f45(x45741,f917(x45743,a905)),x45745),x45747)),f333(f16(f917(x45744,a905),x45743),f333(f333(f45(x45742,f917(x45744,a905)),x45746),x45748)))) % 173.51/173.27 [4606]E(f32(x46061,x46062,x46063,x46064,x46065,x46066,x46067,x46068,x46069,a25),x46062) % 173.51/173.27 [4515]E(f333(f333(f271(x45151,x45152,x45153,x45154),f333(f333(f271(x45151,x45155,x45156,f916(x45152,x45153)),x45157),x45158)),x45159),f333(f333(f271(x45151,x45155,x45156,x45154),x45157),f333(f333(f7(x45155,f917(x45152,f917(x45153,x45154)),f917(x45156,x45154)),f333(f333(f8(f917(x45156,f916(x45152,x45153)),f917(f917(x45152,f917(x45153,x45154)),f917(x45156,x45154)),x45155),f271(x45156,x45152,x45153,x45154)),x45158)),x45159))) % 173.51/173.27 [4544]E(f333(f79(f916(x45441,x45442),f916(x45443,x45444),f916(x45445,x45446),f270(x45441,x45443,x45442,x45444,x45447,x45448)),f270(x45445,x45441,x45446,x45442,x45449,x454410)),f270(x45445,x45443,x45446,x45444,f333(f79(x45441,x45443,x45445,x45447),x45449),f333(f79(x45442,x45444,x45446,x45448),x454410))) % 173.51/173.27 [4607]E(f32(x46071,x46072,x46073,x46074,x46075,x46076,x46077,x46078,x46079,f31(x460710,x460711)),f333(f333(x46075,x460710),x460711)) % 173.51/173.27 [4608]E(f32(x46081,x46082,x46083,x46084,x46085,x46086,x46087,x46088,x46089,f30(x460810,x460811)),f333(f333(x46087,x460810),x460811)) % 173.51/173.27 [4609]E(f32(x46091,x46092,x46093,x46094,x46095,x46096,x46097,x46098,x46099,f26(x460910,x460911)),f333(f333(x46093,x460910),x460911)) % 173.51/173.27 [4550]E(f333(f270(x45501,x45502,x45503,x45504,x45505,x45506),f333(f270(x45507,x45501,x45508,x45503,x45509,x455010),x455011)),f333(f270(x45507,x45502,x45508,x45504,f333(f79(x45501,x45502,x45507,x45505),x45509),f333(f79(x45503,x45504,x45508,x45506),x455010)),x455011)) % 173.51/173.27 [4610]E(f32(x46101,x46102,x46103,x46104,x46105,x46106,x46107,x46108,x46109,f28(x461010,x461011,x461012)),f333(f333(f333(x46106,x461010),x461011),x461012)) % 173.51/173.27 [4611]E(f32(x46111,x46112,x46113,x46114,x46115,x46116,x46117,x46118,x46119,f27(x461110,x461111,x461112)),f333(f333(f333(x46114,x461110),x461111),x461112)) % 173.51/173.27 [4720]~P7(x47201)+P7(f914(x47201)) % 173.51/173.27 [4721]~P66(x47211)+P66(f914(x47211)) % 173.51/173.27 [4722]~P104(x47221)+P104(f911(x47221)) % 173.51/173.27 [4725]~P145(x47251)+~E(f85(x47251),f2(x47251)) % 173.51/173.27 [4727]~E(x47271,f2(a110))+E(f333(a22,x47271),f2(a1)) % 173.51/173.27 [4728]~E(x47281,f2(a1))+E(f89(a1,x47281),f2(a1)) % 173.51/173.27 [4734]~P107(x47341)+P30(x47341,f2(x47341)) % 173.51/173.27 [4736]~P110(x47361)+P16(x47361,f124(x47361)) % 173.51/173.27 [4745]P106(x47451)+P106(f333(a328,x47451)) % 173.51/173.27 [4794]~P107(x47941)+~P30(x47941,f85(x47941)) % 173.51/173.27 [4837]~P106(x48371)+~P106(f333(a328,x48371)) % 173.51/173.27 [4858]E(f333(a115,x48581),f2(a910))+~P106(f333(a201,x48581)) % 173.51/173.27 [4924]~P101(x49241)+P17(x49241,x49241,f121(x49241)) % 173.51/173.27 [4925]~P102(x49251)+P17(x49251,x49251,f112(x49251)) % 173.51/173.27 [4926]~P97(x49261)+P17(x49261,x49261,f88(x49261)) % 173.51/173.27 [4927]~P110(x49271)+P17(x49271,x49271,f244(x49271)) % 173.51/173.27 [4928]~P110(x49281)+P17(x49281,x49281,f245(x49281)) % 173.51/173.27 [4929]~P76(x49291)+P18(x49291,x49291,f88(x49291)) % 173.51/173.27 [4731]~E(x47311,f2(a910))+E(f333(f111(a1),x47311),f2(a1)) % 173.51/173.27 [4738]~P95(x47381)+E(f333(f114(x47381),a90),f2(x47381)) % 173.51/173.27 [4741]~E(f605(x47411),f2(a910))+E(f333(f173(a910),x47411),f2(a910)) % 173.51/173.27 [4742]~P111(x47421)+E(f248(x47421,f246(x47421)),f244(x47421)) % 173.51/173.27 [4743]~P111(x47431)+E(f249(x47431,f246(x47431)),f245(x47431)) % 173.51/173.27 [4744]~P91(x47441)+E(f89(x47441,f2(x47441)),f2(x47441)) % 173.51/173.27 [4753]~P107(x47531)+E(f333(f111(x47531),f2(a910)),f2(x47531)) % 173.51/173.27 [4754]~P107(x47541)+E(f333(f111(x47541),f85(a910)),f85(x47541)) % 173.51/173.27 [4755]~P139(x47551)+E(f333(f113(x47551),f2(a1)),f2(x47551)) % 173.51/173.27 [4756]~P139(x47561)+E(f333(f113(x47561),f85(a1)),f85(x47561)) % 173.51/173.27 [4757]E(x47571,f2(a910))+~E(f333(f111(a1),x47571),f2(a1)) % 173.51/173.27 [4788]~P84(x47881)+E(f333(f86(x47881),f196(x47881)),f254(x47881)) % 173.51/173.27 [4789]~P84(x47891)+E(f333(f86(x47891),f254(x47891)),f196(x47891)) % 173.51/173.27 [4790]~P71(x47901)+E(f333(f86(x47901),f2(x47901)),f2(x47901)) % 173.51/173.27 [4791]~P87(x47911)+E(f333(f82(x47911),f2(x47911)),f2(x47911)) % 173.51/173.27 [4792]~P120(x47921)+E(f333(f82(x47921),f85(x47921)),f85(x47921)) % 173.51/173.27 [4793]~P82(x47931)+E(f333(f173(x47931),f124(x47931)),f2(x47931)) % 173.51/173.27 [4811]~P39(x48111)+P43(f333(f180(a1),x48111)) % 173.51/173.27 [4842]~P95(x48421)+E(f333(f86(x48421),f85(x48421)),f333(f114(x48421),a108)) % 173.51/173.27 [4857]~P95(x48571)+P30(x48571,f333(f114(x48571),a90)) % 173.51/173.27 [4883]P39(x48831)+~P43(f333(f180(a1),x48831)) % 173.51/173.27 [4930]E(f333(f111(a1),f333(a115,x49301)),x49301)+P106(f333(a201,x49301)) % 173.51/173.27 [4949]~P111(x49491)+E(f100(x49491,x49491,f5(x49491)),f101(x49491)) % 173.51/173.27 [5001]~P115(x50011)+E(f257(x50011,f85(x50011),f88(x50011)),f256(x50011)) % 173.51/173.27 [5034]~P95(x50341)+~P30(x50341,f333(f114(x50341),a108)) % 173.51/173.27 [5180]E(f333(f82(a1),x51801),x51801)+P106(f333(f333(f247(a1),x51801),f2(a1))) % 173.51/173.27 [5198]~E(f333(a115,x51981),f2(a910))+P106(f333(f333(f246(a1),x51981),f2(a1))) % 173.51/173.27 [5262]~P106(f333(a201,x52621))+P106(f333(f333(f247(a1),x52621),f2(a1))) % 173.51/173.27 [5302]~P139(x53021)+P106(f333(f333(f335(x53021),f2(x53021)),f120(x53021))) % 173.51/173.27 [5303]~P107(x53031)+P106(f333(f333(f335(x53031),f2(x53031)),f194(x53031))) % 173.51/173.27 [5304]~P139(x53041)+P106(f333(f333(f335(x53041),f85(x53041)),f120(x53041))) % 173.51/173.27 [5305]~P107(x53051)+P106(f333(f333(f335(x53051),f85(x53051)),f194(x53051))) % 173.51/173.27 [5306]~P119(x53061)+P106(f333(f333(f246(x53061),f2(x53061)),f85(x53061))) % 173.51/173.27 [5307]~P119(x53071)+P106(f333(f333(f247(x53071),f2(x53071)),f85(x53071))) % 173.51/173.27 [5362]E(x53621,f2(a910))+~P106(f333(f333(f246(a910),x53621),f2(a910))) % 173.51/173.27 [5403]E(f333(a115,x54031),f2(a910))+~P106(f333(f333(f246(a1),x54031),f2(a1))) % 173.51/173.27 [5464]P106(f333(a201,x54641))+~P106(f333(f333(f247(a1),x54641),f2(a1))) % 173.51/173.27 [5471]~P110(x54711)+P18(x54711,f911(x54711),f156(x54711,x54711,f5(x54711))) % 173.51/173.27 [5487]P43(x54871)+~P106(f333(f333(f246(a1),f2(a1)),f338(x54871))) % 173.51/173.27 [5492]E(f333(f82(a1),x54921),f333(f86(a1),x54921))+~P106(f333(f333(f247(a1),x54921),f2(a1))) % 173.51/173.27 [5660]~P119(x56601)+~P106(f333(f333(f246(x56601),f85(x56601)),f2(x56601))) % 173.51/173.27 [5661]~P119(x56611)+~P106(f333(f333(f247(x56611),f85(x56611)),f2(x56611))) % 173.51/173.27 [5672]~E(x56721,f2(a910))+P106(f333(f333(f246(a1),f333(f111(a1),x56721)),f2(a1))) % 173.51/173.27 [5673]~E(x56731,f2(a1))+P106(f333(f333(f247(a1),f333(f82(a1),x56731)),f85(a1))) % 173.51/173.27 [5792]~P82(x57921)+E(f150(x57921,x57921,f87(x57921),f2(x57921)),f173(x57921)) % 173.51/173.27 [5963]~P103(x59631)+P27(a910,x59631,f111(x59631),f254(f917(a910,a905))) % 173.51/173.27 [6160]E(x61601,f2(a910))+~P106(f333(f333(f246(a1),f333(f111(a1),x61601)),f2(a1))) % 173.51/173.27 [6161]E(x61611,f2(a1))+~P106(f333(f333(f247(a1),f333(f82(a1),x61611)),f85(a1))) % 173.51/173.27 [6950]~P106(f333(f333(f247(a1),x69501),f2(a1)))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x69501),x69501)),f2(a1))) % 173.51/173.27 [7499]P106(f333(f333(f247(a1),x74991),f2(a1)))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),x74991),x74991)),f2(a1))) % 173.51/173.27 [8049]E(x80491,f333(a3,f2(a910)))+P106(f333(f333(f247(a910),f333(f333(f23(a910),f333(a20,x80491)),f333(a123,f2(a910)))),f333(a20,x80491))) % 173.51/173.27 [8832]~P106(f333(f333(f247(a1),x88321),f2(a1)))+P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x88321),x88321)),a108)),f2(a1))) % 173.51/173.27 [8928]~P106(f333(f333(f247(a1),x89281),f2(a1)))+P106(f333(f333(f247(a1),f333(f333(f87(a1),f333(f333(f87(a1),f85(a1)),x89281)),x89281)),f2(a1))) % 173.51/173.27 [9267]P106(f333(f333(f247(a1),x92671),f2(a1)))+~P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92671),x92671)),a108)),f2(a1))) % 173.51/173.27 [9329]P106(f333(f333(f247(a1),x93291),f2(a1)))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),f333(f333(f87(a1),f85(a1)),x93291)),x93291)),f2(a1))) % 173.51/173.27 [4831]~E(a90,x48311)+E(f333(f333(f87(a1),x48311),x48311),a90) % 173.51/173.27 [4832]~E(x48321,a90)+E(f333(f333(f87(a1),x48321),x48321),a90) % 173.51/173.27 [4843]E(x48431,f2(a1))+E(f333(f333(f42(a1),x48431),x48431),f85(a1)) % 173.51/173.27 [4978]E(x49781,a90)+~E(f333(f333(f87(a1),x49781),x49781),a90) % 173.51/173.27 [4979]E(a90,x49791)+~E(f333(f333(f87(a1),x49791),x49791),a90) % 173.51/173.27 [4991]~P8(x49911)+E(f44(x49911,f196(f917(x49911,a905))),f254(x49911)) % 173.51/173.27 [4992]~P8(x49921)+E(f44(x49921,f254(f917(x49921,a905))),f196(x49921)) % 173.51/173.27 [4993]~P8(x49931)+E(f43(x49931,f196(f917(x49931,a905))),f196(x49931)) % 173.51/173.27 [4994]~P8(x49941)+E(f43(x49941,f254(f917(x49941,a905))),f254(x49941)) % 173.51/173.27 [4995]~P110(x49951)+E(f147(x49951,f196(f917(x49951,a905))),f124(x49951)) % 173.51/173.27 [5137]E(x51371,f2(a910))+P106(f333(f333(f247(a910),f2(a910)),x51371)) % 173.51/173.27 [5155]~P9(x51551)+P106(f333(f333(f246(a1),f2(a1)),x51551)) % 173.51/173.27 [5189]~E(f333(f114(a910),x51891),f2(a910))+P106(f333(f333(f246(a1),x51891),a90)) % 173.51/173.27 [5194]P43(x51941)+P106(f333(f333(f335(a1),f338(x51941)),x51941)) % 173.51/173.27 [5195]E(x51951,f333(a3,f2(a910)))+P106(f333(f333(f246(a110),f85(a110)),x51951)) % 173.51/173.27 [5235]P106(f333(a201,x52351))+P106(f333(f333(f246(a1),f2(a1)),x52351)) % 173.51/173.27 [5284]E(f333(f111(a1),f333(a115,x52841)),f2(a1))+P106(f333(f333(f246(a1),f2(a1)),x52841)) % 173.51/173.27 [5343]E(f333(f111(a1),f333(f114(a910),x53431)),f333(f114(a1),x53431))+P106(f333(a201,f333(f114(a1),x53431))) % 173.51/173.27 [5368]E(f333(f114(a910),x53681),f2(a910))+~P106(f333(a201,f333(f114(a1),x53681))) % 173.51/173.27 [5369]E(f333(f114(a910),x53691),f2(a910))+~P106(f333(f333(f246(a1),x53691),a90)) % 173.51/173.27 [5400]P9(x54001)+~P106(f333(f333(f246(a1),f2(a1)),x54001)) % 173.51/173.27 [5474]E(f333(a123,f340(x54741)),x54741)+~P106(f333(f333(f247(a910),f2(a910)),x54741)) % 173.51/173.27 [5481]E(f333(a123,f333(f114(a910),x54811)),f85(a910))+~P106(f333(a201,f333(f114(a1),x54811))) % 173.51/173.27 [5488]E(f333(f111(a1),f451(x54881)),x54881)+~P106(f333(f333(f247(a1),f2(a1)),x54881)) % 173.51/173.27 [5495]~E(x54951,f333(a3,f2(a910)))+~P106(f333(f333(f246(a110),f85(a110)),x54951)) % 173.51/173.27 [5502]E(f333(f111(a1),f333(f114(a910),x55021)),f2(a1))+~P106(f333(a201,f333(f114(a1),x55021))) % 173.51/173.27 [5527]E(f333(f173(a910),x55271),f2(a910))+P106(f333(f333(f335(a910),f605(x55271)),f333(f180(a910),x55271))) % 173.51/173.27 [5547]E(f333(f111(a1),f333(a115,x55471)),x55471)+~P106(f333(f333(f246(a1),f2(a1)),x55471)) % 173.51/173.27 [5555]~P106(f333(a201,x55551))+~P106(f333(f333(f246(a1),f2(a1)),x55551)) % 173.51/173.27 [5653]E(f333(f333(f87(a910),f85(a910)),f333(f114(a910),x56531)),f85(a910))+~P106(f333(f333(f247(a1),x56531),a90)) % 173.51/173.27 [5714]E(x57141,f2(a910))+~P106(f333(f333(f247(a910),x57141),f333(a123,f2(a910)))) % 173.51/173.27 [5753]E(f333(f333(f23(a910),f333(f114(a910),x57531)),f85(a910)),f2(a910))+~P106(f333(f333(f246(a1),x57531),a90)) % 173.51/173.27 [5754]E(f333(f333(f87(a910),f333(f114(a910),x57541)),f85(a910)),f85(a910))+~P106(f333(f333(f247(a1),x57541),a90)) % 173.51/173.27 [5764]~P43(x57641)+E(f333(f41(a910),f333(f316(a1,a910,a115),x57641)),f333(f41(a1),x57641)) % 173.51/173.27 [5793]~P110(x57931)+E(f249(x57931,f333(f7(x57931,x57931,a905),f246(x57931))),f244(x57931)) % 173.51/173.27 [5794]~P110(x57941)+E(f248(x57941,f333(f7(x57941,x57941,a905),f246(x57941))),f245(x57941)) % 173.51/173.27 [5804]E(f51(a910,f333(a123,f2(a910)),f333(f114(a910),x58041)),f333(a123,f2(a910)))+~P106(f333(a201,f333(f114(a1),x58041))) % 173.51/173.27 [5813]~P106(f333(f333(f247(a1),f2(a1)),x58131))+P106(f333(f333(f246(a1),f85(a1)),x58131)) % 173.51/173.27 [5814]P106(f333(f333(f247(a1),f2(a1)),x58141))+~P106(f333(f333(f246(a1),f85(a1)),x58141)) % 173.51/173.27 [5825]E(f333(a123,f333(f333(f23(a910),x58251),f85(a910))),x58251)+~P106(f333(f333(f247(a910),f2(a910)),x58251)) % 173.51/173.27 [5881]P106(f333(f333(f247(a910),f2(a910)),f451(x58811)))+~P106(f333(f333(f247(a1),f2(a1)),x58811)) % 173.51/173.27 [5940]E(f51(a1,f333(f114(a1),a108),x59401),f333(f333(f23(a1),x59401),f85(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x59401)) % 173.51/173.27 [5976]~P106(f333(f333(f247(a1),a90),x59761))+P106(f333(f333(f247(a910),f2(a910)),f333(f114(a910),x59761))) % 173.51/173.27 [6026]P106(f333(f333(f247(a910),f2(a910)),f333(a115,x60261)))+~P106(f333(f333(f247(a1),f2(a1)),x60261)) % 173.51/173.27 [6075]~P106(f333(f333(f247(a910),f2(a910)),x60751))+P106(f333(f333(f247(a1),f2(a1)),f333(f111(a1),x60751))) % 173.51/173.27 [6113]~P106(f333(f333(f247(a910),f2(a910)),f333(a115,x61131)))+P106(f333(f333(f247(a1),f2(a1)),x61131)) % 173.51/173.27 [6128]~P43(x61281)+E(f333(f316(a910,a1,f111(a1)),f333(f316(a1,a910,a115),x61281)),x61281) % 173.51/173.27 [6141]P106(f333(f333(f247(a1),a90),x61411))+~P106(f333(f333(f247(a910),f2(a910)),f333(f114(a910),x61411))) % 173.51/173.27 [6198]P106(f333(f333(f247(a910),f2(a910)),x61981))+~P106(f333(f333(f247(a1),f2(a1)),f333(f111(a1),x61981))) % 173.51/173.27 [6309]E(f333(f316(a910,a1,f111(a1)),f333(f289(a910),f333(a115,x63091))),f333(f308(a1,f2(a1)),x63091))+~P106(f333(f333(f246(a1),f2(a1)),x63091)) % 173.51/173.27 [6325]~P119(x63251)+P106(f333(f333(f247(x63251),f2(x63251)),f333(f333(f87(x63251),f85(x63251)),f85(x63251)))) % 173.51/173.27 [6374]P106(f333(f333(f247(a910),f333(a123,f2(a910))),f333(a115,x63741)))+~P106(f333(f333(f247(a1),f85(a1)),x63741)) % 173.51/173.27 [6471]E(x64711,f2(a1))+P106(f333(f55(f2(a1),x64711),f333(f333(f265(a1,a1),f2(a1)),f2(a1)))) % 173.51/173.27 [6639]~P106(f333(f333(f247(a910),f333(a123,f2(a910))),f333(a115,x66391)))+P106(f333(f333(f247(a1),f85(a1)),x66391)) % 173.51/173.27 [7061]~P116(x70611)+P40(x70611,f333(f252(f916(x70611,x70611)),f333(f269(x70611,x70611,a905),f247(x70611)))) % 173.51/173.27 [5701]E(f333(f114(a910),f333(f333(f23(a1),x57011),a108)),f333(a123,f333(f114(a910),x57011)))+P106(f333(a201,f333(f114(a1),x57011))) % 173.51/173.27 [5717]~P39(x57171)+E(f333(f333(f162(a910,a1),f111(a1)),f333(f333(f162(a1,a910),a115),x57171)),x57171) % 173.51/173.27 [5831]E(f333(f86(a1),f333(f111(a1),f333(a123,f443(x58311)))),x58311)+~P106(f333(f333(f247(a1),x58311),f2(a1))) % 173.51/173.27 [5841]E(f333(f333(f87(a910),f85(a910)),f333(f114(a910),x58411)),f333(f114(a910),f333(f333(f23(a1),x58411),a108)))+P106(f333(f333(f247(a1),x58411),a90)) % 173.51/173.27 [5883]E(f333(f333(f42(a1),f333(f114(a1),a108)),x58831),f333(f114(a1),a108))+~P106(f333(f333(f247(a1),f2(a1)),x58831)) % 173.51/173.27 [5972]E(f333(f333(f23(a910),f333(f114(a910),x59721)),f85(a910)),f333(f114(a910),f333(f333(f87(a1),x59721),a108)))+P106(f333(f333(f246(a1),x59721),a90)) % 173.51/173.27 [5973]E(f333(f333(f87(a910),f333(f114(a910),x59731)),f85(a910)),f333(f114(a910),f333(f333(f23(a1),x59731),a108)))+P106(f333(f333(f247(a1),x59731),a90)) % 173.51/173.27 [6014]E(f333(a115,f333(f333(f87(a1),f85(a1)),x60141)),f333(a123,f333(a115,x60141)))+~P106(f333(f333(f246(a1),f2(a1)),x60141)) % 173.51/173.27 [6047]E(f333(a123,f333(f333(f23(a910),x60471),f333(a123,f2(a910)))),x60471)+~P106(f333(f333(f247(a910),f2(a910)),x60471)) % 173.51/173.27 [6261]E(f51(a910,f333(a123,f2(a910)),f333(f114(a910),x62611)),f333(a115,f51(a1,f85(a1),f333(f114(a1),x62611))))+P106(f333(a201,f333(f114(a1),x62611))) % 173.51/173.27 [6302]~P106(f333(f333(f246(a1),a90),x63021))+P106(f333(f333(f246(a1),a90),f333(f333(f87(a1),x63021),x63021))) % 173.51/173.27 [6303]~P106(f333(f333(f247(a1),a108),x63031))+P106(f333(f333(f246(a1),a108),f333(f333(f87(a1),x63031),x63031))) % 173.51/173.27 [6304]~P106(f333(f333(f247(a1),a90),x63041))+P106(f333(f333(f247(a1),a90),f333(f333(f87(a1),x63041),x63041))) % 173.51/173.27 [6305]~P106(f333(f333(f247(a1),a108),x63051))+P106(f333(f333(f247(a1),a108),f333(f333(f87(a1),x63051),x63051))) % 173.51/173.27 [6484]~P106(f333(f67(x64841),f254(f917(x64841,a905))))+P106(f333(f67(f914(x64841)),f254(f917(f914(x64841),a905)))) % 173.51/173.27 [6572]~P106(f333(f333(f246(a1),f2(a1)),x65721))+P106(f333(f333(f247(a1),f2(a1)),f333(f333(f87(a1),f85(a1)),x65721))) % 173.51/173.27 [6579]E(f333(f264(a1,a1),f53(f85(a1),f333(f114(a1),x65791))),f333(f333(f42(a1),f85(a1)),f333(f114(a1),x65791)))+~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x65791))) % 173.51/173.27 [6599]E(f333(f268(a1,a1),f53(f85(a1),f333(f114(a1),x65991))),f51(a1,f85(a1),f333(f114(a1),x65991)))+~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x65991))) % 173.51/173.27 [6610]P106(f333(f67(x66101),f254(f917(x66101,a905))))+~P106(f333(f67(f914(x66101)),f254(f917(f914(x66101),a905)))) % 173.51/173.27 [6640]P106(f333(f333(f246(a1),a90),x66401))+~P106(f333(f333(f246(a1),a90),f333(f333(f87(a1),x66401),x66401))) % 173.51/173.27 [6641]P106(f333(f333(f247(a1),a90),x66411))+~P106(f333(f333(f247(a1),a90),f333(f333(f87(a1),x66411),x66411))) % 173.51/173.27 [6642]P106(f333(f333(f247(a1),a108),x66421))+~P106(f333(f333(f246(a1),a108),f333(f333(f87(a1),x66421),x66421))) % 173.51/173.27 [6643]P106(f333(f333(f247(a1),a108),x66431))+~P106(f333(f333(f247(a1),a108),f333(f333(f87(a1),x66431),x66431))) % 173.51/173.27 [6954]~P106(f333(f67(x69541),f254(f917(x69541,a905))))+P106(f333(f333(f247(a910),f2(a910)),f333(f41(x69541),f254(f917(x69541,a905))))) % 173.51/173.27 [7538]P106(f333(f67(a910),x75381))+~P106(f333(f67(a1),f333(f316(a910,a1,f111(a1)),x75381))) % 173.51/173.27 [5628]~E(a108,x56281)+E(f333(f333(f23(a1),f333(f333(f87(a1),x56281),x56281)),a108),a108) % 173.51/173.27 [5629]~E(x56291,a108)+E(f333(f333(f23(a1),f333(f333(f87(a1),x56291),x56291)),a108),a108) % 173.51/173.27 [6136]E(x61361,a108)+~E(f333(f333(f23(a1),f333(f333(f87(a1),x61361),x61361)),a108),a108) % 173.51/173.27 [6137]E(a108,x61371)+~E(f333(f333(f23(a1),f333(f333(f87(a1),x61371),x61371)),a108),a108) % 173.51/173.27 [6539]~E(f333(f114(a910),x65391),f2(a910))+P106(f333(a201,f333(f114(a1),f333(f333(f87(a1),x65391),a108)))) % 173.51/173.27 [6884]~P106(f333(a201,f333(f114(a1),x68841)))+P106(f333(a201,f333(f114(a1),f333(f333(f87(a1),x68841),x68841)))) % 173.51/173.27 [6885]~P106(f333(f333(f246(a1),x68851),a90))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x68851),x68851)),a90)) % 173.51/173.27 [6886]~P106(f333(f333(f246(a1),x68861),a108))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x68861),x68861)),a108)) % 173.51/173.27 [6887]~P106(f333(f333(f247(a1),x68871),a90))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x68871),x68871)),a90)) % 173.51/173.27 [6888]~P106(f333(f333(f246(a1),x68881),a108))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x68881),x68881)),a108)) % 173.51/173.27 [7206]E(f333(f114(a910),x72061),f2(a910))+~P106(f333(a201,f333(f114(a1),f333(f333(f87(a1),x72061),a108)))) % 173.51/173.27 [7452]~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x74521)))+P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),f333(f333(f87(a1),x74521),x74521)))) % 173.51/173.27 [7453]P106(f333(a201,f333(f114(a1),x74531)))+~P106(f333(a201,f333(f114(a1),f333(f333(f87(a1),x74531),x74531)))) % 173.51/173.27 [7454]P106(f333(f333(f246(a1),x74541),a90))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),x74541),x74541)),a90)) % 173.51/173.27 [7455]P106(f333(f333(f246(a1),x74551),a108))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),x74551),x74551)),a108)) % 173.51/173.27 [7456]P106(f333(f333(f246(a1),x74561),a108))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),x74561),x74561)),a108)) % 173.51/173.27 [7457]P106(f333(f333(f247(a1),x74571),a90))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),x74571),x74571)),a90)) % 173.51/173.27 [7816]E(f333(a118,f599(x78161)),x78161)+~P106(f333(f333(f335(f917(f916(a910,a910),a905)),x78161),a109)) % 173.51/173.27 [6458]~P95(x64581)+E(f333(f114(x64581),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f85(x64581)) % 173.51/173.27 [6934]~P106(f333(a201,f333(f114(a1),x69341)))+E(f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),x69341),x69341)),a108)),f2(a910)) % 173.51/173.27 [7994]~P106(f333(f333(f247(a1),f333(f114(a1),x79941)),f2(a1)))+E(f333(f264(a1,a1),f333(a57,f56(f333(f86(a1),f85(a1)),f333(f86(a1),f333(f114(a1),x79941))))),f333(f333(f42(a1),f85(a1)),f333(f114(a1),x79941))) % 173.51/173.27 [8007]~P106(f333(f333(f247(a1),f333(f114(a1),x80071)),f2(a1)))+E(f333(f268(a1,a1),f333(a57,f56(f333(f86(a1),f85(a1)),f333(f86(a1),f333(f114(a1),x80071))))),f51(a1,f85(a1),f333(f114(a1),x80071))) % 173.51/173.27 [8056]~P106(f333(f333(f246(a1),a90),x80561))+P106(f333(f333(f246(a1),a90),f333(f333(f23(a1),f333(f333(f87(a1),x80561),x80561)),a108))) % 173.51/173.27 [8057]~P106(f333(f333(f246(a1),a108),x80571))+P106(f333(f333(f246(a1),a108),f333(f333(f23(a1),f333(f333(f87(a1),x80571),x80571)),a108))) % 173.51/173.27 [8058]~P106(f333(f333(f246(a1),a90),x80581))+P106(f333(f333(f247(a1),a90),f333(f333(f23(a1),f333(f333(f87(a1),x80581),x80581)),a108))) % 173.51/173.27 [8059]~P106(f333(f333(f247(a1),a108),x80591))+P106(f333(f333(f247(a1),a108),f333(f333(f23(a1),f333(f333(f87(a1),x80591),x80591)),a108))) % 173.51/173.27 [8362]~P95(x83621)+~P30(x83621,f333(f114(x83621),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))) % 173.51/173.27 [8547]P106(f333(f333(f246(a1),a90),x85471))+~P106(f333(f333(f246(a1),a90),f333(f333(f23(a1),f333(f333(f87(a1),x85471),x85471)),a108))) % 173.51/173.27 [8548]P106(f333(f333(f246(a1),a90),x85481))+~P106(f333(f333(f247(a1),a90),f333(f333(f23(a1),f333(f333(f87(a1),x85481),x85481)),a108))) % 173.51/173.27 [8549]P106(f333(f333(f246(a1),a108),x85491))+~P106(f333(f333(f246(a1),a108),f333(f333(f23(a1),f333(f333(f87(a1),x85491),x85491)),a108))) % 173.51/173.27 [8550]P106(f333(f333(f247(a1),a108),x85501))+~P106(f333(f333(f247(a1),a108),f333(f333(f23(a1),f333(f333(f87(a1),x85501),x85501)),a108))) % 173.51/173.27 [8878]E(f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),x88781),x88781)),a108)),f333(f333(f93(a910,a910),f333(f114(a910),x88781)),f333(f333(f8(a910,a910,a910),a123),f333(f333(f18(a910,a910,a910),f87(a910)),f5(a910)))))+P106(f333(a201,f333(f114(a1),x88781))) % 173.51/173.27 [9770]E(x97701,f196(f917(f916(a910,a910),a905)))+P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x97701),f196(f917(f916(a910,a910),a905)))),a75)) % 173.51/173.27 [8806]~P106(f333(a201,f333(f114(a1),x88061)))+P106(f333(a201,f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),x88061),x88061)),a108)))) % 173.51/173.27 [8807]~P106(f333(f333(f247(a1),x88071),a90))+P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x88071),x88071)),a108)),a90)) % 173.51/173.27 [8808]~P106(f333(f333(f246(a1),x88081),a108))+P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x88081),x88081)),a108)),a108)) % 173.51/173.27 [8809]~P106(f333(f333(f247(a1),x88091),a90))+P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x88091),x88091)),a108)),a90)) % 173.51/173.27 [8810]~P106(f333(f333(f247(a1),x88101),a108))+P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x88101),x88101)),a108)),a108)) % 173.51/173.27 [8919]~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x89191)))+P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),x89191),x89191)),a108)))) % 173.51/173.27 [9088]~P95(x90881)+E(f333(f333(f87(x90881),f85(x90881)),f85(x90881)),f333(f114(x90881),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))) % 173.51/173.27 [9251]P106(f333(a201,f333(f114(a1),x92511)))+~P106(f333(a201,f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92511),x92511)),a108)))) % 173.51/173.27 [9252]P106(f333(f333(f246(a1),x92521),a108))+~P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92521),x92521)),a108)),a108)) % 173.51/173.27 [9253]P106(f333(f333(f247(a1),x92531),a90))+~P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92531),x92531)),a108)),a90)) % 173.51/173.27 [9254]P106(f333(f333(f247(a1),x92541),a90))+~P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92541),x92541)),a108)),a90)) % 173.51/173.27 [9255]P106(f333(f333(f247(a1),x92551),a108))+~P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92551),x92551)),a108)),a108)) % 173.51/173.27 [9816]~P106(f333(f67(f916(a910,a910)),x98161))+P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),f196(f917(f916(a910,a910),a905))),x98161)),a76)) % 173.51/173.27 [9588]~P107(x95881)+E(f333(f333(f256(x95881),f2(x95881)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f2(x95881)) % 173.51/173.27 [9589]~P107(x95891)+E(f333(f333(f256(x95891),f85(x95891)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f85(x95891)) % 173.51/173.27 [10039]~P106(f333(f333(f247(a910),f85(a910)),x100391))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f42(a910),x100391),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.27 [10049]~P106(f333(f333(f247(a910),f2(a910)),x100491))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f42(a910),f333(f333(f87(a910),x100491),f85(a910))),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.27 [10089]~E(f51(a910,x100891,f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f85(a910))+P106(f333(f333(f247(a910),f2(a910)),f51(a910,x100891,f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.27 [10110]E(f51(a910,x101101,f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f85(a910))+~P106(f333(f333(f247(a910),f2(a910)),f51(a910,x101101,f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.27 [4762]~P10(x47621,x47622)+P46(x47621,x47622) % 173.51/173.27 [4763]~P40(x47631,x47632)+P61(x47631,x47632) % 173.51/173.27 [4764]~P47(x47641,x47642)+P61(x47641,x47642) % 173.51/173.27 [4766]~P10(x47661,x47662)+P53(x47661,x47662) % 173.51/173.27 [4768]~P10(x47681,x47682)+P54(x47681,x47682) % 173.51/173.27 [4718]E(x47181,x47182)+~E(f34(x47181),f34(x47182)) % 173.51/173.27 [4719]E(x47191,x47192)+~E(f35(x47191),f35(x47192)) % 173.51/173.27 [4723]~E(x47231,x47232)+E(f278(x47231,x47232),f85(a110)) % 173.51/173.27 [4726]E(f228(x47261,x47262),x47261)+~E(x47262,f2(a910)) % 173.51/173.27 [4733]~E(x47332,f124(x47331))+E(f160(x47331,x47332),f124(x47331)) % 173.51/173.27 [4752]~E(f160(x47522,x47521),f124(x47522))+E(x47521,f124(x47522)) % 173.51/173.27 [4772]~P1(x47722)+P1(f917(x47721,x47722)) % 173.51/173.27 [4773]~P2(x47732)+P2(f917(x47731,x47732)) % 173.51/173.27 [4774]~P98(x47742)+P3(f917(x47741,x47742)) % 173.51/173.27 [4775]~P2(x47752)+P101(f917(x47751,x47752)) % 173.51/173.27 [4776]~P2(x47762)+P102(f917(x47761,x47762)) % 173.51/173.27 [4777]~P99(x47772)+P99(f917(x47771,x47772)) % 173.51/173.27 [4778]~P108(x47782)+P108(f917(x47781,x47782)) % 173.51/173.27 [4779]~P98(x47792)+P100(f917(x47791,x47792)) % 173.51/173.27 [4780]~P109(x47802)+P109(f917(x47801,x47802)) % 173.51/173.27 [4781]~P84(x47812)+P84(f917(x47811,x47812)) % 173.51/173.27 [4782]~P85(x47822)+P85(f917(x47821,x47822)) % 173.51/173.27 [4783]~P5(x47832)+P5(f917(x47831,x47832)) % 173.51/173.27 [4784]~P111(x47842)+P111(f917(x47841,x47842)) % 173.51/173.27 [4785]~P112(x47852)+P112(f917(x47851,x47852)) % 173.51/173.27 [4786]~P8(x47862)+P8(f917(x47861,x47862)) % 173.51/173.27 [4787]~P98(x47872)+P98(f917(x47871,x47872)) % 173.51/173.27 [4800]E(x48001,x48002)+~E(f333(a123,x48001),f333(a123,x48002)) % 173.51/173.27 [4801]E(x48011,x48012)+~E(f333(a118,x48011),f333(a118,x48012)) % 173.51/173.27 [4802]E(x48021,x48022)+~E(f333(a3,x48021),f333(a3,x48022)) % 173.51/173.27 [4804]E(x48041,x48042)+~E(f333(a20,x48041),f333(a20,x48042)) % 173.51/173.27 [4859]P42(x48591,x48592)+~E(f752(x48592,x48591),f753(x48592,x48591)) % 173.51/173.27 [4889]~P61(x48891,x48892)+P42(x48891,f313(x48891,x48892)) % 173.51/173.27 [4890]~P55(x48901,x48902)+P55(x48901,f313(x48901,x48902)) % 173.51/173.27 [4903]~P64(x49031)+E(f51(x49031,x49032,x49032),f2(x49031)) % 173.51/173.27 [4937]~P40(x49371,x49372)+P40(f911(x49371),f154(x49371,x49372)) % 173.51/173.27 [4938]~P40(x49381,x49382)+P40(f911(x49381),f153(x49381,x49382)) % 173.51/173.27 [4939]~P41(x49391,x49392)+P41(f911(x49391),f155(x49391,x49392)) % 173.51/173.27 [4940]~P41(x49401,x49402)+P41(f911(x49401),f166(x49401,x49402)) % 173.51/173.27 [4941]~P55(x49411,x49412)+P55(f911(x49411),f166(x49411,x49412)) % 173.51/173.27 [5039]~P40(x50391,x50392)+P40(f917(x50391,a905),f326(x50391,x50392)) % 173.51/173.27 [5040]~P40(x50401,x50402)+P40(f917(x50401,a905),f324(x50401,x50402)) % 173.51/173.27 [5164]~P9(x51641)+P43(f309(a1,x51641,x51642)) % 173.51/173.27 [5265]~P40(x52651,x52652)+P63(x52651,f73(x52651,x52651,x52652)) % 173.51/173.27 [5758]~P4(x57581)+P27(x57581,x57581,f86(x57581),x57582) % 173.51/173.27 [4747]~E(x47472,f124(x47471))+E(f333(f175(x47471),x47472),f124(x47471)) % 173.51/173.27 [4748]~E(x47482,f124(x47481))+E(f333(f176(x47481),x47482),f124(x47481)) % 173.51/173.27 [4806]E(x48061,f333(a115,x48062))+~E(f333(f111(a1),x48061),x48062) % 173.51/173.27 [4809]E(x48091,f124(x48092))+~E(f333(f175(x48092),x48091),f124(x48092)) % 173.51/173.27 [4810]E(x48101,f124(x48102))+~E(f333(f176(x48102),x48101),f124(x48102)) % 173.51/173.27 [4828]~P95(x48281)+E(f333(f114(x48281),x48282),f333(f113(x48281),x48282)) % 173.51/173.27 [4836]~P66(x48361)+P106(f333(f67(x48361),x48362)) % 173.51/173.27 [4844]~E(f712(x48442,x48441),f124(x48441))+E(f187(x48441,x48442),f124(f911(x48441))) % 173.51/173.27 [4853]~E(x48532,f124(x48531))+E(f333(f180(x48531),x48532),f196(f917(x48531,a905))) % 173.51/173.27 [4854]~E(x48542,f124(x48541))+E(f196(f917(x48541,a905)),f333(f180(x48541),x48542)) % 173.51/173.27 [4856]E(x48561,x48562)+~E(f333(f111(a1),x48561),f333(f111(a1),x48562)) % 173.51/173.27 [4860]E(f226(x48601,x48602),f2(a910))+P106(f333(f67(x48601),x48602)) % 173.51/173.27 [4878]~P120(x48781)+E(f89(x48781,f89(x48781,x48782)),f89(x48781,x48782)) % 173.51/173.27 [4892]~P117(x48921)+E(f333(f333(f256(x48921),x48922),f85(a910)),x48922) % 173.51/173.27 [4893]~P83(x48931)+E(f333(f333(f256(x48931),x48932),f85(a910)),x48932) % 173.51/173.27 [4894]~P55(x48941,x48942)+E(f333(f293(x48941,x48941),x48942),x48942) % 173.51/173.27 [4898]E(x48981,x48982)+E(f278(x48981,x48982),f333(f333(f87(a110),x48982),f85(a110))) % 173.51/173.27 [4901]E(f333(f41(x49011),x49012),f2(a910))+P106(f333(f67(x49011),x49012)) % 173.51/173.27 [4904]~E(f160(x49041,x49042),x49042)+P106(f333(f145(x49041),x49042)) % 173.51/173.27 [4907]~P3(x49071)+E(f333(f333(f121(x49071),x49072),f196(x49071)),x49072) % 173.51/173.27 [4908]~P100(x49081)+E(f333(f333(f112(x49081),x49082),f254(x49081)),x49082) % 173.51/173.27 [4909]~P71(x49091)+E(f333(f333(f23(x49091),x49092),f2(x49091)),x49092) % 173.51/173.27 [4910]~P72(x49101)+E(f333(f333(f87(x49101),x49102),f2(x49101)),x49102) % 173.51/173.27 [4911]~P117(x49111)+E(f333(f333(f87(x49111),x49112),f2(x49111)),x49112) % 173.51/173.27 [4912]~P82(x49121)+E(f333(f333(f87(x49121),x49122),f2(x49121)),x49122) % 173.51/173.27 [4913]~P117(x49131)+E(f333(f333(f88(x49131),x49132),f85(x49131)),x49132) % 173.51/173.27 [4914]~P78(x49141)+E(f333(f333(f88(x49141),x49142),f85(x49141)),x49142) % 173.51/173.27 [4915]~P83(x49151)+E(f333(f333(f88(x49151),x49152),f85(x49151)),x49152) % 173.51/173.27 [4916]~P122(x49161)+E(f333(f333(f296(x49161),x49162),f85(x49161)),x49162) % 173.51/173.27 [4917]~P64(x49171)+E(f333(f333(f42(x49171),x49172),f85(x49171)),x49172) % 173.51/173.27 [4918]~P117(x49181)+E(f333(f333(f256(x49181),x49182),f2(a910)),f85(x49181)) % 173.51/173.27 [4919]~P115(x49191)+E(f333(f333(f256(x49191),x49192),f2(a910)),f85(x49191)) % 173.51/173.27 [4920]~E(x49202,f196(f917(x49201,a905)))+E(f333(f41(x49201),x49202),f2(a910)) % 173.51/173.27 [4931]~P64(x49311)+E(f51(x49311,x49312,f2(x49311)),x49312) % 173.51/173.27 [4942]~P100(x49421)+E(f333(f333(f121(x49421),x49422),f254(x49421)),f254(x49421)) % 173.51/173.27 [4943]~P3(x49431)+E(f333(f333(f112(x49431),x49432),f196(x49431)),f196(x49431)) % 173.51/173.27 [4944]~P117(x49441)+E(f333(f333(f88(x49441),x49442),f2(x49441)),f2(x49441)) % 173.51/173.27 [4945]~P129(x49451)+E(f333(f333(f88(x49451),x49452),f2(x49451)),f2(x49451)) % 173.51/173.27 [4946]~P123(x49461)+E(f333(f333(f296(x49461),x49462),f2(x49461)),f2(x49461)) % 173.51/173.27 [4947]~P64(x49471)+E(f333(f333(f42(x49471),x49472),f2(x49471)),f2(x49471)) % 173.51/173.27 [4950]~P64(x49501)+E(f51(x49501,x49502,f85(x49501)),f2(x49501)) % 173.51/173.27 [4951]~P64(x49511)+E(f51(x49511,f2(x49511),x49512),f2(x49511)) % 173.51/173.27 [4980]E(x49801,f2(a910))+E(f61(x49802,x49801,f124(x49802)),f124(f911(x49802))) % 173.51/173.27 [5003]P55(x50031,x50032)+~E(f333(f293(x50031,x50031),x50032),x50032) % 173.51/173.27 [5004]P40(x50041,x50042)+~E(f606(x50042,x50041),f196(f917(x50041,a905))) % 173.51/173.27 [5005]E(x50051,f124(x50052))+~E(f333(f180(x50052),x50051),f196(f917(x50052,a905))) % 173.51/173.27 [5006]E(x50061,f124(x50062))+~E(f196(f917(x50062,a905)),f333(f180(x50062),x50061)) % 173.51/173.27 [5009]~E(x50091,x50092)+P106(f333(f333(a330,x50091),x50092)) % 173.51/173.27 [5019]P106(x50191)+P106(f333(f333(a336,x50191),x50192)) % 173.51/173.27 [5020]E(x50201,f124(x50202))+E(f333(f333(f172(x50202),x50201),f2(a910)),f333(f149(x50202),x50201)) % 173.51/173.27 [5023]E(f160(x50231,x50232),x50232)+~P106(f333(f145(x50231),x50232)) % 173.51/173.27 [5030]~P106(x50302)+P106(f333(f333(a336,x50301),x50302)) % 173.51/173.27 [5031]~P106(x50312)+P106(f333(f333(a332,x50311),x50312)) % 173.51/173.27 [5032]~P106(x50321)+P106(f333(f333(a332,x50321),x50322)) % 173.51/173.27 [5042]~E(f713(x50422,x50421),f719(x50422,x50421))+P106(f333(f145(x50421),x50422)) % 173.51/173.27 [5049]E(f333(f252(x50491),x50492),f196(f917(x50491,a905)))+P106(f333(x50492,f571(x50492))) % 173.51/173.27 [5050]E(f196(f917(x50501,a905)),f333(f252(x50501),x50502))+P106(f333(x50502,f572(x50502))) % 173.51/173.27 [5119]~P120(x51191)+E(f333(f333(f88(x51191),x51192),f89(x51191,x51192)),f333(f82(x51191),x51192)) % 173.51/173.27 [5130]~E(x51301,f2(a1))+E(f52(x51301,x51302),f333(f333(f265(a1,a1),f2(a1)),f2(a1))) % 173.51/173.27 [5160]~P61(x51601,x51602)+P61(x51601,f333(f293(x51601,x51601),x51602)) % 173.51/173.27 [5161]~P41(x51611,x51612)+P41(x51611,f333(f293(x51611,x51611),x51612)) % 173.51/173.27 [5162]~P42(x51621,x51622)+P42(x51621,f333(f293(x51621,x51621),x51622)) % 173.51/173.27 [5163]~P55(x51631,x51632)+P55(x51631,f333(f293(x51631,x51631),x51632)) % 173.51/173.27 [5185]E(x51851,x51852)+~P106(f333(f333(a330,x51851),x51852)) % 173.51/173.27 [5196]P106(x51961)+~P106(f333(f333(a331,x51962),x51961)) % 173.51/173.27 [5197]P106(x51971)+~P106(f333(f333(a331,x51971),x51972)) % 173.51/173.27 [5202]~P108(x52021)+P106(f333(f333(f246(x52021),x52022),f254(x52021))) % 173.51/173.27 [5206]E(x52061,x52062)+~E(f333(x52061,f442(x52062,x52061)),f333(x52062,f442(x52062,x52061))) % 173.51/173.27 [5237]E(x52371,f2(a910))+E(f228(x52371,f51(a910,x52372,x52371)),f228(x52372,x52371)) % 173.51/173.27 [5242]~P110(x52421)+P16(x52421,f333(f333(f159(x52421),x52422),f124(x52421))) % 173.51/173.27 [5244]E(x52441,f2(a1))+P106(f333(f55(x52442,x52441),f52(x52442,x52441))) % 173.51/173.27 [5263]~E(x52631,x52632)+P106(f333(f333(f247(a910),x52631),f333(a123,x52632))) % 173.51/173.27 [5273]~E(x52731,f2(a910))+P106(f333(f333(f247(a910),x52731),f333(a123,x52732))) % 173.51/173.27 [5283]P106(f333(x52831,x52832))+P106(f333(f333(f246(a1),f2(a1)),f437(x52831))) % 173.51/173.27 [5348]P61(x53481,x53482)+~P61(x53481,f333(f293(x53481,x53481),x53482)) % 173.51/173.27 [5349]P41(x53491,x53492)+~P41(x53491,f333(f293(x53491,x53491),x53492)) % 173.51/173.27 [5350]P42(x53501,x53502)+~P42(x53501,f333(f293(x53501,x53501),x53502)) % 173.51/173.27 [5351]P55(x53511,x53512)+~P55(x53511,f333(f293(x53511,x53511),x53512)) % 173.51/173.27 [5355]~E(f51(a910,x53552,x53551),f2(a910))+E(f333(f333(f88(a910),x53551),f449(x53551,x53552)),x53552) % 173.51/173.27 [5356]~E(f51(a1,x53562,x53561),f2(a1))+E(f333(f333(f88(a1),x53561),f450(x53561,x53562)),x53562) % 173.51/173.27 [5381]~P106(f333(x53811,x53812))+P106(f333(f333(f246(a1),f2(a1)),f362(x53811))) % 173.51/173.27 [5392]E(f333(f333(f23(a910),f333(a115,x53921)),f333(a115,x53922)),f333(a115,x53921))+~P106(f333(a201,x53922)) % 173.51/173.27 [5421]E(f279(x54211,x54212),f85(a110))+~P106(f333(f333(f246(a110),x54211),f85(a110))) % 173.51/173.27 [5513]E(f333(f333(f172(x55131),x55132),f713(x55132,x55131)),f333(f333(f172(x55131),x55132),f719(x55132,x55131)))+P106(f333(f145(x55131),x55132)) % 173.51/173.27 [5556]~P106(f333(x55561,f97(x55562,x55561)))+P106(f333(x55561,f607(x55562,x55561))) % 173.51/173.27 [5618]P63(x56181,x56182)+~P106(f333(f321(x56181,x56182),f593(x56182,x56181))) % 173.51/173.27 [5765]~E(f333(a123,f51(a910,x57651,x57652)),x57652)+E(f51(a910,f333(a123,x57651),x57652),f2(a910)) % 173.51/173.27 [5820]P40(x58201,x58202)+P106(f333(f333(f335(x58201),f627(x58202,x58201)),f628(x58202,x58201))) % 173.51/173.27 [5827]~P139(x58271)+P106(f333(f333(f335(x58271),f333(f111(x58271),x58272)),f120(x58271))) % 173.51/173.27 [5828]~P107(x58281)+P106(f333(f333(f335(x58281),f333(f111(x58281),x58282)),f194(x58281))) % 173.51/173.27 [5829]~P139(x58291)+P106(f333(f333(f335(x58291),f333(f113(x58291),x58292)),f120(x58291))) % 173.51/173.27 [5830]~P95(x58301)+P106(f333(f333(f335(x58301),f333(f114(x58301),x58302)),f120(x58301))) % 173.51/173.27 [5961]~P41(x59611,x59612)+E(f333(f333(f295(x59611,x59611,x59611),x59612),f313(x59611,x59612)),x59612) % 173.51/173.27 [5975]E(f333(a123,f51(a910,x59751,x59752)),x59752)+E(f51(a910,f333(a123,x59751),x59752),f333(a123,f51(a910,x59751,x59752))) % 173.51/173.27 [6386]P40(x63861,x63862)+~P106(f333(f333(f335(x63861),f585(x63862,x63861)),f322(x63861,x63862))) % 173.51/173.27 [6424]~P119(x64241)+~P106(f333(f333(f247(x64241),f333(f111(x64241),x64242)),f2(x64241))) % 173.51/173.27 [6425]~P87(x64251)+~P106(f333(f333(f247(x64251),f333(f82(x64251),x64252)),f2(x64251))) % 173.51/173.27 [6512]P106(f333(f333(f247(a1),x65121),f51(a1,x65122,x65121)))+~P106(f333(f333(f247(a1),x65121),f2(a1))) % 173.51/173.27 [6612]E(f333(f333(f315(a910),f333(a123,x66121)),f309(a910,x66122,x66121)),f309(a910,x66122,f333(a123,x66121)))+~P106(f333(f333(f246(a910),x66122),f333(a123,x66121))) % 173.51/173.27 [6701]~P110(x67011)+P16(x67011,f158(x67011,x67011,f5(x67011),x67012)) % 173.51/173.27 [6829]E(f333(f175(x68291),x68292),x68292)+~P106(f333(f333(f246(a910),f333(f197(f911(x68291)),x68292)),f85(a910))) % 173.51/173.27 [6848]~P87(x68481)+P106(f333(f333(f246(x68481),f333(f86(x68481),f333(f82(x68481),x68482))),f2(x68481))) % 173.51/173.27 [6880]~P40(x68801,x68802)+P40(x68801,f333(f333(f295(x68801,x68801,x68801),x68802),f313(x68801,x68802))) % 173.51/173.27 [6881]~P55(x68811,x68812)+P55(x68811,f333(f333(f295(x68811,x68811,x68811),x68812),f313(x68811,x68812))) % 173.51/173.27 [7099]~P106(f333(f333(f247(a1),x70992),f2(a1)))+P106(f333(f333(f246(a1),f51(a1,x70991,x70992)),f2(a1))) % 173.51/173.27 [7496]~P107(x74961)+E(f198(x74961,f333(f333(f7(x74961,x74961,x74961),f87(x74961)),f85(x74961)),x74962,f2(x74961)),f333(f111(x74961),x74962)) % 173.51/173.27 [7524]~P127(x75241)+~P106(f333(f333(f247(x75241),f333(f333(f88(x75241),x75242),x75242)),f2(x75241))) % 173.51/173.27 [10201]~P120(x102011)+~P106(f333(f333(f247(x102011),f333(f333(f256(x102011),x102012),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f2(x102011))) % 173.51/173.27 [4807]~E(x48072,f124(x48071))+E(f333(f197(f911(x48071)),x48072),f2(a910)) % 173.51/173.27 [4845]~E(x48451,f2(a910))+E(f333(f333(f87(a910),x48451),x48452),x48452) % 173.51/173.27 [4846]~E(x48462,f2(a910))+E(f333(f333(f88(a910),x48461),x48462),f2(a910)) % 173.51/173.27 [4848]~E(x48481,f2(a910))+E(f333(f333(f88(a910),x48481),x48482),f2(a910)) % 173.51/173.27 [4849]~E(x48492,f2(a910))+E(f333(f333(f256(a910),x48491),x48492),f85(a910)) % 173.51/173.27 [4850]~E(x48502,f2(a1))+E(f333(f333(f42(a1),x48501),x48502),f2(a1)) % 173.51/173.27 [4861]E(x48611,f124(x48612))+~E(f333(f197(f911(x48612)),x48611),f2(a910)) % 173.51/173.27 [4862]~P2(x48621)+E(f333(f333(f121(x48621),x48622),x48622),x48622) % 173.51/173.27 [4864]~P101(x48641)+E(f333(f333(f121(x48641),x48642),x48642),x48642) % 173.51/173.27 [4865]~P2(x48651)+E(f333(f333(f112(x48651),x48652),x48652),x48652) % 173.51/173.27 [4867]~P102(x48671)+E(f333(f333(f112(x48671),x48672),x48672),x48672) % 173.51/173.27 [4869]~P97(x48691)+E(f333(f333(f88(x48691),x48692),x48692),x48692) % 173.51/173.27 [4871]~P110(x48711)+E(f333(f333(f244(x48711),x48712),x48712),x48712) % 173.51/173.27 [4873]~P110(x48731)+E(f333(f333(f245(x48731),x48732),x48732),x48732) % 173.51/173.27 [4891]~P71(x48911)+E(f333(f333(f23(x48911),x48912),x48912),f2(x48911)) % 173.51/173.27 [4905]~P84(x49051)+E(f333(f86(x49051),f333(f86(x49051),x49052)),x49052) % 173.51/173.27 [4906]~P71(x49061)+E(f333(f86(x49061),f333(f86(x49061),x49062)),x49062) % 173.51/173.27 [4923]~E(x49232,f2(a910))+E(f333(f333(f256(a910),x49231),x49232),f333(a123,f2(a910))) % 173.51/173.27 [4959]~P3(x49591)+E(f333(f333(f121(x49591),f196(x49591)),x49592),x49592) % 173.51/173.27 [4960]~P100(x49601)+E(f333(f333(f112(x49601),f254(x49601)),x49602),x49602) % 173.51/173.27 [4961]~P72(x49611)+E(f333(f333(f87(x49611),f2(x49611)),x49612),x49612) % 173.51/173.27 [4962]~P117(x49621)+E(f333(f333(f87(x49621),f2(x49621)),x49622),x49622) % 173.51/173.27 [4963]~P82(x49631)+E(f333(f333(f87(x49631),f2(x49631)),x49632),x49632) % 173.51/173.27 [4964]~P117(x49641)+E(f333(f333(f88(x49641),f85(x49641)),x49642),x49642) % 173.51/173.27 [4965]~P78(x49651)+E(f333(f333(f88(x49651),f85(x49651)),x49652),x49652) % 173.51/173.27 [4966]~P83(x49661)+E(f333(f333(f88(x49661),f85(x49661)),x49662),x49662) % 173.51/173.27 [4984]~P100(x49841)+E(f333(f333(f121(x49841),f254(x49841)),x49842),f254(x49841)) % 173.51/173.27 [4985]~P3(x49851)+E(f333(f333(f112(x49851),f196(x49851)),x49852),f196(x49851)) % 173.51/173.27 [4986]~P117(x49861)+E(f333(f333(f88(x49861),f2(x49861)),x49862),f2(x49861)) % 173.51/173.27 [4987]~P129(x49871)+E(f333(f333(f88(x49871),f2(x49871)),x49872),f2(x49871)) % 173.51/173.27 [4988]~P83(x49881)+E(f333(f333(f256(x49881),f85(x49881)),x49882),f85(x49881)) % 173.51/173.27 [4989]~P122(x49891)+E(f333(f333(f296(x49891),f2(x49891)),x49892),f2(x49891)) % 173.51/173.27 [4990]~P64(x49901)+E(f333(f333(f42(x49901),f2(x49901)),x49902),f2(x49901)) % 173.51/173.27 [4998]E(x49981,f124(x49982))+E(f152(x49982,f333(f176(x49982),x49981)),f333(f149(x49982),x49981)) % 173.51/173.27 [4999]E(x49991,f124(x49992))+E(f333(f149(x49992),f333(f176(x49992),x49991)),f152(x49992,x49991)) % 173.51/173.27 [5000]E(x50001,f2(a910))+~E(f333(f333(f87(a910),x50002),x50001),x50002) % 173.51/173.27 [5007]~P139(x50071)+E(f333(f113(x50071),f333(f111(a1),x50072)),f333(f111(x50071),x50072)) % 173.51/173.27 [5008]~P95(x50081)+E(f333(f113(x50081),f333(f114(a1),x50082)),f333(f114(x50081),x50082)) % 173.51/173.27 [5015]E(x50151,f2(a910))+~E(f333(f333(f87(a910),x50152),x50151),f2(a910)) % 173.51/173.27 [5016]E(x50161,f2(a910))+~E(f333(f333(f87(a910),x50161),x50162),f2(a910)) % 173.51/173.27 [5017]E(x50171,f85(a910))+~E(f333(f333(f88(a910),x50172),x50171),f85(a910)) % 173.51/173.27 [5018]E(x50181,f85(a910))+~E(f333(f333(f88(a910),x50181),x50182),f85(a910)) % 173.51/173.27 [5035]~P87(x50351)+E(f333(f82(x50351),f333(f86(x50351),x50352)),f333(f82(x50351),x50352)) % 173.51/173.27 [5036]~P120(x50361)+E(f333(f82(x50361),f333(f111(x50361),x50362)),f333(f111(x50361),x50362)) % 173.51/173.27 [5037]~P87(x50371)+E(f333(f82(x50371),f333(f82(x50371),x50372)),f333(f82(x50371),x50372)) % 173.51/173.27 [5038]~P72(x50381)+E(f333(f173(x50381),f333(f176(x50381),x50382)),f333(f173(x50381),x50382)) % 173.51/173.27 [5043]~E(x50431,f333(a123,f2(a910)))+E(f333(f333(f256(a910),x50431),x50432),f333(a123,f2(a910))) % 173.51/173.27 [5052]~P71(x50521)+E(f333(f333(f23(x50521),f2(x50521)),x50522),f333(f86(x50521),x50522)) % 173.51/173.27 [5053]~E(x50532,f2(a910))+E(f147(a910,f333(f308(a910,x50531),x50532)),f124(a910)) % 173.51/173.27 [5062]~P95(x50621)+E(f333(f333(f87(x50621),x50622),f333(f114(x50621),a90)),x50622) % 173.51/173.27 [5063]E(x50631,f2(a1))+E(f53(f333(f82(a1),x50632),f333(f82(a1),x50631)),f59(x50632,x50631)) % 173.51/173.27 [5079]~E(x50791,x50792)+P106(f333(f333(f246(a910),x50791),x50792)) % 173.51/173.27 [5086]~E(x50861,f2(a110))+E(f333(f333(f87(a910),f333(a20,x50861)),x50862),x50862) % 173.51/173.27 [5087]~E(f333(f114(a1),x50872),f333(f111(a1),x50871))+E(x50871,f333(a115,f333(f114(a1),x50872))) % 173.51/173.27 [5100]~P9(x51001)+P9(f333(f333(f256(a1),x51001),x51002)) % 173.51/173.27 [5101]~P84(x51011)+E(f333(f333(f121(x51011),x51012),f333(f86(x51011),x51012)),f254(x51011)) % 173.51/173.27 [5102]~P84(x51021)+E(f333(f333(f112(x51021),x51022),f333(f86(x51021),x51022)),f196(x51021)) % 173.51/173.27 [5103]~P71(x51031)+E(f333(f333(f87(x51031),x51032),f333(f86(x51031),x51032)),f2(x51031)) % 173.51/173.27 [5127]E(x51271,f2(a910))+~E(f333(f86(a1),f333(f111(a1),x51272)),f333(f111(a1),x51271)) % 173.51/173.27 [5128]E(x51281,f2(a910))+~E(f333(f86(a1),f333(f111(a1),x51281)),f333(f111(a1),x51282)) % 173.51/173.27 [5138]E(f203(x51381,x51382),f2(a1))+P106(f333(f333(f246(a1),x51382),x51381)) % 173.51/173.27 [5139]E(f186(x51391,x51392),f124(a1))+P106(f333(f333(f246(a1),x51391),x51392)) % 173.51/173.27 [5152]E(x51521,f333(a123,f2(a910)))+~E(f333(f333(f88(a910),x51522),x51521),f333(a123,f2(a910))) % 173.51/173.27 [5153]E(x51531,f333(a123,f2(a910)))+~E(f333(f333(f88(a910),x51531),x51532),f333(a123,f2(a910))) % 173.51/173.27 [5154]~P109(x51541)+P106(f333(f333(f246(x51541),x51542),x51542)) % 173.51/173.27 [5157]~P95(x51571)+E(f333(f333(f88(x51571),x51572),f333(f114(x51571),a108)),f333(f86(x51571),x51572)) % 173.51/173.27 [5177]~P139(x51771)+E(f333(f86(x51771),f333(f113(x51771),x51772)),f333(f113(x51771),f333(f86(a1),x51772))) % 173.51/173.27 [5178]~P95(x51781)+E(f333(f86(x51781),f333(f114(x51781),x51782)),f333(f114(x51781),f333(f86(a1),x51782))) % 173.51/173.27 [5207]~E(x52071,f333(a123,x52072))+P106(f333(f333(f247(a910),f2(a910)),x52071)) % 173.51/173.27 [5225]~P110(x52251)+E(f333(f86(f917(x52251,a905)),f333(f289(x52251),x52252)),f333(f290(x52251),x52252)) % 173.51/173.27 [5226]~P110(x52261)+E(f333(f86(f917(x52261,a905)),f333(f307(x52261),x52262)),f333(f310(x52261),x52262)) % 173.51/173.27 [5227]~P110(x52271)+E(f333(f86(f917(x52271,a905)),f333(f310(x52271),x52272)),f333(f307(x52271),x52272)) % 173.51/173.27 [5228]~P110(x52281)+E(f333(f86(f917(x52281,a905)),f333(f290(x52281),x52282)),f333(f289(x52281),x52282)) % 173.51/173.27 [5236]~E(f333(f111(a1),x52362),x52361)+P106(f333(f333(f246(a1),f2(a1)),x52361)) % 173.51/173.27 [5243]~E(x52432,f2(a1))+E(f59(x52431,x52432),f333(f333(f265(a1,a1),f2(a1)),f333(f82(a1),x52431))) % 173.51/173.27 [5245]~P1(x52451)+P106(f333(f333(f246(x52451),f196(x52451)),x52452)) % 173.51/173.27 [5278]E(x52781,x52782)+~E(f333(f333(f87(a1),x52781),x52781),f333(f333(f87(a1),x52782),x52782)) % 173.51/173.27 [5282]~P106(f333(x52821,x52822))+P106(f333(x52821,f333(a115,f362(x52821)))) % 173.51/173.27 [5308]~P120(x53081)+E(f333(f333(f88(x53081),f89(x53081,x53082)),f333(f82(x53081),x53082)),x53082) % 173.51/173.27 [5310]E(x53101,x53102)+~P106(f333(f333(f202(a25),x53101),x53102)) % 173.51/173.27 [5317]~E(x53172,f2(a910))+E(f92(f916(a910,a910),f54(x53171,x53172)),f333(f333(f265(a910,a910),f2(a910)),x53171)) % 173.51/173.27 [5322]~E(x53221,x53222)+~P106(f333(f333(f247(a910),x53221),x53222)) % 173.51/173.27 [5323]~E(x53231,x53232)+~P106(f333(f333(f247(a1),x53231),x53232)) % 173.51/173.27 [5326]~P107(x53261)+E(f333(f333(f87(x53261),f85(x53261)),f333(f111(x53261),x53262)),f333(f111(x53261),f333(a123,x53262))) % 173.51/173.27 [5330]~E(x53301,f2(a910))+~P106(f333(f333(f247(a910),x53302),x53301)) % 173.51/173.27 [5344]E(f160(x53441,x53442),x53442)+~E(f333(f197(f911(x53441)),f160(x53441,x53442)),f333(f197(f911(x53441)),x53442)) % 173.51/173.27 [5345]E(f333(f41(x53451),f333(f180(x53451),x53452)),f333(f197(f911(x53451)),x53452))+~P106(f333(f145(x53451),x53452)) % 173.51/173.27 [5360]~P106(f333(x53601,f363(x53601)))+P106(f333(x53601,f333(f111(a1),x53602))) % 173.51/173.27 [5371]E(f279(x53711,x53712),f85(a110))+~P106(f333(f333(f247(a110),x53712),x53711)) % 173.51/173.27 [5372]E(f186(x53721,x53722),f124(a1))+~P106(f333(f333(f247(a1),x53722),x53721)) % 173.51/173.27 [5373]E(f137(x53731,x53732),f126(a1))+~P106(f333(f333(f247(a1),x53731),x53732)) % 173.51/173.27 [5375]~P112(x53751)+E(f309(x53751,x53752,x53752),f333(f333(f315(x53751),x53752),f196(f917(x53751,a905)))) % 173.51/173.27 [5395]~E(f333(f333(f23(a910),x53951),x53952),f2(a910))+P106(f333(f333(f246(a910),x53951),x53952)) % 173.51/173.27 [5418]~E(x54182,f2(a910))+E(f61(x54181,x54182,f124(x54181)),f333(f333(f159(f911(x54181)),f124(x54181)),f124(f911(x54181)))) % 173.51/173.27 [5422]~P109(x54221)+~P106(f333(f333(f247(x54221),x54222),x54222)) % 173.51/173.27 [5424]~E(f51(a1,x54241,x54242),f2(a1))+E(f51(a1,x54241,f333(f86(a1),x54242)),f2(a1)) % 173.51/173.27 [5426]~E(f51(a1,x54261,x54262),f2(a1))+E(f51(a1,f333(f86(a1),x54261),x54262),f2(a1)) % 173.51/173.27 [5434]E(f333(f308(a910,x54341),f333(a123,x54342)),f196(f917(a910,a905)))+P106(f333(f333(f246(a910),x54341),x54342)) % 173.51/173.27 [5456]E(f147(a910,f333(f308(a910,x54561),x54562)),f124(a910))+P106(f333(f333(f247(a910),x54561),x54562)) % 173.51/173.27 [5461]~E(f333(f41(x54611),f333(f180(x54611),x54612)),f333(f197(f911(x54611)),x54612))+P106(f333(f145(x54611),x54612)) % 173.51/173.27 [5465]~P106(f333(f145(x54651),x54652))+P106(f333(f145(x54651),f333(f175(x54651),x54652))) % 173.51/173.27 [5466]~P106(f333(f145(x54661),x54662))+P106(f333(f145(x54661),f333(f179(x54661),x54662))) % 173.51/173.27 [5467]~P106(f333(f145(x54671),x54672))+P106(f333(f145(x54671),f333(f176(x54671),x54672))) % 173.51/173.27 [5475]P106(f333(x54751,x54752))+~P106(f333(x54751,f333(a115,f437(x54751)))) % 173.51/173.27 [5476]P106(f333(f333(f246(a910),x54762),x54761))+P106(f333(f333(f246(a910),x54761),x54762)) % 173.51/173.27 [5477]P106(f333(f333(f246(a1),x54772),x54771))+P106(f333(f333(f246(a1),x54771),x54772)) % 173.51/173.27 [5479]~P87(x54791)+P106(f333(f333(f246(x54791),x54792),f333(f82(x54791),x54792))) % 173.51/173.27 [5482]P106(f333(x54821,f364(x54821)))+~P106(f333(x54821,f333(f111(a1),x54822))) % 173.51/173.27 [5506]E(f333(f333(f23(a910),x55061),x55062),f2(a910))+~P106(f333(f333(f246(a910),x55061),x55062)) % 173.51/173.27 [5507]E(f333(f333(f42(a910),x55071),x55072),f2(a910))+~P106(f333(f333(f247(a910),x55071),x55072)) % 173.51/173.27 [5525]E(f51(a910,x55251,x55252),x55251)+~P106(f333(f333(f247(a910),x55251),x55252)) % 173.51/173.27 [5533]E(f51(a1,x55331,f333(f86(a1),x55332)),f297(x55331,x55332))+P106(f333(f333(f246(a1),f2(a1)),x55332)) % 173.51/173.27 [5545]E(f333(f333(f23(a1),x55451),x55452),f203(x55451,x55452))+~P106(f333(f333(f246(a1),x55452),x55451)) % 173.51/173.27 [5563]P106(f333(f333(f246(a1),f2(a1)),f363(x55631)))+P106(f333(x55631,f333(f111(a1),x55632))) % 173.51/173.27 [5576]~P119(x55761)+P106(f333(f333(f246(x55761),f2(x55761)),f333(f111(x55761),x55762))) % 173.51/173.27 [5577]~P87(x55771)+P106(f333(f333(f246(x55771),f2(x55771)),f333(f82(x55771),x55772))) % 173.51/173.27 [5604]E(f333(f333(f87(a910),x56041),f341(x56042,x56041)),x56042)+~P106(f333(f333(f246(a910),x56041),x56042)) % 173.51/173.27 [5616]~E(f333(f114(a1),x56161),f333(f111(a1),x56162))+P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x56161))) % 173.51/173.27 [5619]E(f309(a1,x56191,x56192),f196(f917(a1,a905)))+~P106(f333(f333(f247(a1),x56192),x56191)) % 173.51/173.27 [5622]~P120(x56221)+E(f333(f333(f88(x56221),f333(f82(x56221),x56222)),f333(f82(x56221),x56222)),f333(f333(f88(x56221),x56222),x56222)) % 173.51/173.27 [5627]E(f147(a910,f333(f308(a910,x56271),f333(a123,x56272))),f124(a910))+P106(f333(f333(f246(a910),x56271),x56272)) % 173.51/173.27 [5631]E(f333(f333(f42(a1),x56311),x56312),f298(x56311,x56312))+~P106(f333(f333(f246(a1),f2(a1)),x56312)) % 173.51/173.27 [5651]P106(f333(f145(x56511),x56512))+~P106(f333(f145(x56511),f333(f175(x56511),x56512))) % 173.51/173.27 [5652]P106(f333(f145(x56521),x56522))+~P106(f333(f145(x56521),f333(f176(x56521),x56522))) % 173.51/173.27 [5674]P106(f333(f67(a910),x56741))+P106(f333(f333(f335(a910),f869(x56741,x56742)),x56741)) % 173.51/173.27 [5675]P106(f333(f67(a910),x56751))+P106(f333(f333(f335(a910),f880(x56751,x56752)),x56751)) % 173.51/173.27 [5678]P106(f333(f333(f247(a910),x56782),f333(a123,x56781)))+P106(f333(f333(f247(a910),x56781),x56782)) % 173.51/173.27 [5679]E(f51(a1,x56791,x56792),f297(x56791,x56792))+~P106(f333(f333(f246(a1),f2(a1)),x56792)) % 173.51/173.27 [5682]E(f147(a910,f333(f308(a910,x56821),x56822)),f124(a910))+~P106(f333(f333(f246(a910),x56822),x56821)) % 173.51/173.27 [5683]~P4(x56831)+E(f333(f316(x56831,x56831,f86(x56831)),f333(f289(x56831),x56832)),f333(f310(x56831),f333(f86(x56831),x56832))) % 173.51/173.27 [5684]~P4(x56841)+E(f333(f316(x56841,x56841,f86(x56841)),f333(f307(x56841),x56842)),f333(f290(x56841),f333(f86(x56841),x56842))) % 173.51/173.27 [5685]~P4(x56851)+E(f333(f316(x56851,x56851,f86(x56851)),f333(f310(x56851),x56852)),f333(f289(x56851),f333(f86(x56851),x56852))) % 173.51/173.27 [5686]~P4(x56861)+E(f333(f316(x56861,x56861,f86(x56861)),f333(f290(x56861),x56862)),f333(f307(x56861),f333(f86(x56861),x56862))) % 173.51/173.27 [5697]E(x56971,f196(f917(x56972,a905)))+P106(f333(f333(f335(x56972),f720(x56971,x56972)),x56971)) % 173.51/173.27 [5698]E(x56981,f196(f917(x56982,a905)))+P106(f333(f333(f335(x56982),f721(x56981,x56982)),x56981)) % 173.51/173.27 [5709]~P106(f333(f333(f247(a910),x57091),x57092))+P106(f333(f333(f246(a910),x57091),x57092)) % 173.51/173.27 [5710]~P106(f333(f333(f247(a1),x57101),x57102))+P106(f333(f333(f246(a1),x57101),x57102)) % 173.51/173.27 [5726]E(f53(x57261,x57262),f333(f333(f265(a1,a1),f2(a1)),x57261))+~P106(f333(f333(f247(a1),x57261),x57262)) % 173.51/173.27 [5728]E(f227(f333(f86(a1),x57281),f333(f86(a1),x57282)),f227(x57281,x57282))+~P106(f333(f333(f247(a1),x57282),f2(a1))) % 173.51/173.27 [5739]E(x57391,x57392)+~E(f333(a3,f333(a123,f333(a20,x57391))),f333(a3,f333(a123,f333(a20,x57392)))) % 173.51/173.27 [5744]E(f53(x57441,x57442),f333(f333(f265(a1,a1),f2(a1)),x57441))+~P106(f333(f333(f246(a1),x57442),f2(a1))) % 173.51/173.27 [5771]E(f51(a910,f333(f114(a910),x57711),f333(f114(a910),x57712)),f2(a910))+~P106(f333(a201,f333(f114(a1),x57711))) % 173.51/173.27 [5785]P106(f333(f333(f246(a1),f2(a1)),f364(x57851)))+~P106(f333(x57851,f333(f111(a1),x57852))) % 173.51/173.27 [5818]P43(f309(a1,x58181,x58182))+~P106(f333(f333(f246(a1),f2(a1)),x58181)) % 173.51/173.27 [5823]~P106(f333(f67(x58231),x58232))+P106(f333(f67(f917(x58231,a905)),f333(f314(x58231),x58232))) % 173.51/173.27 [5836]E(f333(f333(f87(a1),x58361),f333(f111(a1),f379(x58362,x58361))),x58362)+~P106(f333(f333(f246(a1),x58361),x58362)) % 173.51/173.27 [5844]P106(f333(f333(f246(a910),x58441),x58442))+P106(f333(f333(f246(a910),f333(a123,x58442)),x58441)) % 173.51/173.27 [5887]E(f333(f333(f42(a910),f333(f114(a910),x58871)),f333(f114(a910),x58872)),f2(a910))+~P106(f333(a201,f333(f114(a1),x58871))) % 173.51/173.27 [5888]E(f333(f333(f88(a910),f333(f114(a910),x58881)),f333(f114(a910),x58882)),f2(a910))+~P106(f333(f333(f247(a1),x58881),a90)) % 173.51/173.27 [5890]P106(f333(f333(f246(a910),x58901),f333(a123,x58902)))+~P106(f333(f333(f246(a910),x58901),x58902)) % 173.51/173.27 [5892]P106(f333(f333(f247(a910),x58921),f333(a123,x58922)))+~P106(f333(f333(f246(a910),x58921),x58922)) % 173.51/173.27 [5894]P106(f333(f333(f247(a910),x58941),f333(a123,x58942)))+~P106(f333(f333(f247(a910),x58941),x58942)) % 173.51/173.27 [5897]~E(x58971,x58972)+P106(f333(f333(f247(a1),x58971),f333(f333(f87(a1),x58972),f85(a1)))) % 173.51/173.27 [5900]E(f51(a1,x59001,x59002),f2(a1))+E(f333(f333(f23(a1),x59002),f51(a1,x59001,x59002)),f51(a1,f333(f86(a1),x59001),x59002)) % 173.51/173.27 [5909]E(x59091,f124(x59092))+P106(f333(f333(f335(x59092),f152(x59092,x59091)),f333(f180(x59092),x59091))) % 173.51/173.27 [5921]E(f92(f916(a910,a910),f54(x59211,x59212)),f333(f333(f265(a910,a910),f2(a910)),x59211))+~P106(f333(f333(f247(a910),x59211),x59212)) % 173.51/173.27 [5955]E(f333(f333(f23(a910),f333(f114(a910),x59551)),f333(f114(a910),x59552)),f333(f114(a910),x59551))+~P106(f333(f333(f247(a1),x59552),a90)) % 173.51/173.27 [5956]E(f333(f333(f87(a910),f333(f114(a910),x59561)),f333(f114(a910),x59562)),f333(f114(a910),x59562))+~P106(f333(f333(f247(a1),x59561),a90)) % 173.51/173.27 [5962]E(f333(a123,f333(f333(f87(a910),x59621),f344(x59622,x59621))),x59622)+~P106(f333(f333(f247(a910),x59621),x59622)) % 173.51/173.27 [5985]P106(f333(x59851,x59852))+~P106(f333(x59851,f333(a96,f603(x59852,x59851)))) % 173.51/173.27 [5993]~P106(f333(f333(f247(a910),x59931),f333(a123,x59932)))+P106(f333(f333(f246(a910),x59931),x59932)) % 173.51/173.27 [6038]E(f333(f333(f315(a910),x60381),f333(f308(a910,x60382),x60381)),f333(f308(a910,x60382),f333(a123,x60381)))+~P106(f333(f333(f246(a910),x60382),x60381)) % 173.51/173.27 [6040]E(x60401,f124(x60402))+E(f333(f333(f142(x60402),f125(x60402,x60401)),f333(f333(f159(x60402),f152(x60402,x60401)),f124(x60402))),x60401) % 173.51/173.27 [6057]P106(f333(f67(x60571),x60572))+~P106(f333(f333(f247(a910),f2(a910)),f333(f41(x60571),x60572))) % 173.51/173.27 [6059]~E(x60591,f196(f917(x60592,a905)))+~P106(f333(f333(f247(a910),f2(a910)),f333(f41(x60592),x60591))) % 173.51/173.27 [6071]~P106(f333(f333(f247(a910),x60711),x60712))+P106(f333(f333(f246(a910),f333(a123,x60711)),x60712)) % 173.51/173.27 [6076]~P110(x60761)+E(f158(x60761,x60761,f5(x60761),f160(x60761,x60762)),f147(x60761,f333(f180(x60761),x60762))) % 173.51/173.27 [6079]E(x60791,f124(x60792))+P106(f333(f333(f335(x60792),f333(f149(x60792),x60791)),f333(f180(x60792),x60791))) % 173.51/173.27 [6085]~P119(x60851)+P106(f333(f333(f247(x60851),x60852),f333(f333(f87(x60851),x60852),f85(x60851)))) % 173.51/173.27 [6087]~P87(x60871)+P106(f333(f333(f246(x60871),f333(f86(x60871),x60872)),f333(f82(x60871),x60872))) % 173.51/173.27 [6120]P106(f333(f67(a910),x61201))+~P106(f333(f333(f246(a910),f880(x61201,x61202)),x61202)) % 173.51/173.27 [6121]P106(f333(f67(a910),x61211))+~P106(f333(f333(f247(a910),f869(x61211,x61212)),x61212)) % 173.51/173.27 [6125]~P106(f333(f67(f916(x61251,x61251)),x61252))+P106(f333(f67(x61251),f333(f288(x61251),x61252))) % 173.51/173.27 [6182]~P106(f333(f333(f247(a910),x61822),f333(a123,x61821)))+~P106(f333(f333(f247(a910),x61821),x61822)) % 173.51/173.27 [6183]~P112(x61831)+E(f333(f333(f112(f917(x61831,a905)),f333(f307(x61831),x61832)),f333(f290(x61831),x61832)),f333(f333(f315(x61831),x61832),f196(f917(x61831,a905)))) % 173.51/173.27 [6195]P106(f333(f67(x61951),x61952))+~P106(f333(f67(f917(x61951,a905)),f333(f314(x61951),x61952))) % 173.51/173.27 [6218]P106(f333(f333(f246(a910),f333(a123,x62181)),f333(a123,x62182)))+~P106(f333(f333(f246(a910),x62181),x62182)) % 173.51/173.27 [6219]P106(f333(f333(f246(a910),f333(a20,x62191)),f333(a20,x62192)))+~P106(f333(f333(f246(a110),x62191),x62192)) % 173.51/173.27 [6220]P106(f333(f333(f246(a110),f333(a3,x62201)),f333(a3,x62202)))+~P106(f333(f333(f246(a910),x62201),x62202)) % 173.51/173.27 [6222]P106(f333(f333(f247(a910),f333(a123,x62221)),f333(a123,x62222)))+~P106(f333(f333(f247(a910),x62221),x62222)) % 173.51/173.27 [6223]P106(f333(f333(f247(a910),f333(a20,x62231)),f333(a20,x62232)))+~P106(f333(f333(f247(a110),x62231),x62232)) % 173.51/173.27 [6224]P106(f333(f333(f247(a110),f333(a3,x62241)),f333(a3,x62242)))+~P106(f333(f333(f247(a910),x62241),x62242)) % 173.51/173.27 [6227]E(x62271,x62272)+~E(f333(f316(a910,a1,f111(a1)),x62271),f333(f316(a910,a1,f111(a1)),x62272)) % 173.51/173.27 [6243]P106(f333(f333(f246(a910),x62431),x62432))+~P106(f333(f333(f246(a910),f333(a123,x62431)),x62432)) % 173.51/173.27 [6246]P106(f333(f333(f247(a910),x62461),x62462))+~P106(f333(f333(f246(a910),f333(a123,x62461)),x62462)) % 173.51/173.27 [6247]P106(f333(f333(f247(a910),x62471),x62472))+~P106(f333(f333(f247(a910),f333(a123,x62471)),x62472)) % 173.51/173.27 [6264]E(f51(a1,x62641,x62642),f2(a1))+E(f333(f333(f23(a1),f51(a1,x62641,x62642)),x62642),f51(a1,x62641,f333(f86(a1),x62642))) % 173.51/173.27 [6328]E(f333(f41(f917(x63281,a905)),f333(f314(x63281),x63282)),f333(f333(f256(a910),f333(a123,f333(a123,f2(a910)))),f333(f41(x63281),x63282)))+~P106(f333(f67(x63281),x63282)) % 173.51/173.27 [6331]E(x63311,f124(x63312))+E(f333(f333(f172(x63312),x63311),f333(f333(f23(a910),f333(f197(f911(x63312)),x63311)),f85(a910))),f152(x63312,x63311)) % 173.51/173.27 [6353]E(x63531,f124(x63532))+E(f333(f333(f142(x63532),f333(f179(x63532),x63531)),f333(f333(f159(x63532),f333(f149(x63532),x63531)),f124(x63532))),f333(f175(x63532),x63531)) % 173.51/173.27 [6383]~P106(f333(f67(x63831),f43(f917(x63831,a905),x63832)))+P106(f333(f67(f917(x63831,a905)),x63832)) % 173.51/173.27 [6406]P106(f333(f333(f246(a910),f333(f114(a910),x64061)),f333(f114(a910),x64062)))+~P106(f333(f333(f246(a1),x64061),a90)) % 173.51/173.27 [6426]~P106(f333(f333(f247(a1),x64261),x64262))+P106(f333(f333(f246(a1),x64261),f333(f333(f23(a1),x64262),f85(a1)))) % 173.51/173.27 [6427]~P106(f333(f333(f246(a1),x64271),x64272))+P106(f333(f333(f247(a1),x64271),f333(f333(f87(a1),x64272),f85(a1)))) % 173.51/173.27 [6428]~P106(f333(f333(f247(a1),x64281),x64282))+P106(f333(f333(f247(a1),x64281),f333(f333(f87(a1),x64282),f85(a1)))) % 173.51/173.27 [6430]~P106(f333(f333(f246(a1),x64301),x64302))+P106(f333(f333(f246(a910),f333(f114(a910),x64301)),f333(f114(a910),x64302))) % 173.51/173.27 [6432]~P106(f333(f333(f246(a910),x64321),x64322))+P106(f333(f333(f246(a1),f333(f111(a1),x64321)),f333(f111(a1),x64322))) % 173.51/173.27 [6433]~P106(f333(f333(f246(a1),x64331),x64332))+P106(f333(f333(f246(a1),f333(f114(a1),x64331)),f333(f114(a1),x64332))) % 173.51/173.27 [6435]~P106(f333(f333(f247(a910),x64351),x64352))+P106(f333(f333(f247(a1),f333(f111(a1),x64351)),f333(f111(a1),x64352))) % 173.51/173.27 [6436]~P106(f333(f333(f247(a1),x64361),x64362))+P106(f333(f333(f247(a1),f333(f114(a1),x64361)),f333(f114(a1),x64362))) % 173.51/173.27 [6455]~P106(f333(f333(f246(a910),x64551),x64552))+~P106(f333(f333(f246(a910),f333(a123,x64552)),x64551)) % 173.51/173.27 [6497]~P106(f333(f333(f246(a910),f333(a123,x64971)),f333(a123,x64972)))+P106(f333(f333(f246(a910),x64971),x64972)) % 173.51/173.27 [6498]~P106(f333(f333(f246(a110),f333(a3,x64981)),f333(a3,x64982)))+P106(f333(f333(f246(a910),x64981),x64982)) % 173.51/173.27 [6499]~P106(f333(f333(f246(a910),f333(a20,x64991)),f333(a20,x64992)))+P106(f333(f333(f246(a110),x64991),x64992)) % 173.51/173.27 [6501]~P106(f333(f333(f247(a910),f333(a123,x65011)),f333(a123,x65012)))+P106(f333(f333(f247(a910),x65011),x65012)) % 173.51/173.27 [6502]~P106(f333(f333(f247(a110),f333(a3,x65021)),f333(a3,x65022)))+P106(f333(f333(f247(a910),x65021),x65022)) % 173.51/173.27 [6503]~P106(f333(f333(f247(a910),f333(a115,x65031)),f333(a115,x65032)))+P106(f333(f333(f247(a1),x65031),x65032)) % 173.51/173.27 [6504]~P106(f333(f333(f247(a910),f333(a20,x65041)),f333(a20,x65042)))+P106(f333(f333(f247(a110),x65041),x65042)) % 173.51/173.27 [6545]~P106(f333(f333(f247(a910),f333(a115,x65452)),f333(a115,x65451)))+P106(f333(f333(f247(a1),f2(a1)),x65451)) % 173.51/173.27 [6578]P106(f333(f333(f246(a1),f2(a1)),f51(a1,x65781,x65782)))+~P106(f333(f333(f247(a1),f2(a1)),x65782)) % 173.51/173.27 [6737]P40(x67371,x67372)+~E(f333(f333(f295(x67371,x67371,x67371),x67372),x67372),f196(f917(f916(x67371,x67371),a905))) % 173.51/173.27 [6749]~P40(x67491,x67492)+P40(x67491,f333(f333(f295(x67491,x67491,x67491),x67492),x67492)) % 173.51/173.27 [6761]P106(f333(f333(f246(a1),x67611),x67612))+~P106(f333(f333(f247(a1),x67611),f333(f333(f87(a1),x67612),f85(a1)))) % 173.51/173.27 [6762]P106(f333(f333(f247(a1),x67621),x67622))+~P106(f333(f333(f246(a1),x67621),f333(f333(f23(a1),x67622),f85(a1)))) % 173.51/173.27 [6765]P106(f333(f333(f246(a910),x67651),x67652))+~P106(f333(f333(f246(a1),f333(f111(a1),x67651)),f333(f111(a1),x67652))) % 173.51/173.27 [6766]P106(f333(f333(f246(a1),x67661),x67662))+~P106(f333(f333(f246(a1),f333(f114(a1),x67661)),f333(f114(a1),x67662))) % 173.51/173.27 [6768]P106(f333(f333(f247(a910),x67681),x67682))+~P106(f333(f333(f247(a1),f333(f111(a1),x67681)),f333(f111(a1),x67682))) % 173.51/173.27 [6769]P106(f333(f333(f247(a1),x67691),x67692))+~P106(f333(f333(f247(a910),f333(f114(a910),x67691)),f333(f114(a910),x67692))) % 173.51/173.27 [6770]P106(f333(f333(f247(a1),x67701),x67702))+~P106(f333(f333(f247(a1),f333(f114(a1),x67701)),f333(f114(a1),x67702))) % 173.51/173.27 [6861]~E(f743(x68612,x68611),f124(x68611))+E(f333(f150(f911(x68611),f911(x68611),f142(x68611),f124(x68611)),x68612),f124(x68611)) % 173.51/173.27 [6862]~E(f748(x68622,x68621),f124(x68621))+E(f333(f150(f911(x68621),f911(x68621),f142(x68621),f124(x68621)),x68622),f124(x68621)) % 173.51/173.27 [6867]~P8(x68671)+E(f333(f150(x68671,x68671,f112(x68671),f254(x68671)),x68672),f44(x68671,f333(f180(x68671),x68672))) % 173.51/173.27 [6868]~P8(x68681)+E(f333(f150(x68681,x68681,f121(x68681),f196(x68681)),x68682),f43(x68681,f333(f180(x68681),x68682))) % 173.51/173.27 [6882]E(x68821,f2(a110))+E(f333(f333(f87(a910),f333(a20,f333(f333(f23(a110),x68821),f85(a110)))),f333(a123,x68822)),f333(f333(f87(a910),f333(a20,x68821)),x68822)) % 173.51/173.27 [6931]P106(f333(f333(f247(a1),f333(f333(f23(a1),x69311),x69312)),f2(a1)))+~P106(f333(f333(f247(a1),x69311),x69312)) % 173.51/173.27 [6956]~P110(x69561)+E(f333(f333(f121(f917(x69561,a905)),f333(f333(f315(x69561),x69562),f196(f917(x69561,a905)))),f333(f310(x69561),x69562)),f333(f290(x69561),x69562)) % 173.51/173.27 [7029]~P63(x70291,x70292)+P40(x70291,f333(f252(f916(x70291,x70291)),f333(f269(x70291,x70291,a905),x70292))) % 173.51/173.27 [7030]~P63(x70301,x70302)+P61(x70301,f333(f252(f916(x70301,x70301)),f333(f269(x70301,x70301,a905),x70302))) % 173.51/173.27 [7031]~P53(x70311,x70312)+P41(x70311,f333(f252(f916(x70311,x70311)),f333(f269(x70311,x70311,a905),x70312))) % 173.51/173.27 [7032]~P54(x70321,x70322)+P55(x70321,f333(f252(f916(x70321,x70321)),f333(f269(x70321,x70321,a905),x70322))) % 173.51/173.27 [7033]E(x70331,f196(f917(x70332,a905)))+~P106(f333(f333(f246(f917(x70332,a905)),x70331),f196(f917(x70332,a905)))) % 173.51/173.27 [7114]~P106(f333(f333(f247(a910),f2(a910)),x71142))+P106(f333(f333(f246(a910),f51(a910,x71141,x71142)),x71142)) % 173.51/173.27 [7115]~P106(f333(f333(f246(a1),f2(a1)),x71151))+P106(f333(f333(f246(a1),f51(a1,x71151,x71152)),x71151)) % 173.51/173.27 [7116]~P106(f333(f333(f247(a910),f2(a910)),x71162))+P106(f333(f333(f247(a910),f51(a910,x71161,x71162)),x71162)) % 173.51/173.27 [7118]~P106(f333(f333(f247(a1),f2(a1)),x71182))+P106(f333(f333(f247(a1),f51(a1,x71181,x71182)),x71182)) % 173.51/173.27 [7196]~P112(x71961)+E(f333(f333(f23(f917(x71961,a905)),f333(f333(f315(x71961),x71962),f196(f917(x71961,a905)))),f333(f289(x71961),x71962)),f333(f333(f315(x71961),x71962),f196(f917(x71961,a905)))) % 173.51/173.27 [7268]~P46(x72681,x72682)+P56(x72681,f254(f917(x72681,a905)),f333(f252(f916(x72681,x72681)),f333(f269(x72681,x72681,a905),x72682))) % 173.51/173.27 [7269]P106(f333(x72691,x72692))+P106(f333(f333(f335(f917(f916(a910,a910),a905)),f603(x72692,x72691)),a109)) % 173.51/173.27 [7314]E(f333(f333(f142(a910),f147(a910,f333(f308(a910,x73141),x73142))),f333(f333(f159(a910),x73142),f124(a910))),f147(a910,f333(f308(a910,x73141),f333(a123,x73142))))+~P106(f333(f333(f246(a910),x73141),x73142)) % 173.51/173.27 [7461]E(x74611,f2(a910))+~E(f333(f150(a910,a910,f87(a910),x74611),x74612),f2(a910)) % 173.51/173.27 [7488]~P106(f333(f333(f247(a1),f333(f333(f23(a1),x74881),x74882)),f2(a1)))+P106(f333(f333(f247(a1),x74881),x74882)) % 173.51/173.27 [7515]P40(x75151,x75152)+~P40(x75151,f333(f333(f295(x75151,x75151,x75151),x75152),x75152)) % 173.51/173.27 [7541]~P106(f333(f333(f246(a910),f333(a123,x75411)),x75412))+P106(f193(a905,a250,f333(f246(a910),x75411),x75412)) % 173.51/173.27 [7694]P27(a910,a910,f333(f333(f7(a910,a910,a910),f23(a910)),x76941),x76942)+P106(f333(f333(f335(a910),f871(x76941,x76942)),x76942)) % 173.51/173.27 [7750]E(f333(f333(f333(f71(a910,x77501,f87(a910)),f333(f16(a910,x77501),f85(a910))),f2(a910)),x77502),f333(f41(x77501),x77502))+~P106(f333(f67(x77501),x77502)) % 173.51/173.27 [7791]P27(a910,a910,f333(f333(f7(a910,a910,a910),f23(a910)),x77911),x77912)+~P106(f333(f333(f246(a910),x77911),f871(x77911,x77912))) % 173.51/173.27 [7849]P40(x78491,x78492)+P106(f333(f333(f246(f917(x78491,a905)),f606(x78492,x78491)),f333(f292(x78491,x78491,x78492),f606(x78492,x78491)))) % 173.51/173.27 [7854]P63(x78541,x78542)+~P40(x78541,f333(f252(f916(x78541,x78541)),f333(f269(x78541,x78541,a905),x78542))) % 173.51/173.27 [7855]P53(x78551,x78552)+~P41(x78551,f333(f252(f916(x78551,x78551)),f333(f269(x78551,x78551,a905),x78552))) % 173.51/173.27 [7856]P54(x78561,x78562)+~P55(x78561,f333(f252(f916(x78561,x78561)),f333(f269(x78561,x78561,a905),x78562))) % 173.51/173.27 [7927]P106(f333(f333(f246(a910),f333(a123,x79271)),x79272))+~P106(f193(a905,a250,f333(f246(a910),x79271),x79272)) % 173.51/173.27 [7982]P106(f333(f333(f335(f916(a910,a910)),f333(f333(f265(a910,a910),x79821),x79822)),f313(a910,a323)))+~P106(f333(f333(f246(a910),x79821),x79822)) % 173.51/173.27 [8079]P46(x80791,x80792)+~P56(x80791,f254(f917(x80791,a905)),f333(f252(f916(x80791,x80791)),f333(f269(x80791,x80791,a905),x80792))) % 173.51/173.27 [8140]~P106(f333(f145(x81401),x81402))+P106(f333(f145(f917(x81401,a905)),f333(f333(f162(f911(x81401),f917(x81401,a905)),f180(x81401)),f60(x81401,x81402)))) % 173.51/173.27 [8339]~P40(x83391,f333(f293(x83391,x83391),x83392))+P40(x83391,f333(f293(x83391,x83391),f333(f333(f295(x83391,x83391,x83391),x83392),f313(x83391,x83392)))) % 173.51/173.27 [8439]P28(x84391,a910,f489(x84392,x84391),x84392,f333(f308(a910,f2(a910)),f333(f41(x84391),x84392)))+~P106(f333(f67(x84391),x84392)) % 173.51/173.27 [8440]P28(a910,x84401,f490(x84402,x84401),f333(f308(a910,f2(a910)),f333(f41(x84401),x84402)),x84402)+~P106(f333(f67(x84401),x84402)) % 173.51/173.27 [8457]P28(a910,x84571,f471(x84572,x84571),f309(a910,f85(a910),f333(f41(x84571),x84572)),x84572)+~P106(f333(f67(x84571),x84572)) % 173.51/173.27 [8466]P106(f333(f67(f916(x84661,x84661)),f333(f333(f295(x84661,x84661,x84661),x84662),f313(x84661,x84662))))+~P106(f333(f67(f916(x84661,x84661)),x84662)) % 173.51/173.27 [8493]E(x84931,f2(a1))+P106(f333(f55(x84932,x84931),f333(f333(f265(a1,a1),f333(f333(f42(a1),x84932),x84931)),f51(a1,x84932,x84931)))) % 173.51/173.27 [8506]~P106(f333(f333(f335(f916(a910,a910)),f333(f333(f265(a910,a910),x85061),x85062)),f313(a910,a323)))+P106(f333(f333(f246(a910),x85061),x85062)) % 173.51/173.27 [8525]~P82(x85251)+E(f333(f150(x85251,x85251,f333(f7(x85251,x85251,x85251),f87(x85251)),f2(x85251)),f333(f176(x85251),x85252)),f333(f150(x85251,x85251,f87(x85251),f2(x85251)),x85252)) % 173.51/173.27 [8705]~P110(x87051)+E(f333(f150(f911(x87051),x87051,f333(f7(x87051,f911(x87051),f911(x87051)),f156(x87051,x87051,f5(x87051))),f124(x87051)),x87052),f158(x87051,x87051,f5(x87051),x87052)) % 173.51/173.27 [8817]~P61(x88171,f333(f252(f916(x88171,x88171)),f333(f269(x88171,x88171,a905),x88172)))+P61(x88171,f333(f252(f916(x88171,x88171)),f333(f269(x88171,x88171,a905),f255(x88171,x88171,x88172)))) % 173.51/173.27 [8831]P106(f333(f333(f335(f916(a910,a910)),f333(f333(f265(a910,a910),x88311),x88312)),f333(f333(f295(a910,a910,a910),a323),f313(a910,a323))))+~P106(f333(f333(f247(a910),x88311),x88312)) % 173.51/173.27 [8876]~P106(f333(f67(f916(x88761,x88761)),f333(f333(f295(x88761,x88761,x88761),x88762),f313(x88761,x88762))))+P106(f333(f67(f916(x88761,x88761)),x88762)) % 173.51/173.27 [8934]~P61(x89341,f333(f252(f916(x89341,x89341)),f333(f269(x89341,x89341,a905),f255(x89341,x89341,x89342))))+P61(x89341,f333(f252(f916(x89341,x89341)),f333(f269(x89341,x89341,a905),x89342))) % 173.51/173.27 [9149]P61(x91491,x91492)+P106(f333(f333(f335(f916(x91491,x91491)),f333(f333(f265(x91491,x91491),f620(x91492,x91491)),f620(x91492,x91491))),f333(f333(f295(x91491,x91491,x91491),x91492),f313(x91491,x91492)))) % 173.51/173.27 [9150]P61(x91501,x91502)+P106(f333(f333(f335(f916(x91501,x91501)),f333(f333(f265(x91501,x91501),f622(x91502,x91501)),f622(x91502,x91501))),f333(f333(f295(x91501,x91501,x91501),x91502),f313(x91501,x91502)))) % 173.51/173.27 [9270]~P106(f333(f333(f335(f916(a910,a910)),f333(f333(f265(a910,a910),x92701),x92702)),f333(f333(f295(a910,a910,a910),a323),f313(a910,a323))))+P106(f333(f333(f247(a910),x92701),x92702)) % 173.51/173.27 [5221]~P95(x52211)+E(f333(f333(f87(x52211),f333(f114(x52211),a90)),x52212),x52212) % 173.51/173.27 [5250]~P84(x52501)+E(f333(f333(f121(x52501),f333(f86(x52501),x52502)),x52502),f254(x52501)) % 173.51/173.27 [5251]~P84(x52511)+E(f333(f333(f112(x52511),f333(f86(x52511),x52512)),x52512),f196(x52511)) % 173.51/173.27 [5252]~P6(x52521)+E(f333(f333(f87(x52521),f333(f86(x52521),x52522)),x52522),f2(x52521)) % 173.51/173.27 [5253]~P71(x52531)+E(f333(f333(f87(x52531),f333(f86(x52531),x52532)),x52532),f2(x52531)) % 173.51/173.27 [5286]~P95(x52861)+E(f333(f333(f88(x52861),f333(f114(x52861),a108)),x52862),f333(f86(x52861),x52862)) % 173.51/173.27 [5449]~P114(x54491)+E(f333(f333(f88(x54491),f333(f86(x54491),f85(x54491))),x54492),f333(f86(x54491),x54492)) % 173.51/173.27 [5491]E(f333(f82(a1),x54911),f85(a1))+~E(f333(f82(a1),f333(f333(f88(a1),x54911),x54912)),f85(a1)) % 173.51/173.27 [5579]~P95(x55791)+E(f333(f333(f87(x55791),f85(x55791)),f333(f114(x55791),x55792)),f333(f114(x55791),f333(f333(f23(a1),x55792),a108))) % 173.51/173.27 [5632]~P2(x56321)+E(f13(x56321,f333(f333(f315(x56321),x56322),f196(f917(x56321,a905)))),x56322) % 173.51/173.27 [5633]~P2(x56331)+E(f10(x56331,f333(f333(f315(x56331),x56332),f196(f917(x56331,a905)))),x56332) % 173.51/173.27 [5634]~P110(x56341)+E(f14(x56341,f333(f333(f315(x56341),x56342),f196(f917(x56341,a905)))),x56342) % 173.51/173.27 [5635]~P110(x56351)+E(f15(x56351,f333(f333(f315(x56351),x56352),f196(f917(x56351,a905)))),x56352) % 173.51/173.27 [5636]~P8(x56361)+E(f44(x56361,f333(f333(f315(x56361),x56362),f196(f917(x56361,a905)))),x56362) % 173.51/173.27 [5637]~P8(x56371)+E(f43(x56371,f333(f333(f315(x56371),x56372),f196(f917(x56371,a905)))),x56372) % 173.51/173.27 [5659]E(f333(f333(f87(a910),x56591),f333(f333(f23(a910),x56592),x56591)),x56592)+P106(f333(f333(f247(a910),x56592),x56591)) % 173.51/173.27 [5692]E(x56921,f124(x56922))+P106(f333(f333(f247(a910),f2(a910)),f333(f197(f911(x56922)),x56921))) % 173.51/173.27 [5815]~P110(x58151)+E(f11(x58151,f244(x58151),f333(f333(f315(x58151),x58152),f196(f917(x58151,a905)))),x58152) % 173.51/173.27 [5816]~P110(x58161)+E(f12(x58161,f245(x58161),f333(f333(f315(x58161),x58162),f196(f917(x58161,a905)))),x58162) % 173.51/173.27 [5877]E(f333(f333(f23(a910),x58771),f333(f333(f23(a910),x58771),x58772)),x58772)+~P106(f333(f333(f246(a910),x58772),x58771)) % 173.51/173.27 [5878]E(f333(f333(f87(a910),x58781),f333(f333(f23(a910),x58782),x58781)),x58782)+~P106(f333(f333(f246(a910),x58781),x58782)) % 173.51/173.27 [5899]E(f51(a910,f333(f333(f23(a910),x58991),x58992),x58992),f51(a910,x58991,x58992))+P106(f333(f333(f247(a910),x58991),x58992)) % 173.51/173.27 [5910]E(f333(f86(a1),f333(f333(f42(a1),x59101),f333(f86(a1),x59102))),f298(x59101,x59102))+P106(f333(f333(f246(a1),f2(a1)),x59102)) % 173.51/173.27 [5912]~E(x59122,f2(a910))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f256(a910),x59121),x59122))) % 173.51/173.27 [5964]~P95(x59641)+E(f333(f333(f87(x59641),f333(f86(x59641),f85(x59641))),f333(f114(x59641),x59642)),f333(f114(x59641),f333(f333(f87(a1),x59642),a108))) % 173.51/173.27 [5965]E(f333(f333(f256(a910),f333(f114(a910),x59651)),x59652),f333(f333(f256(a910),f2(a910)),x59652))+~P106(f333(a201,f333(f114(a1),x59651))) % 173.51/173.27 [6063]E(f333(f149(a910),f147(a910,f333(f308(a910,x60631),x60632))),x60631)+~P106(f333(f333(f247(a910),x60631),x60632)) % 173.51/173.27 [6080]E(f333(f333(f88(a910),f333(f114(a910),x60801)),f333(f114(a910),x60802)),f333(f114(a910),f333(f333(f88(a1),x60801),x60802)))+P106(f333(f333(f247(a1),x60801),a90)) % 173.51/173.27 [6086]~P127(x60861)+P106(f333(f333(f246(x60861),f2(x60861)),f333(f333(f88(x60861),x60862),x60862))) % 173.51/173.27 [6098]E(f333(f333(f23(a910),f333(a123,x60981)),x60982),f333(a123,f333(f333(f23(a910),x60981),x60982)))+~P106(f333(f333(f246(a910),x60982),x60981)) % 173.51/173.27 [6101]E(f51(a910,f333(f333(f23(a910),x61011),x61012),x61012),f51(a910,x61011,x61012))+~P106(f333(f333(f246(a910),x61012),x61011)) % 173.51/173.27 [6156]E(f333(f333(f256(a910),f333(a115,x61561)),x61562),f333(a115,f333(f333(f256(a1),x61561),x61562)))+~P106(f333(f333(f246(a1),f2(a1)),x61561)) % 173.51/173.27 [6173]P106(f333(f145(x61731),x61732))+P106(f333(f333(f247(a910),f713(x61732,x61731)),f333(f197(f911(x61731)),x61732))) % 173.51/173.27 [6174]P106(f333(f145(x61741),x61742))+P106(f333(f333(f247(a910),f719(x61742,x61741)),f333(f197(f911(x61741)),x61742))) % 173.51/173.27 [6189]~E(x61891,f124(x61892))+~P106(f333(f333(f247(a910),f2(a910)),f333(f197(f911(x61892)),x61891))) % 173.51/173.27 [6200]E(f152(a910,f147(a910,f333(f308(a910,x62001),x62002))),f333(f333(f23(a910),x62002),f85(a910)))+~P106(f333(f333(f247(a910),x62001),x62002)) % 173.51/173.27 [6203]E(f333(f333(f87(a1),x62031),f333(f111(a1),f333(a123,f372(x62032,x62031)))),x62032)+~P106(f333(f333(f247(a1),x62031),x62032)) % 173.51/173.27 [6210]E(x62101,f2(a910))+E(f333(f333(f88(a910),x62102),f333(f333(f256(a910),x62102),f333(f333(f23(a910),x62101),f85(a910)))),f333(f333(f256(a910),x62102),x62101)) % 173.51/173.27 [6237]E(f333(f333(f88(a910),f333(a115,x62371)),f333(a115,x62372)),f333(a115,f333(f333(f88(a1),x62371),x62372)))+~P106(f333(f333(f246(a1),f2(a1)),x62371)) % 173.51/173.27 [6238]E(f333(f333(f42(a910),f333(a115,x62381)),f333(a115,x62382)),f333(a115,f333(f333(f42(a1),x62381),x62382)))+~P106(f333(f333(f246(a1),f2(a1)),x62381)) % 173.51/173.27 [6252]~P117(x62521)+E(f333(f333(f87(x62521),x62522),x62522),f333(f333(f88(x62521),f333(f333(f87(x62521),f85(x62521)),f85(x62521))),x62522)) % 173.51/173.27 [6273]E(f333(f333(f23(a1),f333(f111(a1),x62731)),f333(f111(a1),x62732)),f333(f111(a1),f333(f333(f23(a910),x62731),x62732)))+~P106(f333(f333(f246(a910),x62732),x62731)) % 173.51/173.27 [6275]E(f333(f333(f265(a1,a1),f333(f114(a1),a108)),f333(f333(f87(a1),x62751),x62752)),f56(x62751,x62752))+~P106(f333(f333(f246(a1),x62752),f2(a1))) % 173.51/173.27 [6306]E(f187(x63061,x63062),f124(f911(x63061)))+P106(f333(f333(f335(f911(x63061)),f712(x63062,x63061)),f333(f180(f911(x63061)),x63062))) % 173.51/173.27 [6315]E(f127(a1,f333(f138(a1),x63151),f137(x63152,f333(f333(f87(a1),x63151),f85(a1)))),f137(x63152,x63151))+P106(f333(f333(f247(a1),x63152),x63151)) % 173.51/173.27 [6389]E(f333(f333(f159(a1),x63891),f186(f333(f333(f87(a1),x63891),f85(a1)),x63892)),f186(x63891,x63892))+~P106(f333(f333(f246(a1),x63891),x63892)) % 173.51/173.27 [6429]~P106(f333(f333(f247(a910),x64292),x64291))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f23(a910),x64291),x64292))) % 173.51/173.27 [6460]~P106(f333(f333(f247(a910),x64601),f333(a115,x64602)))+P106(f333(f333(f247(a1),f333(f111(a1),x64601)),x64602)) % 173.51/173.27 [6488]~P110(x64881)+E(f333(f333(f121(f917(x64881,a905)),f333(f289(x64881),x64882)),f333(f333(f315(x64881),x64882),f196(f917(x64881,a905)))),f333(f307(x64881),x64882)) % 173.51/173.27 [6489]~P106(f333(f333(f246(a1),f2(a1)),x64891))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f256(a1),x64891),x64892))) % 173.51/173.27 [6492]~P106(f333(f333(f247(a910),f2(a910)),x64921))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f256(a910),x64921),x64922))) % 173.51/173.27 [6521]~E(f333(x65211,f2(a910)),f2(a910))+E(f333(f333(f6(a910,a910),x65211),f309(a910,f333(a123,f2(a910)),x65212)),f333(f333(f6(a910,a910),x65211),f309(a910,f2(a910),x65212))) % 173.51/173.27 [6586]~P95(x65861)+E(f333(f333(f88(x65861),f333(f333(f87(x65861),f85(x65861)),f85(x65861))),f333(f114(x65861),x65862)),f333(f114(x65861),f333(f333(f87(a1),x65862),x65862))) % 173.51/173.27 [6601]E(f333(f333(f315(a1),x66011),f309(a1,f333(f333(f87(a1),x66011),f85(a1)),x66012)),f309(a1,x66011,x66012))+P106(f333(f333(f247(a1),x66012),x66011)) % 173.51/173.27 [6602]P106(f333(f333(f247(a910),x66021),f333(a115,x66022)))+~P106(f333(f333(f247(a1),f333(f111(a1),x66021)),x66022)) % 173.51/173.27 [6706]E(f333(a115,f333(f333(f42(a1),f333(f114(a1),x67061)),f333(f114(a1),x67062))),f333(f333(f42(a910),f333(f114(a910),x67061)),f333(f114(a910),x67062)))+P106(f333(a201,f333(f114(a1),x67061))) % 173.51/173.27 [6763]P106(f333(f333(f247(a910),x67631),x67632))+~P106(f333(f333(f247(a910),f2(a910)),f333(f333(f23(a910),x67632),x67631))) % 173.51/173.27 [6806]P106(f333(f333(f247(a910),f2(a910)),x68061))+~P106(f333(f333(f247(a910),f2(a910)),f333(f333(f88(a910),x68062),x68061))) % 173.51/173.27 [6807]P106(f333(f333(f247(a910),f2(a910)),x68071))+~P106(f333(f333(f247(a910),f2(a910)),f333(f333(f88(a910),x68071),x68072))) % 173.51/173.27 [6824]~P106(f333(f333(f246(a1),x68241),f2(a1)))+E(f333(f333(f88(a910),f333(a115,f333(f86(a1),x68241))),f333(a115,f333(f86(a1),x68242))),f333(a115,f333(f333(f88(a1),x68241),x68242))) % 173.51/173.27 [6879]~E(x68792,f196(f917(x68791,a905)))+P106(f333(f333(f246(f917(x68791,a905)),x68792),f333(f86(f917(x68791,a905)),x68792))) % 173.51/173.27 [6941]~P95(x69411)+E(f333(f333(f87(x69411),f333(f333(f87(x69411),f2(x69411)),f333(f114(x69411),x69412))),f333(f114(x69411),x69412)),f333(f114(x69411),f333(f333(f87(a1),x69412),x69412))) % 173.51/173.27 [6995]~P106(f333(f333(f247(a1),x69951),x69952))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x69951),f85(a1))),x69952)) % 173.51/173.27 [7062]E(x70621,f2(a910))+~P106(f333(f333(f246(a1),f333(f111(a1),x70622)),f333(f86(a1),f333(f111(a1),x70621)))) % 173.51/173.27 [7063]E(x70631,f2(a910))+~P106(f333(f333(f246(a1),f333(f111(a1),x70631)),f333(f86(a1),f333(f111(a1),x70632)))) % 173.51/173.27 [7164]E(f333(f333(f265(a1,a1),f333(f114(a1),a108)),f333(f333(f87(a1),x71641),x71642)),f56(x71641,x71642))+~P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),x71641),x71642))) % 173.51/173.27 [7208]~P29(x72081,x72082)+P40(x72081,f333(f264(f917(f916(x72081,x72081),a905),f917(f916(x72081,x72081),a905)),x72082)) % 173.51/173.27 [7226]~P106(f333(f333(f246(a910),f333(a123,f2(a910))),x72261))+P106(f333(f333(f246(a910),f333(a123,f2(a910))),f333(f333(f256(a910),x72261),x72262))) % 173.51/173.27 [7403]~P106(f333(f333(f246(a1),x74031),x74032))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x74031),x74031)),f333(f333(f87(a1),x74032),x74032))) % 173.51/173.27 [7408]~P106(f333(f333(f247(a1),x74081),x74082))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x74081),x74081)),f333(f333(f87(a1),x74082),x74082))) % 173.51/173.27 [7462]~P106(f333(f333(f247(a910),f2(a910)),x74621))+P106(f333(f333(f247(a910),f333(f333(f23(a910),x74621),f333(a123,x74622))),x74621)) % 173.51/173.27 [7497]P106(f333(f333(f246(a910),f333(a123,f2(a910))),x74971))+~P106(f333(f333(f246(a910),f333(a123,f2(a910))),f333(f333(f88(a910),x74972),x74971))) % 173.51/173.27 [7498]P106(f333(f333(f246(a910),f333(a123,f2(a910))),x74981))+~P106(f333(f333(f246(a910),f333(a123,f2(a910))),f333(f333(f88(a910),x74981),x74982))) % 173.51/173.27 [7502]P106(f333(f333(f246(a910),f333(f333(f172(a910),x75021),x75022)),f333(f173(a910),x75021)))+~P106(f333(f333(f247(a910),x75022),f333(f197(f911(a910)),x75021))) % 173.51/173.27 [7540]P106(f333(f333(f247(a1),x75401),x75402))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),x75401),f85(a1))),x75402)) % 173.51/173.27 [7583]P106(f333(f67(x75831),f254(f917(x75831,a905))))+~P106(f333(f67(f917(x75832,x75831)),f254(f917(f917(x75832,x75831),a905)))) % 173.51/173.27 [7584]P106(f333(f67(x75841),f254(f917(x75841,a905))))+~P106(f333(f67(f918(x75842,x75841)),f254(f917(f918(x75842,x75841),a905)))) % 173.51/173.27 [7585]P106(f333(f67(x75851),f254(f917(x75851,a905))))+~P106(f333(f67(f918(x75851,x75852)),f254(f917(f918(x75851,x75852),a905)))) % 173.51/173.27 [7624]E(x76241,f196(f917(x76242,a905)))+~P106(f333(f333(f246(f917(x76242,a905)),x76241),f333(f86(f917(x76242,a905)),x76241))) % 173.51/173.27 [7760]E(f333(f150(f911(x77601),f911(x77601),f142(x77601),f124(x77601)),x77602),f124(x77601))+P106(f333(f333(f335(f911(x77601)),f743(x77602,x77601)),f333(f180(f911(x77601)),x77602))) % 173.51/173.27 [7761]E(f333(f150(f911(x77611),f911(x77611),f142(x77611),f124(x77611)),x77612),f124(x77611))+P106(f333(f333(f335(f911(x77611)),f748(x77612,x77611)),f333(f180(f911(x77611)),x77612))) % 173.51/173.27 [8000]P106(f333(f333(f246(a1),x80001),x80002))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),x80001),x80001)),f333(f333(f87(a1),x80002),x80002))) % 173.51/173.27 [8005]P106(f333(f333(f247(a1),x80051),x80052))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),x80051),x80051)),f333(f333(f87(a1),x80052),x80052))) % 173.51/173.27 [8099]~P117(x80991)+E(f333(f333(f88(x80991),f333(f333(f87(x80991),f85(x80991)),f85(x80991))),f333(f333(f6(a910,x80991),f111(x80991)),f309(a910,f85(a910),x80992))),f333(f333(f88(x80991),f333(f111(x80991),x80992)),f333(f333(f87(x80991),f333(f111(x80991),x80992)),f85(x80991)))) % 173.51/173.27 [8154]P106(f333(f333(f335(a910),x81541),x81542))+~P106(f333(f333(f335(a1),f333(f111(a1),x81541)),f333(f316(a910,a1,f111(a1)),x81542))) % 173.51/173.27 [8310]~P106(f333(f67(x83101),x83102))+E(f333(f316(a910,x83101,f898(x83102,x83101)),f333(f252(a910),f333(f333(f7(a910,a910,a905),f247(a910)),f899(x83102,x83101)))),x83102) % 173.51/173.27 [8601]P57(x86011,x86012)+P106(f333(f333(f335(f916(x86011,x86011)),f333(f333(f265(x86011,x86011),f538(x86012,x86011)),f538(x86012,x86011))),x86012)) % 173.51/173.27 [8602]P41(x86021,x86022)+P106(f333(f333(f335(f916(x86021,x86021)),f333(f333(f265(x86021,x86021),f833(x86022,x86021)),f836(x86022,x86021))),x86022)) % 173.51/173.27 [8603]P41(x86031,x86032)+P106(f333(f333(f335(f916(x86031,x86031)),f333(f333(f265(x86031,x86031),f836(x86032,x86031)),f837(x86032,x86031))),x86032)) % 173.51/173.27 [8604]P42(x86041,x86042)+P106(f333(f333(f335(f916(x86041,x86041)),f333(f333(f265(x86041,x86041),f753(x86042,x86041)),f752(x86042,x86041))),x86042)) % 173.51/173.27 [8605]P42(x86051,x86052)+P106(f333(f333(f335(f916(x86051,x86051)),f333(f333(f265(x86051,x86051),f752(x86052,x86051)),f753(x86052,x86051))),x86052)) % 173.51/173.27 [8606]P55(x86061,x86062)+P106(f333(f333(f335(f916(x86061,x86061)),f333(f333(f265(x86061,x86061),f852(x86062,x86061)),f853(x86062,x86061))),x86062)) % 173.51/173.27 [8748]~P95(x87481)+E(f333(f333(f23(x87481),f85(x87481)),f333(f114(x87481),x87482)),f333(f114(x87481),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f86(a1),x87482)))) % 173.51/173.27 [8873]~P106(f333(f333(f247(f917(a910,a905)),x88731),x88732))+P106(f333(f333(f247(f917(a1,a905)),f333(f316(a910,a1,f111(a1)),x88731)),f333(f316(a910,a1,f111(a1)),x88732))) % 173.51/173.27 [8907]~P106(f333(f333(f247(a1),x89071),x89072))+P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x89071),x89071)),a108)),f333(f333(f87(a1),x89072),x89072))) % 173.51/173.27 [8909]~P106(f333(f333(f247(a1),x89091),x89092))+P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x89091),x89091)),a108)),f333(f333(f87(a1),x89092),x89092))) % 173.51/173.27 [8982]~P106(f333(f333(f335(a910),x89821),f333(f180(a910),x89822)))+P106(f333(f333(f246(a910),x89821),f333(f150(a910,a910,f87(a910),f2(a910)),x89822))) % 173.51/173.27 [9079]P49(x90791,x90792)+~P106(f333(f333(f335(f916(x90791,x90791)),f333(f333(f265(x90791,x90791),f540(x90792,x90791)),f540(x90792,x90791))),x90792)) % 173.51/173.27 [9080]P41(x90801,x90802)+~P106(f333(f333(f335(f916(x90801,x90801)),f333(f333(f265(x90801,x90801),f833(x90802,x90801)),f837(x90802,x90801))),x90802)) % 173.51/173.27 [9081]P55(x90811,x90812)+~P106(f333(f333(f335(f916(x90811,x90811)),f333(f333(f265(x90811,x90811),f853(x90812,x90811)),f852(x90812,x90811))),x90812)) % 173.51/173.27 [9232]~P106(f333(f333(f246(f917(a1,a905)),f333(f316(a910,a1,f111(a1)),x92321)),f333(f316(a910,a1,f111(a1)),x92322)))+P106(f333(f333(f246(f917(a910,a905)),x92321),x92322)) % 173.51/173.27 [9233]~P106(f333(f333(f247(f917(a1,a905)),f333(f316(a910,a1,f111(a1)),x92331)),f333(f316(a910,a1,f111(a1)),x92332)))+P106(f333(f333(f247(f917(a910,a905)),x92331),x92332)) % 173.51/173.27 [9319]P106(f333(f333(f247(a1),x93191),x93192))+~P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x93191),x93191)),a108)),f333(f333(f87(a1),x93192),x93192))) % 173.51/173.27 [9321]P106(f333(f333(f247(a1),x93211),x93212))+~P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x93211),x93211)),a108)),f333(f333(f87(a1),x93212),x93212))) % 173.51/173.27 [10221]~P104(x102211)+E(f127(f911(x102211),f333(f138(f911(x102211)),f124(x102211)),f333(f333(f333(f107(f912(f911(x102211))),f333(f333(f247(a1),f2(a1)),x102212)),f333(f129(f916(x102211,f911(x102211)),f911(x102211),f139(x102211,f911(x102211),f140(x102211,f333(f333(f23(a1),x102212),f85(a1))),f140(f911(x102211),f333(f333(f23(a1),x102212),f85(a1))))),f333(f269(x102211,f911(x102211),f912(f911(x102211))),f333(f333(f8(f917(f911(x102211),f911(x102211)),f917(f911(x102211),f912(f911(x102211))),x102211),f333(f8(f911(x102211),f912(f911(x102211)),f911(x102211)),f138(f911(x102211)))),f159(x102211))))),f126(f911(x102211)))),f140(f911(x102211),x102212)) % 173.51/173.27 [10243]~P106(f333(f67(x102431),x102432))+E(f333(f197(f911(x102431)),f97(f911(x102431),f333(f333(f18(f911(x102431),a905,a905),f333(f333(f8(a905,f917(a905,a905),f911(x102431)),a331),f333(f333(f7(f911(x102431),f917(x102431,a905),a905),f333(f333(f8(f917(x102431,a905),f917(f917(x102431,a905),a905),f911(x102431)),a330),f180(x102431))),x102432))),f145(x102431)))),f226(x102431,x102432)) % 173.51/173.27 [6199]E(f333(f333(f87(a910),f333(f333(f23(a910),x61991),x61992)),x61992),x61991)+~P106(f333(f333(f246(a910),x61992),x61991)) % 173.51/173.27 [6269]E(f333(f333(f42(a910),f333(f333(f88(a910),x62691),x62692)),x62692),x62691)+~P106(f333(f333(f247(a910),f2(a910)),x62692)) % 173.51/173.27 [6270]E(f333(f333(f42(a910),f333(f333(f88(a910),x62701),x62702)),x62701),x62702)+~P106(f333(f333(f247(a910),f2(a910)),x62701)) % 173.51/173.27 [6274]~P72(x62741)+E(f333(f333(f6(a910,x62741),f333(f172(x62741),x62742)),f333(f308(a910,f2(a910)),f333(f197(f911(x62741)),x62742))),f333(f173(x62741),x62742)) % 173.51/173.27 [6381]E(f51(a910,f333(a123,f333(f333(f88(a910),x63811),x63812)),x63811),f85(a910))+~P106(f333(f333(f247(a910),f85(a910)),x63811)) % 173.51/173.27 [6387]E(f333(a123,f333(f333(f87(a910),f333(f114(a910),x63871)),x63872)),f333(f333(f87(a910),f85(a910)),x63872))+~P106(f333(a201,f333(f114(a1),x63871))) % 173.51/173.27 [6417]E(f333(a115,f333(f333(f256(a1),f333(f114(a1),x64171)),x64172)),f333(f333(f256(a910),f333(f114(a910),x64171)),x64172))+P106(f333(a201,f333(f114(a1),x64171))) % 173.51/173.27 [6655]E(f333(f333(f23(a910),x66551),f333(f114(a910),f333(f333(f87(a1),x66552),a108))),f333(f333(f23(a910),f333(a123,x66551)),f333(f114(a910),x66552)))+~P106(f333(f333(f247(a1),a90),x66552)) % 173.51/173.27 [6736]E(x67361,f2(a910))+E(f333(a123,f333(f333(f87(a910),f333(f333(f23(a910),x67361),f85(a910))),x67362)),f333(f333(f87(a910),x67361),x67362)) % 173.51/173.27 [6776]E(x67761,f2(a1))+P106(f333(f333(f247(a1),f2(a1)),f333(f333(f256(a1),f333(f82(a1),x67761)),x67762))) % 173.51/173.27 [6791]~E(x67912,f2(a910))+P106(f333(f333(f247(a1),f2(a1)),f333(f333(f256(a1),f333(f82(a1),x67911)),x67912))) % 173.51/173.27 [6827]E(x68271,f2(a910))+E(f333(f333(f87(a910),x68272),f333(f333(f88(a910),f333(f333(f23(a910),x68271),f85(a910))),x68272)),f333(f333(f88(a910),x68271),x68272)) % 173.51/173.27 [6872]~P106(f333(f333(f246(a1),x68721),x68722))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x68721),a108)),x68722)) % 173.51/173.27 [6998]E(f333(f333(f159(a910),x69981),f147(a910,f333(f308(a910,f333(a123,x69981)),x69982))),f147(a910,f333(f308(a910,x69981),x69982)))+~P106(f333(f333(f247(a910),x69981),x69982)) % 173.51/173.27 [7199]E(x71991,x71992)+~E(f333(f333(f23(a1),f333(f333(f87(a1),x71991),x71991)),a108),f333(f333(f23(a1),f333(f333(f87(a1),x71992),x71992)),a108)) % 173.51/173.27 [7202]E(x72021,f124(x72022))+E(f275(x72022,f333(f333(f162(x72022,f916(a110,x72022)),f333(f265(a110,x72022),f85(a110))),x72021)),f282(x72022,x72021)) % 173.51/173.27 [7433]P106(f333(f333(f246(a1),x74331),x74332))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),x74331),a108)),x74332)) % 173.51/173.27 [7904]~P106(f333(f333(f247(a910),x79041),x79042))+P106(f333(f333(f335(f916(a910,a910)),f333(f333(f265(a910,a910),x79041),x79042)),a251)) % 173.51/173.27 [8128]~P106(f333(f333(f247(a110),f2(a110)),x81281))+P106(f333(f333(f247(a110),f333(f264(a110,f916(a110,a110)),f333(f276(x81281),x81282))),x81281)) % 173.51/173.27 [8393]~P41(x83931,x83932)+P41(x83931,f333(f333(f121(f917(f916(x83931,x83931),a905)),x83932),f313(x83931,f196(f917(f916(x83931,x83931),a905))))) % 173.51/173.27 [8394]~P42(x83941,x83942)+P42(x83941,f333(f333(f121(f917(f916(x83941,x83941),a905)),x83942),f313(x83941,f196(f917(f916(x83941,x83941),a905))))) % 173.51/173.27 [8443]~P87(x84431)+P106(f333(f333(f246(x84431),f333(f82(x84431),f333(f173(x84431),x84432))),f333(f173(x84431),f333(f333(f162(x84431,x84431),f82(x84431)),x84432)))) % 173.51/173.27 [8468]P106(f333(f333(f247(a910),x84681),x84682))+~P106(f333(f333(f335(f916(a910,a910)),f333(f333(f265(a910,a910),x84681),x84682)),a251)) % 173.51/173.27 [8628]E(f333(f333(f265(x86281,x86281),f647(x86282,x86281)),f647(x86282,x86281)),x86282)+~P106(f333(f333(f335(f916(x86281,x86281)),x86282),f313(x86281,f196(f917(f916(x86281,x86281),a905))))) % 173.51/173.27 [8671]E(f333(f308(a910,x86711),f333(f333(f87(a910),x86711),f333(f41(a910),x86712))),x86712)+~P106(f333(f333(f246(f917(a910,a905)),x86712),f333(f308(a910,x86711),f333(f333(f87(a910),x86711),f333(f41(a910),x86712))))) % 173.51/173.27 [8900]P42(x89001,x89002)+~P42(x89001,f333(f333(f121(f917(f916(x89001,x89001),a905)),x89002),f313(x89001,f196(f917(f916(x89001,x89001),a905))))) % 173.51/173.27 [9027]E(f333(f333(f42(a1),f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),x90271),x90271)),a108))),f333(f114(a1),f333(f333(f87(a1),x90272),x90272))),f333(f333(f42(a1),f333(f114(a1),x90271)),f333(f114(a1),x90272)))+~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x90272))) % 173.51/173.27 [9131]~P41(x91311,x91312)+P106(f333(f333(f246(f917(f916(x91311,x91311),a905)),f333(f333(f295(x91311,x91311,x91311),x91312),x91312)),x91312)) % 173.51/173.27 [9160]E(f185(f911(x91601),f333(f333(f8(a905,a905,f911(x91601)),a328),f333(f333(f7(f911(x91601),f911(x91601),a905),a330),f124(x91601))),x91602),f187(x91601,f187(x91601,x91602)))+~P16(a910,f333(f176(a910),f333(f333(f162(f911(x91601),a910),f197(f911(x91601))),x91602))) % 173.51/173.27 [9163]E(f333(f333(f42(a1),f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),x91631),x91631)),a108))),f333(f114(a1),f333(f333(f87(a1),x91632),x91632))),f333(f333(f42(a1),f333(f333(f87(a1),f333(f114(a1),x91631)),f85(a1))),f333(f114(a1),x91632)))+P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x91632))) % 173.51/173.27 [10018]P106(f333(a201,x100182))+E(f333(f333(f93(a1,a910),f333(f333(f23(a1),x100181),x100182)),f333(f333(f18(a1,a910,a910),f333(f333(f7(a1,a910,f917(a910,a910)),f333(f333(f8(a905,f917(a910,f917(a910,a910)),a1),f107(a910)),a201)),f2(a910))),a115)),f333(f333(f23(a910),f333(a115,x100181)),f333(a115,x100182))) % 173.51/173.27 [10026]E(f333(f333(f93(a1,a910),f333(f114(a1),f333(f333(f87(a1),x100261),f333(f86(a1),x100262)))),f333(f333(f18(a1,a910,a910),f333(f333(f7(a1,a910,f917(a910,a910)),f333(f333(f8(a905,f917(a910,f917(a910,a910)),a1),f107(a910)),a201)),f2(a910))),a115)),f333(f333(f23(a910),f333(f114(a910),x100261)),f333(f114(a910),x100262)))+P106(f333(f333(f247(a1),x100262),a90)) % 173.51/173.27 [10027]~P29(x100271,x100272)+P106(f333(f333(f246(f917(f916(x100271,x100271),a905)),f333(f333(f295(x100271,x100271,x100271),f333(f264(f917(f916(x100271,x100271),a905),f917(f916(x100271,x100271),a905)),x100272)),f333(f268(f917(f916(x100271,x100271),a905),f917(f916(x100271,x100271),a905)),x100272))),f333(f264(f917(f916(x100271,x100271),a905),f917(f916(x100271,x100271),a905)),x100272))) % 173.51/173.27 [10090]~E(f333(f41(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,f917(a910,a905),a905),f335(a910)),x100901))),f333(f333(f7(a910,a910,a905),f247(a910)),f333(a123,x100902))))),f2(a910))+~P106(f333(f333(f335(a910),f2(a910)),x100901)) % 173.51/173.27 [10148]E(f51(a1,f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),x101481),x101481)),a108)),f333(f114(a1),f333(f333(f87(a1),x101482),x101482))),f333(f333(f87(a1),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f51(a1,f333(f114(a1),x101481),f333(f114(a1),x101482)))),f85(a1)))+~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x101482))) % 173.51/173.27 [10157]E(f51(a1,f333(f114(a1),f333(f333(f23(a1),f333(f333(f87(a1),x101571),x101571)),a108)),f333(f114(a1),f333(f333(f87(a1),x101572),x101572))),f333(f333(f23(a1),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f51(a1,f333(f333(f87(a1),f333(f114(a1),x101571)),f85(a1)),f333(f114(a1),x101572)))),f85(a1)))+P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x101572))) % 173.51/173.27 [10210]~P8(x102101)+E(f43(x102101,f333(f252(x102101),f333(f333(f8(f917(x102101,a905),a905,x102101),f95(x102101)),f333(f333(f8(f917(x102101,a905),f917(x102101,a905),x102101),f333(f18(x102101,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102101),a336),f333(f333(f7(x102101,f917(x102101,a905),a905),f335(x102101)),x102102)))),f246(x102101))))),f44(x102101,x102102)) % 173.51/173.27 [10236]~P40(x102361,x102362)+P63(x102361,f333(f333(f7(x102361,f917(f916(x102361,x102361),a905),f917(x102361,a905)),f333(f333(f8(f917(x102361,f917(f917(f916(x102361,x102361),a905),a905)),f917(f917(f916(x102361,x102361),a905),f917(x102361,a905)),x102361),f7(x102361,f917(f916(x102361,x102361),a905),a905)),f333(f333(f8(f917(x102361,f916(x102361,x102361)),f917(x102361,f917(f917(f916(x102361,x102361),a905),a905)),x102361),f333(f8(f916(x102361,x102361),f917(f917(f916(x102361,x102361),a905),a905),x102361),f335(f916(x102361,x102361)))),f265(x102361,x102361)))),x102362)) % 173.51/173.27 [10237]~P11(x102371,f254(f917(x102371,a905)),x102372)+P10(x102371,f333(f333(f7(x102371,f917(f916(x102371,x102371),a905),f917(x102371,a905)),f333(f333(f8(f917(x102371,f917(f917(f916(x102371,x102371),a905),a905)),f917(f917(f916(x102371,x102371),a905),f917(x102371,a905)),x102371),f7(x102371,f917(f916(x102371,x102371),a905),a905)),f333(f333(f8(f917(x102371,f916(x102371,x102371)),f917(x102371,f917(f917(f916(x102371,x102371),a905),a905)),x102371),f333(f8(f916(x102371,x102371),f917(f917(f916(x102371,x102371),a905),a905),x102371),f335(f916(x102371,x102371)))),f265(x102371,x102371)))),x102372)) % 173.51/173.27 [10275]P40(x102751,x102752)+~P63(x102751,f333(f333(f7(x102751,f917(f916(x102751,x102751),a905),f917(x102751,a905)),f333(f333(f8(f917(x102751,f917(f917(f916(x102751,x102751),a905),a905)),f917(f917(f916(x102751,x102751),a905),f917(x102751,a905)),x102751),f7(x102751,f917(f916(x102751,x102751),a905),a905)),f333(f333(f8(f917(x102751,f916(x102751,x102751)),f917(x102751,f917(f917(f916(x102751,x102751),a905),a905)),x102751),f333(f8(f916(x102751,x102751),f917(f917(f916(x102751,x102751),a905),a905),x102751),f335(f916(x102751,x102751)))),f265(x102751,x102751)))),x102752)) % 173.51/173.27 [10276]P11(x102761,f254(f917(x102761,a905)),x102762)+~P10(x102761,f333(f333(f7(x102761,f917(f916(x102761,x102761),a905),f917(x102761,a905)),f333(f333(f8(f917(x102761,f917(f917(f916(x102761,x102761),a905),a905)),f917(f917(f916(x102761,x102761),a905),f917(x102761,a905)),x102761),f7(x102761,f917(f916(x102761,x102761),a905),a905)),f333(f333(f8(f917(x102761,f916(x102761,x102761)),f917(x102761,f917(f917(f916(x102761,x102761),a905),a905)),x102761),f333(f8(f916(x102761,x102761),f917(f917(f916(x102761,x102761),a905),a905),x102761),f335(f916(x102761,x102761)))),f265(x102761,x102761)))),x102762)) % 173.51/173.27 [7383]E(f333(f333(f87(a910),f333(f114(a910),f333(f333(f23(a1),x73831),a108))),x73832),f333(a123,f333(f333(f87(a910),f333(f114(a910),x73831)),x73832)))+P106(f333(a201,f333(f114(a1),x73831))) % 173.51/173.27 [7819]~P95(x78191)+E(f333(f333(f87(x78191),f333(f333(f87(x78191),f85(x78191)),f333(f114(x78191),x78192))),f333(f114(x78191),x78192)),f333(f114(x78191),f333(f333(f23(a1),f333(f333(f87(a1),x78192),x78192)),a108))) % 173.51/173.27 [8470]~P106(f333(f333(f246(a1),x84701),x84702))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x84701),x84701)),f333(f333(f23(a1),f333(f333(f87(a1),x84702),x84702)),a108))) % 173.51/173.27 [8472]~P106(f333(f333(f246(a1),x84721),x84722))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x84721),x84721)),f333(f333(f23(a1),f333(f333(f87(a1),x84722),x84722)),a108))) % 173.51/173.27 [8911]P106(f333(f333(f246(a1),x89111),x89112))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),x89111),x89111)),f333(f333(f23(a1),f333(f333(f87(a1),x89112),x89112)),a108))) % 173.51/173.27 [8913]P106(f333(f333(f246(a1),x89131),x89132))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),x89131),x89131)),f333(f333(f23(a1),f333(f333(f87(a1),x89132),x89132)),a108))) % 173.51/173.27 [9221]~P106(f333(f333(f246(a1),x92211),x92212))+P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92211),x92211)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),x92212),x92212)),a108))) % 173.51/173.27 [9223]~P106(f333(f333(f247(a1),x92231),x92232))+P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x92231),x92231)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),x92232),x92232)),a108))) % 173.51/173.27 [9498]P106(f333(f333(f246(a1),x94981),x94982))+~P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),x94981),x94981)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),x94982),x94982)),a108))) % 173.51/173.27 [9500]P106(f333(f333(f247(a1),x95001),x95002))+~P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),x95001),x95001)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),x95002),x95002)),a108))) % 173.51/173.27 [9533]~P106(f333(f67(x95331),x95332))+P106(f333(f67(f917(x95331,a905)),f333(f252(f917(x95331,a905)),f333(f333(f7(f917(x95331,a905),f917(x95331,a905),a905),f246(f917(x95331,a905))),x95332)))) % 173.51/173.27 [9583]~E(f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),x95831),f196(f917(f916(a910,a910),a905)))),f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),x95832),f196(f917(f916(a910,a910),a905)))))+P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),x95831),x95832)),a119)) % 173.51/173.27 [9672]E(f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),x96721),f196(f917(f916(a910,a910),a905)))),f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),x96722),f196(f917(f916(a910,a910),a905)))))+~P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),x96721),x96722)),a119)) % 173.51/173.27 [9716]P106(f333(f333(f246(a1),f2(a1)),f687(x97161,x97162)))+E(f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x97161)),f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x97162))) % 173.51/173.27 [10220]~P8(x102201)+E(f44(x102201,f333(f252(x102201),f333(f333(f8(f917(x102201,a905),a905,x102201),f95(x102201)),f333(f333(f8(f917(x102201,a905),f917(x102201,a905),x102201),f333(f18(x102201,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102201),a336),f333(f333(f7(x102201,f917(x102201,a905),a905),f335(x102201)),x102202)))),f333(f7(x102201,x102201,a905),f246(x102201)))))),f43(x102201,x102202)) % 173.51/173.27 [10242]P106(f333(f333(f335(a910),f2(a910)),x102421))+E(f333(f41(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,f917(a910,a905),a905),f333(f333(f8(a910,f917(f917(a910,a905),a905),a910),f335(a910)),a123)),x102421))),f333(f333(f7(a910,a910,a905),f247(a910)),x102422)))),f333(f41(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,f917(a910,a905),a905),f335(a910)),x102421))),f333(f333(f7(a910,a910,a905),f247(a910)),f333(a123,x102422)))))) % 173.51/173.27 [7688]~P95(x76881)+E(f333(f333(f88(x76881),x76882),f333(f114(x76881),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),x76882) % 173.51/173.27 [7952]~P95(x79521)+E(f333(f333(f87(x79521),f333(f114(x79521),x79522)),f85(x79521)),f333(f114(x79521),f333(f333(f87(a1),x79522),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))) % 173.51/173.27 [8097]P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x80972)))+E(f333(f333(f256(a1),x80971),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),x80972),x80972)),a108))),f85(a1)) % 173.51/173.27 [9558]~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x95582)))+E(f333(f333(f256(a1),x95581),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),x95582),x95582)),a108))),f333(f333(f93(a1,a1),f333(f333(f256(a1),x95581),f333(f114(a910),x95582))),f333(f333(f18(a1,a1,a1),f333(f333(f8(a1,f917(a1,a1),a1),f88(a1)),f333(f88(a1),x95581))),f5(a1)))) % 173.51/173.27 [9940]~P106(f333(f333(f246(a910),f698(x99402,x99401)),f333(x99401,f698(x99402,x99401))))+P106(f333(f67(a910),f333(f252(a910),f333(f333(f7(a910,a910,a905),f333(f333(f8(a910,f917(a910,a905),a910),f246(a910)),x99401)),x99402)))) % 173.51/173.27 [10080]~P106(f333(f333(f246(a910),f333(f114(a910),x100801)),f333(a123,x100802)))+P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x100801),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),f246(a910)),a115)),x100802)))) % 173.51/173.27 [10081]~P106(f333(f333(f247(a910),f333(f114(a910),x100811)),f333(a123,x100812)))+P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x100811),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),f247(a910)),a115)),x100812)))) % 173.51/173.27 [10132]P106(f333(f333(f246(a910),f333(f114(a910),x101321)),f333(a123,x101322)))+~P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x101321),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),f246(a910)),a115)),x101322)))) % 173.51/173.27 [10133]P106(f333(f333(f247(a910),f333(f114(a910),x101331)),f333(a123,x101332)))+~P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x101331),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),f247(a910)),a115)),x101332)))) % 173.51/173.27 [10163]~P106(f333(f333(f246(a910),f333(a123,x101632)),f333(f114(a910),x101631)))+P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x101631),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f8(a910,a905,a1),f333(f246(a910),x101632)),a115))))) % 173.51/173.27 [10164]~P106(f333(f333(f247(a910),f333(a123,x101642)),f333(f114(a910),x101641)))+P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x101641),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f8(a910,a905,a1),f333(f247(a910),x101642)),a115))))) % 173.51/173.27 [10208]P106(f333(f333(f246(a910),f333(a123,x102081)),f333(f114(a910),x102082)))+~P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x102082),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f8(a910,a905,a1),f333(f246(a910),x102081)),a115))))) % 173.51/173.27 [10209]P106(f333(f333(f247(a910),f333(a123,x102091)),f333(f114(a910),x102092)))+~P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x102092),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f8(a910,a905,a1),f333(f247(a910),x102091)),a115))))) % 173.51/173.27 [10285]~P106(f333(f333(f335(a910),f2(a910)),x102851))+E(f333(a123,f333(f41(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,f917(a910,a905),a905),f333(f333(f8(a910,f917(f917(a910,a905),a905),a910),f335(a910)),a123)),x102851))),f333(f333(f7(a910,a910,a905),f247(a910)),x102852))))),f333(f41(a910),f333(f252(a910),f333(f333(f18(a910,a905,a905),f333(f333(f8(a905,f917(a905,a905),a910),a331),f333(f333(f7(a910,f917(a910,a905),a905),f335(a910)),x102851))),f333(f333(f7(a910,a910,a905),f247(a910)),f333(a123,x102852)))))) % 173.51/173.27 [8654]~P95(x86541)+E(f333(f333(f88(x86541),f333(f114(x86541),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),x86542),x86542) % 173.51/173.27 [8714]~P95(x87141)+E(f333(f333(f87(x87141),f85(x87141)),f333(f114(x87141),x87142)),f333(f114(x87141),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),x87142))) % 173.51/173.27 [8778]~P95(x87781)+E(f333(f333(f23(x87781),f333(f114(x87781),x87782)),f85(x87781)),f333(f114(x87781),f333(f333(f87(a1),x87782),f333(f86(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.27 [8930]~P106(f333(f333(f247(a910),f333(f114(a910),a90)),x89302))+E(f333(f333(f23(a910),x89301),f333(f333(f23(a910),x89302),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f23(a910),f333(a123,x89301)),x89302)) % 173.51/173.27 [9601]~P117(x96011)+E(f333(f333(f88(x96011),x96012),x96012),f333(f333(f256(x96011),x96012),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.27 [9602]~P83(x96021)+E(f333(f333(f256(x96021),x96022),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f88(x96021),x96022),x96022)) % 173.51/173.27 [9604]~P95(x96041)+E(f333(f333(f88(x96041),x96042),f333(f114(x96041),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f87(x96041),x96042),x96042)) % 173.51/173.27 [9857]~P139(x98571)+E(f333(f333(f256(x98571),f333(f86(x98571),x98572)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f256(x98571),x98572),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.27 [9858]~P120(x98581)+E(f333(f333(f256(x98581),f333(f82(x98581),x98582)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f256(x98581),x98582),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.27 [9854]~P95(x98541)+E(f333(f333(f88(x98541),f333(f114(x98541),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x98542),f333(f333(f87(x98541),x98542),x98542)) % 173.51/173.27 [9972]~P120(x99721)+E(f333(f82(x99721),f333(f333(f256(x99721),x99722),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x99721),x99722),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.27 [10036]~P120(x100361)+P106(f333(f333(f246(x100361),f2(x100361)),f333(f333(f256(x100361),x100362),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.27 [10199]~E(f333(a123,x101992),f333(f114(a910),x101991))+P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x101991),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),a330),a115)),x101992))))) % 173.51/173.27 [10200]~E(f333(f114(a910),x102001),f333(a123,x102002))+P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x102001),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),a330),a115)),x102002))))) % 173.51/173.27 [10245]E(f333(a123,x102451),f333(f114(a910),x102452))+~P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x102452),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),a330),a115)),x102451))))) % 173.51/173.27 [10246]E(f333(f114(a910),x102461),f333(a123,x102462))+~P106(f333(f333(f93(a1,a905),f333(f114(a1),f333(f333(f87(a1),x102461),a108))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a336),f333(f333(f8(a905,a905,a1),a328),a201))),f333(f333(f7(a1,a910,a905),f333(f333(f8(a910,f917(a910,a905),a1),a330),a115)),x102462))))) % 173.51/173.27 [10032]~P95(x100321)+E(f333(f333(f256(x100321),f333(f114(x100321),a108)),f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x100322)),f85(x100321)) % 173.51/173.27 [10033]~P139(x100331)+E(f333(f333(f256(x100331),f333(f86(x100331),f85(x100331))),f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x100332)),f85(x100331)) % 173.51/173.27 [10038]~P83(x100381)+E(f333(f333(f256(x100381),x100382),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),a108))),f333(f333(f88(x100381),f333(f333(f88(x100381),x100382),x100382)),x100382)) % 173.51/173.27 [10224]~P106(f333(f333(f246(a1),f2(a1)),x102242))+E(f51(a1,f333(f333(f87(a1),f85(a1)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102241)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102242)),f333(f333(f87(a1),f85(a1)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f51(a1,x102241,x102242)))) % 173.51/173.27 [10248]~P106(f333(f333(f246(a1),f2(a1)),x102482))+E(f333(f333(f42(a1),f333(f333(f87(a1),f85(a1)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102481))),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102482)),f333(f333(f42(a1),x102481),x102482)) % 173.51/173.27 [10250]~P106(f333(f333(f246(a1),x102502),f2(a1)))+E(f333(f333(f42(a1),f333(f333(f87(a1),f85(a1)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102501))),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102502)),f333(f333(f42(a1),f333(f333(f87(a1),x102501),f85(a1))),x102502)) % 173.51/173.27 [10251]~P106(f333(f333(f246(a1),x102512),f2(a1)))+E(f51(a1,f333(f333(f87(a1),f85(a1)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102511)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102512)),f333(f333(f23(a1),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f51(a1,f333(f333(f87(a1),x102511),f85(a1)),x102512))),f85(a1))) % 173.51/173.27 [10123]~P95(x101231)+E(f333(f333(f256(x101231),f333(f114(x101231),a108)),f333(a123,f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101232))),f333(f114(x101231),a108)) % 173.51/173.27 [10125]~P139(x101251)+E(f333(f333(f256(x101251),f333(f86(x101251),f85(x101251))),f333(a123,f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101252))),f333(f86(x101251),f85(x101251))) % 173.51/173.27 [5089]P41(x50891,x50892)+~P11(x50891,x50893,x50892) % 173.51/173.27 [5091]P55(x50911,x50912)+~P11(x50911,x50913,x50912) % 173.51/173.27 [5258]~P26(x52581,x52582,x52583)+P31(x52581,x52582,x52583) % 173.51/173.27 [5260]~P11(x52601,x52602,x52603)+P56(x52601,x52602,x52603) % 173.51/173.27 [8169]~E(x81692,x81693)+P37(x81691,x81691,a330,x81692,x81693) % 173.51/173.27 [8727]E(x87271,x87272)+~P37(x87273,x87273,a330,x87271,x87272) % 173.51/173.27 [4896]E(f177(x48961,x48962,x48963),f124(x48961))+~E(x48962,f2(a910)) % 173.51/173.27 [5065]~E(f177(x50652,x50651,x50653),f124(x50652))+E(x50651,f2(a910)) % 173.51/173.27 [5264]~P40(x52641,x52643)+P40(x52641,f327(x52641,x52642,x52643)) % 173.51/173.27 [5374]~P33(x53741,x53742,x53743)+P34(a1,x53741,f186(x53742,x53743)) % 173.51/173.27 [5429]P32(x54291,x54292,x54293)+~P32(x54291,f333(a123,x54292),x54293) % 173.51/173.27 [5447]P33(x54471,x54472,x54473)+~P34(a1,x54471,f186(x54472,x54473)) % 173.51/173.27 [5514]~P11(x55141,x55142,x55143)+P11(f911(x55141),f169(x55141,x55142),f166(x55141,x55143)) % 173.51/173.27 [5515]~P56(x55151,x55152,x55153)+P56(f911(x55151),f169(x55151,x55152),f166(x55151,x55153)) % 173.51/173.27 [5624]P59(x56241,x56242,x56243)+~E(f573(x56243,x56242,x56241),f574(x56243,x56242,x56241)) % 173.51/173.27 [5625]P58(x56251,x56252,x56253)+~E(f616(x56253,x56252,x56251),f617(x56253,x56252,x56251)) % 173.51/173.27 [6560]P31(x65601,x65602,x65603)+~P32(x65601,f525(x65603,x65602,x65601),f537(x65603,x65602,x65601)) % 173.51/173.27 [8175]~E(x81752,x81753)+P28(x81751,x81751,f33(x81751),x81752,x81753) % 173.51/173.27 [8735]E(x87351,x87352)+~P28(x87353,x87353,f33(x87353),x87351,x87352) % 173.51/173.27 [4851]~E(f333(f176(x48512),x48511),x48513)+E(x48511,f333(f176(x48512),x48513)) % 173.51/173.27 [4852]~E(x48522,f333(f176(x48521),x48523))+E(f333(f176(x48521),x48522),x48523) % 173.51/173.27 [4902]E(x49021,x49022)+~E(f333(f176(x49023),x49021),f333(f176(x49023),x49022)) % 173.51/173.27 [5115]~P46(x51153,x51151)+P106(f333(f333(x51151,x51152),x51152)) % 173.51/173.27 [5116]~P10(x51163,x51161)+P106(f333(f333(x51161,x51162),x51162)) % 173.51/173.27 [5118]~P63(x51181,x51182)+P106(f333(f321(x51181,x51182),x51183)) % 173.51/173.27 [5181]~P40(x51811,x51812)+P40(f911(x51811),f333(f151(x51811,x51812),x51813)) % 173.51/173.27 [5186]~P106(f333(x51862,x51863))+~E(f333(f252(x51861),x51862),f196(f917(x51861,a905))) % 173.51/173.27 [5187]~P106(f333(x51872,x51873))+~E(f196(f917(x51871,a905)),f333(f252(x51871),x51872)) % 173.51/173.27 [5199]E(x51991,f2(a910))+E(f152(x51992,f177(x51992,x51991,x51993)),x51993) % 173.51/173.27 [5217]~P106(f333(x52171,x52173))+P106(f333(x52171,f97(x52172,x52171))) % 173.51/173.27 [5218]~P106(f333(x52181,x52183))+P106(f333(x52181,f783(x52181,x52182))) % 173.51/173.27 [5230]E(x52301,f2(a910))+E(f333(f149(x52302),f177(x52302,x52301,x52303)),x52303) % 173.51/173.27 [5337]~E(x53372,x53373)+P106(f333(f333(f335(x53371),x53372),f333(a330,x53373))) % 173.51/173.27 [5352]P106(f333(x53521,x53522))+~P106(f333(x53521,f846(x53521,x53523))) % 173.51/173.27 [5353]~E(x53532,f2(a910))+E(f333(f180(x53531),f177(x53531,x53532,x53533)),f196(f917(x53531,a905))) % 173.51/173.27 [5396]E(f333(f176(x53961),x53962),f333(f333(f159(x53961),x53963),f124(x53961)))+~E(x53962,f333(f333(f159(x53961),x53963),f124(x53961))) % 173.51/173.27 [5397]~E(x53973,f333(f333(f159(x53971),x53972),f124(x53971)))+E(f333(f333(f159(x53971),x53972),f124(x53971)),f333(f176(x53971),x53973)) % 173.51/173.27 [5443]~P36(x54431,x54432,x54433)+P36(x54431,x54432,f333(f176(x54431),x54433)) % 173.51/173.27 [5444]~P34(x54441,x54442,x54443)+P34(x54441,x54442,f333(f176(x54441),x54443)) % 173.51/173.27 [5448]E(f333(f41(x54481),f339(x54482,x54483,x54481)),x54482)+~E(f333(f41(x54481),x54483),f333(a123,x54482)) % 173.51/173.27 [5454]~P40(x54541,x54543)+P106(f333(f333(f335(x54541),x54542),f322(x54541,x54543))) % 173.51/173.27 [5458]~E(f333(f176(x54582),x54581),f333(f333(f159(x54582),x54583),f124(x54582)))+E(x54581,f333(f333(f159(x54582),x54583),f124(x54582))) % 173.51/173.27 [5459]~E(f333(f333(f159(x54592),x54593),f124(x54592)),f333(f176(x54592),x54591))+E(x54591,f333(f333(f159(x54592),x54593),f124(x54592))) % 173.51/173.27 [5480]E(f92(f916(a910,a910),f54(x54801,x54802)),x54803)+~P106(f333(f54(x54801,x54802),x54803)) % 173.51/173.27 [5518]P36(x55181,x55182,x55183)+~P36(x55181,x55182,f333(f176(x55181),x55183)) % 173.51/173.27 [5519]P34(x55191,x55192,x55193)+~P34(x55191,x55192,f333(f176(x55191),x55193)) % 173.51/173.27 [5578]~E(x55782,f124(x55781))+P106(f333(f333(f335(f911(x55781)),x55782),f169(x55781,x55783))) % 173.51/173.27 [5587]~P56(x55871,x55872,x55873)+P56(x55871,x55872,f333(f293(x55871,x55871),x55873)) % 173.51/173.27 [5588]~P59(x55881,x55882,x55883)+P59(x55881,x55882,f333(f293(x55881,x55881),x55883)) % 173.51/173.27 [5605]~P64(x56051)+E(f51(x56051,f51(x56051,x56052,x56053),x56053),f51(x56051,x56052,x56053)) % 173.51/173.27 [5703]E(x57031,x57032)+~P106(f333(f333(f335(x57033),x57031),f333(a330,x57032))) % 173.51/173.27 [5749]~P107(x57491)+E(f198(x57491,x57492,f2(a910),x57493),x57493) % 173.51/173.27 [5769]P56(x57691,x57692,x57693)+~P56(x57691,x57692,f333(f293(x57691,x57691),x57693)) % 173.51/173.27 [5770]P59(x57701,x57702,x57703)+~P59(x57701,x57702,f333(f293(x57701,x57701),x57703)) % 173.51/173.27 [5774]~P110(x57742)+E(f158(x57741,x57742,x57743,f124(x57741)),f124(x57741)) % 173.51/173.27 [5786]E(f178(x57861,x57862,f160(x57861,x57863)),f160(x57861,f178(x57861,x57862,x57863)))+~P106(f333(f145(x57861),x57863)) % 173.51/173.27 [5886]E(f333(f144(x58861,x58862),x58863),f124(x58861))+P106(f333(x58862,f736(x58863,x58862,x58861))) % 173.51/173.27 [5944]E(f74(x59441,x59442,x59443),x59442)+P106(f333(x59443,f784(x59442,x59441,x59443))) % 173.51/173.27 [6031]~P106(f333(f145(x60311),x60312))+P106(f333(f145(x60311),f184(x60311,x60312,x60313))) % 173.51/173.27 [6032]~P106(f333(f145(x60321),x60323))+P106(f333(f145(x60321),f178(x60321,x60322,x60323))) % 173.51/173.27 [6033]~P106(f333(f145(x60331),x60333))+P106(f333(f145(x60331),f185(x60331,x60332,x60333))) % 173.51/173.27 [6034]~P106(f333(f145(x60341),x60343))+P106(f333(f145(x60341),f148(x60341,x60342,x60343))) % 173.51/173.27 [6035]~P146(x60351,x60352,x60353)+P106(f333(x60351,f51(a1,x60352,x60353))) % 173.51/173.27 [6051]~P36(x60513,x60511,x60512)+P106(f333(x60511,f785(x60512,x60511,x60513))) % 173.51/173.27 [6052]~P38(x60523,x60521,x60522)+P106(f333(x60521,f800(x60522,x60521,x60523))) % 173.51/173.27 [6053]~P38(x60533,x60531,x60532)+P106(f333(x60531,f812(x60532,x60531,x60533))) % 173.51/173.27 [6054]~P36(x60543,x60541,x60542)+P106(f333(x60541,f839(x60542,x60541,x60543))) % 173.51/173.27 [6055]~P36(x60553,x60551,x60552)+P106(f333(x60551,f841(x60551,x60552,x60553))) % 173.51/173.27 [6074]E(f333(f144(x60741,x60742),x60743),f185(x60741,x60742,x60743))+P106(f333(x60742,f769(x60743,x60742,x60741))) % 173.51/173.27 [6116]~P106(f333(f145(x61161),x61163))+P106(f333(f145(f911(x61161)),f61(x61161,x61162,x61163))) % 173.51/173.27 [6150]~P112(x61501)+E(f333(f333(f112(f917(x61501,a905)),f333(f289(x61501),x61502)),f309(x61501,x61502,x61503)),f196(f917(x61501,a905))) % 173.51/173.27 [6151]~P112(x61511)+E(f333(f333(f112(f917(x61511,a905)),f333(f307(x61511),x61512)),f311(x61511,x61512,x61513)),f196(f917(x61511,a905))) % 173.51/173.27 [6152]~P112(x61521)+E(f333(f333(f112(f917(x61521,a905)),f333(f307(x61521),x61522)),f312(x61521,x61522,x61523)),f196(f917(x61521,a905))) % 173.51/173.27 [6377]E(f333(f144(x63771,x63772),x63773),x63773)+~P106(f333(x63772,f751(x63773,x63772,x63771))) % 173.51/173.27 [6379]E(f333(f333(f315(x63791),f355(x63792,x63793,x63791)),f339(x63792,x63793,x63791)),x63793)+~E(f333(f41(x63791),x63793),f333(a123,x63792)) % 173.51/173.27 [6395]P146(x63951,x63952,x63953)+~P106(f333(x63951,f51(a1,x63952,x63953))) % 173.51/173.27 [6444]P34(x64441,x64442,x64443)+~P106(f333(x64442,f801(x64443,x64442,x64441))) % 173.51/173.27 [6445]P34(x64451,x64452,x64453)+~P106(f333(x64452,f810(x64452,x64453,x64451))) % 173.51/173.27 [6446]P34(x64461,x64462,x64463)+~P106(f333(x64462,f811(x64463,x64462,x64461))) % 173.51/173.27 [6447]P33(x64471,x64472,x64473)+~P106(f333(x64471,f824(x64473,x64472,x64471))) % 173.51/173.27 [6449]E(f185(x64491,x64492,x64493),x64493)+~P106(f333(x64492,f764(x64493,x64492,x64491))) % 173.51/173.27 [6528]~P106(f333(x65282,f737(x65283,x65282,x65281)))+P106(f333(f260(x65281,x65282),x65283)) % 173.51/173.27 [6529]~P106(f333(x65292,f738(x65293,x65292,x65291)))+P106(f333(f168(x65291,x65292),x65293)) % 173.51/173.27 [6777]~P106(f333(f321(x67771,x67772),f548(x67773,x67772,x67771)))+P106(f333(f321(x67771,x67772),x67773)) % 173.51/173.27 [6778]~P106(f333(f321(x67781,x67782),f551(x67783,x67782,x67781)))+P106(f333(f321(x67781,x67782),x67783)) % 173.51/173.27 [7384]~P64(x73841)+E(f333(f333(f87(x73841),f333(f333(f88(x73841),x73842),f333(f333(f42(x73841),x73843),x73842))),f51(x73841,x73843,x73842)),x73843) % 173.51/173.27 [7413]P33(x74131,x74132,x74133)+P106(f333(f333(f335(a1),f824(x74133,x74132,x74131)),f309(a1,x74132,x74133))) % 173.51/173.27 [7841]E(f333(f333(f265(x78411,x78411),f560(x78412,x78413,x78411)),f560(x78412,x78413,x78411)),x78413)+~P106(f333(f333(f335(f916(x78411,x78411)),x78413),f253(x78411,x78412))) % 173.51/173.27 [7960]~P106(f333(f333(f335(x79601),f586(x79603,x79602,x79601)),f322(x79601,x79603)))+P106(f333(f333(f335(x79601),x79602),f322(x79601,x79603))) % 173.51/173.27 [7961]~P106(f333(f333(f335(x79611),f645(x79613,x79612,x79611)),f322(x79611,x79613)))+P106(f333(f333(f335(x79611),x79612),f322(x79611,x79613))) % 173.51/173.27 [7962]~P106(f333(f333(f335(x79621),f646(x79623,x79622,x79621)),f322(x79621,x79623)))+P106(f333(f333(f335(x79621),x79622),f322(x79621,x79623))) % 173.51/173.27 [8055]P36(a1,x80551,f186(x80552,x80553))+P33(f333(f79(a905,a905,a1,a328),x80551),x80552,x80553) % 173.51/173.27 [8150]~P64(x81501)+E(f333(f333(f87(x81501),f333(f333(f88(x81501),f333(f333(f42(x81501),x81502),x81503)),x81503)),f51(x81501,x81502,x81503)),x81502) % 173.51/173.27 [8196]~E(f333(f41(x81961),x81962),f333(a123,x81963))+~P106(f333(f333(f335(x81961),f355(x81963,x81962,x81961)),f339(x81963,x81962,x81961))) % 173.51/173.27 [8646]~P36(a1,x86461,f186(x86462,x86463))+~P33(f333(f79(a905,a905,a1,a328),x86461),x86462,x86463) % 173.51/173.27 [8833]P106(f333(f333(f246(f917(f916(x88331,x88331),a905)),f313(x88331,x88332)),f313(x88331,x88333)))+~P106(f333(f333(f246(f917(f916(x88331,x88331),a905)),x88332),f313(x88331,x88333))) % 173.51/173.27 [9127]E(x91271,f124(x91272))+~P106(f333(f333(f335(f916(f911(x91272),f911(x91272))),f333(f333(f265(f911(x91272),f911(x91272)),x91271),f124(x91272))),f166(x91272,x91273))) % 173.51/173.27 [9154]E(x91541,f124(x91542))+~P106(f333(f333(f335(f916(f911(x91542),f911(x91542))),f333(f333(f265(f911(x91542),f911(x91542)),f124(x91542)),x91541)),f166(x91542,x91543))) % 173.51/173.27 [9283]E(f333(f333(f159(x92831),f734(x92832,x92833,x92831)),f735(x92832,x92833,x92831)),x92833)+~P106(f333(f333(f335(f916(f911(x92831),f911(x92831))),f333(f333(f265(f911(x92831),f911(x92831)),f124(x92831)),x92833)),f155(x92831,x92832))) % 173.51/173.27 [9526]~P127(x95261)+~P106(f333(f333(f247(x95261),f333(f333(f87(x95261),f333(f333(f88(x95261),x95262),x95262)),f333(f333(f88(x95261),x95263),x95263))),f2(x95261))) % 173.51/173.27 [9576]P106(f333(f67(x95761),x95762))+~P106(f333(f333(f335(f916(f917(x95761,a905),f917(x95761,a905))),f333(f333(f265(f917(x95761,a905),f917(x95761,a905)),x95763),x95762)),f320(x95761))) % 173.51/173.27 [9882]~P50(x98821,x98822,x98823)+P106(f333(f333(f246(a1),f333(f333(f79(f916(a1,a1),a1,x98821,f264(a1,a1)),f224(x98821)),f242(x98821,x98822,f239(x98821,x98823)))),f2(a1))) % 173.51/173.27 [9883]~P51(x98831,x98832,x98833)+P106(f333(f333(f247(a1),f333(f333(f79(f916(a1,a1),a1,x98831,f264(a1,a1)),f224(x98831)),f242(x98831,x98832,f239(x98831,x98833)))),f2(a1))) % 173.51/173.27 [10001]P51(x100011,x100012,x100013)+~P106(f333(f333(f247(a1),f333(f333(f79(f916(a1,a1),a1,x100011,f264(a1,a1)),f224(x100011)),f242(x100011,x100012,f239(x100011,x100013)))),f2(a1))) % 173.51/173.27 [10002]P50(x100021,x100022,x100023)+~P106(f333(f333(f246(a1),f333(f333(f79(f916(a1,a1),a1,x100021,f264(a1,a1)),f224(x100021)),f242(x100021,x100022,f239(x100021,x100023)))),f2(a1))) % 173.51/173.27 [10339]~P120(x103391)+~P106(f333(f333(f247(x103391),f333(f333(f87(x103391),f333(f333(f256(x103391),x103392),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x103391),x103393),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f2(x103391))) % 173.51/173.27 [4881]~E(x48813,f124(x48811))+E(f333(f333(f142(x48811),x48812),x48813),x48812) % 173.51/173.27 [4882]~E(x48822,f124(x48821))+E(f333(f333(f142(x48821),x48822),x48823),x48823) % 173.51/173.27 [4888]~E(x48882,f2(a910))+E(f333(f333(f183(x48881),x48882),x48883),f124(x48881)) % 173.51/173.27 [4897]~E(x48973,f124(x48971))+E(f333(f333(f183(x48971),x48972),x48973),f124(x48971)) % 173.51/173.27 [4936]~E(x49361,x49363)+E(x49361,f333(f333(f142(x49362),f124(x49362)),x49363)) % 173.51/173.27 [5028]~P1(x50282)+E(f333(f196(f917(x50281,x50282)),x50283),f196(x50282)) % 173.51/173.27 [5029]~P108(x50292)+E(f333(f254(f917(x50291,x50292)),x50293),f254(x50292)) % 173.51/173.27 [5047]E(x50471,f124(x50472))+~E(f333(f333(f142(x50472),x50473),x50471),x50473) % 173.51/173.27 [5048]E(x50481,f124(x50482))+~E(f333(f333(f142(x50482),x50481),x50483),x50483) % 173.51/173.27 [5056]E(x50561,f124(x50562))+~E(f333(f333(f142(x50562),x50563),x50561),f124(x50562)) % 173.51/173.27 [5057]E(x50571,f124(x50572))+~E(f333(f333(f142(x50572),x50571),x50573),f124(x50572)) % 173.51/173.27 [5082]~E(x50822,f2(a910))+E(f333(f333(f88(a910),x50821),x50822),f333(f333(f88(a910),x50823),x50822)) % 173.51/173.27 [5084]~E(x50841,f2(a910))+E(f333(f333(f88(a910),x50841),x50842),f333(f333(f88(a910),x50841),x50843)) % 173.51/173.27 [5140]~P2(x51401)+E(f333(f333(f121(x51401),x51402),x51403),f333(f333(f121(x51401),x51403),x51402)) % 173.51/173.27 [5142]~P101(x51421)+E(f333(f333(f121(x51421),x51422),x51423),f333(f333(f121(x51421),x51423),x51422)) % 173.51/173.27 [5143]~P2(x51431)+E(f333(f333(f112(x51431),x51432),x51433),f333(f333(f112(x51431),x51433),x51432)) % 173.51/173.27 [5145]~P102(x51451)+E(f333(f333(f112(x51451),x51452),x51453),f333(f333(f112(x51451),x51453),x51452)) % 173.51/173.27 [5146]~P117(x51461)+E(f333(f333(f87(x51461),x51462),x51463),f333(f333(f87(x51461),x51463),x51462)) % 173.51/173.27 [5147]~P117(x51471)+E(f333(f333(f88(x51471),x51472),x51473),f333(f333(f88(x51471),x51473),x51472)) % 173.51/173.27 [5149]~P110(x51491)+E(f333(f333(f244(x51491),x51492),x51493),f333(f333(f244(x51491),x51493),x51492)) % 173.51/173.27 [5151]~P110(x51511)+E(f333(f333(f245(x51511),x51512),x51513),f333(f333(f245(x51511),x51513),x51512)) % 173.51/173.27 [5212]E(f51(a910,x52121,x52122),f2(a910))+~E(x52121,f333(f333(f88(a910),x52122),x52123)) % 173.51/173.27 [5213]E(f51(a1,x52131,x52132),f2(a1))+~E(x52131,f333(f333(f88(a1),x52132),x52133)) % 173.51/173.27 [5276]E(x52761,x52762)+~E(f333(f333(f87(a910),x52763),x52761),f333(f333(f87(a910),x52763),x52762)) % 173.51/173.27 [5277]E(x52771,x52772)+~E(f333(f333(f87(a910),x52771),x52773),f333(f333(f87(a910),x52772),x52773)) % 173.51/173.27 [5287]~P84(x52871)+E(f333(f333(f112(x52871),x52872),f333(f86(x52871),x52873)),f333(f333(f23(x52871),x52872),x52873)) % 173.51/173.27 [5288]~P6(x52881)+E(f333(f333(f87(x52881),x52882),f333(f86(x52881),x52883)),f333(f333(f23(x52881),x52882),x52883)) % 173.51/173.27 [5289]~P71(x52891)+E(f333(f333(f87(x52891),x52892),f333(f86(x52891),x52893)),f333(f333(f23(x52891),x52892),x52893)) % 173.51/173.27 [5290]~P114(x52901)+E(f333(f333(f87(x52901),x52902),f333(f86(x52901),x52903)),f333(f333(f23(x52901),x52902),x52903)) % 173.51/173.27 [5291]~P71(x52911)+E(f333(f333(f23(x52911),x52912),f333(f86(x52911),x52913)),f333(f333(f87(x52911),x52912),x52913)) % 173.51/173.27 [5331]~P106(f333(x53313,x53312))+P106(f333(f333(f335(x53311),x53312),x53313)) % 173.51/173.27 [5333]~P72(x53332)+E(f333(f333(f6(x53331,x53332),x53333),f196(f917(x53331,a905))),f2(x53332)) % 173.51/173.27 [5335]~P78(x53352)+E(f333(f333(f9(x53351,x53352),x53353),f196(f917(x53351,a905))),f85(x53352)) % 173.51/173.27 [5386]~E(x53862,f333(f333(f87(a910),x53861),x53863))+P106(f333(f333(f246(a910),x53861),x53862)) % 173.51/173.27 [5389]~E(x53892,f196(f917(x53891,a905)))+E(f333(f333(f66(x53891),x53892),x53893),f196(f917(f917(x53891,a905),a905))) % 173.51/173.27 [5390]~E(x53902,f196(f917(x53901,a905)))+E(f196(f917(f917(x53901,a905),a905)),f333(f333(f66(x53901),x53902),x53903)) % 173.51/173.27 [5462]~E(f333(f291(x54622,x54623),x54621),f196(f917(x54623,a905)))+E(x54621,f196(f917(f916(x54622,x54623),a905))) % 173.51/173.27 [5463]~E(f333(f263(x54632,x54633),x54631),f196(f917(x54632,a905)))+E(x54631,f196(f917(f916(x54632,x54633),a905))) % 173.51/173.27 [5493]E(f333(f291(x54931,x54932),x54933),f196(f917(x54932,a905)))+~E(x54933,f196(f917(f916(x54931,x54932),a905))) % 173.51/173.27 [5494]E(f333(f263(x54941,x54942),x54943),f196(f917(x54941,a905)))+~E(x54943,f196(f917(f916(x54941,x54942),a905))) % 173.51/173.27 [5497]E(f281(x54971,x54972,x54973),f333(f333(f23(a110),x54972),x54973))+P106(f333(f333(f247(a110),x54972),x54973)) % 173.51/173.27 [5512]P106(f333(x55121,x55122))+~P106(f333(f333(f335(x55123),x55122),x55121)) % 173.51/173.27 [5550]E(x55501,x55502)+~E(f333(f86(f917(x55503,a905)),x55501),f333(f86(f917(x55503,a905)),x55502)) % 173.51/173.27 [5559]~E(x55591,f196(f917(x55592,a905)))+~P106(f333(f333(f335(x55592),x55593),x55591)) % 173.51/173.27 [5589]~E(x55892,f333(f333(f87(a1),x55891),f333(f111(a1),x55893)))+P106(f333(f333(f246(a1),x55891),x55892)) % 173.51/173.27 [5603]E(f333(f333(f315(x56031),x56032),x56033),x56033)+~P106(f333(f333(f335(x56031),x56032),x56033)) % 173.51/173.27 [5614]E(x56141,f196(f917(x56142,a905)))+~E(f333(f333(f66(x56142),x56141),x56143),f196(f917(f917(x56142,a905),a905))) % 173.51/173.27 [5615]E(x56151,f196(f917(x56152,a905)))+~E(f196(f917(f917(x56152,a905),a905)),f333(f333(f66(x56152),x56151),x56153)) % 173.51/173.27 [5621]~P113(x56211)+E(f333(f333(f88(x56211),f333(f86(x56211),x56212)),f333(f86(x56211),x56213)),f333(f333(f88(x56211),x56212),x56213)) % 173.51/173.27 [5623]~P67(x56231)+E(f333(f333(f296(x56231),f333(f86(x56231),x56232)),f333(f86(x56231),x56233)),f333(f333(f296(x56231),x56232),x56233)) % 173.51/173.27 [5655]~P106(f333(x56553,x56552))+P106(f333(f333(f335(x56551),x56552),f333(f252(x56551),x56553))) % 173.51/173.27 [5677]E(x56771,f2(a910))+E(f333(f180(x56772),f177(x56772,x56771,x56773)),f333(f333(f315(x56772),x56773),f196(f917(x56772,a905)))) % 173.51/173.27 [5696]E(f178(x56961,x56962,x56963),x56963)+P106(f333(f333(f335(x56961),x56962),f333(f180(x56961),x56963))) % 173.51/173.27 [5778]~P106(f333(f145(x57781),x57783))+P106(f333(f145(x57781),f333(f144(x57781,x57782),x57783))) % 173.51/173.27 [5821]~P64(x58211)+E(f333(f333(f42(x58211),f51(x58211,x58212,x58213)),x58213),f2(x58211)) % 173.51/173.27 [5840]E(f184(x58401,f333(f333(f159(x58401),x58402),f124(x58401)),x58403),f124(x58401))+P106(f333(f333(f335(a910),f2(a910)),x58403)) % 173.51/173.27 [5846]E(x58461,f2(a910))+E(f333(f179(x58462),f177(x58462,x58461,x58463)),f177(x58462,f333(f333(f23(a910),x58461),f85(a910)),x58463)) % 173.51/173.27 [5896]E(f333(f333(f159(x58961),x58962),x58963),f148(x58961,x58962,x58963))+P106(f333(f333(f335(x58961),x58962),f333(f180(x58961),x58963))) % 173.51/173.27 [5905]E(x59051,x59052)+~E(f333(f333(f88(a910),f333(a123,x59053)),x59051),f333(f333(f88(a910),f333(a123,x59053)),x59052)) % 173.51/173.27 [5906]~E(x59062,f333(f333(f87(a1),x59061),f333(f111(a1),f333(a123,x59063))))+P106(f333(f333(f247(a1),x59061),x59062)) % 173.51/173.27 [6013]~E(x60133,f124(x60131))+E(f333(f333(f333(f191(f911(x60131),f911(x60131)),x60132),f175(x60131)),x60133),f124(x60131)) % 173.51/173.27 [6017]P106(f333(x60171,x60172))+~P106(f333(f333(f335(x60173),x60172),f333(f252(x60173),x60171))) % 173.51/173.27 [6046]E(x60461,x60462)+~E(f333(f333(f315(x60463),x60461),f196(f917(x60463,a905))),f333(f333(f315(x60463),x60462),f196(f917(x60463,a905)))) % 173.51/173.27 [6060]~P112(x60601)+E(f333(f333(f112(f917(x60601,a905)),f333(f289(x60601),x60602)),f333(f308(x60601,x60602),x60603)),f196(f917(x60601,a905))) % 173.51/173.27 [6100]E(f148(x61001,x61002,x61003),x61003)+~P106(f333(f333(f335(x61001),x61002),f333(f180(x61001),x61003))) % 173.51/173.27 [6124]~P4(x61241)+E(f333(f316(x61241,x61241,f86(x61241)),f333(f308(x61241,x61242),x61243)),f311(x61241,f333(f86(x61241),x61243),f333(f86(x61241),x61242))) % 173.51/173.27 [6135]E(f333(f197(f911(x61351)),f178(x61351,x61352,x61353)),f333(f197(f911(x61351)),x61353))+P106(f333(f333(f335(x61351),x61352),f333(f180(x61351),x61353))) % 173.51/173.27 [6188]~P112(x61881)+E(f333(f333(f112(f917(x61881,a905)),f333(f308(x61881,x61882),x61883)),f333(f290(x61881),x61883)),f196(f917(x61881,a905))) % 173.51/173.27 [6208]~P4(x62081)+E(f333(f316(x62081,x62081,f86(x62081)),f309(x62081,x62082,x62083)),f309(x62081,f333(f86(x62081),x62083),f333(f86(x62081),x62082))) % 173.51/173.27 [6209]~P4(x62091)+E(f333(f316(x62091,x62091,f86(x62091)),f312(x62091,x62092,x62093)),f312(x62091,f333(f86(x62091),x62093),f333(f86(x62091),x62092))) % 173.51/173.27 [6271]E(f184(x62711,f333(f333(f159(x62711),x62712),f124(x62711)),x62713),f333(f333(f159(x62711),x62712),f124(x62711)))+~P106(f333(f333(f335(a910),f2(a910)),x62713)) % 173.51/173.27 [6278]~P4(x62781)+E(f333(f316(x62781,x62781,f86(x62781)),f311(x62781,x62782,x62783)),f333(f308(x62781,f333(f86(x62781),x62783)),f333(f86(x62781),x62782))) % 173.51/173.27 [6298]~P65(x62981)+E(f51(x62981,f333(f86(x62981),f51(x62981,x62982,x62983)),x62983),f51(x62981,f333(f86(x62981),x62982),x62983)) % 173.51/173.27 [6392]~P106(f333(f67(f916(x63922,x63921)),x63923))+P106(f333(f67(x63921),f333(f291(x63922,x63921),x63923))) % 173.51/173.27 [6393]~P106(f333(f67(f916(x63931,x63932)),x63933))+P106(f333(f67(x63931),f333(f263(x63931,x63932),x63933))) % 173.51/173.27 [6399]~P112(x63991)+E(f333(f333(f112(f917(x63991,a905)),f309(x63991,x63992,x63993)),f333(f310(x63991),x63993)),f196(f917(x63991,a905))) % 173.51/173.27 [6400]~P112(x64001)+E(f333(f333(f112(f917(x64001,a905)),f311(x64001,x64002,x64003)),f333(f310(x64001),x64003)),f196(f917(x64001,a905))) % 173.51/173.27 [6401]~P112(x64011)+E(f333(f333(f112(f917(x64011,a905)),f312(x64011,x64012,x64013)),f333(f290(x64011),x64013)),f196(f917(x64011,a905))) % 173.51/173.27 [6469]E(f333(f333(f172(x64691),x64692),f683(x64692,x64693,x64691)),x64693)+~P106(f333(f333(f335(x64691),x64693),f333(f180(x64691),x64692))) % 173.51/173.27 [6611]E(x66111,f124(x66112))+~E(f333(f333(f333(f191(f911(x66112),f911(x66112)),x66113),f175(x66112)),x66111),f124(x66112)) % 173.51/173.27 [6716]~P106(f333(f67(f916(x67162,x67161)),x67163))+P106(f333(f67(f916(x67161,x67162)),f333(f293(x67162,x67161),x67163))) % 173.51/173.27 [6863]P59(x68631,x68632,x68633)+P106(f333(f333(f335(x68631),f574(x68633,x68632,x68631)),x68632)) % 173.51/173.27 [6864]P59(x68641,x68642,x68643)+P106(f333(f333(f335(x68641),f573(x68643,x68642,x68641)),x68642)) % 173.51/173.27 [6875]P106(f333(f321(x68751,x68752),x68753))+P106(f333(f333(x68752,f548(x68753,x68752,x68751)),x68753)) % 173.51/173.27 [6876]P106(f333(f321(x68761,x68762),x68763))+P106(f333(f333(x68762,f551(x68763,x68762,x68761)),x68763)) % 173.51/173.27 [6907]E(f333(f197(f911(x69071)),f178(x69071,x69072,x69073)),f333(f333(f23(a910),f333(f197(f911(x69071)),x69073)),f85(a910)))+~P106(f333(f333(f335(x69071),x69072),f333(f180(x69071),x69073))) % 173.51/173.27 [6946]P106(f333(f260(x69461,x69462),x69463))+P106(f333(f333(f335(x69461),f737(x69463,x69462,x69461)),x69463)) % 173.51/173.27 [6955]~P106(f333(f67(f916(x69552,x69551)),f333(f293(x69551,x69552),x69553)))+P106(f333(f67(f916(x69551,x69552)),x69553)) % 173.51/173.27 [7010]~P106(f333(f333(f335(x70101),x70102),f333(f180(x70101),f125(x70101,x70103))))+P106(f333(f333(f335(x70101),x70102),f333(f180(x70101),x70103))) % 173.51/173.27 [7015]P31(x70151,x70152,x70153)+P106(f333(f333(f335(f909(x70151)),f537(x70153,x70152,x70151)),x70153)) % 173.51/173.27 [7046]E(f333(f144(x70461,x70462),x70463),x70463)+P106(f333(f333(f335(x70461),f751(x70463,x70462,x70461)),f333(f180(x70461),x70463))) % 173.51/173.27 [7060]E(f333(f144(x70601,x70602),x70603),f124(x70601))+P106(f333(f333(f335(x70601),f736(x70603,x70602,x70601)),f333(f180(x70601),x70603))) % 173.51/173.27 [7083]P34(x70831,x70832,x70833)+P106(f333(f333(f335(x70831),f801(x70833,x70832,x70831)),f333(f180(x70831),x70833))) % 173.51/173.27 [7084]P34(x70841,x70842,x70843)+P106(f333(f333(f335(x70841),f811(x70843,x70842,x70841)),f333(f180(x70841),x70843))) % 173.51/173.27 [7085]P34(x70851,x70852,x70853)+P106(f333(f333(f335(x70851),f810(x70852,x70853,x70851)),f333(f180(x70851),x70853))) % 173.51/173.27 [7088]E(f185(x70881,x70882,x70883),x70883)+P106(f333(f333(f335(x70881),f764(x70883,x70882,x70881)),f333(f180(x70881),x70883))) % 173.51/173.27 [7165]P106(f333(f168(x71651,x71652),x71653))+P106(f333(f333(f335(x71651),f738(x71653,x71652,x71651)),f333(f180(x71651),x71653))) % 173.51/173.27 [7174]~P36(x71741,x71743,x71742)+P106(f333(f333(f335(x71741),f785(x71742,x71743,x71741)),f333(f180(x71741),x71742))) % 173.51/173.27 [7175]~P38(x71751,x71753,x71752)+P106(f333(f333(f335(x71751),f800(x71752,x71753,x71751)),f333(f180(x71751),x71752))) % 173.51/173.27 [7176]~P38(x71761,x71763,x71762)+P106(f333(f333(f335(x71761),f812(x71762,x71763,x71761)),f333(f180(x71761),x71762))) % 173.51/173.27 [7177]~P36(x71771,x71773,x71772)+P106(f333(f333(f335(x71771),f839(x71772,x71773,x71771)),f333(f180(x71771),x71772))) % 173.51/173.27 [7178]~P36(x71781,x71782,x71783)+P106(f333(f333(f335(x71781),f841(x71782,x71783,x71781)),f333(f180(x71781),x71783))) % 173.51/173.27 [7212]P106(f333(f333(f335(x72121),x72122),f685(x72123,x72122,x72121)))+~P106(f333(f333(f335(x72121),x72122),f43(f917(x72121,a905),x72123))) % 173.51/173.27 [7213]~P72(x72131)+E(f333(f333(f87(x72131),f333(f333(f6(a910,x72131),x72132),f333(f289(a910),x72133))),f333(x72132,x72133)),f333(f333(f6(a910,x72131),x72132),f333(f289(a910),f333(a123,x72133)))) % 173.51/173.27 [7302]~P36(x73022,x73021,x73023)+P106(f333(x73021,f333(f333(f172(x73022),x73023),f797(x73023,x73021,x73022)))) % 173.51/173.27 [7315]~P106(f333(f333(f335(x73151),x73152),f671(x73152,x73153,x73151)))+P106(f333(f333(f335(x73151),x73152),f44(f917(x73151,a905),x73153))) % 173.51/173.27 [7348]~P72(x73481)+E(f333(f333(f87(x73481),f333(f333(f6(a910,x73481),x73482),f333(f307(a910),x73483))),f333(x73482,f333(a123,x73483))),f333(f333(f6(a910,x73481),x73482),f333(f307(a910),f333(a123,x73483)))) % 173.51/173.27 [7485]P106(f333(f333(f335(f911(x74851)),x74852),f169(x74851,x74853)))+P106(f333(f333(f335(x74851),f703(x74853,x74852,x74851)),f333(f180(x74851),x74852))) % 173.51/173.27 [7500]~P106(f333(f333(f335(f911(x75001)),x75002),f169(x75001,f322(x75001,x75003))))+P106(f333(f333(f335(f911(x75001)),x75002),f322(f911(x75001),f165(x75001,x75003)))) % 173.51/173.27 [7525]~P106(f333(f333(f335(f911(x75251)),x75252),f322(f911(x75251),f165(x75251,x75253))))+P106(f333(f333(f335(f911(x75251)),x75252),f169(x75251,f322(x75251,x75253)))) % 173.51/173.27 [7558]E(f333(f333(f333(f191(f911(x75581),f911(x75581)),x75582),f175(x75581)),x75583),x75583)+~P106(f333(f333(f246(a910),f333(f197(f911(x75581)),x75583)),f85(a910))) % 173.51/173.27 [7592]E(f333(f333(f142(x75921),f804(x75922,x75923,x75921)),f333(f333(f159(x75921),x75923),f805(x75922,x75923,x75921))),x75922)+~P106(f333(f333(f335(x75921),x75923),f333(f180(x75921),x75922))) % 173.51/173.27 [7593]E(f333(f333(f142(x75931),f798(x75932,x75933,x75931)),f333(f333(f159(x75931),x75933),f799(x75932,x75933,x75931))),x75932)+~P106(f333(f333(f335(x75931),x75933),f333(f180(x75931),x75932))) % 173.51/173.27 [7594]E(f333(f333(f142(x75941),f806(x75942,x75943,x75941)),f333(f333(f159(x75941),x75943),f807(x75942,x75943,x75941))),x75942)+~P106(f333(f333(f335(x75941),x75943),f333(f180(x75941),x75942))) % 173.51/173.27 [7616]~P27(x76161,x76162,x76163,f254(f917(x76161,a905)))+P27(f911(x76161),f911(x76162),f333(f162(x76161,x76162),x76163),f254(f917(f911(x76161),a905))) % 173.51/173.27 [7762]E(x77621,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),x77622)),x77623)),f333(f268(a910,a910),x77622)))+~P106(f333(f54(x77621,x77623),x77622)) % 173.51/173.27 [7770]P27(x77701,x77702,x77703,f254(f917(x77701,a905)))+~P27(f911(x77701),f911(x77702),f333(f162(x77701,x77702),x77703),f254(f917(f911(x77701),a905))) % 173.51/173.27 [7809]~P106(f333(f333(f202(x78091),x78092),x78093))+P106(f333(f333(f333(f333(a204,x78091),x78092),f389(x78093,x78092,x78091)),x78093)) % 173.51/173.27 [7810]~P106(f333(f333(f202(x78101),x78102),x78103))+P106(f333(f333(f333(f333(a204,x78101),x78102),f515(x78103,x78102,x78101)),x78103)) % 173.51/173.27 [7815]P106(f333(f333(f335(f917(x78151,a905)),f671(x78152,x78153,x78151)),x78153))+P106(f333(f333(f335(x78151),x78152),f44(f917(x78151,a905),x78153))) % 173.51/173.27 [7908]P106(f333(f333(f335(f911(x79081)),x79082),f169(x79081,x79083)))+~P106(f333(f333(f335(x79081),f703(x79083,x79082,x79081)),x79083)) % 173.51/173.27 [8009]P34(x80091,x80092,x80093)+~P106(f333(x80092,f333(f333(f172(x80091),x80093),f803(x80093,x80092,x80091)))) % 173.51/173.27 [8034]E(x80341,x80342)+~E(f333(f333(f7(x80343,f917(x80343,a905),a905),f335(x80343)),x80341),f333(f333(f7(x80343,f917(x80343,a905),a905),f335(x80343)),x80342)) % 173.51/173.27 [8042]~P106(f333(f333(f335(f916(x80421,x80421)),x80423),f253(x80421,x80422)))+P106(f333(f333(f335(x80421),f560(x80422,x80423,x80421)),x80422)) % 173.51/173.27 [8044]~P106(f333(f333(f335(x80441),x80443),f43(f917(x80441,a905),x80442)))+P106(f333(f333(f335(f917(x80441,a905)),f685(x80442,x80443,x80441)),x80442)) % 173.51/173.27 [8170]P27(x81701,x81702,f99(x81702,x81701,f254(f917(x81702,a905)),x81703),f254(f917(x81701,a905)))+~E(f333(f316(x81702,x81701,x81703),f254(f917(x81702,a905))),f254(f917(x81701,a905))) % 173.51/173.27 [8225]~P106(f333(f333(f335(x82251),x82252),f333(f180(x82251),f798(x82253,x82252,x82251))))+~P106(f333(f333(f335(x82251),x82252),f333(f180(x82251),x82253))) % 173.51/173.27 [8226]~P106(f333(f333(f335(x82261),x82262),f333(f180(x82261),f807(x82263,x82262,x82261))))+~P106(f333(f333(f335(x82261),x82262),f333(f180(x82261),x82263))) % 173.51/173.27 [8414]E(x84141,f124(x84142))+P106(f333(f333(f335(x84142),f333(f264(x84142,f916(a110,a110)),f333(f282(x84142,x84141),x84143))),f333(f180(x84142),x84141))) % 173.51/173.27 [8511]~P75(x85111)+E(f333(f150(x85111,x85111,f333(f7(x85111,x85111,x85111),f87(x85111)),x85112),f333(f176(x85111),x85113)),f333(f150(x85111,x85111,f87(x85111),x85112),x85113)) % 173.51/173.27 [8715]~P27(x87152,x87151,x87153,f254(f917(x87152,a905)))+E(f333(f316(x87151,x87152,f99(x87152,x87151,f254(f917(x87152,a905)),x87153)),f254(f917(x87151,a905))),f254(f917(x87152,a905))) % 173.51/173.27 [9033]~P110(x90331)+E(f333(f180(x90331),f157(x90331,x90331,f5(x90331),x90332,x90333)),f333(f333(f315(x90331),x90332),f333(f180(x90331),x90333))) % 173.51/173.27 [9044]~E(f333(x90443,f333(f99(x90441,x90442,f254(f917(x90441,a905)),x90443),f872(x90443,x90442,x90441))),f872(x90443,x90442,x90441))+E(f333(f316(x90441,x90442,x90443),f254(f917(x90441,a905))),f254(f917(x90442,a905))) % 173.51/173.27 [9046]P106(f333(f333(f247(a910),f2(a910)),f619(x90461,x90462,x90463)))+~P106(f333(f333(f335(f916(x90463,x90463)),x90462),f333(f333(f295(x90463,x90463,x90463),x90461),f313(x90463,x90461)))) % 173.51/173.27 [9340]~P61(x93401,x93402)+~P106(f333(f333(f335(f916(x93401,x93401)),f333(f333(f265(x93401,x93401),x93403),x93403)),f333(f333(f295(x93401,x93401,x93401),x93402),f313(x93401,x93402)))) % 173.51/173.27 [9481]~E(f333(f333(f112(f917(f916(x94811,x94811),a905)),f333(f293(x94811,x94811),x94812)),f313(x94811,x94812)),f196(f917(f916(x94811,x94811),a905)))+~P106(f333(f333(f335(f916(x94811,x94811)),f333(f333(f265(x94811,x94811),x94813),x94813)),f333(f333(f295(x94811,x94811,x94811),x94812),f313(x94811,x94812)))) % 173.51/173.27 [9664]~P106(f333(f67(x96641),x96642))+P106(f333(f333(f246(a910),f333(f41(x96641),f333(f333(f23(f917(x96641,a905)),x96642),f333(f333(f315(x96641),x96643),f196(f917(x96641,a905)))))),f333(f41(x96641),x96642))) % 173.51/173.27 [5201]~E(x52013,f124(x52011))+E(f152(x52011,f333(f333(f159(x52011),x52012),x52013)),x52012) % 173.51/173.27 [5209]~E(x52093,f124(x52091))+E(f125(x52091,f333(f333(f159(x52091),x52092),x52093)),f124(x52091)) % 173.51/173.27 [5239]E(x52391,f124(x52392))+E(f152(x52392,f333(f333(f159(x52392),x52393),x52391)),f152(x52392,x52391)) % 173.51/173.27 [5241]E(x52411,f124(x52412))+E(f152(x52412,f333(f333(f142(x52412),x52413),x52411)),f152(x52412,x52411)) % 173.51/173.27 [5246]~E(x52463,f124(x52461))+E(f125(x52461,f333(f333(f142(x52461),x52462),x52463)),f125(x52461,x52462)) % 173.51/173.27 [5248]~E(x52483,f124(x52481))+E(f152(x52481,f333(f333(f142(x52481),x52482),x52483)),f152(x52481,x52482)) % 173.51/173.27 [5281]E(x52811,f124(x52812))+E(f333(f149(x52812),f333(f333(f142(x52812),x52811),x52813)),f333(f149(x52812),x52811)) % 173.51/173.27 [5311]~E(x53112,f124(x53111))+E(f333(f149(x53111),f333(f333(f142(x53111),x53112),x53113)),f333(f149(x53111),x53113)) % 173.51/173.27 [5363]~P2(x53631)+E(f333(f333(f121(x53631),x53632),f333(f333(f112(x53631),x53632),x53633)),x53632) % 173.51/173.27 [5364]~P2(x53641)+E(f333(f333(f112(x53641),x53642),f333(f333(f121(x53641),x53642),x53643)),x53642) % 173.51/173.27 [5365]~P110(x53651)+E(f333(f333(f244(x53651),x53652),f333(f333(f245(x53651),x53652),x53653)),x53652) % 173.51/173.27 [5366]~P110(x53661)+E(f333(f333(f245(x53661),x53662),f333(f333(f244(x53661),x53662),x53663)),x53662) % 173.51/173.27 [5384]~P64(x53841)+E(f51(x53841,f333(f333(f88(x53841),x53842),x53843),x53843),f2(x53841)) % 173.51/173.27 [5385]~P64(x53851)+E(f51(x53851,f333(f333(f88(x53851),x53852),x53853),x53852),f2(x53851)) % 173.51/173.27 [5457]~P6(x54571)+E(f333(f86(x54571),f333(f333(f23(x54571),x54572),x54573)),f333(f333(f23(x54571),x54573),x54572)) % 173.51/173.27 [5516]E(x55161,f124(x55162))+E(f125(x55162,f333(f333(f159(x55162),x55163),x55161)),f333(f333(f159(x55162),x55163),f125(x55162,x55161))) % 173.51/173.27 [5517]E(x55171,f124(x55172))+E(f125(x55172,f333(f333(f142(x55172),x55173),x55171)),f333(f333(f142(x55172),x55173),f125(x55172,x55171))) % 173.51/173.27 [5520]~P8(x55201)+E(f44(x55201,f333(f333(f315(x55201),x55202),x55203)),f333(f333(f112(x55201),x55202),f44(x55201,x55203))) % 173.51/173.27 [5521]~P8(x55211)+E(f43(x55211,f333(f333(f315(x55211),x55212),x55213)),f333(f333(f121(x55211),x55212),f43(x55211,x55213))) % 173.51/173.27 [5564]~P2(x55641)+E(f333(f333(f121(x55641),x55642),f333(f333(f121(x55641),x55642),x55643)),f333(f333(f121(x55641),x55642),x55643)) % 173.51/173.27 [5566]~P101(x55661)+E(f333(f333(f121(x55661),x55662),f333(f333(f121(x55661),x55662),x55663)),f333(f333(f121(x55661),x55662),x55663)) % 173.51/173.27 [5567]~P2(x55671)+E(f333(f333(f112(x55671),x55672),f333(f333(f112(x55671),x55672),x55673)),f333(f333(f112(x55671),x55672),x55673)) % 173.51/173.27 [5569]~P102(x55691)+E(f333(f333(f112(x55691),x55692),f333(f333(f112(x55691),x55692),x55693)),f333(f333(f112(x55691),x55692),x55693)) % 173.51/173.27 [5570]~P97(x55701)+E(f333(f333(f88(x55701),x55702),f333(f333(f88(x55701),x55702),x55703)),f333(f333(f88(x55701),x55702),x55703)) % 173.51/173.27 [5572]~P110(x55721)+E(f333(f333(f244(x55721),x55722),f333(f333(f244(x55721),x55722),x55723)),f333(f333(f244(x55721),x55722),x55723)) % 173.51/173.27 [5574]~P110(x55741)+E(f333(f333(f245(x55741),x55742),f333(f333(f245(x55741),x55742),x55743)),f333(f333(f245(x55741),x55742),x55743)) % 173.51/173.27 [5581]~P64(x55811)+E(f51(x55811,f333(f333(f87(x55811),x55812),x55813),x55813),f51(x55811,x55812,x55813)) % 173.51/173.27 [5582]~P64(x55821)+E(f51(x55821,f333(f333(f87(x55821),x55822),x55823),x55822),f51(x55821,x55823,x55822)) % 173.51/173.27 [5590]~P113(x55901)+E(f333(f333(f88(x55901),x55902),f333(f86(x55901),x55903)),f333(f86(x55901),f333(f333(f88(x55901),x55902),x55903))) % 173.51/173.27 [5591]~P67(x55911)+E(f333(f333(f296(x55911),x55912),f333(f86(x55911),x55913)),f333(f86(x55911),f333(f333(f296(x55911),x55912),x55913))) % 173.51/173.27 [5592]~P82(x55921)+E(f333(f333(f87(x55921),x55922),f333(f173(x55921),x55923)),f333(f173(x55921),f333(f333(f159(x55921),x55922),x55923))) % 173.51/173.27 [5620]~P113(x56201)+E(f333(f333(f88(x56201),f333(f86(x56201),x56202)),x56203),f333(f333(f88(x56201),x56202),f333(f86(x56201),x56203))) % 173.51/173.27 [5626]~P11(x56261,x56262,x56263)+E(f43(f917(x56261,a905),f333(f333(f66(x56261),x56262),x56263)),x56262) % 173.51/173.27 [5688]~P115(x56881)+E(f333(f333(f88(x56881),x56882),f333(f333(f256(x56881),x56882),x56883)),f333(f333(f256(x56881),x56882),f333(a123,x56883))) % 173.51/173.27 [5689]~P117(x56891)+E(f333(f333(f88(x56891),x56892),f333(f333(f256(x56891),x56892),x56893)),f333(f333(f256(x56891),x56892),f333(a123,x56893))) % 173.51/173.27 [5699]~P71(x56991)+E(f333(f333(f87(x56991),f333(f86(x56991),x56992)),f333(f333(f87(x56991),x56992),x56993)),x56993) % 173.51/173.27 [5722]~P107(x57221)+E(f333(f333(f256(x57221),f333(f111(x57221),x57222)),x57223),f333(f111(x57221),f333(f333(f256(a910),x57222),x57223))) % 173.51/173.27 [5723]~P139(x57231)+E(f333(f333(f256(x57231),f333(f113(x57231),x57232)),x57233),f333(f113(x57231),f333(f333(f256(a1),x57232),x57233))) % 173.51/173.27 [5729]~P87(x57291)+E(f333(f82(x57291),f333(f333(f23(x57291),x57292),x57293)),f333(f82(x57291),f333(f333(f23(x57291),x57293),x57292))) % 173.51/173.27 [5731]~P120(x57311)+E(f333(f333(f88(x57311),f89(x57311,x57312)),f89(x57311,x57313)),f89(x57311,f333(f333(f88(x57311),x57312),x57313))) % 173.51/173.27 [5735]E(x57351,f124(x57352))+E(f333(f333(f142(x57352),f333(f179(x57352),x57351)),x57353),f333(f179(x57352),f333(f333(f142(x57352),x57351),x57353))) % 173.51/173.27 [5740]~E(x57402,f333(a123,f333(f333(f87(a910),x57401),x57403)))+P106(f333(f333(f247(a910),x57401),x57402)) % 173.51/173.27 [5741]~P113(x57411)+E(f333(f333(f88(x57411),f333(f86(x57411),x57412)),x57413),f333(f86(x57411),f333(f333(f88(x57411),x57412),x57413))) % 173.51/173.27 [5742]~P122(x57421)+E(f333(f333(f296(x57421),f333(f86(x57421),x57422)),x57423),f333(f86(x57421),f333(f333(f296(x57421),x57422),x57423))) % 173.51/173.27 [5743]~P120(x57431)+E(f333(f333(f256(x57431),f333(f82(x57431),x57432)),x57433),f333(f82(x57431),f333(f333(f256(x57431),x57432),x57433))) % 173.51/173.27 [5839]E(f768(x58391,x58392,x58393),f774(x58391,x58392,x58393))+E(f333(f333(f112(f917(x58393,a905)),x58392),x58391),f196(f917(x58393,a905))) % 173.51/173.27 [5854]~P72(x58542)+E(f333(f333(f6(x58541,x58542),f333(f16(x58542,x58541),f2(x58542))),x58543),f2(x58542)) % 173.51/173.27 [5855]~P78(x58552)+E(f333(f333(f9(x58551,x58552),f333(f16(x58552,x58551),f85(x58552))),x58553),f85(x58552)) % 173.51/173.27 [5857]~P107(x58571)+E(f333(f333(f87(x58571),f333(f111(x58571),x58572)),f333(f111(x58571),x58573)),f333(f111(x58571),f333(f333(f87(a910),x58572),x58573))) % 173.51/173.27 [5858]~P107(x58581)+E(f333(f333(f88(x58581),f333(f111(x58581),x58582)),f333(f111(x58581),x58583)),f333(f111(x58581),f333(f333(f88(a910),x58582),x58583))) % 173.51/173.27 [5859]~P139(x58591)+E(f333(f333(f23(x58591),f333(f113(x58591),x58592)),f333(f113(x58591),x58593)),f333(f113(x58591),f333(f333(f23(a1),x58592),x58593))) % 173.51/173.27 [5860]~P139(x58601)+E(f333(f333(f87(x58601),f333(f113(x58601),x58602)),f333(f113(x58601),x58603)),f333(f113(x58601),f333(f333(f87(a1),x58602),x58603))) % 173.51/173.27 [5861]~P139(x58611)+E(f333(f333(f88(x58611),f333(f113(x58611),x58612)),f333(f113(x58611),x58613)),f333(f113(x58611),f333(f333(f88(a1),x58612),x58613))) % 173.51/173.27 [5862]~P95(x58621)+E(f333(f333(f23(x58621),f333(f114(x58621),x58622)),f333(f114(x58621),x58623)),f333(f114(x58621),f333(f333(f23(a1),x58622),x58623))) % 173.51/173.27 [5865]~P95(x58651)+E(f333(f333(f87(x58651),f333(f114(x58651),x58652)),f333(f114(x58651),x58653)),f333(f114(x58651),f333(f333(f87(a1),x58652),x58653))) % 173.51/173.27 [5866]~P95(x58661)+E(f333(f333(f88(x58661),f333(f114(x58661),x58662)),f333(f114(x58661),x58663)),f333(f114(x58661),f333(f333(f88(a1),x58662),x58663))) % 173.51/173.27 [5913]~E(x59133,x59132)+P106(f333(f333(f246(f917(x59131,a905)),x59132),x59133)) % 173.51/173.27 [5919]~E(x59192,x59193)+P106(f333(f333(f246(f917(x59191,a905)),x59192),x59193)) % 173.51/173.27 [5924]~P84(x59241)+E(f333(f333(f112(x59241),f333(f86(x59241),x59242)),f333(f86(x59241),x59243)),f333(f86(x59241),f333(f333(f121(x59241),x59242),x59243))) % 173.51/173.27 [5925]~P84(x59251)+E(f333(f333(f121(x59251),f333(f86(x59251),x59252)),f333(f86(x59251),x59253)),f333(f86(x59251),f333(f333(f112(x59251),x59252),x59253))) % 173.51/173.27 [5926]~P71(x59261)+E(f333(f333(f87(x59261),f333(f86(x59261),x59262)),f333(f86(x59261),x59263)),f333(f86(x59261),f333(f333(f87(x59261),x59263),x59262))) % 173.51/173.27 [5927]~P6(x59271)+E(f333(f333(f87(x59271),f333(f86(x59271),x59272)),f333(f86(x59271),x59273)),f333(f86(x59271),f333(f333(f87(x59271),x59272),x59273))) % 173.51/173.27 [5928]~P80(x59281)+E(f333(f333(f245(x59281),f333(f86(x59281),x59282)),f333(f86(x59281),x59283)),f333(f86(x59281),f333(f333(f244(x59281),x59282),x59283))) % 173.51/173.27 [5929]~P80(x59291)+E(f333(f333(f244(x59291),f333(f86(x59291),x59292)),f333(f86(x59291),x59293)),f333(f86(x59291),f333(f333(f245(x59291),x59292),x59293))) % 173.51/173.27 [5930]~P120(x59301)+E(f333(f333(f88(x59301),f333(f82(x59301),x59302)),f333(f82(x59301),x59303)),f333(f82(x59301),f333(f333(f88(x59301),x59302),x59303))) % 173.51/173.27 [5931]~P69(x59311)+E(f333(f333(f296(x59311),f333(f82(x59311),x59312)),f333(f82(x59311),x59313)),f333(f82(x59311),f333(f333(f296(x59311),x59312),x59313))) % 173.51/173.27 [5932]~P82(x59321)+E(f333(f333(f87(x59321),f333(f173(x59321),x59322)),f333(f173(x59321),x59323)),f333(f173(x59321),f333(f333(f142(x59321),x59322),x59323))) % 173.51/173.27 [5933]E(x59331,f196(f917(x59332,a905)))+~E(f333(f333(f121(f917(x59332,a905)),x59333),x59331),f196(f917(x59332,a905))) % 173.51/173.27 [5934]E(x59341,f196(f917(x59342,a905)))+~E(f333(f333(f121(f917(x59342,a905)),x59341),x59343),f196(f917(x59342,a905))) % 173.51/173.27 [5935]~P147(x59351,x59352,x59353)+P106(f333(x59351,f333(f333(f42(a1),x59352),x59353))) % 173.51/173.27 [5987]~P106(f333(f67(x59871),x59873))+P106(f333(f67(x59871),f333(f333(f315(x59871),x59872),x59873))) % 173.51/173.27 [5988]~P106(f333(f145(x59881),x59883))+P106(f333(f145(x59881),f333(f333(f183(x59881),x59882),x59883))) % 173.51/173.27 [5989]~P106(f333(f145(x59891),x59893))+P106(f333(f145(x59891),f333(f333(f146(x59891),x59892),x59893))) % 173.51/173.27 [6018]~P2(x60181)+P106(f333(f333(f246(x60181),x60182),f333(f333(f121(x60181),x60183),x60182))) % 173.51/173.27 [6019]~P101(x60191)+P106(f333(f333(f246(x60191),x60192),f333(f333(f121(x60191),x60193),x60192))) % 173.51/173.27 [6020]~P2(x60201)+P106(f333(f333(f246(x60201),x60202),f333(f333(f121(x60201),x60202),x60203))) % 173.51/173.27 [6021]~P101(x60211)+P106(f333(f333(f246(x60211),x60212),f333(f333(f121(x60211),x60212),x60213))) % 173.51/173.27 [6022]~P110(x60221)+P106(f333(f333(f246(x60221),x60222),f333(f333(f245(x60221),x60223),x60222))) % 173.51/173.27 [6023]~P110(x60231)+P106(f333(f333(f246(x60231),x60232),f333(f333(f245(x60231),x60232),x60233))) % 173.51/173.27 [6036]~E(x60361,f2(a910))+E(f333(f333(f42(a910),f333(f333(f88(a910),x60361),x60362)),f333(f333(f88(a910),x60361),x60363)),f2(a910)) % 173.51/173.27 [6103]P106(f333(x61031,x61032))+P106(f333(f333(f202(f30(x61031,x61033)),x61032),x61032)) % 173.51/173.27 [6118]~P95(x61181)+E(f333(f333(f23(x61181),f333(f114(x61181),x61182)),f333(f114(x61181),x61183)),f333(f114(x61181),f333(f333(f87(a1),x61182),f333(f86(a1),x61183)))) % 173.51/173.27 [6175]E(x61751,f2(a910))+E(f333(f333(f42(a910),f333(f333(f88(a910),x61751),x61752)),f333(f333(f88(a910),x61751),x61753)),f333(f333(f42(a910),x61752),x61753)) % 173.51/173.27 [6206]E(f160(x62061,f333(f333(f159(x62061),x62062),x62063)),f333(f333(f159(x62061),x62062),f160(x62061,x62063)))+P106(f333(f333(f335(x62061),x62062),f333(f180(x62061),x62063))) % 173.51/173.27 [6241]P147(x62411,x62412,x62413)+~P106(f333(x62411,f333(f333(f42(a1),x62412),x62413))) % 173.51/173.27 [6311]E(x63111,f124(x63112))+E(f333(f333(f159(x63112),f333(f149(x63112),x63111)),f333(f333(f183(x63112),x63113),f333(f179(x63112),x63111))),f333(f333(f183(x63112),f333(a123,x63113)),x63111)) % 173.51/173.27 [6318]E(f333(f333(f23(f917(x63181,a905)),x63182),x63183),x63182)+~E(f333(f333(f112(f917(x63181,a905)),x63182),x63183),f196(f917(x63181,a905))) % 173.51/173.27 [6332]E(f160(x63321,f333(f333(f159(x63321),x63322),x63323)),f160(x63321,x63323))+~P106(f333(f333(f335(x63321),x63322),f333(f180(x63321),x63323))) % 173.51/173.27 [6362]~P106(f333(f333(f246(a910),x63621),x63623))+P106(f333(f333(f246(a910),x63621),f333(f333(f87(a910),x63622),x63623))) % 173.51/173.27 [6364]~P106(f333(f333(f246(a910),x63641),x63642))+P106(f333(f333(f246(a910),x63641),f333(f333(f87(a910),x63642),x63643))) % 173.51/173.27 [6366]~P106(f333(f333(f247(a910),x63661),x63663))+P106(f333(f333(f247(a910),x63661),f333(f333(f87(a910),x63662),x63663))) % 173.51/173.27 [6368]~P106(f333(f333(f247(a910),x63681),x63682))+P106(f333(f333(f247(a910),x63681),f333(f333(f87(a910),x63682),x63683))) % 173.51/173.27 [6407]P106(f333(f67(x64071),x64072))+~P106(f333(f67(x64071),f333(f333(f315(x64071),x64073),x64072))) % 173.51/173.27 [6408]P106(f333(f145(x64081),x64082))+~P106(f333(f145(x64081),f333(f333(f159(x64081),x64083),x64082))) % 173.51/173.27 [6409]P106(f333(f145(x64091),x64092))+~P106(f333(f145(x64091),f333(f333(f142(x64091),x64093),x64092))) % 173.51/173.27 [6410]P106(f333(f145(x64101),x64102))+~P106(f333(f145(x64101),f333(f333(f142(x64101),x64102),x64103))) % 173.51/173.27 [6459]~P117(x64591)+E(f333(f333(f87(x64591),x64592),f333(f333(f88(x64591),x64593),x64592)),f333(f333(f88(x64591),f333(f333(f87(x64591),x64593),f85(x64591))),x64592)) % 173.51/173.27 [6505]~E(x65051,x65052)+~P106(f333(f333(f247(f917(x65053,a905)),x65051),x65052)) % 173.51/173.27 [6551]P106(f333(f333(f335(x65511),x65512),x65513))+P106(f333(f333(f335(x65511),x65512),f333(f86(f917(x65511,a905)),x65513))) % 173.51/173.27 [6557]E(f152(x65571,f333(f333(f146(x65571),x65572),x65573)),f152(x65571,x65573))+~P106(f333(f333(f247(a910),x65572),f333(f197(f911(x65571)),x65573))) % 173.51/173.27 [6558]E(f333(f333(f183(x65581),x65582),f125(x65581,x65583)),f333(f333(f183(x65581),x65582),x65583))+~P106(f333(f333(f247(a910),x65582),f333(f197(f911(x65581)),x65583))) % 173.51/173.27 [6613]E(f333(f333(f333(f191(f911(x66131),f911(x66131)),x66132),f175(x66131)),x66133),x66133)+~E(f51(a910,x66132,f333(f197(f911(x66131)),x66133)),f2(a910)) % 173.51/173.27 [6620]~P11(x66201,x66203,x66202)+E(f333(f333(f295(x66201,x66201,x66201),f333(f293(x66201,x66201),x66202)),x66202),x66202) % 173.51/173.27 [6662]~E(f333(f333(f121(f917(x66621,a905)),x66622),x66623),x66623)+P106(f333(f333(f246(f917(x66621,a905)),x66622),x66623)) % 173.51/173.27 [6667]~P58(x66671,x66671,x66673)+P58(x66671,x66671,f333(f333(f191(f916(x66671,x66671),a905),x66672),x66673)) % 173.51/173.27 [6671]~P106(f333(f333(f335(x66711),x66713),f333(f180(x66711),x66712)))+P106(f333(f333(f247(a910),f2(a910)),f333(f197(f911(x66711)),x66712))) % 173.51/173.27 [6697]~P87(x66971)+E(f333(f82(x66971),f333(f333(f87(x66971),f333(f82(x66971),x66972)),f333(f82(x66971),x66973))),f333(f333(f87(x66971),f333(f82(x66971),x66972)),f333(f82(x66971),x66973))) % 173.51/173.27 [6709]E(f333(f333(f42(a910),f333(f333(f88(a910),x67091),x67092)),f333(f333(f88(a910),x67091),x67093)),f333(f333(f42(a910),x67092),x67093))+~P106(f333(f333(f247(a910),f2(a910)),x67091)) % 173.51/173.27 [6756]E(x67561,x67562)+~P106(f333(f333(f333(f333(a204,a25),x67561),x67563),x67562)) % 173.51/173.27 [6844]~P106(f333(f67(x68441),x68443))+E(f333(f333(f70(x68441,f917(x68441,a905),f315(x68441)),x68442),x68443),f333(f333(f121(f917(x68441,a905)),x68443),x68442)) % 173.51/173.27 [6900]E(f333(f333(f121(f917(x69001,a905)),x69002),x69003),x69002)+~P106(f333(f333(f246(f917(x69001,a905)),x69003),x69002)) % 173.51/173.27 [6902]E(f333(f333(f121(f917(x69021,a905)),x69022),x69023),x69023)+~P106(f333(f333(f246(f917(x69021,a905)),x69022),x69023)) % 173.51/173.27 [6903]E(f333(f333(f112(f917(x69031,a905)),x69032),x69033),x69033)+~P106(f333(f333(f246(f917(x69031,a905)),x69033),x69032)) % 173.51/173.27 [6904]E(f333(f333(f112(f917(x69041,a905)),x69042),x69043),x69042)+~P106(f333(f333(f246(f917(x69041,a905)),x69042),x69043)) % 173.51/173.27 [6953]~P106(f333(f145(x69531),x69532))+E(f333(f333(f23(f917(x69531,a905)),f333(f180(x69531),x69532)),f333(f333(f315(x69531),x69533),f196(f917(x69531,a905)))),f333(f180(x69531),f178(x69531,x69533,x69532))) % 173.51/173.27 [7005]P40(x70051,x70052)+~P40(x70051,f333(f333(f191(f916(x70051,x70051),a905),x70053),x70052)) % 173.51/173.27 [7071]P106(f333(f55(x70711,x70712),f333(a57,x70713)))+~P106(f333(f55(f333(f86(a1),x70711),f333(f86(a1),x70712)),x70713)) % 173.51/173.27 [7076]E(f333(f333(f23(f917(x70761,a905)),f333(f333(f315(x70761),x70762),x70763)),f333(f333(f315(x70761),x70762),f196(f917(x70761,a905)))),x70763)+P106(f333(f333(f335(x70761),x70762),x70763)) % 173.51/173.27 [7097]E(f333(f333(f112(f917(x70971,a905)),f333(f180(x70971),x70972)),f333(f180(x70971),x70973)),f196(f917(x70971,a905)))+~P106(f333(f145(x70971),f333(f333(f142(x70971),x70972),x70973))) % 173.51/173.27 [7112]~P106(f333(f333(f335(x71121),x71122),f333(f180(x71121),x71123)))+~P106(f333(f145(x71121),f333(f333(f159(x71121),x71122),x71123))) % 173.51/173.27 [7184]P34(x71841,x71842,x71843)+P106(f333(f333(f247(a910),f803(x71843,x71842,x71841)),f333(f197(f911(x71841)),x71843))) % 173.51/173.27 [7194]E(f333(f333(f112(f917(x71941,a905)),x71942),x71943),f196(f917(x71941,a905)))+P106(f333(f333(f335(x71941),f768(x71943,x71942,x71941)),x71942)) % 173.51/173.27 [7195]E(f333(f333(f112(f917(x71951,a905)),x71952),x71953),f196(f917(x71951,a905)))+P106(f333(f333(f335(x71951),f774(x71953,x71952,x71951)),x71953)) % 173.51/173.27 [7198]E(f125(x71981,f333(f333(f183(x71981),x71982),x71983)),f333(f333(f183(x71981),f333(f333(f23(a910),x71982),f85(a910))),x71983))+~P106(f333(f333(f246(a910),x71982),f333(f197(f911(x71981)),x71983))) % 173.51/173.27 [7257]~P36(x72573,x72572,x72571)+P106(f333(f333(f247(a910),f797(x72571,x72572,x72573)),f333(f197(f911(x72573)),x72571))) % 173.51/173.27 [7275]P106(f333(f333(f247(a910),f2(a910)),x72751))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x72752),x72751)),f333(f333(f88(a910),x72753),x72751))) % 173.51/173.27 [7276]P106(f333(f333(f247(a910),f2(a910)),x72761))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x72761),x72762)),f333(f333(f88(a910),x72761),x72763))) % 173.51/173.27 [7279]~P106(f333(f333(f335(x72791),x72792),x72793))+~P106(f333(f333(f335(x72791),x72792),f333(f86(f917(x72791,a905)),x72793))) % 173.51/173.27 [7285]~P106(f333(f333(f247(f917(x72851,a905)),x72852),x72853))+P106(f333(f333(f246(f917(x72851,a905)),x72852),x72853)) % 173.51/173.27 [7392]~P106(f333(f333(f246(a910),x73923),x73922))+P106(f333(f333(f246(a910),f333(f333(f23(a910),x73921),x73922)),f333(f333(f23(a910),x73921),x73923))) % 173.51/173.27 [7393]~P106(f333(f333(f246(a910),x73931),x73933))+P106(f333(f333(f246(a910),f333(f333(f23(a910),x73931),x73932)),f333(f333(f23(a910),x73933),x73932))) % 173.51/173.27 [7394]~P106(f333(f333(f246(a910),x73942),x73943))+P106(f333(f333(f246(a910),f333(f333(f87(a910),x73941),x73942)),f333(f333(f87(a910),x73941),x73943))) % 173.51/173.27 [7395]~P106(f333(f333(f246(a910),x73951),x73953))+P106(f333(f333(f246(a910),f333(f333(f87(a910),x73951),x73952)),f333(f333(f87(a910),x73953),x73952))) % 173.51/173.27 [7397]~P106(f333(f333(f246(a910),x73972),x73973))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x73971),x73972)),f333(f333(f88(a910),x73971),x73973))) % 173.51/173.27 [7399]~P106(f333(f333(f246(a910),x73991),x73993))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x73991),x73992)),f333(f333(f88(a910),x73993),x73992))) % 173.51/173.27 [7400]~P106(f333(f333(f246(a910),x74001),x74003))+P106(f333(f333(f246(a910),f333(f333(f42(a910),x74001),x74002)),f333(f333(f42(a910),x74003),x74002))) % 173.51/173.27 [7401]~P106(f333(f333(f246(a1),x74012),x74013))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x74011),x74012)),f333(f333(f87(a1),x74011),x74013))) % 173.51/173.27 [7404]~P106(f333(f333(f247(a910),x74042),x74043))+P106(f333(f333(f247(a910),f333(f333(f87(a910),x74041),x74042)),f333(f333(f87(a910),x74041),x74043))) % 173.51/173.27 [7405]~P106(f333(f333(f247(a910),x74051),x74053))+P106(f333(f333(f247(a910),f333(f333(f87(a910),x74051),x74052)),f333(f333(f87(a910),x74053),x74052))) % 173.51/173.27 [7406]~P106(f333(f333(f247(a1),x74061),x74063))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x74061),x74062)),f333(f333(f87(a1),x74063),x74062))) % 173.51/173.27 [7484]E(x74841,x74842)+~P106(f333(f333(f335(x74843),x74841),f333(f333(f315(x74843),x74842),f196(f917(x74843,a905))))) % 173.51/173.27 [7486]~E(f333(f333(f112(f917(x74861,a905)),x74862),x74863),f196(f917(x74861,a905)))+P106(f333(f333(f246(f917(x74861,a905)),x74862),f333(f86(f917(x74861,a905)),x74863))) % 173.51/173.27 [7492]P106(f333(f333(f335(f917(x74921,a905)),x74922),f333(f314(x74921),x74923)))+~P106(f333(f333(f246(f917(x74921,a905)),x74922),x74923)) % 173.51/173.27 [7542]E(f333(f333(f159(x75421),f333(f333(f172(x75421),x75422),x75423)),f333(f333(f146(x75421),f333(a123,x75423)),x75422)),f333(f333(f146(x75421),x75423),x75422))+~P106(f333(f333(f247(a910),x75423),f333(f197(f911(x75421)),x75422))) % 173.51/173.27 [7568]P106(f333(f333(f335(f916(x75681,x75681)),x75682),f313(x75681,x75683)))+~P106(f333(f333(f335(f916(x75681,x75681)),x75682),x75683)) % 173.51/173.27 [7578]~P106(f333(f333(f335(f917(x75781,a905)),x75782),f333(f314(x75781),x75783)))+P106(f333(f333(f246(f917(x75781,a905)),x75782),x75783)) % 173.51/173.27 [7622]P106(f333(f333(f246(f917(x76221,a905)),x76222),f43(f917(x76221,a905),x76223)))+~P106(f333(f333(f335(f917(x76221,a905)),x76222),x76223)) % 173.51/173.27 [7644]~P139(x76441)+E(f333(f333(f88(x76441),f333(f333(f256(x76441),f333(f86(x76441),f85(x76441))),x76442)),f333(f333(f256(x76441),x76443),x76442)),f333(f333(f256(x76441),f333(f86(x76441),x76443)),x76442)) % 173.51/173.27 [7666]E(f333(f333(f172(x76661),x76662),f333(f333(f23(a910),f333(f197(f911(x76661)),x76662)),f333(a123,x76663))),f333(f333(f172(x76661),f333(f176(x76661),x76662)),x76663))+~P106(f333(f333(f247(a910),x76663),f333(f197(f911(x76661)),x76662))) % 173.51/173.27 [7683]~E(f333(f333(f112(f917(x76831,a905)),f642(x76833,x76832,x76831)),x76833),f196(f917(x76831,a905)))+E(f333(f333(f112(f917(x76831,a905)),f43(f917(x76831,a905),x76832)),x76833),f196(f917(x76831,a905))) % 173.51/173.27 [7745]~P106(f333(f333(f335(x77453),x77452),f333(f180(x77453),x77451)))+P106(f333(f333(f247(a910),f683(x77451,x77452,x77453)),f333(f197(f911(x77453)),x77451))) % 173.51/173.27 [7753]P106(f333(f333(f335(x77531),f333(f333(f172(x77531),x77532),x77533)),f333(f180(x77531),x77532)))+~P106(f333(f333(f247(a910),x77533),f333(f197(f911(x77531)),x77532))) % 173.51/173.27 [7852]~P106(f333(x78522,f765(x78523,x78522,x78521)))+E(f333(f333(f146(x78521),f333(f197(f911(x78521)),f185(x78521,x78522,x78523))),x78523),f124(x78521)) % 173.51/173.27 [7865]P106(f333(f333(f246(f917(f911(x78651),a905)),f169(x78651,x78652)),f169(x78651,x78653)))+~P106(f333(f333(f246(f917(x78651,a905)),x78652),x78653)) % 173.51/173.27 [7866]P106(f333(f333(f246(f917(f911(x78661),a905)),f168(x78661,x78662)),f168(x78661,x78663)))+~P106(f333(f333(f246(f917(x78661,a905)),x78662),x78663)) % 173.51/173.27 [7894]E(f333(f333(f112(f917(x78941,a905)),f43(f917(x78941,a905),x78942)),x78943),f196(f917(x78941,a905)))+P106(f333(f333(f335(f917(x78941,a905)),f642(x78943,x78942,x78941)),x78942)) % 173.51/173.27 [7896]~P106(f333(f333(f335(f917(x78961,a905)),x78963),x78962))+P106(f333(f333(f246(f917(x78961,a905)),f44(f917(x78961,a905),x78962)),x78963)) % 173.51/173.27 [7898]E(f333(f333(f112(f917(x78981,a905)),x78982),x78983),f196(f917(x78981,a905)))+~P106(f333(f333(f246(f917(x78981,a905)),x78982),f333(f86(f917(x78981,a905)),x78983))) % 173.51/173.27 [7947]E(f333(f333(f23(a910),f333(f333(f87(a910),f333(f173(a910),x79471)),x79472)),f333(f333(f172(a910),x79471),x79473)),f333(f173(a910),f333(f333(f167(a910,x79471),x79473),x79472)))+~P106(f333(f333(f247(a910),x79473),f333(f197(f911(a910)),x79471))) % 173.51/173.27 [7998]P106(f333(f333(f246(a910),x79981),x79982))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),x79983),x79981)),f333(f333(f87(a910),x79983),x79982))) % 173.51/173.27 [8001]P106(f333(f333(f247(a910),x80011),x80012))+~P106(f333(f333(f247(a910),f333(f333(f87(a910),x80013),x80011)),f333(f333(f87(a910),x80013),x80012))) % 173.51/173.27 [8002]P106(f333(f333(f247(a910),x80021),x80022))+~P106(f333(f333(f247(a910),f333(f333(f88(a910),x80023),x80021)),f333(f333(f88(a910),x80023),x80022))) % 173.51/173.27 [8003]P106(f333(f333(f247(a910),x80031),x80032))+~P106(f333(f333(f247(a910),f333(f333(f88(a910),x80031),x80033)),f333(f333(f88(a910),x80032),x80033))) % 173.51/173.27 [8032]P106(f333(f333(f247(a910),f2(a910)),x80321))+~P106(f333(f333(f247(a910),f333(f333(f88(a910),x80322),x80321)),f333(f333(f88(a910),x80323),x80321))) % 173.51/173.27 [8033]P106(f333(f333(f247(a910),f2(a910)),x80331))+~P106(f333(f333(f247(a910),f333(f333(f88(a910),x80331),x80332)),f333(f333(f88(a910),x80331),x80333))) % 173.51/173.27 [8107]E(f259(x81071,x81072,x81073),x81072)+~P106(f333(f333(f246(f917(x81071,a905)),x81073),f333(f333(f315(x81071),x81072),f196(f917(x81071,a905))))) % 173.51/173.27 [8163]~P106(f333(f145(x81631),x81633))+E(f333(f144(x81631,f333(f333(f8(a905,a905,x81631),a328),f333(a330,x81632))),x81633),f178(x81631,x81632,x81633)) % 173.51/173.27 [8188]E(f333(f333(f146(x81881),f333(f197(f911(x81881)),f185(x81881,x81882,x81883))),x81883),f124(x81881))+P106(f333(f333(f335(x81881),f765(x81883,x81882,x81881)),f333(f180(x81881),x81883))) % 173.51/173.27 [8192]E(f333(f333(f142(x81921),f333(f333(f183(x81921),x81922),x81923)),f333(f333(f159(x81921),f333(f333(f172(x81921),x81923),x81922)),f124(x81921))),f333(f333(f183(x81921),f333(a123,x81922)),x81923))+~P106(f333(f333(f247(a910),x81922),f333(f197(f911(x81921)),x81923))) % 173.51/173.27 [8253]E(f333(f144(x82531,f333(f333(f8(a905,a905,x82531),a328),f333(a330,x82532))),x82533),x82533)+P106(f333(f333(f335(x82531),x82532),f333(f180(x82531),x82533))) % 173.51/173.27 [8261]P106(f333(f333(f246(f917(f917(x82611,a905),a905)),f260(x82611,x82612)),f260(x82611,x82613)))+~P106(f333(f333(f246(f917(x82611,a905)),x82612),x82613)) % 173.51/173.27 [8301]~P106(f333(f145(x83011),x83013))+P106(f333(f145(x83011),f333(f333(f333(f191(f911(x83011),f911(x83011)),x83012),f175(x83011)),x83013))) % 173.51/173.27 [8307]~P106(f333(f333(f247(a910),x83072),x83073))+P106(f333(f333(f247(a910),f333(f333(f88(a910),f333(a123,x83071)),x83072)),f333(f333(f88(a910),f333(a123,x83071)),x83073))) % 173.51/173.27 [8327]P106(f333(f333(f246(f917(f917(x83271,a905),a905)),f333(f314(x83271),x83272)),f333(f314(x83271),x83273)))+~P106(f333(f333(f246(f917(x83271,a905)),x83272),x83273)) % 173.51/173.27 [8398]~E(f333(f316(x83981,x83982,x83983),f254(f917(x83981,a905))),f254(f917(x83982,a905)))+E(f333(f79(x83981,x83982,x83982,x83983),f99(x83981,x83982,f254(f917(x83981,a905)),x83983)),f33(x83982)) % 173.51/173.27 [8492]~P106(f333(f333(f246(f917(x84921,a905)),x84923),x84922))+P106(f333(f333(f246(f917(x84921,a905)),f333(f86(f917(x84921,a905)),x84922)),f333(f86(f917(x84921,a905)),x84923))) % 173.51/173.27 [8528]E(f333(f316(a910,a910,f333(f333(f7(a910,a910,a910),f23(a910)),x85281)),f333(f308(a910,x85282),x85283)),f333(f308(a910,f333(f333(f23(a910),x85282),x85281)),f333(f333(f23(a910),x85283),x85281)))+~P106(f333(f333(f247(a910),x85281),x85283)) % 173.51/173.27 [8556]~P82(x85561)+E(f333(f333(f87(x85561),x85562),f333(f150(x85561,x85561,f87(x85561),f2(x85561)),x85563)),f333(f150(x85561,x85561,f87(x85561),x85562),x85563)) % 173.51/173.27 [8640]~P87(x86401)+P106(f333(f333(f246(x86401),f333(f82(x86401),f333(f333(f23(x86401),x86402),x86403))),f333(f333(f87(x86401),f333(f82(x86401),x86402)),f333(f82(x86401),x86403)))) % 173.51/173.27 [8641]~P87(x86411)+P106(f333(f333(f246(x86411),f333(f82(x86411),f333(f333(f87(x86411),x86412),x86413))),f333(f333(f87(x86411),f333(f82(x86411),x86412)),f333(f82(x86411),x86413)))) % 173.51/173.27 [8652]E(f333(f333(f87(a1),f333(f333(f88(a1),x86521),f51(a1,f333(f333(f42(a1),x86522),x86521),x86523))),f51(a1,x86522,x86521)),f51(a1,x86522,f333(f333(f88(a1),x86521),x86523)))+~P106(f333(f333(f247(a1),f2(a1)),x86523)) % 173.51/173.27 [8658]E(f333(f333(f142(x86581),f333(f333(f183(x86581),x86582),x86583)),f333(f333(f159(x86581),f333(f149(x86581),f333(f333(f146(x86581),x86582),x86583))),f124(x86581))),f333(f333(f183(x86581),f333(a123,x86582)),x86583))+~P106(f333(f333(f247(a910),x86582),f333(f197(f911(x86581)),x86583))) % 173.51/173.27 [8678]E(f333(f277(x86781,f333(f333(f162(x86781,f916(a110,x86781)),f333(f265(a110,x86781),f85(a110))),x86782)),f333(a3,x86783)),f333(f333(f172(x86781),x86782),x86783))+~P106(f333(f333(f247(a910),x86783),f333(f197(f911(x86781)),x86782))) % 173.51/173.27 [8745]P106(f333(f333(f335(f916(x87451,x87451)),x87452),f333(f333(f295(x87451,x87451,x87451),x87453),f313(x87451,x87453))))+~P106(f333(f333(f335(f916(x87451,x87451)),x87452),x87453)) % 173.51/173.27 [8756]E(f333(f316(x87561,x87562,x87563),f254(f917(x87561,a905))),f254(f917(x87562,a905)))+~E(f333(f79(x87561,x87562,x87562,x87563),f99(x87561,x87562,f254(f917(x87561,a905)),x87563)),f33(x87562)) % 173.51/173.27 [8767]P106(f333(f333(f246(a910),x87671),x87672))+~P106(f333(f333(f246(a910),f333(f333(f88(a910),f333(a123,x87673)),x87671)),f333(f333(f88(a910),f333(a123,x87673)),x87672))) % 173.51/173.27 [8783]P106(f333(f333(f246(f917(x87831,a905)),x87832),x87833))+~P106(f333(f333(f246(f917(x87831,a905)),f333(f86(f917(x87831,a905)),x87833)),f333(f86(f917(x87831,a905)),x87832))) % 173.51/173.27 [8805]P106(f333(f145(x88051),x88052))+~P106(f333(f145(x88051),f333(f333(f333(f191(f911(x88051),f911(x88051)),x88053),f175(x88051)),x88052))) % 173.51/173.27 [8877]E(f333(f292(x88771,x88771,f313(x88771,x88772)),x88773),x88773)+~P106(f333(f333(f246(f917(x88771,a905)),f333(f292(x88771,x88771,x88772),x88773)),x88773)) % 173.51/173.27 [8925]~P110(x89251)+P16(x89251,f333(f144(x89251,f333(f333(f7(x89251,x89251,a905),a330),f333(x89252,x89253))),x89253)) % 173.51/173.27 [8932]~P106(f333(f333(f246(a910),x89321),x89322))+P106(f333(f333(f246(a910),x89321),f333(f150(a910,a910,f87(a910),x89322),x89323))) % 173.51/173.27 [9018]~P106(f333(f333(f335(f916(x90181,x90181)),x90182),f313(x90181,x90183)))+P106(f333(f333(f335(f916(x90181,x90181)),x90182),f333(f333(f191(f916(x90181,x90181),a905),f618(x90183,x90182,x90181)),x90183))) % 173.51/173.27 [9111]~P82(x91111)+E(f333(f333(f87(x91111),x91112),f333(f150(x91111,x91111,f333(f7(x91111,x91111,x91111),f87(x91111)),f2(x91111)),f333(f176(x91111),x91113))),f333(f150(x91111,x91111,f87(x91111),x91112),x91113)) % 173.51/173.27 [9236]~P28(x92362,x92361,x92363,f254(f917(x92362,a905)),f254(f917(x92361,a905)))+E(f99(x92361,x92362,f254(f917(x92361,a905)),f99(x92362,x92361,f254(f917(x92362,a905)),x92363)),x92363) % 173.51/173.27 [9387]P58(x93871,x93872,x93873)+P106(f333(f333(f335(f916(x93871,x93872)),f333(f333(f265(x93871,x93872),f623(x93873,x93872,x93871)),f617(x93873,x93872,x93871))),x93873)) % 173.51/173.27 [9388]P58(x93881,x93882,x93883)+P106(f333(f333(f335(f916(x93881,x93882)),f333(f333(f265(x93881,x93882),f623(x93883,x93882,x93881)),f616(x93883,x93882,x93881))),x93883)) % 173.51/173.27 [9464]~P106(f333(f333(f335(f916(x94641,x94641)),x94642),f333(f333(f295(x94641,x94641,x94641),x94643),f313(x94641,x94643))))+P106(f333(f333(f335(f916(x94641,x94641)),x94642),f333(f333(f191(f916(x94641,x94641),a905),f619(x94643,x94642,x94641)),x94643))) % 173.51/173.27 [9465]~P106(f333(x94651,f333(f333(f172(x94652),x94653),f333(f197(f911(x94652)),f185(x94652,x94651,x94653)))))+~P106(f333(f333(f247(a910),f333(f197(f911(x94652)),f185(x94652,x94651,x94653))),f333(f197(f911(x94652)),x94653))) % 173.51/173.27 [9556]~P106(f333(f333(f246(f917(x95561,a905)),x95562),x95563))+P106(f333(f333(f246(f917(x95561,a905)),f333(f333(f7(x95561,f917(x95561,a905),a905),f335(x95561)),x95562)),f333(f333(f7(x95561,f917(x95561,a905),a905),f335(x95561)),x95563))) % 173.51/173.27 [9614]~P106(f333(f333(f335(f916(f917(x96141,a905),f917(x96141,a905))),f333(f333(f265(f917(x96141,a905),f917(x96141,a905)),x96142),x96143)),f320(x96141)))+P106(f333(f333(f247(f917(x96141,a905)),x96142),x96143)) % 173.51/173.27 [9639]P59(x96391,x96392,x96393)+~P106(f333(f333(f335(f916(x96391,x96391)),f333(f333(f265(x96391,x96391),f574(x96393,x96392,x96391)),f573(x96393,x96392,x96391))),x96393)) % 173.51/173.27 [9640]P59(x96401,x96402,x96403)+~P106(f333(f333(f335(f916(x96401,x96401)),f333(f333(f265(x96401,x96401),f573(x96403,x96402,x96401)),f574(x96403,x96402,x96401))),x96403)) % 173.51/173.27 [9680]~P106(f333(f333(f335(f916(f911(x96801),f911(x96801))),f333(f333(f265(f911(x96801),f911(x96801)),x96802),x96802)),f155(x96801,x96803)))+P106(f333(f333(f335(f916(x96801,x96801)),f333(f333(f265(x96801,x96801),f702(x96802,x96803,x96801)),f702(x96802,x96803,x96801))),x96803)) % 173.51/173.27 [9737]P106(f333(f333(f246(f917(x97371,a905)),x97372),x97373))+~P106(f333(f333(f246(f917(x97371,a905)),f333(f333(f7(x97371,f917(x97371,a905),a905),f335(x97371)),x97372)),f333(f333(f7(x97371,f917(x97371,a905),a905),f335(x97371)),x97373))) % 173.51/173.27 [9820]E(f333(f333(f23(a910),f333(f333(f6(a910,a910),x98201),f333(f289(a910),x98202))),f333(f333(f6(a910,a910),x98203),f333(f289(a910),x98202))),f333(f333(f6(a910,a910),f333(f333(f18(a910,a910,a910),f333(f333(f8(a910,f917(a910,a910),a910),f23(a910)),x98201)),x98203)),f333(f289(a910),x98202)))+~P106(f333(f333(f246(a910),f333(x98203,f378(x98202,x98201,x98203))),f333(x98201,f378(x98202,x98201,x98203)))) % 173.51/173.27 [5775]~P71(x57751)+E(f333(f333(f23(x57751),f333(f333(f87(x57751),x57752),x57753)),x57753),x57752) % 173.51/173.27 [5776]~P71(x57761)+E(f333(f333(f87(x57761),f333(f333(f23(x57761),x57762),x57763)),x57763),x57762) % 173.51/173.27 [5995]~P71(x59951)+E(f333(f333(f87(x59951),x59952),f333(f333(f87(x59951),f333(f86(x59951),x59952)),x59953)),x59953) % 173.51/173.27 [6077]~P83(x60771)+E(f333(f333(f88(x60771),f333(f333(f256(x60771),x60772),x60773)),x60772),f333(f333(f256(x60771),x60772),f333(a123,x60773))) % 173.51/173.27 [6078]~P117(x60781)+E(f333(f333(f88(x60781),f333(f333(f256(x60781),x60782),x60783)),x60782),f333(f333(f256(x60781),x60782),f333(a123,x60783))) % 173.51/173.27 [6295]~P120(x62951)+E(f333(f82(x62951),f333(f333(f256(x62951),f333(f86(x62951),x62952)),x62953)),f333(f82(x62951),f333(f333(f256(x62951),x62952),x62953))) % 173.51/173.27 [6346]~P83(x63461)+E(f333(f333(f88(x63461),f333(f333(f256(x63461),x63462),x63463)),x63462),f333(f333(f88(x63461),x63462),f333(f333(f256(x63461),x63462),x63463))) % 173.51/173.27 [6398]E(f333(f333(f23(a110),f333(f333(f87(a110),x63981),x63982)),x63983),f281(x63981,x63982,x63983))+~P106(f333(f333(f247(a110),x63982),x63983)) % 173.51/173.27 [6421]~E(f333(f333(f146(x64211),x64213),x64212),f124(x64211))+P106(f333(f333(f246(a910),f333(f197(f911(x64211)),x64212)),x64213)) % 173.51/173.27 [6556]E(f333(f333(f88(a910),f333(f114(a910),x65561)),f333(f333(f88(a910),f333(f114(a910),x65562)),x65563)),f2(a910))+~P106(f333(f333(f247(a1),x65561),a90)) % 173.51/173.27 [6573]~P67(x65731)+E(f333(f333(f256(x65731),f333(f333(f296(x65731),f85(x65731)),x65732)),x65733),f333(f333(f296(x65731),f85(x65731)),f333(f333(f256(x65731),x65732),x65733))) % 173.51/173.27 [6649]E(f333(f333(f23(a910),f333(f333(f87(a910),x66491),x66492)),x66493),f333(f333(f23(a910),x66491),f333(f333(f23(a910),x66493),x66492)))+~P106(f333(f333(f246(a910),x66492),x66493)) % 173.51/173.27 [6651]E(f333(f333(f23(a910),f333(f333(f87(a910),x66511),x66512)),x66513),f333(f333(f87(a910),x66511),f333(f333(f23(a910),x66512),x66513)))+~P106(f333(f333(f246(a910),x66513),x66512)) % 173.51/173.27 [6688]~P2(x66881)+P106(f333(f333(f246(x66881),f333(f333(f112(x66881),x66882),x66883)),x66883)) % 173.51/173.27 [6689]~P102(x66891)+P106(f333(f333(f246(x66891),f333(f333(f112(x66891),x66892),x66893)),x66893)) % 173.51/173.27 [6690]~P2(x66901)+P106(f333(f333(f246(x66901),f333(f333(f112(x66901),x66902),x66903)),x66902)) % 173.51/173.27 [6691]~P102(x66911)+P106(f333(f333(f246(x66911),f333(f333(f112(x66911),x66912),x66913)),x66912)) % 173.51/173.27 [6692]~P110(x66921)+P106(f333(f333(f246(x66921),f333(f333(f244(x66921),x66922),x66923)),x66923)) % 173.51/173.27 [6693]~P110(x66931)+P106(f333(f333(f246(x66931),f333(f333(f244(x66931),x66932),x66933)),x66932)) % 173.51/173.27 [6708]E(f333(f333(f42(a1),f333(f333(f42(a1),x67081),x67082)),x67083),f333(f333(f42(a1),x67081),f333(f333(f88(a1),x67082),x67083)))+~P106(f333(f333(f247(a1),f2(a1)),x67083)) % 173.51/173.27 [6759]~P117(x67591)+E(f333(f333(f87(x67591),f333(f333(f88(x67591),x67592),x67593)),x67593),f333(f333(f88(x67591),f333(f333(f87(x67591),x67592),f85(x67591))),x67593)) % 173.51/173.27 [6760]~P95(x67601)+E(f333(f333(f88(x67601),f333(f86(x67601),f333(f114(x67601),x67602))),x67603),f333(f333(f88(x67601),f333(f114(x67601),f333(f86(a1),x67602))),x67603)) % 173.51/173.27 [6830]~P82(x68301)+E(f333(f173(x68301),f333(f333(f162(x68302,x68301),f333(f16(x68301,x68302),f2(x68301))),x68303)),f2(x68301)) % 173.51/173.27 [6845]E(f333(f333(f87(a910),f333(f114(a910),x68451)),f333(f333(f87(a910),f333(f114(a910),x68452)),x68453)),f333(f333(f87(a910),f333(f114(a910),x68452)),x68453))+~P106(f333(a201,f333(f114(a1),x68451))) % 173.51/173.27 [6859]~P8(x68591)+E(f44(x68591,f333(f333(f315(x68591),x68592),f333(f333(f315(x68591),x68593),f196(f917(x68591,a905))))),f333(f333(f112(x68591),x68592),x68593)) % 173.51/173.27 [6860]~P8(x68601)+E(f43(x68601,f333(f333(f315(x68601),x68602),f333(f333(f315(x68601),x68603),f196(f917(x68601,a905))))),f333(f333(f121(x68601),x68602),x68603)) % 173.51/173.27 [6883]E(f333(f333(f183(x68831),x68832),x68833),x68833)+~P106(f333(f333(f246(a910),f333(f197(f911(x68831)),x68833)),x68832)) % 173.51/173.27 [6895]E(f333(f333(f146(x68951),x68952),x68953),f124(x68951))+~P106(f333(f333(f246(a910),f333(f197(f911(x68951)),x68953)),x68952)) % 173.51/173.27 [6906]E(f333(f333(f87(a910),f333(f333(f23(a910),x69061),x69062)),x69063),f333(f333(f23(a910),f333(f333(f87(a910),x69061),x69063)),x69062))+~P106(f333(f333(f246(a910),x69062),x69061)) % 173.51/173.27 [6920]~P106(f333(f333(f247(a910),x69201),x69203))+P106(f333(f333(f247(a910),f333(f333(f23(a910),x69201),x69202)),x69203)) % 173.51/173.27 [6947]~P110(x69471)+E(f178(x69471,x69472,f333(f333(f156(x69471,x69471,f5(x69471)),x69472),x69473)),x69473) % 173.51/173.27 [7034]E(f333(f333(f23(a910),f333(f333(f87(a910),x70341),x70342)),f333(a123,x70343)),f333(f333(f23(a910),x70341),f333(a123,f333(f333(f23(a910),x70343),x70342))))+~P106(f333(f333(f246(a910),x70342),x70343)) % 173.51/173.27 [7035]~P120(x70351)+P106(f333(f333(f246(x70351),f2(x70351)),f333(f333(f256(x70351),f333(f82(x70351),x70352)),x70353))) % 173.51/173.27 [7081]P26(x70811,x70812,x70813)+~P106(f333(f333(f246(f917(f909(x70811),a905)),x70813),x70812)) % 173.51/173.27 [7123]~P106(f333(f67(x71231),x71233))+P106(f333(f67(x71231),f333(f333(f112(f917(x71231,a905)),x71232),x71233))) % 173.51/173.27 [7124]~P106(f333(f67(x71241),x71242))+P106(f333(f67(x71241),f333(f333(f112(f917(x71241,a905)),x71242),x71243))) % 173.51/173.27 [7125]~P106(f333(f67(x71251),x71252))+P106(f333(f67(x71251),f333(f333(f23(f917(x71251,a905)),x71252),x71253))) % 173.51/173.27 [7265]~P40(x72651,x72653)+P40(x72651,f333(f333(f112(f917(f916(x72651,x72651),a905)),x72652),x72653)) % 173.51/173.27 [7266]~P40(x72661,x72662)+P40(x72661,f333(f333(f112(f917(f916(x72661,x72661),a905)),x72662),x72663)) % 173.51/173.27 [7388]~P2(x73881)+E(f13(x73881,f333(f180(x73881),f333(f333(f159(x73881),x73882),x73883))),f333(f150(x73881,x73881,f121(x73881),x73882),x73883)) % 173.51/173.27 [7389]~P2(x73891)+E(f10(x73891,f333(f180(x73891),f333(f333(f159(x73891),x73892),x73893))),f333(f150(x73891,x73891,f112(x73891),x73892),x73893)) % 173.51/173.27 [7390]~P110(x73901)+E(f14(x73901,f333(f180(x73901),f333(f333(f159(x73901),x73902),x73903))),f333(f150(x73901,x73901,f244(x73901),x73902),x73903)) % 173.51/173.27 [7391]~P110(x73911)+E(f15(x73911,f333(f180(x73911),f333(f333(f159(x73911),x73912),x73913))),f333(f150(x73911,x73911,f245(x73911),x73912),x73913)) % 173.51/173.27 [7451]~P106(f333(f67(x74511),x74512))+P106(f333(f333(f246(a910),f333(f41(x74511),x74512)),f333(f41(x74511),f333(f333(f315(x74511),x74513),x74512)))) % 173.51/173.27 [7458]E(f333(f333(f121(f917(a910,a905)),f333(f308(a910,x74581),x74582)),f333(f308(a910,x74582),f333(f333(f87(a910),x74582),x74583))),f333(f308(a910,x74581),f333(f333(f87(a910),x74582),x74583)))+~P106(f333(f333(f246(a910),x74581),x74582)) % 173.51/173.27 [7467]P106(f333(f333(f246(a910),x74671),x74672))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),x74673),x74671)),x74672)) % 173.51/173.27 [7468]P106(f333(f333(f246(a910),x74681),x74682))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),x74681),x74683)),x74682)) % 173.51/173.27 [7469]P106(f333(f333(f247(a910),x74691),x74692))+~P106(f333(f333(f247(a910),f333(f333(f87(a910),x74691),x74693)),x74692)) % 173.51/173.27 [7509]~P110(x75091)+E(f11(x75091,f244(x75091),f333(f180(x75091),f333(f333(f159(x75091),x75092),x75093))),f333(f150(x75091,x75091,f244(x75091),x75092),x75093)) % 173.51/173.27 [7510]~P110(x75101)+E(f12(x75101,f245(x75101),f333(f180(x75101),f333(f333(f159(x75101),x75102),x75103))),f333(f150(x75101,x75101,f245(x75101),x75102),x75103)) % 173.51/173.27 [7514]~E(x75142,f196(f917(f916(x75141,x75141),a905)))+P106(f333(f333(f246(f917(f916(x75141,x75141),a905)),x75142),x75143)) % 173.51/173.27 [7617]E(f333(f333(f121(f917(x76171,a905)),x76172),f333(f333(f23(f917(x76171,a905)),x76173),x76172)),x76173)+~P106(f333(f333(f246(f917(x76171,a905)),x76172),x76173)) % 173.51/173.27 [7618]~P106(f333(f333(f246(a910),x76181),f333(f333(f87(a910),x76183),x76182)))+P106(f333(f333(f246(a910),f333(f333(f23(a910),x76181),x76182)),x76183)) % 173.51/173.27 [7619]~P106(f333(f333(f247(a910),x76191),f333(f333(f23(a910),x76193),x76192)))+P106(f333(f333(f247(a910),f333(f333(f87(a910),x76191),x76192)),x76193)) % 173.51/173.27 [7673]E(x76731,f124(x76732))+E(f333(f149(x76732),f333(f333(f333(f191(f911(x76732),f911(x76732)),x76733),f175(x76732)),x76731)),f333(f333(f172(x76732),x76731),f51(a910,x76733,f333(f197(f911(x76732)),x76731)))) % 173.51/173.27 [7682]E(f333(f333(f315(x76821),x76822),f333(f333(f23(f917(x76821,a905)),x76823),f333(f333(f315(x76821),x76822),f196(f917(x76821,a905))))),x76823)+~P106(f333(f333(f335(x76821),x76822),x76823)) % 173.51/173.27 [7843]P106(f333(f333(f246(a910),x78431),f333(f333(f87(a910),x78432),x78433)))+~P106(f333(f333(f246(a910),f333(f333(f23(a910),x78431),x78433)),x78432)) % 173.51/173.27 [7844]P106(f333(f333(f247(a910),x78441),f333(f333(f23(a910),x78442),x78443)))+~P106(f333(f333(f247(a910),f333(f333(f87(a910),x78441),x78443)),x78442)) % 173.51/173.27 [7869]P106(f333(f67(x78691),x78692))+~P106(f333(f67(x78691),f333(f333(f121(f917(x78691,a905)),x78693),x78692))) % 173.51/173.27 [7870]P106(f333(f67(x78701),x78702))+~P106(f333(f67(x78701),f333(f333(f121(f917(x78701,a905)),x78702),x78703))) % 173.51/173.27 [7946]~P49(x79461,x79463)+P106(f333(f333(f335(f916(x79461,x79461)),f333(f333(f265(x79461,x79461),x79462),x79462)),x79463)) % 173.51/173.27 [8080]E(f333(f333(f172(a910),f147(a910,f333(f308(a910,x80801),x80802))),x80803),f333(f333(f87(a910),x80801),x80803))+~P106(f333(f333(f247(a910),f333(f333(f87(a910),x80801),x80803)),x80802)) % 173.51/173.27 [8152]E(f333(f333(f183(a910),x81521),f147(a910,f333(f308(a910,x81522),x81523))),f147(a910,f333(f308(a910,x81522),f333(f333(f87(a910),x81522),x81521))))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),x81522),x81521)),x81523)) % 173.51/173.27 [8208]~P95(x82081)+E(f333(f333(f256(x82081),x82082),f333(f114(a910),f333(f333(f87(a1),x82083),x82083))),f333(f333(f93(x82081,x82081),f333(f333(f256(x82081),x82082),f333(f114(a910),x82083))),f333(f333(f18(x82081,x82081,x82081),f88(x82081)),f5(x82081)))) % 173.51/173.27 [8473]E(f333(f333(f142(x84731),f333(f333(f183(x84731),x84732),x84733)),f333(f333(f159(x84731),f333(f333(f172(x84731),x84733),x84732)),f333(f333(f146(x84731),f333(a123,x84732)),x84733))),x84733)+~P106(f333(f333(f247(a910),x84732),f333(f197(f911(x84731)),x84733))) % 173.51/173.27 [8480]P106(f333(f333(f246(f917(x84801,a905)),f321(x84801,x84802)),f321(x84801,x84803)))+~P106(f333(f333(f246(f917(x84801,f917(x84801,a905))),x84803),x84802)) % 173.51/173.27 [8481]~P59(x84811,x84812,x84813)+P59(x84811,x84812,f333(f333(f23(f917(f916(x84811,x84811),a905)),x84813),f313(x84811,f196(f917(f916(x84811,x84811),a905))))) % 173.51/173.27 [8500]P106(f333(f333(f246(f917(x85001,a905)),f322(x85001,x85002)),f322(x85001,x85003)))+~P106(f333(f333(f246(f917(f916(x85001,x85001),a905)),x85003),x85002)) % 173.51/173.27 [8507]~P127(x85071)+P106(f333(f333(f246(x85071),f2(x85071)),f333(f333(f87(x85071),f333(f333(f88(x85071),x85072),x85072)),f333(f333(f88(x85071),x85073),x85073)))) % 173.51/173.27 [8543]P106(f333(f333(f246(f917(x85431,a905)),f333(f288(x85431),x85432)),f333(f288(x85431),x85433)))+~P106(f333(f333(f246(f917(f916(x85431,x85431),a905)),x85432),x85433)) % 173.51/173.27 [8577]~P57(x85771,x85772)+~P106(f333(f333(f335(f916(x85771,x85771)),f333(f333(f265(x85771,x85771),x85773),x85773)),x85772)) % 173.51/173.27 [8579]~P40(x85791,x85792)+~P106(f333(f333(f335(f916(x85791,x85791)),f333(f333(f265(x85791,x85791),x85793),x85793)),x85792)) % 173.51/173.27 [8642]P106(f333(f333(f246(f917(x86421,a905)),f44(f917(x86421,a905),x86422)),f44(f917(x86421,a905),x86423)))+~P106(f333(f333(f246(f917(f917(x86421,a905),a905)),x86423),x86422)) % 173.51/173.27 [8643]P106(f333(f333(f246(f917(x86431,a905)),f43(f917(x86431,a905),x86432)),f43(f917(x86431,a905),x86433)))+~P106(f333(f333(f246(f917(f917(x86431,a905),a905)),x86432),x86433)) % 173.51/173.27 [8697]~P11(x86971,x86973,x86972)+P106(f333(f333(f246(f917(f916(x86971,x86971),a905)),x86972),f333(f333(f267(x86971,x86971),x86973),f333(f16(f917(x86971,a905),x86971),x86973)))) % 173.51/173.27 [8698]~P56(x86981,x86983,x86982)+P106(f333(f333(f246(f917(f916(x86981,x86981),a905)),x86982),f333(f333(f267(x86981,x86981),x86983),f333(f16(f917(x86981,a905),x86981),x86983)))) % 173.51/173.27 [8746]~P87(x87461)+P106(f333(f333(f246(x87461),f333(f333(f23(x87461),f333(f82(x87461),x87462)),f333(f82(x87461),x87463))),f333(f82(x87461),f333(f333(f23(x87461),x87463),x87462)))) % 173.51/173.27 [8747]~P87(x87471)+P106(f333(f333(f246(x87471),f333(f333(f23(x87471),f333(f82(x87471),x87472)),f333(f82(x87471),x87473))),f333(f82(x87471),f333(f333(f23(x87471),x87472),x87473)))) % 173.51/173.27 [8781]P106(f333(f333(f246(f917(f916(x87811,x87811),a905)),f313(x87811,x87812)),f313(x87811,x87813)))+~P106(f333(f333(f246(f917(f916(x87811,x87811),a905)),x87812),x87813)) % 173.51/173.27 [8890]~P27(x88902,x88901,x88903,f254(f917(x88902,a905)))+E(f333(f79(x88901,x88902,x88902,f99(x88902,x88901,f254(f917(x88902,a905)),x88903)),x88903),f33(x88902)) % 173.51/173.27 [8950]P59(x89501,x89502,x89503)+~P59(x89501,x89502,f333(f333(f23(f917(f916(x89501,x89501),a905)),x89503),f313(x89501,f196(f917(f916(x89501,x89501),a905))))) % 173.51/173.27 [8970]P106(f333(f333(f246(f917(f916(f911(x89701),f911(x89701)),a905)),f165(x89701,x89702)),f165(x89701,x89703)))+~P106(f333(f333(f246(f917(f916(x89701,x89701),a905)),x89702),x89703)) % 173.51/173.27 [8971]P106(f333(f333(f246(f917(f916(f911(x89711),f911(x89711)),a905)),f166(x89711,x89712)),f166(x89711,x89713)))+~P106(f333(f333(f246(f917(f916(x89711,x89711),a905)),x89712),x89713)) % 173.51/173.27 [8992]~P56(x89921,x89923,x89922)+P106(f333(f333(f246(f917(f916(x89921,x89921),a905)),x89922),f333(f333(f295(x89921,x89921,x89921),f333(f293(x89921,x89921),x89922)),x89922))) % 173.51/173.27 [9047]~P106(f333(f145(x90471),x90472))+E(f333(f144(x90471,f333(f333(f7(x90471,f917(x90471,a905),a905),f335(x90471)),f333(f180(x90471),f184(x90471,x90472,x90473)))),x90472),f184(x90471,x90472,x90473)) % 173.51/173.27 [9109]E(x91091,x91092)+~P106(f333(f333(f335(f916(x91093,x91093)),f333(f333(f265(x91093,x91093),x91091),x91092)),f313(x91093,f196(f917(f916(x91093,x91093),a905))))) % 173.51/173.27 [9199]P106(f333(f333(f335(x91991),x91992),f322(x91991,x91993)))+P106(f333(f333(f335(f916(x91991,x91991)),f333(f333(f265(x91991,x91991),f586(x91993,x91992,x91991)),x91992)),x91993)) % 173.51/173.27 [9200]P106(f333(f333(f335(x92001),x92002),f322(x92001,x92003)))+P106(f333(f333(f335(f916(x92001,x92001)),f333(f333(f265(x92001,x92001),f645(x92003,x92002,x92001)),x92002)),x92003)) % 173.51/173.27 [9201]P106(f333(f333(f335(x92011),x92012),f322(x92011,x92013)))+P106(f333(f333(f335(f916(x92011,x92011)),f333(f333(f265(x92011,x92011),f646(x92013,x92012,x92011)),x92012)),x92013)) % 173.51/173.27 [9237]P27(x92371,x92372,x92373,f254(f917(x92371,a905)))+~E(f333(f79(x92372,x92371,x92371,f99(x92371,x92372,f254(f917(x92371,a905)),x92373)),x92373),f33(x92371)) % 173.51/173.27 [9292]~P106(f333(f333(f335(f911(x92921)),x92923),f169(x92921,x92922)))+P106(f333(f168(x92921,f333(f333(f7(x92921,f917(x92921,a905),a905),f335(x92921)),x92922)),x92923)) % 173.51/173.27 [9314]P106(f333(x93143,x93142))+E(f333(f252(x93141),f333(f333(f18(x93141,a905,a905),f333(f333(f8(a905,f917(a905,a905),x93141),a331),f333(a330,x93142))),x93143)),f196(f917(x93141,a905))) % 173.51/173.27 [9331]~P87(x93311)+P106(f333(f333(f246(x93311),f333(f82(x93311),f333(f333(f23(x93311),f333(f82(x93311),x93312)),f333(f82(x93311),x93313)))),f333(f82(x93311),f333(f333(f23(x93311),x93312),x93313)))) % 173.51/173.27 [9345]~P106(f333(x93453,x93452))+E(f333(f252(x93451),f333(f333(f18(x93451,a905,a905),f333(f333(f8(a905,f917(a905,a905),x93451),a331),f333(a330,x93452))),x93453)),f333(f333(f315(x93451),x93452),f196(f917(x93451,a905)))) % 173.51/173.27 [9352]~P106(f333(f333(f335(f917(x93521,a905)),x93523),f333(f314(x93521),x93522)))+P106(f333(f260(x93521,f333(f333(f7(x93521,f917(x93521,a905),a905),f335(x93521)),x93522)),x93523)) % 173.51/173.27 [9386]P40(x93861,x93862)+P106(f333(f333(f335(f916(x93861,x93861)),f333(f333(f265(x93861,x93861),f333(f591(x93862,x93861),f333(a123,x93863))),f333(f591(x93862,x93861),x93863))),x93862)) % 173.51/173.27 [9535]P106(f333(f333(f335(f911(x95351)),x95352),f169(x95351,x95353)))+~P106(f333(f168(x95351,f333(f333(f7(x95351,f917(x95351,a905),a905),f335(x95351)),x95353)),x95352)) % 173.51/173.27 [9548]P106(f333(f333(f335(f917(x95481,a905)),x95482),f333(f314(x95481),x95483)))+~P106(f333(f260(x95481,f333(f333(f7(x95481,f917(x95481,a905),a905),f335(x95481)),x95483)),x95482)) % 173.51/173.27 [9609]P106(f333(f333(f335(x96091),f333(f277(x96091,x96092),x96093)),f333(f180(x96091),f333(f333(f162(f916(a110,x96091),x96091),f268(a110,x96091)),x96092))))+~P106(f333(f333(f247(a110),x96093),f333(f173(a110),f333(f333(f162(f916(a110,x96091),a110),f264(a110,x96091)),x96092)))) % 173.51/173.27 [9657]P106(f333(f333(f246(f917(f916(f911(x96571),f911(x96571)),a905)),f166(x96571,x96572)),f333(f333(f267(f911(x96571),f911(x96571)),f169(x96571,x96573)),f333(f16(f917(f911(x96571),a905),f911(x96571)),f169(x96571,x96573)))))+~P106(f333(f333(f246(f917(f916(x96571,x96571),a905)),x96572),f333(f333(f267(x96571,x96571),x96573),f333(f16(f917(x96571,a905),x96571),x96573)))) % 173.51/173.27 [9683]P106(f333(f333(f335(x96831),f333(f264(x96831,f916(a110,a110)),f333(f275(x96831,x96832),x96833))),f333(f180(x96831),f333(f333(f162(f916(a110,x96831),x96831),f268(a110,x96831)),x96832))))+~P106(f333(f333(f247(a110),f2(a110)),f333(f173(a110),f333(f333(f162(f916(a110,x96831),a110),f264(a110,x96831)),x96832)))) % 173.51/173.27 [9705]~P106(f333(f333(f246(f917(f916(x97051,x97051),a905)),x97052),f333(f333(f267(x97051,x97051),x97053),f333(f16(f917(x97051,a905),x97051),x97053))))+P106(f333(f333(f246(f917(f916(x97051,x97051),a905)),f333(f333(f295(x97051,x97051,x97051),x97052),f313(x97051,x97052))),f333(f333(f267(x97051,x97051),x97053),f333(f16(f917(x97051,a905),x97051),x97053)))) % 173.51/173.27 [10004]~P40(x100041,x100042)+~P106(f333(f333(f335(f916(x100041,x100041)),f333(f333(f265(x100041,x100041),f333(x100043,f333(a123,f592(x100042,x100041,x100043)))),f333(x100043,f592(x100042,x100041,x100043)))),x100042)) % 173.51/173.27 [10005]~P40(x100051,x100052)+~P106(f333(f333(f335(f916(x100051,x100051)),f333(f333(f265(x100051,x100051),f333(x100053,f333(a123,f650(x100053,x100052,x100051)))),f333(x100053,f650(x100053,x100052,x100051)))),x100052)) % 173.51/173.27 [10259]P106(f333(f333(f246(f917(f916(f917(x102591,a905),f917(x102591,a905)),a905)),f333(f333(f295(f917(x102591,a905),f917(x102591,a905),f917(x102591,a905)),f326(x102591,x102592)),f333(f333(f121(f917(f916(f917(x102591,a905),f917(x102591,a905)),a905)),f326(x102591,x102593)),f333(f333(f315(f916(f917(x102591,a905),f917(x102591,a905))),f333(f333(f265(f917(x102591,a905),f917(x102591,a905)),f196(f917(x102591,a905))),f196(f917(x102591,a905)))),f196(f917(f916(f917(x102591,a905),f917(x102591,a905)),a905)))))),f326(x102591,x102592)))+~P106(f333(f333(f246(f917(f916(x102591,x102591),a905)),f333(f333(f295(x102591,x102591,x102591),x102592),x102593)),x102592)) % 173.51/173.27 [10260]P106(f333(f333(f246(f917(f916(f917(x102601,a905),f917(x102601,a905)),a905)),f333(f333(f295(f917(x102601,a905),f917(x102601,a905),f917(x102601,a905)),f324(x102601,x102602)),f333(f333(f121(f917(f916(f917(x102601,a905),f917(x102601,a905)),a905)),f324(x102601,x102603)),f333(f333(f315(f916(f917(x102601,a905),f917(x102601,a905))),f333(f333(f265(f917(x102601,a905),f917(x102601,a905)),f196(f917(x102601,a905))),f196(f917(x102601,a905)))),f196(f917(f916(f917(x102601,a905),f917(x102601,a905)),a905)))))),f324(x102601,x102602)))+~P106(f333(f333(f246(f917(f916(x102601,x102601),a905)),f333(f333(f295(x102601,x102601,x102601),x102602),x102603)),x102602)) % 173.51/173.27 [7387]~P106(f333(f333(f246(a910),x73872),x73871))+E(f333(f333(f23(a910),f333(a123,f333(f333(f23(a910),x73871),x73872))),x73873),f333(f333(f23(a910),f333(a123,x73871)),f333(f333(f87(a910),x73872),x73873))) % 173.51/173.27 [7426]~P64(x74261)+E(f333(f333(f87(x74261),f51(x74261,x74262,x74263)),f333(f333(f88(x74261),f333(f333(f42(x74261),x74262),x74263)),x74263)),x74262) % 173.51/173.27 [7623]E(f333(f333(f88(a910),f333(f114(a910),x76231)),f333(f333(f88(a910),f333(f114(a910),x76232)),x76233)),f333(f333(f88(a910),f333(f114(a910),f333(f333(f88(a1),x76231),x76232))),x76233))+P106(f333(f333(f247(a1),x76231),a90)) % 173.51/173.27 [8089]~P106(f333(f333(f246(a910),x80893),x80892))+P106(f333(f333(f246(a910),x80891),f333(f333(f23(a910),f333(f333(f87(a910),x80892),x80891)),x80893))) % 173.51/173.27 [8292]~P106(f333(f333(f246(a910),x82921),x82922))+E(f333(f333(f142(a910),f147(a910,f333(f308(a910,x82921),x82922))),f147(a910,f333(f308(a910,x82922),f333(f333(f87(a910),x82922),x82923)))),f147(a910,f333(f308(a910,x82921),f333(f333(f87(a910),x82922),x82923)))) % 173.51/173.27 [8553]~P106(f333(f67(x85531),x85532))+E(f333(a123,f333(f41(x85531),f333(f333(f23(f917(x85531,a905)),x85532),f333(f333(f315(x85531),x85533),f196(f917(x85531,a905)))))),f333(f41(x85531),f333(f333(f315(x85531),x85533),x85532))) % 173.51/173.27 [8598]~P106(f333(f67(x85981),x85982))+E(f333(f333(f87(a910),f85(a910)),f333(f41(x85981),f333(f333(f23(f917(x85981,a905)),x85982),f333(f333(f315(x85981),x85983),f196(f917(x85981,a905)))))),f333(f41(x85981),f333(f333(f315(x85981),x85983),x85982))) % 173.51/173.27 [8789]E(f333(f333(f23(a910),f333(f41(x87891),x87892)),f333(f41(x87891),f333(f333(f112(f917(x87891,a905)),x87892),x87893))),f333(f41(x87891),f333(f333(f23(f917(x87891,a905)),x87892),x87893)))+~P106(f333(f67(x87891),f333(f333(f112(f917(x87891,a905)),x87892),x87893))) % 173.51/173.27 [9042]~P9(f333(x90422,f445(x90422,x90423,x90421)))+E(f333(f111(a1),f333(f333(f6(x90421,a910),f333(f333(f8(a1,a910,x90421),a115),x90422)),x90423)),f333(f333(f6(x90421,a1),x90422),x90423)) % 173.51/173.27 [9043]~P9(f333(x90432,f503(x90432,x90433,x90431)))+E(f333(f111(a1),f333(f333(f9(x90431,a910),f333(f333(f8(a1,a910,x90431),a115),x90432)),x90433)),f333(f333(f9(x90431,a1),x90432),x90433)) % 173.51/173.27 [9091]~P106(f333(f67(x90911),x90913))+P106(f333(f333(f246(a910),f333(f333(f23(a910),f333(f41(x90911),x90912)),f333(f41(x90911),x90913))),f333(f41(x90911),f333(f333(f23(f917(x90911,a905)),x90912),x90913)))) % 173.51/173.27 [9119]P106(f333(f333(f335(x91191),f445(x91192,x91193,x91191)),x91193))+E(f333(f111(a1),f333(f333(f6(x91191,a910),f333(f333(f8(a1,a910,x91191),a115),x91192)),x91193)),f333(f333(f6(x91191,a1),x91192),x91193)) % 173.51/173.27 [9120]P106(f333(f333(f335(x91201),f503(x91202,x91203,x91201)),x91203))+E(f333(f111(a1),f333(f333(f9(x91201,a910),f333(f333(f8(a1,a910,x91201),a115),x91202)),x91203)),f333(f333(f9(x91201,a1),x91202),x91203)) % 173.51/173.27 [9191]E(f92(x91911,f333(f333(f7(x91911,f917(x91911,a905),a905),f335(x91911)),f333(f333(f23(f917(x91911,a905)),x91912),f333(f333(f315(x91911),x91913),f196(f917(x91911,a905)))))),f259(x91911,x91913,x91912))+P106(f333(f333(f246(f917(x91911,a905)),x91912),f333(f333(f315(x91911),x91913),f196(f917(x91911,a905))))) % 173.51/173.27 [9549]E(f333(f333(f162(f911(x95491),x95491),f333(f333(f7(f911(x95491),a910,x95491),f172(x95491)),x95492)),f333(f144(f911(x95491),f333(f333(f8(a910,a905,f911(x95491)),f333(f247(a910),x95492)),f197(f911(x95491)))),x95493)),f333(f333(f172(f911(x95491)),f187(x95491,x95493)),x95492))+~P106(f333(f333(f247(a910),x95492),f333(f197(f911(f911(x95491))),f187(x95491,x95493)))) % 173.51/173.27 [9629]E(f333(f144(x96291,x96292),x96293),f185(x96291,x96292,x96293))+P106(f333(f333(f335(x96291),f769(x96293,x96292,x96291)),f333(f180(x96291),f333(f333(f146(x96291),f333(f197(f911(x96291)),f185(x96291,x96292,x96293))),x96293)))) % 173.51/173.27 [9780]E(f333(f333(f146(x97801),f333(f197(f911(x97801)),f185(x97801,x97802,x97803))),x97803),f124(x97801))+~P106(f333(x97802,f333(f149(x97801),f333(f333(f146(x97801),f333(f197(f911(x97801)),f185(x97801,x97802,x97803))),x97803)))) % 173.51/173.27 [9872]~P106(f333(f333(f335(f916(x98721,x98721)),x98722),f313(x98721,x98723)))+P106(f333(f333(f335(f916(x98721,x98721)),x98722),f333(f333(f45(a910,f917(f916(x98721,x98721),a905)),f254(f917(a910,a905))),f333(f333(f7(a910,f917(f916(x98721,x98721),a905),f917(f916(x98721,x98721),a905)),f191(f916(x98721,x98721),a905)),x98723)))) % 173.51/173.27 [9933]~P106(f333(f333(f246(f917(x99331,a905)),f333(f333(f45(a910,f917(x99331,a905)),f333(f308(a910,f2(a910)),f495(x99333,x99332,x99331))),x99332)),x99333))+P106(f333(f333(f246(f917(x99331,a905)),f333(f333(f45(a910,f917(x99331,a905)),f254(f917(a910,a905))),x99332)),x99333)) % 173.51/173.27 [9979]~P106(f333(f333(f247(a1),f2(a1)),x99793))+P106(f333(f333(f247(a1),x99791),f333(f333(f87(a1),x99792),f333(f333(f88(a1),f333(f333(f87(a1),f333(f82(a1),f333(f333(f23(a1),x99792),x99791))),f85(a1))),x99793)))) % 173.51/173.27 [9991]~P40(x99911,f333(f333(f121(f917(f916(x99911,x99911),a905)),x99912),x99913))+P40(x99911,f333(f333(f121(f917(f916(x99911,x99911),a905)),f333(f333(f121(f917(f916(x99911,x99911),a905)),f333(f333(f295(x99911,x99911,x99911),x99912),x99912)),f333(f333(f295(x99911,x99911,x99911),x99913),x99912))),x99913)) % 173.51/173.27 [10071]P40(x100711,f333(f333(f121(f917(f916(x100711,x100711),a905)),x100712),x100713))+~P40(x100711,f333(f333(f121(f917(f916(x100711,x100711),a905)),f333(f333(f121(f917(f916(x100711,x100711),a905)),f333(f333(f295(x100711,x100711,x100711),x100712),x100712)),f333(f333(f295(x100711,x100711,x100711),x100713),x100712))),x100713)) % 173.51/173.27 [9633]~P139(x96331)+E(f333(f113(x96331),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x96332),x96333)),f196(f917(f916(a910,a910),a905)))))),f333(f333(f23(x96331),f333(f111(x96331),x96332)),f333(f111(x96331),x96333))) % 173.51/173.27 [9725]P106(f333(x97253,x97252))+E(f333(f252(x97251),f333(f333(f18(x97251,a905,a905),f333(f333(f8(a905,f917(a905,a905),x97251),a331),f333(f333(f7(x97251,x97251,a905),a330),x97252))),x97253)),f196(f917(x97251,a905))) % 173.51/173.27 [9727]~P106(f333(x97273,x97272))+E(f333(f252(x97271),f333(f333(f18(x97271,a905,a905),f333(f333(f8(a905,f917(a905,a905),x97271),a331),f333(f333(f7(x97271,x97271,a905),a330),x97272))),x97273)),f333(f333(f315(x97271),x97272),f196(f917(x97271,a905)))) % 173.51/173.27 [9958]E(x99581,x99582)+P106(f333(f333(f255(x99583,x99583,f333(f333(f8(f917(x99583,a905),f917(x99583,a905),x99583),f333(f8(a905,a905,x99583),a328)),a330)),x99581),x99582)) % 173.51/173.27 [10051]~E(x100511,x100512)+~P106(f333(f333(f255(x100513,x100513,f333(f333(f8(f917(x100513,a905),f917(x100513,a905),x100513),f333(f8(a905,a905,x100513),a328)),a330)),x100511),x100512)) % 173.51/173.27 [10063]~P106(f333(f67(x100631),x100633))+E(f333(f333(f70(x100631,f917(x100631,a905),f333(f333(f8(f917(x100631,a905),f917(f917(x100631,a905),f917(x100631,a905)),x100631),f333(f7(f917(x100631,a905),f917(x100631,a905),f917(x100631,a905)),f23(f917(x100631,a905)))),f333(f333(f7(x100631,f917(x100631,a905),f917(x100631,a905)),f315(x100631)),f196(f917(x100631,a905))))),x100632),x100633),f333(f333(f23(f917(x100631,a905)),x100632),x100633)) % 173.51/173.27 [10097]~P106(f333(f333(f247(a1),f2(a1)),x100973))+P106(f333(f333(f247(a1),f333(f333(f23(a1),x100971),f333(f333(f88(a1),f333(f333(f87(a1),f333(f82(a1),f333(f333(f23(a1),x100971),x100972))),f85(a1))),x100973))),x100972)) % 173.51/173.27 [10335]~P106(f333(f333(f335(x103351),x103353),f322(x103351,x103352)))+P106(f333(f321(x103351,f333(f333(f7(x103351,f917(f916(x103351,x103351),a905),f917(x103351,a905)),f333(f333(f8(f917(x103351,f917(f917(f916(x103351,x103351),a905),a905)),f917(f917(f916(x103351,x103351),a905),f917(x103351,a905)),x103351),f7(x103351,f917(f916(x103351,x103351),a905),a905)),f333(f333(f8(f917(x103351,f916(x103351,x103351)),f917(x103351,f917(f917(f916(x103351,x103351),a905),a905)),x103351),f333(f8(f916(x103351,x103351),f917(f917(f916(x103351,x103351),a905),a905),x103351),f335(f916(x103351,x103351)))),f265(x103351,x103351)))),x103352)),x103353)) % 173.51/173.27 [10349]P106(f333(f333(f335(x103491),x103492),f322(x103491,x103493)))+~P106(f333(f321(x103491,f333(f333(f7(x103491,f917(f916(x103491,x103491),a905),f917(x103491,a905)),f333(f333(f8(f917(x103491,f917(f917(f916(x103491,x103491),a905),a905)),f917(f917(f916(x103491,x103491),a905),f917(x103491,a905)),x103491),f7(x103491,f917(f916(x103491,x103491),a905),a905)),f333(f333(f8(f917(x103491,f916(x103491,x103491)),f917(x103491,f917(f917(f916(x103491,x103491),a905),a905)),x103491),f333(f8(f916(x103491,x103491),f917(f917(f916(x103491,x103491),a905),a905),x103491),f335(f916(x103491,x103491)))),f265(x103491,x103491)))),x103493)),x103492)) % 173.51/173.27 [9931]~P106(f333(f67(x99311),f333(f252(x99311),x99313)))+P106(f333(f67(x99311),f333(f252(x99311),f333(f333(f18(x99311,a905,a905),f333(f333(f8(a905,f917(a905,a905),x99311),a331),x99312)),x99313)))) % 173.51/173.27 [9932]~P106(f333(f67(x99321),f333(f252(x99321),x99322)))+P106(f333(f67(x99321),f333(f252(x99321),f333(f333(f18(x99321,a905,a905),f333(f333(f8(a905,f917(a905,a905),x99321),a331),x99322)),x99323)))) % 173.51/173.27 [10024]P106(f333(f67(x100241),f333(f252(x100241),x100242)))+~P106(f333(f67(x100241),f333(f252(x100241),f333(f333(f18(x100241,a905,a905),f333(f333(f8(a905,f917(a905,a905),x100241),a332),x100243)),x100242)))) % 173.51/173.27 [10025]P106(f333(f67(x100251),f333(f252(x100251),x100252)))+~P106(f333(f67(x100251),f333(f252(x100251),f333(f333(f18(x100251,a905,a905),f333(f333(f8(a905,f917(a905,a905),x100251),a332),x100252)),x100253)))) % 173.51/173.27 [10314]~P106(f333(f67(x103141),x103142))+P106(f333(f67(f911(x103141)),f333(f252(f911(x103141)),f333(f333(f18(f911(x103141),a905,a905),f333(f333(f8(a905,f917(a905,a905),f911(x103141)),a331),f333(f333(f7(f911(x103141),f917(x103141,a905),a905),f333(f333(f8(f917(x103141,a905),f917(f917(x103141,a905),a905),f911(x103141)),f246(f917(x103141,a905))),f180(x103141))),x103142))),f333(f333(f7(f911(x103141),a910,a905),f333(f333(f8(a910,f917(a910,a905),f911(x103141)),a330),f197(f911(x103141)))),x103143))))) % 173.51/173.27 [10315]~P106(f333(f67(x103151),x103152))+P106(f333(f67(f911(x103151)),f333(f252(f911(x103151)),f333(f333(f18(f911(x103151),a905,a905),f333(f333(f8(a905,f917(a905,a905),f911(x103151)),a331),f333(f333(f7(f911(x103151),f917(x103151,a905),a905),f333(f333(f8(f917(x103151,a905),f917(f917(x103151,a905),a905),f911(x103151)),f246(f917(x103151,a905))),f180(x103151))),x103152))),f333(f333(f7(f911(x103151),a910,a905),f333(f333(f8(a910,f917(a910,a905),f911(x103151)),f246(a910)),f197(f911(x103151)))),x103153))))) % 173.51/173.27 [10040]~P117(x100401)+E(f333(f333(f256(x100401),x100402),f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x100403)),f333(f333(f88(x100401),f333(f333(f256(x100401),x100402),x100403)),f333(f333(f256(x100401),x100402),x100403))) % 173.51/173.27 [10076]~P83(x100761)+E(f333(f333(f256(x100761),f333(f333(f256(x100761),x100762),x100763)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f256(x100761),x100762),f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x100763))) % 173.51/173.27 [10124]~P139(x101241)+E(f333(f333(f256(x101241),f333(f86(x101241),x101242)),f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101243)),f333(f333(f256(x101241),x101242),f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101243))) % 173.51/173.27 [10266]~P120(x102661)+P106(f333(f333(f246(x102661),f2(x102661)),f333(f333(f87(x102661),f333(f333(f256(x102661),x102662),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x102661),x102663),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))))) % 173.51/173.27 [10134]~P117(x101341)+E(f333(f333(f256(x101341),x101342),f333(a123,f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101343))),f333(f333(f88(x101341),x101342),f333(f333(f88(x101341),f333(f333(f256(x101341),x101342),x101343)),f333(f333(f256(x101341),x101342),x101343)))) % 173.51/173.27 [10187]~P83(x101871)+E(f333(f333(f88(x101871),x101872),f333(f333(f256(x101871),f333(f333(f256(x101871),x101872),x101873)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x101871),x101872),f333(a123,f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101873)))) % 173.51/173.27 [10223]~P120(x102231)+P106(f333(f333(f246(x102231),f2(x102231)),f333(f333(f256(x102231),x102232),f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102233)))) % 173.51/173.27 [10292]~P95(x102921)+E(f333(f333(f23(x102921),f333(f333(f87(x102921),f333(f333(f256(x102921),x102922),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x102921),x102923),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f333(f333(f88(x102921),f333(f333(f88(x102921),f333(f114(x102921),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102922)),x102923)),f333(f333(f256(x102921),f333(f333(f23(x102921),x102922),x102923)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.27 [10293]~P95(x102931)+E(f333(f333(f87(x102931),f333(f333(f87(x102931),f333(f333(f256(x102931),x102932),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x102931),x102933),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f333(f333(f88(x102931),f333(f333(f88(x102931),f333(f114(x102931),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x102932)),x102933)),f333(f333(f256(x102931),f333(f333(f87(x102931),x102932),x102933)),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.27 [10401]~P32(x104011,x104012,x104013)+P106(f106(x104011,a905,f333(f333(f8(f917(a907,f917(f917(x104011,f917(a906,a905)),f917(x104011,a905))),f917(a907,f917(f917(x104011,f917(a906,a905)),a905)),f917(x104011,f917(a906,a905))),f333(f8(f917(f917(x104011,f917(a906,a905)),f917(x104011,a905)),f917(f917(x104011,f917(a906,a905)),a905),a907),f333(f8(f917(x104011,a905),a905,f917(x104011,f917(a906,a905))),f95(x104011)))),f333(f333(f8(f917(a907,f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905)))),f917(a907,f917(f917(x104011,f917(a906,a905)),f917(x104011,a905))),f917(x104011,f917(a906,a905))),f333(f8(f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),f917(f917(x104011,f917(a906,a905)),f917(x104011,a905)),a907),f333(f8(f917(x104011,f917(a906,a905)),f917(x104011,a905),f917(x104011,f917(a906,a905))),f333(f8(f917(a906,a905),a905,x104011),f95(a906))))),f333(f333(f7(f917(x104011,f917(a906,a905)),f917(a907,f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905)))),f917(a907,f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))))),f333(f333(f8(f917(f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905)))),f917(f917(a907,f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905)))),f917(a907,f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))))),f917(x104011,f917(a906,a905))),f8(f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),a907)),f333(f333(f8(f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),f917(f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905)))),f917(x104011,f917(a906,a905))),f8(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905)))),f333(f333(f8(f917(x104011,f917(f917(a906,a905),f917(a906,a905))),f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),f917(x104011,f917(a906,a905))),f18(x104011,f917(a906,a905),f917(a906,a905))),f333(f333(f8(f917(x104011,f917(a906,f917(a905,a905))),f917(x104011,f917(f917(a906,a905),f917(a906,a905))),f917(x104011,f917(a906,a905))),f333(f8(f917(a906,f917(a905,a905)),f917(f917(a906,a905),f917(a906,a905)),x104011),f18(a906,a905,a905))),f333(f8(f917(a906,a905),f917(a906,f917(a905,a905)),x104011),f333(f8(a905,f917(a905,a905),a906),a336))))))),f333(f333(f8(f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,f917(a906,a905)))),f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),a907),f333(f8(f917(x104011,f917(a906,f917(a906,a905))),f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,a905))),f333(f8(f917(a906,f917(a906,a905)),f917(a906,a905),x104011),f333(f8(f917(a906,a905),a905,a906),f95(a906))))),f333(f333(f8(f917(f917(a906,a905),f917(a906,f917(a906,a905))),f917(f917(x104011,f917(a906,a905)),f917(x104011,f917(a906,f917(a906,a905)))),a907),f8(f917(a906,a905),f917(a906,f917(a906,a905)),x104011)),f333(f333(f8(f917(a906,f917(f917(a906,a905),f917(a906,a905))),f917(f917(a906,a905),f917(a906,f917(a906,a905))),a907),f7(a906,f917(a906,a905),f917(a906,a905))),f333(f333(f8(f917(a906,f917(a906,f917(a905,a905))),f917(a906,f917(f917(a906,a905),f917(a906,a905))),a907),f333(f8(f917(a906,f917(a905,a905)),f917(f917(a906,a905),f917(a906,a905)),a906),f18(a906,a905,a905))),f333(f333(f8(f917(a906,f917(a906,a905)),f917(a906,f917(a906,f917(a905,a905))),a907),f333(f8(f917(a906,a905),f917(a906,f917(a905,a905)),a906),f333(f8(a905,f917(a905,a905),a906),a336))),f333(f333(f7(a907,a910,f917(a906,f917(a906,a905))),f333(f333(f8(f917(a906,f917(a910,f917(a906,a905))),f917(a910,f917(a906,f917(a906,a905))),a907),f7(a906,a910,f917(a906,a905))),a204)),x104012))))))))),x104013)) % 173.51/173.27 [10403]P32(x104031,x104032,x104033)+~P106(f106(x104031,a905,f333(f333(f8(f917(a907,f917(f917(x104031,f917(a906,a905)),f917(x104031,a905))),f917(a907,f917(f917(x104031,f917(a906,a905)),a905)),f917(x104031,f917(a906,a905))),f333(f8(f917(f917(x104031,f917(a906,a905)),f917(x104031,a905)),f917(f917(x104031,f917(a906,a905)),a905),a907),f333(f8(f917(x104031,a905),a905,f917(x104031,f917(a906,a905))),f95(x104031)))),f333(f333(f8(f917(a907,f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905)))),f917(a907,f917(f917(x104031,f917(a906,a905)),f917(x104031,a905))),f917(x104031,f917(a906,a905))),f333(f8(f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),f917(f917(x104031,f917(a906,a905)),f917(x104031,a905)),a907),f333(f8(f917(x104031,f917(a906,a905)),f917(x104031,a905),f917(x104031,f917(a906,a905))),f333(f8(f917(a906,a905),a905,x104031),f95(a906))))),f333(f333(f7(f917(x104031,f917(a906,a905)),f917(a907,f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905)))),f917(a907,f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))))),f333(f333(f8(f917(f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905)))),f917(f917(a907,f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905)))),f917(a907,f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))))),f917(x104031,f917(a906,a905))),f8(f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),a907)),f333(f333(f8(f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),f917(f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905)))),f917(x104031,f917(a906,a905))),f8(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905)))),f333(f333(f8(f917(x104031,f917(f917(a906,a905),f917(a906,a905))),f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),f917(x104031,f917(a906,a905))),f18(x104031,f917(a906,a905),f917(a906,a905))),f333(f333(f8(f917(x104031,f917(a906,f917(a905,a905))),f917(x104031,f917(f917(a906,a905),f917(a906,a905))),f917(x104031,f917(a906,a905))),f333(f8(f917(a906,f917(a905,a905)),f917(f917(a906,a905),f917(a906,a905)),x104031),f18(a906,a905,a905))),f333(f8(f917(a906,a905),f917(a906,f917(a905,a905)),x104031),f333(f8(a905,f917(a905,a905),a906),a336))))))),f333(f333(f8(f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,f917(a906,a905)))),f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),a907),f333(f8(f917(x104031,f917(a906,f917(a906,a905))),f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,a905))),f333(f8(f917(a906,f917(a906,a905)),f917(a906,a905),x104031),f333(f8(f917(a906,a905),a905,a906),f95(a906))))),f333(f333(f8(f917(f917(a906,a905),f917(a906,f917(a906,a905))),f917(f917(x104031,f917(a906,a905)),f917(x104031,f917(a906,f917(a906,a905)))),a907),f8(f917(a906,a905),f917(a906,f917(a906,a905)),x104031)),f333(f333(f8(f917(a906,f917(f917(a906,a905),f917(a906,a905))),f917(f917(a906,a905),f917(a906,f917(a906,a905))),a907),f7(a906,f917(a906,a905),f917(a906,a905))),f333(f333(f8(f917(a906,f917(a906,f917(a905,a905))),f917(a906,f917(f917(a906,a905),f917(a906,a905))),a907),f333(f8(f917(a906,f917(a905,a905)),f917(f917(a906,a905),f917(a906,a905)),a906),f18(a906,a905,a905))),f333(f333(f8(f917(a906,f917(a906,a905)),f917(a906,f917(a906,f917(a905,a905))),a907),f333(f8(f917(a906,a905),f917(a906,f917(a905,a905)),a906),f333(f8(a905,f917(a905,a905),a906),a336))),f333(f333(f7(a907,a910,f917(a906,f917(a906,a905))),f333(f333(f8(f917(a906,f917(a910,f917(a906,a905))),f917(a910,f917(a906,f917(a906,a905))),a907),f7(a906,a910,f917(a906,a905))),a204)),x104032))))))))),x104033)) % 173.51/173.27 [4822]E(x48221,x48222)+~E(f31(x48223,x48221),f31(x48224,x48222)) % 173.51/173.27 [4823]E(x48231,x48232)+~E(f31(x48231,x48233),f31(x48232,x48234)) % 173.51/173.27 [4824]E(x48241,x48242)+~E(f30(x48243,x48241),f30(x48244,x48242)) % 173.51/173.27 [4825]E(x48251,x48252)+~E(f30(x48251,x48253),f30(x48252,x48254)) % 173.51/173.27 [4826]E(x48261,x48262)+~E(f26(x48263,x48261),f26(x48264,x48262)) % 173.51/173.27 [4827]E(x48271,x48272)+~E(f26(x48271,x48273),f26(x48272,x48274)) % 173.51/173.27 [7888]P27(x78881,x78882,x78883,x78884)+~E(f808(x78884,x78883,x78882,x78881),f815(x78884,x78883,x78882,x78881)) % 173.51/173.27 [8186]P37(x81861,x81862,x81863,x81864,f124(x81862))+~E(x81864,f124(x81861)) % 173.51/173.27 [8187]P37(x81871,x81872,x81873,f124(x81871),x81874)+~E(x81874,f124(x81872)) % 173.51/173.27 [8736]~P37(x87362,x87363,x87364,x87361,f124(x87363))+E(x87361,f124(x87362)) % 173.51/173.27 [8737]~P37(x87373,x87372,x87374,f124(x87373),x87371)+E(x87371,f124(x87372)) % 173.51/173.27 [5205]~P19(x52053,x52051,x52054)+E(f333(f333(x52051,x52052),x52052),x52052) % 173.51/173.27 [5455]P106(f333(x54552,x54554))+E(f333(f144(x54551,x54552),f177(x54551,x54553,x54554)),f124(x54551)) % 173.51/173.27 [5490]~E(x54904,f196(f917(x54901,a905)))+E(f333(f316(x54901,x54902,x54903),x54904),f196(f917(x54902,a905))) % 173.51/173.27 [5727]~P106(f333(x57272,x57274))+E(f333(f144(x57271,x57272),f177(x57271,x57273,x57274)),f177(x57271,x57273,x57274)) % 173.51/173.27 [5756]~E(f333(f316(x57562,x57563,x57564),x57561),f196(f917(x57563,a905)))+E(x57561,f196(f917(x57562,a905))) % 173.51/173.27 [6037]~P110(x60372)+E(f333(f333(f156(x60371,x60372,x60373),x60374),f124(x60371)),f333(f333(f159(x60371),x60374),f124(x60371))) % 173.51/173.27 [6391]~E(x63911,f196(f917(x63912,a905)))+~P106(f333(f68(x63912,x63913,x63911),x63914)) % 173.51/173.27 [6414]~P62(x64141,x64143,x64144,x64142)+P106(f333(f67(x64141),x64142)) % 173.51/173.27 [6416]~P62(x64161,x64163,x64162,x64164)+P106(f333(f67(x64161),x64162)) % 173.51/173.27 [6423]~P62(x64232,x64233,x64234,x64231)+~E(x64231,f196(f917(x64232,a905))) % 173.51/173.27 [6454]~P112(x64541)+E(f333(f333(f112(f917(x64541,a905)),f333(f308(x64541,x64542),x64543)),f309(x64541,x64543,x64544)),f196(f917(x64541,a905))) % 173.51/173.27 [6480]~P106(f333(f333(x64803,x64804),x64802))+P106(f333(f333(f335(x64801),x64802),f299(x64801,x64803,x64804))) % 173.51/173.27 [6481]~P106(f333(f333(x64813,x64814),x64812))+P106(f333(f333(f335(x64811),x64812),f300(x64811,x64813,x64814))) % 173.51/173.27 [6482]~P106(f333(f333(x64823,x64822),x64824))+P106(f333(f333(f335(x64821),x64822),f301(x64821,x64823,x64824))) % 173.51/173.27 [6483]~P106(f333(f333(x64833,x64832),x64834))+P106(f333(f333(f335(x64831),x64832),f304(x64831,x64833,x64834))) % 173.51/173.27 [6547]~P52(x65474,x65471,x65472,x65473)+P106(f333(f333(x65471,x65472),x65473)) % 173.51/173.27 [6624]~P112(x66241)+E(f333(f333(f112(f917(x66241,a905)),f309(x66241,x66242,x66243)),f311(x66241,x66243,x66244)),f196(f917(x66241,a905))) % 173.51/173.27 [6625]~P112(x66251)+E(f333(f333(f112(f917(x66251,a905)),f309(x66251,x66252,x66253)),f312(x66251,x66253,x66254)),f196(f917(x66251,a905))) % 173.51/173.27 [6626]~P112(x66261)+E(f333(f333(f112(f917(x66261,a905)),f311(x66261,x66262,x66263)),f311(x66261,x66263,x66264)),f196(f917(x66261,a905))) % 173.51/173.27 [6627]~P112(x66271)+E(f333(f333(f112(f917(x66271,a905)),f311(x66271,x66272,x66273)),f312(x66271,x66273,x66274)),f196(f917(x66271,a905))) % 173.51/173.27 [6628]~P112(x66281)+E(f333(f333(f112(f917(x66281,a905)),f312(x66281,x66282,x66283)),f309(x66281,x66283,x66284)),f196(f917(x66281,a905))) % 173.51/173.27 [6665]P106(f333(f333(x66651,x66652),f604(x66652,x66651)))+~P106(f333(f261(x66653,x66654,x66651),x66652)) % 173.51/173.27 [6669]~P52(x66691,x66692,x66693,x66694)+~P106(f333(f333(x66692,x66694),x66693)) % 173.51/173.27 [6745]~P110(x67452)+E(f333(f180(x67451),f158(x67451,x67452,x67453,x67454)),f333(f180(x67451),x67454)) % 173.51/173.27 [6796]~P107(x67961)+E(f198(x67961,x67962,f333(a123,x67963),x67964),f198(x67961,x67962,x67963,f333(x67962,x67964))) % 173.51/173.27 [6854]~P106(f333(f333(f335(x68544),x68543),f299(x68544,x68541,x68542)))+P106(f333(f333(x68541,x68542),x68543)) % 173.51/173.27 [6855]~P106(f333(f333(f335(x68554),x68553),f300(x68554,x68551,x68552)))+P106(f333(f333(x68551,x68552),x68553)) % 173.51/173.27 [6856]~P106(f333(f333(f335(x68564),x68562),f301(x68564,x68561,x68563)))+P106(f333(f333(x68561,x68562),x68563)) % 173.51/173.27 [6857]~P106(f333(f333(f335(x68574),x68572),f304(x68574,x68571,x68573)))+P106(f333(f333(x68571,x68572),x68573)) % 173.51/173.27 [6932]E(f333(f41(f918(x69321,x69322)),f319(x69321,x69322,x69323,x69324)),f2(a910))+P106(f333(f67(x69322),x69324)) % 173.51/173.27 [6933]E(f333(f41(f918(x69331,x69332)),f319(x69331,x69332,x69333,x69334)),f2(a910))+P106(f333(f67(x69331),x69333)) % 173.51/173.27 [7132]~P17(x71324,x71321,x71322)+E(f333(f79(x71321,x71321,x71321,f333(x71322,x71323)),f333(x71322,x71323)),f333(x71322,x71323)) % 173.51/173.27 [7372]E(f284(x73721,x73722,x73723,x73724),f333(f265(f917(a110,f917(a905,f914(f912(x73721)))),f916(a110,a110)),f47(x73721)))+~P106(f333(f333(f246(a110),x73723),f2(a110))) % 173.51/173.27 [7926]~P106(f333(x79261,x79264))+P106(f333(x79261,f102(x79262,a910,x79263,x79261))) % 173.51/173.27 [8010]~E(x80102,x80103)+P106(f333(f333(f335(f916(x80101,x80101)),f333(f333(f265(x80101,x80101),x80102),x80103)),f313(x80101,x80104))) % 173.51/173.27 [8040]~P27(x80401,x80402,x80403,f254(f917(x80401,a905)))+E(f333(f84(x80401,x80402,f254(f917(x80401,a905)),x80403),f333(x80403,x80404)),x80404) % 173.51/173.27 [8041]~P27(x80411,x80412,x80413,f254(f917(x80411,a905)))+E(f333(f99(x80411,x80412,f254(f917(x80411,a905)),x80413),f333(x80413,x80414)),x80414) % 173.51/173.27 [8132]~P106(f333(f333(f335(f911(x81321)),f333(f333(f159(x81321),x81324),x81322)),f169(x81321,x81323)))+P106(f333(f333(f335(f911(x81321)),x81322),f169(x81321,x81323))) % 173.51/173.27 [8133]~P106(f333(f333(f335(f911(x81331)),f333(f333(f142(x81331),x81334),x81332)),f169(x81331,x81333)))+P106(f333(f333(f335(f911(x81331)),x81332),f169(x81331,x81333))) % 173.51/173.27 [8134]~P106(f333(f333(f335(f911(x81341)),f333(f333(f142(x81341),x81342),x81344)),f169(x81341,x81343)))+P106(f333(f333(f335(f911(x81341)),x81342),f169(x81341,x81343))) % 173.51/173.27 [8148]~P110(x81481)+P16(x81481,f333(f333(f162(x81482,x81481),x81483),f158(x81482,x81481,x81483,x81484))) % 173.51/173.27 [8248]P27(x82484,x82483,x82481,x82482)+E(f333(x82481,f808(x82482,x82481,x82483,x82484)),f333(x82481,f815(x82482,x82481,x82483,x82484))) % 173.51/173.27 [8358]~P27(x83582,x83581,x83584,x83583)+P27(x83581,x83582,f84(x83582,x83581,x83583,x83584),f333(f316(x83582,x83581,x83584),x83583)) % 173.51/173.27 [8498]P40(f916(x84982,x84984),f287(x84982,x84984,x84981,x84983))+P106(f333(x84981,f594(x84982,x84983,x84984,x84981))) % 173.51/173.27 [8623]E(x86231,x86232)+~P106(f333(f333(f335(f916(x86233,x86233)),f333(f333(f265(x86233,x86233),x86231),x86232)),f253(x86233,x86234))) % 173.51/173.27 [8689]~P106(f333(f67(f918(x86893,x86891)),f319(x86893,x86891,x86894,x86892)))+P106(f333(f67(x86891),x86892)) % 173.51/173.27 [8690]~P106(f333(f67(f918(x86901,x86903)),f319(x86901,x86903,x86902,x86904)))+P106(f333(f67(x86901),x86902)) % 173.51/173.27 [8699]~P27(x86991,x86992,x86993,x86994)+P28(x86991,x86992,x86993,x86994,f333(f316(x86991,x86992,x86993),x86994)) % 173.51/173.27 [8790]~P28(x87902,x87903,x87904,x87901,f196(f917(x87903,a905)))+E(x87901,f196(f917(x87902,a905))) % 173.51/173.27 [8791]~P28(x87913,x87912,x87914,f196(f917(x87913,a905)),x87911)+E(x87911,f196(f917(x87912,a905))) % 173.51/173.27 [8882]P40(f916(x88821,x88822),f287(x88821,x88822,x88823,x88824))+~P40(x88822,f333(x88824,f594(x88821,x88824,x88822,x88823))) % 173.51/173.27 [9469]E(f333(f333(f167(x94691,x94692),f717(x94693,x94694,x94692,x94691)),f718(x94693,x94694,x94692,x94691)),x94694)+~P106(f333(f333(f335(f916(f911(x94691),f911(x94691))),f333(f333(f265(f911(x94691),f911(x94691)),x94692),x94694)),f165(x94691,x94693))) % 173.51/173.27 [9470]~P106(f333(x94703,x94704))+P106(f333(f333(f246(a910),f333(x94701,f102(x94702,a910,x94701,x94703))),f333(x94701,x94704))) % 173.51/173.27 [9476]~P106(f333(f333(f335(f916(f911(x94761),f911(x94761))),f333(f333(f265(f911(x94761),f911(x94761)),x94762),x94763)),f153(x94761,x94764)))+P106(f333(f333(f335(f916(f911(x94761),f911(x94761))),f333(f333(f265(f911(x94761),f911(x94761)),x94762),x94763)),f155(x94761,x94764))) % 173.51/173.27 [9586]P106(f333(f67(x95861),x95862))+~P106(f333(f333(f335(f916(f917(x95861,a905),f917(x95861,a905))),f333(f333(f265(f917(x95861,a905),f917(x95861,a905)),x95863),x95862)),f324(x95861,x95864))) % 173.51/173.27 [9587]P106(f333(f67(x95871),x95872))+~P106(f333(f333(f335(f916(f917(x95871,a905),f917(x95871,a905))),f333(f333(f265(f917(x95871,a905),f917(x95871,a905)),x95872),x95873)),f324(x95871,x95874))) % 173.51/173.27 [9590]~E(x95901,f196(f917(x95902,a905)))+~P106(f333(f333(f335(f916(f917(x95902,a905),f917(x95902,a905))),f333(f333(f265(f917(x95902,a905),f917(x95902,a905)),x95903),x95901)),f324(x95902,x95904))) % 173.51/173.27 [10235]P14(x102351,x102352,x102353,x102354)+~P106(f333(f333(f269(x102351,x102351,a905),f333(f333(f7(x102351,f917(x102351,x102352),f917(x102351,a905)),f333(f333(f8(f917(x102352,a905),f917(f917(x102351,x102352),f917(x102351,a905)),x102351),f8(x102352,a905,x102351)),f333(f333(f8(x102352,f917(x102352,a905),x102351),a330),x102354))),x102354)),f532(x102354,x102353,x102352,x102351))) % 173.51/173.27 [5107]~E(x51072,f124(x51071))+E(f333(f333(f167(x51071,x51072),x51073),x51074),f124(x51071)) % 173.51/173.27 [5108]~E(x51084,f124(x51081))+E(f333(f333(f162(x51081,x51082),x51083),x51084),f124(x51082)) % 173.51/173.27 [5339]E(x53391,f124(x53392))+~E(f333(f333(f162(x53392,x53393),x53394),x53391),f124(x53393)) % 173.51/173.27 [5340]E(x53401,f124(x53402))+~E(f333(f333(f167(x53402,x53401),x53403),x53404),f124(x53402)) % 173.51/173.27 [5376]E(x53761,x53762)+~E(f333(f333(f142(x53763),x53764),x53761),f333(f333(f142(x53763),x53764),x53762)) % 173.51/173.27 [5377]E(x53771,x53772)+~E(f333(f333(f142(x53773),x53771),x53774),f333(f333(f142(x53773),x53772),x53774)) % 173.51/173.27 [5526]P106(f333(x55263,x55262))+E(f178(x55261,x55262,f333(f144(x55261,x55263),x55264)),f333(f144(x55261,x55263),x55264)) % 173.51/173.27 [5528]~P106(f333(x55282,x55283))+P36(x55281,x55282,f333(f333(f159(x55281),x55283),x55284)) % 173.51/173.27 [5537]E(x55371,x55372)+~E(f147(a910,f333(f308(a910,x55371),x55373)),f333(f333(f159(a910),x55372),x55374)) % 173.51/173.27 [5583]~P29(x55832,x55833)+P29(x55831,f333(f333(f80(x55832,x55831),x55833),x55834)) % 173.51/173.27 [5584]~P40(x55842,x55843)+P40(x55841,f333(f333(f294(x55842,x55841),x55843),x55844)) % 173.51/173.27 [5585]~P41(x55852,x55853)+P41(x55851,f333(f333(f294(x55852,x55851),x55853),x55854)) % 173.51/173.27 [5586]~P55(x55862,x55863)+P55(x55861,f333(f333(f294(x55862,x55861),x55863),x55864)) % 173.51/173.27 [5711]~P36(x57111,x57112,x57114)+P36(x57111,x57112,f333(f333(f159(x57111),x57113),x57114)) % 173.51/173.27 [5712]~P36(x57121,x57122,x57124)+P36(x57121,x57122,f333(f333(f142(x57121),x57123),x57124)) % 173.51/173.27 [5713]~P36(x57131,x57132,x57133)+P36(x57131,x57132,f333(f333(f142(x57131),x57133),x57134)) % 173.51/173.27 [5797]~E(x57971,f124(x57972))+~E(f333(f333(f142(x57972),x57973),f333(f333(f159(x57972),x57974),f124(x57972))),x57971) % 173.51/173.27 [5822]~P34(x58223,x58221,f333(f333(f159(x58223),x58222),x58224))+P106(f333(x58221,x58222)) % 173.51/173.27 [5832]E(f125(x58321,x58322),x58323)+~E(f333(f333(f142(x58321),x58323),f333(f333(f159(x58321),x58324),f124(x58321))),x58322) % 173.51/173.27 [5833]E(f152(x58331,x58332),x58333)+~E(f333(f333(f142(x58331),x58334),f333(f333(f159(x58331),x58333),f124(x58331))),x58332) % 173.51/173.27 [5941]~E(f147(a910,f333(f308(a910,x59411),x59412)),f333(f333(f159(a910),x59413),x59414))+P106(f333(f333(f247(a910),x59411),x59412)) % 173.51/173.27 [5950]P34(x59501,x59502,x59503)+~P34(x59501,x59502,f333(f333(f159(x59501),x59504),x59503)) % 173.51/173.27 [5951]P34(x59511,x59512,x59513)+~P34(x59511,x59512,f333(f333(f142(x59511),x59514),x59513)) % 173.51/173.27 [5952]P34(x59521,x59522,x59523)+~P34(x59521,x59522,f333(f333(f142(x59521),x59523),x59524)) % 173.51/173.27 [6142]E(x61421,f333(f333(f142(x61422),f333(f176(x61422),x61423)),f333(f333(f159(x61422),x61424),f124(x61422))))+~E(f333(f176(x61422),x61421),f333(f333(f159(x61422),x61424),x61423)) % 173.51/173.27 [6313]~P112(x63131)+E(f333(f333(f112(f917(x63131,a905)),f333(f308(x63131,x63132),x63133)),f333(f308(x63131,x63133),x63134)),f196(f917(x63131,a905))) % 173.51/173.27 [6324]E(f333(f333(f172(x63241),f177(x63241,x63242,x63243)),x63244),x63243)+~P106(f333(f333(f247(a910),x63244),x63242)) % 173.51/173.27 [6351]~P72(x63511)+E(f333(f173(x63511),f333(f333(f162(a1,x63511),x63512),f186(x63513,x63514))),f333(f333(f6(a1,x63511),x63512),f333(f180(a1),f186(x63513,x63514)))) % 173.51/173.27 [6352]~P72(x63521)+E(f333(f333(f6(a1,x63521),x63522),f333(f180(a1),f186(x63523,x63524))),f333(f173(x63521),f333(f333(f162(a1,x63521),x63522),f186(x63523,x63524)))) % 173.51/173.27 [6493]~E(x64932,f333(f333(f142(x64931),f333(f176(x64931),x64934)),f333(f333(f159(x64931),x64933),f124(x64931))))+E(f333(f176(x64931),x64932),f333(f333(f159(x64931),x64933),x64934)) % 173.51/173.27 [6509]~P21(x65092,x65093,x65094,x65091)+E(f333(x65091,f196(f917(x65092,a905))),f33(x65093)) % 173.51/173.27 [6536]~P112(x65361)+E(f333(f333(f112(f917(x65361,a905)),f312(x65361,x65362,x65363)),f333(f308(x65361,x65363),x65364)),f196(f917(x65361,a905))) % 173.51/173.27 [6746]E(x67461,f196(f917(x67462,a905)))+~E(f319(x67463,x67462,x67464,x67461),f196(f917(f918(x67463,x67462),a905))) % 173.51/173.27 [6747]E(x67471,f196(f917(x67472,a905)))+~E(f319(x67472,x67473,x67471,x67474),f196(f917(f918(x67472,x67473),a905))) % 173.51/173.27 [6815]~P110(x68152)+E(f333(f197(f911(x68151)),f158(x68151,x68152,x68153,x68154)),f333(f197(f911(x68151)),x68154)) % 173.51/173.27 [6826]~P106(f333(f262(x68263,x68264,x68261),x68262))+P106(f333(f333(x68261,f596(x68262,x68261)),x68262)) % 173.51/173.27 [6865]~P106(f333(f67(x68652),x68654))+P106(f333(f67(x68651),f333(f316(x68652,x68651,x68653),x68654))) % 173.51/173.27 [7093]~P27(x70932,x70931,x70933,x70934)+E(f333(f41(x70931),f333(f316(x70932,x70931,x70933),x70934)),f333(f41(x70932),x70934)) % 173.51/173.27 [7111]E(f333(f316(x71111,x71112,x71113),f333(f317(x71111,x71112,x71113),x71114)),x71114)+~E(f333(f316(x71111,x71112,x71113),f254(f917(x71111,a905))),f254(f917(x71112,a905))) % 173.51/173.27 [7523]~P27(x75231,x75232,x75233,f254(f917(x75231,a905)))+E(f333(f317(x75231,x75232,x75233),f333(f316(x75231,x75232,x75233),x75234)),x75234) % 173.51/173.27 [7801]E(x78011,x78012)+~P106(f333(f333(f335(x78013),x78011),f333(f180(x78013),f177(x78013,x78014,x78012)))) % 173.51/173.27 [7812]~E(x78121,f2(a910))+~P106(f333(f333(f335(x78122),x78123),f333(f180(x78122),f177(x78122,x78121,x78124)))) % 173.51/173.27 [7846]P106(f333(x78461,x78462))+~P106(f333(f333(f335(x78463),x78462),f333(f180(x78463),f185(x78463,x78461,x78464)))) % 173.51/173.27 [7957]~P106(f333(f333(f335(f911(x79571)),f333(f333(f159(x79571),x79572),x79574)),f169(x79571,x79573)))+P106(f333(f333(f335(x79571),x79572),x79573)) % 173.51/173.27 [8086]~P106(f333(f333(f335(x80861),x80862),f333(f180(x80861),f184(x80861,x80863,x80864))))+P106(f333(f333(f335(x80861),x80862),f333(f180(x80861),x80863))) % 173.51/173.27 [8087]~P106(f333(f333(f335(x80871),x80872),f333(f180(x80871),f178(x80871,x80874,x80873))))+P106(f333(f333(f335(x80871),x80872),f333(f180(x80871),x80873))) % 173.51/173.27 [8088]~P106(f333(f333(f335(x80881),x80882),f333(f180(x80881),f185(x80881,x80884,x80883))))+P106(f333(f333(f335(x80881),x80882),f333(f180(x80881),x80883))) % 173.51/173.27 [8098]E(f333(f197(f911(x80981)),x80982),x80983)+~P106(f333(f333(f335(f911(x80981)),x80982),f333(f180(f911(x80981)),f61(x80981,x80983,x80984)))) % 173.51/173.27 [8199]P106(f333(x81993,x81992))+E(f333(f144(x81991,f333(f333(f8(a905,a905,x81991),a328),f333(a330,x81992))),f333(f144(x81991,x81993),x81994)),f333(f144(x81991,x81993),x81994)) % 173.51/173.27 [8308]E(f333(f333(f172(x83081),f185(x83081,x83082,x83083)),x83084),f333(f333(f172(x83081),x83083),x83084))+~P106(f333(f333(f247(a910),x83084),f333(f197(f911(x83081)),f185(x83081,x83082,x83083)))) % 173.51/173.27 [8396]~P72(x83961)+E(f333(f333(f6(a910,x83961),f333(f333(f8(a910,x83961,a910),x83962),a123)),f333(f308(a910,x83963),x83964)),f333(f333(f6(a910,x83961),x83962),f333(f308(a910,f333(a123,x83963)),f333(a123,x83964)))) % 173.51/173.27 [8406]~P72(x84061)+E(f333(f333(f6(a910,x84061),f333(f333(f8(a910,x84061,a910),x84062),a123)),f309(a910,x84063,x84064)),f333(f333(f6(a910,x84061),x84062),f309(a910,f333(a123,x84063),f333(a123,x84064)))) % 173.51/173.27 [8536]~P27(x85361,x85363,x85364,f254(f917(x85361,a905)))+P27(x85361,f917(x85362,x85363),f333(f333(f8(x85363,f917(x85362,x85363),x85361),f16(x85363,x85362)),x85364),f254(f917(x85361,a905))) % 173.51/173.27 [8631]~P27(x86312,x86311,x86314,x86313)+E(f333(f316(x86311,x86312,f84(x86312,x86311,x86313,x86314)),f333(f316(x86312,x86311,x86314),x86313)),x86313) % 173.51/173.27 [8691]~P106(f333(f333(f335(f916(x86911,x86911)),f333(f333(f265(x86911,x86911),x86912),x86914)),f253(x86911,x86913)))+P106(f333(f333(f335(x86911),x86912),x86913)) % 173.51/173.27 [8814]~P27(x88142,x88141,x88143,f254(f917(x88142,a905)))+E(f333(f316(x88141,x88142,f99(x88142,x88141,f254(f917(x88142,a905)),x88143)),f333(f316(x88142,x88141,x88143),x88144)),x88144) % 173.51/173.27 [8888]~P28(x88881,x88882,x88883,x88884,f254(f917(x88882,a905)))+E(f333(f316(x88881,x88882,x88883),f254(f917(x88881,a905))),f254(f917(x88882,a905))) % 173.51/173.27 [8921]~E(f333(f333(f6(x89211,a910),x89214),x89213),f333(a123,x89212))+P106(f333(f333(f335(x89211),f493(x89212,x89213,x89214,x89211)),x89213)) % 173.51/173.27 [8942]~E(f333(f333(f6(x89424,a910),x89421),x89423),f333(a123,x89422))+P106(f333(f333(f247(a910),f2(a910)),f333(x89421,f493(x89422,x89423,x89421,x89424)))) % 173.51/173.27 [8953]~P106(f333(f67(x89532),x89534))+P106(f333(f333(f246(a910),f333(f41(x89531),f333(f316(x89532,x89531,x89533),x89534))),f333(f41(x89532),x89534))) % 173.51/173.27 [8954]E(f333(f333(f265(x89541,x89542),f688(x89543,x89544,x89542,x89541)),f689(x89543,x89544,x89542,x89541)),x89544)+~P106(f333(f333(f335(f916(x89541,x89542)),x89544),f333(f293(x89542,x89541),x89543))) % 173.51/173.27 [8962]P27(x89621,x89622,x89623,x89624)+P106(f333(f333(f335(x89621),f808(x89624,x89623,x89622,x89621)),x89624)) % 173.51/173.27 [8963]P27(x89631,x89632,x89633,x89634)+P106(f333(f333(f335(x89631),f815(x89634,x89633,x89632,x89631)),x89634)) % 173.51/173.27 [9032]P14(x90321,x90322,x90323,x90324)+P106(f333(f333(f335(f916(x90321,x90321)),f532(x90324,x90323,x90322,x90321)),x90323)) % 173.51/173.27 [9095]P106(f333(x90951,x90952))+~P106(f333(x90951,f333(f333(f265(x90953,x90954),f541(x90954,x90953,x90951)),f542(x90954,x90953,x90951)))) % 173.51/173.27 [9114]E(f333(f197(f911(x91141)),x91142),f333(f197(f911(x91141)),x91143))+~P106(f333(f333(f335(f916(f911(x91141),f911(x91141))),f333(f333(f265(f911(x91141),f911(x91141)),x91142),x91143)),f153(x91141,x91144))) % 173.51/173.27 [9115]E(f333(f197(f911(x91151)),x91152),f333(f197(f911(x91151)),x91153))+~P106(f333(f333(f335(f916(f911(x91151),f911(x91151))),f333(f333(f265(f911(x91151),f911(x91151)),x91152),x91153)),f165(x91151,x91154))) % 173.51/173.27 [9118]E(f333(f197(f911(x91181)),x91182),f333(f197(f911(x91181)),x91183))+~P106(f333(f333(f335(f916(f911(x91181),f911(x91181))),f333(f333(f265(f911(x91181),f911(x91181)),x91182),x91183)),f166(x91181,x91184))) % 173.51/173.27 [9195]P106(f333(f333(f246(a910),f163(x91951,x91952,x91953)),f163(x91951,x91954,x91953)))+P106(f333(f333(f335(x91951),f716(x91954,x91952,x91953,x91951)),f333(f180(x91951),x91953))) % 173.51/173.27 [9198]E(f333(f197(f911(x91981)),x91982),f333(f197(f911(x91981)),x91983))+~P106(f333(f333(f335(f916(f911(x91981),f911(x91981))),f333(f333(f265(f911(x91981),f911(x91981)),x91982),x91983)),f313(f911(x91981),f165(x91981,x91984)))) % 173.51/173.27 [9437]~P27(x94371,x94372,x94373,x94374)+~P106(f333(f333(f247(a910),f333(f41(x94372),f333(f316(x94371,x94372,x94373),x94374))),f333(f41(x94371),x94374))) % 173.51/173.27 [9489]~P106(f333(f333(f335(f916(f911(x94891),f911(x94891))),f333(f333(f265(f911(x94891),f911(x94891)),x94892),x94893)),f165(x94891,x94894)))+P106(f333(f333(f335(f916(f911(x94891),f911(x94891))),f333(f333(f265(f911(x94891),f911(x94891)),x94892),x94893)),f166(x94891,f313(x94891,x94894)))) % 173.51/173.27 [9493]~P106(f333(f333(f335(f916(f911(x94931),f911(x94931))),f333(f333(f265(f911(x94931),f911(x94931)),x94932),x94933)),f166(x94931,x94934)))+P106(f333(f333(f335(f916(f911(x94931),f911(x94931))),f333(f333(f265(f911(x94931),f911(x94931)),x94932),x94933)),f313(f911(x94931),f165(x94931,x94934)))) % 173.51/173.27 [9509]P106(f333(f333(f335(f916(x95091,x95091)),f333(f333(f265(x95091,x95091),x95092),x95093)),f313(x95091,x95094)))+~P106(f333(f333(f335(f916(x95091,x95091)),f333(f333(f265(x95091,x95091),x95092),x95093)),f333(f333(f295(x95091,x95091,x95091),x95094),f313(x95091,x95094)))) % 173.51/173.27 [9706]E(f333(f333(f142(x97061),f729(x97062,x97063,x97064,x97061)),f333(f333(f159(x97061),f730(x97062,x97063,x97064,x97061)),f732(x97062,x97063,x97064,x97061))),x97064)+~P106(f333(f333(f335(f916(f911(x97061),f911(x97061))),f333(f333(f265(f911(x97061),f911(x97061)),x97064),x97063)),f165(x97061,x97062))) % 173.51/173.27 [9707]E(f333(f333(f142(x97071),f729(x97072,x97073,x97074,x97071)),f333(f333(f159(x97071),f731(x97072,x97073,x97074,x97071)),f732(x97072,x97073,x97074,x97071))),x97073)+~P106(f333(f333(f335(f916(f911(x97071),f911(x97071))),f333(f333(f265(f911(x97071),f911(x97071)),x97074),x97073)),f165(x97071,x97072))) % 173.51/173.27 [9787]P106(f333(f333(f335(f916(x97871,x97871)),f333(f333(f265(x97871,x97871),x97872),f633(x97873,x97874,x97872,x97871))),f313(x97871,x97873)))+~P106(f333(f333(f335(f916(x97871,x97871)),f333(f333(f265(x97871,x97871),x97872),x97874)),f333(f333(f295(x97871,x97871,x97871),x97873),f313(x97871,x97873)))) % 173.51/173.27 [9855]P106(f333(f333(f246(a910),f163(x98551,x98552,x98553)),f163(x98551,x98554,x98553)))+~P106(f333(f333(f247(a910),f333(x98552,f716(x98554,x98552,x98553,x98551))),f333(x98554,f716(x98554,x98552,x98553,x98551)))) % 173.51/173.27 [9927]P106(f333(f333(f335(f916(x99271,x99271)),f333(f333(f265(x99271,x99271),f632(x99272,x99273,x99274,x99271)),x99273)),f313(x99271,x99272)))+~P106(f333(f333(f335(f916(x99271,x99271)),f333(f333(f265(x99271,x99271),x99274),x99273)),f333(f333(f295(x99271,x99271,x99271),x99272),f313(x99271,x99272)))) % 173.51/173.27 [5359]~E(x53592,x53593)+E(f178(x53591,x53592,f333(f333(f159(x53591),x53593),x53594)),x53594) % 173.51/173.27 [5483]P106(f333(x54832,x54833))+E(f185(x54831,x54832,f333(f333(f159(x54831),x54833),x54834)),f124(x54831)) % 173.51/173.27 [5549]~P85(x55492)+E(f333(f333(f86(f917(x55491,x55492)),x55493),x55494),f333(f86(x55492),f333(x55493,x55494))) % 173.51/173.27 [5560]~E(x55602,f2(a910))+E(f333(f333(f146(x55601),x55602),f333(f333(f159(x55601),x55603),x55604)),f333(f333(f159(x55601),x55603),x55604)) % 173.51/173.27 [5561]P106(f333(x55612,x55613))+E(f333(f144(x55611,x55612),f333(f333(f159(x55611),x55613),x55614)),f333(f144(x55611,x55612),x55614)) % 173.51/173.27 [5694]~E(x56942,x56944)+P106(f333(f333(f333(f315(x56941),x56942),x56943),x56944)) % 173.51/173.27 [5702]E(x57021,f124(x57022))+E(f152(x57023,f333(f333(f162(x57022,x57023),x57024),x57021)),f333(x57024,f152(x57022,x57021))) % 173.51/173.27 [5716]~E(x57161,f69(x57162,x57164))+E(f333(x57161,f333(f333(f315(x57162),x57163),f196(f917(x57162,a905)))),x57163) % 173.51/173.27 [5751]E(x57511,f124(x57512))+E(f333(f149(x57513),f333(f333(f162(x57512,x57513),x57514),x57511)),f333(x57514,f333(f149(x57512),x57511))) % 173.51/173.27 [5852]~P106(f333(x58523,x58524))+P106(f333(f333(f333(f315(x58521),x58522),x58523),x58524)) % 173.51/173.27 [5968]~P20(x59682,x59684,x59681)+E(f333(x59681,f333(f333(f315(x59682),x59683),f196(f917(x59682,a905)))),x59683) % 173.51/173.27 [5992]~E(x59922,x59923)+P106(f333(f333(f335(x59921),x59922),f333(f333(f315(x59921),x59923),x59924))) % 173.51/173.27 [5996]~P2(x59961)+E(f333(f333(f121(x59961),x59962),f333(f333(f121(x59961),x59963),x59964)),f333(f333(f121(x59961),x59963),f333(f333(f121(x59961),x59962),x59964))) % 173.51/173.27 [5998]~P101(x59981)+E(f333(f333(f121(x59981),x59982),f333(f333(f121(x59981),x59983),x59984)),f333(f333(f121(x59981),x59983),f333(f333(f121(x59981),x59982),x59984))) % 173.51/173.27 [5999]~P2(x59991)+E(f333(f333(f112(x59991),x59992),f333(f333(f112(x59991),x59993),x59994)),f333(f333(f112(x59991),x59993),f333(f333(f112(x59991),x59992),x59994))) % 173.51/173.27 [6001]~P102(x60011)+E(f333(f333(f112(x60011),x60012),f333(f333(f112(x60011),x60013),x60014)),f333(f333(f112(x60011),x60013),f333(f333(f112(x60011),x60012),x60014))) % 173.51/173.27 [6002]~P117(x60021)+E(f333(f333(f87(x60021),x60022),f333(f333(f87(x60021),x60023),x60024)),f333(f333(f87(x60021),x60023),f333(f333(f87(x60021),x60022),x60024))) % 173.51/173.27 [6003]~P117(x60031)+E(f333(f333(f88(x60031),x60032),f333(f333(f88(x60031),x60033),x60034)),f333(f333(f88(x60031),x60033),f333(f333(f88(x60031),x60032),x60034))) % 173.51/173.27 [6005]~P110(x60051)+E(f333(f333(f244(x60051),x60052),f333(f333(f244(x60051),x60053),x60054)),f333(f333(f244(x60051),x60053),f333(f333(f244(x60051),x60052),x60054))) % 173.51/173.27 [6007]~P110(x60071)+E(f333(f333(f245(x60071),x60072),f333(f333(f245(x60071),x60073),x60074)),f333(f333(f245(x60071),x60073),f333(f333(f245(x60071),x60072),x60074))) % 173.51/173.27 [6012]E(x60121,x60122)+E(f178(x60123,x60121,f333(f333(f159(x60123),x60122),x60124)),f333(f333(f159(x60123),x60122),f178(x60123,x60121,x60124))) % 173.51/173.27 [6025]~P106(f333(x60252,x60253))+E(f333(f144(x60251,x60252),f333(f333(f159(x60251),x60253),x60254)),f333(f333(f159(x60251),x60253),f333(f144(x60251,x60252),x60254))) % 173.51/173.27 [6162]~P106(f333(x61622,x61623))+E(f185(x61621,x61622,f333(f333(f159(x61621),x61623),x61624)),f333(f333(f159(x61621),x61623),f185(x61621,x61622,x61624))) % 173.51/173.27 [6211]P26(x62111,x62112,x62113)+~P26(x62111,x62112,f333(f333(f315(f909(x62111)),x62114),x62113)) % 173.51/173.27 [6225]E(x62251,f196(f917(x62252,a905)))+E(f333(f333(f45(x62252,f917(x62253,a905)),x62251),f333(f16(f917(x62253,a905),x62252),x62254)),x62254) % 173.51/173.27 [6226]E(x62261,f196(f917(x62262,a905)))+E(f333(f333(f46(x62262,f917(x62263,a905)),x62261),f333(f16(f917(x62263,a905),x62262),x62264)),x62264) % 173.51/173.27 [6235]~E(x62354,f196(f917(x62352,a905)))+E(f333(f333(f267(x62351,x62352),x62353),f333(f16(f917(x62352,a905),x62351),x62354)),f196(f917(f916(x62351,x62352),a905))) % 173.51/173.27 [6236]~E(x62363,f196(f917(x62361,a905)))+E(f333(f333(f267(x62361,x62362),x62363),f333(f16(f917(x62362,a905),x62361),x62364)),f196(f917(f916(x62361,x62362),a905))) % 173.51/173.27 [6286]E(x62861,f2(a910))+E(f333(f333(f146(x62862),x62861),f333(f333(f159(x62862),x62863),x62864)),f333(f333(f146(x62862),f333(f333(f23(a910),x62861),f85(a910))),x62864)) % 173.51/173.27 [6307]E(x63071,f196(f917(x63072,a905)))+E(f333(f316(x63072,x63073,f333(f16(x63073,x63072),x63074)),x63071),f333(f333(f315(x63073),x63074),f196(f917(x63073,a905)))) % 173.51/173.27 [6310]E(f333(f317(x63101,x63102,f333(f16(x63102,x63101),x63103)),x63104),f196(f917(x63101,a905)))+P106(f333(f333(f335(x63102),x63103),x63104)) % 173.51/173.27 [6375]~E(x63753,f196(f917(x63751,a905)))+E(f333(f333(f45(x63751,f917(x63752,a905)),x63753),f333(f16(f917(x63752,a905),x63751),x63754)),f196(f917(x63752,a905))) % 173.51/173.27 [6376]~E(x63763,f196(f917(x63761,a905)))+E(f333(f333(f46(x63761,f917(x63762,a905)),x63763),f333(f16(f917(x63762,a905),x63761),x63764)),f254(f917(x63762,a905))) % 173.51/173.27 [6378]~P64(x63781)+E(f51(x63781,f333(f333(f88(x63781),x63782),x63783),f333(f333(f88(x63781),x63782),x63784)),f333(f333(f88(x63781),x63782),f51(x63781,x63783,x63784))) % 173.51/173.27 [6546]E(f333(f317(x65461,x65462,f333(f16(x65462,x65461),x65463)),x65464),f254(f917(x65461,a905)))+~P106(f333(f333(f335(x65462),x65463),x65464)) % 173.51/173.27 [6571]~P106(f333(f333(f335(x65711),x65712),x65714))+P106(f333(f333(f335(x65711),x65712),f333(f333(f315(x65711),x65713),x65714))) % 173.51/173.27 [6576]P106(f333(x65761,x65762))+~P106(f333(f168(x65763,x65761),f333(f333(f159(x65763),x65762),x65764))) % 173.51/173.27 [6585]~E(x65853,f333(f333(f23(a910),f333(f197(f911(x65851)),x65852)),f85(a910)))+E(f125(x65851,f333(f333(f167(x65851,x65852),x65853),x65854)),f125(x65851,x65852)) % 173.51/173.27 [6603]~P110(x66031)+E(f333(f333(f112(f917(x66031,a905)),f333(f307(x66031),x66032)),f309(x66031,x66033,x66034)),f309(x66031,x66033,f333(f333(f244(x66031),x66032),x66034))) % 173.51/173.27 [6604]~P110(x66041)+E(f333(f333(f112(f917(x66041,a905)),f333(f290(x66041),x66042)),f309(x66041,x66043,x66044)),f309(x66041,f333(f333(f245(x66041),x66042),x66043),x66044)) % 173.51/173.27 [6619]E(f333(f333(f112(f917(x66191,a905)),x66192),f333(f333(f315(x66191),x66193),x66194)),f333(f333(f112(f917(x66191,a905)),x66192),x66194))+P106(f333(f333(f335(x66191),x66193),x66192)) % 173.51/173.27 [6631]E(f178(x66311,x66312,f333(f333(f142(x66311),x66313),x66314)),f333(f333(f142(x66311),x66313),f178(x66311,x66312,x66314)))+P106(f333(f333(f335(x66311),x66312),f333(f180(x66311),x66313))) % 173.51/173.27 [6636]~P83(x66361)+E(f333(f333(f88(x66361),f333(f333(f256(x66361),x66362),x66363)),f333(f333(f256(x66361),x66362),x66364)),f333(f333(f256(x66361),x66362),f333(f333(f87(a910),x66363),x66364))) % 173.51/173.27 [6637]~P117(x66371)+E(f333(f333(f88(x66371),f333(f333(f256(x66371),x66372),x66373)),f333(f333(f256(x66371),x66372),x66374)),f333(f333(f256(x66371),x66372),f333(f333(f87(a910),x66373),x66374))) % 173.51/173.27 [6674]~P99(x66741)+E(f333(f333(f112(x66741),f333(f333(f121(x66741),x66742),x66743)),f333(f333(f121(x66741),x66742),x66744)),f333(f333(f121(x66741),x66742),f333(f333(f112(x66741),x66743),x66744))) % 173.51/173.27 [6675]~P99(x66751)+E(f333(f333(f121(x66751),f333(f333(f112(x66751),x66752),x66753)),f333(f333(f112(x66751),x66752),x66754)),f333(f333(f112(x66751),x66752),f333(f333(f121(x66751),x66753),x66754))) % 173.51/173.27 [6676]~P117(x66761)+E(f333(f333(f87(x66761),f333(f333(f88(x66761),x66762),x66763)),f333(f333(f88(x66761),x66762),x66764)),f333(f333(f88(x66761),x66762),f333(f333(f87(x66761),x66763),x66764))) % 173.51/173.27 [6677]~P110(x66771)+E(f333(f333(f245(x66771),f333(f333(f244(x66771),x66772),x66773)),f333(f333(f244(x66771),x66772),x66774)),f333(f333(f244(x66771),x66772),f333(f333(f245(x66771),x66773),x66774))) % 173.51/173.27 [6678]~P110(x66781)+E(f333(f333(f244(x66781),f333(f333(f245(x66781),x66782),x66783)),f333(f333(f245(x66781),x66782),x66784)),f333(f333(f245(x66781),x66782),f333(f333(f244(x66781),x66783),x66784))) % 173.51/173.27 [6711]~P64(x67111)+E(f51(x67111,f333(f333(f88(x67111),x67112),x67113),f333(f333(f88(x67111),x67114),x67113)),f333(f333(f88(x67111),f51(x67111,x67112,x67114)),x67113)) % 173.51/173.27 [6714]~E(f333(f197(f911(x67141)),x67143),f333(f197(f911(x67142)),x67144))+E(f333(f333(f162(f916(x67141,x67142),x67142),f268(x67141,x67142)),f333(f333(f189(x67141,x67142),x67143),x67144)),x67144) % 173.51/173.27 [6715]~E(f333(f197(f911(x67151)),x67153),f333(f197(f911(x67152)),x67154))+E(f333(f333(f162(f916(x67151,x67152),x67151),f264(x67151,x67152)),f333(f333(f189(x67151,x67152),x67153),x67154)),x67153) % 173.51/173.27 [6720]P106(f333(f168(x67201,x67202),x67203))+~P106(f333(f168(x67201,x67202),f333(f333(f159(x67201),x67204),x67203))) % 173.51/173.27 [6721]P106(f333(f168(x67211,x67212),x67213))+~P106(f333(f168(x67211,x67212),f333(f333(f142(x67211),x67214),x67213))) % 173.51/173.27 [6722]P106(f333(f168(x67221,x67222),x67223))+~P106(f333(f168(x67221,x67222),f333(f333(f142(x67221),x67223),x67224))) % 173.51/173.27 [6727]~P65(x67271)+E(f51(x67271,f333(f333(f23(x67271),x67272),f51(x67271,x67273,x67274)),x67274),f51(x67271,f333(f333(f23(x67271),x67272),x67273),x67274)) % 173.51/173.27 [6729]~P64(x67291)+E(f51(x67291,f333(f333(f88(x67291),x67292),f51(x67291,x67293,x67294)),x67294),f51(x67291,f333(f333(f88(x67291),x67292),x67293),x67294)) % 173.51/173.27 [6730]~P64(x67301)+E(f51(x67301,f333(f333(f87(x67301),x67302),f51(x67301,x67303,x67304)),x67304),f51(x67301,f333(f333(f87(x67301),x67302),x67303),x67304)) % 173.51/173.27 [6809]~P110(x68091)+E(f333(f333(f112(f917(x68091,a905)),f309(x68091,x68092,x68093)),f333(f307(x68091),x68094)),f309(x68091,x68092,f333(f333(f244(x68091),x68093),x68094))) % 173.51/173.27 [6810]~P110(x68101)+E(f333(f333(f112(f917(x68101,a905)),f309(x68101,x68102,x68103)),f333(f290(x68101),x68104)),f309(x68101,f333(f333(f245(x68101),x68102),x68104),x68103)) % 173.51/173.27 [6813]~E(f333(f197(f911(x68131)),x68133),f333(f197(f911(x68132)),x68134))+E(f333(f333(f189(x68131,x68132),f333(f176(x68131),x68133)),f333(f176(x68132),x68134)),f333(f176(f916(x68131,x68132)),f333(f333(f189(x68131,x68132),x68133),x68134))) % 173.51/173.27 [6823]E(x68231,f333(f333(f23(a910),f333(f197(f911(x68232)),x68233)),f85(a910)))+E(f125(x68232,f333(f333(f167(x68232,x68233),x68231),x68234)),f333(f333(f167(x68232,f125(x68232,x68233)),x68231),x68234)) % 173.51/173.27 [6837]~P106(f333(f145(x68372),x68374))+P106(f333(f145(f916(x68371,x68372)),f333(f333(f189(x68371,x68372),x68373),x68374))) % 173.51/173.27 [6838]~P106(f333(f145(x68381),x68383))+P106(f333(f145(f916(x68381,x68382)),f333(f333(f189(x68381,x68382),x68383),x68384))) % 173.51/173.27 [6926]E(x69261,f333(f333(f333(a205,x69262),x69263),f333(x69264,x69262)))+~P106(f333(f333(f202(f26(x69263,x69264)),x69262),x69261)) % 173.51/173.27 [7096]E(f333(f333(f42(a910),x70961),x70962),x70963)+~P106(f333(f54(x70961,x70962),f333(f333(f265(a910,a910),x70963),x70964))) % 173.51/173.27 [7119]E(f51(a910,x71191,x71192),x71193)+~P106(f333(f54(x71191,x71192),f333(f333(f265(a910,a910),x71194),x71193))) % 173.51/173.27 [7122]P106(f333(f145(x71221),x71222))+~P106(f333(f145(x71223),f333(f333(f162(x71221,x71223),x71224),x71222))) % 173.51/173.27 [7130]~P26(x71301,x71302,f333(f333(f315(f909(x71301)),x71303),x71304))+P26(x71301,x71302,f333(f333(f315(f909(x71301)),x71303),f196(f917(f909(x71301),a905)))) % 173.51/173.27 [7135]P106(f333(f333(f202(x71351),x71352),x71353))+~P106(f333(f333(f333(f333(a204,x71351),x71352),x71354),x71353)) % 173.51/173.27 [7207]E(f178(x72071,x72072,f333(f333(f142(x72071),x72073),x72074)),f333(f333(f142(x72071),f178(x72071,x72072,x72073)),x72074))+~P106(f333(f333(f335(x72071),x72072),f333(f180(x72071),x72073))) % 173.51/173.27 [7297]~P65(x72971)+E(f51(x72971,f333(f333(f23(x72971),f51(x72971,x72972,x72973)),x72974),x72973),f51(x72971,f333(f333(f23(x72971),x72972),x72974),x72973)) % 173.51/173.27 [7300]~P64(x73001)+E(f51(x73001,f333(f333(f87(x73001),f51(x73001,x73002,x73003)),x73004),x73003),f51(x73001,f333(f333(f87(x73001),x73002),x73004),x73003)) % 173.51/173.27 [7301]~P64(x73011)+E(f51(x73011,f333(f333(f88(x73011),f51(x73011,x73012,x73013)),x73014),x73013),f51(x73011,f333(f333(f88(x73011),x73012),x73014),x73013)) % 173.51/173.27 [7494]~E(x74941,f333(f333(f159(x74942),x74943),x74944))+~P106(f333(f333(f246(a910),f333(f197(f911(x74942)),x74941)),f333(f197(f911(x74942)),x74944))) % 173.51/173.27 [7695]P27(x76951,x76952,x76953,f333(f180(x76951),x76954))+~P106(f333(f145(x76952),f333(f333(f162(x76951,x76952),x76953),x76954))) % 173.51/173.27 [7768]~P106(f333(f333(f246(f917(x77681,a905)),x77682),x77684))+P106(f333(f333(f246(f917(x77681,a905)),x77682),f333(f333(f315(x77681),x77683),x77684))) % 173.51/173.27 [7802]~P65(x78021)+E(f51(x78021,f333(f333(f23(x78021),f51(x78021,x78022,x78023)),f51(x78021,x78024,x78023)),x78023),f51(x78021,f333(f333(f23(x78021),x78022),x78024),x78023)) % 173.51/173.27 [7803]~P64(x78031)+E(f51(x78031,f333(f333(f87(x78031),f51(x78031,x78032,x78033)),f51(x78031,x78034,x78033)),x78033),f51(x78031,f333(f333(f87(x78031),x78032),x78034),x78033)) % 173.51/173.27 [7804]~P64(x78041)+E(f51(x78041,f333(f333(f88(x78041),f51(x78041,x78042,x78043)),f51(x78041,x78044,x78043)),x78043),f51(x78041,f333(f333(f88(x78041),x78042),x78044),x78043)) % 173.51/173.27 [7905]P106(f333(f333(f333(f333(a204,x79051),x79052),f333(a123,x79053)),x79054))+~P106(f333(f333(f333(f333(a204,x79051),x79052),x79053),x79054)) % 173.51/173.27 [7912]~E(f333(x79124,f469(x79124,x79123,x79121,x79122)),f196(f917(x79122,a905)))+E(f333(f333(f45(x79121,f917(x79122,a905)),x79123),x79124),f196(f917(x79122,a905))) % 173.51/173.27 [7913]~E(f333(x79134,f643(x79134,x79133,x79131,x79132)),f254(f917(x79132,a905)))+E(f333(f333(f46(x79131,f917(x79132,a905)),x79133),x79134),f254(f917(x79132,a905))) % 173.51/173.27 [7914]~E(f333(x79144,f488(x79144,x79143,x79142,x79141)),f196(f917(x79142,a905)))+E(f333(f333(f45(x79141,f917(x79142,a905)),x79143),x79144),f196(f917(x79142,a905))) % 173.51/173.27 [7915]~E(f333(x79154,f644(x79154,x79153,x79152,x79151)),f254(f917(x79152,a905)))+E(f333(f333(f46(x79151,f917(x79152,a905)),x79153),x79154),f254(f917(x79152,a905))) % 173.51/173.27 [8309]P106(f333(x83091,x83092))+~P106(f333(f333(f335(x83093),x83092),f333(f333(f112(f917(x83093,a905)),x83094),f333(f252(x83093),x83091)))) % 173.51/173.27 [8347]~P106(f333(f333(f246(f917(x83471,a905)),x83473),x83474))+P106(f333(f333(f246(f917(x83471,a905)),f333(f333(f315(x83471),x83472),x83473)),f333(f333(f315(x83471),x83472),x83474))) % 173.51/173.27 [8357]E(f333(x83571,f860(x83571,x83572,x83573)),x83573)+~P106(f333(f333(f335(x83574),x83573),f333(f316(x83572,x83574,x83571),f254(f917(x83572,a905))))) % 173.51/173.27 [8518]P106(f333(f333(f202(x85181),x85182),f384(x85183,x85182,x85184,x85181)))+~P106(f333(f333(f202(f31(x85181,x85184)),x85182),x85183)) % 173.51/173.27 [8519]P106(f333(f333(f202(x85191),x85192),f393(x85193,x85192,x85194,x85191)))+~P106(f333(f333(f202(f31(x85191,x85194)),x85192),x85193)) % 173.51/173.27 [8529]P106(f333(x85292,x85293))+E(f333(f333(f146(x85291),f333(f197(f911(x85291)),f185(x85291,x85292,f333(f333(f159(x85291),x85293),x85294)))),f333(f333(f159(x85291),x85293),x85294)),f333(f333(f159(x85291),x85293),x85294)) % 173.51/173.27 [8645]~P106(f333(f333(f247(a910),f333(x86454,x86452)),f333(x86454,x86453)))+P106(f333(f333(f335(f916(x86451,x86451)),f333(f333(f265(x86451,x86451),x86452),x86453)),f333(f333(f294(a910,x86451),a251),x86454))) % 173.51/173.27 [8740]~P106(f333(x87402,f787(x87404,x87402,x87403,x87401)))+E(f185(x87401,x87402,f333(f333(f142(x87401),x87403),x87404)),f333(f333(f142(x87401),x87403),f185(x87401,x87402,x87404))) % 173.51/173.27 [8818]P27(f911(x88181),f911(x88182),f333(f162(x88181,x88182),x88183),x88184)+~P27(x88181,x88182,x88183,f43(f917(x88181,a905),f333(f316(f911(x88181),f917(x88181,a905),f180(x88181)),x88184))) % 173.51/173.27 [8892]~P106(f333(x88922,x88923))+E(f333(f333(f146(x88921),f333(f197(f911(x88921)),f185(x88921,x88922,f333(f333(f159(x88921),x88923),x88924)))),f333(f333(f159(x88921),x88923),x88924)),f333(f333(f146(x88921),f333(f197(f911(x88921)),f185(x88921,x88922,x88924))),x88924)) % 173.51/173.27 [8933]~E(x89332,x89333)+E(f333(f144(x89331,f333(f333(f8(a905,a905,x89331),a328),f333(a330,x89332))),f333(f333(f159(x89331),x89333),x89334)),f333(f144(x89331,f333(f333(f8(a905,a905,x89331),a328),f333(a330,x89332))),x89334)) % 173.51/173.27 [8943]E(f333(f333(f45(x89431,f917(x89432,a905)),x89433),x89434),f196(f917(x89432,a905)))+P106(f333(f333(f335(x89431),f469(x89434,x89433,x89431,x89432)),x89433)) % 173.51/173.27 [8944]E(f333(f333(f46(x89441,f917(x89442,a905)),x89443),x89444),f254(f917(x89442,a905)))+P106(f333(f333(f335(x89441),f643(x89444,x89443,x89441,x89442)),x89443)) % 173.51/173.27 [8945]E(f333(f333(f45(x89451,f917(x89452,a905)),x89453),x89454),f196(f917(x89452,a905)))+P106(f333(f333(f335(x89451),f488(x89454,x89453,x89452,x89451)),x89453)) % 173.51/173.27 [8946]E(f333(f333(f46(x89461,f917(x89462,a905)),x89463),x89464),f254(f917(x89462,a905)))+P106(f333(f333(f335(x89461),f644(x89464,x89463,x89462,x89461)),x89463)) % 173.51/173.27 [8984]P106(f333(f333(f247(a910),f333(x89841,x89842)),f333(x89841,x89843)))+~P106(f333(f333(f335(f916(x89844,x89844)),f333(f333(f265(x89844,x89844),x89842),x89843)),f333(f333(f294(a910,x89844),a251),x89841))) % 173.51/173.27 [9010]E(f185(x90101,x90102,f333(f333(f142(x90101),x90103),x90104)),f333(f333(f142(x90101),x90103),f185(x90101,x90102,x90104)))+P106(f333(f333(f335(x90101),f787(x90104,x90102,x90103,x90101)),f333(f180(x90101),x90103))) % 173.51/173.27 [9050]P106(f333(f333(f202(x90501),f384(x90502,x90503,x90501,x90504)),x90502))+~P106(f333(f333(f202(f31(x90504,x90501)),x90503),x90502)) % 173.51/173.27 [9051]P106(f333(f333(f202(x90511),f393(x90512,x90513,x90511,x90514)),x90512))+~P106(f333(f333(f202(f31(x90514,x90511)),x90513),x90512)) % 173.51/173.27 [9069]~P28(x90691,x90692,x90693,f254(f917(x90691,a905)),f254(f917(x90692,a905)))+E(f333(f316(x90691,x90692,x90693),f333(f86(f917(x90691,a905)),x90694)),f333(f86(f917(x90692,a905)),f333(f316(x90691,x90692,x90693),x90694))) % 173.51/173.27 [9184]P106(f333(f333(f335(x91841),f524(x91842,x91843,x91844,x91841)),x91843))+~P106(f333(f333(f335(f917(x91841,a905)),x91844),f333(f333(f66(x91841),x91843),x91842))) % 173.51/173.27 [9187]E(x91871,x91872)+~P106(f333(f333(f335(f916(x91873,x91873)),f333(f333(f265(x91873,x91873),x91871),x91872)),f333(f333(f191(f916(x91873,x91873),a905),f2(a910)),x91874))) % 173.51/173.27 [9269]E(f333(f292(x92691,x92691,x92692),f333(f333(f315(x92691),f524(x92692,x92693,x92694,x92691)),f196(f917(x92691,a905)))),x92694)+~P106(f333(f333(f335(f917(x92691,a905)),x92694),f333(f333(f66(x92691),x92693),x92692))) % 173.51/173.27 [9274]~P106(f333(f333(f335(f916(x92741,x92741)),f333(f333(f265(x92741,x92741),x92743),x92742)),f313(x92741,x92744)))+P106(f333(f333(f335(f916(x92741,x92741)),f333(f333(f265(x92741,x92741),x92742),x92743)),f313(x92741,f333(f293(x92741,x92741),x92744)))) % 173.51/173.27 [9288]~P64(x92881)+E(f333(f333(f87(x92881),f333(f333(f87(x92881),f333(f333(f88(x92881),x92882),f333(f333(f42(x92881),x92883),x92882))),f51(x92881,x92883,x92882))),x92884),f333(f333(f87(x92881),x92883),x92884)) % 173.51/173.27 [9298]~P106(f333(f333(f335(x92981),x92983),x92984))+P106(f333(f333(f335(f917(x92981,a905)),f333(f292(x92981,x92981,x92982),f333(f333(f315(x92981),x92983),f196(f917(x92981,a905))))),f333(f333(f66(x92981),x92984),x92982))) % 173.51/173.27 [9310]P106(f333(f333(f335(f916(x93101,x93101)),f333(f333(f265(x93101,x93101),x93102),x93103)),f313(x93101,x93104)))+~P106(f333(f333(f335(f916(x93101,x93101)),f333(f333(f265(x93101,x93101),x93103),x93102)),f313(x93101,f333(f293(x93101,x93101),x93104)))) % 173.51/173.27 [9399]E(f333(f333(f167(x93991,f333(f176(x93991),x93992)),f333(f333(f23(a910),f333(f333(f23(a910),f333(f197(f911(x93991)),x93992)),x93993)),f85(a910))),x93994),f333(f176(x93991),f333(f333(f167(x93991,x93992),x93993),x93994)))+~P106(f333(f333(f247(a910),x93993),f333(f197(f911(x93991)),x93992))) % 173.51/173.27 [9402]~P106(f333(x94022,f779(x94024,x94022,x94023,x94021)))+E(f333(f333(f146(x94021),f333(f197(f911(x94021)),f185(x94021,x94022,f333(f333(f142(x94021),x94023),x94024)))),f333(f333(f142(x94021),x94023),x94024)),f333(f333(f146(x94021),f333(f197(f911(x94021)),f185(x94021,x94022,x94024))),x94024)) % 173.51/173.27 [9445]~P27(x94452,x94451,x94453,f254(f917(x94452,a905)))+P106(f333(f333(f246(f917(x94451,a905)),f333(f316(x94452,x94451,x94453),f333(f86(f917(x94452,a905)),x94454))),f333(f86(f917(x94451,a905)),f333(f316(x94452,x94451,x94453),x94454)))) % 173.51/173.27 [9460]~P8(x94601)+E(f333(f150(x94601,x94602,f333(f7(x94602,x94601,x94601),f333(f333(f8(x94601,f917(x94601,x94601),x94602),f121(x94601)),x94603)),f196(x94601)),x94604),f333(f333(f45(x94602,x94601),f333(f180(x94602),x94604)),x94603)) % 173.51/173.27 [9461]~P8(x94611)+E(f333(f150(x94611,x94612,f333(f7(x94612,x94611,x94611),f333(f333(f8(x94611,f917(x94611,x94611),x94612),f112(x94611)),x94613)),f254(x94611)),x94614),f333(f333(f46(x94612,x94611),f333(f180(x94612),x94614)),x94613)) % 173.51/173.27 [9473]E(f333(f333(f146(x94731),f333(f197(f911(x94731)),f185(x94731,x94732,f333(f333(f142(x94731),x94733),x94734)))),f333(f333(f142(x94731),x94733),x94734)),f333(f333(f146(x94731),f333(f197(f911(x94731)),f185(x94731,x94732,x94734))),x94734))+P106(f333(f333(f335(x94731),f779(x94734,x94732,x94733,x94731)),f333(f180(x94731),x94733))) % 173.51/173.27 [9543]~P106(f333(f333(f335(f916(f911(x95434),f911(x95434))),f333(f333(f265(f911(x95434),f911(x95434)),x95433),x95432)),f165(x95434,x95431)))+P106(f333(f333(f247(a910),f717(x95431,x95432,x95433,x95434)),f333(f197(f911(x95434)),x95433))) % 173.51/173.27 [9544]~P64(x95441)+E(f333(f333(f87(x95441),f333(f333(f87(x95441),f333(f333(f88(x95441),f333(f333(f42(x95441),x95442),x95443)),x95443)),f51(x95441,x95442,x95443))),x95444),f333(f333(f87(x95441),x95442),x95444)) % 173.51/173.27 [9572]~P106(f333(f333(f335(f916(f911(x95721),f911(x95721))),f333(f333(f265(f911(x95721),f911(x95721)),x95722),x95723)),f333(f293(f911(x95721),f911(x95721)),f165(x95721,x95724))))+P106(f333(f333(f335(f916(f911(x95721),f911(x95721))),f333(f333(f265(f911(x95721),f911(x95721)),x95722),x95723)),f165(x95721,f333(f293(x95721,x95721),x95724)))) % 173.51/173.27 [9573]P106(f333(f333(f335(f916(f911(x95731),f911(x95731))),f333(f333(f265(f911(x95731),f911(x95731)),x95732),x95733)),f333(f293(f911(x95731),f911(x95731)),f165(x95731,x95734))))+~P106(f333(f333(f335(f916(f911(x95731),f911(x95731))),f333(f333(f265(f911(x95731),f911(x95731)),x95732),x95733)),f165(x95731,f333(f293(x95731,x95731),x95734)))) % 173.51/173.27 [9612]~P106(f333(f333(f335(x96121),x96123),f333(f263(x96121,x96122),x96124)))+P106(f333(f333(f335(f916(x96121,x96122)),f333(f333(f265(x96121,x96122),x96123),f601(x96124,x96122,x96123,x96121))),x96124)) % 173.51/173.27 [9613]~P106(f333(f333(f335(x96131),x96133),f333(f263(x96131,x96132),x96134)))+P106(f333(f333(f335(f916(x96131,x96132)),f333(f333(f265(x96131,x96132),x96133),f602(x96134,x96132,x96133,x96131))),x96134)) % 173.51/173.27 [9782]~P106(f333(f333(f335(f916(x97821,x97821)),f333(f333(f265(x97821,x97821),x97822),x97824)),f333(f333(f295(x97821,x97821,x97821),x97823),f313(x97821,x97823))))+P106(f333(f333(f335(f916(x97821,x97821)),f333(f333(f265(x97821,x97821),x97822),f632(x97823,x97824,x97822,x97821))),x97823)) % 173.51/173.27 [9947]~P106(f333(f333(f335(f916(x99472,x99471)),x99474),f333(f293(x99471,x99472),x99473)))+P106(f333(f333(f335(f916(x99471,x99472)),f333(f333(f265(x99471,x99472),f689(x99473,x99474,x99471,x99472)),f688(x99473,x99474,x99471,x99472))),x99473)) % 173.51/173.27 [9971]~P106(f333(f333(f335(f916(f911(x99711),f911(x99711))),f333(f333(f265(f911(x99711),f911(x99711)),x99714),x99713)),f165(x99711,x99712)))+P106(f333(f333(f335(f916(x99711,x99711)),f333(f333(f265(x99711,x99711),f730(x99712,x99713,x99714,x99711)),f731(x99712,x99713,x99714,x99711))),x99712)) % 173.51/173.27 [10065]~P106(f333(f333(f335(f916(f911(x100651),f911(x100651))),f333(f333(f265(f911(x100651),f911(x100651)),x100652),x100654)),f165(x100651,x100653)))+P106(f333(f333(f335(f916(x100651,x100651)),f333(f333(f265(x100651,x100651),f333(f333(f172(x100651),x100652),f717(x100653,x100654,x100652,x100651))),f718(x100653,x100654,x100652,x100651))),x100653)) % 173.51/173.27 [10087]~P106(f333(f67(x100872),x100874))+E(f333(f333(f333(f71(f917(x100871,a905),x100872,f121(f917(x100871,a905))),f333(f333(f7(x100872,f917(x100871,a905),f917(x100871,a905)),f333(f333(f8(x100871,f917(f917(x100871,a905),f917(x100871,a905)),x100872),f315(x100871)),x100873)),f196(f917(x100871,a905)))),f196(f917(x100871,a905))),x100874),f333(f316(x100872,x100871,x100873),x100874)) % 173.51/173.27 [10188]~P27(x101881,x101882,x101883,f254(f917(x101881,a905)))+P106(f333(f333(f246(f917(x101881,a905)),f333(f317(x101881,x101882,x101883),f333(f333(f315(x101882),x101884),f196(f917(x101882,a905))))),f333(f333(f315(x101881),f92(x101881,f333(f333(f7(x101881,x101882,a905),f333(f333(f8(x101882,f917(x101882,a905),x101881),a330),x101883)),x101884))),f196(f917(x101881,a905))))) % 173.51/173.27 [5760]~E(f333(f333(f142(x57601),x57602),x57604),x57603)+E(f333(f333(f183(x57601),f333(f197(f911(x57601)),x57602)),x57603),x57602) % 173.51/173.27 [5761]~E(f333(f333(f142(x57612),x57613),x57611),x57614)+E(x57611,f333(f333(f146(x57612),f333(f197(f911(x57612)),x57613)),x57614)) % 173.51/173.27 [5772]~E(x57724,f2(a910))+E(f333(f333(f172(x57721),f333(f333(f159(x57721),x57722),x57723)),x57724),x57722) % 173.51/173.27 [6299]~P117(x62991)+E(f333(f333(f256(x62991),f333(f333(f256(x62991),x62992),x62993)),x62994),f333(f333(f256(x62991),x62992),f333(f333(f88(a910),x62993),x62994))) % 173.51/173.27 [6300]~P83(x63001)+E(f333(f333(f256(x63001),f333(f333(f256(x63001),x63002),x63003)),x63004),f333(f333(f256(x63001),x63002),f333(f333(f88(a910),x63003),x63004))) % 173.51/173.27 [6308]E(x63081,f2(a910))+E(f333(f333(f172(x63082),f333(f333(f159(x63082),x63083),x63084)),x63081),f333(f333(f172(x63082),x63084),f333(f333(f23(a910),x63081),f85(a910)))) % 173.51/173.27 [6335]~P122(x63351)+E(f333(f333(f296(x63351),f333(f333(f88(x63351),x63352),x63353)),x63354),f333(f333(f88(x63351),x63352),f333(f333(f296(x63351),x63353),x63354))) % 173.51/173.27 [6336]~P2(x63361)+E(f333(f333(f121(x63361),f333(f333(f121(x63361),x63362),x63363)),x63364),f333(f333(f121(x63361),x63362),f333(f333(f121(x63361),x63363),x63364))) % 173.51/173.27 [6338]~P101(x63381)+E(f333(f333(f121(x63381),f333(f333(f121(x63381),x63382),x63383)),x63384),f333(f333(f121(x63381),x63382),f333(f333(f121(x63381),x63383),x63384))) % 173.51/173.27 [6339]~P2(x63391)+E(f333(f333(f112(x63391),f333(f333(f112(x63391),x63392),x63393)),x63394),f333(f333(f112(x63391),x63392),f333(f333(f112(x63391),x63393),x63394))) % 173.51/173.27 [6341]~P102(x63411)+E(f333(f333(f112(x63411),f333(f333(f112(x63411),x63412),x63413)),x63414),f333(f333(f112(x63411),x63412),f333(f333(f112(x63411),x63413),x63414))) % 173.51/173.27 [6342]~P75(x63421)+E(f333(f333(f87(x63421),f333(f333(f87(x63421),x63422),x63423)),x63424),f333(f333(f87(x63421),x63422),f333(f333(f87(x63421),x63423),x63424))) % 173.51/173.27 [6343]~P117(x63431)+E(f333(f333(f87(x63431),f333(f333(f87(x63431),x63432),x63433)),x63434),f333(f333(f87(x63431),x63432),f333(f333(f87(x63431),x63433),x63434))) % 173.51/173.27 [6344]~P117(x63441)+E(f333(f333(f88(x63441),f333(f333(f88(x63441),x63442),x63443)),x63444),f333(f333(f88(x63441),x63442),f333(f333(f88(x63441),x63443),x63444))) % 173.51/173.27 [6345]~P76(x63451)+E(f333(f333(f88(x63451),f333(f333(f88(x63451),x63452),x63453)),x63454),f333(f333(f88(x63451),x63452),f333(f333(f88(x63451),x63453),x63454))) % 173.51/173.27 [6348]~P110(x63481)+E(f333(f333(f244(x63481),f333(f333(f244(x63481),x63482),x63483)),x63484),f333(f333(f244(x63481),x63482),f333(f333(f244(x63481),x63483),x63484))) % 173.51/173.27 [6350]~P110(x63501)+E(f333(f333(f245(x63501),f333(f333(f245(x63501),x63502),x63503)),x63504),f333(f333(f245(x63501),x63502),f333(f333(f245(x63501),x63503),x63504))) % 173.51/173.27 [6359]~P64(x63591)+E(f51(x63591,f333(f333(f87(x63591),x63592),f333(f333(f88(x63591),x63593),x63594)),x63594),f51(x63591,x63592,x63594)) % 173.51/173.27 [6360]~P64(x63601)+E(f51(x63601,f333(f333(f87(x63601),x63602),f333(f333(f88(x63601),x63603),x63604)),x63603),f51(x63601,x63602,x63603)) % 173.51/173.27 [6494]E(f333(f333(f172(x64941),f333(f333(f183(x64941),x64942),x64943)),x64944),f333(f333(f172(x64941),x64943),x64944))+~P106(f333(f333(f247(a910),x64944),x64942)) % 173.51/173.27 [6670]~E(x66702,x66704)+P106(f333(f333(f180(x66701),f333(f333(f159(x66701),x66702),x66703)),x66704)) % 173.51/173.27 [6672]~P117(x66721)+E(f333(f333(f87(x66721),f333(f333(f87(x66721),x66722),x66723)),x66724),f333(f333(f87(x66721),f333(f333(f87(x66721),x66722),x66724)),x66723)) % 173.51/173.27 [6673]~P117(x66731)+E(f333(f333(f88(x66731),f333(f333(f88(x66731),x66732),x66733)),x66734),f333(f333(f88(x66731),f333(f333(f88(x66731),x66732),x66734)),x66733)) % 173.51/173.27 [6733]~P107(x67332)+E(f333(f333(f6(x67331,x67332),f333(f16(x67332,x67331),x67333)),x67334),f333(f333(f88(x67332),f333(f111(x67332),f333(f41(x67331),x67334))),x67333)) % 173.51/173.27 [6898]E(f333(f333(f112(f917(x68981,a905)),f333(f333(f315(x68981),x68982),x68983)),x68984),f333(f333(f112(f917(x68981,a905)),x68983),x68984))+P106(f333(f333(f335(x68981),x68982),x68984)) % 173.51/173.27 [6965]~P99(x69651)+E(f333(f333(f112(x69651),f333(f333(f121(x69651),x69652),x69653)),f333(f333(f121(x69651),x69654),x69653)),f333(f333(f121(x69651),f333(f333(f112(x69651),x69652),x69654)),x69653)) % 173.51/173.27 [6966]~P99(x69661)+E(f333(f333(f121(x69661),f333(f333(f112(x69661),x69662),x69663)),f333(f333(f112(x69661),x69664),x69663)),f333(f333(f112(x69661),f333(f333(f121(x69661),x69662),x69664)),x69663)) % 173.51/173.27 [6967]~P4(x69671)+E(f333(f333(f244(x69671),f333(f333(f23(x69671),x69672),x69673)),f333(f333(f23(x69671),x69674),x69673)),f333(f333(f23(x69671),f333(f333(f244(x69671),x69672),x69674)),x69673)) % 173.51/173.27 [6968]~P4(x69681)+E(f333(f333(f245(x69681),f333(f333(f23(x69681),x69682),x69683)),f333(f333(f23(x69681),x69684),x69683)),f333(f333(f23(x69681),f333(f333(f245(x69681),x69682),x69684)),x69683)) % 173.51/173.27 [6969]~P89(x69691)+E(f333(f333(f244(x69691),f333(f333(f87(x69691),x69692),x69693)),f333(f333(f87(x69691),x69694),x69693)),f333(f333(f87(x69691),f333(f333(f244(x69691),x69692),x69694)),x69693)) % 173.51/173.27 [6970]~P89(x69701)+E(f333(f333(f245(x69701),f333(f333(f87(x69701),x69702),x69703)),f333(f333(f87(x69701),x69704),x69703)),f333(f333(f87(x69701),f333(f333(f245(x69701),x69702),x69704)),x69703)) % 173.51/173.27 [6972]~P118(x69721)+E(f333(f333(f87(x69721),f333(f333(f88(x69721),x69722),x69723)),f333(f333(f88(x69721),x69724),x69723)),f333(f333(f88(x69721),f333(f333(f87(x69721),x69722),x69724)),x69723)) % 173.51/173.27 [6973]~P110(x69731)+E(f333(f333(f245(x69731),f333(f333(f244(x69731),x69732),x69733)),f333(f333(f244(x69731),x69734),x69733)),f333(f333(f244(x69731),f333(f333(f245(x69731),x69732),x69734)),x69733)) % 173.51/173.27 [6974]~P110(x69741)+E(f333(f333(f244(x69741),f333(f333(f245(x69741),x69742),x69743)),f333(f333(f245(x69741),x69744),x69743)),f333(f333(f245(x69741),f333(f333(f244(x69741),x69742),x69744)),x69743)) % 173.51/173.27 [6975]~P117(x69751)+E(f333(f333(f88(x69751),f333(f333(f256(x69751),x69752),x69753)),f333(f333(f256(x69751),x69754),x69753)),f333(f333(f256(x69751),f333(f333(f88(x69751),x69752),x69754)),x69753)) % 173.51/173.27 [6976]~P78(x69761)+E(f333(f333(f88(x69761),f333(f333(f256(x69761),x69762),x69763)),f333(f333(f256(x69761),x69764),x69763)),f333(f333(f256(x69761),f333(f333(f88(x69761),x69762),x69764)),x69763)) % 173.51/173.27 [6977]~P67(x69771)+E(f333(f333(f296(x69771),f333(f333(f256(x69771),x69772),x69773)),f333(f333(f256(x69771),x69774),x69773)),f333(f333(f256(x69771),f333(f333(f296(x69771),x69772),x69774)),x69773)) % 173.51/173.27 [6978]~P122(x69781)+E(f333(f333(f23(x69781),f333(f333(f296(x69781),x69782),x69783)),f333(f333(f296(x69781),x69784),x69783)),f333(f333(f296(x69781),f333(f333(f23(x69781),x69782),x69784)),x69783)) % 173.51/173.27 [6979]~P122(x69791)+E(f333(f333(f87(x69791),f333(f333(f296(x69791),x69792),x69793)),f333(f333(f296(x69791),x69794),x69793)),f333(f333(f296(x69791),f333(f333(f87(x69791),x69792),x69794)),x69793)) % 173.51/173.27 [6980]~P117(x69801)+E(f333(f333(f87(x69801),f333(f333(f88(x69801),x69802),x69803)),f333(f333(f88(x69801),x69804),x69803)),f333(f333(f88(x69801),f333(f333(f87(x69801),x69802),x69804)),x69803)) % 173.51/173.27 [7011]E(f333(f333(f167(x70111,x70112),x70113),x70114),x70112)+~P106(f333(f333(f246(a910),f333(f197(f911(x70111)),x70112)),x70113)) % 173.51/173.27 [7037]~P106(f333(x70373,x70374))+P106(f333(f333(f333(f121(f917(x70371,a905)),x70372),x70373),x70374)) % 173.51/173.27 [7039]~P106(f333(x70392,x70394))+P106(f333(f333(f333(f121(f917(x70391,a905)),x70392),x70393),x70394)) % 173.51/173.27 [7059]E(f333(f333(f172(x70591),f333(f333(f142(x70591),x70592),x70593)),x70594),f333(f333(f172(x70591),x70592),x70594))+~P106(f333(f333(f247(a910),x70594),f333(f197(f911(x70591)),x70592))) % 173.51/173.27 [7069]E(f333(f333(f23(f917(x70691,a905)),f333(f333(f315(x70691),x70692),x70693)),x70694),f333(f333(f23(f917(x70691,a905)),x70693),x70694))+~P106(f333(f333(f335(x70691),x70692),x70694)) % 173.51/173.27 [7109]~E(f147(a910,f333(f308(a910,x71091),x71092)),f333(f333(f159(a910),x71094),x71093))+E(f147(a910,f333(f308(a910,f333(f333(f87(a910),x71091),f85(a910))),x71092)),x71093) % 173.51/173.27 [7131]~P106(f333(f333(f180(x71311),x71313),x71314))+P106(f333(f333(f180(x71311),f333(f333(f159(x71311),x71312),x71313)),x71314)) % 173.51/173.27 [7182]E(x71821,f2(a910))+E(f333(f333(f159(x71822),x71823),f333(f333(f183(x71822),f333(f333(f23(a910),x71821),f85(a910))),x71824)),f333(f333(f183(x71822),x71821),f333(f333(f159(x71822),x71823),x71824))) % 173.51/173.27 [7281]E(f333(f333(f172(x72811),x72812),f333(f333(f23(a910),x72813),f333(f197(f911(x72811)),x72814))),f333(f333(f172(x72811),f333(f333(f142(x72811),x72814),x72812)),x72813))+P106(f333(f333(f247(a910),x72813),f333(f197(f911(x72811)),x72814))) % 173.51/173.27 [7311]E(f333(f333(f112(f917(x73111,a905)),x73112),f333(f333(f315(x73111),x73113),x73114)),f333(f333(f315(x73111),x73113),f333(f333(f112(f917(x73111,a905)),x73112),x73114)))+~P106(f333(f333(f335(x73111),x73113),x73112)) % 173.51/173.27 [7349]E(f333(f333(f172(x73491),f333(f333(f167(x73491,x73492),x73493),x73494)),x73493),x73494)+~P106(f333(f333(f247(a910),x73493),f333(f197(f911(x73491)),x73492))) % 173.51/173.27 [7370]E(x73701,f196(f917(x73702,a905)))+E(f333(f316(f916(x73703,x73702),x73703,f264(x73703,x73702)),f333(f333(f267(x73703,x73702),x73704),f333(f16(f917(x73702,a905),x73703),x73701))),x73704) % 173.51/173.27 [7371]E(x73711,f196(f917(x73712,a905)))+E(f333(f316(f916(x73712,x73713),x73713,f268(x73712,x73713)),f333(f333(f267(x73712,x73713),x73711),f333(f16(f917(x73713,a905),x73712),x73714))),x73714) % 173.51/173.27 [7442]E(f333(f333(f23(f917(x74421,a905)),f333(f333(f315(x74421),x74422),x74423)),x74424),f333(f333(f315(x74421),x74422),f333(f333(f23(f917(x74421,a905)),x74423),x74424)))+P106(f333(f333(f335(x74421),x74422),x74424)) % 173.51/173.27 [7472]P106(f333(x74721,x74722))+P106(f333(f333(f333(f333(a204,f30(x74721,x74723)),x74722),x74724),x74722)) % 173.51/173.27 [7479]~E(x74794,f196(f917(x74792,a905)))+E(f333(f316(f916(x74791,x74792),x74791,f264(x74791,x74792)),f333(f333(f267(x74791,x74792),x74793),f333(f16(f917(x74792,a905),x74791),x74794))),f196(f917(x74791,a905))) % 173.51/173.27 [7480]~E(x74803,f196(f917(x74801,a905)))+E(f333(f316(f916(x74801,x74802),x74802,f268(x74801,x74802)),f333(f333(f267(x74801,x74802),x74803),f333(f16(f917(x74802,a905),x74801),x74804))),f196(f917(x74802,a905))) % 173.51/173.27 [7532]~P106(f333(f333(f335(x75321),x75322),x75324))+P106(f333(f333(f335(x75321),x75322),f333(f333(f121(f917(x75321,a905)),x75323),x75324))) % 173.51/173.27 [7535]~P106(f333(f333(f335(x75351),x75352),x75353))+P106(f333(f333(f335(x75351),x75352),f333(f333(f121(f917(x75351,a905)),x75353),x75354))) % 173.51/173.27 [7553]E(f333(f333(f112(f917(x75531,a905)),f333(f333(f315(x75531),x75532),x75533)),x75534),f333(f333(f315(x75531),x75532),f333(f333(f112(f917(x75531,a905)),x75533),x75534)))+~P106(f333(f333(f335(x75531),x75532),x75534)) % 173.51/173.27 [7826]P106(f333(x78261,x78262))+~P106(f333(f333(f333(f112(f917(x78263,a905)),x78264),x78261),x78262)) % 173.51/173.27 [7827]P106(f333(x78271,x78272))+~P106(f333(f333(f333(f112(f917(x78273,a905)),x78271),x78274),x78272)) % 173.51/173.27 [7828]E(f333(f333(f6(x78281,a910),x78282),f333(f333(f23(f917(x78281,a905)),x78283),f333(f333(f315(x78281),x78284),f196(f917(x78281,a905))))),f333(f333(f6(x78281,a910),x78282),x78283))+P106(f333(f333(f335(x78281),x78284),x78283)) % 173.51/173.27 [7834]~P72(x78341)+E(f333(f173(x78341),f333(f333(f162(a910,x78341),x78342),f147(a910,f333(f308(a910,x78343),x78344)))),f333(f333(f6(a910,x78341),x78342),f333(f180(a910),f147(a910,f333(f308(a910,x78343),x78344))))) % 173.51/173.27 [7835]~P72(x78351)+E(f333(f333(f6(a910,x78351),x78352),f333(f180(a910),f147(a910,f333(f308(a910,x78353),x78354)))),f333(f173(x78351),f333(f333(f162(a910,x78351),x78352),f147(a910,f333(f308(a910,x78353),x78354))))) % 173.51/173.27 [7950]~E(x79503,x79504)+P106(f333(f68(x79501,x79502,f333(f333(f315(x79501),x79503),f196(f917(x79501,a905)))),x79504)) % 173.51/173.27 [8047]P106(f333(f333(f335(x80471),x80472),f333(f180(x80471),x80473)))+~P106(f333(f333(f335(x80471),x80472),f333(f180(x80471),f333(f333(f183(x80471),x80474),x80473)))) % 173.51/173.27 [8048]P106(f333(f333(f335(x80481),x80482),f333(f180(x80481),x80483)))+~P106(f333(f333(f335(x80481),x80482),f333(f180(x80481),f333(f333(f146(x80481),x80484),x80483)))) % 173.51/173.27 [8121]P106(f333(f333(f335(x81211),x81212),x81213))+~P106(f333(f333(f335(x81211),x81212),f333(f333(f112(f917(x81211,a905)),x81214),x81213))) % 173.51/173.27 [8124]P106(f333(f333(f335(x81241),x81242),x81243))+~P106(f333(f333(f335(x81241),x81242),f333(f333(f112(f917(x81241,a905)),x81243),x81244))) % 173.51/173.27 [8127]P106(f333(f333(f335(x81271),x81272),x81273))+~P106(f333(f333(f335(x81271),x81272),f333(f333(f23(f917(x81271,a905)),x81273),x81274))) % 173.51/173.27 [8145]E(f333(f333(f142(x81451),f333(f333(f183(x81451),x81452),x81453)),f333(f333(f159(x81451),x81454),f333(f333(f146(x81451),f333(a123,x81452)),x81453))),f333(f333(f167(x81451,x81453),x81452),x81454))+~P106(f333(f333(f247(a910),x81452),f333(f197(f911(x81451)),x81453))) % 173.51/173.27 [8168]P106(f333(f333(f335(x81681),x81682),x81683))+~P106(f333(f333(f246(f917(x81681,a905)),f333(f333(f315(x81681),x81682),x81684)),x81683)) % 173.51/173.27 [8204]~P106(f333(f333(f335(x82041),x82042),x82043))+~P106(f333(f333(f335(x82041),x82042),f333(f333(f23(f917(x82041,a905)),x82044),x82043))) % 173.51/173.27 [8236]~P106(f333(f333(f247(a910),x82364),f333(f197(f911(x82361)),x82363)))+P106(f333(f333(f335(x82361),x82362),f333(f180(x82361),f333(f333(f167(x82361,x82363),x82364),x82362)))) % 173.51/173.27 [8288]E(f333(f333(f172(x82881),f333(f333(f146(x82881),x82882),x82883)),x82884),f333(f333(f172(x82881),x82883),f333(f333(f87(a910),x82882),x82884)))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),x82882),x82884)),f333(f197(f911(x82881)),x82883))) % 173.51/173.27 [8297]~P107(x82972)+E(f333(f333(f6(x82971,x82972),f333(f333(f8(a910,x82972,x82971),f111(x82972)),x82973)),x82974),f333(f111(x82972),f333(f333(f6(x82971,a910),x82973),x82974))) % 173.51/173.27 [8298]~P139(x82982)+E(f333(f333(f6(x82981,x82982),f333(f333(f8(a1,x82982,x82981),f113(x82982)),x82983)),x82984),f333(f113(x82982),f333(f333(f6(x82981,a1),x82983),x82984))) % 173.51/173.27 [8349]~P70(x83492)+E(f333(f333(f9(x83491,x83492),f333(f333(f8(x83492,x83492,x83491),f82(x83492)),x83493)),x83494),f333(f82(x83492),f333(f333(f9(x83491,x83492),x83493),x83494))) % 173.51/173.27 [8350]~P6(x83502)+E(f333(f333(f6(x83501,x83502),f333(f333(f8(x83502,x83502,x83501),f86(x83502)),x83503)),x83504),f333(f86(x83502),f333(f333(f6(x83501,x83502),x83503),x83504))) % 173.51/173.27 [8352]E(f333(f333(f6(x83521,a910),x83522),f333(f333(f23(f917(x83521,a905)),x83523),f333(f333(f315(x83521),x83524),f196(f917(x83521,a905))))),f333(f333(f23(a910),f333(f333(f6(x83521,a910),x83522),x83523)),f333(x83522,x83524)))+~P106(f333(f333(f335(x83521),x83524),x83523)) % 173.51/173.27 [8372]P106(f333(f333(f246(f917(x83721,a905)),x83722),x83723))+~P106(f333(f333(f246(f917(x83721,a905)),f333(f333(f315(x83721),x83724),x83722)),x83723)) % 173.51/173.27 [8496]~E(f333(f316(x84962,x84963,x84961),f254(f917(x84962,a905))),f254(f917(x84963,a905)))+E(f333(x84961,f333(f99(x84962,x84963,f254(f917(x84962,a905)),x84961),x84964)),x84964) % 173.51/173.27 [8586]P40(x85861,x85862)+~P40(x85861,f333(f333(f315(f916(x85861,x85861)),f333(f333(f265(x85861,x85861),x85863),x85864)),x85862)) % 173.51/173.27 [8587]P61(x85871,x85872)+~P61(x85871,f333(f333(f315(f916(x85871,x85871)),f333(f333(f265(x85871,x85871),x85873),x85874)),x85872)) % 173.51/173.27 [8595]~P110(x85951)+E(f333(f333(f156(x85951,x85951,f5(x85951)),x85952),f333(f333(f156(x85951,x85951,f5(x85951)),x85953),x85954)),f333(f333(f156(x85951,x85951,f5(x85951)),x85953),f333(f333(f156(x85951,x85951,f5(x85951)),x85952),x85954))) % 173.51/173.27 [8610]E(x86101,x86102)+~P106(f333(f68(x86103,x86104,f333(f333(f315(x86103),x86101),f196(f917(x86103,a905)))),x86102)) % 173.51/173.27 [8619]E(f333(f333(f142(x86191),f333(f333(f183(x86191),x86192),x86193)),f333(f333(f183(x86191),x86194),f333(f333(f146(x86191),x86192),x86193))),f333(f333(f183(x86191),f333(f333(f87(a910),x86192),x86194)),x86193))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),x86192),x86194)),f333(f197(f911(x86191)),x86193))) % 173.51/173.27 [8661]P106(f333(f67(x86611),x86612))+~E(x86612,f333(f316(a910,x86611,x86613),f333(f252(a910),f333(f333(f7(a910,a910,a905),f247(a910)),x86614)))) % 173.51/173.27 [8681]~P92(x86811)+E(f333(f150(x86811,x86811,f87(x86811),f333(f333(f87(x86811),x86812),x86813)),x86814),f333(f333(f87(x86811),x86812),f333(f150(x86811,x86811,f87(x86811),x86813),x86814))) % 173.51/173.27 [8716]P106(f333(f333(f246(f917(x87161,a905)),f333(f263(x87161,x87162),x87163)),f333(f263(x87161,x87162),x87164)))+~P106(f333(f333(f246(f917(f916(x87161,x87162),a905)),x87163),x87164)) % 173.51/173.27 [8728]~P106(f333(f333(f246(a910),x87282),x87284))+P106(f333(f333(f246(f917(x87281,a905)),f333(f180(x87281),f333(f333(f183(x87281),x87282),x87283))),f333(f180(x87281),f333(f333(f183(x87281),x87284),x87283)))) % 173.51/173.27 [8729]~P106(f333(f333(f246(a910),x87294),x87292))+P106(f333(f333(f246(f917(x87291,a905)),f333(f180(x87291),f333(f333(f146(x87291),x87292),x87293))),f333(f180(x87291),f333(f333(f146(x87291),x87294),x87293)))) % 173.51/173.27 [8787]~P106(f333(f67(x87871),f333(f333(f23(f917(x87871,a905)),x87872),x87874)))+P106(f333(f67(x87871),f333(f333(f23(f917(x87871,a905)),x87872),f333(f333(f315(x87871),x87873),x87874)))) % 173.51/173.27 [8829]P106(f333(f333(f335(f916(x88291,x88291)),x88292),f313(x88291,x88293)))+~P106(f333(f333(f335(f916(x88291,x88291)),x88292),f333(f333(f191(f916(x88291,x88291),a905),x88294),x88293))) % 173.51/173.27 [8914]~P106(f333(f67(x89141),f333(f333(f23(f917(x89141,a905)),x89142),f333(f333(f315(x89141),x89144),x89143))))+P106(f333(f67(x89141),f333(f333(f23(f917(x89141,a905)),x89142),x89143))) % 173.51/173.27 [9140]~P2(x91401)+P106(f333(f333(f246(x91401),f333(f333(f121(x91401),x91402),f333(f333(f112(x91401),x91403),x91404))),f333(f333(f112(x91401),f333(f333(f121(x91401),x91402),x91403)),f333(f333(f121(x91401),x91402),x91404)))) % 173.51/173.27 [9141]~P110(x91411)+P106(f333(f333(f246(x91411),f333(f333(f245(x91411),x91412),f333(f333(f244(x91411),x91413),x91414))),f333(f333(f244(x91411),f333(f333(f245(x91411),x91412),x91413)),f333(f333(f245(x91411),x91412),x91414)))) % 173.51/173.27 [9294]E(x92941,x92942)+~P106(f333(f333(f335(f916(x92943,x92943)),f333(f333(f265(x92943,x92943),x92941),x92942)),f333(f180(f916(x92943,x92943)),f333(f333(f189(x92943,x92943),x92944),x92944)))) % 173.51/173.27 [9325]~P106(f333(f333(f335(f916(x93251,x93251)),f333(f333(f265(x93251,x93251),x93253),x93252)),f313(x93251,x93254)))+~P40(x93251,f333(f333(f315(f916(x93251,x93251)),f333(f333(f265(x93251,x93251),x93252),x93253)),x93254)) % 173.51/173.27 [9326]~P106(f333(f333(f335(f916(x93261,x93261)),f333(f333(f265(x93261,x93261),x93263),x93262)),f313(x93261,x93264)))+~P61(x93261,f333(f333(f315(f916(x93261,x93261)),f333(f333(f265(x93261,x93261),x93262),x93263)),x93264)) % 173.51/173.27 [9330]E(x93301,x93302)+E(f333(f144(x93303,f333(f333(f8(a905,a905,x93303),a328),f333(a330,x93301))),f333(f333(f159(x93303),x93302),x93304)),f333(f333(f159(x93303),x93302),f333(f144(x93303,f333(f333(f8(a905,a905,x93303),a328),f333(a330,x93301))),x93304))) % 173.51/173.27 [9358]~P28(x93582,x93581,x93583,f254(f917(x93582,a905)),f254(f917(x93581,a905)))+E(f333(f316(x93581,x93582,f99(x93582,x93581,f254(f917(x93582,a905)),x93583)),x93584),f333(f317(x93582,x93581,x93583),x93584)) % 173.51/173.27 [9374]~P2(x93741)+P106(f333(f333(f246(x93741),f333(f333(f121(x93741),f333(f333(f112(x93741),x93742),x93743)),f333(f333(f112(x93741),x93742),x93744))),f333(f333(f112(x93741),x93742),f333(f333(f121(x93741),x93743),x93744)))) % 173.51/173.27 [9375]~P110(x93751)+P106(f333(f333(f246(x93751),f333(f333(f245(x93751),f333(f333(f244(x93751),x93752),x93753)),f333(f333(f244(x93751),x93752),x93754))),f333(f333(f244(x93751),x93752),f333(f333(f245(x93751),x93753),x93754)))) % 173.51/173.27 [9439]~P28(x94392,x94391,x94394,f254(f917(x94392,a905)),f254(f917(x94391,a905)))+E(f333(f252(x94391),f333(f333(f8(x94392,a905,x94391),x94393),f99(x94392,x94391,f254(f917(x94392,a905)),x94394))),f333(f316(x94392,x94391,x94394),f333(f252(x94392),x94393))) % 173.51/173.27 [9456]~E(f333(f316(x94562,x94561,x94563),f254(f917(x94562,a905))),f254(f917(x94561,a905)))+P106(f333(f333(f246(f917(x94561,a905)),f333(f86(f917(x94561,a905)),f333(f316(x94562,x94561,x94563),x94564))),f333(f316(x94562,x94561,x94563),f333(f86(f917(x94562,a905)),x94564)))) % 173.51/173.27 [9795]P106(f333(f333(f335(f916(x97951,x97951)),f333(f333(f265(x97951,x97951),x97952),x97953)),f333(f293(x97951,x97951),f333(f333(f295(x97951,x97951,x97951),x97954),f313(x97951,x97954)))))+~P106(f333(f333(f335(f916(x97951,x97951)),f333(f333(f265(x97951,x97951),x97952),x97953)),f333(f333(f295(x97951,x97951,x97951),f333(f293(x97951,x97951),x97954)),f313(x97951,f333(f293(x97951,x97951),x97954))))) % 173.51/173.27 [9796]~P106(f333(f333(f335(f916(x97961,x97961)),f333(f333(f265(x97961,x97961),x97962),x97963)),f333(f293(x97961,x97961),f333(f333(f295(x97961,x97961,x97961),x97964),f313(x97961,x97964)))))+P106(f333(f333(f335(f916(x97961,x97961)),f333(f333(f265(x97961,x97961),x97962),x97963)),f333(f333(f295(x97961,x97961,x97961),f333(f293(x97961,x97961),x97964)),f313(x97961,f333(f293(x97961,x97961),x97964))))) % 173.51/173.27 [9817]~P106(f333(f333(f335(x98172),x98174),f333(f291(x98171,x98172),x98173)))+P106(f333(f333(f335(f916(x98171,x98172)),f333(f333(f265(x98171,x98172),f597(x98173,x98171,x98174,x98172)),x98174)),x98173)) % 173.51/173.27 [9818]~P106(f333(f333(f335(x98182),x98184),f333(f291(x98181,x98182),x98183)))+P106(f333(f333(f335(f916(x98181,x98182)),f333(f333(f265(x98181,x98182),f598(x98183,x98181,x98184,x98182)),x98184)),x98183)) % 173.51/173.27 [9843]~P106(f333(f333(f335(x98431),x98434),f333(f333(f121(f917(x98431,a905)),x98432),x98433)))+P106(f333(f333(f333(f121(f917(x98431,a905)),f333(f333(f7(x98431,f917(x98431,a905),a905),f335(x98431)),x98432)),f333(f333(f7(x98431,f917(x98431,a905),a905),f335(x98431)),x98433)),x98434)) % 173.51/173.27 [9844]~P106(f333(f333(f335(x98441),x98444),f333(f333(f112(f917(x98441,a905)),x98442),x98443)))+P106(f333(f333(f333(f112(f917(x98441,a905)),f333(f333(f7(x98441,f917(x98441,a905),a905),f335(x98441)),x98442)),f333(f333(f7(x98441,f917(x98441,a905),a905),f335(x98441)),x98443)),x98444)) % 173.51/173.27 [9925]~P106(f333(f333(f335(f916(x99251,x99251)),f333(f333(f265(x99251,x99251),x99254),x99253)),f333(f333(f295(x99251,x99251,x99251),x99252),f313(x99251,x99252))))+P106(f333(f333(f335(f916(x99251,x99251)),f333(f333(f265(x99251,x99251),f633(x99252,x99253,x99254,x99251)),x99253)),x99252)) % 173.51/173.27 [9959]P106(f333(f333(f335(x99591),x99592),f333(f333(f121(f917(x99591,a905)),x99593),x99594)))+~P106(f333(f333(f333(f121(f917(x99591,a905)),f333(f333(f7(x99591,f917(x99591,a905),a905),f335(x99591)),x99593)),f333(f333(f7(x99591,f917(x99591,a905),a905),f335(x99591)),x99594)),x99592)) % 173.51/173.27 [9960]P106(f333(f333(f335(x99601),x99602),f333(f333(f112(f917(x99601,a905)),x99603),x99604)))+~P106(f333(f333(f333(f112(f917(x99601,a905)),f333(f333(f7(x99601,f917(x99601,a905),a905),f335(x99601)),x99603)),f333(f333(f7(x99601,f917(x99601,a905),a905),f335(x99601)),x99604)),x99602)) % 173.51/173.27 [10240]P35(x102401,f333(f333(f7(x102401,f917(f916(x102401,x102401),a905),f917(x102401,a905)),f333(f333(f8(f917(x102401,f917(f917(f916(x102401,x102401),a905),a905)),f917(f917(f916(x102401,x102401),a905),f917(x102401,a905)),x102401),f7(x102401,f917(f916(x102401,x102401),a905),a905)),f333(f333(f8(f917(x102401,f916(x102401,x102401)),f917(x102401,f917(f917(f916(x102401,x102401),a905),a905)),x102401),f333(f8(f916(x102401,x102401),f917(f917(f916(x102401,x102401),a905),a905),x102401),f335(f916(x102401,x102401)))),f265(x102401,x102401)))),x102402),x102403,x102404)+~P106(f333(f333(f335(f916(f911(x102401),f911(x102401))),f333(f333(f265(f911(x102401),f911(x102401)),x102403),x102404)),f166(x102401,x102402))) % 173.51/173.28 [10244]P62(x102441,f333(f333(f7(x102441,f917(f916(x102441,x102441),a905),f917(x102441,a905)),f333(f333(f8(f917(x102441,f917(f917(f916(x102441,x102441),a905),a905)),f917(f917(f916(x102441,x102441),a905),f917(x102441,a905)),x102441),f7(x102441,f917(f916(x102441,x102441),a905),a905)),f333(f333(f8(f917(x102441,f916(x102441,x102441)),f917(x102441,f917(f917(f916(x102441,x102441),a905),a905)),x102441),f333(f8(f916(x102441,x102441),f917(f917(f916(x102441,x102441),a905),a905),x102441),f335(f916(x102441,x102441)))),f265(x102441,x102441)))),x102442),x102443,x102444)+~P106(f333(f333(f335(f916(f917(x102441,a905),f917(x102441,a905))),f333(f333(f265(f917(x102441,a905),f917(x102441,a905)),x102443),x102444)),f324(x102441,x102442))) % 173.51/173.28 [10274]E(x102741,x102742)+~E(f333(f333(f7(x102743,f917(f916(x102743,x102744),a905),f917(x102744,a905)),f333(f333(f8(f917(x102744,f917(f917(f916(x102743,x102744),a905),a905)),f917(f917(f916(x102743,x102744),a905),f917(x102744,a905)),x102743),f7(x102744,f917(f916(x102743,x102744),a905),a905)),f333(f333(f8(f917(x102744,f916(x102743,x102744)),f917(x102744,f917(f917(f916(x102743,x102744),a905),a905)),x102743),f333(f8(f916(x102743,x102744),f917(f917(f916(x102743,x102744),a905),a905),x102744),f335(f916(x102743,x102744)))),f265(x102743,x102744)))),x102741),f333(f333(f7(x102743,f917(f916(x102743,x102744),a905),f917(x102744,a905)),f333(f333(f8(f917(x102744,f917(f917(f916(x102743,x102744),a905),a905)),f917(f917(f916(x102743,x102744),a905),f917(x102744,a905)),x102743),f7(x102744,f917(f916(x102743,x102744),a905),a905)),f333(f333(f8(f917(x102744,f916(x102743,x102744)),f917(x102744,f917(f917(f916(x102743,x102744),a905),a905)),x102743),f333(f8(f916(x102743,x102744),f917(f917(f916(x102743,x102744),a905),a905),x102744),f335(f916(x102743,x102744)))),f265(x102743,x102744)))),x102742)) % 173.51/173.28 [10278]~P35(x102781,f333(f333(f7(x102781,f917(f916(x102781,x102781),a905),f917(x102781,a905)),f333(f333(f8(f917(x102781,f917(f917(f916(x102781,x102781),a905),a905)),f917(f917(f916(x102781,x102781),a905),f917(x102781,a905)),x102781),f7(x102781,f917(f916(x102781,x102781),a905),a905)),f333(f333(f8(f917(x102781,f916(x102781,x102781)),f917(x102781,f917(f917(f916(x102781,x102781),a905),a905)),x102781),f333(f8(f916(x102781,x102781),f917(f917(f916(x102781,x102781),a905),a905),x102781),f335(f916(x102781,x102781)))),f265(x102781,x102781)))),x102784),x102782,x102783)+P106(f333(f333(f335(f916(f911(x102781),f911(x102781))),f333(f333(f265(f911(x102781),f911(x102781)),x102782),x102783)),f166(x102781,x102784))) % 173.51/173.28 [10279]~P62(x102791,f333(f333(f7(x102791,f917(f916(x102791,x102791),a905),f917(x102791,a905)),f333(f333(f8(f917(x102791,f917(f917(f916(x102791,x102791),a905),a905)),f917(f917(f916(x102791,x102791),a905),f917(x102791,a905)),x102791),f7(x102791,f917(f916(x102791,x102791),a905),a905)),f333(f333(f8(f917(x102791,f916(x102791,x102791)),f917(x102791,f917(f917(f916(x102791,x102791),a905),a905)),x102791),f333(f8(f916(x102791,x102791),f917(f917(f916(x102791,x102791),a905),a905),x102791),f335(f916(x102791,x102791)))),f265(x102791,x102791)))),x102794),x102792,x102793)+P106(f333(f333(f335(f916(f917(x102791,a905),f917(x102791,a905))),f333(f333(f265(f917(x102791,a905),f917(x102791,a905)),x102792),x102793)),f324(x102791,x102794))) % 173.51/173.28 [7603]~P95(x76031)+E(f333(f333(f87(x76031),f333(f114(x76031),x76032)),f333(f333(f23(x76031),f333(f114(x76031),x76033)),x76034)),f333(f333(f23(x76031),f333(f114(x76031),f333(f333(f87(a1),x76032),x76033))),x76034)) % 173.51/173.28 [7604]~P95(x76041)+E(f333(f333(f87(x76041),f333(f114(x76041),x76042)),f333(f333(f87(x76041),f333(f114(x76041),x76043)),x76044)),f333(f333(f87(x76041),f333(f114(x76041),f333(f333(f87(a1),x76042),x76043))),x76044)) % 173.51/173.28 [7605]~P95(x76051)+E(f333(f333(f88(x76051),f333(f114(x76051),x76052)),f333(f333(f88(x76051),f333(f114(x76051),x76053)),x76054)),f333(f333(f88(x76051),f333(f114(x76051),f333(f333(f88(a1),x76052),x76053))),x76054)) % 173.51/173.28 [7645]~P107(x76451)+E(f333(f173(x76451),f333(f333(f162(x76452,x76451),f333(f16(x76451,x76452),x76453)),x76454)),f333(f333(f88(x76451),f333(f111(x76451),f333(f197(f911(x76452)),x76454))),x76453)) % 173.51/173.28 [7883]E(f333(f277(x78831,f333(f333(f159(f916(a110,x78831)),x78832),x78833)),x78834),f333(f268(a110,x78831),x78832))+~P106(f333(f333(f247(a110),x78834),f333(f264(a110,x78831),x78832))) % 173.51/173.28 [7928]~P95(x79281)+E(f333(f333(f87(x79281),f333(f114(x79281),x79282)),f333(f333(f23(x79281),x79283),f333(f114(x79281),x79284))),f333(f333(f87(x79281),f333(f114(x79281),f333(f333(f87(a1),x79282),f333(f86(a1),x79284)))),x79283)) % 173.51/173.28 [8060]E(f333(f277(x80601,x80602),f333(f333(f23(a110),x80603),f333(f264(a110,x80601),x80604))),f333(f277(x80601,f333(f333(f159(f916(a110,x80601)),x80604),x80602)),x80603))+P106(f333(f333(f247(a110),x80603),f333(f264(a110,x80601),x80604))) % 173.51/173.28 [8502]~P106(f333(f333(f335(x85021),x85022),f333(f180(x85021),f125(x85021,x85024))))+P106(f333(f333(f335(x85021),x85022),f333(f180(x85021),f125(x85021,f333(f333(f142(x85021),x85023),x85024))))) % 173.51/173.28 [8503]~P106(f333(f333(f335(x85031),x85032),f333(f180(x85031),f125(x85031,x85033))))+P106(f333(f333(f335(x85031),x85032),f333(f180(x85031),f125(x85031,f333(f333(f142(x85031),x85033),x85034))))) % 173.51/173.28 [8524]E(f333(f333(f121(f917(x85241,a905)),f333(f333(f112(f917(x85241,a905)),x85242),x85243)),x85244),f333(f333(f112(f917(x85241,a905)),x85242),f333(f333(f121(f917(x85241,a905)),x85243),x85244)))+~P106(f333(f333(f246(f917(x85241,a905)),x85244),x85242)) % 173.51/173.28 [8843]~E(f333(f333(f121(f917(x88431,a905)),f333(f333(f112(f917(x88431,a905)),x88433),x88434)),x88432),f333(f333(f112(f917(x88431,a905)),x88433),f333(f333(f121(f917(x88431,a905)),x88434),x88432)))+P106(f333(f333(f246(f917(x88431,a905)),x88432),x88433)) % 173.51/173.28 [9148]~P106(f333(f333(f246(f917(x91481,a905)),x91482),f333(f333(f121(f917(x91481,a905)),x91483),x91484)))+P106(f333(f333(f246(f917(x91481,a905)),f333(f333(f23(f917(x91481,a905)),x91482),x91483)),x91484)) % 173.51/173.28 [9266]~E(f333(f316(x92661,x92662,x92663),f254(f917(x92661,a905))),f254(f917(x92662,a905)))+E(f333(f316(x92661,x92662,x92663),f333(f316(x92662,x92661,f99(x92661,x92662,f254(f917(x92661,a905)),x92663)),x92664)),x92664) % 173.51/173.28 [9271]P106(f333(f333(f246(f917(x92711,a905)),x92712),f333(f333(f121(f917(x92711,a905)),x92713),x92714)))+~P106(f333(f333(f246(f917(x92711,a905)),f333(f333(f23(f917(x92711,a905)),x92712),x92713)),x92714)) % 173.51/173.28 [9354]~P87(x93541)+E(f333(f82(x93541),f333(f333(f6(x93542,x93541),f333(f333(f8(x93541,x93541,x93542),f82(x93541)),x93543)),x93544)),f333(f333(f6(x93542,x93541),f333(f333(f8(x93541,x93541,x93542),f82(x93541)),x93543)),x93544)) % 173.51/173.28 [9534]~P87(x95341)+P106(f333(f333(f246(x95341),f2(x95341)),f333(f333(f6(x95342,x95341),f333(f333(f8(x95341,x95341,x95342),f82(x95341)),x95343)),x95344))) % 173.51/173.28 [9538]~P6(x95381)+E(f333(f173(x95381),f333(f333(f162(x95382,x95381),f333(f79(x95381,x95381,x95382,f86(x95381)),x95383)),x95384)),f333(f86(x95381),f333(f173(x95381),f333(f333(f162(x95382,x95381),x95383),x95384)))) % 173.51/173.28 [9682]~P87(x96821)+P106(f333(f333(f246(x96821),f333(f82(x96821),f333(f333(f6(x96822,x96821),x96823),x96824))),f333(f333(f6(x96822,x96821),f333(f333(f8(x96821,x96821,x96822),f82(x96821)),x96823)),x96824))) % 173.51/173.28 [9718]~E(f333(f333(f87(a910),x97181),x97184),f333(f333(f87(a910),x97183),x97182))+P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),f333(f333(f265(a910,a910),x97181),x97182)),f333(f333(f265(a910,a910),x97183),x97184))),a119)) % 173.51/173.28 [9719]~P106(f333(f333(f247(a910),x97191),x97193))+P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),f333(f333(f265(a910,a910),x97191),x97192)),f333(f333(f265(a910,a910),x97193),x97194))),a39)) % 173.51/173.28 [9720]~P106(f333(f333(f247(a910),x97201),x97203))+P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),f333(f333(f265(a910,a910),x97201),x97202)),f333(f333(f265(a910,a910),x97203),x97204))),a77)) % 173.51/173.28 [9868]E(f333(f333(f87(a910),x98681),x98682),f333(f333(f87(a910),x98683),x98684))+~P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),f333(f333(f265(a910,a910),x98681),x98684)),f333(f333(f265(a910,a910),x98683),x98682))),a119)) % 173.51/173.28 [9898]E(f333(f333(f172(x98981),f333(f333(f146(x98981),f333(f197(f911(x98981)),f185(x98981,x98982,x98983))),x98983)),x98984),f333(f333(f172(x98981),x98983),f333(f333(f87(a910),x98984),f333(f197(f911(x98981)),f185(x98981,x98982,x98983)))))+~P106(f333(f333(f247(a910),x98984),f333(f197(f911(x98981)),f333(f333(f146(x98981),f333(f197(f911(x98981)),f185(x98981,x98982,x98983))),x98983)))) % 173.51/173.28 [9915]~P106(f333(f333(f335(x99152),x99154),f333(f333(f45(x99151,f917(x99152,a905)),f254(f917(x99151,a905))),x99153)))+P106(f333(f333(f333(f45(x99151,f917(x99152,a905)),f254(f917(x99151,a905))),f333(f333(f8(f917(x99152,a905),f917(x99152,a905),x99151),f333(f7(x99152,f917(x99152,a905),a905),f335(x99152))),x99153)),x99154)) % 173.51/173.28 [9916]~P106(f333(f333(f335(x99162),x99164),f333(f333(f46(x99161,f917(x99162,a905)),f254(f917(x99161,a905))),x99163)))+P106(f333(f333(f333(f46(x99161,f917(x99162,a905)),f254(f917(x99161,a905))),f333(f333(f8(f917(x99162,a905),f917(x99162,a905),x99161),f333(f7(x99162,f917(x99162,a905),a905),f335(x99162))),x99163)),x99164)) % 173.51/173.28 [9986]~P106(f333(f55(x99861,x99862),f333(f333(f265(a1,a1),x99864),x99863)))+P106(f333(f55(f333(f86(a1),x99861),x99862),f333(f333(f265(a1,a1),f333(f333(f333(f107(a1),f333(f333(a330,x99863),f2(a1))),f333(f86(a1),x99864)),f333(f333(f23(a1),f333(f86(a1),x99864)),f85(a1)))),f333(f333(f333(f107(a1),f333(f333(a330,x99863),f2(a1))),f2(a1)),f333(f333(f23(a1),x99862),x99863))))) % 173.51/173.28 [9996]P106(f333(f333(f335(x99961),x99962),f333(f333(f45(x99963,f917(x99961,a905)),f254(f917(x99963,a905))),x99964)))+~P106(f333(f333(f333(f45(x99963,f917(x99961,a905)),f254(f917(x99963,a905))),f333(f333(f8(f917(x99961,a905),f917(x99961,a905),x99963),f333(f7(x99961,f917(x99961,a905),a905),f335(x99961))),x99964)),x99962)) % 173.51/173.28 [9997]P106(f333(f333(f335(x99971),x99972),f333(f333(f46(x99973,f917(x99971,a905)),f254(f917(x99973,a905))),x99974)))+~P106(f333(f333(f333(f46(x99973,f917(x99971,a905)),f254(f917(x99973,a905))),f333(f333(f8(f917(x99971,a905),f917(x99971,a905),x99973),f333(f7(x99971,f917(x99971,a905),a905),f335(x99971))),x99974)),x99972)) % 173.51/173.28 [10009]E(f333(f333(f45(a910,f917(x100091,a905)),f254(f917(a910,a905))),x100092),f333(f333(f45(a910,f917(x100091,a905)),f254(f917(a910,a905))),x100093))+~E(f333(f333(f45(a910,f917(x100091,a905)),f333(f308(a910,f2(a910)),f496(x100092,x100094,x100093,x100091))),x100093),f333(f333(f45(a910,f917(x100091,a905)),f333(f308(a910,f2(a910)),f333(f333(f87(a910),f496(x100092,x100094,x100093,x100091)),x100094))),x100092)) % 173.51/173.28 [10347]~P106(f333(f333(f246(f917(f916(x103471,x103472),a905)),x103473),x103474))+P106(f333(f333(f246(f917(x103471,f917(x103472,a905))),f333(f333(f7(x103471,f917(f916(x103471,x103472),a905),f917(x103472,a905)),f333(f333(f8(f917(x103472,f917(f917(f916(x103471,x103472),a905),a905)),f917(f917(f916(x103471,x103472),a905),f917(x103472,a905)),x103471),f7(x103472,f917(f916(x103471,x103472),a905),a905)),f333(f333(f8(f917(x103472,f916(x103471,x103472)),f917(x103472,f917(f917(f916(x103471,x103472),a905),a905)),x103471),f333(f8(f916(x103471,x103472),f917(f917(f916(x103471,x103472),a905),a905),x103472),f335(f916(x103471,x103472)))),f265(x103471,x103472)))),x103473)),f333(f333(f7(x103471,f917(f916(x103471,x103472),a905),f917(x103472,a905)),f333(f333(f8(f917(x103472,f917(f917(f916(x103471,x103472),a905),a905)),f917(f917(f916(x103471,x103472),a905),f917(x103472,a905)),x103471),f7(x103472,f917(f916(x103471,x103472),a905),a905)),f333(f333(f8(f917(x103472,f916(x103471,x103472)),f917(x103472,f917(f917(f916(x103471,x103472),a905),a905)),x103471),f333(f8(f916(x103471,x103472),f917(f917(f916(x103471,x103472),a905),a905),x103472),f335(f916(x103471,x103472)))),f265(x103471,x103472)))),x103474))) % 173.51/173.28 [10364]P106(f333(f333(f246(f917(f916(x103641,x103642),a905)),x103643),x103644))+~P106(f333(f333(f246(f917(x103641,f917(x103642,a905))),f333(f333(f7(x103641,f917(f916(x103641,x103642),a905),f917(x103642,a905)),f333(f333(f8(f917(x103642,f917(f917(f916(x103641,x103642),a905),a905)),f917(f917(f916(x103641,x103642),a905),f917(x103642,a905)),x103641),f7(x103642,f917(f916(x103641,x103642),a905),a905)),f333(f333(f8(f917(x103642,f916(x103641,x103642)),f917(x103642,f917(f917(f916(x103641,x103642),a905),a905)),x103641),f333(f8(f916(x103641,x103642),f917(f917(f916(x103641,x103642),a905),a905),x103642),f335(f916(x103641,x103642)))),f265(x103641,x103642)))),x103643)),f333(f333(f7(x103641,f917(f916(x103641,x103642),a905),f917(x103642,a905)),f333(f333(f8(f917(x103642,f917(f917(f916(x103641,x103642),a905),a905)),f917(f917(f916(x103641,x103642),a905),f917(x103642,a905)),x103641),f7(x103642,f917(f916(x103641,x103642),a905),a905)),f333(f333(f8(f917(x103642,f916(x103641,x103642)),f917(x103642,f917(f917(f916(x103641,x103642),a905),a905)),x103641),f333(f8(f916(x103641,x103642),f917(f917(f916(x103641,x103642),a905),a905),x103642),f335(f916(x103641,x103642)))),f265(x103641,x103642)))),x103644))) % 173.51/173.28 [9405]~P106(f333(f333(f335(f916(x94051,x94051)),x94052),f313(x94051,x94054)))+P106(f333(f333(f335(f916(x94051,x94051)),x94052),f313(x94051,f333(f333(f121(f917(f916(x94051,x94051),a905)),x94053),x94054)))) % 173.51/173.28 [9406]~P106(f333(f333(f335(f916(x94061,x94061)),x94062),f313(x94061,x94063)))+P106(f333(f333(f335(f916(x94061,x94061)),x94062),f313(x94061,f333(f333(f121(f917(f916(x94061,x94061),a905)),x94063),x94064)))) % 173.51/173.28 [10103]~P106(f333(f333(f246(a910),f333(f333(f87(a910),x101031),x101034)),f333(f333(f87(a910),x101033),x101032)))+P106(f333(f333(f246(a1),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101031),x101032)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101033),x101034)),f196(f917(f916(a910,a910),a905))))))) % 173.51/173.28 [10104]~P106(f333(f333(f247(a910),f333(f333(f87(a910),x101041),x101044)),f333(f333(f87(a910),x101043),x101042)))+P106(f333(f333(f247(a1),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101041),x101042)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101043),x101044)),f196(f917(f916(a910,a910),a905))))))) % 173.51/173.28 [10184]P106(f333(f333(f246(a910),f333(f333(f87(a910),x101841),x101842)),f333(f333(f87(a910),x101843),x101844)))+~P106(f333(f333(f246(a1),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101841),x101844)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101843),x101842)),f196(f917(f916(a910,a910),a905))))))) % 173.51/173.28 [10185]P106(f333(f333(f247(a910),f333(f333(f87(a910),x101851),x101852)),f333(f333(f87(a910),x101853),x101854)))+~P106(f333(f333(f247(a1),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101851),x101854)),f196(f917(f916(a910,a910),a905)))))),f333(a96,f333(f292(f916(a910,a910),f916(a910,a910),a119),f333(f333(f315(f916(a910,a910)),f333(f333(f265(a910,a910),x101853),x101852)),f196(f917(f916(a910,a910),a905))))))) % 173.51/173.28 [10225]P106(f333(f333(f246(f917(x102251,a905)),f333(f333(f45(a910,f917(x102251,a905)),f254(f917(a910,a905))),x102252)),f333(f333(f45(a910,f917(x102251,a905)),f254(f917(a910,a905))),x102253)))+~P106(f333(f333(f246(f917(x102251,a905)),f333(f333(f45(a910,f917(x102251,a905)),f333(f308(a910,f2(a910)),f492(x102253,x102254,x102252,x102251))),x102252)),f333(f333(f45(a910,f917(x102251,a905)),f333(f308(a910,f2(a910)),f333(f333(f87(a910),f492(x102253,x102254,x102252,x102251)),x102254))),x102253))) % 173.51/173.28 [10282]P106(f333(f333(f246(a110),x102824),f2(a110)))+E(f333(f333(f271(f916(a110,a110),f916(x102821,f917(a913,a329)),f916(a110,a110),f916(f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110))),f333(x102822,x102823)),f333(f333(f8(f917(f917(a110,f917(a905,f914(f912(x102821)))),f917(f916(a110,a110),f916(f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110)))),f917(f916(a110,a110),f916(f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110))),f916(x102821,f917(a913,a329))),f333(f271(f916(a110,a110),f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110),f916(f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110))),f284(x102821,x102822,f333(f333(f23(a110),x102824),f85(a110)),x102823))),f333(f333(f8(f917(f917(a110,f917(a905,f914(f912(x102821)))),f917(a110,f917(a905,f914(f912(x102821))))),f917(f917(a110,f917(a905,f914(f912(x102821)))),f917(f916(a110,a110),f916(f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110)))),f916(x102821,f917(a913,a329))),f333(f8(f917(a110,f917(a905,f914(f912(x102821)))),f917(f916(a110,a110),f916(f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110))),f917(a110,f917(a905,f914(f912(x102821))))),f265(f917(a110,f917(a905,f914(f912(x102821)))),f916(a110,a110)))),f333(f333(f8(f917(a110,f917(a905,f914(f912(x102821)))),f917(f917(a110,f917(a905,f914(f912(x102821)))),f917(a110,f917(a905,f914(f912(x102821))))),f916(x102821,f917(a913,a329))),f50(x102821)),f333(f333(f8(x102821,f917(a110,f917(a905,f914(f912(x102821)))),f916(x102821,f917(a913,a329))),f48(x102821)),f264(x102821,f917(a913,a329))))))),f284(x102821,x102822,x102824,x102823)) % 173.51/173.28 [10336]~P106(f333(f333(f335(x103362),x103364),f333(f291(x103361,x103362),x103363)))+P106(f333(f262(x103361,x103362,f333(f333(f7(x103361,f917(f916(x103361,x103362),a905),f917(x103362,a905)),f333(f333(f8(f917(x103362,f917(f917(f916(x103361,x103362),a905),a905)),f917(f917(f916(x103361,x103362),a905),f917(x103362,a905)),x103361),f7(x103362,f917(f916(x103361,x103362),a905),a905)),f333(f333(f8(f917(x103362,f916(x103361,x103362)),f917(x103362,f917(f917(f916(x103361,x103362),a905),a905)),x103361),f333(f8(f916(x103361,x103362),f917(f917(f916(x103361,x103362),a905),a905),x103362),f335(f916(x103361,x103362)))),f265(x103361,x103362)))),x103363)),x103364)) % 173.51/173.28 [10337]~P106(f333(f333(f335(x103371),x103374),f333(f263(x103371,x103372),x103373)))+P106(f333(f261(x103371,x103372,f333(f333(f7(x103371,f917(f916(x103371,x103372),a905),f917(x103372,a905)),f333(f333(f8(f917(x103372,f917(f917(f916(x103371,x103372),a905),a905)),f917(f917(f916(x103371,x103372),a905),f917(x103372,a905)),x103371),f7(x103372,f917(f916(x103371,x103372),a905),a905)),f333(f333(f8(f917(x103372,f916(x103371,x103372)),f917(x103372,f917(f917(f916(x103371,x103372),a905),a905)),x103371),f333(f8(f916(x103371,x103372),f917(f917(f916(x103371,x103372),a905),a905),x103372),f335(f916(x103371,x103372)))),f265(x103371,x103372)))),x103373)),x103374)) % 173.51/173.28 [10350]P106(f333(f333(f335(x103501),x103502),f333(f291(x103503,x103501),x103504)))+~P106(f333(f262(x103503,x103501,f333(f333(f7(x103503,f917(f916(x103503,x103501),a905),f917(x103501,a905)),f333(f333(f8(f917(x103501,f917(f917(f916(x103503,x103501),a905),a905)),f917(f917(f916(x103503,x103501),a905),f917(x103501,a905)),x103503),f7(x103501,f917(f916(x103503,x103501),a905),a905)),f333(f333(f8(f917(x103501,f916(x103503,x103501)),f917(x103501,f917(f917(f916(x103503,x103501),a905),a905)),x103503),f333(f8(f916(x103503,x103501),f917(f917(f916(x103503,x103501),a905),a905),x103501),f335(f916(x103503,x103501)))),f265(x103503,x103501)))),x103504)),x103502)) % 173.51/173.28 [10351]P106(f333(f333(f335(x103511),x103512),f333(f263(x103511,x103513),x103514)))+~P106(f333(f261(x103511,x103513,f333(f333(f7(x103511,f917(f916(x103511,x103513),a905),f917(x103513,a905)),f333(f333(f8(f917(x103513,f917(f917(f916(x103511,x103513),a905),a905)),f917(f917(f916(x103511,x103513),a905),f917(x103513,a905)),x103511),f7(x103513,f917(f916(x103511,x103513),a905),a905)),f333(f333(f8(f917(x103513,f916(x103511,x103513)),f917(x103513,f917(f917(f916(x103511,x103513),a905),a905)),x103511),f333(f8(f916(x103511,x103513),f917(f917(f916(x103511,x103513),a905),a905),x103513),f335(f916(x103511,x103513)))),f265(x103511,x103513)))),x103514)),x103512)) % 173.51/173.28 [10019]P106(f333(f168(x100191,x100192),x100193))+~P106(f333(f168(x100191,f333(f333(f18(x100191,a905,a905),f333(f333(f8(a905,f917(a905,a905),x100191),a331),x100194)),x100192)),x100193)) % 173.51/173.28 [10020]P106(f333(f168(x100201,x100202),x100203))+~P106(f333(f168(x100201,f333(f333(f18(x100201,a905,a905),f333(f333(f8(a905,f917(a905,a905),x100201),a331),x100202)),x100204)),x100203)) % 173.51/173.28 [10105]~P117(x101051)+E(f333(f333(f88(x101051),f333(f333(f87(x101051),f85(x101051)),f85(x101051))),f333(f333(f6(a910,x101051),f333(f333(f8(x101051,x101051,a910),f333(f87(x101051),x101052)),f333(f333(f7(a910,x101051,x101051),f333(f333(f8(x101051,f917(x101051,x101051),a910),f88(x101051)),f111(x101051))),x101053))),f333(f289(a910),x101054))),f333(f333(f88(x101051),f333(f111(x101051),x101054)),f333(f333(f87(x101051),x101052),f333(f333(f87(x101051),x101052),f333(f333(f88(x101051),f333(f111(x101051),f333(f333(f23(a910),x101054),f85(a910)))),x101053))))) % 173.51/173.28 [10247]P106(f333(x102471,f595(x102472,x102473,x102474,x102471)))+P40(x102472,f333(f252(f916(x102472,x102472)),f333(f269(x102472,x102472,a905),f333(f333(f8(f917(x102472,a905),f917(x102472,a905),x102472),f333(f18(x102472,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102472),a331),x102471))),f333(f333(f7(x102472,f917(x102472,x102472),f917(x102472,a905)),f333(f333(f8(f917(x102472,a905),f917(f917(x102472,x102472),f917(x102472,a905)),x102472),f8(x102472,a905,x102472)),a330)),x102473))))) % 173.51/173.28 [10261]~P106(f333(f333(f247(a910),f333(x102614,f333(x102613,f595(x102611,x102613,x102614,x102612)))),f333(x102614,f595(x102611,x102613,x102614,x102612))))+P40(x102611,f333(f252(f916(x102611,x102611)),f333(f269(x102611,x102611,a905),f333(f333(f8(f917(x102611,a905),f917(x102611,a905),x102611),f333(f18(x102611,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102611),a331),x102612))),f333(f333(f7(x102611,f917(x102611,x102611),f917(x102611,a905)),f333(f333(f8(f917(x102611,a905),f917(f917(x102611,x102611),f917(x102611,a905)),x102611),f8(x102611,a905,x102611)),a330)),x102613))))) % 173.51/173.28 [10321]~P8(x103211)+E(f44(x103211,f333(f252(x103211),f333(f333(f8(f917(f917(x103212,x103211),a905),a905,x103211),f94(f917(x103212,x103211))),f333(f333(f8(f917(f917(x103212,x103211),a905),f917(f917(x103212,x103211),a905),x103211),f333(f18(f917(x103212,x103211),a905,a905),f333(f333(f8(a905,f917(a905,a905),f917(x103212,x103211)),a331),f333(f333(f7(f917(x103212,x103211),f917(f917(x103212,x103211),a905),a905),f335(f917(x103212,x103211))),x103213)))),f333(f333(f7(x103211,f917(f917(x103212,x103211),x103211),f917(f917(x103212,x103211),a905)),f333(f333(f8(f917(x103211,a905),f917(f917(f917(x103212,x103211),x103211),f917(f917(x103212,x103211),a905)),x103211),f8(x103211,a905,f917(x103212,x103211))),a330)),f333(f333(f7(f917(x103212,x103211),x103212,x103211),f5(f917(x103212,x103211))),x103214)))))),f333(f44(f917(x103212,x103211),x103213),x103214)) % 173.51/173.28 [10322]~P8(x103221)+E(f44(x103221,f333(f252(x103221),f333(f333(f8(f917(f917(x103222,x103221),a905),a905,x103221),f94(f917(x103222,x103221))),f333(f333(f8(f917(f917(x103222,x103221),a905),f917(f917(x103222,x103221),a905),x103221),f333(f18(f917(x103222,x103221),a905,a905),f333(f333(f8(a905,f917(a905,a905),f917(x103222,x103221)),a331),f333(f333(f7(f917(x103222,x103221),f917(f917(x103222,x103221),a905),a905),f335(f917(x103222,x103221))),x103223)))),f333(f333(f7(x103221,f917(f917(x103222,x103221),x103221),f917(f917(x103222,x103221),a905)),f333(f333(f8(f917(x103221,a905),f917(f917(f917(x103222,x103221),x103221),f917(f917(x103222,x103221),a905)),x103221),f8(x103221,a905,f917(x103222,x103221))),a330)),f333(f333(f7(f917(x103222,x103221),x103222,x103221),f5(f917(x103222,x103221))),x103224)))))),f333(f44(f917(x103222,x103221),x103223),x103224)) % 173.51/173.28 [10323]~P8(x103231)+E(f43(x103231,f333(f252(x103231),f333(f333(f8(f917(f917(x103232,x103231),a905),a905,x103231),f94(f917(x103232,x103231))),f333(f333(f8(f917(f917(x103232,x103231),a905),f917(f917(x103232,x103231),a905),x103231),f333(f18(f917(x103232,x103231),a905,a905),f333(f333(f8(a905,f917(a905,a905),f917(x103232,x103231)),a331),f333(f333(f7(f917(x103232,x103231),f917(f917(x103232,x103231),a905),a905),f335(f917(x103232,x103231))),x103233)))),f333(f333(f7(x103231,f917(f917(x103232,x103231),x103231),f917(f917(x103232,x103231),a905)),f333(f333(f8(f917(x103231,a905),f917(f917(f917(x103232,x103231),x103231),f917(f917(x103232,x103231),a905)),x103231),f8(x103231,a905,f917(x103232,x103231))),a330)),f333(f333(f7(f917(x103232,x103231),x103232,x103231),f5(f917(x103232,x103231))),x103234)))))),f333(f43(f917(x103232,x103231),x103233),x103234)) % 173.51/173.28 [10324]~P8(x103241)+E(f43(x103241,f333(f252(x103241),f333(f333(f8(f917(f917(x103242,x103241),a905),a905,x103241),f94(f917(x103242,x103241))),f333(f333(f8(f917(f917(x103242,x103241),a905),f917(f917(x103242,x103241),a905),x103241),f333(f18(f917(x103242,x103241),a905,a905),f333(f333(f8(a905,f917(a905,a905),f917(x103242,x103241)),a331),f333(f333(f7(f917(x103242,x103241),f917(f917(x103242,x103241),a905),a905),f335(f917(x103242,x103241))),x103243)))),f333(f333(f7(x103241,f917(f917(x103242,x103241),x103241),f917(f917(x103242,x103241),a905)),f333(f333(f8(f917(x103241,a905),f917(f917(f917(x103242,x103241),x103241),f917(f917(x103242,x103241),a905)),x103241),f8(x103241,a905,f917(x103242,x103241))),a330)),f333(f333(f7(f917(x103242,x103241),x103242,x103241),f5(f917(x103242,x103241))),x103244)))))),f333(f43(f917(x103242,x103241),x103243),x103244)) % 173.51/173.28 [10378]~P106(f333(f333(f335(f916(x103781,x103781)),f333(f333(f265(x103781,x103781),x103783),x103784)),f333(f333(f121(f917(f916(x103781,x103781),a905)),x103782),f313(x103781,f196(f917(f916(x103781,x103781),a905))))))+P106(f333(f333(f333(f333(f121(f917(x103781,f917(x103781,a905))),f333(f333(f7(x103781,f917(f916(x103781,x103781),a905),f917(x103781,a905)),f333(f333(f8(f917(x103781,f917(f917(f916(x103781,x103781),a905),a905)),f917(f917(f916(x103781,x103781),a905),f917(x103781,a905)),x103781),f7(x103781,f917(f916(x103781,x103781),a905),a905)),f333(f333(f8(f917(x103781,f916(x103781,x103781)),f917(x103781,f917(f917(f916(x103781,x103781),a905),a905)),x103781),f333(f8(f916(x103781,x103781),f917(f917(f916(x103781,x103781),a905),a905),x103781),f335(f916(x103781,x103781)))),f265(x103781,x103781)))),x103782)),a330),x103783),x103784)) % 173.51/173.28 [10386]P106(f333(f333(f335(f916(x103861,x103861)),f333(f333(f265(x103861,x103861),x103862),x103863)),f333(f333(f121(f917(f916(x103861,x103861),a905)),x103864),f313(x103861,f196(f917(f916(x103861,x103861),a905))))))+~P106(f333(f333(f333(f333(f121(f917(x103861,f917(x103861,a905))),f333(f333(f7(x103861,f917(f916(x103861,x103861),a905),f917(x103861,a905)),f333(f333(f8(f917(x103861,f917(f917(f916(x103861,x103861),a905),a905)),f917(f917(f916(x103861,x103861),a905),f917(x103861,a905)),x103861),f7(x103861,f917(f916(x103861,x103861),a905),a905)),f333(f333(f8(f917(x103861,f916(x103861,x103861)),f917(x103861,f917(f917(f916(x103861,x103861),a905),a905)),x103861),f333(f8(f916(x103861,x103861),f917(f917(f916(x103861,x103861),a905),a905),x103861),f335(f916(x103861,x103861)))),f265(x103861,x103861)))),x103864)),a330),x103862),x103863)) % 173.51/173.28 [10233]~P111(x102333)+E(f97(x102331,f333(f333(f18(x102331,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102331),a331),x102332)),f333(f333(f8(f917(x102331,a905),a905,x102331),f95(x102331)),f333(f333(f8(f917(x102331,a905),f917(x102331,a905),x102331),f333(f18(x102331,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102331),a336),x102332))),f333(f333(f8(x102333,f917(x102331,a905),x102331),f333(f7(x102331,x102333,a905),f333(f333(f8(x102333,f917(x102333,a905),x102331),f246(x102333)),x102334))),x102334))))),f333(f100(x102331,x102333,x102334),x102332)) % 173.51/173.28 [10277]~P111(x102773)+E(f97(x102771,f333(f333(f18(x102771,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102771),a331),x102772)),f333(f333(f8(f917(x102771,a905),a905,x102771),f95(x102771)),f333(f333(f8(f917(x102771,a905),f917(x102771,a905),x102771),f333(f18(x102771,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102771),a336),x102772))),f333(f333(f7(x102771,f917(x102771,x102773),f917(x102771,a905)),f333(f333(f8(f917(x102773,a905),f917(f917(x102771,x102773),f917(x102771,a905)),x102771),f8(x102773,a905,x102771)),f333(f333(f8(x102773,f917(x102773,a905),x102771),f246(x102773)),x102774))),x102774))))),f102(x102771,x102773,x102774,x102772)) % 173.51/173.28 [10332]E(f333(f333(f159(f911(x103321)),f333(f333(f159(x103321),x103322),f333(f150(f911(x103321),f911(x103321),f142(x103321),f124(x103321)),f333(f333(f162(f911(x103321),f911(x103321)),f164(f911(x103321),x103321,f124(x103321),f333(f333(f8(f911(x103321),f917(f911(x103321),f911(x103321)),x103321),f16(f911(x103321),f911(x103321))),f333(f333(f7(x103321,f911(x103321),f911(x103321)),f159(x103321)),f124(x103321))))),x103323)))),f187(x103321,f333(f333(f159(f911(x103321)),x103324),f333(f150(f911(f911(x103321)),f911(f911(x103321)),f142(f911(x103321)),f124(f911(x103321))),f333(f333(f162(f911(x103321),f911(f911(x103321))),f164(f911(f911(x103321)),x103321,f124(f911(x103321)),f333(f16(f917(f911(x103321),f911(f911(x103321))),x103321),f333(f333(f7(f911(x103321),f911(f911(x103321)),f911(f911(x103321))),f159(f911(x103321))),f124(f911(x103321)))))),x103323))))),f187(x103321,f333(f333(f159(f911(x103321)),f333(f333(f159(x103321),x103322),x103324)),x103323)))+~P106(f333(f321(f911(f911(x103321)),f188(x103321)),f333(f333(f159(f911(x103321)),f333(f333(f159(x103321),x103322),x103324)),x103323))) % 173.51/173.28 [10377]~P106(f333(f67(x103772),f333(f252(x103772),x103774)))+P106(f333(f67(x103771),f333(f252(x103771),f333(f333(f8(f917(x103772,a905),a905,x103771),f94(x103772)),f333(f333(f7(x103771,f917(x103772,a905),f917(x103772,a905)),f333(f333(f8(f917(x103772,f917(a905,a905)),f917(f917(x103772,a905),f917(x103772,a905)),x103771),f18(x103772,a905,a905)),f333(f333(f8(f917(x103772,a905),f917(x103772,f917(a905,a905)),x103771),f333(f8(a905,f917(a905,a905),x103772),a331)),f333(f333(f7(x103771,f917(x103772,x103771),f917(x103772,a905)),f333(f333(f8(f917(x103771,a905),f917(f917(x103772,x103771),f917(x103772,a905)),x103771),f8(x103771,a905,x103772)),a330)),x103773)))),x103774))))) % 173.51/173.28 [8880]P27(x88801,x88802,x88803,x88804)+~P28(x88801,x88802,x88803,x88804,x88805) % 173.51/173.28 [5410]E(x54101,x54102)+~E(f177(x54103,x54101,x54104),f177(x54103,x54102,x54105)) % 173.51/173.28 [5411]E(x54111,x54112)+~E(f136(x54113,x54114,x54111),f136(x54113,x54115,x54112)) % 173.51/173.28 [5412]E(x54121,x54122)+~E(f136(x54123,x54121,x54124),f136(x54123,x54122,x54125)) % 173.51/173.28 [8198]~E(f333(x81983,x81984),x81985)+E(f81(x81981,x81982,x81983,x81984,x81985),x81983) % 173.51/173.28 [8738]~E(f81(x87384,x87385,x87381,x87382,x87383),x87381)+E(f333(x87381,x87382),x87383) % 173.51/173.28 [9372]~P28(x93722,x93721,x93724,x93723,x93725)+P28(x93721,x93722,f84(x93722,x93721,x93723,x93724),x93725,x93723) % 173.51/173.28 [9373]~P28(x93732,x93731,x93734,x93733,x93735)+P28(x93731,x93732,f99(x93732,x93731,x93733,x93734),x93735,x93733) % 173.51/173.28 [6192]P106(f333(f262(x61921,x61922,x61923),x61924))+~P106(f333(f333(x61923,x61925),x61924)) % 173.51/173.28 [6194]P106(f333(f261(x61941,x61942,x61943),x61944))+~P106(f333(f333(x61943,x61944),x61945)) % 173.51/173.28 [6660]~E(x66605,f2(a110))+E(f333(f210(x66601,x66602,x66603,x66604),x66605),f126(x66602)) % 173.51/173.28 [6661]~E(x66615,f2(a110))+E(f333(f208(x66611,x66612,x66613,x66614),x66615),f134(x66612)) % 173.51/173.28 [6798]~E(x67983,f2(a110))+E(f333(f280(x67981,x67982,x67983,x67984),x67985),f333(f265(x67981,x67982),x67985)) % 173.51/173.28 [7839]~P22(x78394,x78391,x78392,x78395)+E(f333(f79(x78391,x78391,x78391,f333(x78392,x78393)),f333(x78392,x78393)),f333(x78392,x78393)) % 173.51/173.28 [8237]~P18(x82375,x82371,x82372)+E(f333(f79(x82371,x82371,x82371,f333(x82372,x82373)),f333(x82372,x82374)),f333(f79(x82371,x82371,x82371,f333(x82372,x82374)),f333(x82372,x82373))) % 173.51/173.28 [8566]P106(f333(f333(f335(f916(x85661,x85661)),f333(f333(f265(x85661,x85661),x85662),x85663)),f327(x85661,x85664,x85665)))+~P106(f333(f333(f247(a910),f333(x85664,x85662)),f333(x85664,x85663))) % 173.51/173.28 [8667]~P106(f333(f333(f335(x86674),x86673),f302(x86674,x86671,x86672,x86675)))+P106(f333(f333(x86671,x86672),x86673)) % 173.51/173.28 [8668]~P106(f333(f333(f335(x86684),x86683),f305(x86684,x86681,x86682,x86685)))+P106(f333(f333(x86681,x86682),x86683)) % 173.51/173.28 [8669]~P106(f333(f333(f335(x86694),x86692),f302(x86694,x86691,x86695,x86693)))+P106(f333(f333(x86691,x86692),x86693)) % 173.51/173.28 [8670]~P106(f333(f333(f335(x86704),x86702),f305(x86704,x86701,x86705,x86703)))+P106(f333(f333(x86701,x86702),x86703)) % 173.51/173.28 [8750]~P28(x87501,x87503,x87505,x87502,x87504)+E(f333(f41(x87501),x87502),f333(f41(x87503),x87504)) % 173.51/173.28 [8799]~P28(x87991,x87992,x87993,x87994,x87995)+E(f333(f316(x87991,x87992,x87993),x87994),x87995) % 173.51/173.28 [8819]~P60(x88192,x88191,x88195,x88193,x88194)+E(f333(f316(x88191,x88192,x88193),x88194),f254(f917(x88192,a905))) % 173.51/173.28 [9284]~P37(x92841,x92842,x92843,x92844,x92845)+P37(x92841,x92842,x92843,f333(f176(x92841),x92844),f333(f176(x92842),x92845)) % 173.51/173.28 [9286]~P37(x92861,x92862,x92863,f333(f176(x92861),x92864),x92865)+P37(x92861,x92862,x92863,x92864,f333(f176(x92862),x92865)) % 173.51/173.28 [9287]~P37(x92871,x92872,x92873,x92874,f333(f176(x92872),x92875))+P37(x92871,x92872,x92873,f333(f176(x92871),x92874),x92875) % 173.51/173.28 [9293]P37(x92931,x92932,x92933,x92934,x92935)+~P37(x92931,x92932,x92933,f333(f176(x92931),x92934),f333(f176(x92932),x92935)) % 173.51/173.28 [9708]P106(f333(f333(f335(f916(f911(x97081),f911(x97081))),f333(f333(f265(f911(x97081),f911(x97081)),f333(f333(f159(x97081),x97082),x97083)),f333(f333(f159(x97081),x97082),x97084))),f165(x97081,x97085)))+~P106(f333(f333(f335(f916(f911(x97081),f911(x97081))),f333(f333(f265(f911(x97081),f911(x97081)),x97083),x97084)),f165(x97081,x97085))) % 173.51/173.28 [9709]P106(f333(f333(f335(f916(f911(x97091),f911(x97091))),f333(f333(f265(f911(x97091),f911(x97091)),f333(f333(f142(x97091),x97092),x97093)),f333(f333(f142(x97091),x97092),x97094))),f155(x97091,x97095)))+~P106(f333(f333(f335(f916(f911(x97091),f911(x97091))),f333(f333(f265(f911(x97091),f911(x97091)),x97093),x97094)),f155(x97091,x97095))) % 173.51/173.28 [9905]E(f333(f333(f159(x99051),f697(x99052,x99053,x99054,x99055,x99051)),f699(x99052,x99053,x99054,x99055,x99051)),x99055)+~P106(f333(f333(f335(f916(f911(x99051),f911(x99051))),f333(f333(f265(f911(x99051),f911(x99051)),x99055),f333(f333(f159(x99051),x99054),x99053))),f166(x99051,x99052))) % 173.51/173.28 [9928]E(f333(f333(f159(x99281),f700(x99282,x99283,x99284,x99285,x99281)),f701(x99282,x99283,x99284,x99285,x99281)),x99283)+~P106(f333(f333(f335(f916(f911(x99281),f911(x99281))),f333(f333(f265(f911(x99281),f911(x99281)),f333(f333(f159(x99281),x99285),x99284)),x99283)),f166(x99281,x99282))) % 173.51/173.28 [10077]~P106(f333(f333(f335(f916(f911(x100771),f911(x100771))),f333(f333(f265(f911(x100771),f911(x100771)),f333(f333(f159(x100771),x100775),x100772)),x100774)),f166(x100771,x100773)))+P106(f333(f333(f335(f916(f911(x100771),f911(x100771))),f333(f333(f265(f911(x100771),f911(x100771)),x100772),f701(x100773,x100774,x100772,x100775,x100771))),f166(x100771,x100773))) % 173.51/173.28 [10149]~P106(f333(f333(f335(f916(f911(x101491),f911(x101491))),f333(f333(f265(f911(x101491),f911(x101491)),x101495),f333(f333(f159(x101491),x101494),x101493))),f166(x101491,x101492)))+P106(f333(f333(f335(f916(f911(x101491),f911(x101491))),f333(f333(f265(f911(x101491),f911(x101491)),f699(x101492,x101493,x101494,x101495,x101491)),x101493)),f166(x101491,x101492))) % 173.51/173.28 [10326]P106(f333(f333(f335(f916(x103261,x103261)),f333(f333(f265(x103261,x103261),f333(x103262,f333(f333(f87(a910),x103263),x103264))),f333(x103262,x103263))),f313(x103261,x103265)))+~P106(f333(f333(f335(f916(x103261,x103261)),f333(f333(f265(x103261,x103261),f333(x103262,f333(a123,f621(x103264,x103263,x103265,x103262,x103261)))),f333(x103262,f621(x103264,x103263,x103265,x103262,x103261)))),f313(x103261,x103265))) % 173.51/173.28 [5378]E(x53781,x53782)+~E(f333(f333(f159(x53783),x53784),x53781),f333(f333(f159(x53783),x53785),x53782)) % 173.51/173.28 [5379]E(x53791,x53792)+~E(f333(f333(f159(x53793),x53791),x53794),f333(f333(f159(x53793),x53792),x53795)) % 173.51/173.28 [5427]P106(f333(x54271,x54272))+~E(f333(f144(x54273,x54271),x54274),f333(f333(f159(x54273),x54272),x54275)) % 173.51/173.28 [5428]P106(f333(x54281,x54282))+~E(f333(f333(f159(x54283),x54282),x54284),f333(f144(x54283,x54281),x54285)) % 173.51/173.28 [5580]~E(f333(f333(f146(x55801),x55803),x55802),f333(f333(f159(x55801),x55804),x55805))+E(f333(f333(f172(x55801),x55802),x55803),x55804) % 173.51/173.28 [5715]~P17(x57154,x57155,x57151)+E(f333(f333(x57151,x57152),f333(f333(x57151,x57152),x57153)),f333(f333(x57151,x57152),x57153)) % 173.51/173.28 [6249]~E(x62494,f2(a110))+E(f333(f333(f128(x62491,x62492,x62493),x62494),x62495),f333(f333(f265(f911(x62492),x62491),f124(x62492)),x62495)) % 173.51/173.28 [6317]~P110(x63172)+~E(f333(f333(f156(x63171,x63172,x63173),x63174),x63175),f124(x63171)) % 173.51/173.28 [6699]E(x66991,x66992)+~E(f333(f333(f142(x66993),x66994),f333(f333(f159(x66993),x66991),f124(x66993))),f333(f333(f142(x66993),x66995),f333(f333(f159(x66993),x66992),f124(x66993)))) % 173.51/173.28 [6700]E(x67001,x67002)+~E(f333(f333(f142(x67003),x67001),f333(f333(f159(x67003),x67004),f124(x67003))),f333(f333(f142(x67003),x67002),f333(f333(f159(x67003),x67005),f124(x67003)))) % 173.51/173.28 [7009]E(f333(f333(f315(x70091),f333(x70092,x70093)),f333(f316(x70094,x70091,x70092),x70095)),f333(f316(x70094,x70091,x70092),x70095))+~P106(f333(f333(f335(x70094),x70093),x70095)) % 173.51/173.28 [7016]~P106(f333(x70164,f333(x70163,x70165)))+P106(f333(f333(f317(x70161,x70162,x70163),x70164),x70165)) % 173.51/173.28 [7019]~P106(f333(f333(x70193,x70195),x70194))+P106(f333(f333(f255(x70191,x70192,x70193),x70194),x70195)) % 173.51/173.28 [7113]~E(f333(f316(x71131,x71132,x71133),x71134),x71135)+E(f333(f316(f917(x71131,a905),f917(x71132,a905),f316(x71131,x71132,x71133)),f333(f314(x71131),x71134)),f333(f314(x71132),x71135)) % 173.51/173.28 [7450]P27(x74501,x74502,x74503,x74504)+~P27(x74501,x74502,x74503,f333(f333(f315(x74501),x74505),x74504)) % 173.51/173.28 [7516]P106(f333(x75161,x75162))+~P106(f333(f333(f103(x75163,x75164,x75161),x75165),x75162)) % 173.51/173.28 [7557]~P106(f333(f333(f335(x75574),x75573),x75575))+P106(f333(f333(f335(x75571),f333(x75572,x75573)),f333(f316(x75574,x75571,x75572),x75575))) % 173.51/173.28 [7579]~P110(x75792)+E(f158(x75791,x75792,x75793,f333(f144(x75791,x75794),x75795)),f333(f144(x75791,x75794),f158(x75791,x75792,x75793,x75795))) % 173.51/173.28 [7610]P106(f333(x76101,f333(x76102,x76103)))+~P106(f333(f333(f317(x76104,x76105,x76102),x76101),x76103)) % 173.51/173.28 [7613]P106(f333(f333(x76131,x76132),x76133))+~P106(f333(f333(f255(x76134,x76135,x76131),x76133),x76132)) % 173.51/173.28 [7614]P106(f333(f333(x76141,x76142),x76143))+~P106(f333(f333(f103(x76144,x76141,x76145),x76142),x76143)) % 173.51/173.28 [7675]~P106(f333(f333(f335(x76753),f333(x76754,x76752)),x76755))+P106(f333(f333(f335(x76751),x76752),f333(f317(x76751,x76753,x76754),x76755))) % 173.51/173.28 [8074]~P106(f333(f333(f335(x80745),x80743),f333(f317(x80745,x80741,x80742),x80744)))+P106(f333(f333(f335(x80741),f333(x80742,x80743)),x80744)) % 173.51/173.28 [8377]~P18(x83772,x83771,x83773)+E(f333(f150(x83771,x83772,f333(f7(x83772,x83771,x83771),x83773),x83774),f160(x83772,x83775)),f333(f333(f70(x83772,x83771,x83773),x83774),f333(f180(x83772),x83775))) % 173.51/173.28 [8399]E(f333(x83991,f714(x83992,x83991,x83993,x83994)),x83994)+~P106(f333(f333(f335(x83995),x83994),f333(f316(x83993,x83995,x83991),x83992))) % 173.51/173.28 [8400]E(f333(x84001,f762(x84002,x84001,x84003,x84004)),x84004)+~P106(f333(f333(f335(x84005),x84004),f333(f316(x84003,x84005,x84001),x84002))) % 173.51/173.28 [8713]~E(x87132,f333(f333(f159(x87131),x87134),x87135))+P106(f333(f333(f335(f916(f911(x87131),f911(x87131))),f333(f333(f265(f911(x87131),f911(x87131)),f124(x87131)),x87132)),f155(x87131,x87133))) % 173.51/173.28 [8761]E(f333(x87611,f333(f99(x87612,x87613,x87614,x87611),x87615)),x87615)+~P106(f333(f333(f335(x87613),x87615),f333(f316(x87612,x87613,x87611),x87614))) % 173.51/173.28 [8764]P27(x87641,x87642,f99(x87642,x87641,x87643,x87644),x87645)+~P106(f333(f333(f246(f917(x87641,a905)),x87645),f333(f316(x87642,x87641,x87644),x87643))) % 173.51/173.28 [8771]~P37(x87711,x87713,x87715,x87712,x87714)+E(f333(f197(f911(x87711)),x87712),f333(f197(f911(x87713)),x87714)) % 173.51/173.28 [8782]P106(f333(f333(f246(f917(x87821,a905)),f333(f333(f46(x87822,f917(x87821,a905)),x87823),x87824)),f333(x87824,x87825)))+~P106(f333(f333(f335(x87822),x87825),x87823)) % 173.51/173.28 [8835]~P60(x88351,x88352,x88353,x88355,x88354)+E(f333(f316(x88351,x88352,x88353),f254(f917(x88351,a905))),x88354) % 173.51/173.28 [9064]E(f333(f144(x90641,x90642),f789(x90643,x90644,x90645,x90642,x90641)),x90643)+~E(f333(f144(x90641,x90642),x90645),f333(f333(f159(x90641),x90644),x90643)) % 173.51/173.28 [9065]E(f333(f144(x90651,x90652),f790(x90653,x90652,x90654,x90655,x90651)),x90654)+~E(f333(f333(f159(x90651),x90655),x90654),f333(f144(x90651,x90652),x90653)) % 173.51/173.28 [9171]E(f333(f197(f911(x91711)),x91712),x91713)+~P106(f333(f333(f335(f916(f911(x91711),f911(x91711))),f333(f333(f265(f911(x91711),f911(x91711)),x91714),x91712)),f333(f151(x91711,x91715),x91713))) % 173.51/173.28 [9172]E(f333(f197(f911(x91721)),x91722),x91723)+~P106(f333(f333(f335(f916(f911(x91721),f911(x91721))),f333(f333(f265(f911(x91721),f911(x91721)),x91722),x91724)),f333(f151(x91721,x91725),x91723))) % 173.51/173.28 [9241]P106(f333(f333(f335(x92411),f714(x92412,x92413,x92411,x92414)),x92412))+~P106(f333(f333(f335(x92415),x92414),f333(f316(x92411,x92415,x92413),x92412))) % 173.51/173.28 [9242]P106(f333(f333(f335(x92421),f762(x92422,x92423,x92421,x92424)),x92422))+~P106(f333(f333(f335(x92425),x92424),f333(f316(x92421,x92425,x92423),x92422))) % 173.51/173.28 [9403]E(f333(f316(x94031,x94032,x94033),f862(x94034,x94033,x94031,x94035,x94032)),x94035)+~P106(f333(f333(f246(f917(x94032,a905)),x94035),f333(f316(x94031,x94032,x94033),x94034))) % 173.51/173.28 [9726]P106(f333(f333(f335(f916(f911(x97261),f911(x97261))),f333(f333(f265(f911(x97261),f911(x97261)),f333(f333(f159(x97261),x97262),x97263)),f333(f333(f159(x97261),x97262),x97264))),f313(f911(x97261),f165(x97261,x97265))))+~P106(f333(f333(f335(f916(f911(x97261),f911(x97261))),f333(f333(f265(f911(x97261),f911(x97261)),x97263),x97264)),f313(f911(x97261),f165(x97261,x97265)))) % 173.51/173.28 [9758]~E(f333(x97583,f741(x97585,x97584,x97583,x97582,x97581)),f333(x97585,f741(x97585,x97584,x97583,x97582,x97581)))+E(f333(f333(f162(x97581,x97582),x97583),x97584),f333(f333(f162(x97581,x97582),x97585),x97584)) % 173.51/173.28 [9774]P106(f333(f333(f202(x97741),f333(f333(f333(a205,x97742),f34(x97743)),f333(x97744,x97742))),f579(x97745,x97742,x97741,x97744,x97743)))+~P106(f333(f333(f202(f27(x97743,x97744,x97741)),x97742),f333(f333(f333(a205,x97745),f34(x97743)),f206(x97742,x97743)))) % 173.51/173.28 [9834]~E(f333(f144(x98341,x98345),x98344),f333(f333(f159(x98341),x98343),x98342))+E(f333(f333(f142(x98341),f793(x98342,x98343,x98344,x98345,x98341)),f333(f333(f159(x98341),x98343),f789(x98342,x98343,x98344,x98345,x98341))),x98344) % 173.51/173.28 [9835]~E(f333(f333(f159(x98351),x98355),x98354),f333(f144(x98351,x98353),x98352))+E(f333(f333(f142(x98351),f791(x98352,x98353,x98354,x98355,x98351)),f333(f333(f159(x98351),x98355),f790(x98352,x98353,x98354,x98355,x98351))),x98352) % 173.51/173.28 [9839]E(f333(f333(f162(x98391,x98392),x98393),x98394),f333(f333(f162(x98391,x98392),x98395),x98394))+P106(f333(f333(f335(x98391),f741(x98393,x98394,x98395,x98392,x98391)),f333(f180(x98391),x98394))) % 173.51/173.28 [9869]~P106(f333(f333(f335(x98695),x98694),f333(f292(x98691,x98695,x98693),x98692)))+P106(f333(f333(f335(x98691),f536(x98692,x98693,x98691,x98694,x98695)),x98692)) % 173.51/173.28 [9870]~P106(f333(f333(f335(x98705),x98704),f333(f292(x98701,x98705,x98703),x98702)))+P106(f333(f333(f335(x98701),f581(x98702,x98703,x98701,x98704,x98705)),x98702)) % 173.51/173.28 [9899]~P106(f333(f333(f246(f917(x98995,a905)),x98994),f333(f316(x98991,x98995,x98993),x98992)))+P106(f333(f333(f246(f917(x98991,a905)),f862(x98992,x98993,x98991,x98994,x98995)),x98992)) % 173.51/173.28 [9919]E(f333(f333(f333(a205,f579(x99191,x99192,x99193,x99194,x99195)),f34(x99195)),f206(x99192,x99195)),f333(f333(f333(a205,x99191),f34(x99195)),f206(x99192,x99195)))+~P106(f333(f333(f202(f27(x99195,x99194,x99193)),x99192),f333(f333(f333(a205,x99191),f34(x99195)),f206(x99192,x99195)))) % 173.51/173.28 [10327]E(x103271,f2(a110))+E(f235(f916(f911(x103272),x103273),f916(x103272,x103273),f333(f333(f265(f911(x103272),x103273),f124(x103272)),x103274),f333(f269(x103272,x103273,f916(f911(x103272),x103273)),f333(f333(f7(x103272,f917(x103273,f916(f911(x103272),x103273)),f917(x103273,f916(f911(x103272),x103273))),f333(f333(f8(f917(f916(f911(x103272),x103273),f916(f911(x103272),x103273)),f917(f917(x103273,f916(f911(x103272),x103273)),f917(x103273,f916(f911(x103272),x103273))),x103272),f8(f916(f911(x103272),x103273),f916(f911(x103272),x103273),x103273)),f333(f333(f8(f917(f911(x103272),f917(x103273,f916(f911(x103272),x103273))),f917(f916(f911(x103272),x103273),f916(f911(x103272),x103273)),x103272),f269(f911(x103272),x103273,f916(f911(x103272),x103273))),f333(f333(f8(f917(f911(x103272),f911(x103272)),f917(f911(x103272),f917(x103273,f916(f911(x103272),x103273))),x103272),f333(f8(f911(x103272),f917(x103273,f916(f911(x103272),x103273)),f911(x103272)),f265(f911(x103272),x103273))),f159(x103272))))),f333(f128(x103273,x103272,x103275),f333(f333(f23(a110),x103271),f85(a110))))),f333(x103275,x103274)),f333(f333(f128(x103273,x103272,x103275),x103271),x103274)) % 173.51/173.28 [6131]E(x61311,x61312)+~E(f333(f268(x61313,x61314),f333(f333(f265(x61313,x61314),x61315),x61311)),x61312) % 173.51/173.28 [6132]E(x61321,x61322)+~E(f333(f264(x61323,x61324),f333(f333(f265(x61323,x61324),x61321),x61325)),x61322) % 173.51/173.28 [6390]~E(x63903,f333(f333(f142(x63901),x63904),f333(f333(f159(x63901),x63902),x63905)))+P106(f333(f333(f335(x63901),x63902),f333(f180(x63901),x63903))) % 173.51/173.28 [6785]E(f333(f316(x67851,x67852,f333(f16(x67852,x67851),x67853)),x67854),f333(f333(f315(x67852),x67853),f196(f917(x67852,a905))))+~P106(f333(f333(f335(x67851),x67855),x67854)) % 173.51/173.28 [6853]E(f333(f333(f121(f917(x68531,a905)),f333(f180(x68531),x68532)),f333(f180(x68531),x68533)),f333(f180(x68531),x68534))+~E(f174(x68531,x68535,x68534),f333(f333(f265(f911(x68531),f911(x68531)),x68532),x68533)) % 173.51/173.28 [6952]~P110(x69522)+E(f333(f197(f911(x69521)),f333(f333(f156(x69521,x69522,x69523),x69524),x69525)),f333(a123,f333(f197(f911(x69521)),x69525))) % 173.51/173.28 [6964]~P110(x69642)+E(f333(f180(x69641),f333(f333(f156(x69641,x69642,x69643),x69644),x69645)),f333(f333(f315(x69641),x69644),f333(f180(x69641),x69645))) % 173.51/173.28 [7235]~P117(x72351)+E(f333(f333(f87(x72351),f333(f333(f87(x72351),x72352),x72353)),f333(f333(f87(x72351),x72354),x72355)),f333(f333(f87(x72351),f333(f333(f87(x72351),x72352),x72354)),f333(f333(f87(x72351),x72353),x72355))) % 173.51/173.28 [7236]~P117(x72361)+E(f333(f333(f88(x72361),f333(f333(f88(x72361),x72362),x72363)),f333(f333(f88(x72361),x72364),x72365)),f333(f333(f88(x72361),f333(f333(f88(x72361),x72362),x72364)),f333(f333(f88(x72361),x72363),x72365))) % 173.51/173.28 [7237]~P67(x72371)+E(f333(f333(f296(x72371),f333(f333(f88(x72371),x72372),x72373)),f333(f333(f88(x72371),x72374),x72375)),f333(f333(f88(x72371),f333(f333(f296(x72371),x72372),x72374)),f333(f333(f296(x72371),x72373),x72375))) % 173.51/173.28 [7251]~P110(x72511)+E(f309(x72511,f333(f333(f245(x72511),x72512),x72513),f333(f333(f244(x72511),x72514),x72515)),f333(f333(f112(f917(x72511,a905)),f309(x72511,x72512,x72514)),f309(x72511,x72513,x72515))) % 173.51/173.28 [7252]~P110(x72521)+E(f311(x72521,f333(f333(f245(x72521),x72522),x72523),f333(f333(f244(x72521),x72524),x72525)),f333(f333(f112(f917(x72521,a905)),f311(x72521,x72522,x72524)),f311(x72521,x72523,x72525))) % 173.51/173.28 [7253]~P110(x72531)+E(f312(x72531,f333(f333(f245(x72531),x72532),x72533),f333(f333(f244(x72531),x72534),x72535)),f333(f333(f112(f917(x72531,a905)),f312(x72531,x72532,x72534)),f312(x72531,x72533,x72535))) % 173.51/173.28 [7254]~P110(x72541)+E(f333(f333(f112(f917(x72541,a905)),f333(f308(x72541,x72542),x72543)),f333(f308(x72541,x72544),x72545)),f333(f308(x72541,f333(f333(f245(x72541),x72542),x72544)),f333(f333(f244(x72541),x72543),x72545))) % 173.51/173.28 [7373]~P106(f333(x73731,f530(x73733,x73732,x73731)))+P106(f333(x73731,f333(f333(f265(x73732,x73733),x73734),x73735))) % 173.51/173.28 [7482]~E(x74822,f333(x74824,x74825))+P106(f333(f333(f335(x74821),x74822),f333(f316(x74823,x74821,x74824),f254(f917(x74823,a905))))) % 173.51/173.28 [7554]~P17(x75543,x75542,x75544)+P17(x75541,x75542,f333(f333(f8(x75543,f917(x75542,x75542),x75541),x75544),x75545)) % 173.51/173.28 [7555]~P18(x75553,x75552,x75554)+P18(x75551,x75552,f333(f333(f8(x75553,f917(x75552,x75552),x75551),x75554),x75555)) % 173.51/173.28 [7692]~P27(x76921,x76922,x76923,x76924)+P27(x76921,x76922,x76923,f333(f333(f23(f917(x76921,a905)),x76924),x76925)) % 173.51/173.28 [7848]~P106(f333(f333(x78483,x78484),x78485))+P106(f333(f333(f269(x78481,x78482,a905),x78483),f333(f333(f265(x78481,x78482),x78484),x78485))) % 173.51/173.28 [7963]~P106(f333(x79632,x79634))+~E(f333(f333(f146(x79631),f333(f197(f911(x79631)),f185(x79631,x79632,x79633))),x79633),f333(f333(f159(x79631),x79634),x79635)) % 173.51/173.28 [7983]P27(x79831,x79832,x79833,x79834)+~P27(x79831,x79832,x79833,f333(f333(f121(f917(x79831,a905)),x79835),x79834)) % 173.51/173.28 [7984]P27(x79841,x79842,x79843,x79844)+~P27(x79841,x79842,x79843,f333(f333(f121(f917(x79841,a905)),x79844),x79845)) % 173.51/173.28 [8031]~P110(x80312)+E(f333(f333(f156(x80311,x80312,x80313),x80314),f158(x80311,x80312,x80313,x80315)),f158(x80311,x80312,x80313,f333(f333(f159(x80311),x80314),x80315))) % 173.51/173.28 [8353]~P17(x83532,x83531,x83533)+E(f333(f150(x83531,x83532,f333(f7(x83532,x83531,x83531),x83533),x83534),x83535),f333(f333(f70(x83532,x83531,x83533),x83534),f333(f180(x83532),x83535))) % 173.51/173.28 [8382]~E(f333(f333(f146(x83821),f333(f197(f911(x83821)),f185(x83821,x83822,x83823))),x83823),f333(f333(f159(x83821),x83824),x83825))+E(f333(f333(f142(x83821),f185(x83821,x83822,x83823)),f333(f333(f159(x83821),x83824),x83825)),x83823) % 173.51/173.28 [8410]P106(f333(f333(x84101,x84102),x84103))+~P106(f333(f333(f269(x84104,x84105,a905),x84101),f333(f333(f265(x84104,x84105),x84102),x84103))) % 173.51/173.28 [8897]P106(f333(f333(f246(f917(x88971,a905)),f333(f316(x88972,x88971,x88973),x88974)),f333(f316(x88972,x88971,x88973),x88975)))+~P106(f333(f333(f246(f917(x88972,a905)),x88974),x88975)) % 173.51/173.28 [8898]P106(f333(f333(f246(f917(x88981,a905)),f333(f317(x88981,x88982,x88983),x88984)),f333(f317(x88981,x88982,x88983),x88985)))+~P106(f333(f333(f246(f917(x88982,a905)),x88984),x88985)) % 173.51/173.28 [8977]E(x89771,f2(a110))+E(f333(f333(f271(x89772,x89773,x89772,f916(x89773,x89772)),f333(x89774,x89775)),f280(x89773,x89772,f333(f333(f23(a110),x89771),f85(a110)),x89774)),f333(f280(x89773,x89772,x89771,x89774),x89775)) % 173.51/173.28 [9282]P106(f333(f333(f202(f27(x92821,x92822,x92823)),x92824),f333(f333(f333(a205,x92825),f34(x92821)),f206(x92824,x92821))))+~P106(f333(f333(f202(x92823),f333(f333(f333(a205,x92824),f34(x92821)),f333(x92822,x92824))),x92825)) % 173.51/173.28 [9315]P32(x93151,x93152,f333(f333(f333(f98(x93151),x93153),x93154),x93155))+P106(f333(f333(x93153,f465(x93155,x93154,x93153,x93152)),f477(x93155,x93154,x93153,x93152))) % 173.51/173.28 [9564]P32(x95641,x95642,f333(f333(f333(f98(x95641),x95643),x95644),x95645))+~P106(f333(f333(x95645,f465(x95645,x95644,x95643,x95642)),f480(x95645,x95644,x95643,x95642))) % 173.51/173.28 [9567]~P106(f333(f333(f335(x95672),x95675),f333(f316(x95671,x95672,x95674),x95673)))+P106(f333(f333(f335(x95671),f333(f99(x95671,x95672,x95673,x95674),x95675)),x95673)) % 173.51/173.28 [9631]P32(x96311,x96312,f333(f333(f333(f98(x96311),x96313),x96314),x96315))+P106(f333(f333(f333(f333(a204,x96314),f477(x96315,x96314,x96313,x96312)),x96312),f480(x96315,x96314,x96313,x96312))) % 173.51/173.28 [9659]~P106(f333(f67(x96593),f333(f316(x96592,x96593,x96595),f254(f917(x96592,a905)))))+P106(f333(f67(x96591),f333(f316(x96592,x96591,f333(f333(f8(x96593,x96591,x96592),x96594),x96595)),f254(f917(x96592,a905))))) % 173.51/173.28 [9686]P106(f333(f333(f246(f917(f917(x96861,a905),a905)),f333(f316(f917(x96862,a905),f917(x96861,a905),f316(x96862,x96861,x96863)),f333(f314(x96862),x96864))),f333(f314(x96861),x96865)))+~P106(f333(f333(f246(f917(x96861,a905)),f333(f316(x96862,x96861,x96863),x96864)),x96865)) % 173.51/173.28 [9740]P106(f333(f333(f202(x97401),f333(f333(f333(a205,x97402),f34(x97403)),f333(x97404,x97402))),f611(x97405,x97402,x97401,x97404,x97403)))+~P106(f333(f333(f202(f27(x97403,x97404,x97401)),x97402),x97405)) % 173.51/173.28 [9766]E(x97661,x97662)+~P106(f333(f72(x97663,x97664,x97665,x97661,f196(f917(x97663,a905))),x97662)) % 173.51/173.28 [9783]E(f333(f333(f265(x97831,x97832),f580(x97833,x97834,x97835,x97832,x97831)),f582(x97833,x97834,x97835,x97832,x97831)),x97835)+~P106(f333(f333(f335(f916(x97831,x97832)),x97835),f333(f333(f267(x97831,x97832),x97834),x97833))) % 173.51/173.28 [9874]P106(f333(f333(f335(x98741),f580(x98742,x98743,x98744,x98745,x98741)),x98743))+~P106(f333(f333(f335(f916(x98741,x98745)),x98744),f333(f333(f267(x98741,x98745),x98743),x98742))) % 173.51/173.28 [9906]E(f333(f333(f333(a205,f611(x99061,x99062,x99063,x99064,x99065)),f34(x99065)),f206(x99062,x99065)),x99061)+~P106(f333(f333(f202(f27(x99065,x99064,x99063)),x99062),x99061)) % 173.51/173.28 [9975]P26(x99755,x99754,f333(f333(f315(f909(x99755)),f333(f333(f333(f98(x99755),x99751),x99753),x99752)),f196(f917(f909(x99755),a905))))+P106(f333(f333(x99751,f565(x99752,x99753,x99754,x99755,x99751)),f675(x99752,x99753,x99754,x99755,x99751))) % 173.51/173.28 [10028]P106(f333(f333(f335(x100281),f582(x100282,x100283,x100284,x100281,x100285)),f333(x100282,f580(x100282,x100283,x100284,x100281,x100285))))+~P106(f333(f333(f335(f916(x100285,x100281)),x100284),f333(f333(f267(x100285,x100281),x100283),x100282))) % 173.51/173.28 [10054]P106(f333(f333(f335(f916(x100541,x100541)),f333(f333(f265(x100541,x100541),x100542),f636(x100543,x100544,x100545,x100542,x100541))),x100543))+~P106(f333(f333(f335(f916(x100541,x100541)),f333(f333(f265(x100541,x100541),x100542),x100545)),f333(f333(f191(f916(x100541,x100541),a905),f333(a123,x100544)),x100543))) % 173.51/173.28 [10055]P106(f333(f333(f335(f916(x100551,x100551)),f333(f333(f265(x100551,x100551),x100552),f638(x100553,x100554,x100555,x100552,x100551))),x100553))+~P106(f333(f333(f335(f916(x100551,x100551)),f333(f333(f265(x100551,x100551),x100552),x100555)),f333(f333(f191(f916(x100551,x100551),a905),f333(a123,x100554)),x100553))) % 173.51/173.28 [10072]~P106(f333(f333(f335(f916(f911(x100721),f911(x100721))),f333(f333(f265(f911(x100721),f911(x100721)),f333(f333(f159(x100721),x100722),x100725)),x100724)),f166(x100721,x100723)))+P106(f333(f333(f335(f916(x100721,x100721)),f333(f333(f265(x100721,x100721),x100722),f700(x100723,x100724,x100725,x100722,x100721))),x100723)) % 173.51/173.28 [10074]~P26(x100741,x100742,f333(f333(f315(f909(x100741)),f333(f333(f333(f98(x100741),f103(x100741,x100743,x100744)),x100745),x100743)),f196(f917(f909(x100741),a905))))+P26(x100741,x100742,f333(f333(f315(f909(x100741)),f333(f333(f333(f98(x100741),x100743),f30(x100744,x100745)),f103(x100741,x100743,f333(f79(a905,a905,a906,a328),x100744)))),f196(f917(f909(x100741),a905)))) % 173.51/173.28 [10075]~P31(x100751,x100752,f333(f333(f315(f909(x100751)),f333(f333(f333(f98(x100751),f103(x100751,x100753,x100754)),x100755),x100753)),f196(f917(f909(x100751),a905))))+P31(x100751,x100752,f333(f333(f315(f909(x100751)),f333(f333(f333(f98(x100751),x100753),f30(x100754,x100755)),f103(x100751,x100753,f333(f79(a905,a905,a906,a328),x100754)))),f196(f917(f909(x100751),a905)))) % 173.51/173.28 [10353]P26(x103531,x103532,f333(f333(f315(f909(x103531)),f333(f333(f333(f98(x103531),x103533),x103534),x103535)),f196(f917(f909(x103531),a905))))+~P26(x103531,x103532,f333(f333(f315(f909(x103531)),f333(f333(f333(f98(x103531),f333(f16(f917(a906,a905),x103531),f333(f333(f7(a906,a906,a905),a330),f675(x103535,x103534,x103532,x103531,x103533)))),x103534),f333(f16(f917(a906,a905),x103531),f333(x103535,f565(x103535,x103534,x103532,x103531,x103533))))),f196(f917(f909(x103531),a905)))) % 173.51/173.28 [6466]P106(f333(x64662,x64664))+E(f185(x64661,x64662,f333(f333(f142(x64661),x64663),f333(f333(f159(x64661),x64664),x64665))),f185(x64661,x64662,x64663)) % 173.51/173.28 [6515]~P2(x65152)+E(f333(f333(f333(f121(f917(x65151,x65152)),x65153),x65154),x65155),f333(f333(f121(x65152),f333(x65153,x65155)),f333(x65154,x65155))) % 173.51/173.28 [6517]~P2(x65172)+E(f333(f333(f333(f112(f917(x65171,x65172)),x65173),x65174),x65175),f333(f333(f112(x65172),f333(x65173,x65175)),f333(x65174,x65175))) % 173.51/173.28 [6519]~P5(x65192)+E(f333(f333(f333(f23(f917(x65191,x65192)),x65193),x65194),x65195),f333(f333(f23(x65192),f333(x65193,x65195)),f333(x65194,x65195))) % 173.51/173.28 [6537]E(x65371,x65372)+E(f333(f333(f172(x65373),f333(f333(f167(x65373,x65374),x65371),x65375)),x65372),f333(f333(f172(x65373),x65374),x65372)) % 173.51/173.28 [6803]~E(x68034,f196(f917(x68033,a905)))+E(f333(f333(f121(f917(x68031,a905)),x68032),f333(f333(f45(x68033,f917(x68031,a905)),x68034),x68035)),x68032) % 173.51/173.28 [6804]~E(x68044,f196(f917(x68043,a905)))+E(f333(f333(f112(f917(x68041,a905)),x68042),f333(f333(f46(x68043,f917(x68041,a905)),x68044),x68045)),x68042) % 173.51/173.28 [6805]~E(x68054,f196(f917(x68053,a905)))+E(f333(f333(f23(f917(x68051,a905)),x68052),f333(f333(f45(x68053,f917(x68051,a905)),x68054),x68055)),x68052) % 173.51/173.28 [6819]~E(x68194,f196(f917(x68193,a905)))+E(f333(f333(f315(x68191),x68192),f333(f333(f45(x68193,f917(x68191,a905)),x68194),x68195)),f333(f333(f315(x68191),x68192),f196(f917(x68191,a905)))) % 173.51/173.28 [7601]E(f333(f333(f172(x76011),f333(f333(f162(x76012,x76011),x76013),x76014)),x76015),f333(x76013,f333(f333(f172(x76012),x76014),x76015)))+~P106(f333(f333(f247(a910),x76015),f333(f197(f911(x76012)),x76014))) % 173.51/173.28 [7663]E(f333(f333(f121(f917(x76631,a905)),f333(x76632,x76633)),f333(f333(f45(x76634,f917(x76631,a905)),x76635),x76632)),f333(f333(f45(x76634,f917(x76631,a905)),x76635),x76632))+~P106(f333(f333(f335(x76634),x76633),x76635)) % 173.51/173.28 [7664]E(f333(f333(f112(f917(x76641,a905)),f333(x76642,x76643)),f333(f333(f46(x76644,f917(x76641,a905)),x76645),x76642)),f333(f333(f46(x76644,f917(x76641,a905)),x76645),x76642))+~P106(f333(f333(f335(x76644),x76643),x76645)) % 173.51/173.28 [8274]~E(x82743,f196(f917(x82741,a905)))+E(f333(f333(f45(x82741,f917(x82742,a905)),x82743),f333(f333(f8(f917(x82742,a905),f917(x82742,a905),x82741),f333(f315(x82742),x82744)),x82745)),f196(f917(x82742,a905))) % 173.51/173.28 [8280]~P106(f333(f333(f335(x82804),x82803),x82805))+P106(f333(f333(f246(f917(x82801,a905)),f333(x82802,x82803)),f333(f333(f45(x82804,f917(x82801,a905)),x82805),x82802))) % 173.51/173.28 [8335]E(x83351,f333(f333(f333(a205,x83352),x83353),f333(x83354,x83352)))+~P106(f333(f333(f333(f333(a204,f26(x83353,x83354)),x83352),x83355),x83351)) % 173.51/173.28 [8409]~E(f333(x84094,x84092),x84095)+P106(f333(f333(f335(x84091),x84092),f333(f317(x84091,x84093,x84094),f333(f333(f315(x84093),x84095),f196(f917(x84093,a905)))))) % 173.51/173.28 [8456]~P58(x84561,x84562,f333(f293(x84562,x84561),x84563))+E(f333(f333(f112(f917(x84561,a905)),f333(f292(x84562,x84561,x84563),x84564)),f333(f292(x84562,x84561,x84563),x84565)),f333(f292(x84562,x84561,x84563),f333(f333(f112(f917(x84562,a905)),x84564),x84565))) % 173.51/173.28 [8533]E(x85331,f2(a110))+E(f333(f129(x85332,x85333,f333(x85334,f333(f333(f23(a110),x85331),f85(a110)))),f333(f333(f7(x85332,a110,f912(x85333)),x85335),x85331)),f333(f210(x85332,x85333,x85334,x85335),x85331)) % 173.51/173.28 [8576]E(x85761,f196(f917(x85762,a905)))+E(f333(f333(f45(x85762,f917(x85763,a905)),x85761),f333(f333(f8(f917(x85763,a905),f917(x85763,a905),x85762),f333(f315(x85763),x85764)),x85765)),f333(f333(f315(x85763),x85764),f333(f333(f45(x85762,f917(x85763,a905)),x85761),x85765))) % 173.51/173.28 [8632]~P27(x86322,x86321,x86323,f254(f917(x86322,a905)))+E(f333(f333(f112(f917(x86321,a905)),f333(f316(x86322,x86321,x86323),x86324)),f333(f316(x86322,x86321,x86323),x86325)),f333(f316(x86322,x86321,x86323),f333(f333(f112(f917(x86322,a905)),x86324),x86325))) % 173.51/173.28 [8633]~P27(x86332,x86331,x86333,f254(f917(x86332,a905)))+E(f333(f333(f23(f917(x86331,a905)),f333(f316(x86332,x86331,x86333),x86334)),f333(f316(x86332,x86331,x86333),x86335)),f333(f316(x86332,x86331,x86333),f333(f333(f23(f917(x86332,a905)),x86334),x86335))) % 173.51/173.28 [8700]~P106(f333(f333(f73(x87001,x87002,x87005),x87003),x87004))+P106(f333(f333(f335(f916(x87001,x87002)),f333(f333(f265(x87001,x87002),x87003),x87004)),x87005)) % 173.51/173.28 [8732]P106(f333(f333(f335(x87321),x87322),f333(f291(x87323,x87321),x87324)))+~P106(f333(f333(f335(f916(x87323,x87321)),f333(f333(f265(x87323,x87321),x87325),x87322)),x87324)) % 173.51/173.28 [8734]P106(f333(f333(f335(x87341),x87342),f333(f263(x87341,x87343),x87344)))+~P106(f333(f333(f335(f916(x87341,x87343)),f333(f333(f265(x87341,x87343),x87342),x87345)),x87344)) % 173.51/173.28 [8881]P106(f333(f333(f73(x88811,x88812,x88813),x88814),x88815))+~P106(f333(f333(f335(f916(x88811,x88812)),f333(f333(f265(x88811,x88812),x88814),x88815)),x88813)) % 173.51/173.28 [8920]E(f333(x89201,x89202),x89203)+~P106(f333(f333(f335(x89204),x89202),f333(f317(x89204,x89205,x89201),f333(f333(f315(x89205),x89203),f196(f917(x89205,a905)))))) % 173.51/173.28 [9168]P106(f333(f333(f335(f916(x91681,x91682)),f333(f333(f265(x91681,x91682),x91683),x91684)),f333(f293(x91682,x91681),x91685)))+~P106(f333(f333(f335(f916(x91682,x91681)),f333(f333(f265(x91682,x91681),x91684),x91683)),x91685)) % 173.51/173.28 [9186]~P106(f333(f333(x91861,x91865),x91864))+P106(f333(f333(x91861,f333(f268(x91862,x91863),f333(f333(f265(x91862,x91863),x91864),x91865))),f333(f264(x91862,x91863),f333(f333(f265(x91862,x91863),x91864),x91865)))) % 173.51/173.28 [9216]~P106(f333(f333(f335(f916(x92162,x92161)),f333(f333(f265(x92162,x92161),x92164),x92163)),f333(f293(x92161,x92162),x92165)))+P106(f333(f333(f335(f916(x92161,x92162)),f333(f333(f265(x92161,x92162),x92163),x92164)),x92165)) % 173.51/173.28 [9249]~P106(f333(f333(f335(f916(x92493,x92491)),f333(f333(f265(x92493,x92491),x92495),x92492)),x92494))+P106(f333(f333(f335(x92491),x92492),f333(f292(x92493,x92491,x92494),f333(f333(f315(x92493),x92495),f196(f917(x92493,a905)))))) % 173.51/173.28 [9296]P106(f333(f333(f335(f916(x92961,x92962)),f333(f333(f265(x92961,x92962),x92963),x92964)),x92965))+~P106(f333(f333(f335(x92962),x92964),f333(f292(x92961,x92962,x92965),f333(f333(f315(x92961),x92963),f196(f917(x92961,a905)))))) % 173.51/173.28 [9383]~P72(x93831)+E(f333(f333(f6(a910,x93831),x93832),f309(a910,f333(f333(f87(a910),x93833),x93834),f333(f333(f87(a910),x93835),x93834))),f333(f333(f6(a910,x93831),f333(f333(f8(a910,x93831,a910),x93832),f333(f333(f7(a910,a910,a910),f87(a910)),x93834))),f309(a910,x93833,x93835))) % 173.51/173.28 [9408]~P72(x94081)+E(f333(f333(f6(a910,x94081),x94082),f333(f308(a910,f333(f333(f87(a910),x94083),x94084)),f333(f333(f87(a910),x94085),x94084))),f333(f333(f6(a910,x94081),f333(f333(f8(a910,x94081,a910),x94082),f333(f333(f7(a910,a910,a910),f87(a910)),x94084))),f333(f308(a910,x94083),x94085))) % 173.51/173.28 [9466]~P27(x94661,x94662,x94663,f254(f917(x94661,a905)))+E(f333(f333(f162(x94661,x94662),x94663),f333(f144(x94661,f333(f333(f8(a905,a905,x94661),a328),f333(a330,x94664))),x94665)),f333(f144(x94662,f333(f333(f8(a905,a905,x94662),a328),f333(a330,f333(x94663,x94664)))),f333(f333(f162(x94661,x94662),x94663),x94665))) % 173.51/173.28 [9486]~P27(x94861,x94862,x94863,f333(f333(f315(x94861),x94864),f333(f180(x94861),x94865)))+E(f333(f333(f162(x94861,x94862),x94863),f333(f144(x94861,f333(f333(f8(a905,a905,x94861),a328),f333(a330,x94864))),x94865)),f333(f144(x94862,f333(f333(f8(a905,a905,x94862),a328),f333(a330,f333(x94863,x94864)))),f333(f333(f162(x94861,x94862),x94863),x94865))) % 173.51/173.28 [9647]P106(f333(f333(f335(f916(f911(x96471),f911(x96471))),f333(f333(f265(f911(x96471),f911(x96471)),f333(f333(f159(x96471),x96472),x96473)),f333(f333(f159(x96471),x96474),x96473))),f165(x96471,x96475)))+~P106(f333(f333(f335(f916(x96471,x96471)),f333(f333(f265(x96471,x96471),x96472),x96474)),x96475)) % 173.51/173.28 [9687]P106(f333(f333(f333(f333(a204,x96871),x96872),x96873),f448(x96874,x96873,x96872,x96875,x96871)))+~P106(f333(f333(f333(f333(a204,f31(x96871,x96875)),x96872),x96873),x96874)) % 173.51/173.28 [9688]P106(f333(f333(f333(f333(a204,x96881),x96882),x96883),f497(x96884,x96883,x96882,x96885,x96881)))+~P106(f333(f333(f333(f333(a204,f31(x96881,x96885)),x96882),x96883),x96884)) % 173.51/173.28 [9778]E(f333(f333(f315(x97781),f459(x97782,x97783,x97784,x97785,x97781)),f460(x97782,x97783,x97784,x97785,x97781)),f333(f333(f315(x97781),x97784),x97783))+~P106(f333(f68(x97781,x97785,f333(f333(f315(x97781),x97784),x97783)),x97782)) % 173.51/173.28 [9779]E(f333(f333(f315(x97791),f461(x97792,x97793,x97794,x97795,x97791)),f462(x97792,x97793,x97794,x97795,x97791)),f333(f333(f315(x97791),x97794),x97793))+~P106(f333(f68(x97791,x97795,f333(f333(f315(x97791),x97794),x97793)),x97792)) % 173.51/173.28 [9860]P106(f333(f333(f335(x98601),f659(x98602,x98603,x98604,x98605,x98601)),x98604))+P106(f333(f333(f333(f46(x98601,f917(x98605,a905)),x98604),x98603),x98602)) % 173.51/173.28 [9865]P106(f333(f333(f335(x98651),f660(x98652,x98653,x98651,x98654,x98655)),x98653))+P106(f333(f333(f335(x98655),x98654),f333(f333(f46(x98651,f917(x98655,a905)),x98653),x98652))) % 173.51/173.28 [9873]P106(f333(f333(f335(x98731),f657(x98732,x98733,x98731,x98734,x98735)),x98733))+P106(f333(f333(f246(f917(x98735,a905)),x98734),f333(f333(f46(x98731,f917(x98735,a905)),x98733),x98732))) % 173.51/173.28 [9875]P106(f333(f333(x98751,f482(x98752,x98751,x98753,x98754,x98755)),x98752))+~P106(f333(f333(f333(f45(x98755,f917(x98754,a905)),x98753),x98751),x98752)) % 173.51/173.28 [9879]P106(f333(f333(f335(x98791),f482(x98792,x98793,x98794,x98795,x98791)),x98794))+~P106(f333(f333(f333(f45(x98791,f917(x98795,a905)),x98794),x98793),x98792)) % 173.51/173.28 [9880]P56(x98804,f333(f333(f46(x98801,f917(x98804,a905)),x98805),x98803),f333(f333(f46(x98801,f917(f916(x98804,x98804),a905)),x98805),x98802))+P106(f333(f333(f335(x98801),f820(x98802,x98803,x98804,x98805,x98801)),x98805)) % 173.51/173.28 [9891]P106(f333(f333(f335(x98911),f487(x98912,x98913,x98911,x98914,x98915)),x98913))+~P106(f333(f333(f335(x98915),x98914),f333(f333(f45(x98911,f917(x98915,a905)),x98913),x98912))) % 173.51/173.28 [9897]P106(f333(f333(f335(x98971),x98972),f333(x98973,f487(x98973,x98974,x98975,x98972,x98971))))+~P106(f333(f333(f335(x98971),x98972),f333(f333(f45(x98975,f917(x98971,a905)),x98974),x98973))) % 173.51/173.28 [9980]~P106(f333(f333(x99804,f659(x99805,x99804,x99803,x99802,x99801)),x99805))+P106(f333(f333(f333(f46(x99801,f917(x99802,a905)),x99803),x99804),x99805)) % 173.51/173.28 [9983]~P106(f333(f333(f335(x99831),x99832),f333(x99835,f660(x99835,x99834,x99833,x99832,x99831))))+P106(f333(f333(f335(x99831),x99832),f333(f333(f46(x99833,f917(x99831,a905)),x99834),x99835))) % 173.51/173.28 [9987]~P56(x99871,f333(x99874,f820(x99875,x99874,x99871,x99873,x99872)),f333(x99875,f820(x99875,x99874,x99871,x99873,x99872)))+P56(x99871,f333(f333(f46(x99872,f917(x99871,a905)),x99873),x99874),f333(f333(f46(x99872,f917(f916(x99871,x99871),a905)),x99873),x99875)) % 173.51/173.28 [9988]~P106(f333(f333(f246(f917(x99881,a905)),x99882),f333(x99885,f657(x99885,x99884,x99883,x99882,x99881))))+P106(f333(f333(f246(f917(x99881,a905)),x99882),f333(f333(f46(x99883,f917(x99881,a905)),x99884),x99885))) % 173.51/173.28 [10034]P106(f333(f333(f333(f333(a204,x100341),f448(x100342,x100343,x100344,x100341,x100345)),x100343),x100342))+~P106(f333(f333(f333(f333(a204,f31(x100345,x100341)),x100344),x100343),x100342)) % 173.51/173.28 [10035]P106(f333(f333(f333(f333(a204,x100351),f497(x100352,x100353,x100354,x100351,x100355)),x100353),x100352))+~P106(f333(f333(f333(f333(a204,f31(x100355,x100351)),x100354),x100353),x100352)) % 173.51/173.28 [10058]~P106(f333(f333(f335(x100581),f459(x100585,x100584,x100583,x100582,x100581)),f460(x100585,x100584,x100583,x100582,x100581)))+~P106(f333(f68(x100581,x100582,f333(f333(f315(x100581),x100583),x100584)),x100585)) % 173.51/173.28 [10059]~P106(f333(f333(f335(x100591),f461(x100595,x100594,x100593,x100592,x100591)),f462(x100595,x100594,x100593,x100592,x100591)))+~P106(f333(f68(x100591,x100592,f333(f333(f315(x100591),x100593),x100594)),x100595)) % 173.51/173.28 [10060]~P106(f333(f333(f335(f916(x100601,x100601)),f333(f333(f265(x100601,x100601),x100602),x100605)),f333(f333(f191(f916(x100601,x100601),a905),f333(a123,x100604)),x100603)))+P106(f333(f333(f335(f916(x100601,x100601)),f333(f333(f265(x100601,x100601),x100602),f637(x100603,x100604,x100605,x100602,x100601))),f333(f333(f191(f916(x100601,x100601),a905),x100604),x100603))) % 173.51/173.28 [10066]P106(f333(f72(x100661,x100661,x100662,f459(x100663,x100664,x100665,x100662,x100661),f460(x100663,x100664,x100665,x100662,x100661)),x100663))+~P106(f333(f68(x100661,x100662,f333(f333(f315(x100661),x100665),x100664)),x100663)) % 173.51/173.28 [10067]P106(f333(f72(x100671,x100671,x100672,f461(x100673,x100674,x100675,x100672,x100671),f462(x100673,x100674,x100675,x100672,x100671)),x100673))+~P106(f333(f68(x100671,x100672,f333(f333(f315(x100671),x100675),x100674)),x100673)) % 173.51/173.28 [10079]~P110(x100791)+P16(x100791,f333(f333(f162(x100792,x100791),x100793),f333(f144(x100792,f333(f333(f7(x100792,x100791,a905),f333(f333(f8(x100791,f917(x100791,a905),x100792),a330),x100793)),f333(x100794,x100795))),x100795))) % 173.51/173.28 [10121]~P106(f333(f333(f335(x101212),x101215),f333(f292(x101211,x101212,x101214),x101213)))+P106(f333(f333(f335(f916(x101211,x101212)),f333(f333(f265(x101211,x101212),f536(x101213,x101214,x101211,x101215,x101212)),x101215)),x101214)) % 173.51/173.28 [10122]~P106(f333(f333(f335(x101222),x101225),f333(f292(x101221,x101222,x101224),x101223)))+P106(f333(f333(f335(f916(x101221,x101222)),f333(f333(f265(x101221,x101222),f581(x101223,x101224,x101221,x101225,x101222)),x101225)),x101224)) % 173.51/173.28 [10142]~P106(f333(f333(f335(f916(x101421,x101421)),f333(f333(f265(x101421,x101421),x101425),x101424)),f333(f333(f191(f916(x101421,x101421),a905),f333(a123,x101423)),x101422)))+P106(f333(f333(f335(f916(x101421,x101421)),f333(f333(f265(x101421,x101421),f637(x101422,x101423,x101424,x101425,x101421)),x101424)),x101422)) % 173.51/173.28 [10145]~P106(f333(f333(f335(f916(x101451,x101451)),f333(f333(f265(x101451,x101451),x101455),x101454)),f333(f333(f191(f916(x101451,x101451),a905),f333(a123,x101453)),x101452)))+P106(f333(f333(f335(f916(x101451,x101451)),f333(f333(f265(x101451,x101451),f636(x101452,x101453,x101454,x101455,x101451)),x101454)),f333(f333(f191(f916(x101451,x101451),a905),x101453),x101452))) % 173.51/173.28 [10146]~P106(f333(f333(f335(f916(x101461,x101461)),f333(f333(f265(x101461,x101461),x101465),x101464)),f333(f333(f191(f916(x101461,x101461),a905),f333(a123,x101463)),x101462)))+P106(f333(f333(f335(f916(x101461,x101461)),f333(f333(f265(x101461,x101461),f638(x101462,x101463,x101464,x101465,x101461)),x101464)),f333(f333(f191(f916(x101461,x101461),a905),x101463),x101462))) % 173.51/173.28 [10147]~P106(f333(f333(f335(f916(f911(x101471),f911(x101471))),f333(f333(f265(f911(x101471),f911(x101471)),x101475),f333(f333(f159(x101471),x101474),x101473))),f166(x101471,x101472)))+P106(f333(f333(f335(f916(x101471,x101471)),f333(f333(f265(x101471,x101471),f697(x101472,x101473,x101474,x101475,x101471)),x101474)),x101472)) % 173.51/173.28 [7684]~E(x76843,f196(f917(x76842,a905)))+E(f333(f333(f121(f917(x76841,a905)),f333(f333(f45(x76842,f917(x76841,a905)),x76843),x76844)),x76845),x76845) % 173.51/173.28 [7685]~E(x76853,f196(f917(x76852,a905)))+E(f333(f333(f112(f917(x76851,a905)),f333(f333(f46(x76852,f917(x76851,a905)),x76853),x76854)),x76855),x76855) % 173.51/173.28 [8116]~E(x81163,f196(f917(x81162,a905)))+E(f333(f333(f23(f917(x81161,a905)),f333(f333(f46(x81162,f917(x81161,a905)),x81163),x81164)),x81165),f333(f333(f23(f917(x81161,a905)),f254(f917(x81161,a905))),x81165)) % 173.51/173.28 [8247]E(f333(f333(f167(x82471,f333(f333(f142(x82471),x82472),x82473)),x82474),x82475),f333(f333(f142(x82471),f333(f333(f167(x82471,x82472),x82474),x82475)),x82473))+~P106(f333(f333(f247(a910),x82474),f333(f197(f911(x82471)),x82472))) % 173.51/173.28 [8523]E(f333(f333(f172(x85231),f333(f333(f162(a910,x85231),x85232),f147(a910,f333(f308(a910,x85233),x85234)))),x85235),f333(x85232,f333(f333(f87(a910),x85233),x85235)))+~P106(f333(f333(f247(a910),x85235),f333(f333(f23(a910),x85234),x85233))) % 173.51/173.28 [8537]E(x85371,f2(a110))+E(f132(x85372,x85373,f333(x85374,f333(f333(f23(a110),x85371),f85(a110))),f333(f333(f7(x85372,a110,f912(f914(x85373))),x85375),x85371)),f333(f208(x85372,x85373,x85374,x85375),x85371)) % 173.51/173.28 [8563]~E(x85633,f196(f917(x85631,a905)))+E(f333(f333(f45(x85631,f917(x85632,a905)),x85633),f333(f333(f8(f917(x85632,a905),f917(x85632,a905),x85631),f333(f121(f917(x85632,a905)),x85634)),x85635)),f196(f917(x85632,a905))) % 173.51/173.28 [8564]~E(x85643,f196(f917(x85641,a905)))+E(f333(f333(f46(x85641,f917(x85642,a905)),x85643),f333(f333(f8(f917(x85642,a905),f917(x85642,a905),x85641),f333(f112(f917(x85642,a905)),x85644)),x85645)),f254(f917(x85642,a905))) % 173.51/173.28 [8565]~E(x85653,f196(f917(x85651,a905)))+E(f333(f333(f46(x85651,f917(x85652,a905)),x85653),f333(f333(f8(f917(x85652,a905),f917(x85652,a905),x85651),f333(f23(f917(x85652,a905)),x85654)),x85655)),f254(f917(x85652,a905))) % 173.51/173.28 [8570]~P143(x85702)+E(f333(f333(f6(x85701,x85702),f333(f333(f8(x85702,x85702,x85701),f333(f88(x85702),x85703)),x85704)),x85705),f333(f333(f88(x85702),x85703),f333(f333(f6(x85701,x85702),x85704),x85705))) % 173.51/173.28 [8865]E(x88651,f196(f917(x88652,a905)))+E(f333(f333(f45(x88652,f917(x88653,a905)),x88651),f333(f333(f8(f917(x88653,a905),f917(x88653,a905),x88652),f333(f121(f917(x88653,a905)),x88654)),x88655)),f333(f333(f121(f917(x88653,a905)),x88654),f333(f333(f45(x88652,f917(x88653,a905)),x88651),x88655))) % 173.51/173.28 [8866]E(x88661,f196(f917(x88662,a905)))+E(f333(f333(f46(x88662,f917(x88663,a905)),x88661),f333(f333(f8(f917(x88663,a905),f917(x88663,a905),x88662),f333(f112(f917(x88663,a905)),x88664)),x88665)),f333(f333(f112(f917(x88663,a905)),x88664),f333(f333(f46(x88662,f917(x88663,a905)),x88661),x88665))) % 173.51/173.28 [8867]E(x88671,f196(f917(x88672,a905)))+E(f333(f333(f46(x88672,f917(x88673,a905)),x88671),f333(f333(f8(f917(x88673,a905),f917(x88673,a905),x88672),f333(f23(f917(x88673,a905)),x88674)),x88675)),f333(f333(f23(f917(x88673,a905)),x88674),f333(f333(f45(x88672,f917(x88673,a905)),x88671),x88675))) % 173.51/173.28 [9074]~P106(f333(f333(f247(a910),f333(x90744,x90742)),f333(x90744,x90743)))+P106(f333(f333(f335(f916(x90741,x90741)),f333(f333(f265(x90741,x90741),x90742),x90743)),f161(x90741,f333(f333(f159(f917(x90741,a910)),x90744),x90745)))) % 173.51/173.28 [9350]~P27(x93502,x93501,x93503,f333(f333(f121(f917(x93502,a905)),x93504),x93505))+E(f333(f333(f112(f917(x93501,a905)),f333(f316(x93502,x93501,x93503),f333(f333(f23(f917(x93502,a905)),x93504),x93505))),f333(f316(x93502,x93501,x93503),f333(f333(f23(f917(x93502,a905)),x93505),x93504))),f196(f917(x93501,a905))) % 173.51/173.28 [9611]~P27(x96113,x96111,x96115,f254(f917(x96113,a905)))+E(f333(f79(x96111,x96112,x96113,f333(f79(x96113,x96112,x96111,x96114),f99(x96113,x96111,f254(f917(x96113,a905)),x96115))),x96115),x96114) % 173.51/173.28 [9643]~P106(f333(f333(f246(f917(x96433,a905)),f333(f292(x96431,x96433,x96434),x96432)),x96435))+P106(f333(f333(f246(f917(x96431,a905)),x96432),f333(f86(f917(x96431,a905)),f333(f292(x96433,x96431,f333(f293(x96431,x96433),x96434)),f333(f86(f917(x96433,a905)),x96435))))) % 173.51/173.28 [9669]~P27(x96691,x96692,x96693,f333(f333(f315(x96691),x96694),x96695))+~P106(f333(f333(f335(x96692),f333(x96693,x96694)),f333(f316(x96691,x96692,x96693),f333(f333(f23(f917(x96691,a905)),x96695),f333(f333(f315(x96691),x96694),f196(f917(x96691,a905))))))) % 173.51/173.28 [9730]P106(f333(f333(f246(f917(x97301,a905)),f333(f292(x97302,x97301,x97303),x97304)),x97305))+~P106(f333(f333(f246(f917(x97302,a905)),x97304),f333(f86(f917(x97302,a905)),f333(f292(x97301,x97302,f333(f293(x97302,x97301),x97303)),f333(f86(f917(x97301,a905)),x97305))))) % 173.51/173.28 [9805]~P87(x98051)+P106(f333(f333(f246(x98051),f333(f82(x98051),f333(f333(f23(x98051),f333(f333(f87(x98051),x98052),x98053)),f333(f333(f87(x98051),x98054),x98055)))),f333(f333(f87(x98051),f333(f82(x98051),f333(f333(f23(x98051),x98052),x98054))),f333(f82(x98051),f333(f333(f23(x98051),x98053),x98055))))) % 173.51/173.28 [9913]P106(f333(f333(f335(x99131),f491(x99132,x99133,x99134,x99131,x99135)),x99134))+P106(f333(f333(f246(f917(x99135,a905)),f333(f333(f45(x99131,f917(x99135,a905)),x99134),x99133)),x99132)) % 173.51/173.28 [10099]~P106(f333(f333(f246(f917(x100991,a905)),f333(x100994,f491(x100995,x100994,x100993,x100992,x100991))),x100995))+P106(f333(f333(f246(f917(x100991,a905)),f333(f333(f45(x100992,f917(x100991,a905)),x100993),x100994)),x100995)) % 173.51/173.28 [8680]E(f333(f333(f142(x86801),x86802),f333(f333(f167(x86801,x86803),f333(f333(f23(a910),x86804),f333(f197(f911(x86801)),x86802))),x86805)),f333(f333(f167(x86801,f333(f333(f142(x86801),x86802),x86803)),x86804),x86805))+P106(f333(f333(f247(a910),x86804),f333(f197(f911(x86801)),x86802))) % 173.51/173.28 [8707]~P142(x87071)+E(f333(f333(f87(x87071),f333(f333(f88(x87071),x87072),x87073)),f333(f333(f87(x87071),f333(f333(f88(x87071),x87074),x87073)),x87075)),f333(f333(f87(x87071),f333(f333(f88(x87071),f333(f333(f87(x87071),x87072),x87074)),x87073)),x87075)) % 173.51/173.28 [9305]~P143(x93051)+E(f333(f173(x93051),f333(f333(f162(x93052,x93051),f333(f333(f8(x93051,x93051,x93052),f333(f88(x93051),x93053)),x93054)),x93055)),f333(f333(f88(x93051),x93053),f333(f173(x93051),f333(f333(f162(x93052,x93051),x93054),x93055)))) % 173.51/173.28 [9485]E(f333(f197(f911(x94851)),f333(f333(f183(x94851),f333(f333(f244(a910),f333(f197(f911(x94851)),x94852)),f333(f197(f911(x94853)),x94854))),x94852)),f333(f197(f911(x94853)),f333(f333(f183(x94853),f333(f333(f244(a910),f333(f197(f911(x94851)),x94852)),f333(f197(f911(x94853)),x94854))),x94854)))+P106(f333(x94855,f333(f333(f189(x94851,x94853),x94852),x94854))) % 173.51/173.28 [9741]~P143(x97412)+E(f333(f333(f6(x97411,x97412),f333(f333(f7(x97411,x97412,x97412),f333(f333(f8(x97412,f917(x97412,x97412),x97411),f88(x97412)),x97413)),x97414)),x97415),f333(f333(f88(x97412),f333(f333(f6(x97411,x97412),x97413),x97415)),x97414)) % 173.51/173.28 [9742]~P68(x97422)+E(f333(f333(f6(x97421,x97422),f333(f333(f7(x97421,x97422,x97422),f333(f333(f8(x97422,f917(x97422,x97422),x97421),f296(x97422)),x97423)),x97424)),x97425),f333(f333(f296(x97422),f333(f333(f6(x97421,x97422),x97423),x97425)),x97424)) % 173.51/173.28 [9749]~P6(x97492)+E(f333(f333(f6(x97491,x97492),f333(f333(f18(x97491,x97492,x97492),f333(f333(f8(x97492,f917(x97492,x97492),x97491),f23(x97492)),x97493)),x97494)),x97495),f333(f333(f23(x97492),f333(f333(f6(x97491,x97492),x97493),x97495)),f333(f333(f6(x97491,x97492),x97494),x97495))) % 173.51/173.28 [9750]~P72(x97502)+E(f333(f333(f6(x97501,x97502),f333(f333(f18(x97501,x97502,x97502),f333(f333(f8(x97502,f917(x97502,x97502),x97501),f87(x97502)),x97503)),x97504)),x97505),f333(f333(f87(x97502),f333(f333(f6(x97501,x97502),x97503),x97505)),f333(f333(f6(x97501,x97502),x97504),x97505))) % 173.51/173.28 [9751]~P78(x97512)+E(f333(f333(f9(x97511,x97512),f333(f333(f18(x97511,x97512,x97512),f333(f333(f8(x97512,f917(x97512,x97512),x97511),f88(x97512)),x97513)),x97514)),x97515),f333(f333(f88(x97512),f333(f333(f9(x97511,x97512),x97513),x97515)),f333(f333(f9(x97511,x97512),x97514),x97515))) % 173.51/173.28 [9790]~E(x97903,f196(f917(x97901,a905)))+E(f333(f333(f45(x97901,f917(x97902,a905)),x97903),f333(f333(f7(x97901,f917(x97902,a905),f917(x97902,a905)),f333(f333(f8(f917(x97902,a905),f917(f917(x97902,a905),f917(x97902,a905)),x97901),f121(f917(x97902,a905))),x97904)),x97905)),f196(f917(x97902,a905))) % 173.51/173.28 [9791]~E(x97913,f196(f917(x97911,a905)))+E(f333(f333(f46(x97911,f917(x97912,a905)),x97913),f333(f333(f7(x97911,f917(x97912,a905),f917(x97912,a905)),f333(f333(f8(f917(x97912,a905),f917(f917(x97912,a905),f917(x97912,a905)),x97911),f112(f917(x97912,a905))),x97914)),x97915)),f254(f917(x97912,a905))) % 173.51/173.28 [9792]~E(x97923,f196(f917(x97921,a905)))+E(f333(f333(f46(x97921,f917(x97922,a905)),x97923),f333(f333(f7(x97921,f917(x97922,a905),f917(x97922,a905)),f333(f333(f8(f917(x97922,a905),f917(f917(x97922,a905),f917(x97922,a905)),x97921),f23(f917(x97922,a905))),x97924)),x97925)),f254(f917(x97922,a905))) % 173.51/173.28 [9813]E(x98131,f196(f917(x98132,a905)))+E(f333(f333(f45(x98132,f917(x98133,a905)),x98131),f333(f333(f7(x98132,f917(x98133,a905),f917(x98133,a905)),f333(f333(f8(f917(x98133,a905),f917(f917(x98133,a905),f917(x98133,a905)),x98132),f121(f917(x98133,a905))),x98134)),x98135)),f333(f333(f121(f917(x98133,a905)),f333(f333(f45(x98132,f917(x98133,a905)),x98131),x98134)),x98135)) % 173.51/173.28 [9814]E(x98141,f196(f917(x98142,a905)))+E(f333(f333(f46(x98142,f917(x98143,a905)),x98141),f333(f333(f7(x98142,f917(x98143,a905),f917(x98143,a905)),f333(f333(f8(f917(x98143,a905),f917(f917(x98143,a905),f917(x98143,a905)),x98142),f112(f917(x98143,a905))),x98144)),x98145)),f333(f333(f112(f917(x98143,a905)),f333(f333(f46(x98142,f917(x98143,a905)),x98141),x98144)),x98145)) % 173.51/173.28 [9815]E(x98151,f196(f917(x98152,a905)))+E(f333(f333(f46(x98152,f917(x98153,a905)),x98151),f333(f333(f7(x98152,f917(x98153,a905),f917(x98153,a905)),f333(f333(f8(f917(x98153,a905),f917(f917(x98153,a905),f917(x98153,a905)),x98152),f23(f917(x98153,a905))),x98154)),x98155)),f333(f333(f23(f917(x98153,a905)),f333(f333(f46(x98152,f917(x98153,a905)),x98151),x98154)),x98155)) % 173.51/173.28 [9355]~P106(f333(f333(f246(a910),x93551),x93554))+E(f333(f333(f23(a910),f333(f333(f87(a910),f333(f333(f88(a910),x93551),x93552)),x93553)),f333(f333(f87(a910),f333(f333(f88(a910),x93554),x93552)),x93555)),f333(f333(f23(a910),x93553),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x93554),x93551)),x93552)),x93555))) % 173.51/173.28 [9962]~P143(x99621)+E(f333(f173(x99621),f333(f333(f162(x99622,x99621),f333(f333(f7(x99622,x99621,x99621),f333(f333(f8(x99621,f917(x99621,x99621),x99622),f88(x99621)),x99623)),x99624)),x99625)),f333(f333(f88(x99621),f333(f173(x99621),f333(f333(f162(x99622,x99621),x99623),x99625))),x99624)) % 173.51/173.28 [9968]~P6(x99681)+E(f333(f173(x99681),f333(f333(f162(x99682,x99681),f333(f333(f18(x99682,x99681,x99681),f333(f333(f8(x99681,f917(x99681,x99681),x99682),f23(x99681)),x99683)),x99684)),x99685)),f333(f333(f23(x99681),f333(f173(x99681),f333(f333(f162(x99682,x99681),x99683),x99685))),f333(f173(x99681),f333(f333(f162(x99682,x99681),x99684),x99685)))) % 173.51/173.28 [9969]~P72(x99691)+E(f333(f173(x99691),f333(f333(f162(x99692,x99691),f333(f333(f18(x99692,x99691,x99691),f333(f333(f8(x99691,f917(x99691,x99691),x99692),f87(x99691)),x99693)),x99694)),x99695)),f333(f333(f87(x99691),f333(f173(x99691),f333(f333(f162(x99692,x99691),x99693),x99695))),f333(f173(x99691),f333(f333(f162(x99692,x99691),x99694),x99695)))) % 173.51/173.28 [10112]P106(f333(x101121,f333(f333(f189(x101122,x101123),x101124),x101125)))+~P106(f333(x101121,f333(f333(f189(x101122,x101123),f333(f333(f183(x101122),f333(f333(f244(a910),f333(f197(f911(x101122)),x101124)),f333(f197(f911(x101123)),x101125))),x101124)),f333(f333(f183(x101123),f333(f333(f244(a910),f333(f197(f911(x101122)),x101124)),f333(f197(f911(x101123)),x101125))),x101125)))) % 173.51/173.28 [10363]~P106(f333(f333(f335(f916(x103632,x103631)),f333(f333(f265(x103632,x103631),x103634),x103635)),f333(f293(x103631,x103632),x103633)))+P106(f333(f333(f255(x103631,x103632,f333(f333(f7(x103631,f917(f916(x103631,x103632),a905),f917(x103632,a905)),f333(f333(f8(f917(x103632,f917(f917(f916(x103631,x103632),a905),a905)),f917(f917(f916(x103631,x103632),a905),f917(x103632,a905)),x103631),f7(x103632,f917(f916(x103631,x103632),a905),a905)),f333(f333(f8(f917(x103632,f916(x103631,x103632)),f917(x103632,f917(f917(f916(x103631,x103632),a905),a905)),x103631),f333(f8(f916(x103631,x103632),f917(f917(f916(x103631,x103632),a905),a905),x103632),f335(f916(x103631,x103632)))),f265(x103631,x103632)))),x103633)),x103634),x103635)) % 173.51/173.28 [10373]P106(f333(f333(f335(f916(x103731,x103732)),f333(f333(f265(x103731,x103732),x103733),x103734)),f333(f293(x103732,x103731),x103735)))+~P106(f333(f333(f255(x103732,x103731,f333(f333(f7(x103732,f917(f916(x103732,x103731),a905),f917(x103731,a905)),f333(f333(f8(f917(x103731,f917(f917(f916(x103732,x103731),a905),a905)),f917(f917(f916(x103732,x103731),a905),f917(x103731,a905)),x103732),f7(x103731,f917(f916(x103732,x103731),a905),a905)),f333(f333(f8(f917(x103731,f916(x103732,x103731)),f917(x103731,f917(f917(f916(x103732,x103731),a905),a905)),x103732),f333(f8(f916(x103732,x103731),f917(f917(f916(x103732,x103731),a905),a905),x103731),f335(f916(x103732,x103731)))),f265(x103732,x103731)))),x103735)),x103733),x103734)) % 173.51/173.28 [9610]~P106(f333(f333(f246(a910),x96104),x96101))+E(f333(f333(f23(a910),f333(f333(f87(a910),f333(f333(f88(a910),x96101),x96102)),x96103)),f333(f333(f87(a910),f333(f333(f88(a910),x96104),x96102)),x96105)),f333(f333(f23(a910),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x96101),x96104)),x96102)),x96103)),x96105)) % 173.51/173.28 [5404]E(x54041,x54042)+~E(f28(x54043,x54044,x54041),f28(x54045,x54046,x54042)) % 173.51/173.28 [5405]E(x54051,x54052)+~E(f28(x54053,x54051,x54054),f28(x54055,x54052,x54056)) % 173.51/173.28 [5406]E(x54061,x54062)+~E(f28(x54061,x54063,x54064),f28(x54062,x54065,x54066)) % 173.51/173.28 [5407]E(x54071,x54072)+~E(f27(x54073,x54074,x54071),f27(x54075,x54076,x54072)) % 173.51/173.28 [5408]E(x54081,x54082)+~E(f27(x54083,x54081,x54084),f27(x54085,x54082,x54086)) % 173.51/173.28 [5409]E(x54091,x54092)+~E(f27(x54091,x54093,x54094),f27(x54092,x54095,x54096)) % 173.51/173.28 [7381]E(x73811,x73812)+~E(f232(x73813,x73814,x73815,x73811),f232(x73813,x73814,x73816,x73812)) % 173.51/173.28 [7382]E(x73821,x73822)+~E(f232(x73823,x73824,x73821,x73825),f232(x73823,x73824,x73822,x73826)) % 173.51/173.28 [8505]~P21(x85055,x85051,x85052,x85056)+E(f333(f79(x85051,x85051,x85051,f333(x85052,x85053)),f333(x85052,x85054)),f333(f79(x85051,x85051,x85051,f333(x85052,x85054)),f333(x85052,x85053))) % 173.51/173.28 [8751]~P60(x87514,x87515,x87512,x87511,x87516)+E(f333(x87511,f333(x87512,x87513)),x87513) % 173.51/173.28 [8918]P27(x89181,x89182,x89183,x89184)+~P27(x89181,x89185,f333(f79(x89182,x89185,x89181,x89186),x89183),x89184) % 173.51/173.28 [8991]~E(x89916,x89914)+E(f333(f81(x89911,x89912,x89913,x89914,x89915),x89916),x89915) % 173.51/173.28 [8997]E(x89971,x89972)+E(f333(f81(x89973,x89974,x89975,x89972,x89976),x89971),f333(x89975,x89971)) % 173.51/173.28 [9009]~P27(x90094,x90092,f333(f79(x90091,x90092,x90094,x90093),x90095),x90096)+P27(x90091,x90092,x90093,f333(f316(x90094,x90091,x90095),x90096)) % 173.51/173.28 [9752]P106(f333(f67(x97521),x97522))+~P106(f333(f72(x97521,x97523,x97524,x97525,x97522),x97526)) % 173.51/173.28 [9761]~P106(f333(f333(f335(x97614),x97613),f306(x97614,x97615,x97611,x97612,x97616)))+P106(f333(f333(x97611,x97612),x97613)) % 173.51/173.28 [9762]~P106(f333(f333(f335(x97624),x97623),f303(x97624,x97621,x97625,x97622,x97626)))+P106(f333(f333(x97621,x97622),x97623)) % 173.51/173.28 [9763]~P106(f333(f333(f335(x97634),x97632),f306(x97634,x97631,x97635,x97636,x97633)))+P106(f333(f333(x97631,x97632),x97633)) % 173.51/173.28 [9764]~P106(f333(f333(f335(x97644),x97642),f303(x97644,x97645,x97641,x97646,x97643)))+P106(f333(f333(x97641,x97642),x97643)) % 173.51/173.28 [5902]E(x59021,x59022)+~E(f333(f333(f265(x59023,x59024),x59025),x59021),f333(f333(f265(x59023,x59024),x59026),x59022)) % 173.51/173.28 [5904]E(x59041,x59042)+~E(f333(f333(f265(x59043,x59044),x59041),x59045),f333(f333(f265(x59043,x59044),x59042),x59046)) % 173.51/173.28 [6030]~P18(x60305,x60306,x60301)+E(f333(f333(x60301,x60302),f333(f333(x60301,x60303),x60304)),f333(f333(x60301,x60303),f333(f333(x60301,x60302),x60304))) % 173.51/173.28 [7444]~P35(x74444,x74441,f333(f333(f159(x74444),x74442),x74445),f333(f333(f159(x74444),x74443),x74446))+P106(f333(f333(x74441,x74442),x74443)) % 173.51/173.28 [7798]P35(x77981,x77982,x77983,x77984)+~P35(x77981,x77982,f333(f333(f159(x77981),x77985),x77983),f333(f333(f159(x77981),x77986),x77984)) % 173.51/173.28 [8856]~P60(x88565,x88561,x88562,x88566,x88564)+P106(f333(f333(f335(x88561),f333(x88562,x88563)),x88564)) % 173.51/173.28 [9038]E(f333(f83(x90381,x90382,x90383,x90384,x90385),x90386),f333(x90383,x90386))+P106(f333(f333(f335(x90381),x90386),x90385)) % 173.51/173.28 [9062]~E(x90623,f333(f333(f159(x90621),x90625),x90626))+P106(f333(f333(f335(f916(f911(x90621),f911(x90621))),f333(f333(f265(f911(x90621),f911(x90621)),x90622),f333(f333(f142(x90621),x90622),x90623))),f155(x90621,x90624))) % 173.51/173.28 [9068]E(f333(f83(x90681,x90682,x90683,x90684,x90685),x90686),f333(x90684,x90686))+~P106(f333(f333(f335(x90681),x90686),x90685)) % 173.51/173.28 [9311]~P37(x93111,x93112,x93113,x93115,x93116)+P37(x93111,x93112,x93113,f333(f333(f183(x93111),x93114),x93115),f333(f333(f183(x93112),x93114),x93116)) % 173.51/173.28 [9312]~P37(x93121,x93122,x93123,x93125,x93126)+P37(x93121,x93122,x93123,f333(f333(f146(x93121),x93124),x93125),f333(f333(f146(x93122),x93124),x93126)) % 173.51/173.28 [9577]E(f333(f316(x95771,x95772,f81(x95771,x95772,x95773,x95774,x95775)),x95776),f333(f316(x95771,x95772,x95773),x95776))+P106(f333(f333(f335(x95771),x95774),x95776)) % 173.51/173.28 [9580]E(f333(f333(f162(x95801,x95802),f81(x95801,x95802,x95803,x95804,x95805)),x95806),f333(f333(f162(x95801,x95802),x95803),x95806))+P106(f333(f333(f335(x95801),x95804),f333(f180(x95801),x95806))) % 173.51/173.28 [9825]~P25(x98254,x98252,x98255,x98253,x98256,x98251)+E(f333(x98251,f196(f917(x98252,a905))),x98253) % 173.51/173.28 [10061]~E(f333(x100614,f333(f264(x100611,x100613),x100615)),f333(x100616,f333(f264(x100611,x100613),x100615)))+E(f333(f270(x100611,x100612,x100613,x100613,x100614,f33(x100613)),x100615),f333(f270(x100611,x100612,x100613,x100613,x100616,f33(x100613)),x100615)) % 173.51/173.28 [10062]~E(f333(x100624,f333(f268(x100621,x100622),x100625)),f333(x100626,f333(f268(x100621,x100622),x100625)))+E(f333(f270(x100621,x100621,x100622,x100623,f33(x100621),x100624),x100625),f333(f270(x100621,x100621,x100622,x100623,f33(x100621),x100626),x100625)) % 173.51/173.28 [10094]P106(f333(f333(f333(f333(a204,x100941),f333(f333(f333(a205,x100942),f34(x100943)),f333(x100944,x100942))),x100945),f570(x100946,x100945,x100942,x100941,x100944,x100943)))+~P106(f333(f333(f333(f333(a204,f27(x100943,x100944,x100941)),x100942),x100945),f333(f333(f333(a205,x100946),f34(x100943)),f206(x100942,x100943)))) % 173.51/173.28 [10108]~E(f333(f270(x101082,x101086,x101083,x101083,x101081,f33(x101083)),x101084),f333(f270(x101082,x101086,x101083,x101083,x101085,f33(x101083)),x101084))+E(f333(x101081,f333(f264(x101082,x101083),x101084)),f333(x101085,f333(f264(x101082,x101083),x101084))) % 173.51/173.28 [10109]~E(f333(f270(x101092,x101092,x101093,x101096,f33(x101092),x101091),x101094),f333(f270(x101092,x101092,x101093,x101096,f33(x101092),x101095),x101094))+E(f333(x101091,f333(f268(x101092,x101093),x101094)),f333(x101095,f333(f268(x101092,x101093),x101094))) % 173.51/173.28 [10186]E(f333(f333(f333(a205,f570(x101861,x101862,x101863,x101864,x101865,x101866)),f34(x101866)),f206(x101863,x101866)),f333(f333(f333(a205,x101861),f34(x101866)),f206(x101863,x101866)))+~P106(f333(f333(f333(f333(a204,f27(x101866,x101865,x101864)),x101863),x101862),f333(f333(f333(a205,x101861),f34(x101866)),f206(x101863,x101866)))) % 173.51/173.28 [8958]P106(f333(f333(f335(x89581),x89582),x89583))+~P106(f333(f333(f335(f916(x89581,x89584)),f333(f333(f265(x89581,x89584),x89582),x89585)),f333(f333(f267(x89581,x89584),x89583),x89586))) % 173.51/173.28 [8974]P106(f333(f333(f335(x89741),x89742),f333(x89743,x89744)))+~P106(f333(f333(f335(f916(x89745,x89741)),f333(f333(f265(x89745,x89741),x89744),x89742)),f333(f333(f267(x89745,x89741),x89746),x89743))) % 173.51/173.28 [9430]P106(f333(f333(f335(f916(x94301,x94301)),f333(f333(f265(x94301,x94301),f333(x94302,x94303)),f333(x94302,x94304))),x94305))+~P106(f333(f333(f335(f916(x94306,x94306)),f333(f333(f265(x94306,x94306),x94303),x94304)),f333(f333(f294(x94301,x94306),x94305),x94302))) % 173.51/173.28 [9453]~P106(f333(f333(f335(f916(x94534,x94534)),f333(f333(f265(x94534,x94534),f333(x94536,x94532)),f333(x94536,x94533))),x94535))+P106(f333(f333(f335(f916(x94531,x94531)),f333(f333(f265(x94531,x94531),x94532),x94533)),f333(f333(f294(x94534,x94531),x94535),x94536))) % 173.51/173.28 [10111]E(f333(f333(f265(x101111,x101112),f690(x101113,x101114,x101115,x101116,x101112,x101111)),f691(x101113,x101114,x101115,x101116,x101112,x101111)),x101116)+~P106(f333(f333(f335(f916(x101111,x101112)),x101116),f333(f333(f295(x101111,x101115,x101112),x101114),x101113))) % 173.51/173.28 [10116]~E(f333(x101163,f796(x101164,x101162,x101166,x101163,x101165,x101161)),f333(x101166,f796(x101164,x101162,x101166,x101163,x101165,x101161)))+E(f333(f333(f112(f917(x101161,a905)),f333(f317(x101161,x101162,x101163),x101164)),x101165),f333(f333(f112(f917(x101161,a905)),f333(f317(x101161,x101162,x101166),x101164)),x101165)) % 173.51/173.28 [10178]E(f333(f333(f112(f917(x101781,a905)),f333(f317(x101781,x101782,x101783),x101784)),x101785),f333(f333(f112(f917(x101781,a905)),f333(f317(x101781,x101782,x101786),x101784)),x101785))+P106(f333(f333(f335(x101781),f796(x101784,x101782,x101783,x101786,x101785,x101781)),x101785)) % 173.51/173.28 [10319]~P106(f333(f333(f335(f916(x103191,x103196)),x103195),f333(f333(f295(x103191,x103192,x103196),x103194),x103193)))+P106(f333(f333(f335(f916(x103191,x103192)),f333(f333(f265(x103191,x103192),f690(x103193,x103194,x103192,x103195,x103196,x103191)),f692(x103193,x103194,x103192,x103195,x103196,x103191))),x103194)) % 173.51/173.28 [10320]~P106(f333(f333(f335(f916(x103206,x103202)),x103205),f333(f333(f295(x103206,x103201,x103202),x103204),x103203)))+P106(f333(f333(f335(f916(x103201,x103202)),f333(f333(f265(x103201,x103202),f692(x103203,x103204,x103201,x103205,x103202,x103206)),f691(x103203,x103204,x103201,x103205,x103202,x103206))),x103203)) % 173.51/173.28 [7871]~P8(x78712)+E(f333(f333(f45(x78711,x78712),x78713),f333(f333(f7(x78711,x78714,x78712),x78715),x78716)),f333(f333(f333(f45(x78711,f917(x78714,x78712)),x78713),x78715),x78716)) % 173.51/173.28 [7872]~P8(x78722)+E(f333(f333(f46(x78721,x78722),x78723),f333(f333(f7(x78721,x78724,x78722),x78725),x78726)),f333(f333(f333(f46(x78721,f917(x78724,x78722)),x78723),x78725),x78726)) % 173.51/173.28 [8662]E(f333(f333(f45(x86621,f917(x86622,a905)),x86623),f333(f333(f8(f917(x86622,a905),f917(x86622,a905),x86621),f333(f315(x86622),x86624)),x86625)),f333(f333(f315(x86622),x86624),f333(f333(f45(x86621,f917(x86622,a905)),x86623),x86625)))+~P106(f333(f333(f335(x86621),x86626),x86623)) % 173.51/173.28 [9125]~P8(x91252)+E(f333(f333(f45(x91251,x91252),x91253),f333(f333(f8(f917(x91254,x91252),x91252,x91251),f333(f45(x91254,x91252),x91255)),f333(f7(x91254,x91251,x91252),x91256))),f333(f333(f45(x91254,x91252),x91255),f333(f333(f8(f917(x91251,x91252),x91252,x91254),f333(f45(x91251,x91252),x91253)),x91256))) % 173.51/173.28 [9126]~P8(x91262)+E(f333(f333(f46(x91261,x91262),x91263),f333(f333(f8(f917(x91264,x91262),x91262,x91261),f333(f46(x91264,x91262),x91265)),f333(f7(x91264,x91261,x91262),x91266))),f333(f333(f46(x91264,x91262),x91265),f333(f333(f8(f917(x91261,x91262),x91262,x91264),f333(f46(x91261,x91262),x91263)),x91266))) % 173.51/173.28 [9337]P106(f333(f333(f335(x93371),x93372),f333(f180(x93371),x93373)))+~P106(f333(f333(f335(f916(x93374,x93371)),f333(f333(f265(x93374,x93371),x93375),x93372)),f333(f180(f916(x93374,x93371)),f333(f333(f189(x93374,x93371),x93376),x93373)))) % 173.51/173.28 [9338]P106(f333(f333(f335(x93381),x93382),f333(f180(x93381),x93383)))+~P106(f333(f333(f335(f916(x93381,x93384)),f333(f333(f265(x93381,x93384),x93382),x93385)),f333(f180(f916(x93381,x93384)),f333(f333(f189(x93381,x93384),x93383),x93386)))) % 173.51/173.28 [9446]P106(f333(f333(f246(f917(x94461,a905)),f333(f292(x94462,x94461,x94463),x94464)),x94465))+~P106(f333(f333(f246(f917(f916(x94462,x94461),a905)),x94463),f333(f333(f267(x94462,x94461),x94466),f333(f16(f917(x94461,a905),x94462),x94465)))) % 173.51/173.28 [9454]~P28(x94544,x94542,x94545,f254(f917(x94544,a905)),f254(f917(x94542,a905)))+E(f333(f333(f46(x94541,f917(x94542,a905)),x94543),f333(f333(f8(f917(x94544,a905),f917(x94542,a905),x94541),f316(x94544,x94542,x94545)),x94546)),f333(f316(x94544,x94542,x94545),f333(f333(f46(x94541,f917(x94544,a905)),x94543),x94546))) % 173.51/173.28 [9646]P106(f333(f333(f335(f916(f911(x96461),f911(x96461))),f333(f333(f265(f911(x96461),f911(x96461)),f333(f333(f159(x96461),x96462),x96463)),f333(f333(f159(x96461),x96464),x96465))),f155(x96461,x96466)))+~P106(f333(f333(f335(f916(x96461,x96461)),f333(f333(f265(x96461,x96461),x96462),x96464)),x96466)) % 173.51/173.28 [9679]P106(f333(f333(f333(f333(a204,f27(x96791,x96792,x96793)),x96794),x96795),f333(f333(f333(a205,x96796),f34(x96791)),f206(x96794,x96791))))+~P106(f333(f333(f333(f333(a204,x96793),f333(f333(f333(a205,x96794),f34(x96791)),f333(x96792,x96794))),x96795),x96796)) % 173.51/173.28 [10091]P106(f333(f333(f333(f333(a204,x100911),f333(f333(f333(a205,x100912),f34(x100913)),f333(x100914,x100912))),x100915),f626(x100916,x100915,x100912,x100911,x100914,x100913)))+~P106(f333(f333(f333(f333(a204,f27(x100913,x100914,x100911)),x100912),x100915),x100916)) % 173.51/173.28 [10107]E(f333(f333(f265(x101071,x101072),f612(x101073,x101074,x101075,x101072,x101071,x101076)),f615(x101073,x101074,x101075,x101072,x101071,x101076)),x101076)+P106(f333(f333(f335(x101075),x101074),f333(f333(f269(x101071,x101072,f917(x101075,a905)),x101073),x101076))) % 173.51/173.28 [10113]E(f333(f333(f265(x101131,x101132),f613(x101133,x101134,x101132,x101131,x101135,x101136)),f614(x101133,x101134,x101132,x101131,x101135,x101136)),x101133)+~P106(f333(f333(f335(x101136),x101135),f333(f333(f269(x101131,x101132,f917(x101136,a905)),x101134),x101133))) % 173.51/173.28 [10183]E(f333(f333(f333(a205,f626(x101831,x101832,x101833,x101834,x101835,x101836)),f34(x101836)),f206(x101833,x101836)),x101831)+~P106(f333(f333(f333(f333(a204,f27(x101836,x101835,x101834)),x101833),x101832),x101831)) % 173.51/173.28 [10272]P106(f333(f333(f335(x102721),x102722),f333(f333(x102723,f613(x102724,x102723,x102725,x102726,x102722,x102721)),f614(x102724,x102723,x102725,x102726,x102722,x102721))))+~P106(f333(f333(f335(x102721),x102722),f333(f333(f269(x102726,x102725,f917(x102721,a905)),x102723),x102724))) % 173.51/173.28 [10294]~P106(f333(f333(f335(x102941),x102942),f333(f333(x102945,f612(x102945,x102942,x102941,x102944,x102943,x102946)),f615(x102945,x102942,x102941,x102944,x102943,x102946))))+P106(f333(f333(f335(x102941),x102942),f333(f333(f269(x102943,x102944,f917(x102941,a905)),x102945),x102946))) % 173.51/173.28 [8555]E(x85551,x85552)+E(f333(f333(f167(x85553,f333(f333(f167(x85553,x85554),x85551),x85555)),x85552),x85556),f333(f333(f167(x85553,f333(f333(f167(x85553,x85554),x85552),x85556)),x85551),x85555)) % 173.51/173.28 [9715]~P106(f333(f333(f335(x97153),x97156),x97155))+E(f333(f333(f315(x97151),x97152),f333(f316(x97153,x97151,x97154),f333(f333(f23(f917(x97153,a905)),x97155),f333(f333(f315(x97153),x97156),f196(f917(x97153,a905)))))),f333(f316(x97153,x97151,f81(x97153,x97151,x97154,x97156,x97152)),x97155)) % 173.51/173.28 [9209]~P106(f333(f333(x92094,x92095),x92096))+P106(f333(f333(f333(f333(f121(f917(x92091,f917(x92092,a905))),x92093),x92094),x92095),x92096)) % 173.51/173.28 [9211]~P106(f333(f333(x92113,x92115),x92116))+P106(f333(f333(f333(f333(f121(f917(x92111,f917(x92112,a905))),x92113),x92114),x92115),x92116)) % 173.51/173.28 [9506]P106(f333(f333(x95061,x95062),x95063))+~P106(f333(f333(f333(f333(f112(f917(x95064,f917(x95065,a905))),x95066),x95061),x95062),x95063)) % 173.51/173.28 [9507]P106(f333(f333(x95071,x95072),x95073))+~P106(f333(f333(f333(f333(f112(f917(x95074,f917(x95075,a905))),x95071),x95076),x95072),x95073)) % 173.51/173.28 [9950]~P72(x99502)+E(f333(f333(f6(x99501,x99502),f333(f333(f7(x99501,f917(x99503,a905),x99502),f333(f333(f8(f917(x99503,x99502),f917(f917(x99503,a905),x99502),x99501),f6(x99503,x99502)),x99504)),x99505)),x99506),f333(f333(f6(f916(x99501,x99503),x99502),f333(f269(x99501,x99503,x99502),x99504)),f333(f333(f267(x99501,x99503),x99506),f333(f16(f917(x99503,a905),x99501),x99505)))) % 173.51/173.28 [9951]~P78(x99512)+E(f333(f333(f9(x99511,x99512),f333(f333(f7(x99511,f917(x99513,a905),x99512),f333(f333(f8(f917(x99513,x99512),f917(f917(x99513,a905),x99512),x99511),f9(x99513,x99512)),x99514)),x99515)),x99516),f333(f333(f9(f916(x99511,x99513),x99512),f333(f269(x99511,x99513,x99512),x99514)),f333(f333(f267(x99511,x99513),x99516),f333(f16(f917(x99513,a905),x99511),x99515)))) % 173.51/173.28 [10088]~P72(x100882)+E(f333(f333(f6(x100881,x100882),f333(f333(f7(x100881,f917(x100883,a905),x100882),f333(f333(f8(f917(x100883,x100882),f917(f917(x100883,a905),x100882),x100881),f6(x100883,x100882)),f333(f7(x100883,x100881,x100882),x100884))),x100885)),x100886),f333(f333(f6(x100883,x100882),f333(f333(f7(x100883,f917(x100881,a905),x100882),f333(f333(f8(f917(x100881,x100882),f917(f917(x100881,a905),x100882),x100883),f6(x100881,x100882)),x100884)),x100886)),x100885)) % 173.51/173.28 [10384]~P106(f333(f333(f335(f916(x103841,x103842)),f333(f333(f265(x103841,x103842),x103845),x103846)),f333(f333(f121(f917(f916(x103841,x103842),a905)),x103843),x103844)))+P106(f333(f333(f333(f333(f121(f917(x103841,f917(x103842,a905))),f333(f333(f7(x103841,f917(f916(x103841,x103842),a905),f917(x103842,a905)),f333(f333(f8(f917(x103842,f917(f917(f916(x103841,x103842),a905),a905)),f917(f917(f916(x103841,x103842),a905),f917(x103842,a905)),x103841),f7(x103842,f917(f916(x103841,x103842),a905),a905)),f333(f333(f8(f917(x103842,f916(x103841,x103842)),f917(x103842,f917(f917(f916(x103841,x103842),a905),a905)),x103841),f333(f8(f916(x103841,x103842),f917(f917(f916(x103841,x103842),a905),a905),x103842),f335(f916(x103841,x103842)))),f265(x103841,x103842)))),x103843)),f333(f333(f7(x103841,f917(f916(x103841,x103842),a905),f917(x103842,a905)),f333(f333(f8(f917(x103842,f917(f917(f916(x103841,x103842),a905),a905)),f917(f917(f916(x103841,x103842),a905),f917(x103842,a905)),x103841),f7(x103842,f917(f916(x103841,x103842),a905),a905)),f333(f333(f8(f917(x103842,f916(x103841,x103842)),f917(x103842,f917(f917(f916(x103841,x103842),a905),a905)),x103841),f333(f8(f916(x103841,x103842),f917(f917(f916(x103841,x103842),a905),a905),x103842),f335(f916(x103841,x103842)))),f265(x103841,x103842)))),x103844)),x103845),x103846)) % 173.51/173.28 [10385]~P106(f333(f333(f335(f916(x103851,x103852)),f333(f333(f265(x103851,x103852),x103855),x103856)),f333(f333(f112(f917(f916(x103851,x103852),a905)),x103853),x103854)))+P106(f333(f333(f333(f333(f112(f917(x103851,f917(x103852,a905))),f333(f333(f7(x103851,f917(f916(x103851,x103852),a905),f917(x103852,a905)),f333(f333(f8(f917(x103852,f917(f917(f916(x103851,x103852),a905),a905)),f917(f917(f916(x103851,x103852),a905),f917(x103852,a905)),x103851),f7(x103852,f917(f916(x103851,x103852),a905),a905)),f333(f333(f8(f917(x103852,f916(x103851,x103852)),f917(x103852,f917(f917(f916(x103851,x103852),a905),a905)),x103851),f333(f8(f916(x103851,x103852),f917(f917(f916(x103851,x103852),a905),a905),x103852),f335(f916(x103851,x103852)))),f265(x103851,x103852)))),x103853)),f333(f333(f7(x103851,f917(f916(x103851,x103852),a905),f917(x103852,a905)),f333(f333(f8(f917(x103852,f917(f917(f916(x103851,x103852),a905),a905)),f917(f917(f916(x103851,x103852),a905),f917(x103852,a905)),x103851),f7(x103852,f917(f916(x103851,x103852),a905),a905)),f333(f333(f8(f917(x103852,f916(x103851,x103852)),f917(x103852,f917(f917(f916(x103851,x103852),a905),a905)),x103851),f333(f8(f916(x103851,x103852),f917(f917(f916(x103851,x103852),a905),a905),x103852),f335(f916(x103851,x103852)))),f265(x103851,x103852)))),x103854)),x103855),x103856)) % 173.51/173.28 [10391]P106(f333(f333(f335(f916(x103911,x103912)),f333(f333(f265(x103911,x103912),x103913),x103914)),f333(f333(f121(f917(f916(x103911,x103912),a905)),x103915),x103916)))+~P106(f333(f333(f333(f333(f121(f917(x103911,f917(x103912,a905))),f333(f333(f7(x103911,f917(f916(x103911,x103912),a905),f917(x103912,a905)),f333(f333(f8(f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),f917(f917(f916(x103911,x103912),a905),f917(x103912,a905)),x103911),f7(x103912,f917(f916(x103911,x103912),a905),a905)),f333(f333(f8(f917(x103912,f916(x103911,x103912)),f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),x103911),f333(f8(f916(x103911,x103912),f917(f917(f916(x103911,x103912),a905),a905),x103912),f335(f916(x103911,x103912)))),f265(x103911,x103912)))),x103915)),f333(f333(f7(x103911,f917(f916(x103911,x103912),a905),f917(x103912,a905)),f333(f333(f8(f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),f917(f917(f916(x103911,x103912),a905),f917(x103912,a905)),x103911),f7(x103912,f917(f916(x103911,x103912),a905),a905)),f333(f333(f8(f917(x103912,f916(x103911,x103912)),f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),x103911),f333(f8(f916(x103911,x103912),f917(f917(f916(x103911,x103912),a905),a905),x103912),f335(f916(x103911,x103912)))),f265(x103911,x103912)))),x103916)),x103913),x103914)) % 173.51/173.28 [10392]P106(f333(f333(f335(f916(x103921,x103922)),f333(f333(f265(x103921,x103922),x103923),x103924)),f333(f333(f112(f917(f916(x103921,x103922),a905)),x103925),x103926)))+~P106(f333(f333(f333(f333(f112(f917(x103921,f917(x103922,a905))),f333(f333(f7(x103921,f917(f916(x103921,x103922),a905),f917(x103922,a905)),f333(f333(f8(f917(x103922,f917(f917(f916(x103921,x103922),a905),a905)),f917(f917(f916(x103921,x103922),a905),f917(x103922,a905)),x103921),f7(x103922,f917(f916(x103921,x103922),a905),a905)),f333(f333(f8(f917(x103922,f916(x103921,x103922)),f917(x103922,f917(f917(f916(x103921,x103922),a905),a905)),x103921),f333(f8(f916(x103921,x103922),f917(f917(f916(x103921,x103922),a905),a905),x103922),f335(f916(x103921,x103922)))),f265(x103921,x103922)))),x103925)),f333(f333(f7(x103921,f917(f916(x103921,x103922),a905),f917(x103922,a905)),f333(f333(f8(f917(x103922,f917(f917(f916(x103921,x103922),a905),a905)),f917(f917(f916(x103921,x103922),a905),f917(x103922,a905)),x103921),f7(x103922,f917(f916(x103921,x103922),a905),a905)),f333(f333(f8(f917(x103922,f916(x103921,x103922)),f917(x103922,f917(f917(f916(x103921,x103922),a905),a905)),x103921),f333(f8(f916(x103921,x103922),f917(f917(f916(x103921,x103922),a905),a905),x103922),f335(f916(x103921,x103922)))),f265(x103921,x103922)))),x103926)),x103923),x103924)) % 173.51/173.28 [10380]~P106(f333(f333(f335(f916(x103802,x103803)),f333(f333(f265(x103802,x103803),x103805),x103806)),f333(f333(f45(x103801,f917(f916(x103802,x103803),a905)),f254(f917(x103801,a905))),x103804)))+P106(f333(f333(f333(f333(f45(x103801,f917(x103802,f917(x103803,a905))),f254(f917(x103801,a905))),f333(f333(f8(f917(f916(x103802,x103803),a905),f917(x103802,f917(x103803,a905)),x103801),f333(f7(x103802,f917(f916(x103802,x103803),a905),f917(x103803,a905)),f333(f333(f8(f917(x103803,f917(f917(f916(x103802,x103803),a905),a905)),f917(f917(f916(x103802,x103803),a905),f917(x103803,a905)),x103802),f7(x103803,f917(f916(x103802,x103803),a905),a905)),f333(f333(f8(f917(x103803,f916(x103802,x103803)),f917(x103803,f917(f917(f916(x103802,x103803),a905),a905)),x103802),f333(f8(f916(x103802,x103803),f917(f917(f916(x103802,x103803),a905),a905),x103803),f335(f916(x103802,x103803)))),f265(x103802,x103803))))),x103804)),x103805),x103806)) % 173.51/173.28 [10381]~P106(f333(f333(f335(f916(x103812,x103813)),f333(f333(f265(x103812,x103813),x103815),x103816)),f333(f333(f46(x103811,f917(f916(x103812,x103813),a905)),f254(f917(x103811,a905))),x103814)))+P106(f333(f333(f333(f333(f46(x103811,f917(x103812,f917(x103813,a905))),f254(f917(x103811,a905))),f333(f333(f8(f917(f916(x103812,x103813),a905),f917(x103812,f917(x103813,a905)),x103811),f333(f7(x103812,f917(f916(x103812,x103813),a905),f917(x103813,a905)),f333(f333(f8(f917(x103813,f917(f917(f916(x103812,x103813),a905),a905)),f917(f917(f916(x103812,x103813),a905),f917(x103813,a905)),x103812),f7(x103813,f917(f916(x103812,x103813),a905),a905)),f333(f333(f8(f917(x103813,f916(x103812,x103813)),f917(x103813,f917(f917(f916(x103812,x103813),a905),a905)),x103812),f333(f8(f916(x103812,x103813),f917(f917(f916(x103812,x103813),a905),a905),x103813),f335(f916(x103812,x103813)))),f265(x103812,x103813))))),x103814)),x103815),x103816)) % 173.51/173.28 [10388]P106(f333(f333(f335(f916(x103881,x103882)),f333(f333(f265(x103881,x103882),x103883),x103884)),f333(f333(f45(x103885,f917(f916(x103881,x103882),a905)),f254(f917(x103885,a905))),x103886)))+~P106(f333(f333(f333(f333(f45(x103885,f917(x103881,f917(x103882,a905))),f254(f917(x103885,a905))),f333(f333(f8(f917(f916(x103881,x103882),a905),f917(x103881,f917(x103882,a905)),x103885),f333(f7(x103881,f917(f916(x103881,x103882),a905),f917(x103882,a905)),f333(f333(f8(f917(x103882,f917(f917(f916(x103881,x103882),a905),a905)),f917(f917(f916(x103881,x103882),a905),f917(x103882,a905)),x103881),f7(x103882,f917(f916(x103881,x103882),a905),a905)),f333(f333(f8(f917(x103882,f916(x103881,x103882)),f917(x103882,f917(f917(f916(x103881,x103882),a905),a905)),x103881),f333(f8(f916(x103881,x103882),f917(f917(f916(x103881,x103882),a905),a905),x103882),f335(f916(x103881,x103882)))),f265(x103881,x103882))))),x103886)),x103883),x103884)) % 173.51/173.28 [10389]P106(f333(f333(f335(f916(x103891,x103892)),f333(f333(f265(x103891,x103892),x103893),x103894)),f333(f333(f46(x103895,f917(f916(x103891,x103892),a905)),f254(f917(x103895,a905))),x103896)))+~P106(f333(f333(f333(f333(f46(x103895,f917(x103891,f917(x103892,a905))),f254(f917(x103895,a905))),f333(f333(f8(f917(f916(x103891,x103892),a905),f917(x103891,f917(x103892,a905)),x103895),f333(f7(x103891,f917(f916(x103891,x103892),a905),f917(x103892,a905)),f333(f333(f8(f917(x103892,f917(f917(f916(x103891,x103892),a905),a905)),f917(f917(f916(x103891,x103892),a905),f917(x103892,a905)),x103891),f7(x103892,f917(f916(x103891,x103892),a905),a905)),f333(f333(f8(f917(x103892,f916(x103891,x103892)),f917(x103892,f917(f917(f916(x103891,x103892),a905),a905)),x103891),f333(f8(f916(x103891,x103892),f917(f917(f916(x103891,x103892),a905),a905),x103892),f335(f916(x103891,x103892)))),f265(x103891,x103892))))),x103896)),x103893),x103894)) % 173.51/173.28 [7550]E(f333(x75501,f333(x75502,x75503)),f333(x75504,x75503))+~E(f333(f79(x75505,x75506,x75507,x75501),x75502),x75504) % 173.51/173.28 [9731]E(x97311,x97312)+E(f81(x97313,x97314,f81(x97313,x97314,x97315,x97311,x97316),x97312,x97317),f81(x97313,x97314,f81(x97313,x97314,x97315,x97312,x97317),x97311,x97316)) % 173.51/173.28 [9824]~P24(x98243,x98244,x98241,x98245,x98246,x98247)+E(f333(f333(x98241,x98242),x98242),x98242) % 173.51/173.28 [6133]~E(f333(f333(f162(x61331,x61335),x61336),x61332),f333(f333(f162(x61333,x61335),x61337),x61334))+E(f333(f197(f911(x61331)),x61332),f333(f197(f911(x61333)),x61334)) % 173.51/173.28 [8592]E(f333(x85921,f333(x85922,x85923)),f333(x85924,x85923))+~E(f333(f79(x85925,x85926,x85927,x85921),x85922),f333(f79(x85926,x85926,x85927,f33(x85926)),x85924)) % 173.51/173.28 [8947]~P37(x89474,x89475,x89471,f333(f333(f159(x89474),x89472),x89476),f333(f333(f159(x89475),x89473),x89477))+P106(f333(f333(x89471,x89472),x89473)) % 173.51/173.28 [9344]P37(x93441,x93442,x93443,x93444,x93445)+~P37(x93441,x93442,x93443,f333(f333(f159(x93441),x93446),x93444),f333(f333(f159(x93442),x93447),x93445)) % 173.51/173.28 [9984]P106(f333(f333(x99841,x99842),f590(x99843,x99842,x99844,x99841)))+~P106(f333(f333(f266(x99845,x99846,x99847,x99841,x99844),x99842),x99843)) % 173.51/173.28 [10006]P106(f333(f333(x100061,f590(x100062,x100063,x100061,x100064)),x100062))+~P106(f333(f333(f266(x100065,x100066,x100067,x100064,x100061),x100063),x100062)) % 173.51/173.28 [6178]E(x61781,x61782)+~E(f333(f333(f333(f98(x61783),x61784),x61785),x61781),f333(f333(f333(f98(x61783),x61786),x61787),x61782)) % 173.51/173.28 [6179]E(x61791,x61792)+~E(f333(f333(f333(f98(x61793),x61794),x61791),x61795),f333(f333(f333(f98(x61793),x61796),x61792),x61797)) % 173.51/173.28 [6180]E(x61801,x61802)+~E(f333(f333(f333(f98(x61803),x61801),x61804),x61805),f333(f333(f333(f98(x61803),x61802),x61806),x61807)) % 173.51/173.28 [9072]~P22(x90726,x90721,x90723,x90727)+E(f333(f79(x90721,x90721,x90722,f333(x90723,x90724)),f333(f79(x90721,x90721,x90722,f333(x90723,x90724)),x90725)),f333(f79(x90721,x90721,x90722,f333(x90723,x90724)),x90725)) % 173.51/173.28 [9457]~P37(x94573,x94572,x94574,f333(f333(f162(x94571,x94573),x94575),x94576),x94577)+P37(x94571,x94572,f333(f333(f8(x94573,f917(x94572,a905),x94571),x94574),x94575),x94576,x94577) % 173.51/173.28 [9482]P37(x94821,x94822,x94823,f333(f333(f162(x94824,x94821),x94825),x94826),x94827)+~P37(x94824,x94822,f333(f333(f8(x94821,f917(x94822,a905),x94824),x94823),x94825),x94826,x94827) % 173.51/173.28 [9071]~P106(f333(f333(f335(x90711),x90712),f333(f333(x90715,x90716),x90717)))+P106(f333(f333(f335(x90711),x90712),f333(f333(f269(x90713,x90714,f917(x90711,a905)),x90715),f333(f333(f265(x90713,x90714),x90716),x90717)))) % 173.51/173.28 [9367]P106(f333(f333(f333(x93671,x93672),x93673),x93674))+~P106(f333(f333(f333(f269(x93675,x93676,f917(x93677,a905)),x93671),f333(f333(f265(x93675,x93676),x93672),x93673)),x93674)) % 173.51/173.28 [9521]P106(f333(f333(f335(x95211),f333(f333(x95212,x95213),x95214)),f333(f316(f916(x95215,x95216),x95211,f333(f269(x95215,x95216,x95211),x95212)),x95217)))+~P106(f333(f333(f335(f916(x95215,x95216)),f333(f333(f265(x95215,x95216),x95213),x95214)),x95217)) % 173.51/173.28 [9871]P106(f333(f333(f335(f916(f911(x98711),f911(x98711))),f333(f333(f265(f911(x98711),f911(x98711)),f333(f333(f142(x98711),x98712),f333(f333(f159(x98711),x98713),x98714))),f333(f333(f142(x98711),x98712),f333(f333(f159(x98711),x98715),x98716)))),f155(x98711,x98717)))+~P106(f333(f333(f335(f916(x98711,x98711)),f333(f333(f265(x98711,x98711),x98713),x98715)),x98717)) % 173.51/173.28 [9936]~P37(x99361,x99363,x99364,x99366,f333(f333(f162(x99362,x99363),x99365),x99367))+P37(x99361,x99362,f333(f333(f7(x99361,f917(x99362,x99363),f917(x99362,a905)),f333(f333(f8(f917(x99363,a905),f917(f917(x99362,x99363),f917(x99362,a905)),x99361),f8(x99363,a905,x99362)),x99364)),x99365),x99366,x99367) % 173.51/173.28 [10010]P37(x100101,x100102,x100103,x100104,f333(f333(f162(x100105,x100102),x100106),x100107))+~P37(x100101,x100105,f333(f333(f7(x100101,f917(x100105,x100102),f917(x100105,a905)),f333(f333(f8(f917(x100102,a905),f917(f917(x100105,x100102),f917(x100105,a905)),x100101),f8(x100102,a905,x100105)),x100103)),x100106),x100104,x100107) % 173.51/173.28 [10306]P106(f333(f333(f335(x103061),f661(x103062,x103063,x103064,x103065,x103066,x103067,x103061)),x103065))+P106(f333(f333(f333(f333(f46(x103061,f917(x103067,f917(x103066,a905))),x103065),x103064),x103063),x103062)) % 173.51/173.28 [10307]P106(f333(f333(f335(x103071),f831(x103072,x103073,x103074,x103075,x103076,x103077,x103071)),x103077))+P106(f333(f333(f333(f333(f46(x103071,f917(x103073,f917(x103072,a905))),x103077),x103076),x103075),x103074)) % 173.51/173.28 [10308]P106(f333(f333(f335(x103081),f498(x103082,x103083,x103084,x103085,x103086,x103087,x103081)),x103085))+~P106(f333(f333(f333(f333(f45(x103081,f917(x103087,f917(x103086,a905))),x103085),x103084),x103083),x103082)) % 173.51/173.28 [10309]P106(f333(f333(f335(x103091),f832(x103092,x103093,x103094,x103095,x103096,x103097,x103091)),x103095))+~P106(f333(f333(f333(f333(f45(x103091,f917(x103097,f917(x103096,a905))),x103095),x103094),x103093),x103092)) % 173.51/173.28 [10342]P106(f333(f333(f333(x103421,f498(x103422,x103423,x103421,x103424,x103425,x103426,x103427)),x103423),x103422))+~P106(f333(f333(f333(f333(f45(x103427,f917(x103426,f917(x103425,a905))),x103424),x103421),x103423),x103422)) % 173.51/173.28 [10343]P106(f333(f333(f333(x103431,f832(x103432,x103433,x103431,x103434,x103435,x103436,x103437)),x103433),x103432))+~P106(f333(f333(f333(f333(f45(x103437,f917(x103436,f917(x103435,a905))),x103434),x103431),x103433),x103432)) % 173.51/173.28 [10360]~P106(f333(f333(f333(x103605,f661(x103607,x103606,x103605,x103604,x103603,x103602,x103601)),x103606),x103607))+P106(f333(f333(f333(f333(f46(x103601,f917(x103602,f917(x103603,a905))),x103604),x103605),x103606),x103607)) % 173.51/173.28 [10361]~P106(f333(f333(f333(x103615,f831(x103613,x103612,x103617,x103616,x103615,x103614,x103611)),x103616),x103617))+P106(f333(f333(f333(f333(f46(x103611,f917(x103612,f917(x103613,a905))),x103614),x103615),x103616),x103617)) % 173.51/173.28 [10379]~P106(f333(f333(f335(f916(x103791,x103793)),f333(f333(f265(x103791,x103793),x103796),x103797)),f333(f333(f295(x103791,x103792,x103793),x103794),x103795)))+P106(f333(f333(f266(x103791,x103792,x103793,f333(f333(f7(x103791,f917(f916(x103791,x103792),a905),f917(x103792,a905)),f333(f333(f8(f917(x103792,f917(f917(f916(x103791,x103792),a905),a905)),f917(f917(f916(x103791,x103792),a905),f917(x103792,a905)),x103791),f7(x103792,f917(f916(x103791,x103792),a905),a905)),f333(f333(f8(f917(x103792,f916(x103791,x103792)),f917(x103792,f917(f917(f916(x103791,x103792),a905),a905)),x103791),f333(f8(f916(x103791,x103792),f917(f917(f916(x103791,x103792),a905),a905),x103792),f335(f916(x103791,x103792)))),f265(x103791,x103792)))),x103794),f333(f333(f7(x103792,f917(f916(x103792,x103793),a905),f917(x103793,a905)),f333(f333(f8(f917(x103793,f917(f917(f916(x103792,x103793),a905),a905)),f917(f917(f916(x103792,x103793),a905),f917(x103793,a905)),x103792),f7(x103793,f917(f916(x103792,x103793),a905),a905)),f333(f333(f8(f917(x103793,f916(x103792,x103793)),f917(x103793,f917(f917(f916(x103792,x103793),a905),a905)),x103792),f333(f8(f916(x103792,x103793),f917(f917(f916(x103792,x103793),a905),a905),x103793),f335(f916(x103792,x103793)))),f265(x103792,x103793)))),x103795)),x103796),x103797)) % 173.51/173.28 [10387]P106(f333(f333(f335(f916(x103871,x103872)),f333(f333(f265(x103871,x103872),x103873),x103874)),f333(f333(f295(x103871,x103875,x103872),x103876),x103877)))+~P106(f333(f333(f266(x103871,x103875,x103872,f333(f333(f7(x103871,f917(f916(x103871,x103875),a905),f917(x103875,a905)),f333(f333(f8(f917(x103875,f917(f917(f916(x103871,x103875),a905),a905)),f917(f917(f916(x103871,x103875),a905),f917(x103875,a905)),x103871),f7(x103875,f917(f916(x103871,x103875),a905),a905)),f333(f333(f8(f917(x103875,f916(x103871,x103875)),f917(x103875,f917(f917(f916(x103871,x103875),a905),a905)),x103871),f333(f8(f916(x103871,x103875),f917(f917(f916(x103871,x103875),a905),a905),x103875),f335(f916(x103871,x103875)))),f265(x103871,x103875)))),x103876),f333(f333(f7(x103875,f917(f916(x103875,x103872),a905),f917(x103872,a905)),f333(f333(f8(f917(x103872,f917(f917(f916(x103875,x103872),a905),a905)),f917(f917(f916(x103875,x103872),a905),f917(x103872,a905)),x103875),f7(x103872,f917(f916(x103875,x103872),a905),a905)),f333(f333(f8(f917(x103872,f916(x103875,x103872)),f917(x103872,f917(f917(f916(x103875,x103872),a905),a905)),x103875),f333(f8(f916(x103875,x103872),f917(f917(f916(x103875,x103872),a905),a905),x103872),f335(f916(x103875,x103872)))),f265(x103875,x103872)))),x103877)),x103873),x103874)) % 173.51/173.28 [10318]~P143(x103182)+E(f333(f333(f6(x103181,x103182),f333(f333(f7(x103181,f917(x103183,a905),x103182),f333(f333(f8(f917(x103183,x103182),f917(f917(x103183,a905),x103182),x103181),f6(x103183,x103182)),f333(f333(f7(x103181,f917(x103183,x103182),f917(x103183,x103182)),f333(f333(f8(f917(x103182,x103182),f917(f917(x103183,x103182),f917(x103183,x103182)),x103181),f8(x103182,x103182,x103183)),f333(f333(f8(x103182,f917(x103182,x103182),x103181),f88(x103182)),x103184))),x103185))),x103186)),x103187),f333(f333(f88(x103182),f333(f333(f6(x103181,x103182),x103184),x103187)),f333(f333(f6(x103183,x103182),x103185),x103186))) % 173.51/173.28 [9404]~P21(x94047,x94041,x94043,x94048)+E(f333(f79(x94041,x94041,x94042,f333(x94043,x94044)),f333(f79(x94041,x94041,x94042,f333(x94043,x94045)),x94046)),f333(f79(x94041,x94041,x94042,f333(x94043,x94045)),f333(f79(x94041,x94041,x94042,f333(x94043,x94044)),x94046))) % 173.51/173.28 [10375]P26(x103751,x103752,f333(f333(f315(f909(x103751)),f333(f333(f333(f98(x103751),f333(f333(f8(f917(a906,a905),f917(a906,a905),x103751),f333(f18(a906,a905,a905),f333(f333(f8(a905,f917(a905,a905),a906),a331),f333(a330,x103753)))),f333(f333(f7(x103751,f917(a906,a906),f917(a906,a905)),f333(f333(f8(f917(a906,a905),f917(f917(a906,a906),f917(a906,a905)),x103751),f8(a906,a905,a906)),x103754)),f333(f333(f18(a906,a910,a906),f333(f333(f7(a906,a908,f917(a910,a906)),a205),f34(x103755))),x103756)))),f27(x103755,x103756,x103757)),x103758)),f196(f917(f909(x103751),a905))))+~P26(x103751,x103752,f333(f333(f315(f909(x103751)),f333(f333(f333(f98(x103751),x103754),x103757),f333(f333(f7(x103751,f917(a906,a906),f917(a906,a905)),f333(f333(f8(f917(a906,a905),f917(f917(a906,a906),f917(a906,a905)),x103751),f8(a906,a905,a906)),x103758)),f333(f333(f7(a906,a910,a906),f333(f333(f7(a906,a908,f917(a910,a906)),a205),f34(x103755))),f206(x103753,x103755))))),f196(f917(f909(x103751),a905)))) % 173.51/173.28 [10382]E(f333(f333(f265(x103821,x103822),f333(x103823,f583(x103824,x103825,x103823,x103826,x103827,x103828,x103822,x103821))),f333(x103825,f584(x103824,x103825,x103823,x103826,x103827,x103828,x103822,x103821))),x103828)+~P106(f333(f333(f335(f916(x103821,x103822)),x103828),f333(f316(f916(x103827,x103826),f916(x103821,x103822),f270(x103827,x103821,x103826,x103822,x103823,x103825)),x103824))) % 173.51/173.28 [10396]~P106(f333(f333(f335(f916(x103968,x103967)),x103966),f333(f316(f916(x103961,x103962),f916(x103968,x103967),f270(x103961,x103968,x103962,x103967,x103965,x103964)),x103963)))+P106(f333(f333(f335(f916(x103961,x103962)),f333(f333(f265(x103961,x103962),f583(x103963,x103964,x103965,x103962,x103961,x103966,x103967,x103968)),f584(x103963,x103964,x103965,x103962,x103961,x103966,x103967,x103968))),x103963)) % 173.51/173.28 [9861]P106(f333(f333(f335(f916(f916(x98611,x98612),f916(x98611,x98612))),f333(f333(f265(f916(x98611,x98612),f916(x98611,x98612)),f333(f333(f265(x98611,x98612),x98613),x98614)),f333(f333(f265(x98611,x98612),x98615),x98616))),f325(x98611,x98612,x98617,x98618)))+~P106(f333(f333(f335(f916(x98611,x98611)),f333(f333(f265(x98611,x98611),x98613),x98615)),x98617)) % 173.51/173.28 [10372]E(f333(f150(x103721,x103722,f333(f7(x103722,x103721,x103721),x103723),f333(x103724,x103725)),x103726),f333(x103724,f333(f150(x103727,x103722,f333(f7(x103722,x103727,x103727),x103728),x103725),x103726)))+P106(f333(f333(f335(x103722),f780(x103725,x103728,x103724,x103723,x103727,x103721,x103726,x103722)),f333(f180(x103722),x103726))) % 173.51/173.28 [10390]~E(f333(f79(x103901,x103901,x103907,f333(x103903,f780(x103905,x103908,x103904,x103903,x103907,x103901,x103906,x103902))),x103904),f333(f79(x103907,x103901,x103907,x103904),f333(x103908,f780(x103905,x103908,x103904,x103903,x103907,x103901,x103906,x103902))))+E(f333(f150(x103901,x103902,f333(f7(x103902,x103901,x103901),x103903),f333(x103904,x103905)),x103906),f333(x103904,f333(f150(x103907,x103902,f333(f7(x103902,x103907,x103907),x103908),x103905),x103906))) % 173.51/173.28 [8597]E(f333(x85971,f333(x85972,x85973)),f333(x85974,f333(x85975,x85973)))+~E(f333(f79(x85976,x85977,x85978,x85971),x85972),f333(f79(x85979,x85977,x85978,x85974),x85975)) % 173.51/173.28 [10241]P106(f333(f333(f335(f916(x102411,x102412)),f333(f333(f265(x102411,x102412),f333(x102413,x102414)),f333(x102415,x102416))),f333(f316(f916(x102417,x102418),f916(x102411,x102412),f270(x102417,x102411,x102418,x102412,x102413,x102415)),x102419)))+~P106(f333(f333(f335(f916(x102417,x102418)),f333(f333(f265(x102417,x102418),x102414),x102416)),x102419)) % 173.51/173.28 [8893]~E(f333(x88934,f333(x88935,x88936)),f333(x88939,f333(x889310,x889311)))+E(f333(f333(f79(x88931,x88932,x88933,x88934),x88935),x88936),f333(f333(f79(x88937,x88932,x88938,x88939),x889310),x889311)) % 173.51/173.28 [4729]~P102(x47291)+~P110(x47291)+E(f112(x47291),f244(x47291)) % 173.51/173.28 [4730]~P101(x47301)+~P110(x47301)+E(f121(x47301),f245(x47301)) % 173.51/173.28 [4977]~P120(x49771)+~P95(x49771)+E(f333(f82(x49771),f333(f114(x49771),a108)),f85(x49771)) % 173.51/173.28 [5261]E(x52611,f2(a1))+E(f89(a1,x52611),f333(f86(a1),f85(a1)))+P106(f333(f333(f247(a1),f2(a1)),x52611)) % 173.51/173.28 [5470]E(x54701,f2(a1))+E(f89(a1,x54701),f85(a1))+~P106(f333(f333(f247(a1),f2(a1)),x54701)) % 173.51/173.28 [7448]~P43(x74481)+P106(f333(f67(a1),x74481))+~P106(f333(f67(a910),f333(f316(a1,a910,a115),x74481))) % 173.51/173.28 [9823]E(x98231,f196(f917(f916(a910,a910),a905)))+~P106(f333(f67(f916(a910,a910)),x98231))+P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),f196(f917(f916(a910,a910),a905))),x98231)),a40)) % 173.51/173.28 [9985]E(x99851,f2(a910))+E(x99851,f333(a123,f2(a910)))+~P106(f333(f333(f247(a910),x99851),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.28 [10269]E(x102691,f2(a110))+E(f333(f333(f87(a1),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(a22,f333(f333(f42(a110),x102691),f333(f114(a110),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))))),f85(a1)),f333(a22,x102691))+E(f51(a110,x102691,f333(f114(a110),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f2(a110)) % 173.51/173.28 [10118]E(x101181,f2(a110))+~E(f51(a110,x101181,f333(f114(a110),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f2(a110))+E(f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(a22,f333(f333(f42(a110),x101181),f333(f114(a110),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f333(a22,x101181)) % 173.51/173.28 [4805]~P61(x48051,x48052)+P47(x48051,x48052)+~P48(a905) % 173.51/173.28 [4739]~P107(x47391)+P30(x47391,x47392)+~E(x47392,f2(x47391)) % 173.51/173.28 [4740]~P110(x47401)+P16(x47401,x47402)+~E(x47402,f124(x47401)) % 173.51/173.28 [4749]~P120(x47491)+~E(x47492,f2(x47491))+E(f89(x47491,x47492),f2(x47491)) % 173.51/173.28 [4750]~P91(x47501)+~E(x47502,f2(x47501))+E(f89(x47501,x47502),f2(x47501)) % 173.51/173.28 [4758]~P107(x47582)+~P30(x47582,x47581)+E(x47581,f2(x47582)) % 173.51/173.28 [4798]~P120(x47982)+~E(f89(x47982,x47981),f2(x47982))+E(x47981,f2(x47982)) % 173.51/173.28 [4812]~P7(x48122)+~P7(x48121)+P7(f917(x48121,x48122)) % 173.51/173.28 [4813]~P7(x48132)+~P7(x48131)+P7(f916(x48131,x48132)) % 173.51/173.28 [4814]~P7(x48142)+~P7(x48141)+P7(f918(x48141,x48142)) % 173.51/173.28 [4815]~P66(x48152)+~P66(x48151)+P66(f917(x48151,x48152)) % 173.51/173.28 [4816]~P66(x48162)+~P66(x48161)+P66(f916(x48161,x48162)) % 173.51/173.28 [4817]~P66(x48172)+~P66(x48171)+P66(f918(x48171,x48172)) % 173.51/173.28 [4818]~P9(x48182)+~P9(x48181)+P9(f203(x48181,x48182)) % 173.51/173.28 [4819]~P104(x48192)+~P104(x48191)+P104(f916(x48191,x48192)) % 173.51/173.28 [4948]~P110(x49481)+~P16(x49481,x49482)+P16(x49481,f160(x49481,x49482)) % 173.51/173.28 [5190]~P9(x51902)+~P9(x51901)+P9(f51(a1,x51901,x51902)) % 173.51/173.28 [4760]~P80(x47601)+~E(x47602,f2(x47601))+E(f333(f86(x47601),x47602),x47602) % 173.51/173.28 [4770]~P139(x47701)+~E(x47702,f2(a1))+E(f333(f113(x47701),x47702),f2(x47701)) % 173.51/173.28 [4771]~P94(x47711)+~E(x47712,f2(a1))+E(f333(f113(x47711),x47712),f2(x47711)) % 173.51/173.28 [4795]~P71(x47951)+~E(f2(x47951),x47952)+E(f333(f86(x47951),x47952),f2(x47951)) % 173.51/173.28 [4796]~P71(x47961)+~E(x47962,f2(x47961))+E(f333(f86(x47961),x47962),f2(x47961)) % 173.51/173.28 [4797]~P87(x47971)+~E(x47972,f2(x47971))+E(f333(f82(x47971),x47972),f2(x47971)) % 173.51/173.28 [4821]~P80(x48212)+E(x48211,f2(x48212))+~E(f333(f86(x48212),x48211),x48211) % 173.51/173.28 [4829]E(x48291,f333(a115,x48292))+~E(x48291,f2(a910))+~E(x48292,f333(f111(a1),x48291)) % 173.51/173.28 [4830]E(f333(a115,x48301),x48302)+~E(x48302,f2(a910))+~E(x48301,f333(f111(a1),x48302)) % 173.51/173.28 [4834]~P94(x48342)+E(x48341,f2(a1))+~E(f333(f113(x48342),x48341),f2(x48342)) % 173.51/173.28 [4838]~P71(x48382)+E(x48381,f2(x48382))+~E(f333(f86(x48382),x48381),f2(x48382)) % 173.51/173.28 [4839]~P87(x48392)+E(x48391,f2(x48392))+~E(f333(f82(x48392),x48391),f2(x48392)) % 173.51/173.28 [4840]~P71(x48401)+E(f2(x48401),x48402)+~E(f333(f86(x48401),x48402),f2(x48401)) % 173.51/173.28 [5024]~P110(x50241)+~P16(x50241,x50242)+P16(x50241,f333(f179(x50241),x50242)) % 173.51/173.28 [5051]~P106(x50512)+~P106(x50511)+P106(f333(f333(a331,x50511),x50512)) % 173.51/173.28 [5085]~E(f85(a910),f2(a910))+E(f333(f41(x50851),x50852),f2(a910))+~P106(f333(f67(x50851),x50852)) % 173.51/173.28 [5121]~P143(x51211)+~P115(x51211)+E(f333(f333(f256(x51211),f2(x51211)),f333(a123,x51212)),f2(x51211)) % 173.51/173.28 [5158]~P110(x51581)+P16(x51581,f147(x51581,x51582))+~P106(f333(f67(x51581),x51582)) % 173.51/173.28 [5159]~P110(x51591)+P16(x51591,f772(x51592,x51591))+~P106(f333(f67(x51591),x51592)) % 173.51/173.28 [5182]~P110(x51821)+E(f333(f180(x51821),f147(x51821,x51822)),x51822)+~P106(f333(f67(x51821),x51822)) % 173.51/173.28 [5183]~P110(x51831)+E(f333(f180(x51831),f772(x51832,x51831)),x51832)+~P106(f333(f67(x51831),x51832)) % 173.51/173.28 [5211]P106(x52111)+P106(x52112)+~P106(f333(f333(a332,x52112),x52111)) % 173.51/173.28 [5224]E(x52241,f196(f917(x52242,a905)))+~E(f333(f41(x52242),x52241),f2(a910))+~P106(f333(f67(x52242),x52241)) % 173.51/173.28 [5229]P106(x52291)+~P106(x52292)+~P106(f333(f333(a336,x52292),x52291)) % 173.51/173.28 [5279]~P77(x52791)+E(f333(f82(x52791),x52792),x52792)+P106(f333(f333(f247(x52791),x52792),f2(x52791))) % 173.51/173.28 [5341]~P7(x53412)+~P106(f333(f62(x53412),x53411))+P106(f333(x53411,f845(x53411,x53412))) % 173.51/173.28 [5342]~P7(x53422)+~P106(f333(f62(x53422),x53421))+P106(f333(x53421,f868(x53421,x53422))) % 173.51/173.28 [5382]E(x53821,f124(x53822))+P106(f333(f145(x53822),f125(x53822,x53821)))+~P106(f333(f145(x53822),x53821)) % 173.51/173.28 [5387]~P110(x53871)+~P106(f333(f67(x53871),x53872))+P106(f333(f145(x53871),f147(x53871,x53872))) % 173.51/173.28 [5388]~P110(x53881)+~P106(f333(f67(x53881),x53882))+P106(f333(f145(x53881),f772(x53882,x53881))) % 173.51/173.28 [5393]~P139(x53931)+E(f333(f111(x53931),f333(a115,x53932)),f333(f113(x53931),x53932))+P106(f333(f333(f247(a1),x53932),f2(a1))) % 173.51/173.28 [5420]P10(x54202,x54201)+E(f333(x54201,f559(x54201)),f333(x54201,f568(x54201)))+P106(f333(f333(x54201,f559(x54201)),f568(x54201))) % 173.51/173.28 [5433]E(f333(f111(a1),f441(x54331,x54332)),x54331)+P106(f333(x54332,f333(a115,x54331)))+~P106(f333(x54332,f2(a910))) % 173.51/173.28 [5445]~P7(x54451)+~P106(f333(x54452,f847(x54452,x54451)))+P106(f333(f63(x54451),x54452)) % 173.51/173.28 [5446]~P7(x54461)+~P106(f333(x54462,f865(x54462,x54461)))+P106(f333(f63(x54461),x54462)) % 173.51/173.28 [5478]~P120(x54781)+~E(f89(x54781,x54782),f333(f86(x54781),f85(x54781)))+P106(f333(f333(f247(x54781),x54782),f2(x54781))) % 173.51/173.28 [5551]~E(x55512,f2(a1))+E(f227(x55511,x55512),f333(f333(f265(a1,a1),f2(a1)),f85(a1)))+P106(f333(f333(f247(a1),x55512),f2(a1))) % 173.51/173.28 [5552]~E(x55521,f2(a1))+E(f227(x55521,x55522),f333(f333(f265(a1,a1),f2(a1)),f85(a1)))+P106(f333(f333(f247(a1),x55522),f2(a1))) % 173.51/173.28 [5602]E(f333(f111(a1),f441(x56021,x56022)),x56021)+P106(f333(x56022,f333(a115,x56021)))+P106(f333(f333(f247(a1),x56021),f2(a1))) % 173.51/173.28 [5666]~P120(x56661)+E(f89(x56661,x56662),f333(f86(x56661),f85(x56661)))+~P106(f333(f333(f247(x56661),x56662),f2(x56661))) % 173.51/173.28 [5667]~P87(x56671)+E(f333(f82(x56671),x56672),f333(f86(x56671),x56672))+~P106(f333(f333(f246(x56671),x56672),f2(x56671))) % 173.51/173.28 [5668]~P87(x56681)+E(f333(f82(x56681),x56682),f333(f86(x56681),x56682))+~P106(f333(f333(f247(x56681),x56682),f2(x56681))) % 173.51/173.28 [5669]~P77(x56691)+E(f333(f82(x56691),x56692),f333(f86(x56691),x56692))+~P106(f333(f333(f247(x56691),x56692),f2(x56691))) % 173.51/173.28 [5766]~P106(f333(x57661,f441(x57662,x57661)))+P106(f333(x57661,f333(a115,x57662)))+~P106(f333(x57661,f2(a910))) % 173.51/173.28 [5773]E(x57731,f2(a910))+E(f333(a123,f343(x57732,x57731)),x57731)+~P106(f333(f333(f247(a910),x57731),f333(a123,x57732))) % 173.51/173.28 [5777]P10(x57771,x57772)+~E(f333(x57772,f559(x57772)),f333(x57772,f568(x57772)))+~P106(f333(f333(x57772,f559(x57772)),f568(x57772))) % 173.51/173.28 [5795]~P110(x57951)+P16(x57951,x57952)+P106(f333(f333(f246(a910),f755(x57952,x57951)),f756(x57952,x57951))) % 173.51/173.28 [5796]~P110(x57961)+P16(x57961,x57962)+P106(f333(f333(f246(a910),f763(x57962,x57961)),f767(x57962,x57961))) % 173.51/173.28 [5882]~P87(x58821)+~E(x58822,f2(x58821))+P106(f333(f333(f246(x58821),f333(f82(x58821),x58822)),f2(x58821))) % 173.51/173.28 [5966]~P106(f333(x59661,f441(x59662,x59661)))+P106(f333(x59661,f333(a115,x59662)))+P106(f333(f333(f247(a1),x59662),f2(a1))) % 173.51/173.28 [5990]~P106(f333(x59901,f333(a115,x59902)))+P106(f333(x59901,f2(a910)))+~P106(f333(f333(f247(a1),x59902),f2(a1))) % 173.51/173.28 [6327]~P120(x63271)+~P106(f333(f333(f247(x63271),x63272),f2(x63271)))+P106(f333(f333(f247(x63271),f89(x63271,x63272)),f2(x63271))) % 173.51/173.28 [6441]~P120(x64411)+P106(f333(f333(f246(x64411),f333(f113(x64411),x64412)),f2(x64411)))+~P106(f333(f333(f246(a1),x64412),f2(a1))) % 173.51/173.28 [6442]~P120(x64421)+P106(f333(f333(f247(x64421),f333(f113(x64421),x64422)),f2(x64421)))+~P106(f333(f333(f247(a1),x64422),f2(a1))) % 173.51/173.28 [6450]~P87(x64502)+E(x64501,f2(x64502))+~P106(f333(f333(f246(x64502),f333(f82(x64502),x64501)),f2(x64502))) % 173.51/173.28 [6526]~P139(x65261)+~P106(f333(f333(f335(x65261),x65262),f120(x65261)))+P106(f333(f333(f335(x65261),f333(f86(x65261),x65262)),f120(x65261))) % 173.51/173.28 [6559]~P120(x65591)+~P106(f333(f333(f247(x65591),f89(x65591,x65592)),f2(x65591)))+P106(f333(f333(f247(x65591),x65592),f2(x65591))) % 173.51/173.28 [6731]~P120(x67312)+~P106(f333(f333(f246(x67312),f333(f113(x67312),x67311)),f2(x67312)))+P106(f333(f333(f246(a1),x67311),f2(a1))) % 173.51/173.28 [6732]~P120(x67322)+~P106(f333(f333(f247(x67322),f333(f113(x67322),x67321)),f2(x67322)))+P106(f333(f333(f247(a1),x67321),f2(a1))) % 173.51/173.28 [7228]~P80(x72281)+~P106(f333(f333(f246(x72281),x72282),f2(x72281)))+P106(f333(f333(f246(x72281),f333(f333(f87(x72281),x72282),x72282)),f2(x72281))) % 173.51/173.28 [7229]~P80(x72291)+~P106(f333(f333(f247(x72291),x72292),f2(x72291)))+P106(f333(f333(f247(x72291),f333(f333(f87(x72291),x72292),x72292)),f2(x72291))) % 173.51/173.28 [7230]~P120(x72301)+~P106(f333(f333(f247(x72301),x72302),f2(x72301)))+P106(f333(f333(f247(x72301),f333(f333(f87(x72301),x72302),x72302)),f2(x72301))) % 173.51/173.28 [7792]~P80(x77921)+~P106(f333(f333(f246(x77921),f333(f333(f87(x77921),x77922),x77922)),f2(x77921)))+P106(f333(f333(f246(x77921),x77922),f2(x77921))) % 173.51/173.28 [7793]~P80(x77931)+~P106(f333(f333(f247(x77931),f333(f333(f87(x77931),x77932),x77932)),f2(x77931)))+P106(f333(f333(f247(x77931),x77932),f2(x77931))) % 173.51/173.28 [7794]~P120(x77941)+~P106(f333(f333(f247(x77941),f333(f333(f87(x77941),x77942),x77942)),f2(x77941)))+P106(f333(f333(f247(x77941),x77942),f2(x77941))) % 173.51/173.28 [4875]~E(x48752,f2(a910))+~E(x48751,f2(a910))+E(f333(f333(f87(a910),x48751),x48752),f2(a910)) % 173.51/173.28 [4876]~E(x48762,f85(a910))+~E(x48761,f85(a910))+E(f333(f333(f88(a910),x48761),x48762),f85(a910)) % 173.51/173.28 [4877]~E(x48772,f85(a1))+~E(x48771,f85(a1))+E(f333(f333(f88(a1),x48771),x48772),f85(a1)) % 173.51/173.28 [4932]~P122(x49322)+E(x49321,f2(x49322))+E(f333(f333(f296(x49322),x49321),x49321),f85(x49322)) % 173.51/173.28 [4933]~P64(x49332)+E(x49331,f2(x49332))+E(f333(f333(f42(x49332),x49331),x49331),f85(x49332)) % 173.51/173.28 [4934]~P123(x49342)+E(x49341,f2(x49342))+E(f333(f333(f296(x49342),x49341),x49341),f85(x49342)) % 173.51/173.28 [4953]~P80(x49531)+~E(x49532,f2(x49531))+E(f333(f333(f87(x49531),x49532),x49532),f2(x49531)) % 173.51/173.28 [4956]~P141(x49561)+~E(x49562,f85(x49561))+E(f333(f333(f88(x49561),x49562),x49562),f85(x49561)) % 173.51/173.28 [4957]~P123(x49571)+~E(x49572,f2(x49571))+E(f333(f333(f296(x49571),x49572),x49572),f2(x49571)) % 173.51/173.28 [5002]~E(x50022,f2(a910))+~E(x50021,f2(a910))+E(f333(f86(a1),f333(f111(a1),x50021)),f333(f111(a1),x50022)) % 173.51/173.28 [5021]E(x50211,f85(a910))+E(x50212,f2(a910))+~E(f333(f333(f88(a910),x50212),x50211),x50212) % 173.51/173.28 [5033]E(x50331,f2(a910))+E(x50332,f2(a910))+~E(f333(f333(f88(a910),x50332),x50331),f2(a910)) % 173.51/173.28 [5060]~E(x50602,f2(a910))+~E(x50601,f333(a123,f2(a910)))+E(f333(f333(f87(a910),x50601),x50602),f333(a123,f2(a910))) % 173.51/173.28 [5061]~E(x50611,f2(a910))+~E(x50612,f333(a123,f2(a910)))+E(f333(f333(f87(a910),x50611),x50612),f333(a123,f2(a910))) % 173.51/173.28 [5068]E(x50681,f85(a1))+E(x50682,f333(f114(a1),a108))+~E(f333(f333(f88(a1),x50681),x50682),f85(a1)) % 173.51/173.28 [5069]E(x50691,f85(a1))+E(x50692,f333(f114(a1),a108))+~E(f333(f333(f88(a1),x50692),x50691),f85(a1)) % 173.51/173.28 [5070]E(x50701,f85(a1))+E(x50701,f333(f114(a1),a108))+~E(f333(f333(f88(a1),x50702),x50701),f85(a1)) % 173.51/173.28 [5072]E(x50721,f85(a1))+E(x50721,f333(f114(a1),a108))+~E(f333(f333(f88(a1),x50721),x50722),f85(a1)) % 173.51/173.28 [5093]~P80(x50932)+E(x50931,f2(x50932))+~E(f333(f333(f87(x50932),x50931),x50931),f2(x50932)) % 173.51/173.28 [5099]~E(x50991,f333(f114(a1),a108))+~E(x50992,f333(f114(a1),a108))+E(f333(f333(f88(a1),x50991),x50992),f85(a1)) % 173.51/173.28 [5110]E(x51101,f2(a910))+E(x51102,f2(a910))+~E(f333(f333(f87(a910),x51102),x51101),f333(a123,f2(a910))) % 173.51/173.28 [5120]~P67(x51201)+~P95(x51201)+E(f333(f333(f296(x51201),x51202),f333(f114(x51201),a90)),f2(x51201)) % 173.51/173.28 [5126]~P141(x51261)+~E(x51262,f333(f86(x51261),f85(x51261)))+E(f333(f333(f88(x51261),x51262),x51262),f85(x51261)) % 173.51/173.28 [5131]~P9(x51312)+~P9(x51311)+P9(f333(f333(f87(a1),x51311),x51312)) % 173.51/173.28 [5132]~P9(x51322)+~P9(x51321)+P9(f333(f333(f88(a1),x51321),x51322)) % 173.51/173.28 [5133]~P9(x51332)+~P9(x51331)+P9(f333(f333(f42(a1),x51331),x51332)) % 173.51/173.28 [5135]~E(x51352,f2(a1))+E(x51351,f2(a1))+E(f52(x51351,x51352),f333(f333(f265(a1,a1),f2(a1)),x51351)) % 173.51/173.28 [5156]~E(x51562,f333(a123,f2(a910)))+~E(x51561,f333(a123,f2(a910)))+E(f333(f333(f88(a910),x51561),x51562),f333(a123,f2(a910))) % 173.51/173.28 [5173]E(x51731,f2(a910))+E(x51732,f333(a123,f2(a910)))+~E(f333(f333(f256(a910),x51732),x51731),f333(a123,f2(a910))) % 173.51/173.28 [5174]E(x51741,f2(a910))+E(x51741,f333(a123,f2(a910)))+~E(f333(f333(f87(a910),x51742),x51741),f333(a123,f2(a910))) % 173.51/173.28 [5175]E(x51751,f2(a910))+E(x51751,f333(a123,f2(a910)))+~E(f333(f333(f87(a910),x51751),x51752),f333(a123,f2(a910))) % 173.51/173.28 [5184]~P67(x51841)+~P95(x51841)+E(f333(f333(f296(x51841),x51842),f333(f114(x51841),a108)),f333(f86(x51841),x51842)) % 173.51/173.28 [5203]E(x52031,f333(a115,x52032))+~E(x52031,f2(a910))+P106(f333(f333(f246(a1),f2(a1)),x52032)) % 173.51/173.28 [5204]E(f333(a115,x52041),x52042)+~E(x52042,f2(a910))+P106(f333(f333(f246(a1),f2(a1)),x52041)) % 173.51/173.28 [5220]E(x52201,f333(a123,f2(a910)))+E(x52202,f333(a123,f2(a910)))+~E(f333(f333(f87(a910),x52201),x52202),f333(a123,f2(a910))) % 173.51/173.28 [5231]~E(x52311,f333(a115,x52312))+E(x52311,f2(a910))+P106(f333(f333(f246(a1),f2(a1)),x52312)) % 173.51/173.28 [5232]~E(f333(a115,x52322),x52321)+E(x52321,f2(a910))+P106(f333(f333(f246(a1),f2(a1)),x52322)) % 173.51/173.28 [5254]~P2(x52541)+E(f333(f69(x52541,f121(x52541)),x52542),f13(x52541,x52542))+~P106(f333(f67(x52541),x52542)) % 173.51/173.28 [5255]~P2(x52551)+E(f333(f69(x52551,f112(x52551)),x52552),f10(x52551,x52552))+~P106(f333(f67(x52551),x52552)) % 173.51/173.28 [5256]~P110(x52561)+E(f333(f69(x52561,f244(x52561)),x52562),f14(x52561,x52562))+~P106(f333(f67(x52561),x52562)) % 173.51/173.28 [5257]~P110(x52571)+E(f333(f69(x52571,f245(x52571)),x52572),f15(x52571,x52572))+~P106(f333(f67(x52571),x52572)) % 173.51/173.28 [5336]E(x53361,x53362)+~E(f333(f333(f23(a910),x53362),x53361),f2(a910))+~E(f333(f333(f23(a910),x53361),x53362),f2(a910)) % 173.51/173.28 [5354]P9(x53541)+~P43(x53542)+~P106(f333(f333(f335(a1),x53541),x53542)) % 173.51/173.28 [5383]~P120(x53831)+~E(f89(x53831,x53832),f85(x53831))+P106(f333(f333(f247(x53831),f2(x53831)),x53832)) % 173.51/173.28 [5394]~P95(x53941)+E(f333(f111(x53941),f333(f114(a910),x53942)),f333(f114(x53941),x53942))+P106(f333(a201,f333(f114(a1),x53942))) % 173.51/173.28 [5399]~P47(x53991,x53992)+P48(a905)+P106(f333(f67(f916(x53991,x53991)),x53992)) % 173.51/173.28 [5472]~P110(x54721)+E(f333(f69(x54721,f244(x54721)),x54722),f11(x54721,f244(x54721),x54722))+~P106(f333(f67(x54721),x54722)) % 173.51/173.28 [5473]~P110(x54731)+E(f333(f69(x54731,f245(x54731)),x54732),f12(x54731,f245(x54731),x54732))+~P106(f333(f67(x54731),x54732)) % 173.51/173.28 [5485]E(x54851,x54852)+P106(f333(f333(f247(a910),x54852),x54851))+P106(f333(f333(f247(a910),x54851),x54852)) % 173.51/173.28 [5486]E(x54861,x54862)+P106(f333(f333(f247(a1),x54862),x54861))+P106(f333(f333(f247(a1),x54861),x54862)) % 173.51/173.28 [5538]~P95(x55381)+E(f333(f111(x55381),f333(f114(a910),x55382)),f2(x55381))+~P106(f333(a201,f333(f114(a1),x55382))) % 173.51/173.28 [5541]~E(x55412,f333(a115,x55411))+E(x55411,f333(f111(a1),x55412))+~P106(f333(f333(f246(a1),f2(a1)),x55411)) % 173.51/173.28 [5542]~E(f333(a115,x55421),x55422)+E(x55421,f333(f111(a1),x55422))+~P106(f333(f333(f246(a1),f2(a1)),x55421)) % 173.51/173.28 [5543]~E(x55431,f333(a115,x55432))+E(f333(f111(a1),x55431),x55432)+~P106(f333(f333(f246(a1),f2(a1)),x55432)) % 173.51/173.28 [5553]E(x55531,f333(a115,x55532))+~E(x55532,f333(f111(a1),x55531))+~P106(f333(f333(f246(a1),f2(a1)),x55532)) % 173.51/173.28 [5554]E(f333(a115,x55541),x55542)+~E(x55541,f333(f111(a1),x55542))+~P106(f333(f333(f246(a1),f2(a1)),x55541)) % 173.51/173.28 [5593]~P87(x55932)+E(x55931,f2(x55932))+P106(f333(f333(f247(x55932),f2(x55932)),f333(f82(x55932),x55931))) % 173.51/173.28 [5658]~P120(x56581)+E(f89(x56581,x56582),f85(x56581))+~P106(f333(f333(f247(x56581),f2(x56581)),x56582)) % 173.51/173.28 [5662]~P95(x56621)+E(f333(f111(x56621),f333(f114(a910),x56622)),f2(x56621))+P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x56622))) % 173.51/173.28 [5670]~P87(x56701)+E(f333(f82(x56701),x56702),x56702)+~P106(f333(f333(f246(x56701),f2(x56701)),x56702)) % 173.51/173.28 [5671]~P87(x56711)+E(f333(f82(x56711),x56712),x56712)+~P106(f333(f333(f247(x56711),f2(x56711)),x56712)) % 173.51/173.28 [5680]E(x56801,f2(a910))+~E(f147(a910,f333(f308(a910,x56802),x56801)),f124(a910))+P106(f333(f333(f246(a910),x56801),x56802)) % 173.51/173.28 [5690]~P72(x56901)+E(f333(f333(f6(x56901,x56901),f5(x56901)),f333(f180(x56901),x56902)),f333(f173(x56901),x56902))+~P106(f333(f145(x56901),x56902)) % 173.51/173.28 [5693]~P139(x56931)+E(f333(f111(x56931),f333(a115,x56932)),f333(f113(x56931),x56932))+~P106(f333(f333(f246(a1),f2(a1)),x56932)) % 173.51/173.28 [5720]E(x57201,x57202)+P106(f333(f333(f247(a910),x57201),x57202))+~P106(f333(f333(f246(a910),x57201),x57202)) % 173.51/173.28 [5721]E(x57211,x57212)+P106(f333(f333(f247(a1),x57211),x57212))+~P106(f333(f333(f246(a1),x57211),x57212)) % 173.51/173.28 [5724]E(x57241,f85(a1))+~E(f333(f333(f88(a1),x57242),x57241),f85(a1))+~P106(f333(f333(f247(a1),f2(a1)),x57242)) % 173.51/173.28 [5725]E(x57251,f85(a1))+~E(f333(f333(f88(a1),x57251),x57252),f85(a1))+~P106(f333(f333(f247(a1),f2(a1)),x57251)) % 173.51/173.28 [5763]~P43(x57632)+P106(f333(f333(f246(a1),f2(a1)),x57631))+~P106(f333(f333(f335(a1),x57631),x57632)) % 173.51/173.28 [5782]~P61(x57821,x57822)+P40(x57821,x57822)+~P106(f333(f67(f916(x57821,x57821)),x57822)) % 173.51/173.28 [5784]~P61(x57841,x57842)+P47(x57841,x57842)+~P106(f333(f67(f916(x57841,x57841)),x57842)) % 173.51/173.28 [5826]E(x58261,f196(f917(x58262,a905)))+~P106(f333(f67(x58262),x58261))+P106(f333(f333(f247(a910),f2(a910)),f333(f41(x58262),x58261))) % 173.51/173.28 [5853]~P106(f333(x58531,x58532))+P106(f333(x58531,f2(a910)))+P106(f333(f333(f247(a910),f366(x58532,x58531)),x58532)) % 173.51/173.28 [5876]E(x58761,f2(a910))+~E(f333(f173(a910),x58762),f2(a910))+~P106(f333(f333(f335(a910),x58761),f333(f180(a910),x58762))) % 173.51/173.28 [5942]E(x59421,x59422)+~P106(f333(f333(f246(a910),x59422),x59421))+~P106(f333(f333(f246(a910),x59421),x59422)) % 173.51/173.28 [5943]E(x59431,x59432)+~P106(f333(f333(f246(a1),x59432),x59431))+~P106(f333(f333(f246(a1),x59431),x59432)) % 173.51/173.28 [5945]E(f333(f41(x59451),x59452),f2(a910))+~P106(f333(f67(x59451),x59452))+P106(f333(f333(f335(x59451),f519(x59452,x59451)),x59452)) % 173.51/173.28 [5954]E(f56(x59541,x59542),f52(x59541,x59542))+P106(f333(f333(f246(a1),f2(a1)),x59541))+~P106(f333(f333(f247(a1),f2(a1)),x59542)) % 173.51/173.28 [5979]~P106(f333(x59791,f438(x59791)))+P106(f333(x59791,f333(a115,x59792)))+~P106(f333(f333(f246(a1),f2(a1)),x59792)) % 173.51/173.28 [5981]P106(f333(f333(f246(a910),x59811),f881(x59812)))+~P106(f333(f67(a910),x59812))+~P106(f333(f333(f335(a910),x59811),x59812)) % 173.51/173.28 [5982]P106(f333(f333(f247(a910),x59821),f870(x59822)))+~P106(f333(f67(a910),x59822))+~P106(f333(f333(f335(a910),x59821),x59822)) % 173.51/173.28 [6011]E(x60111,x60112)+~P106(f333(f333(f247(a910),x60111),f333(a123,x60112)))+P106(f333(f333(f247(a910),x60111),x60112)) % 173.51/173.28 [6042]E(x60421,f333(a123,x60422))+~P106(f333(f333(f246(a910),x60421),f333(a123,x60422)))+P106(f333(f333(f246(a910),x60421),x60422)) % 173.51/173.28 [6058]P106(f333(x60581,f439(x60581)))+~P106(f333(x60581,f333(a115,x60582)))+~P106(f333(f333(f246(a1),f2(a1)),x60582)) % 173.51/173.28 [6072]~P106(f333(x60721,x60722))+~P106(f333(f333(f246(a1),f2(a1)),x60722))+P106(f333(x60721,f333(f111(a1),f383(x60721)))) % 173.51/173.28 [6084]~P87(x60842)+~E(x60841,f2(x60842))+~P106(f333(f333(f247(x60842),f2(x60842)),f333(f82(x60842),x60841))) % 173.51/173.28 [6111]~P61(x61111,x61112)+P40(x61111,f333(f293(x61111,x61111),x61112))+~P106(f333(f67(f916(x61111,x61111)),x61112)) % 173.51/173.28 [6119]~P95(x61191)+E(f333(f111(x61191),f333(f114(a910),x61192)),f333(f114(x61191),x61192))+~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x61192))) % 173.51/173.28 [6123]E(f333(a123,x61231),x61232)+~P106(f333(f333(f247(a910),x61231),x61232))+P106(f333(f333(f247(a910),f333(a123,x61231)),x61232)) % 173.51/173.28 [6139]E(f333(f333(f42(a1),x61391),x61392),f2(a1))+~P106(f333(f333(f246(a1),x61391),f2(a1)))+~P106(f333(f333(f247(a1),x61392),x61391)) % 173.51/173.28 [6149]E(f51(a1,x61491,x61492),x61491)+~P106(f333(f333(f246(a1),x61491),f2(a1)))+~P106(f333(f333(f247(a1),x61492),x61491)) % 173.51/173.28 [6163]E(f53(x61631,x61632),f52(x61631,x61632))+~P106(f333(f333(f246(a1),f2(a1)),x61631))+~P106(f333(f333(f246(a1),f2(a1)),x61632)) % 173.51/173.28 [6172]E(f333(f333(f42(a1),x61721),x61722),f2(a1))+~P106(f333(f333(f246(a1),f2(a1)),x61721))+~P106(f333(f333(f247(a1),x61721),x61722)) % 173.51/173.28 [6184]E(f51(a910,f333(f114(a910),x61841),f333(f114(a910),x61842)),f333(f114(a910),x61841))+P106(f333(a201,f333(f114(a1),x61841)))+~P106(f333(a201,f333(f114(a1),x61842))) % 173.51/173.28 [6186]E(f51(a1,x61861,x61862),x61861)+~P106(f333(f333(f246(a1),f2(a1)),x61861))+~P106(f333(f333(f247(a1),x61861),x61862)) % 173.51/173.28 [6187]E(x61871,x61872)+~P106(f333(f333(f247(a910),x61871),f333(a123,x61872)))+~P106(f333(f333(f246(a910),x61872),x61871)) % 173.51/173.28 [6201]~P80(x62011)+~P106(f333(f333(f246(x62011),x62012),f2(x62011)))+P106(f333(f333(f246(x62011),x62012),f333(f86(x62011),x62012))) % 173.51/173.28 [6202]~P120(x62021)+~P106(f333(f333(f247(x62021),x62022),f2(x62021)))+P106(f333(f333(f247(x62021),x62022),f333(f86(x62021),x62022))) % 173.51/173.28 [6212]~P8(x62121)+E(f333(f333(f70(x62121,x62121,f112(x62121)),f254(x62121)),x62122),f44(x62121,x62122))+~P106(f333(f67(x62121),x62122)) % 173.51/173.28 [6213]~P8(x62131)+E(f333(f333(f70(x62131,x62131,f121(x62131)),f196(x62131)),x62132),f43(x62131,x62132))+~P106(f333(f67(x62131),x62132)) % 173.51/173.28 [6228]~P120(x62281)+~P106(f333(f333(f246(a1),f2(a1)),x62282))+P106(f333(f333(f246(x62281),f2(x62281)),f333(f113(x62281),x62282))) % 173.51/173.28 [6229]~P119(x62291)+~P106(f333(f333(f247(a910),f2(a910)),x62292))+P106(f333(f333(f247(x62291),f2(x62291)),f333(f111(x62291),x62292))) % 173.51/173.28 [6230]~P120(x62301)+~P106(f333(f333(f247(a1),f2(a1)),x62302))+P106(f333(f333(f247(x62301),f2(x62301)),f333(f113(x62301),x62302))) % 173.51/173.28 [6233]~P9(x62332)+~P9(x62331)+E(f333(f316(a910,a1,f111(a1)),f309(a910,f333(a115,x62331),f333(a115,x62332))),f309(a1,x62331,x62332)) % 173.51/173.28 [6239]P106(f333(x62391,x62392))+~P106(f333(f333(f246(a1),f2(a1)),x62392))+~P106(f333(x62391,f333(f111(a1),f387(x62391)))) % 173.51/173.28 [6268]E(f333(f333(f87(a910),f333(f114(a910),x62681)),f333(f114(a910),x62682)),f333(f114(a910),x62681))+P106(f333(f333(f247(a1),x62681),a90))+~P106(f333(f333(f247(a1),x62682),a90)) % 173.51/173.28 [6272]~P120(x62721)+P106(f333(f333(f247(x62721),f2(x62721)),f89(x62721,x62722)))+~P106(f333(f333(f247(x62721),f2(x62721)),x62722)) % 173.51/173.28 [6283]~P4(x62831)+~P106(f333(f333(f246(x62831),x62832),f2(x62831)))+P106(f333(f333(f246(x62831),f2(x62831)),f333(f86(x62831),x62832))) % 173.51/173.28 [6284]~P4(x62841)+~P106(f333(f333(f247(x62841),x62842),f2(x62841)))+P106(f333(f333(f247(x62841),f2(x62841)),f333(f86(x62841),x62842))) % 173.51/173.28 [6287]E(x62871,f254(f917(x62872,a905)))+~E(f333(f41(x62872),x62871),f333(f41(x62872),f254(f917(x62872,a905))))+~P106(f333(f67(x62872),f254(f917(x62872,a905)))) % 173.51/173.28 [6319]~P80(x63191)+P106(f333(f333(f246(x63191),x63192),f2(x63191)))+~P106(f333(f333(f246(x63191),x63192),f333(f86(x63191),x63192))) % 173.51/173.28 [6320]~P120(x63201)+P106(f333(f333(f247(x63201),x63202),f2(x63201)))+~P106(f333(f333(f247(x63201),x63202),f333(f86(x63201),x63202))) % 173.51/173.28 [6329]~P95(x63291)+P106(f333(f333(f335(x63291),f333(f114(x63291),x63292)),f194(x63291)))+~P106(f333(f333(f246(a1),a90),x63292)) % 173.51/173.28 [6358]E(x63581,f2(a910))+~P106(f333(f333(f247(a910),x63581),f333(a123,x63582)))+P106(f333(f333(f247(a910),f343(x63582,x63581)),x63582)) % 173.51/173.28 [6380]~P120(x63801)+~P106(f333(f333(f247(x63801),f2(x63801)),f89(x63801,x63802)))+P106(f333(f333(f247(x63801),f2(x63801)),x63802)) % 173.51/173.28 [6382]~E(f333(f114(a910),x63822),f333(f114(a910),x63821))+P106(f333(f333(f246(a1),f333(f114(a1),x63821)),f2(a1)))+~P106(f333(a201,f333(f114(a1),x63822))) % 173.51/173.28 [6412]E(f333(f264(a1,a1),f56(x64121,x64122)),f333(f333(f42(a1),x64121),x64122))+~P106(f333(f333(f247(a1),x64121),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x64122)) % 173.51/173.28 [6448]E(f333(f268(a1,a1),f56(x64481,x64482)),f51(a1,x64481,x64482))+~P106(f333(f333(f247(a1),x64481),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x64482)) % 173.51/173.28 [6451]~P120(x64512)+~P106(f333(f333(f246(x64512),f2(x64512)),f333(f113(x64512),x64511)))+P106(f333(f333(f246(a1),f2(a1)),x64511)) % 173.51/173.28 [6452]~P119(x64522)+~P106(f333(f333(f247(x64522),f2(x64522)),f333(f111(x64522),x64521)))+P106(f333(f333(f247(a910),f2(a910)),x64521)) % 173.51/173.28 [6453]~P120(x64532)+~P106(f333(f333(f247(x64532),f2(x64532)),f333(f113(x64532),x64531)))+P106(f333(f333(f247(a1),f2(a1)),x64531)) % 173.51/173.28 [6456]E(f333(f264(a1,a1),f53(x64561,x64562)),f333(f333(f42(a1),x64561),x64562))+~P106(f333(f333(f246(a1),f2(a1)),x64562))+~P106(f333(f333(f247(a1),f2(a1)),x64561)) % 173.51/173.28 [6470]E(f333(f268(a1,a1),f53(x64701,x64702)),f51(a1,x64701,x64702))+~P106(f333(f333(f246(a1),f2(a1)),x64702))+~P106(f333(f333(f247(a1),f2(a1)),x64701)) % 173.51/173.28 [6485]~P4(x64851)+P106(f333(f333(f246(x64851),x64852),f2(x64851)))+~P106(f333(f333(f246(x64851),f2(x64851)),f333(f86(x64851),x64852))) % 173.51/173.28 [6486]~P4(x64861)+P106(f333(f333(f247(x64861),x64862),f2(x64861)))+~P106(f333(f333(f247(x64861),f2(x64861)),f333(f86(x64861),x64862))) % 173.51/173.28 [6513]P106(f333(f55(x65131,x65132),f56(x65131,x65132)))+~P106(f333(f333(f247(a1),x65131),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x65132)) % 173.51/173.28 [6538]P106(f333(f55(x65381,x65382),f53(x65381,x65382)))+~P106(f333(f333(f246(a1),f2(a1)),x65381))+~P106(f333(f333(f247(a1),f2(a1)),x65382)) % 173.51/173.28 [6583]~P4(x65831)+P106(f333(f333(f246(x65831),f333(f86(x65831),x65832)),f2(x65831)))+~P106(f333(f333(f246(x65831),f2(x65831)),x65832)) % 173.51/173.28 [6584]~P4(x65841)+P106(f333(f333(f247(x65841),f333(f86(x65841),x65842)),f2(x65841)))+~P106(f333(f333(f247(x65841),f2(x65841)),x65842)) % 173.51/173.28 [6600]E(f333(f333(f23(a910),f333(a115,x66001)),f333(a115,x66002)),f333(a115,f203(x66001,x66002)))+~P106(f333(f333(f246(a1),f2(a1)),x66002))+~P106(f333(f333(f246(a1),f2(a1)),x66001)) % 173.51/173.28 [6617]P106(f333(f333(f246(a1),f2(a1)),f203(x66171,x66172)))+~P106(f333(f333(f246(a1),f2(a1)),x66172))+~P106(f333(f333(f246(a1),f2(a1)),x66171)) % 173.51/173.28 [6654]~P106(f333(x66541,x66542))+P106(f333(x66541,f2(a910)))+P106(f333(x66541,f333(f333(f87(a910),f366(x66542,x66541)),f85(a910)))) % 173.51/173.28 [6738]E(f333(f114(a910),x67381),f333(f114(a910),x67382))+~P106(f333(f333(f246(a1),f333(f114(a1),x67382)),f2(a1)))+~P106(f333(a201,f333(f114(a1),x67381))) % 173.51/173.28 [6748]~E(x67481,f2(a910))+~E(f726(x67482,x67481),f2(a910))+E(f333(f150(a910,a910,f87(a910),x67481),x67482),f2(a910)) % 173.51/173.28 [6773]~P106(f333(f67(x67731),f629(x67732,x67731)))+~P106(f333(f67(f917(x67731,a905)),x67732))+P106(f333(f67(x67731),f43(f917(x67731,a905),x67732))) % 173.51/173.28 [6779]E(x67791,x67792)+P106(f333(f333(f247(a1),x67791),x67792))+~P106(f333(f333(f247(a1),x67791),f333(f333(f87(a1),x67792),f85(a1)))) % 173.51/173.28 [6780]P106(f333(f333(f246(a910),f333(a115,x67801)),f333(a115,x67802)))+~P106(f333(f333(f246(a1),f2(a1)),x67802))+~P106(f333(f333(f246(a1),x67801),x67802)) % 173.51/173.28 [6781]P106(f333(f333(f246(a910),f333(a115,x67811)),f333(a115,x67812)))+~P106(f333(f333(f247(a1),f2(a1)),x67811))+~P106(f333(f333(f246(a1),x67811),x67812)) % 173.51/173.28 [6783]P106(f333(f333(f247(a910),f333(a115,x67831)),f333(a115,x67832)))+~P106(f333(f333(f246(a1),f2(a1)),x67831))+~P106(f333(f333(f247(a1),x67831),x67832)) % 173.51/173.28 [6784]P106(f333(f333(f247(a910),f333(a115,x67841)),f333(a115,x67842)))+~P106(f333(f333(f247(a1),f2(a1)),x67842))+~P106(f333(f333(f247(a1),x67841),x67842)) % 173.51/173.28 [6795]E(f51(a910,f333(a115,x67951),f333(a115,x67952)),f333(a115,f51(a1,x67951,x67952)))+~P106(f333(f333(f246(a1),f2(a1)),x67952))+~P106(f333(f333(f246(a1),f2(a1)),x67951)) % 173.51/173.28 [6817]~P4(x68171)+~P106(f333(f333(f246(x68171),f333(f86(x68171),x68172)),f2(x68171)))+P106(f333(f333(f246(x68171),f2(x68171)),x68172)) % 173.51/173.28 [6818]~P4(x68181)+~P106(f333(f333(f247(x68181),f333(f86(x68181),x68182)),f2(x68181)))+P106(f333(f333(f247(x68181),f2(x68181)),x68182)) % 173.51/173.28 [6832]~P106(f333(f333(f247(a1),a90),x68322))+~P106(f333(f333(f247(a1),x68321),x68322))+P106(f333(f333(f247(a910),f333(f114(a910),x68321)),f333(f114(a910),x68322))) % 173.51/173.28 [6921]~P106(f333(f333(f246(a1),f2(a1)),x69211))+P106(f333(f333(f247(a910),f333(a115,x69211)),x69212))+~P106(f333(f333(f247(a1),x69211),f333(f111(a1),x69212))) % 173.51/173.28 [6937]E(x69371,f2(a1))+E(f51(a1,x69372,x69371),f2(a1))+E(f333(f333(f23(a1),f333(f86(a1),f333(f333(f42(a1),x69372),x69371))),f85(a1)),f333(f333(f42(a1),x69372),f333(f86(a1),x69371))) % 173.51/173.28 [6951]~P106(f333(f333(f246(a1),f2(a1)),x69511))+~P106(f333(f333(f247(a910),f333(a115,x69511)),x69512))+P106(f333(f333(f247(a1),x69511),f333(f111(a1),x69512))) % 173.51/173.28 [6985]~P106(f333(f333(f246(a910),f333(a115,x69851)),f333(a115,x69852)))+~P106(f333(f333(f246(a1),f2(a1)),x69852))+P106(f333(f333(f246(a1),x69851),x69852)) % 173.51/173.28 [6986]~P106(f333(f333(f246(a910),f333(a115,x69861)),f333(a115,x69862)))+~P106(f333(f333(f247(a1),f2(a1)),x69861))+P106(f333(f333(f246(a1),x69861),x69862)) % 173.51/173.28 [7014]P106(f333(f333(f246(a1),x70141),x70142))+~P106(f333(f333(f246(a910),f333(f114(a910),x70141)),f333(f114(a910),x70142)))+P106(f333(f333(f246(a1),x70141),a90)) % 173.51/173.28 [7042]P106(f333(f333(f246(a1),f2(a1)),f51(a1,x70421,x70422)))+~P106(f333(f333(f246(a1),f2(a1)),x70422))+~P106(f333(f333(f246(a1),f2(a1)),x70421)) % 173.51/173.28 [7139]P106(f333(f333(f247(a1),a90),x71391))+~P106(f333(f333(f247(a1),x71392),x71391))+~P106(f333(f333(f247(a910),f333(f114(a910),x71392)),f333(f114(a910),x71391))) % 173.51/173.28 [7191]E(f333(f333(f265(a1,a1),f333(f333(f42(a1),x71911),x71912)),f51(a1,x71911,x71912)),f56(x71911,x71912))+~P106(f333(f333(f247(a1),x71911),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x71912)) % 173.51/173.28 [7211]E(f333(f333(f265(a1,a1),f333(f333(f42(a1),x72111),x72112)),f51(a1,x72111,x72112)),f53(x72111,x72112))+~P106(f333(f333(f246(a1),f2(a1)),x72112))+~P106(f333(f333(f246(a1),f2(a1)),x72111)) % 173.51/173.28 [7262]~P97(x72622)+E(x72621,f124(x72622))+E(f333(f150(x72622,x72622,f88(x72622),f333(f149(x72622),x72621)),f333(f179(x72622),x72621)),f333(f69(x72622,f88(x72622)),f333(f180(x72622),x72621))) % 173.51/173.28 [7378]~E(x73781,f2(a910))+E(f333(f150(a910,a910,f87(a910),x73781),x73782),f2(a910))+P106(f333(f333(f335(a910),f726(x73782,x73781)),f333(f180(a910),x73782))) % 173.51/173.28 [7428]~P106(f333(f333(f246(a1),x74281),f2(a1)))+P106(f333(f333(f246(a1),f333(f333(f42(a1),x74281),x74282)),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x74282)) % 173.51/173.28 [7429]~P106(f333(f333(f247(a1),x74292),f2(a1)))+P106(f333(f333(f246(a1),f333(f333(f42(a1),x74291),x74292)),f2(a1)))+~P106(f333(f333(f246(a1),f2(a1)),x74291)) % 173.51/173.28 [7430]~P106(f333(f333(f247(a1),x74302),f2(a1)))+P106(f333(f333(f247(a1),f333(f333(f42(a1),x74301),x74302)),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x74301)) % 173.51/173.28 [7432]~P106(f333(f333(f247(a1),x74321),f2(a1)))+P106(f333(f333(f247(a1),f333(f333(f42(a1),x74321),x74322)),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x74322)) % 173.51/173.28 [7438]P106(f333(f333(f335(f917(x74381,a905)),f629(x74382,x74381)),x74382))+~P106(f333(f67(f917(x74381,a905)),x74382))+P106(f333(f67(x74381),f43(f917(x74381,a905),x74382))) % 173.51/173.28 [7529]P27(x75291,x75291,x75292,f254(f917(x75291,a905)))+~E(f333(f316(x75291,x75291,x75292),f254(f917(x75291,a905))),f254(f917(x75291,a905)))+~P106(f333(f67(x75291),f254(f917(x75291,a905)))) % 173.51/173.28 [7649]~P27(x76491,x76491,x76492,f254(f917(x76491,a905)))+E(f333(f316(x76491,x76491,x76492),f254(f917(x76491,a905))),f254(f917(x76491,a905)))+~P106(f333(f67(x76491),f254(f917(x76491,a905)))) % 173.51/173.28 [7786]E(f333(f333(f42(a1),x77861),x77862),f333(f114(a1),a108))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),x77861),x77862)),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x77861)) % 173.51/173.28 [7845]~P106(f333(f333(f247(a1),x78452),f2(a1)))+~P106(f333(f333(f247(a1),f333(f333(f42(a1),x78451),x78452)),f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x78451)) % 173.51/173.28 [7850]E(f333(f333(f87(a1),x78501),x78502),f51(a1,x78501,x78502))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),x78501),x78502)),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x78501)) % 173.51/173.28 [7853]P106(f333(f333(f247(a1),x78531),f2(a1)))+~P106(f333(f333(f247(a1),f333(f333(f42(a1),x78531),x78532)),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x78532)) % 173.51/173.28 [8560]~P110(x85601)+P16(x85601,x85602)+~P106(f333(f333(f246(x85601),f333(f333(f172(x85601),x85602),f755(x85602,x85601))),f333(f333(f172(x85601),x85602),f756(x85602,x85601)))) % 173.51/173.28 [8561]~P110(x85611)+P16(x85611,x85612)+~P106(f333(f333(f246(x85611),f333(f333(f172(x85611),x85612),f763(x85612,x85611))),f333(f333(f172(x85611),x85612),f767(x85612,x85611)))) % 173.51/173.28 [5819]E(x58191,f2(a1))+~E(f51(a1,x58192,x58191),f2(a1))+E(f333(f333(f42(a1),x58192),f333(f86(a1),x58191)),f333(f86(a1),f333(f333(f42(a1),x58192),x58191))) % 173.51/173.28 [5837]~P43(x58372)+~P43(x58371)+P43(f333(f333(f121(f917(a1,a905)),x58371),x58372)) % 173.51/173.28 [5838]~P43(x58382)+~P43(x58381)+P43(f333(f333(f112(f917(a1,a905)),x58381),x58382)) % 173.51/173.28 [5856]~P67(x58561)+~P95(x58561)+E(f333(f86(x58561),f333(f333(f296(x58561),f85(x58561)),x58562)),f333(f333(f296(x58561),f333(f114(x58561),a108)),x58562)) % 173.51/173.28 [5971]E(x59711,f2(a1))+~E(f51(a1,x59712,x59711),f2(a1))+E(f333(f333(f42(a1),f333(f86(a1),x59712)),x59711),f333(f86(a1),f333(f333(f42(a1),x59712),x59711))) % 173.51/173.28 [6105]~P110(x61051)+P16(x61051,x61052)+P106(f333(f333(f247(a910),f756(x61052,x61051)),f333(f197(f911(x61051)),x61052))) % 173.51/173.28 [6106]~P110(x61061)+P16(x61061,x61062)+P106(f333(f333(f247(a910),f767(x61062,x61061)),f333(f197(f911(x61061)),x61062))) % 173.51/173.28 [6262]~P95(x62621)+~E(f333(f114(x62621),x62622),f2(x62621))+P30(x62621,f333(f114(x62621),f333(f333(f87(a1),x62622),f333(f86(a1),a90)))) % 173.51/173.28 [6263]~P95(x62631)+~E(f333(f114(x62631),x62632),f2(x62631))+P30(x62631,f333(f114(x62631),f333(f333(f87(a1),a90),f333(f86(a1),x62632)))) % 173.51/173.28 [6265]E(f333(a57,f53(f333(f86(a1),x62651),f333(f86(a1),x62652))),f52(x62651,x62652))+P106(f333(f333(f246(a1),f2(a1)),x62651))+P106(f333(f333(f247(a1),f2(a1)),x62652)) % 173.51/173.28 [6388]~E(x63882,f2(a910))+~E(x63881,f2(a910))+P106(f333(f333(f246(a1),f333(f111(a1),x63881)),f333(f86(a1),f333(f111(a1),x63882)))) % 173.51/173.28 [6418]E(f333(f333(f87(a910),f333(f114(a910),x64181)),f333(f114(a910),x64182)),f333(f114(a910),f333(f333(f87(a1),x64181),x64182)))+P106(f333(f333(f247(a1),x64181),a90))+P106(f333(f333(f247(a1),x64182),a90)) % 173.51/173.28 [6548]~P80(x65481)+~P106(f333(f333(f246(x65481),f2(x65481)),x65482))+P106(f333(f333(f246(x65481),f333(f86(x65481),x65482)),x65482)) % 173.51/173.28 [6549]~P80(x65491)+~P106(f333(f333(f247(x65491),f2(x65491)),x65492))+P106(f333(f333(f247(x65491),f333(f86(x65491),x65492)),x65492)) % 173.51/173.28 [6724]E(f333(f333(f23(a910),f333(a115,x67241)),f333(a115,x67242)),f333(a115,f333(f333(f23(a1),x67241),x67242)))+~P106(f333(f333(f246(a1),f2(a1)),x67242))+~P106(f333(f333(f246(a1),x67242),x67241)) % 173.51/173.28 [6757]E(f333(a115,f51(a1,f333(f114(a1),x67571),f333(f114(a1),x67572))),f51(a910,f333(f114(a910),x67571),f333(f114(a910),x67572)))+P106(f333(a201,f333(f114(a1),x67571)))+P106(f333(a201,f333(f114(a1),x67572))) % 173.51/173.28 [6774]~P80(x67741)+P106(f333(f333(f246(x67741),f2(x67741)),x67742))+~P106(f333(f333(f246(x67741),f333(f86(x67741),x67742)),x67742)) % 173.51/173.28 [6775]~P80(x67751)+P106(f333(f333(f247(x67751),f2(x67751)),x67752))+~P106(f333(f333(f247(x67751),f333(f86(x67751),x67752)),x67752)) % 173.51/173.28 [6786]~P80(x67861)+~P106(f333(f333(f246(x67861),f2(x67861)),x67862))+P106(f333(f333(f246(x67861),f2(x67861)),f333(f333(f87(x67861),x67862),x67862))) % 173.51/173.28 [6789]~P80(x67891)+~P106(f333(f333(f247(x67891),f2(x67891)),x67892))+P106(f333(f333(f247(x67891),f2(x67891)),f333(f333(f87(x67891),x67892),x67892))) % 173.51/173.28 [6800]E(f333(f333(f87(a910),f333(a115,x68001)),f333(a115,x68002)),f333(a115,f333(f333(f87(a1),x68001),x68002)))+~P106(f333(f333(f246(a1),f2(a1)),x68002))+~P106(f333(f333(f246(a1),f2(a1)),x68001)) % 173.51/173.28 [6812]E(x68121,f2(a910))+P106(f333(f333(f247(a910),f2(a910)),x68122))+~P106(f333(f333(f247(a910),f2(a910)),f333(f333(f256(a910),x68122),x68121))) % 173.51/173.28 [6842]~P95(x68421)+E(f333(f114(x68421),x68422),f2(x68421))+~P30(x68421,f333(f114(x68421),f333(f333(f87(a1),a90),f333(f86(a1),x68422)))) % 173.51/173.28 [6843]~P95(x68431)+E(f333(f114(x68431),x68432),f2(x68431))+~P30(x68431,f333(f114(x68431),f333(f333(f87(a1),x68432),f333(f86(a1),a90)))) % 173.51/173.28 [6899]~P106(f333(f67(x68991),x68992))+~P106(f333(f67(x68991),f254(f917(x68991,a905))))+P106(f333(f67(x68991),f333(f86(f917(x68991,a905)),x68992))) % 173.51/173.28 [6922]~P106(f333(f333(f247(a1),f2(a1)),x69222))+~P106(f333(f333(f246(a1),x69222),x69221))+P106(f333(f333(f247(a1),f2(a1)),f333(f333(f42(a1),x69221),x69222))) % 173.51/173.28 [6923]~P106(f333(f333(f246(a1),x69231),f2(a1)))+~P106(f333(f333(f247(a1),x69232),f2(a1)))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f42(a1),x69231),x69232))) % 173.51/173.28 [6959]~P106(f333(f333(f246(a1),f2(a1)),x69592))+~P106(f333(f333(f246(a1),f2(a1)),x69591))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),x69591),x69592))) % 173.51/173.28 [6960]~P106(f333(f333(f246(a1),f2(a1)),x69602))+~P106(f333(f333(f246(a1),f2(a1)),x69601))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f88(a1),x69601),x69602))) % 173.51/173.28 [6961]~P106(f333(f333(f246(a1),f2(a1)),x69612))+~P106(f333(f333(f246(a1),f2(a1)),x69611))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f42(a1),x69611),x69612))) % 173.51/173.28 [6962]~P106(f333(f333(f246(a1),f2(a1)),x69621))+~P106(f333(f333(f247(a1),f2(a1)),x69622))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f42(a1),x69621),x69622))) % 173.51/173.28 [6963]~P106(f333(f333(f247(a910),f2(a910)),x69632))+~P106(f333(f333(f247(a910),f2(a910)),x69631))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f88(a910),x69631),x69632))) % 173.51/173.28 [7027]E(x70271,f2(a1))+E(f51(a1,x70272,x70271),f2(a1))+E(f333(f333(f23(a1),f333(f86(a1),f333(f333(f42(a1),x70272),x70271))),f85(a1)),f333(f333(f42(a1),f333(f86(a1),x70272)),x70271)) % 173.51/173.28 [7082]P106(f333(f333(f247(a910),f2(a910)),x70821))+P106(f333(f333(f247(a910),f2(a910)),x70822))+~P106(f333(f333(f247(a910),f2(a910)),f333(f333(f87(a910),x70822),x70821))) % 173.51/173.28 [7086]~P80(x70861)+P106(f333(f333(f246(x70861),f2(x70861)),x70862))+~P106(f333(f333(f246(x70861),f2(x70861)),f333(f333(f87(x70861),x70862),x70862))) % 173.51/173.28 [7087]~P80(x70871)+P106(f333(f333(f247(x70871),f2(x70871)),x70872))+~P106(f333(f333(f247(x70871),f2(x70871)),f333(f333(f87(x70871),x70872),x70872))) % 173.51/173.28 [7140]~P106(f333(f67(x71401),x71402))+P106(f333(f67(x71401),f254(f917(x71401,a905))))+~P106(f333(f67(x71401),f333(f86(f917(x71401,a905)),x71402))) % 173.51/173.28 [7203]P106(f333(f333(f246(a1),x72031),f2(a1)))+~P106(f333(f333(f247(a1),x72032),f2(a1)))+~P106(f333(f333(f246(a1),f2(a1)),f333(f333(f42(a1),x72031),x72032))) % 173.51/173.28 [7209]~P106(f333(f333(f247(a1),f2(a1)),x72091))+P106(f333(f333(f246(a1),x72091),x72092))+~P106(f333(f333(f247(a1),f2(a1)),f333(f333(f42(a1),x72092),x72091))) % 173.51/173.28 [7210]~P106(f333(f333(f246(a1),f2(a1)),x72102))+P106(f333(f333(f246(a1),x72101),x72102))+~P106(f333(f333(f247(a1),f2(a1)),f333(f333(f42(a1),x72102),x72101))) % 173.51/173.28 [7239]P106(f333(f333(f246(a1),f2(a1)),x72391))+~P106(f333(f333(f247(a1),f2(a1)),x72392))+~P106(f333(f333(f246(a1),f2(a1)),f333(f333(f42(a1),x72391),x72392))) % 173.51/173.28 [7240]P106(f333(f333(f247(a1),f2(a1)),x72401))+~P106(f333(f333(f246(a1),f2(a1)),x72402))+~P106(f333(f333(f247(a1),f2(a1)),f333(f333(f42(a1),x72402),x72401))) % 173.51/173.28 [7680]~P106(f333(f67(x76802),f254(f917(x76802,a905))))+~P106(f333(f67(x76801),f254(f917(x76801,a905))))+P106(f333(f67(f916(x76801,x76802)),f254(f917(f916(x76801,x76802),a905)))) % 173.51/173.28 [7681]~P106(f333(f67(x76812),f254(f917(x76812,a905))))+~P106(f333(f67(x76811),f254(f917(x76811,a905))))+P106(f333(f67(f918(x76811,x76812)),f254(f917(f918(x76811,x76812),a905)))) % 173.51/173.28 [7751]~P106(f333(f333(f247(a910),f333(a123,f2(a910))),x77511))+~P106(f333(f333(f247(a910),f333(a123,f2(a910))),x77512))+P106(f333(f333(f247(a910),x77511),f333(f333(f88(a910),x77512),x77511))) % 173.51/173.28 [7752]~P106(f333(f333(f247(a910),f333(a123,f2(a910))),x77521))+~P106(f333(f333(f247(a910),f333(a123,f2(a910))),x77522))+P106(f333(f333(f247(a910),x77521),f333(f333(f88(a910),x77521),x77522))) % 173.51/173.28 [7785]E(f333(f41(x77851),f254(f917(x77851,a905))),f333(a123,f2(a910)))+P106(f333(f67(x77852),f254(f917(x77852,a905))))+~P106(f333(f67(f917(x77852,x77851)),f254(f917(f917(x77852,x77851),a905)))) % 173.51/173.28 [7916]~P106(f333(f333(f246(a910),f333(a123,f2(a910))),x79161))+~P106(f333(f333(f246(a910),f333(a123,f2(a910))),x79162))+P106(f333(f333(f246(a910),f333(a123,f2(a910))),f333(f333(f88(a910),x79161),x79162))) % 173.51/173.28 [7917]~P106(f333(f333(f247(a910),f333(a123,f2(a910))),x79172))+~P106(f333(f333(f247(a910),f333(a123,f2(a910))),x79171))+P106(f333(f333(f247(a910),f333(a123,f2(a910))),f333(f333(f88(a910),x79171),x79172))) % 173.51/173.28 [8613]E(x86131,f124(x86132))+~P106(f333(f145(x86132),x86131))+E(f185(x86132,f333(f333(f8(a905,a905,x86132),a328),f333(f333(f7(x86132,x86132,a905),a330),f152(x86132,x86131))),x86131),f125(x86132,x86131)) % 173.51/173.28 [8709]~P43(x87092)+~P43(x87091)+E(f333(f316(a910,a1,f111(a1)),f333(f333(f121(f917(a910,a905)),f333(f316(a1,a910,a115),x87091)),f333(f316(a1,a910,a115),x87092))),f333(f333(f121(f917(a1,a905)),x87091),x87092)) % 173.51/173.28 [8710]~P43(x87102)+~P43(x87101)+E(f333(f316(a910,a1,f111(a1)),f333(f333(f112(f917(a910,a905)),f333(f316(a1,a910,a115),x87101)),f333(f316(a1,a910,a115),x87102))),f333(f333(f112(f917(a1,a905)),x87101),x87102)) % 173.51/173.28 [9398]~P95(x93981)+~E(f333(f114(x93981),x93982),f85(x93981))+P30(x93981,f333(f114(x93981),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f86(a1),x93982)))) % 173.51/173.28 [9644]~P95(x96441)+E(f333(f114(x96441),x96442),f85(x96441))+~P30(x96441,f333(f114(x96441),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f86(a1),x96442)))) % 173.51/173.28 [10394]E(x103941,f2(a1))+E(x103942,f2(a1))+E(f333(f270(a1,a1,a1,a1,f33(a1),f333(f88(a1),f89(a1,x103942))),f333(f333(f333(f107(f916(a1,a1)),f333(f333(a330,f89(a1,x103941)),f89(a1,x103942))),f59(x103941,x103942)),f333(f333(f269(a1,a1,f916(a1,a1)),f333(f333(f18(a1,f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),f333(f333(f8(f917(a1,f917(f916(a1,a1),f916(a1,a1))),f917(f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),a1),f18(a1,f916(a1,a1),f916(a1,a1))),f333(f333(f8(f916(a1,a1),f917(a1,f917(f916(a1,a1),f916(a1,a1))),a1),f333(f7(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f333(f333(f8(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f107(f916(a1,a1))),f333(f333(f7(a1,a1,a905),a330),f2(a1))))),f333(f333(f7(a1,a1,f916(a1,a1)),f333(f333(f8(a1,f917(a1,f916(a1,a1)),a1),f265(a1,a1)),f86(a1))),f2(a1))))),f333(f333(f7(a1,f917(a1,a1),f917(a1,f916(a1,a1))),f333(f333(f8(f917(a1,f916(a1,a1)),f917(f917(a1,a1),f917(a1,f916(a1,a1))),a1),f8(a1,f916(a1,a1),a1)),f333(f333(f8(a1,f917(a1,f916(a1,a1)),a1),f265(a1,a1)),f333(f333(f7(a1,a1,a1),f333(f333(f8(a1,f917(a1,a1),a1),f23(a1)),f86(a1))),f85(a1))))),f333(f23(a1),f333(f82(a1),x103942))))),f59(x103941,x103942)))),f52(x103941,x103942)) % 173.51/173.28 [10395]E(x103951,f2(a1))+E(x103952,f2(a1))+E(f333(f270(a1,a1,a1,a1,f33(a1),f333(f88(a1),f89(a1,x103952))),f333(f333(f333(f107(f916(a1,a1)),f333(f333(a332,f333(f333(a331,f333(f333(f247(a1),f2(a1)),x103952)),f333(f333(f246(a1),f2(a1)),x103951))),f333(f333(a331,f333(f333(f247(a1),x103952),f2(a1))),f333(f333(f247(a1),x103951),f2(a1))))),f59(x103951,x103952)),f333(f333(f269(a1,a1,f916(a1,a1)),f333(f333(f18(a1,f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),f333(f333(f8(f917(a1,f917(f916(a1,a1),f916(a1,a1))),f917(f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),a1),f18(a1,f916(a1,a1),f916(a1,a1))),f333(f333(f8(f916(a1,a1),f917(a1,f917(f916(a1,a1),f916(a1,a1))),a1),f333(f7(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f333(f333(f8(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f107(f916(a1,a1))),f333(f333(f7(a1,a1,a905),a330),f2(a1))))),f333(f333(f7(a1,a1,f916(a1,a1)),f333(f333(f8(a1,f917(a1,f916(a1,a1)),a1),f265(a1,a1)),f86(a1))),f2(a1))))),f333(f333(f7(a1,f917(a1,a1),f917(a1,f916(a1,a1))),f333(f333(f8(f917(a1,f916(a1,a1)),f917(f917(a1,a1),f917(a1,f916(a1,a1))),a1),f8(a1,f916(a1,a1),a1)),f333(f333(f8(a1,f917(a1,f916(a1,a1)),a1),f265(a1,a1)),f333(f333(f7(a1,a1,a1),f333(f333(f8(a1,f917(a1,a1),a1),f23(a1)),f86(a1))),f85(a1))))),f333(f23(a1),f333(f82(a1),x103952))))),f59(x103951,x103952)))),f52(x103951,x103952)) % 173.51/173.28 [5845]~P120(x58451)+~P95(x58451)+E(f333(f82(x58451),f333(f333(f256(x58451),f333(f114(x58451),a108)),x58452)),f85(x58451)) % 173.51/173.28 [6330]~P139(x63301)+~P106(f333(f333(f247(a1),x63302),f2(a1)))+E(f333(f86(x63301),f333(f111(x63301),f333(a115,f333(f86(a1),x63302)))),f333(f113(x63301),x63302)) % 173.51/173.28 [6531]P106(f333(f333(f246(a110),x65311),f85(a110)))+E(f333(f333(f87(a110),f85(a110)),f279(x65311,f333(f333(f42(a110),x65312),x65311))),f279(x65311,x65312))+P106(f333(f333(f247(a110),x65312),x65311)) % 173.51/173.28 [7126]~P94(x71261)+~P106(f333(f333(f335(x71261),x71262),f120(x71261)))+~E(f333(f333(f87(x71261),f333(f333(f87(x71261),f85(x71261)),x71262)),x71262),f2(x71261)) % 173.51/173.28 [7241]~P106(f333(f333(f246(a1),x72412),f2(a1)))+~P106(f333(f333(f247(a1),x72411),f2(a1)))+E(f333(f264(a1,a1),f333(a57,f53(f333(f86(a1),x72411),f333(f86(a1),x72412)))),f333(f333(f42(a1),x72411),x72412)) % 173.51/173.28 [7258]~P106(f333(f333(f246(a1),x72582),f2(a1)))+~P106(f333(f333(f247(a1),x72581),f2(a1)))+E(f333(f268(a1,a1),f333(a57,f53(f333(f86(a1),x72581),f333(f86(a1),x72582)))),f51(a1,x72581,x72582)) % 173.51/173.28 [7264]~P106(f333(f333(f247(a1),x72642),f2(a1)))+E(f333(f264(a1,a1),f333(a57,f56(f333(f86(a1),x72641),f333(f86(a1),x72642)))),f333(f333(f42(a1),x72641),x72642))+~P106(f333(f333(f247(a1),f2(a1)),x72641)) % 173.51/173.28 [7282]~P106(f333(f333(f247(a1),x72822),f2(a1)))+E(f333(f268(a1,a1),f333(a57,f56(f333(f86(a1),x72821),f333(f86(a1),x72822)))),f51(a1,x72821,x72822))+~P106(f333(f333(f247(a1),f2(a1)),x72821)) % 173.51/173.28 [7335]E(f333(f333(f42(a1),f333(f333(f256(a1),x73351),x73352)),x73351),f333(f333(f256(a1),x73351),f333(f333(f23(a910),x73352),f333(a123,f2(a910)))))+~P106(f333(f333(f247(a910),f2(a910)),x73352))+~P106(f333(f333(f247(a1),f2(a1)),x73351)) % 173.51/173.28 [7435]~P106(f333(f333(f247(a910),f2(a910)),x74351))+~P106(f333(f333(f247(a910),f2(a910)),x74352))+P106(f333(f333(f247(a910),f333(f333(f23(a910),x74351),x74352)),x74351)) % 173.51/173.28 [7436]~P106(f333(f333(f247(a910),f2(a910)),x74361))+~P106(f333(f333(f247(a910),f85(a910)),x74362))+P106(f333(f333(f247(a910),f333(f333(f42(a910),x74361),x74362)),x74361)) % 173.51/173.28 [7437]~P106(f333(f333(f247(a1),f2(a1)),x74371))+~P106(f333(f333(f247(a1),f85(a1)),x74372))+P106(f333(f333(f247(a1),f333(f333(f42(a1),x74371),x74372)),x74371)) % 173.51/173.28 [7576]E(x75761,f2(a910))+~E(x75762,f2(a1))+~P106(f333(f333(f247(a1),f2(a1)),f333(f333(f256(a1),f333(f82(a1),x75762)),x75761))) % 173.51/173.28 [7995]~E(x79952,f124(f911(x79951)))+E(f333(f197(f911(f911(x79951))),f187(x79951,x79952)),f2(a910))+~P16(a910,f333(f176(a910),f333(f333(f162(f911(x79951),a910),f197(f911(x79951))),x79952))) % 173.51/173.28 [8249]P106(f333(x82491,x82492))+~P106(f333(x82491,f333(a118,f600(x82491,x82492))))+~P106(f333(f333(f335(f917(f916(a910,a910),a905)),x82492),a109)) % 173.51/173.28 [8267]E(x82671,f124(f911(x82672)))+E(f333(f197(f911(x82672)),f333(f333(f172(f911(x82672)),x82671),f2(a910))),f333(f197(f911(f911(x82672))),f187(x82672,x82671)))+~P16(a910,f333(f176(a910),f333(f333(f162(f911(x82672),a910),f197(f911(x82672))),x82671))) % 173.51/173.28 [8411]~P41(x84111,x84112)+~P42(x84111,x84112)+P41(x84111,f333(f333(f23(f917(f916(x84111,x84111),a905)),x84112),f313(x84111,f196(f917(f916(x84111,x84111),a905))))) % 173.51/173.28 [8994]~P106(f333(f67(x89941),f333(f252(x89941),x89942)))+~P106(f333(f67(x89941),f254(f917(x89941,a905))))+P106(f333(f67(x89941),f333(f252(x89941),f333(f333(f8(a905,a905,x89941),a328),x89942)))) % 173.51/173.28 [9063]E(f333(f333(f265(a910,a910),f333(a123,f333(f333(f42(a910),f333(f333(f23(a910),x90631),x90632)),x90632))),f51(a910,f333(f333(f23(a910),x90631),x90632),x90632)),f92(f916(a910,a910),f54(x90631,x90632)))+~P106(f333(f333(f247(a910),f2(a910)),x90632))+~P106(f333(f333(f246(a910),x90632),x90631)) % 173.51/173.28 [9359]~P106(f333(f67(x93591),f333(f252(x93591),x93592)))+P106(f333(f67(x93591),f254(f917(x93591,a905))))+~P106(f333(f67(x93591),f333(f252(x93591),f333(f333(f8(a905,a905,x93591),a328),x93592)))) % 173.51/173.28 [10101]P29(x101011,x101012)+~P40(x101011,f333(f264(f917(f916(x101011,x101011),a905),f917(f916(x101011,x101011),a905)),x101012))+~P106(f333(f333(f246(f917(f916(x101011,x101011),a905)),f333(f333(f295(x101011,x101011,x101011),f333(f264(f917(f916(x101011,x101011),a905),f917(f916(x101011,x101011),a905)),x101012)),f333(f268(f917(f916(x101011,x101011),a905),f917(f916(x101011,x101011),a905)),x101012))),f333(f264(f917(f916(x101011,x101011),a905),f917(f916(x101011,x101011),a905)),x101012))) % 173.51/173.28 [7364]~P106(f333(f333(f247(a910),f2(a910)),x73642))+P106(f333(f333(f247(a910),x73641),x73642))+E(f333(a123,f333(f333(f42(a910),f333(f333(f23(a910),x73641),x73642)),x73642)),f333(f333(f42(a910),x73641),x73642)) % 173.51/173.28 [7501]~P106(f333(f333(f247(a910),f2(a910)),x75012))+~P106(f333(f333(f246(a910),x75012),x75011))+E(f333(a123,f333(f333(f42(a910),f333(f333(f23(a910),x75011),x75012)),x75012)),f333(f333(f42(a910),x75011),x75012)) % 173.51/173.28 [8474]~P95(x84741)+~P94(x84741)+~P30(x84741,f333(f114(x84741),f333(f333(f23(a1),f333(f333(f87(a1),x84742),x84742)),a108))) % 173.51/173.28 [9268]E(x92681,f2(a910))+E(f333(f333(f269(a910,a910,f916(a910,a910)),f333(f333(f8(a910,f917(a910,f916(a910,a910)),a910),f265(a910,a910)),a123)),f92(f916(a910,a910),f54(f333(f333(f23(a910),x92682),x92681),x92681))),f92(f916(a910,a910),f54(x92682,x92681)))+P106(f333(f333(f247(a910),x92682),x92681)) % 173.51/173.28 [9452]~P41(x94521,x94522)+~P55(x94521,x94522)+P106(f333(f333(f246(f917(f916(x94521,x94521),a905)),f333(f333(f295(x94521,x94521,x94521),f333(f293(x94521,x94521),x94522)),x94522)),x94522)) % 173.51/173.28 [9717]P106(f333(x97172,f687(x97172,x97171)))+P106(f333(x97171,f687(x97172,x97171)))+E(f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x97171)),f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x97172))) % 173.51/173.28 [9721]~P106(f333(x97212,f687(x97212,x97211)))+~P106(f333(x97211,f687(x97212,x97211)))+E(f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x97211)),f333(f252(a1),f333(f333(f18(a1,a905,a905),f333(f333(f8(a905,f917(a905,a905),a1),a331),f333(f246(a1),f2(a1)))),x97212))) % 173.51/173.28 [7709]~P68(x77091)+~P95(x77091)+E(f333(f333(f296(x77091),x77092),f333(f114(x77091),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))),x77092) % 173.51/173.28 [9397]~P95(x93971)+~E(f333(f114(x93971),x93972),f85(x93971))+P30(x93971,f333(f114(x93971),f333(f333(f87(a1),x93972),f333(f86(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.28 [9584]~P141(x95841)+~E(x95842,f2(x95841))+E(f333(f333(f256(x95841),x95842),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f2(x95841)) % 173.51/173.28 [9585]~P141(x95851)+~E(x95852,f85(x95851))+E(f333(f333(f256(x95851),x95852),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f85(x95851)) % 173.51/173.28 [9600]~P141(x96001)+~E(x96002,f333(f86(x96001),f85(x96001)))+E(f333(f333(f256(x96001),x96002),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f85(x96001)) % 173.51/173.28 [9645]~P95(x96451)+E(f333(f114(x96451),x96452),f85(x96451))+~P30(x96451,f333(f114(x96451),f333(f333(f87(a1),x96452),f333(f86(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.28 [10037]~P120(x100372)+E(x100371,f2(x100372))+P106(f333(f333(f247(x100372),f2(x100372)),f333(f333(f256(x100372),x100371),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.28 [10100]~P120(x101002)+~E(x101001,f2(x101002))+~P106(f333(f333(f247(x101002),f2(x101002)),f333(f333(f256(x101002),x101001),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.28 [10126]P106(f333(f333(f246(a1),x101261),f2(a1)))+P106(f333(f333(f247(a1),x101262),x101261))+E(f333(f49(x101261),f53(x101262,f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101261))),f53(x101262,x101261)) % 173.51/173.28 [10127]~P106(f333(f333(f247(a1),f2(a1)),x101271))+P106(f333(f333(f247(a1),x101272),x101271))+E(f333(f49(x101271),f53(x101272,f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101271))),f53(x101272,x101271)) % 173.51/173.28 [10128]P106(f333(f333(f246(a1),x101281),f2(a1)))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),x101282),x101281)))+E(f333(f49(x101281),f56(x101282,f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101281))),f56(x101282,x101281)) % 173.51/173.28 [10129]~P106(f333(f333(f247(a1),f2(a1)),x101291))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),x101292),x101291)))+E(f333(f49(x101291),f56(x101292,f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101291))),f56(x101292,x101291)) % 173.51/173.28 [10130]~P107(x101301)+~P106(f333(f333(f246(a1),f2(a1)),x101302))+E(f333(f111(x101301),f333(a115,f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x101302))),f333(f333(f87(x101301),f333(f111(x101301),f333(a115,x101302))),f333(f111(x101301),f333(a115,x101302)))) % 173.51/173.28 [5191]~P146(x51911,x51912,x51913)+~E(x51913,f2(a1))+P106(f333(x51911,x51912)) % 173.51/173.28 [5309]~E(f556(x53091,x53093,x53092),x53093)+E(f92(x53091,x53092),x53093)+~P106(f333(x53092,x53093)) % 173.51/173.28 [5315]~P110(x53151)+~P16(x53151,x53153)+P16(x53151,f178(x53151,x53152,x53153)) % 173.51/173.28 [5316]~P110(x53161)+~P16(x53161,x53163)+P16(x53161,f185(x53161,x53162,x53163)) % 173.51/173.28 [4885]~P71(x48852)+~E(x48853,f333(f86(x48852),x48851))+E(x48851,f333(f86(x48852),x48853)) % 173.51/173.28 [4887]~P71(x48871)+~E(f333(f86(x48871),x48873),x48872)+E(f333(f86(x48871),x48872),x48873) % 173.51/173.28 [4967]~P84(x49673)+E(x49671,x49672)+~E(f333(f86(x49673),x49671),f333(f86(x49673),x49672)) % 173.51/173.28 [4968]~P71(x49683)+E(x49681,x49682)+~E(f333(f86(x49683),x49681),f333(f86(x49683),x49682)) % 173.51/173.28 [4969]~P110(x49693)+E(x49691,x49692)+~E(f333(f289(x49693),x49691),f333(f289(x49693),x49692)) % 173.51/173.28 [4970]~P103(x49703)+E(x49701,x49702)+~E(f333(f111(x49703),x49701),f333(f111(x49703),x49702)) % 173.51/173.28 [4971]~P110(x49713)+E(x49711,x49712)+~E(f333(f307(x49713),x49711),f333(f307(x49713),x49712)) % 173.51/173.28 [4972]~P110(x49723)+E(x49721,x49722)+~E(f333(f310(x49723),x49721),f333(f310(x49723),x49722)) % 173.51/173.28 [4973]~P110(x49733)+E(x49731,x49732)+~E(f333(f290(x49733),x49731),f333(f290(x49733),x49732)) % 173.51/173.28 [4974]~P94(x49743)+E(x49741,x49742)+~E(f333(f113(x49743),x49741),f333(f113(x49743),x49742)) % 173.51/173.28 [5076]~P7(x50761)+~P106(f333(x50762,x50763))+P106(f333(f62(x50761),x50762)) % 173.51/173.28 [5112]~P7(x51123)+P106(f333(x51121,x51122))+~P106(f333(f63(x51123),x51121)) % 173.51/173.28 [5210]~P147(x52101,x52103,x52102)+~E(x52102,f2(a1))+P106(f333(x52101,f2(a1))) % 173.51/173.28 [5249]~E(x52491,f2(a910))+E(f339(x52491,x52492,x52493),f196(f917(x52493,a905)))+~E(f333(f41(x52493),x52492),f333(a123,x52491)) % 173.51/173.28 [5398]~E(x53982,f2(a910))+E(f333(f264(a910,a910),x53981),f2(a910))+~P106(f333(f54(x53983,x53982),x53981)) % 173.51/173.28 [5442]P106(f333(x54421,x54422))+~E(x54423,f333(f111(a1),x54422))+~P106(f333(x54421,f333(a115,x54423))) % 173.51/173.28 [5908]~E(x59083,f2(a910))+~P106(f333(x59081,x59082))+P106(f333(x59081,f51(a910,x59082,x59083))) % 173.51/173.28 [5967]E(f92(x59671,x59672),x59673)+~P106(f333(x59672,x59673))+P106(f333(x59672,f556(x59671,x59673,x59672))) % 173.51/173.28 [6134]~P104(x61342)+~P104(x61341)+E(f139(x61341,x61342,f140(x61341,x61343),f140(x61342,x61343)),f140(f916(x61341,x61342),x61343)) % 173.51/173.28 [6312]~E(x63123,f2(a910))+P106(f333(x63121,x63122))+~P106(f333(x63121,f51(a910,x63122,x63123))) % 173.51/173.28 [6984]E(x69841,f2(a910))+~P106(f333(x69842,f520(x69841,x69843,x69842)))+P106(f333(x69842,f51(a910,x69843,x69841))) % 173.51/173.28 [7092]~P8(x70921)+~P106(f333(f333(f246(x70921),x70922),f640(x70923,x70922,x70921)))+P106(f333(f333(f246(x70921),x70922),f44(x70921,x70923))) % 173.51/173.28 [7094]~P106(f333(x70941,x70942))+~P106(f333(x70941,f520(x70943,x70942,x70941)))+P106(f333(x70941,f51(a910,x70942,x70943))) % 173.51/173.28 [7197]E(x71971,f124(x71972))+E(f333(f333(f159(x71972),f739(x71973,x71971,x71972)),f740(x71973,x71971,x71972)),x71971)+~P106(f333(f333(f335(f911(x71972)),x71971),f169(x71972,x71973))) % 173.51/173.28 [7227]~P139(x72271)+~P106(f333(f333(f335(x72271),x72272),f120(x72271)))+P106(f333(f333(f335(x72271),f333(f333(f256(x72271),x72272),x72273)),f120(x72271))) % 173.51/173.28 [7547]P40(x75471,x75472)+~P106(f333(f333(f335(x75471),x75473),f628(x75472,x75471)))+P106(f333(f333(f335(x75471),f686(x75472,x75471,x75473)),f628(x75472,x75471))) % 173.51/173.28 [7814]E(x78141,f124(x78142))+~P106(f333(f333(f335(f911(x78142)),x78141),f169(x78142,x78143)))+P106(f333(f333(f335(f911(x78142)),f740(x78143,x78141,x78142)),f169(x78142,x78143))) % 173.51/173.28 [7867]E(x78671,f2(a910))+E(f333(f333(f87(a910),f333(f333(f88(a910),x78671),f521(x78671,x78672,x78673))),f520(x78671,x78672,x78673)),x78672)+P106(f333(x78673,f51(a910,x78672,x78671))) % 173.51/173.28 [7911]~P106(f333(x79113,x79112))+E(f333(f333(f87(a910),f333(f333(f88(a910),x79111),f521(x79111,x79112,x79113))),f520(x79111,x79112,x79113)),x79112)+P106(f333(x79113,f51(a910,x79112,x79111))) % 173.51/173.28 [8051]P106(f333(f333(f247(a1),x80511),f517(x80512,x80513,x80511)))+P106(f333(f333(x80513,f333(f333(f42(a1),x80512),x80511)),f51(a1,x80512,x80511)))+~P106(f333(f333(f247(a1),x80511),f2(a1))) % 173.51/173.28 [8323]P106(f333(f333(x83232,f333(f333(f42(a1),x83231),x83233)),f51(a1,x83231,x83233)))+~P106(f333(f333(f247(a1),x83233),f2(a1)))+P106(f333(f333(f246(a1),f517(x83231,x83232,x83233)),f2(a1))) % 173.51/173.28 [8508]E(f333(f333(f87(a1),f333(f333(f88(a1),x85081),f518(x85082,x85083,x85081))),f517(x85082,x85083,x85081)),x85082)+P106(f333(f333(x85083,f333(f333(f42(a1),x85082),x85081)),f51(a1,x85082,x85081)))+~P106(f333(f333(f247(a1),x85081),f2(a1))) % 173.51/173.28 [8759]~P106(f333(f333(x87591,f518(x87592,x87591,x87593)),f517(x87592,x87591,x87593)))+P106(f333(f333(x87591,f333(f333(f42(a1),x87592),x87593)),f51(a1,x87592,x87593)))+~P106(f333(f333(f247(a1),x87593),f2(a1))) % 173.51/173.28 [9007]~P110(x90071)+~P16(x90071,x90073)+P16(x90071,f157(x90071,x90071,f5(x90071),x90072,x90073)) % 173.51/173.28 [9531]~P126(x95312)+E(x95311,f2(x95312))+~P106(f333(f333(f246(x95312),f333(f333(f87(x95312),f333(f333(f88(x95312),x95313),x95313)),f333(f333(f88(x95312),x95311),x95311))),f2(x95312))) % 173.51/173.28 [9532]~P126(x95322)+E(x95321,f2(x95322))+~P106(f333(f333(f246(x95322),f333(f333(f87(x95322),f333(f333(f88(x95322),x95321),x95321)),f333(f333(f88(x95322),x95323),x95323))),f2(x95322))) % 173.51/173.28 [10330]~P120(x103301)+~P106(f333(f333(f247(x103301),x103302),f2(x103301)))+P106(f333(f333(f247(x103301),f333(f333(f256(x103301),x103302),f333(a123,f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x103303)))),f2(x103301))) % 173.51/173.28 [10340]~P120(x103402)+E(x103401,f2(x103402))+~P106(f333(f333(f246(x103402),f333(f333(f87(x103402),f333(f333(f256(x103402),x103403),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x103402),x103401),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f2(x103402))) % 173.51/173.28 [10341]~P120(x103412)+E(x103411,f2(x103412))+~P106(f333(f333(f246(x103412),f333(f333(f87(x103412),f333(f333(f256(x103412),x103411),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x103412),x103413),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f2(x103412))) % 173.51/173.28 [4921]~E(x49212,x49213)+~P6(x49211)+E(f333(f333(f23(x49211),x49212),x49213),f2(x49211)) % 173.51/173.28 [4922]~E(x49222,x49223)+~P71(x49221)+E(f333(f333(f23(x49221),x49222),x49223),f2(x49221)) % 173.51/173.28 [4935]~P144(x49351)+~E(x49353,f2(x49351))+E(f333(f333(f87(x49351),x49352),x49353),x49352) % 173.51/173.28 [4954]~P140(x49541)+~E(x49543,f2(x49541))+E(f333(f333(f88(x49541),x49542),x49543),f2(x49541)) % 173.51/173.28 [4955]~P140(x49551)+~E(x49552,f2(x49551))+E(f333(f333(f88(x49551),x49552),x49553),f2(x49551)) % 173.51/173.28 [4976]~E(x49763,f124(x49761))+~E(x49762,f124(x49761))+E(f333(f333(f142(x49761),x49762),x49763),f124(x49761)) % 173.51/173.28 [5066]~P144(x50662)+E(x50661,f2(x50662))+~E(f333(f333(f87(x50662),x50663),x50661),x50663) % 173.51/173.28 [5067]~P71(x50671)+~E(x50672,f333(f86(x50671),x50673))+E(f333(f333(f87(x50671),x50672),x50673),f2(x50671)) % 173.51/173.28 [5074]E(x50741,f124(x50742))+E(x50743,f2(a910))+~E(f333(f333(f183(x50742),x50743),x50741),f124(x50742)) % 173.51/173.28 [5080]~P6(x50803)+E(x50801,x50802)+~E(f333(f333(f23(x50803),x50801),x50802),f2(x50803)) % 173.51/173.28 [5081]~P71(x50813)+E(x50811,x50812)+~E(f333(f333(f23(x50813),x50811),x50812),f2(x50813)) % 173.51/173.28 [5094]~P141(x50942)+E(x50941,f2(x50942))+~E(f333(f333(f256(x50942),x50941),x50943),f2(x50942)) % 173.51/173.28 [5095]~P3(x50952)+E(x50951,f196(x50952))+~E(f333(f333(f121(x50952),x50953),x50951),f196(x50952)) % 173.51/173.28 [5096]~P3(x50962)+E(x50961,f196(x50962))+~E(f333(f333(f121(x50962),x50961),x50963),f196(x50962)) % 173.51/173.28 [5097]~P100(x50972)+E(x50971,f254(x50972))+~E(f333(f333(f112(x50972),x50973),x50971),f254(x50972)) % 173.51/173.28 [5098]~P100(x50982)+E(x50981,f254(x50982))+~E(f333(f333(f112(x50982),x50981),x50983),f254(x50982)) % 173.51/173.28 [5165]~P71(x51652)+E(x51651,f333(f86(x51652),x51653))+~E(f333(f333(f87(x51652),x51651),x51653),f2(x51652)) % 173.51/173.28 [5166]~P71(x51661)+E(f333(f86(x51661),x51662),x51663)+~E(f333(f333(f87(x51661),x51662),x51663),f2(x51661)) % 173.51/173.28 [5168]~E(x51682,x51683)+~P109(x51681)+P106(f333(f333(f246(x51681),x51682),x51683)) % 173.51/173.28 [5170]~E(x51702,x51703)+~P112(x51701)+P106(f333(f333(f246(x51701),x51702),x51703)) % 173.51/173.28 [5266]~P121(x52661)+~E(x52662,f333(f86(x52661),x52663))+E(f333(f333(f88(x52661),x52662),x52662),f333(f333(f88(x52661),x52663),x52663)) % 173.51/173.28 [5274]~P110(x52741)+~P16(x52741,x52743)+P16(x52741,f333(f333(f183(x52741),x52742),x52743)) % 173.51/173.28 [5275]~P110(x52751)+~P16(x52751,x52753)+P16(x52751,f333(f333(f146(x52751),x52752),x52753)) % 173.51/173.28 [5313]E(x53131,x53132)+E(x53133,f2(a910))+~E(f333(f333(f88(a910),x53133),x53131),f333(f333(f88(a910),x53133),x53132)) % 173.51/173.28 [5314]E(x53141,x53142)+E(x53143,f2(a910))+~E(f333(f333(f88(a910),x53141),x53143),f333(f333(f88(a910),x53142),x53143)) % 173.51/173.28 [5391]~E(x53912,x53913)+~P112(x53911)+E(f309(x53911,x53912,x53913),f333(f333(f315(x53911),x53912),f196(f917(x53911,a905)))) % 173.51/173.28 [5440]~E(x54401,x54402)+~P110(x54403)+~P106(f333(f333(f247(x54403),x54401),x54402)) % 173.51/173.28 [5441]~E(x54411,x54412)+~P112(x54413)+~P106(f333(f333(f247(x54413),x54411),x54412)) % 173.51/173.28 [5452]~P112(x54521)+E(f333(f308(x54521,x54522),x54523),f196(f917(x54521,a905)))+P106(f333(f333(f247(x54521),x54522),x54523)) % 173.51/173.28 [5498]~P112(x54981)+E(f309(x54981,x54982,x54983),f196(f917(x54981,a905)))+P106(f333(f333(f246(x54981),x54982),x54983)) % 173.51/173.28 [5499]~P112(x54991)+E(f311(x54991,x54992,x54993),f196(f917(x54991,a905)))+P106(f333(f333(f247(x54991),x54992),x54993)) % 173.51/173.28 [5500]~P112(x55001)+E(f196(f917(x55001,a905)),f309(x55001,x55002,x55003))+P106(f333(f333(f246(x55001),x55002),x55003)) % 173.51/173.28 [5501]~P112(x55011)+E(f196(f917(x55011,a905)),f311(x55011,x55012,x55013))+P106(f333(f333(f247(x55011),x55012),x55013)) % 173.51/173.28 [5508]~P101(x55081)+~E(f333(f333(f121(x55081),x55082),x55083),x55083)+P106(f333(f333(f246(x55081),x55082),x55083)) % 173.51/173.28 [5509]~P102(x55091)+~E(f333(f333(f112(x55091),x55092),x55093),x55092)+P106(f333(f333(f246(x55091),x55092),x55093)) % 173.51/173.28 [5510]~P110(x55101)+~E(f333(f333(f244(x55101),x55102),x55103),x55102)+P106(f333(f333(f246(x55101),x55102),x55103)) % 173.51/173.28 [5511]~P110(x55111)+~E(f333(f333(f245(x55111),x55112),x55113),x55113)+P106(f333(f333(f246(x55111),x55112),x55113)) % 173.51/173.28 [5530]~P110(x55301)+P16(x55301,x55302)+~P16(x55301,f333(f333(f159(x55301),x55303),x55302)) % 173.51/173.28 [5531]~P110(x55311)+P16(x55311,x55312)+~P16(x55311,f333(f333(f142(x55311),x55313),x55312)) % 173.51/173.28 [5532]~P110(x55321)+P16(x55321,x55322)+~P16(x55321,f333(f333(f142(x55321),x55322),x55323)) % 173.51/173.28 [5595]~P110(x55951)+P106(f333(f333(f246(x55951),x55953),x55952))+P106(f333(f333(f246(x55951),x55952),x55953)) % 173.51/173.28 [5600]~P110(x56001)+P106(f333(f333(f247(x56001),x56003),x56002))+P106(f333(f333(f246(x56001),x56002),x56003)) % 173.51/173.28 [5638]~P101(x56381)+E(f333(f333(f121(x56381),x56382),x56383),x56382)+~P106(f333(f333(f246(x56381),x56383),x56382)) % 173.51/173.28 [5640]~P101(x56401)+E(f333(f333(f121(x56401),x56402),x56403),x56403)+~P106(f333(f333(f246(x56401),x56402),x56403)) % 173.51/173.28 [5641]~P102(x56411)+E(f333(f333(f112(x56411),x56412),x56413),x56413)+~P106(f333(f333(f246(x56411),x56413),x56412)) % 173.51/173.28 [5643]~P102(x56431)+E(f333(f333(f112(x56431),x56432),x56433),x56432)+~P106(f333(f333(f246(x56431),x56432),x56433)) % 173.51/173.28 [5644]~P110(x56441)+E(f333(f333(f244(x56441),x56442),x56443),x56443)+~P106(f333(f333(f246(x56441),x56443),x56442)) % 173.51/173.28 [5646]~P110(x56461)+E(f333(f333(f244(x56461),x56462),x56463),x56462)+~P106(f333(f333(f246(x56461),x56462),x56463)) % 173.51/173.28 [5647]~P110(x56471)+E(f333(f333(f245(x56471),x56472),x56473),x56472)+~P106(f333(f333(f246(x56471),x56473),x56472)) % 173.51/173.28 [5649]~P110(x56491)+E(f333(f333(f245(x56491),x56492),x56493),x56493)+~P106(f333(f333(f246(x56491),x56492),x56493)) % 173.51/173.28 [5656]~P122(x56562)+E(x56561,f2(x56562))+E(f333(f333(f296(x56562),f333(f86(x56562),x56563)),f333(f86(x56562),x56561)),f333(f333(f296(x56562),x56563),x56561)) % 173.51/173.28 [5704]~P112(x57041)+E(f333(f308(x57041,x57042),x57043),f196(f917(x57041,a905)))+~P106(f333(f333(f246(x57041),x57043),x57042)) % 173.51/173.28 [5736]~P112(x57361)+E(f309(x57361,x57362,x57363),f196(f917(x57361,a905)))+~P106(f333(f333(f247(x57361),x57363),x57362)) % 173.51/173.28 [5737]~P112(x57371)+E(f311(x57371,x57372,x57373),f196(f917(x57371,a905)))+~P106(f333(f333(f246(x57371),x57373),x57372)) % 173.51/173.28 [5738]~P112(x57381)+E(f312(x57381,x57382,x57383),f196(f917(x57381,a905)))+~P106(f333(f333(f246(x57381),x57383),x57382)) % 173.51/173.28 [5788]~E(f333(f333(f23(a910),x57881),x57883),x57882)+E(x57881,f333(f333(f87(a910),x57882),x57883))+~P106(f333(f333(f246(a910),x57883),x57881)) % 173.51/173.28 [5789]~E(x57891,f333(f333(f87(a910),x57893),x57892))+E(f333(f333(f23(a910),x57891),x57892),x57893)+~P106(f333(f333(f246(a910),x57892),x57891)) % 173.51/173.28 [5834]~P106(f333(x58341,x58343))+P106(f333(x58341,f365(x58341,x58342)))+~P106(f333(f333(f246(a910),x58343),x58342)) % 173.51/173.28 [5835]~P106(f333(x58351,x58353))+P106(f333(x58351,f385(x58351,x58352)))+~P106(f333(f333(f247(a910),x58353),x58352)) % 173.51/173.28 [5843]~P112(x58431)+~E(f333(f308(x58431,x58432),x58433),f196(f917(x58431,a905)))+~P106(f333(f333(f247(x58431),x58432),x58433)) % 173.51/173.28 [5848]~P109(x58481)+~P106(f333(f333(f247(x58481),x58482),x58483))+P106(f333(f333(f246(x58481),x58482),x58483)) % 173.51/173.28 [5850]~P112(x58501)+~P106(f333(f333(f247(x58501),x58502),x58503))+P106(f333(f333(f246(x58501),x58502),x58503)) % 173.51/173.28 [5957]~P112(x59571)+~E(f309(x59571,x59572,x59573),f196(f917(x59571,a905)))+~P106(f333(f333(f246(x59571),x59572),x59573)) % 173.51/173.28 [5958]~P112(x59581)+~E(f311(x59581,x59582,x59583),f196(f917(x59581,a905)))+~P106(f333(f333(f247(x59581),x59582),x59583)) % 173.51/173.28 [5959]~P112(x59591)+~E(f196(f917(x59591,a905)),f309(x59591,x59592,x59593))+~P106(f333(f333(f246(x59591),x59592),x59593)) % 173.51/173.28 [5960]~P112(x59601)+~E(f196(f917(x59601,a905)),f311(x59601,x59602,x59603))+~P106(f333(f333(f247(x59601),x59602),x59603)) % 173.51/173.28 [5969]P106(f333(x59691,x59692))+~P106(f333(x59691,f380(x59691,x59693)))+~P106(f333(f333(f246(a910),x59692),x59693)) % 173.51/173.28 [5970]P106(f333(x59701,x59702))+~P106(f333(x59701,f386(x59701,x59703)))+~P106(f333(f333(f247(a910),x59702),x59703)) % 173.51/173.28 [5978]~E(x59781,f333(a123,x59783))+P106(f333(f333(f247(a910),x59781),f333(a123,x59782)))+~P106(f333(f333(f247(a910),x59783),x59782)) % 173.51/173.28 [5994]E(x59941,x59942)+~E(f333(f333(f88(a910),x59943),x59941),f333(f333(f88(a910),x59943),x59942))+~P106(f333(f333(f247(a910),f2(a910)),x59943)) % 173.51/173.28 [6049]E(f333(x60491,f346(x60491,x60492,x60493)),f85(a910))+~E(f333(f333(f6(x60493,a910),x60491),x60492),f85(a910))+~P106(f333(f67(x60493),x60492)) % 173.51/173.28 [6064]~P8(x60641)+P106(f333(f333(f246(x60641),x60642),f43(x60641,x60643)))+~P106(f333(f333(f335(x60641),x60642),x60643)) % 173.51/173.28 [6088]~P109(x60881)+~P106(f333(f333(f247(x60881),x60883),x60882))+~P106(f333(f333(f246(x60881),x60882),x60883)) % 173.51/173.28 [6092]~P109(x60921)+~P106(f333(f333(f247(x60921),x60923),x60922))+~P106(f333(f333(f247(x60921),x60922),x60923)) % 173.51/173.28 [6095]~P110(x60951)+~P106(f333(f333(f247(x60951),x60953),x60952))+~P106(f333(f333(f246(x60951),x60952),x60953)) % 173.51/173.28 [6096]~P110(x60961)+~P106(f333(f333(f247(x60961),x60963),x60962))+~P106(f333(f333(f247(x60961),x60962),x60963)) % 173.51/173.28 [6097]~P112(x60971)+~P106(f333(f333(f247(x60971),x60973),x60972))+~P106(f333(f333(f247(x60971),x60972),x60973)) % 173.51/173.28 [6126]~E(f333(x61262,f350(x61262,x61263,x61261)),f2(a910))+E(f333(f333(f6(x61261,a910),x61262),x61263),f2(a910))+~P106(f333(f67(x61261),x61263)) % 173.51/173.28 [6127]~E(f333(x61272,f453(x61272,x61273,x61271)),f85(a910))+E(f333(f333(f9(x61271,a910),x61272),x61273),f85(a910))+~P106(f333(f67(x61271),x61273)) % 173.51/173.28 [6143]~P111(x61431)+~P106(f333(f333(f247(x61431),x61433),x61432))+P106(f333(f333(f335(x61431),x61432),f333(f310(x61431),x61433))) % 173.51/173.28 [6144]~P111(x61441)+~P106(f333(f333(f246(x61441),x61443),x61442))+P106(f333(f333(f335(x61441),x61442),f333(f290(x61441),x61443))) % 173.51/173.28 [6145]~P111(x61451)+~P106(f333(f333(f247(x61451),x61452),x61453))+P106(f333(f333(f335(x61451),x61452),f333(f289(x61451),x61453))) % 173.51/173.28 [6146]~P111(x61461)+~P106(f333(f333(f246(x61461),x61462),x61463))+P106(f333(f333(f335(x61461),x61462),f333(f307(x61461),x61463))) % 173.51/173.28 [6158]E(f333(x61581,f354(x61581,x61582,x61583)),f333(a123,f2(a910)))+~E(f333(f333(f6(x61583,a910),x61581),x61582),f333(a123,f2(a910)))+~P106(f333(f67(x61583),x61582)) % 173.51/173.28 [6240]~P8(x62401)+~P106(f333(f333(f335(x62401),x62403),x62402))+P106(f333(f333(f246(x62401),f44(x62401,x62402)),x62403)) % 173.51/173.28 [6259]~P106(f333(f333(f246(a910),x62591),x62593))+P106(f333(f333(f246(a910),x62591),x62592))+~P106(f333(f333(f246(a910),x62593),x62592)) % 173.51/173.28 [6260]~P106(f333(f333(f246(a1),x62601),x62603))+P106(f333(f333(f246(a1),x62601),x62602))+~P106(f333(f333(f246(a1),x62603),x62602)) % 173.51/173.28 [6279]~P111(x62791)+~P106(f333(f333(f335(x62791),x62793),f333(f290(x62791),x62792)))+P106(f333(f333(f246(x62791),x62792),x62793)) % 173.51/173.28 [6280]~P111(x62801)+~P106(f333(f333(f335(x62801),x62802),f333(f307(x62801),x62803)))+P106(f333(f333(f246(x62801),x62802),x62803)) % 173.51/173.28 [6281]~P111(x62811)+~P106(f333(f333(f335(x62811),x62813),f333(f310(x62811),x62812)))+P106(f333(f333(f247(x62811),x62812),x62813)) % 173.51/173.28 [6282]~P111(x62821)+~P106(f333(f333(f335(x62821),x62822),f333(f289(x62821),x62823)))+P106(f333(f333(f247(x62821),x62822),x62823)) % 173.51/173.28 [6355]~P106(f333(x63551,x63552))+P106(f333(x63551,f823(x63551)))+~P106(f333(f333(f335(x63553),x63552),f254(f917(x63553,a905)))) % 173.51/173.28 [6394]P106(f333(x63941,x63942))+~P106(f333(x63941,f848(x63941)))+~P106(f333(f333(f335(x63943),x63942),f254(f917(x63943,a905)))) % 173.51/173.28 [6495]~P69(x64951)+P106(f333(f333(f247(x64951),f2(x64951)),f499(x64953,x64952,x64951)))+P106(f333(f333(f246(x64951),x64952),x64953)) % 173.51/173.28 [6496]~P70(x64961)+P106(f333(f333(f247(x64961),f2(x64961)),f813(x64963,x64962,x64961)))+P106(f333(f333(f246(x64961),x64962),x64963)) % 173.51/173.28 [6566]~P4(x65661)+~P106(f333(f333(f246(x65661),x65663),f333(f86(x65661),x65662)))+P106(f333(f333(f246(x65661),x65662),f333(f86(x65661),x65663))) % 173.51/173.28 [6568]~P4(x65681)+~P106(f333(f333(f247(x65681),x65683),f333(f86(x65681),x65682)))+P106(f333(f333(f247(x65681),x65682),f333(f86(x65681),x65683))) % 173.51/173.28 [6580]~P106(f333(f333(f247(a910),x65801),x65803))+~P106(f333(f333(f247(a910),x65803),x65802))+P106(f333(f333(f247(a910),f333(a123,x65801)),x65802)) % 173.51/173.28 [6605]~P119(x66051)+P106(f333(f333(f246(x66051),f333(f111(x66051),x66052)),f333(f111(x66051),x66053)))+~P106(f333(f333(f246(a910),x66052),x66053)) % 173.51/173.28 [6606]~P120(x66061)+P106(f333(f333(f246(x66061),f333(f113(x66061),x66062)),f333(f113(x66061),x66063)))+~P106(f333(f333(f246(a1),x66062),x66063)) % 173.51/173.28 [6608]~P120(x66081)+P106(f333(f333(f247(x66081),f333(f113(x66081),x66082)),f333(f113(x66081),x66083)))+~P106(f333(f333(f247(a1),x66082),x66083)) % 173.51/173.28 [6609]~P119(x66091)+P106(f333(f333(f247(x66091),f333(f111(x66091),x66092)),f333(f111(x66091),x66093)))+~P106(f333(f333(f247(a910),x66092),x66093)) % 173.51/173.28 [6615]~P110(x66151)+E(f333(f333(f121(f917(x66151,a905)),f333(f289(x66151),x66152)),f333(f308(x66151,x66152),x66153)),f333(f289(x66151),x66153))+~P106(f333(f333(f246(x66151),x66152),x66153)) % 173.51/173.28 [6645]~P4(x66451)+~P106(f333(f333(f246(x66451),x66453),x66452))+P106(f333(f333(f246(x66451),f333(f86(x66451),x66452)),f333(f86(x66451),x66453))) % 173.51/173.28 [6647]~P84(x66471)+~P106(f333(f333(f246(x66471),x66473),x66472))+P106(f333(f333(f246(x66471),f333(f86(x66471),x66472)),f333(f86(x66471),x66473))) % 173.51/173.28 [6648]~P4(x66481)+~P106(f333(f333(f247(x66481),x66483),x66482))+P106(f333(f333(f247(x66481),f333(f86(x66481),x66482)),f333(f86(x66481),x66483))) % 173.51/173.28 [6682]~P110(x66821)+E(f333(f333(f121(f917(x66821,a905)),f333(f289(x66821),x66822)),f309(x66821,x66822,x66823)),f333(f307(x66821),x66823))+~P106(f333(f333(f246(x66821),x66822),x66823)) % 173.51/173.28 [6683]~P110(x66831)+E(f333(f333(f121(f917(x66831,a905)),f333(f307(x66831),x66832)),f311(x66831,x66832,x66833)),f333(f307(x66831),x66833))+~P106(f333(f333(f246(x66831),x66832),x66833)) % 173.51/173.28 [6684]~P110(x66841)+E(f333(f333(f121(f917(x66841,a905)),f333(f307(x66841),x66842)),f312(x66841,x66842,x66843)),f333(f289(x66841),x66843))+~P106(f333(f333(f247(x66841),x66842),x66843)) % 173.51/173.28 [6719]~P110(x67191)+E(f333(f333(f121(f917(x67191,a905)),f333(f308(x67191,x67192),x67193)),f333(f290(x67191),x67193)),f333(f290(x67191),x67192))+~P106(f333(f333(f246(x67191),x67192),x67193)) % 173.51/173.28 [6869]~P110(x68691)+E(f333(f333(f121(f917(x68691,a905)),f309(x68691,x68692,x68693)),f333(f310(x68691),x68693)),f333(f290(x68691),x68692))+~P106(f333(f333(f246(x68691),x68692),x68693)) % 173.51/173.28 [6870]~P110(x68701)+E(f333(f333(f121(f917(x68701,a905)),f311(x68701,x68702,x68703)),f333(f310(x68701),x68703)),f333(f310(x68701),x68702))+~P106(f333(f333(f246(x68701),x68702),x68703)) % 173.51/173.28 [6871]~P110(x68711)+E(f333(f333(f121(f917(x68711,a905)),f312(x68711,x68712,x68713)),f333(f290(x68711),x68713)),f333(f310(x68711),x68712))+~P106(f333(f333(f247(x68711),x68712),x68713)) % 173.51/173.28 [6890]P106(f333(x68901,x68902))+~P106(f333(f333(f246(a910),x68902),x68903))+P106(f333(f333(f335(a910),f380(x68901,x68903)),f309(a910,f2(a910),x68903))) % 173.51/173.28 [6924]E(x69241,x69242)+~E(f333(f333(f172(x69243),x69241),f684(x69243,x69242,x69241)),f333(f333(f172(x69243),x69242),f684(x69243,x69242,x69241)))+~E(f333(f197(f911(x69243)),x69241),f333(f197(f911(x69243)),x69242)) % 173.51/173.28 [6929]~E(x69293,f333(f333(f42(a910),x69291),x69292))+~P106(f333(f333(f247(a910),f2(a910)),x69292))+P106(f333(f333(f247(a910),x69291),f333(f333(f88(a910),x69292),f333(a123,x69293)))) % 173.51/173.28 [6945]~P106(f333(x69451,x69453))+~P106(f333(f333(f246(a910),x69453),x69452))+P106(f333(f333(f335(a910),f365(x69451,x69452)),f309(a910,f2(a910),x69452))) % 173.51/173.28 [6982]~P106(f333(x69821,x69823))+P106(f333(x69821,f381(x69821,x69822)))+~P106(f333(f333(f335(a910),x69823),f309(a910,f2(a910),x69822))) % 173.51/173.28 [7000]~P119(x70003)+~P106(f333(f333(f246(x70003),f333(f111(x70003),x70001)),f333(f111(x70003),x70002)))+P106(f333(f333(f246(a910),x70001),x70002)) % 173.51/173.28 [7001]~P120(x70013)+~P106(f333(f333(f246(x70013),f333(f113(x70013),x70011)),f333(f113(x70013),x70012)))+P106(f333(f333(f246(a1),x70011),x70012)) % 173.51/173.28 [7003]~P119(x70033)+~P106(f333(f333(f247(x70033),f333(f111(x70033),x70031)),f333(f111(x70033),x70032)))+P106(f333(f333(f247(a910),x70031),x70032)) % 173.51/173.28 [7004]~P120(x70043)+~P106(f333(f333(f247(x70043),f333(f113(x70043),x70041)),f333(f113(x70043),x70042)))+P106(f333(f333(f247(a1),x70041),x70042)) % 173.51/173.28 [7021]~P119(x70211)+~P106(f333(f333(f247(x70211),f85(x70211)),x70212))+P106(f333(f333(f247(x70211),f85(x70211)),f333(f333(f256(x70211),x70212),f333(a123,x70213)))) % 173.51/173.28 [7023]~P4(x70231)+~P106(f333(f333(f246(x70231),f333(f86(x70231),x70233)),f333(f86(x70231),x70232)))+P106(f333(f333(f246(x70231),x70232),x70233)) % 173.51/173.28 [7024]~P84(x70241)+~P106(f333(f333(f246(x70241),f333(f86(x70241),x70243)),f333(f86(x70241),x70242)))+P106(f333(f333(f246(x70241),x70242),x70243)) % 173.51/173.28 [7025]~P4(x70251)+~P106(f333(f333(f247(x70251),f333(f86(x70251),x70253)),f333(f86(x70251),x70252)))+P106(f333(f333(f247(x70251),x70252),x70253)) % 173.51/173.28 [7051]P106(f333(x70511,x70512))+~P106(f333(x70511,f382(x70511,x70513)))+~P106(f333(f333(f335(a910),x70512),f309(a910,f2(a910),x70513))) % 173.51/173.28 [7070]~P69(x70701)+P106(f333(f333(f247(x70701),f499(x70703,x70702,x70701)),f85(x70701)))+P106(f333(f333(f246(x70701),x70702),x70703)) % 173.51/173.28 [7089]~E(f51(a910,x70893,x70892),f51(a910,x70891,x70892))+E(f333(f333(f87(a910),x70891),f333(f333(f88(a910),x70892),f522(x70891,x70892,x70893))),x70893)+~P106(f333(f333(f246(a910),x70891),x70893)) % 173.51/173.28 [7145]E(f333(f333(f6(x71451,a910),x71452),x71453),f2(a910))+~P106(f333(f67(x71451),x71453))+P106(f333(f333(f335(x71451),f350(x71452,x71453,x71451)),x71453)) % 173.51/173.28 [7146]E(f333(f333(f9(x71461,a910),x71462),x71463),f85(a910))+~P106(f333(f67(x71461),x71463))+P106(f333(f333(f335(x71461),f453(x71462,x71463,x71461)),x71463)) % 173.51/173.28 [7168]~P110(x71681)+~P106(f333(f333(f246(x71681),x71682),x71683))+P106(f333(f333(f246(f917(x71681,a905)),f333(f289(x71681),x71682)),f333(f289(x71681),x71683))) % 173.51/173.28 [7169]~P112(x71691)+~P106(f333(f333(f246(x71691),x71692),x71693))+P106(f333(f333(f246(f917(x71691,a905)),f333(f307(x71691),x71692)),f333(f307(x71691),x71693))) % 173.51/173.28 [7170]~P110(x71701)+~P106(f333(f333(f246(x71701),x71703),x71702))+P106(f333(f333(f246(f917(x71701,a905)),f333(f310(x71701),x71702)),f333(f310(x71701),x71703))) % 173.51/173.28 [7171]~P112(x71711)+~P106(f333(f333(f246(x71711),x71713),x71712))+P106(f333(f333(f246(f917(x71711,a905)),f333(f290(x71711),x71712)),f333(f290(x71711),x71713))) % 173.51/173.28 [7172]~P110(x71721)+~P106(f333(f333(f247(x71721),x71722),x71723))+P106(f333(f333(f247(f917(x71721,a905)),f333(f289(x71721),x71722)),f333(f289(x71721),x71723))) % 173.51/173.28 [7183]~P8(x71831)+P106(f333(f333(f246(x71831),x71832),f44(x71831,x71833)))+P106(f333(f333(f335(x71831),f640(x71833,x71832,x71831)),x71833)) % 173.51/173.28 [7189]~P4(x71891)+P106(f333(f333(f246(x71891),f333(f333(f23(x71891),x71892),x71893)),f2(x71891)))+~P106(f333(f333(f246(x71891),x71892),x71893)) % 173.51/173.28 [7190]~P4(x71901)+P106(f333(f333(f247(x71901),f333(f333(f23(x71901),x71902),x71903)),f2(x71901)))+~P106(f333(f333(f247(x71901),x71902),x71903)) % 173.51/173.28 [7231]P106(f333(x72311,x72312))+P106(f333(f333(f246(a910),f382(x72311,x72313)),x72313))+~P106(f333(f333(f335(a910),x72312),f309(a910,f2(a910),x72313))) % 173.51/173.28 [7271]~E(f333(f333(f6(x72711,a910),x72712),x72713),f85(a910))+~P106(f333(f67(x72711),x72713))+P106(f333(f333(f335(x72711),f346(x72712,x72713,x72711)),x72713)) % 173.51/173.28 [7272]~P106(f333(x72721,x72723))+P106(f333(f333(f246(a910),f381(x72721,x72722)),x72722))+~P106(f333(f333(f335(a910),x72723),f309(a910,f2(a910),x72722))) % 173.51/173.28 [7312]~P8(x73121)+P106(f333(f333(f335(x73121),f641(x73123,x73122,x73121)),x73122))+P106(f333(f333(f246(x73121),f43(x73121,x73122)),x73123)) % 173.51/173.28 [7346]~E(f333(f333(f6(x73461,a910),x73462),x73463),f333(a123,f2(a910)))+~P106(f333(f67(x73461),x73463))+P106(f333(f333(f335(x73461),f354(x73462,x73463,x73461)),x73463)) % 173.51/173.28 [7357]E(x73571,f2(a910))+P106(f333(x73572,f51(a910,x73573,x73571)))+P106(f333(f333(f247(a910),f520(x73571,x73573,x73572)),x73571)) % 173.51/173.28 [7464]~P106(f333(x74641,x74642))+P106(f333(x74641,f51(a910,x74642,x74643)))+P106(f333(f333(f247(a910),f520(x74643,x74642,x74641)),x74643)) % 173.51/173.28 [7580]E(x75801,f124(x75802))+~P106(f333(f333(f335(f911(x75802)),x75801),f169(x75802,x75803)))+P106(f333(f333(f335(x75802),f739(x75803,x75801,x75802)),x75803)) % 173.51/173.28 [7602]~P110(x76021)+E(f333(f333(f121(f917(x76021,a905)),f333(f333(f315(x76021),x76022),f196(f917(x76021,a905)))),f312(x76021,x76022,x76023)),f333(f308(x76021,x76022),x76023))+~P106(f333(f333(f247(x76021),x76022),x76023)) % 173.51/173.28 [7625]~P110(x76251)+E(f333(f333(f121(f917(x76251,a905)),f333(f333(f315(x76251),x76252),f196(f917(x76251,a905)))),f311(x76251,x76252,x76253)),f309(x76251,x76252,x76253))+~P106(f333(f333(f246(x76251),x76252),x76253)) % 173.51/173.28 [7731]~P110(x77311)+P106(f333(f333(f246(x77311),x77312),x77313))+~P106(f333(f333(f246(f917(x77311,a905)),f333(f310(x77311),x77313)),f333(f310(x77311),x77312))) % 173.51/173.28 [7732]~P112(x77321)+P106(f333(f333(f246(x77321),x77322),x77323))+~P106(f333(f333(f246(f917(x77321,a905)),f333(f290(x77321),x77323)),f333(f290(x77321),x77322))) % 173.51/173.28 [7733]~P110(x77331)+P106(f333(f333(f246(x77331),x77332),x77333))+~P106(f333(f333(f246(f917(x77331,a905)),f333(f289(x77331),x77332)),f333(f289(x77331),x77333))) % 173.51/173.28 [7734]~P112(x77341)+P106(f333(f333(f246(x77341),x77342),x77343))+~P106(f333(f333(f246(f917(x77341,a905)),f333(f307(x77341),x77342)),f333(f307(x77341),x77343))) % 173.51/173.28 [7735]~P110(x77351)+P106(f333(f333(f247(x77351),x77352),x77353))+~P106(f333(f333(f247(f917(x77351,a905)),f333(f289(x77351),x77352)),f333(f289(x77351),x77353))) % 173.51/173.28 [7758]~P4(x77581)+~P106(f333(f333(f246(x77581),f333(f333(f23(x77581),x77582),x77583)),f2(x77581)))+P106(f333(f333(f246(x77581),x77582),x77583)) % 173.51/173.28 [7759]~P4(x77591)+~P106(f333(f333(f247(x77591),f333(f333(f23(x77591),x77592),x77593)),f2(x77591)))+P106(f333(f333(f247(x77591),x77592),x77593)) % 173.51/173.28 [7918]E(x79181,f2(a910))+~E(f333(f150(a910,a910,f87(a910),x79182),x79183),f2(a910))+~P106(f333(f333(f335(a910),x79181),f333(f180(a910),x79183))) % 173.51/173.28 [7922]~P8(x79221)+~P106(f333(f333(f246(x79221),f641(x79223,x79222,x79221)),x79223))+P106(f333(f333(f246(x79221),f43(x79221,x79222)),x79223)) % 173.51/173.28 [8077]P106(f333(f333(f246(a1),f2(a1)),f512(x80771,x80772,x80773)))+P106(f333(f333(x80772,f333(f333(f42(a1),x80771),x80773)),f51(a1,x80771,x80773)))+~P106(f333(f333(f247(a1),f2(a1)),x80773)) % 173.51/173.28 [8171]E(x81711,x81712)+~E(f333(f197(f911(x81713)),x81711),f333(f197(f911(x81713)),x81712))+~P106(f333(f333(f269(x81713,x81713,a905),a330),f710(x81713,x81711,x81712))) % 173.51/173.28 [8240]~P40(x82402,x82403)+E(x82401,f196(f917(x82402,a905)))+~P106(f333(f333(f246(f917(x82402,a905)),x82401),f333(f292(x82402,x82402,x82403),x82401))) % 173.51/173.28 [8269]~P70(x82691)+~P106(f333(f333(f246(x82691),x82692),f333(f333(f87(x82691),x82693),f813(x82693,x82692,x82691))))+P106(f333(f333(f246(x82691),x82692),x82693)) % 173.51/173.28 [8305]P56(x83051,x83052,x83053)+P106(f333(f333(f335(x83051),f561(x83053,x83052,x83051)),x83052))+P106(f333(f333(f335(f916(x83051,x83051)),f562(x83053,x83052,x83051)),x83053)) % 173.51/173.28 [8326]P106(f333(f333(x83262,f333(f333(f42(a1),x83261),x83263)),f51(a1,x83261,x83263)))+~P106(f333(f333(f247(a1),f2(a1)),x83263))+P106(f333(f333(f247(a1),f512(x83261,x83262,x83263)),x83263)) % 173.51/173.28 [8351]E(f333(f316(a910,a910,f333(f333(f7(a910,a910,a910),f23(a910)),x83511)),f333(f308(a910,x83512),x83513)),f196(f917(a910,a905)))+P106(f333(f333(f247(a910),x83511),x83513))+P106(f333(f333(f247(a910),x83512),x83513)) % 173.51/173.28 [8463]E(f333(f316(a910,a910,f333(f333(f7(a910,a910,a910),f23(a910)),x84631)),f333(f308(a910,x84632),x84633)),f333(f333(f315(a910),f2(a910)),f196(f917(a910,a905))))+P106(f333(f333(f247(a910),x84631),x84633))+~P106(f333(f333(f247(a910),x84632),x84633)) % 173.51/173.28 [8477]~P110(x84771)+E(f157(x84771,x84771,f5(x84771),x84772,x84773),x84773)+~P106(f333(f333(f335(x84771),x84772),f333(f180(x84771),x84773))) % 173.51/173.28 [8490]P27(x84901,x84901,x84902,x84903)+~P106(f333(f67(x84901),x84903))+~P106(f333(f333(f246(f917(x84901,a905)),x84903),f333(f316(x84901,x84901,x84902),x84903))) % 173.51/173.28 [8515]E(f333(f333(f87(a1),f333(f333(f88(a1),x85151),f513(x85152,x85153,x85151))),f512(x85152,x85153,x85151)),x85152)+P106(f333(f333(x85153,f333(f333(f42(a1),x85152),x85151)),f51(a1,x85152,x85151)))+~P106(f333(f333(f247(a1),f2(a1)),x85151)) % 173.51/173.28 [8766]~P106(f333(f333(x87661,f513(x87662,x87661,x87663)),f512(x87662,x87661,x87663)))+P106(f333(f333(x87661,f333(f333(f42(a1),x87662),x87663)),f51(a1,x87662,x87663)))+~P106(f333(f333(f247(a1),f2(a1)),x87663)) % 173.51/173.28 [9677]~P106(f333(f67(x96771),x96772))+~P106(f333(f333(f335(x96771),x96773),x96772))+P106(f333(f333(f247(a910),f333(f41(x96771),f333(f333(f23(f917(x96771,a905)),x96772),f333(f333(f315(x96771),x96773),f196(f917(x96771,a905)))))),f333(f41(x96771),x96772))) % 173.51/173.28 [10281]P56(x102811,x102812,x102813)+~P106(f333(f333(f269(x102811,x102811,a905),f333(f333(f7(x102811,f917(x102811,a905),f917(x102811,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x102811,a905),f917(x102811,a905)),x102811),f8(a905,a905,x102811)),f333(f333(f8(a905,f917(a905,a905),x102811),a331),f333(f333(f7(x102811,f917(x102811,a905),a905),f335(x102811)),x102812)))),f333(f333(f7(x102811,f917(x102811,a905),a905),f335(x102811)),x102812))),f562(x102813,x102812,x102811)))+P106(f333(f333(f335(x102811),f561(x102813,x102812,x102811)),x102812)) % 173.51/173.28 [5617]~P122(x56172)+E(x56171,f2(x56172))+E(f333(f333(f296(x56172),x56173),f333(f86(x56172),x56171)),f333(f86(x56172),f333(f333(f296(x56172),x56173),x56171))) % 173.51/173.28 [5752]~E(x57523,f196(f917(x57521,a905)))+~E(x57522,f196(f917(x57521,a905)))+E(f333(f333(f121(f917(x57521,a905)),x57522),x57523),f196(f917(x57521,a905))) % 173.51/173.28 [5808]~E(x58083,f2(a910))+~P106(f333(x58081,f2(a910)))+P106(f333(x58081,f333(f333(f42(a910),x58082),x58083))) % 173.51/173.28 [5949]~P70(x59492)+E(x59491,f2(x59492))+E(f333(f333(f296(x59492),f333(f82(x59492),x59493)),f333(f82(x59492),x59491)),f333(f82(x59492),f333(f333(f296(x59492),x59493),x59491))) % 173.51/173.28 [6115]~P106(f333(f67(x61151),x61153))+E(f333(f41(x61151),f333(f333(f315(x61151),x61152),x61153)),f333(a123,f333(f41(x61151),x61153)))+P106(f333(f333(f335(x61151),x61152),x61153)) % 173.51/173.28 [6190]~E(x61902,f2(a910))+P106(f333(x61901,f2(a910)))+~P106(f333(x61901,f333(f333(f42(a910),x61903),x61902))) % 173.51/173.28 [6207]~P106(f333(f67(x62071),x62073))+E(f333(f41(x62071),f333(f333(f315(x62071),x62072),x62073)),f333(f41(x62071),x62073))+~P106(f333(f333(f335(x62071),x62072),x62073)) % 173.51/173.28 [6242]~P106(f333(f67(x62421),x62423))+E(f333(f41(x62421),f333(f333(f315(x62421),x62422),x62423)),f333(f333(f87(a910),f85(a910)),f333(f41(x62421),x62423)))+P106(f333(f333(f335(x62421),x62422),x62423)) % 173.51/173.28 [6356]E(f333(f333(f87(a910),x63561),f351(x63561,x63562,x63563)),x63562)+~P106(f333(x63563,f2(a910)))+P106(f333(x63563,f333(f333(f23(a910),x63562),x63561))) % 173.51/173.28 [6357]E(f333(f333(f87(a910),x63571),f353(x63571,x63572,x63573)),x63572)+~P106(f333(x63573,f2(a910)))+P106(f333(x63573,f333(f333(f23(a910),x63572),x63571))) % 173.51/173.28 [6404]~P8(x64041)+~P106(f333(f67(x64041),x64043))+E(f333(f333(f70(x64041,x64041,f121(x64041)),x64042),x64043),f333(f333(f121(x64041),x64042),f43(x64041,x64043))) % 173.51/173.28 [6405]~P8(x64051)+~P106(f333(f67(x64051),x64053))+E(f333(f333(f70(x64051,x64051,f112(x64051)),x64052),x64053),f333(f333(f112(x64051),x64052),f44(x64051,x64053))) % 173.51/173.28 [6411]~P95(x64111)+~E(f333(f114(x64111),x64112),f333(f114(x64111),x64113))+P30(x64111,f333(f114(x64111),f333(f333(f87(a1),x64112),f333(f86(a1),x64113)))) % 173.51/173.28 [6420]~P139(x64201)+E(f333(f333(f23(x64201),f333(f111(x64201),x64202)),f333(f111(x64201),x64203)),f333(f111(x64201),f333(f333(f23(a910),x64202),x64203)))+~P106(f333(f333(f246(a910),x64203),x64202)) % 173.51/173.28 [6506]E(f333(f333(f87(a910),x65061),f351(x65061,x65062,x65063)),x65062)+P106(f333(f333(f247(a910),x65062),x65061))+P106(f333(x65063,f333(f333(f23(a910),x65062),x65061))) % 173.51/173.28 [6507]E(f333(f333(f87(a910),x65071),f353(x65071,x65072,x65073)),x65072)+P106(f333(f333(f247(a910),x65072),x65071))+P106(f333(x65073,f333(f333(f23(a910),x65072),x65071))) % 173.51/173.28 [6523]~P120(x65231)+E(f333(f333(f88(x65231),f333(f82(x65231),x65232)),x65233),f333(f82(x65231),f333(f333(f88(x65231),x65232),x65233)))+~P106(f333(f333(f246(x65231),f2(x65231)),x65233)) % 173.51/173.28 [6524]~P69(x65241)+E(f333(f333(f296(x65241),f333(f82(x65241),x65242)),x65243),f333(f82(x65241),f333(f333(f296(x65241),x65242),x65243)))+~P106(f333(f333(f247(x65241),f2(x65241)),x65243)) % 173.51/173.28 [6532]~P2(x65321)+~P106(f333(f67(x65321),x65323))+E(f333(f333(f70(x65321,x65321,f121(x65321)),x65322),x65323),f13(x65321,f333(f333(f315(x65321),x65322),x65323))) % 173.51/173.28 [6533]~P2(x65331)+~P106(f333(f67(x65331),x65333))+E(f333(f333(f70(x65331,x65331,f112(x65331)),x65332),x65333),f10(x65331,f333(f333(f315(x65331),x65332),x65333))) % 173.51/173.28 [6534]~P110(x65341)+~P106(f333(f67(x65341),x65343))+E(f333(f333(f70(x65341,x65341,f244(x65341)),x65342),x65343),f14(x65341,f333(f333(f315(x65341),x65342),x65343))) % 173.51/173.28 [6535]~P110(x65351)+~P106(f333(f67(x65351),x65353))+E(f333(f333(f70(x65351,x65351,f245(x65351)),x65352),x65353),f15(x65351,f333(f333(f315(x65351),x65352),x65353))) % 173.51/173.28 [6582]E(x65821,f124(x65822))+~E(f187(x65822,x65823),f124(f911(x65822)))+~P106(f333(f333(f335(f911(x65822)),x65821),f333(f180(f911(x65822)),x65823))) % 173.51/173.28 [6623]~P106(f333(f145(x66231),x66233))+P106(f333(f333(f335(x66231),x66232),f333(f180(x66231),x66233)))+P106(f333(f145(x66231),f333(f333(f159(x66231),x66232),x66233))) % 173.51/173.28 [6634]~P97(x66341)+~P106(f333(f67(x66341),x66343))+E(f333(f69(x66341,f88(x66341)),f333(f333(f315(x66341),x66342),x66343)),f333(f333(f70(x66341,x66341,f88(x66341)),x66342),x66343)) % 173.51/173.28 [6656]~P110(x66561)+~P106(f333(f67(x66561),x66563))+E(f11(x66561,f244(x66561),f333(f333(f315(x66561),x66562),x66563)),f333(f333(f70(x66561,x66561,f244(x66561)),x66562),x66563)) % 173.51/173.28 [6657]~P110(x66571)+~P106(f333(f67(x66571),x66573))+E(f12(x66571,f245(x66571),f333(f333(f315(x66571),x66572),x66573)),f333(f333(f70(x66571,x66571,f245(x66571)),x66572),x66573)) % 173.51/173.28 [6659]P106(f333(x66591,f2(a910)))+~P106(f333(f333(f247(a910),x66592),x66593))+~P106(f333(x66591,f333(f333(f23(a910),x66592),x66593))) % 173.51/173.28 [6680]~P87(x66801)+P106(f333(f333(f246(x66801),x66802),x66803))+~P106(f333(f333(f246(x66801),f333(f82(x66801),x66802)),x66803)) % 173.51/173.28 [6681]~P120(x66811)+P106(f333(f333(f247(x66811),x66812),x66813))+~P106(f333(f333(f247(x66811),f333(f82(x66811),x66812)),x66813)) % 173.51/173.28 [6698]E(x66981,f124(x66982))+E(f333(f149(x66982),f333(f333(f146(x66982),x66983),x66981)),f333(f333(f172(x66982),x66981),x66983))+~P106(f333(f333(f247(a910),x66983),f333(f197(f911(x66982)),x66981))) % 173.51/173.28 [6750]~P106(f333(x67501,x67503))+P106(f333(x67501,f423(x67501,x67502)))+~P106(f333(f333(f335(a910),x67503),f333(f308(a910,f2(a910)),x67502))) % 173.51/173.28 [6771]P106(f333(x67711,x67712))+~P106(f333(f333(f247(a910),x67712),x67713))+P106(f333(f333(f335(a910),f386(x67711,x67713)),f333(f308(a910,f2(a910)),x67713))) % 173.51/173.28 [6787]~P119(x67871)+~P106(f333(f333(f246(x67871),f2(x67871)),x67872))+P106(f333(f333(f246(x67871),f2(x67871)),f333(f333(f256(x67871),x67872),x67873))) % 173.51/173.28 [6788]~P119(x67881)+~P106(f333(f333(f246(x67881),f85(x67881)),x67882))+P106(f333(f333(f246(x67881),f85(x67881)),f333(f333(f256(x67881),x67882),x67883))) % 173.51/173.28 [6790]~P119(x67901)+~P106(f333(f333(f247(x67901),f2(x67901)),x67902))+P106(f333(f333(f247(x67901),f2(x67901)),f333(f333(f256(x67901),x67902),x67903))) % 173.51/173.28 [6814]~P106(f333(x68141,x68143))+~P106(f333(f333(f247(a910),x68143),x68142))+P106(f333(f333(f335(a910),f385(x68141,x68142)),f333(f308(a910,f2(a910)),x68142))) % 173.51/173.28 [6821]P106(f333(f67(x68211),x68212))+~P106(f333(f67(x68211),x68213))+~P106(f333(f333(f246(f917(x68211,a905)),x68212),x68213)) % 173.51/173.28 [6828]P106(f333(x68281,x68282))+~P106(f333(x68281,f388(x68281,x68283)))+~P106(f333(f333(f335(a910),x68282),f333(f308(a910,f2(a910)),x68283))) % 173.51/173.28 [6839]E(x68391,f2(a910))+P106(f333(x68392,f500(x68391,x68393,x68392)))+~P106(f333(x68392,f333(f333(f42(a910),x68393),x68391))) % 173.51/173.28 [6846]~P126(x68462)+E(x68461,f2(x68462))+~E(f333(f333(f87(x68462),f333(f333(f88(x68462),x68463),x68463)),f333(f333(f88(x68462),x68461),x68461)),f2(x68462)) % 173.51/173.28 [6847]~P126(x68472)+E(x68471,f2(x68472))+~E(f333(f333(f87(x68472),f333(f333(f88(x68472),x68471),x68471)),f333(f333(f88(x68472),x68473),x68473)),f2(x68472)) % 173.51/173.28 [6891]E(x68911,f2(a910))+~P106(f333(x68912,f501(x68911,x68913,x68912)))+P106(f333(x68912,f333(f333(f42(a910),x68913),x68911))) % 173.51/173.28 [6896]~P110(x68961)+~P16(x68961,x68963)+P16(x68961,f333(f333(f156(x68961,x68961,f5(x68961)),x68962),x68963)) % 173.51/173.28 [6938]P106(f333(x69381,f500(x69382,x69383,x69381)))+P106(f333(x69381,f2(a910)))+~P106(f333(x69381,f333(f333(f42(a910),x69383),x69382))) % 173.51/173.28 [6944]~P95(x69441)+E(f333(f114(x69441),x69442),f333(f114(x69441),x69443))+~P30(x69441,f333(f114(x69441),f333(f333(f87(a1),x69442),f333(f86(a1),x69443)))) % 173.51/173.28 [7007]E(x70071,f2(a1))+E(x70072,f2(a1))+~P106(f333(f55(x70072,x70072),f333(f333(f265(a1,a1),x70073),x70071))) % 173.51/173.28 [7008]E(x70081,f85(a1))+E(x70082,f2(a1))+~P106(f333(f55(x70082,x70082),f333(f333(f265(a1,a1),x70081),x70083))) % 173.51/173.28 [7022]P106(f333(x70221,x70222))+P106(f333(f333(f247(a910),f388(x70221,x70223)),x70223))+~P106(f333(f333(f335(a910),x70222),f333(f308(a910,f2(a910)),x70223))) % 173.51/173.28 [7047]~P106(f333(x70471,f351(x70473,x70472,x70471)))+~P106(f333(x70471,f2(a910)))+P106(f333(x70471,f333(f333(f23(a910),x70472),x70473))) % 173.51/173.28 [7048]~P106(f333(x70481,f353(x70483,x70482,x70481)))+~P106(f333(x70481,f2(a910)))+P106(f333(x70481,f333(f333(f23(a910),x70482),x70483))) % 173.51/173.28 [7049]~P106(f333(x70491,f501(x70493,x70492,x70491)))+~P106(f333(x70491,f2(a910)))+P106(f333(x70491,f333(f333(f42(a910),x70492),x70493))) % 173.51/173.28 [7066]~P106(f333(x70661,x70663))+P106(f333(f333(f247(a910),f423(x70661,x70662)),x70662))+~P106(f333(f333(f335(a910),x70663),f333(f308(a910,f2(a910)),x70662))) % 173.51/173.28 [7067]E(f333(f333(f23(a910),f333(f333(f23(a910),x70671),x70672)),f333(f333(f23(a910),x70673),x70672)),f333(f333(f23(a910),x70671),x70673))+~P106(f333(f333(f246(a910),x70672),x70671))+~P106(f333(f333(f246(a910),x70672),x70673)) % 173.51/173.28 [7102]~P4(x71021)+~P106(f333(f333(f246(x71021),f333(f86(x71021),x71023)),x71022))+P106(f333(f333(f246(x71021),f333(f86(x71021),x71022)),x71023)) % 173.51/173.28 [7104]~P87(x71041)+~P106(f333(f333(f246(x71041),f333(f82(x71041),x71042)),x71043))+P106(f333(f333(f246(x71041),f333(f86(x71041),x71042)),x71043)) % 173.51/173.28 [7106]~P4(x71061)+~P106(f333(f333(f247(x71061),f333(f86(x71061),x71063)),x71062))+P106(f333(f333(f247(x71061),f333(f86(x71061),x71062)),x71063)) % 173.51/173.28 [7107]~P120(x71071)+~P106(f333(f333(f247(x71071),f333(f82(x71071),x71072)),x71073))+P106(f333(f333(f247(x71071),f333(f86(x71071),x71072)),x71073)) % 173.51/173.28 [7141]~P106(f333(x71413,f351(x71412,x71411,x71413)))+P106(f333(f333(f247(a910),x71411),x71412))+P106(f333(x71413,f333(f333(f23(a910),x71411),x71412))) % 173.51/173.28 [7142]~P106(f333(x71423,f353(x71422,x71421,x71423)))+P106(f333(f333(f247(a910),x71421),x71422))+P106(f333(x71423,f333(f333(f23(a910),x71421),x71422))) % 173.51/173.28 [7193]~E(f668(x71933,x71932,x71931),f669(x71933,x71932,x71931))+E(f333(f333(f112(f917(x71931,a905)),x71932),f43(f917(x71931,a905),x71933)),f196(f917(x71931,a905)))+P106(f333(f333(f335(f917(x71931,a905)),x71932),x71933)) % 173.51/173.28 [7201]~P106(f333(f67(x72011),x72013))+P106(f333(f67(x72011),f44(f917(x72011,a905),x72012)))+~P106(f333(f333(f335(f917(x72011,a905)),x72013),x72012)) % 173.51/173.28 [7260]~P110(x72601)+E(f333(f333(f121(f917(x72601,a905)),f333(f308(x72601,x72602),x72603)),f333(f333(f315(x72601),x72603),f196(f917(x72601,a905)))),f309(x72601,x72602,x72603))+~P106(f333(f333(f246(x72601),x72602),x72603)) % 173.51/173.28 [7261]E(x72611,f2(a910))+P106(f333(f333(f247(a910),f511(x72611,x72613,x72612)),x72611))+P106(f333(x72612,f333(f333(f42(a910),x72613),x72611))) % 173.51/173.28 [7290]P106(f333(f333(f247(a910),f333(f197(f911(x72901)),x72902)),f825(x72903,x72901)))+~P106(f333(f67(f911(x72901)),x72903))+~P106(f333(f333(f335(f911(x72901)),x72902),x72903)) % 173.51/173.28 [7296]E(x72961,x72962)+~P106(f333(f333(f246(f917(x72963,a905)),x72961),x72962))+P106(f333(f333(f247(f917(x72963,a905)),x72961),x72962)) % 173.51/173.28 [7309]E(x73091,x73092)+~E(f333(f197(f911(x73093)),x73091),f333(f197(f911(x73093)),x73092))+P106(f333(f333(f247(a910),f684(x73093,x73091,x73092)),f333(f197(f911(x73093)),x73092))) % 173.51/173.28 [7358]P11(x73581,x73582,x73583)+~E(f333(f263(x73581,x73581),x73583),x73582)+~E(f333(f333(f295(x73581,x73581,x73581),f333(f293(x73581,x73581),x73583)),x73583),x73583) % 173.51/173.28 [7434]~P106(f333(x74341,f2(a910)))+P106(f333(f333(f247(a910),f511(x74343,x74342,x74341)),x74343))+P106(f333(x74341,f333(f333(f42(a910),x74342),x74343))) % 173.51/173.28 [7443]~P110(x74431)+E(f333(f333(f121(f917(x74431,a905)),f312(x74431,x74432,x74433)),f333(f333(f315(x74431),x74433),f196(f917(x74431,a905)))),f311(x74431,x74432,x74433))+~P106(f333(f333(f247(x74431),x74432),x74433)) % 173.51/173.28 [7536]~P106(f333(f67(x75361),x75363))+P106(f333(f333(f246(a910),f333(f41(x75361),x75362)),f333(f41(x75361),x75363)))+~P106(f333(f333(f246(f917(x75361,a905)),x75362),x75363)) % 173.51/173.28 [7537]~P106(f333(f67(x75371),x75373))+P106(f333(f333(f247(a910),f333(f41(x75371),x75372)),f333(f41(x75371),x75373)))+~P106(f333(f333(f247(f917(x75371,a905)),x75372),x75373)) % 173.51/173.28 [7574]~P106(f333(x75743,x75742))+P106(f333(f333(f202(x75741),x75742),f361(x75742,x75741,x75743)))+~P106(f333(f333(f202(f30(x75743,x75741)),x75742),x75742)) % 173.51/173.28 [7668]E(x76681,x76682)+~P106(f333(f333(f246(f917(x76683,a905)),x76682),x76681))+~P106(f333(f333(f246(f917(x76683,a905)),x76681),x76682)) % 173.51/173.28 [7671]~P110(x76711)+P16(x76711,x76712)+~P16(x76711,f333(f333(f156(x76711,x76711,f5(x76711)),x76713),x76712)) % 173.51/173.28 [7740]~P106(f333(f333(f247(a910),x77403),x77402))+~P106(f333(f333(f247(a910),x77403),x77401))+P106(f333(f333(f247(a910),f333(f333(f23(a910),x77401),x77402)),f333(f333(f23(a910),x77401),x77403))) % 173.51/173.28 [7741]~P106(f333(f333(f246(a910),x77412),x77411))+~P106(f333(f333(f247(a910),x77411),x77413))+P106(f333(f333(f247(a910),f333(f333(f23(a910),x77411),x77412)),f333(f333(f23(a910),x77413),x77412))) % 173.51/173.28 [7756]~P106(f333(f333(f247(a1),x77562),f2(a1)))+~P106(f333(f333(f246(a1),x77563),x77561))+P106(f333(f333(f246(a1),f333(f333(f42(a1),x77561),x77562)),f333(f333(f42(a1),x77563),x77562))) % 173.51/173.28 [7773]~P106(f333(f333(f247(a910),f2(a910)),x77733))+~P106(f333(f333(f246(a910),x77733),x77732))+P106(f333(f333(f246(a910),f333(f333(f42(a910),x77731),x77732)),f333(f333(f42(a910),x77731),x77733))) % 173.51/173.28 [7774]~P106(f333(f333(f247(a1),f2(a1)),x77742))+~P106(f333(f333(f246(a1),x77741),x77743))+P106(f333(f333(f246(a1),f333(f333(f42(a1),x77741),x77742)),f333(f333(f42(a1),x77743),x77742))) % 173.51/173.28 [7778]~P106(f333(f333(f247(a910),f2(a910)),x77782))+~P106(f333(f333(f247(a910),x77781),x77783))+P106(f333(f333(f247(a910),f333(f333(f88(a910),x77781),x77782)),f333(f333(f88(a910),x77783),x77782))) % 173.51/173.28 [7779]~P106(f333(f333(f247(a910),f2(a910)),x77791))+~P106(f333(f333(f247(a910),x77792),x77793))+P106(f333(f333(f247(a910),f333(f333(f88(a910),x77791),x77792)),f333(f333(f88(a910),x77791),x77793))) % 173.51/173.28 [7780]~P106(f333(f333(f247(a1),f2(a1)),x77801))+~P106(f333(f333(f247(a1),x77802),x77803))+P106(f333(f333(f247(a1),f333(f333(f88(a1),x77801),x77802)),f333(f333(f88(a1),x77801),x77803))) % 173.51/173.28 [7829]E(x78291,f2(a910))+E(f333(f333(f87(a910),f333(f333(f88(a910),x78291),f501(x78291,x78292,x78293))),f511(x78291,x78292,x78293)),x78292)+P106(f333(x78293,f333(f333(f42(a910),x78292),x78291))) % 173.51/173.28 [7891]E(f333(f333(f87(a910),f333(f333(f88(a910),x78911),f501(x78911,x78912,x78913))),f511(x78911,x78912,x78913)),x78912)+~P106(f333(x78913,f2(a910)))+P106(f333(x78913,f333(f333(f42(a910),x78912),x78911))) % 173.51/173.28 [7909]~P106(f333(f67(x79091),x79093))+P106(f333(f333(f335(x79091),f502(x79092,x79093,x79091)),x79093))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f9(x79091,a910),x79092),x79093))) % 173.51/173.28 [7910]~P106(f333(f67(x79101),x79103))+P106(f333(f333(f335(x79101),f516(x79102,x79103,x79101)),x79103))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f9(x79101,a910),x79102),x79103))) % 173.51/173.28 [8206]E(x82061,f196(f917(x82062,a905)))+E(x82061,f333(f333(f315(x82062),x82063),f196(f917(x82062,a905))))+~P106(f333(f333(f246(f917(x82062,a905)),x82061),f333(f333(f315(x82062),x82063),f196(f917(x82062,a905))))) % 173.51/173.28 [8242]~P106(f333(f333(f247(a910),f2(a910)),x82423))+P106(f333(f333(f246(a910),x82421),x82422))+~P106(f333(f333(f246(a910),f333(f333(f88(a910),x82423),x82421)),f333(f333(f88(a910),x82423),x82422))) % 173.51/173.28 [8243]~P106(f333(f333(f247(a910),f2(a910)),x82433))+P106(f333(f333(f246(a910),x82431),x82432))+~P106(f333(f333(f246(a910),f333(f333(f88(a910),x82431),x82433)),f333(f333(f88(a910),x82432),x82433))) % 173.51/173.28 [8245]~P106(f333(f333(f247(a910),f2(a910)),x82453))+P106(f333(f333(f247(a910),x82451),x82452))+~P106(f333(f333(f247(a910),f333(f333(f256(a910),x82453),x82451)),f333(f333(f256(a910),x82453),x82452))) % 173.51/173.28 [8278]~P106(f333(x82781,x82783))+P106(f333(f333(f202(f30(x82781,x82782)),f361(x82783,x82782,x82781)),x82783))+~P106(f333(f333(f202(f30(x82781,x82782)),x82783),x82783)) % 173.51/173.28 [8286]~E(f333(f333(f112(f917(x82861,a905)),f669(x82863,x82862,x82861)),f668(x82863,x82862,x82861)),f196(f917(x82861,a905)))+E(f333(f333(f112(f917(x82861,a905)),x82862),f43(f917(x82861,a905),x82863)),f196(f917(x82861,a905)))+P106(f333(f333(f335(f917(x82861,a905)),x82862),x82863)) % 173.51/173.28 [8300]E(x83001,f124(x83002))+~E(f333(f150(f911(x83002),f911(x83002),f142(x83002),f124(x83002)),x83003),f124(x83002))+~P106(f333(f333(f335(f911(x83002)),x83001),f333(f180(f911(x83002)),x83003))) % 173.51/173.28 [8356]E(x83561,f196(f917(f917(x83562,a905),a905)))+P106(f333(f333(f335(f917(x83562,a905)),f672(x83563,x83561,x83562)),x83561))+P106(f333(f333(f246(f917(x83562,a905)),f44(f917(x83562,a905),x83561)),x83563)) % 173.51/173.28 [8363]~P72(x83631)+~P78(x83631)+E(f333(f333(f6(a1,x83631),f333(f333(f8(a910,x83631,a1),x83632),a115)),f333(f316(a910,a1,f111(a1)),x83633)),f333(f333(f6(a910,x83631),x83632),x83633)) % 173.51/173.28 [8364]~P72(x83641)+~P78(x83641)+E(f333(f333(f9(a1,x83641),f333(f333(f8(a910,x83641,a1),x83642),a115)),f333(f316(a910,a1,f111(a1)),x83643)),f333(f333(f9(a910,x83641),x83642),x83643)) % 173.51/173.28 [8407]~P106(f333(f67(x84071),x84073))+~P106(f333(f333(f247(a910),f2(a910)),f333(x84072,f502(x84072,x84073,x84071))))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f9(x84071,a910),x84072),x84073))) % 173.51/173.28 [8408]~P106(f333(f67(x84081),x84083))+~P106(f333(f333(f247(a910),f2(a910)),f333(x84082,f516(x84082,x84083,x84081))))+P106(f333(f333(f247(a910),f2(a910)),f333(f333(f9(x84081,a910),x84082),x84083))) % 173.51/173.28 [8444]~P68(x84442)+E(x84441,f85(x84442))+E(f333(f333(f296(x84442),f333(f333(f23(x84442),f333(f333(f256(x84442),x84441),x84443)),f85(x84442))),f333(f333(f23(x84442),x84441),f85(x84442))),f333(f333(f6(a910,x84442),f333(f256(x84442),x84441)),f333(f308(a910,f2(a910)),x84443))) % 173.51/173.28 [8501]E(x85011,f2(a910))+~P106(f333(x85013,f333(f333(f42(a910),x85012),x85011)))+P106(f333(f333(f247(a910),x85012),f333(f333(f88(a910),x85011),f333(a123,f500(x85011,x85012,x85013))))) % 173.51/173.28 [8520]P106(f333(x85201,f2(a910)))+~P106(f333(x85201,f333(f333(f42(a910),x85202),x85203)))+P106(f333(f333(f247(a910),x85202),f333(f333(f88(a910),x85203),f333(a123,f500(x85203,x85202,x85201))))) % 173.51/173.28 [8562]E(x85621,f2(a910))+~P106(f333(x85623,f333(f333(f42(a910),x85622),x85621)))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x85621),f500(x85621,x85622,x85623))),x85622)) % 173.51/173.28 [8599]P106(f333(x85991,f2(a910)))+~P106(f333(x85991,f333(f333(f42(a910),x85993),x85992)))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x85992),f500(x85992,x85993,x85991))),x85993)) % 173.51/173.28 [8607]~P110(x86071)+E(f333(f333(f156(x86071,x86071,f5(x86071)),x86072),x86073),f157(x86071,x86071,f5(x86071),x86072,x86073))+P106(f333(f333(f335(x86071),x86072),f333(f180(x86071),x86073))) % 173.51/173.28 [8644]~E(f333(x86443,f608(x86442,x86443,x86441)),f333(x86443,f610(x86442,x86443,x86441)))+~P63(x86441,f333(x86443,f609(x86442,x86443,x86441)))+P63(x86441,f333(f333(f45(x86442,f917(x86441,f917(x86441,a905))),f254(f917(x86442,a905))),x86443)) % 173.51/173.28 [8653]E(x86531,f196(f917(f917(x86532,a905),a905)))+~P106(f333(f333(f246(f917(x86532,a905)),f672(x86533,x86531,x86532)),x86533))+P106(f333(f333(f246(f917(x86532,a905)),f44(f917(x86532,a905),x86531)),x86533)) % 173.51/173.28 [8712]~P70(x87121)+~P106(f333(f333(f247(x87121),x87122),x87123))+P106(f333(f333(f247(x87121),x87122),f333(f333(f296(x87121),f333(f333(f87(x87121),x87122),x87123)),f333(f333(f87(x87121),f85(x87121)),f85(x87121))))) % 173.51/173.28 [8772]~P106(f333(f333(x87721,f539(x87721,x87723,x87722)),f545(x87721,x87723,x87722)))+P106(f333(f333(x87721,x87722),x87723))+~P106(f333(f321(f916(a1,a1),a58),f333(f333(f265(a1,a1),x87722),x87723))) % 173.51/173.28 [8773]~P106(f333(f333(x87731,f546(x87731,x87733,x87732)),f547(x87731,x87733,x87732)))+P106(f333(f333(x87731,x87732),x87733))+~P106(f333(f321(f916(a1,a1),a64),f333(f333(f265(a1,a1),x87732),x87733))) % 173.51/173.28 [8774]~P106(f333(f333(x87741,f549(x87741,x87743,x87742)),f550(x87741,x87743,x87742)))+P106(f333(f333(x87741,x87742),x87743))+~P106(f333(f321(f916(a1,a1),a233),f333(f333(f265(a1,a1),x87742),x87743))) % 173.51/173.28 [8775]~P106(f333(f333(x87751,f552(x87751,x87753,x87752)),f553(x87751,x87753,x87752)))+P106(f333(f333(x87751,x87752),x87753))+~P106(f333(f321(f916(a910,a910),a231),f333(f333(f265(a910,a910),x87752),x87753))) % 173.51/173.28 [8776]~P106(f333(f333(x87761,f722(x87761,x87763,x87762)),f723(x87761,x87763,x87762)))+P106(f333(f333(x87761,x87762),x87763))+~P106(f333(f321(f916(a1,a1),a190),f333(f333(f265(a1,a1),x87762),x87763))) % 173.51/173.28 [8777]~P106(f333(f333(x87771,f818(x87771,x87773,x87772)),f819(x87771,x87773,x87772)))+P106(f333(f333(x87771,x87772),x87773))+~P106(f333(f321(f916(a1,a1),a141),f333(f333(f265(a1,a1),x87772),x87773))) % 173.51/173.28 [9053]P106(f333(f333(x90531,x90532),x90533))+P106(f333(f321(f916(a910,a910),a231),f333(f333(f265(a910,a910),f552(x90531,x90533,x90532)),f553(x90531,x90533,x90532))))+~P106(f333(f321(f916(a910,a910),a231),f333(f333(f265(a910,a910),x90532),x90533))) % 173.51/173.28 [9054]P106(f333(f333(x90541,x90542),x90543))+P106(f333(f321(f916(a1,a1),a58),f333(f333(f265(a1,a1),f539(x90541,x90543,x90542)),f545(x90541,x90543,x90542))))+~P106(f333(f321(f916(a1,a1),a58),f333(f333(f265(a1,a1),x90542),x90543))) % 173.51/173.28 [9055]P106(f333(f333(x90551,x90552),x90553))+P106(f333(f321(f916(a1,a1),a64),f333(f333(f265(a1,a1),f546(x90551,x90553,x90552)),f547(x90551,x90553,x90552))))+~P106(f333(f321(f916(a1,a1),a64),f333(f333(f265(a1,a1),x90552),x90553))) % 173.51/173.28 [9056]P106(f333(f333(x90561,x90562),x90563))+P106(f333(f321(f916(a1,a1),a233),f333(f333(f265(a1,a1),f549(x90561,x90563,x90562)),f550(x90561,x90563,x90562))))+~P106(f333(f321(f916(a1,a1),a233),f333(f333(f265(a1,a1),x90562),x90563))) % 173.51/173.28 [9057]P106(f333(f333(x90571,x90572),x90573))+P106(f333(f321(f916(a1,a1),a190),f333(f333(f265(a1,a1),f722(x90571,x90573,x90572)),f723(x90571,x90573,x90572))))+~P106(f333(f321(f916(a1,a1),a190),f333(f333(f265(a1,a1),x90572),x90573))) % 173.51/173.28 [9058]P106(f333(f333(x90581,x90582),x90583))+P106(f333(f321(f916(a1,a1),a141),f333(f333(f265(a1,a1),f818(x90581,x90583,x90582)),f819(x90581,x90583,x90582))))+~P106(f333(f321(f916(a1,a1),a141),f333(f333(f265(a1,a1),x90582),x90583))) % 173.51/173.28 [9410]~P106(f333(f67(x94101),x94103))+P106(f333(f333(f335(f916(f917(x94101,a905),f917(x94101,a905))),f333(f333(f265(f917(x94101,a905),f917(x94101,a905)),x94102),x94103)),f320(x94101)))+~P106(f333(f333(f247(f917(x94101,a905)),x94102),x94103)) % 173.51/173.28 [9487]~P63(x94871,f333(x94873,f609(x94872,x94873,x94871)))+P63(x94871,f333(f333(f45(x94872,f917(x94871,f917(x94871,a905))),f254(f917(x94872,a905))),x94873))+~E(f333(f333(f112(f917(x94871,a905)),f261(x94871,x94871,f333(x94873,f608(x94872,x94873,x94871)))),f262(x94871,x94871,f333(x94873,f610(x94872,x94873,x94871)))),f196(f917(x94871,a905))) % 173.51/173.28 [9697]P56(x96971,x96972,x96973)+P106(f333(f333(f335(f916(x96971,x96971)),f562(x96973,x96972,x96971)),x96973))+~P106(f333(f333(f335(f916(x96971,x96971)),f333(f333(f265(x96971,x96971),f561(x96973,x96972,x96971)),f561(x96973,x96972,x96971))),x96973)) % 173.51/173.28 [10283]P56(x102831,x102832,x102833)+~P106(f333(f333(f269(x102831,x102831,a905),f333(f333(f7(x102831,f917(x102831,a905),f917(x102831,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x102831,a905),f917(x102831,a905)),x102831),f8(a905,a905,x102831)),f333(f333(f8(a905,f917(a905,a905),x102831),a331),f333(f333(f7(x102831,f917(x102831,a905),a905),f335(x102831)),x102832)))),f333(f333(f7(x102831,f917(x102831,a905),a905),f335(x102831)),x102832))),f562(x102833,x102832,x102831)))+~P106(f333(f333(f335(f916(x102831,x102831)),f333(f333(f265(x102831,x102831),f561(x102833,x102832,x102831)),f561(x102833,x102832,x102831))),x102833)) % 173.51/173.28 [5790]~P64(x57902)+E(x57901,f2(x57902))+E(f333(f333(f42(x57902),f333(f333(f88(x57902),x57903),x57901)),x57901),x57903) % 173.51/173.28 [5791]~P64(x57912)+E(x57911,f2(x57912))+E(f333(f333(f42(x57912),f333(f333(f88(x57912),x57911),x57913)),x57911),x57913) % 173.51/173.28 [6581]~P72(x65811)+~E(f333(x65812,f2(a910)),f2(x65811))+E(f333(f333(f6(a910,x65811),x65812),f333(f308(a910,f333(a123,f2(a910))),x65813)),f333(f333(f6(a910,x65811),x65812),f333(f308(a910,f2(a910)),x65813))) % 173.51/173.28 [6712]~P64(x67122)+E(x67121,f2(x67122))+E(f333(f333(f42(x67122),f333(f333(f87(x67122),x67123),x67121)),x67121),f333(f333(f87(x67122),f333(f333(f42(x67122),x67123),x67121)),f85(x67122))) % 173.51/173.28 [6713]~P64(x67132)+E(x67131,f2(x67132))+E(f333(f333(f42(x67132),f333(f333(f87(x67132),x67131),x67133)),x67131),f333(f333(f87(x67132),f333(f333(f42(x67132),x67133),x67131)),f85(x67132))) % 173.51/173.28 [6927]~P106(f333(x69273,f2(a1)))+P106(f333(f333(f246(a910),x69271),x69272))+P106(f333(x69273,f333(f111(a1),f333(f333(f23(a910),x69272),x69271)))) % 173.51/173.28 [7028]P106(f333(f333(f247(a910),x70282),x70281))+P106(f333(f333(f246(a910),x70281),x70282))+P106(f333(x70283,f333(f111(a1),f333(f333(f23(a910),x70282),x70281)))) % 173.51/173.28 [7100]E(f333(f333(f87(a910),f333(f114(a910),x71001)),f333(f333(f87(a910),f333(f114(a910),x71002)),x71003)),f333(f333(f87(a910),f333(f114(a910),x71001)),x71003))+P106(f333(a201,f333(f114(a1),x71001)))+~P106(f333(a201,f333(f114(a1),x71002))) % 173.51/173.28 [7180]~E(x71802,f333(f333(f42(a910),x71803),x71801))+~P106(f333(f333(f247(a910),f2(a910)),x71801))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x71801),x71802)),x71803)) % 173.51/173.28 [7293]~P106(f333(f67(x72931),x72933))+~P106(f333(f67(x72931),x72932))+P106(f333(f67(x72931),f333(f333(f121(f917(x72931,a905)),x72932),x72933))) % 173.51/173.28 [7343]~P41(x73431,x73433)+~P41(x73431,x73432)+P41(x73431,f333(f333(f112(f917(f916(x73431,x73431),a905)),x73432),x73433)) % 173.51/173.28 [7344]~P55(x73441,x73443)+~P55(x73441,x73442)+P55(x73441,f333(f333(f121(f917(f916(x73441,x73441),a905)),x73442),x73443)) % 173.51/173.28 [7345]~P55(x73451,x73453)+~P55(x73451,x73452)+P55(x73451,f333(f333(f112(f917(f916(x73451,x73451),a905)),x73452),x73453)) % 173.51/173.28 [7586]~P110(x75861)+~P106(f333(f67(x75861),x75862))+E(f147(x75861,f333(f333(f23(f917(x75861,a905)),x75862),f333(f333(f315(x75861),x75863),f196(f917(x75861,a905))))),f178(x75861,x75863,f147(x75861,x75862))) % 173.51/173.28 [7647]P106(f333(x76471,f2(a1)))+~P106(f333(f333(f247(a910),x76472),x76473))+~P106(f333(x76471,f333(f111(a1),f333(f333(f23(a910),x76472),x76473)))) % 173.51/173.28 [7665]~P106(f333(f67(x76651),x76652))+E(f333(f41(x76651),f333(f333(f23(f917(x76651,a905)),x76652),f333(f333(f315(x76651),x76653),f196(f917(x76651,a905))))),f333(f41(x76651),x76652))+P106(f333(f333(f335(x76651),x76653),x76652)) % 173.51/173.28 [7795]~P119(x77951)+~P106(f333(f333(f247(x77951),f85(x77951)),x77952))+P106(f333(f333(f247(x77951),f85(x77951)),f333(f333(f88(x77951),x77952),f333(f333(f256(x77951),x77952),x77953)))) % 173.51/173.28 [7840]~P106(f333(f67(x78401),x78403))+E(f333(f333(f23(a910),f333(f41(x78401),x78402)),f333(f41(x78401),x78403)),f333(f41(x78401),f333(f333(f23(f917(x78401,a905)),x78402),x78403)))+~P106(f333(f333(f246(f917(x78401,a905)),x78403),x78402)) % 173.51/173.28 [7899]~P106(f333(f333(f246(a910),x78992),x78993))+~P106(f333(f333(f246(a910),x78991),f333(f333(f23(a910),x78993),x78992)))+P106(f333(f333(f246(a910),f333(f333(f87(a910),x78991),x78992)),x78993)) % 173.51/173.28 [7953]P106(f333(f67(x79531),x79532))+~P106(f333(f67(x79531),x79533))+~P106(f333(f67(x79531),f333(f333(f23(f917(x79531,a905)),x79532),x79533))) % 173.51/173.28 [7959]~P106(f333(f67(x79591),x79592))+E(f333(f41(x79591),f333(f333(f23(f917(x79591,a905)),x79592),f333(f333(f315(x79591),x79593),f196(f917(x79591,a905))))),f333(f333(f23(a910),f333(f41(x79591),x79592)),f85(a910)))+~P106(f333(f333(f335(x79591),x79593),x79592)) % 173.51/173.28 [8035]P63(x80351,x80352)+~P63(x80351,x80353)+~P106(f333(f333(f246(f917(x80351,f917(x80351,a905))),x80352),x80353)) % 173.51/173.28 [8076]~P106(f333(f333(f246(a910),x80763),x80762))+P106(f333(f333(f246(a910),x80761),f333(f333(f23(a910),x80762),x80763)))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),x80761),x80763)),x80762)) % 173.51/173.28 [8094]P40(x80941,x80942)+~P40(x80941,x80943)+~P106(f333(f333(f246(f917(f916(x80941,x80941),a905)),x80942),x80943)) % 173.51/173.28 [8095]P61(x80951,x80952)+~P61(x80951,x80953)+~P106(f333(f333(f246(f917(f916(x80951,x80951),a905)),x80952),x80953)) % 173.51/173.28 [8096]P42(x80961,x80962)+~P42(x80961,x80963)+~P106(f333(f333(f246(f917(f916(x80961,x80961),a905)),x80962),x80963)) % 173.51/173.28 [8333]~P119(x83331)+~P106(f333(f333(f247(x83331),f85(x83331)),x83332))+P106(f333(f333(f247(x83331),f333(f333(f256(x83331),x83332),x83333)),f333(f333(f88(x83331),x83332),f333(f333(f256(x83331),x83332),x83333)))) % 173.51/173.28 [8426]~P106(f333(x84261,f2(a1)))+~P106(f333(x84261,f333(f333(f23(a1),f333(f111(a1),x84262)),f333(f111(a1),x84263))))+P106(f333(x84261,f333(f111(a1),f333(f333(f23(a910),x84262),x84263)))) % 173.51/173.28 [8441]~P106(f333(f333(f246(a910),x84413),x84412))+P106(f333(x84411,f333(f333(f23(a1),f333(f111(a1),x84412)),f333(f111(a1),x84413))))+~P106(f333(x84411,f333(f111(a1),f333(f333(f23(a910),x84412),x84413)))) % 173.51/173.28 [8460]P106(f333(f333(f247(a910),x84601),x84602))+~P106(f333(x84603,f333(f333(f23(a1),f333(f111(a1),x84601)),f333(f111(a1),x84602))))+P106(f333(x84603,f333(f111(a1),f333(f333(f23(a910),x84601),x84602)))) % 173.51/173.28 [8512]~P126(x85122)+E(x85121,f2(x85122))+P106(f333(f333(f247(x85122),f2(x85122)),f333(f333(f87(x85122),f333(f333(f88(x85122),x85123),x85123)),f333(f333(f88(x85122),x85121),x85121)))) % 173.51/173.28 [8513]~P126(x85132)+E(x85131,f2(x85132))+P106(f333(f333(f247(x85132),f2(x85132)),f333(f333(f87(x85132),f333(f333(f88(x85132),x85131),x85131)),f333(f333(f88(x85132),x85133),x85133)))) % 173.51/173.28 [8624]~P106(f333(f333(f247(a910),f2(a910)),x86241))+~P106(f333(f333(f247(a1),x86242),x86243))+P106(f333(f333(f247(a1),f333(f333(f88(a1),f333(f111(a1),x86241)),x86242)),f333(f333(f88(a1),f333(f111(a1),x86241)),x86243))) % 173.51/173.28 [8682]E(f333(f333(f112(f917(x86821,a905)),x86822),f43(f917(x86821,a905),x86823)),f196(f917(x86821,a905)))+P106(f333(f333(f335(f917(x86821,a905)),x86822),x86823))+P106(f333(f333(f335(f917(x86821,a905)),f669(x86823,x86822,x86821)),f333(f333(f315(f917(x86821,a905)),x86822),x86823))) % 173.51/173.28 [8683]E(f333(f333(f112(f917(x86831,a905)),x86832),f43(f917(x86831,a905),x86833)),f196(f917(x86831,a905)))+P106(f333(f333(f335(f917(x86831,a905)),x86832),x86833))+P106(f333(f333(f335(f917(x86831,a905)),f668(x86833,x86832,x86831)),f333(f333(f315(f917(x86831,a905)),x86832),x86833))) % 173.51/173.28 [8711]E(x87111,x87112)+~E(f333(f197(f911(x87113)),x87111),f333(f197(f911(x87113)),x87112))+P106(f333(f333(f335(f916(x87113,x87113)),f710(x87113,x87111,x87112)),f333(f180(f916(x87113,x87113)),f333(f333(f189(x87113,x87113),x87112),x87111)))) % 173.51/173.28 [8961]E(f313(x89611,x89612),f313(x89611,x89613))+~P106(f333(f333(f246(f917(f916(x89611,x89611),a905)),x89613),f313(x89611,x89612)))+~P106(f333(f333(f246(f917(f916(x89611,x89611),a905)),x89612),x89613)) % 173.51/173.28 [9029]~P56(x90291,f254(f917(x90291,a905)),x90293)+P106(f333(f333(f246(f917(f916(f911(x90291),f911(x90291)),a905)),f165(x90291,x90292)),f166(x90291,x90293)))+~P106(f333(f333(f246(f917(f916(x90291,x90291),a905)),x90292),x90293)) % 173.51/173.28 [9244]P40(x92441,x92442)+~P106(f333(f333(f335(x92441),x92443),f628(x92442,x92441)))+P106(f333(f333(f335(f916(x92441,x92441)),f333(f333(f265(x92441,x92441),f686(x92442,x92441,x92443)),x92443)),x92442)) % 173.51/173.28 [9279]~P106(f333(f67(x92791),x92792))+P106(f333(f67(f917(x92791,a905)),f333(f333(f66(x92791),x92792),x92793)))+~P106(f333(f333(f246(f917(f916(x92791,x92791),a905)),x92793),f333(f333(f267(x92791,x92791),x92792),f333(f16(f917(x92791,a905),x92791),x92792)))) % 173.51/173.28 [9316]P56(x93161,x93162,x93163)+P106(f333(f333(f335(x93161),f566(x93163,x93162,x93161)),x93162))+~P106(f333(f333(f246(f917(f916(x93161,x93161),a905)),x93163),f333(f333(f267(x93161,x93161),x93162),f333(f16(f917(x93161,a905),x93161),x93162)))) % 173.51/173.28 [9317]P56(x93171,x93172,x93173)+P106(f333(f333(f335(x93171),f567(x93172,x93173,x93171)),x93172))+~P106(f333(f333(f246(f917(f916(x93171,x93171),a905)),x93173),f333(f333(f267(x93171,x93171),x93172),f333(f16(f917(x93171,a905),x93171),x93172)))) % 173.51/173.28 [9349]~P70(x93491)+~P106(f333(f333(f247(x93491),x93492),x93493))+P106(f333(f333(f247(x93491),f333(f333(f296(x93491),f333(f333(f87(x93491),x93492),x93493)),f333(f333(f87(x93491),f85(x93491)),f85(x93491)))),x93493)) % 173.51/173.28 [9377]~P69(x93771)+P106(f333(f333(f246(x93771),x93772),x93773))+~P106(f333(f333(f246(x93771),f333(f333(f88(x93771),f499(x93773,x93772,x93771)),x93772)),x93773)) % 173.51/173.28 [9522]E(f333(f197(f911(f911(x95221))),f333(f144(f911(x95221),f333(f333(f8(a910,a905,f911(x95221)),f333(f247(a910),x95222)),f197(f911(x95221)))),f187(x95221,x95223))),f333(f197(f911(x95221)),f333(f333(f172(f911(x95221)),x95223),x95222)))+~P16(a910,f333(f176(a910),f333(f333(f162(f911(x95221),a910),f197(f911(x95221))),x95223)))+~P106(f333(f333(f247(a910),x95222),f333(f197(f911(f911(x95221))),x95223))) % 173.51/173.28 [9636]~P40(x96361,x96362)+P29(x96361,f333(f333(f265(f917(f916(x96361,x96361),a905),f917(f916(x96361,x96361),a905)),x96362),x96363))+~P106(f333(f333(f246(f917(f916(x96361,x96361),a905)),f333(f333(f295(x96361,x96361,x96361),x96362),x96363)),x96362)) % 173.51/173.28 [9642]E(f333(f333(f162(f911(x96421),x96421),f333(f333(f7(f911(x96421),a910,x96421),f172(x96421)),x96422)),f333(f144(f911(x96421),f333(f333(f8(a910,a905,f911(x96421)),f333(f247(a910),x96422)),f197(f911(x96421)))),f187(x96421,x96423))),f333(f333(f172(f911(x96421)),x96423),x96422))+~P16(a910,f333(f176(a910),f333(f333(f162(f911(x96421),a910),f197(f911(x96421))),x96423)))+~P106(f333(f333(f247(a910),x96422),f333(f197(f911(f911(x96421))),x96423))) % 173.51/173.28 [9788]P56(x97881,x97882,x97883)+~P106(f333(f333(f335(f916(x97881,x97881)),f333(f333(f265(x97881,x97881),f566(x97883,x97882,x97881)),f566(x97883,x97882,x97881))),x97883))+~P106(f333(f333(f246(f917(f916(x97881,x97881),a905)),x97883),f333(f333(f267(x97881,x97881),x97882),f333(f16(f917(x97881,a905),x97881),x97882)))) % 173.51/173.28 [9789]P56(x97891,x97892,x97893)+~P106(f333(f333(f335(f916(x97891,x97891)),f333(f333(f265(x97891,x97891),f567(x97892,x97893,x97891)),f567(x97892,x97893,x97891))),x97893))+~P106(f333(f333(f246(f917(f916(x97891,x97891),a905)),x97893),f333(f333(f267(x97891,x97891),x97892),f333(f16(f917(x97891,a905),x97891),x97892)))) % 173.51/173.28 [9957]~P139(x99571)+~P125(x99571)+E(f333(f333(f296(x99571),f333(f113(x99571),f333(f333(f79(f916(a1,a1),a1,x99572,f264(a1,a1)),f224(x99572)),x99573))),f333(f113(x99571),f333(f333(f79(f916(a1,a1),a1,x99572,f268(a1,a1)),f224(x99572)),x99573))),f234(x99572,x99571,x99573)) % 173.51/173.28 [10158]~E(x101583,f2(a910))+~E(f333(f197(f911(x101581)),f333(f333(f172(f911(x101581)),x101582),f758(x101583,x101581,x101582))),x101583)+E(f333(f333(f162(a910,f911(x101581)),f333(f333(f7(a910,f911(a910),f911(x101581)),f333(f333(f8(f917(a910,x101581),f917(f911(a910),f911(x101581)),a910),f162(a910,x101581)),f333(f7(a910,a910,x101581),f333(f333(f8(f911(x101581),f917(a910,x101581),a910),f172(x101581)),f333(f172(f911(x101581)),x101582))))),f147(a910,f333(f308(a910,f2(a910)),f333(f197(f911(f911(x101581))),x101582))))),f147(a910,f333(f308(a910,f2(a910)),x101583))),f187(x101581,x101582)) % 173.51/173.28 [10159]E(x101591,f124(f911(x101592)))+~E(f333(f197(f911(x101592)),f333(f333(f172(f911(x101592)),x101591),f758(x101593,x101592,x101591))),x101593)+E(f333(f333(f162(a910,f911(x101592)),f333(f333(f7(a910,f911(a910),f911(x101592)),f333(f333(f8(f917(a910,x101592),f917(f911(a910),f911(x101592)),a910),f162(a910,x101592)),f333(f7(a910,a910,x101592),f333(f333(f8(f911(x101592),f917(a910,x101592),a910),f172(x101592)),f333(f172(f911(x101592)),x101591))))),f147(a910,f333(f308(a910,f2(a910)),f333(f197(f911(f911(x101592))),x101591))))),f147(a910,f333(f308(a910,f2(a910)),x101593))),f187(x101592,x101591)) % 173.51/173.28 [10160]~E(x101603,f2(a910))+E(f333(f333(f162(a910,f911(x101601)),f333(f333(f7(a910,f911(a910),f911(x101601)),f333(f333(f8(f917(a910,x101601),f917(f911(a910),f911(x101601)),a910),f162(a910,x101601)),f333(f7(a910,a910,x101601),f333(f333(f8(f911(x101601),f917(a910,x101601),a910),f172(x101601)),f333(f172(f911(x101601)),x101602))))),f147(a910,f333(f308(a910,f2(a910)),f333(f197(f911(f911(x101601))),x101602))))),f147(a910,f333(f308(a910,f2(a910)),x101603))),f187(x101601,x101602))+P106(f333(f333(f247(a910),f758(x101603,x101601,x101602)),f333(f197(f911(f911(x101601))),x101602))) % 173.51/173.28 [10161]E(x101611,f124(f911(x101612)))+E(f333(f333(f162(a910,f911(x101612)),f333(f333(f7(a910,f911(a910),f911(x101612)),f333(f333(f8(f917(a910,x101612),f917(f911(a910),f911(x101612)),a910),f162(a910,x101612)),f333(f7(a910,a910,x101612),f333(f333(f8(f911(x101612),f917(a910,x101612),a910),f172(x101612)),f333(f172(f911(x101612)),x101611))))),f147(a910,f333(f308(a910,f2(a910)),f333(f197(f911(f911(x101612))),x101611))))),f147(a910,f333(f308(a910,f2(a910)),x101613))),f187(x101612,x101611))+P106(f333(f333(f247(a910),f758(x101613,x101612,x101611)),f333(f197(f911(f911(x101612))),x101611))) % 173.51/173.28 [7837]E(f333(f333(f87(a910),f333(f114(a910),x78371)),f333(f333(f87(a910),f333(f114(a910),x78372)),x78373)),f333(f333(f87(a910),f333(f114(a910),f333(f333(f87(a1),x78371),x78372))),x78373))+P106(f333(a201,f333(f114(a1),x78371)))+P106(f333(a201,f333(f114(a1),x78372))) % 173.51/173.28 [8616]~P106(f333(f67(x86161),x86162))+~P106(f333(f333(f335(x86161),x86163),x86162))+E(f333(a123,f333(f41(x86161),f333(f333(f23(f917(x86161,a905)),x86162),f333(f333(f315(x86161),x86163),f196(f917(x86161,a905)))))),f333(f41(x86161),x86162)) % 173.51/173.28 [8634]~P106(f333(f67(x86341),x86342))+~P106(f333(f333(f335(x86341),x86343),x86342))+E(f333(f333(f87(a910),f85(a910)),f333(f41(x86341),f333(f333(f23(f917(x86341,a905)),x86342),f333(f333(f315(x86341),x86343),f196(f917(x86341,a905)))))),f333(f41(x86341),x86342)) % 173.51/173.28 [8720]~P110(x87201)+~P106(f333(f67(x87201),x87203))+E(f333(f333(f156(x87201,x87201,f5(x87201)),x87202),f147(x87201,f333(f333(f23(f917(x87201,a905)),x87203),f333(f333(f315(x87201),x87202),f196(f917(x87201,a905)))))),f147(x87201,f333(f333(f315(x87201),x87202),x87203))) % 173.51/173.28 [8886]~P106(f333(f67(x88861),x88863))+~P106(f333(f67(x88861),x88862))+E(f333(f333(f87(a910),f333(f41(x88861),f333(f333(f121(f917(x88861,a905)),x88862),x88863))),f333(f41(x88861),f333(f333(f112(f917(x88861,a905)),x88862),x88863))),f333(f333(f87(a910),f333(f41(x88861),x88862)),f333(f41(x88861),x88863))) % 173.51/173.28 [10106]~P27(x101061,f917(f917(x101061,a905),a905),f333(f333(f7(x101061,f917(f916(x101061,x101061),a905),f917(f917(x101061,a905),a905)),f333(f333(f8(f917(x101061,a905),f917(f917(f916(x101061,x101061),a905),f917(f917(x101061,a905),a905)),x101061),f66(x101061)),f333(f333(f7(x101061,f917(x101061,a905),f917(x101061,a905)),f315(x101061)),f196(f917(x101061,a905))))),x101063),x101062)+~P106(f333(f67(x101061),x101062))+E(f333(f41(f917(x101061,a905)),f333(f333(f66(x101061),x101062),x101063)),f333(f41(x101061),x101062)) % 173.51/173.28 [8111]~P95(x81111)+P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x81113)))+E(f333(f333(f256(x81111),x81112),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),x81113),x81113)),a108))),f85(x81111)) % 173.51/173.28 [9620]~P95(x96201)+~P106(f333(f333(f246(a1),f2(a1)),f333(f114(a1),x96203)))+E(f333(f333(f256(x96201),x96202),f333(f114(a910),f333(f333(f23(a1),f333(f333(f87(a1),x96203),x96203)),a108))),f333(f333(f93(x96201,x96201),f333(f333(f256(x96201),x96202),f333(f114(a910),x96203))),f333(f333(f18(x96201,x96201,x96201),f333(f333(f8(x96201,f917(x96201,x96201),x96201),f88(x96201)),f333(f88(x96201),x96202))),f5(x96201)))) % 173.51/173.28 [10017]~P106(f333(f145(x100171),x100173))+~P106(f333(f333(f335(x100171),x100172),f333(f180(x100171),x100173)))+E(f333(f333(f146(x100171),f333(f197(f911(x100171)),f185(x100171,f333(f333(f8(a905,a905,x100171),a328),f333(f333(f7(x100171,x100171,a905),a330),x100172)),f333(f176(x100171),x100173)))),f333(f176(x100171),x100173)),f333(f333(f159(x100171),x100172),f333(f176(x100171),f185(x100171,f333(f333(f8(a905,a905,x100171),a328),f333(f333(f7(x100171,x100171,a905),a330),x100172)),x100173)))) % 173.51/173.28 [10085]P106(f333(f333(f246(f917(f916(x100851,x100851),a905)),f313(x100851,x100852)),x100853))+~P106(f333(f333(f246(f917(f916(x100851,x100851),a905)),f313(x100851,f196(f917(f916(x100851,x100851),a905)))),x100853))+~P106(f333(f333(f246(f917(f916(x100851,x100851),a905)),f333(f333(f295(x100851,x100851,x100851),f333(f333(f112(f917(f916(x100851,x100851),a905)),f313(x100851,x100852)),x100853)),x100852)),x100853)) % 173.51/173.28 [9938]~P106(f333(f67(x99381),f333(f252(x99381),x99383)))+~P106(f333(f67(x99381),f333(f252(x99381),x99382)))+P106(f333(f67(x99381),f333(f252(x99381),f333(f333(f18(x99381,a905,a905),f333(f333(f8(a905,f917(a905,a905),x99381),a332),x99382)),x99383)))) % 173.51/173.28 [10222]P106(f333(f333(f246(f917(f916(x102221,x102221),a905)),f333(f333(f295(x102221,x102221,x102221),x102222),f313(x102221,x102222))),x102223))+~P106(f333(f333(f246(f917(f916(x102221,x102221),a905)),x102222),x102223))+~P106(f333(f333(f246(f917(f916(x102221,x102221),a905)),f333(f333(f295(x102221,x102221,x102221),f333(f333(f112(f917(f916(x102221,x102221),a905)),f333(f333(f295(x102221,x102221,x102221),x102222),f313(x102221,x102222))),x102223)),x102222)),x102223)) % 173.51/173.28 [10175]~P120(x101752)+E(x101751,f2(x101752))+~E(f333(f333(f87(x101752),f333(f333(f256(x101752),x101753),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x101752),x101751),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f2(x101752)) % 173.51/173.28 [10176]~P120(x101762)+E(x101761,f2(x101762))+~E(f333(f333(f87(x101762),f333(f333(f256(x101762),x101761),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x101762),x101763),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f2(x101762)) % 173.51/173.28 [10182]~P106(f333(f145(x101821),x101823))+~P106(f333(f333(f335(x101821),x101822),f333(f180(x101821),x101823)))+E(f333(f176(x101821),f333(f179(x101821),f333(f333(f146(x101821),f333(f197(f911(x101821)),f185(x101821,f333(f333(f8(a905,a905,x101821),a328),f333(f333(f7(x101821,x101821,a905),a330),x101822)),x101823))),x101823))),f185(x101821,f333(f333(f8(a905,a905,x101821),a328),f333(f333(f7(x101821,x101821,a905),a330),x101822)),f333(f176(x101821),x101823))) % 173.51/173.28 [10267]~P120(x102672)+E(x102671,f2(x102672))+P106(f333(f333(f247(x102672),f2(x102672)),f333(f333(f87(x102672),f333(f333(f256(x102672),x102673),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x102672),x102671),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))))) % 173.51/173.28 [10268]~P120(x102682)+E(x102681,f2(x102682))+P106(f333(f333(f247(x102682),f2(x102682)),f333(f333(f87(x102682),f333(f333(f256(x102682),x102681),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x102682),x102683),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))))) % 173.51/173.28 [10316]~P120(x103161)+P106(f333(f333(f246(x103161),f2(x103161)),x103162))+~P106(f333(f333(f246(x103161),f2(x103161)),f333(f333(f256(x103161),x103162),f333(a123,f333(f333(f88(a910),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),x103163))))) % 173.51/173.28 [5630]~P26(x56301,x56304,x56303)+P26(x56301,x56302,x56303)+~P26(x56301,x56302,x56304) % 173.51/173.28 [5104]~E(x51042,f97(x51043,x51041))+P106(f333(x51041,x51042))+~P106(f333(x51041,x51044)) % 173.51/173.28 [5347]E(f74(x53473,x53472,x53474),x53472)+E(x53471,f784(x53472,x53473,x53474))+~P106(f333(x53474,x53471)) % 173.51/173.28 [6635]E(f74(x66351,x66352,x66353),f92(x66351,x66353))+~E(f821(x66352,x66351,x66353,x66354),x66354)+~P106(f333(x66353,x66354)) % 173.51/173.28 [6840]~P40(x68402,x68404)+~P40(x68401,x68403)+P40(f916(x68401,x68402),f325(x68401,x68402,x68403,x68404)) % 173.51/173.28 [6841]~P41(x68412,x68414)+~P41(x68411,x68413)+P41(f916(x68411,x68412),f325(x68411,x68412,x68413,x68414)) % 173.51/173.28 [5285]~P10(x52854,x52851)+~E(f333(x52851,x52852),f333(x52851,x52853))+P106(f333(f333(x52851,x52852),x52853)) % 173.51/173.28 [5450]~P10(x54504,x54501)+E(f333(x54501,x54502),f333(x54501,x54503))+~P106(f333(f333(x54501,x54502),x54503)) % 173.51/173.28 [5539]~P20(x55393,x55394,x55391)+E(f333(x55391,x55392),f333(f69(x55393,x55394),x55392))+~P106(f333(f67(x55393),x55392)) % 173.51/173.28 [5540]~P12(x55403,x55404,x55401)+E(f333(x55401,x55402),f333(f69(x55403,x55404),x55402))+~P106(f333(f67(x55403),x55402)) % 173.51/173.28 [5663]~P10(x56634,x56631)+~P106(f333(f333(x56631,x56633),x56632))+P106(f333(f333(x56631,x56632),x56633)) % 173.51/173.28 [5664]~P54(x56644,x56641)+~P106(f333(f333(x56641,x56643),x56642))+P106(f333(f333(x56641,x56642),x56643)) % 173.51/173.28 [5734]E(x57341,x57342)+~E(f333(f264(x57343,x57344),x57341),f333(f264(x57343,x57344),x57342))+~E(f333(f268(x57343,x57344),x57341),f333(f268(x57343,x57344),x57342)) % 173.51/173.28 [5759]E(x57591,x57592)+~P106(f333(f54(x57593,x57594),x57592))+~P106(f333(f54(x57593,x57594),x57591)) % 173.51/173.28 [5948]~P72(x59482)+E(f243(x59481,x59482,x59483,x59484),f2(x59482))+P106(f333(f67(x59481),x59484)) % 173.51/173.28 [6083]~P106(f333(f321(x60831,x60832),x60834))+P106(f333(f321(x60831,x60832),x60833))+~P106(f333(f333(x60832,x60833),x60834)) % 173.51/173.28 [6510]P52(x65101,x65102,x65103,x65104)+P106(f333(f333(x65102,x65104),x65103))+~P106(f333(f333(x65102,x65103),x65104)) % 173.51/173.28 [6874]~P33(x68741,x68743,x68744)+P106(f333(x68741,x68742))+~P106(f333(f333(f335(a1),x68742),f309(a1,x68743,x68744))) % 173.51/173.28 [7948]E(x79481,f2(a910))+~P106(f333(x79482,x79483))+P106(f333(x79482,f816(x79482,x79483,x79481,x79484))) % 173.51/173.28 [8030]~P110(x80302)+~P106(f333(f145(x80301),x80304))+P106(f333(f145(x80301),f158(x80301,x80302,x80303,x80304))) % 173.51/173.28 [8075]E(f74(x80751,x80752,x80753),f92(x80751,x80753))+~P106(f333(x80753,x80754))+P106(f333(x80753,f821(x80752,x80751,x80753,x80754))) % 173.51/173.28 [8259]~P106(f333(f67(x82592),x82594))+~P106(f333(f67(x82591),x82593))+P106(f333(f67(f918(x82591,x82592)),f319(x82591,x82592,x82593,x82594))) % 173.51/173.28 [8260]~P106(f333(f145(x82602),x82604))+~P106(f333(f145(x82601),x82603))+P106(f333(f145(f916(x82601,x82602)),f65(x82601,x82602,x82603,x82604))) % 173.51/173.28 [8263]P106(f333(f333(f335(f911(x82631)),f333(f333(f142(x82631),x82632),x82633)),f169(x82631,x82634)))+~P106(f333(f333(f335(f911(x82631)),x82633),f169(x82631,x82634)))+~P106(f333(f333(f335(f911(x82631)),x82632),f169(x82631,x82634))) % 173.51/173.28 [8546]E(x85461,f2(a910))+P106(f333(x85462,x85463))+~P106(f333(x85462,f817(x85462,x85463,x85461,x85464))) % 173.51/173.28 [8591]~P110(x85913)+~P106(f333(f145(x85911),f158(x85911,x85913,x85914,x85912)))+P106(f333(f145(x85911),x85912)) % 173.51/173.28 [8875]~P106(f333(f333(f335(f916(x88751,x88751)),f333(f333(f265(x88751,x88751),x88752),x88754)),f313(x88751,x88753)))+P106(f333(f333(f335(x88751),x88752),f322(x88751,x88753)))+~P106(f333(f333(f335(x88751),x88754),f322(x88751,x88753))) % 173.51/173.28 [5269]~P72(x52692)+E(f333(f333(f6(x52691,x52692),x52693),x52694),f2(x52692))+P106(f333(f67(x52691),x52694)) % 173.51/173.28 [5272]~P78(x52722)+E(f333(f333(f9(x52721,x52722),x52723),x52724),f85(x52722))+P106(f333(f67(x52721),x52724)) % 173.51/173.28 [5414]~P73(x54143)+E(x54141,x54142)+~E(f333(f333(f87(x54143),x54144),x54141),f333(f333(f87(x54143),x54144),x54142)) % 173.51/173.28 [5415]~P74(x54153)+E(x54151,x54152)+~E(f333(f333(f87(x54153),x54154),x54151),f333(f333(f87(x54153),x54154),x54152)) % 173.51/173.28 [5417]~P73(x54173)+E(x54171,x54172)+~E(f333(f333(f87(x54173),x54171),x54174),f333(f333(f87(x54173),x54172),x54174)) % 173.51/173.28 [5535]~P8(x55353)+E(x55351,f196(f917(x55352,a905)))+E(f333(f333(f45(x55352,x55353),x55351),f333(f16(x55353,x55352),x55354)),x55354) % 173.51/173.28 [5536]~P8(x55363)+E(x55361,f196(f917(x55362,a905)))+E(f333(f333(f46(x55362,x55363),x55361),f333(f16(x55363,x55362),x55364)),x55364) % 173.51/173.28 [5747]~P112(x57473)+E(x57471,x57472)+~E(f309(x57473,x57474,x57471),f333(f333(f315(x57473),x57472),f196(f917(x57473,a905)))) % 173.51/173.28 [5748]~P112(x57483)+E(x57481,x57482)+~E(f309(x57483,x57481,x57482),f333(f333(f315(x57483),x57484),f196(f917(x57483,a905)))) % 173.51/173.28 [5806]~P38(x58063,x58061,x58064)+P38(x58063,x58061,f333(f333(f159(x58063),x58062),x58064))+P106(f333(x58061,x58062)) % 173.51/173.28 [5907]~P34(x59071,x59072,x59074)+~P106(f333(x59072,x59073))+P34(x59071,x59072,f333(f333(f159(x59071),x59073),x59074)) % 173.51/173.28 [6039]P106(f333(x60391,x60392))+~P106(f333(f260(x60393,x60391),x60394))+~P106(f333(f333(f335(x60393),x60392),x60394)) % 173.51/173.28 [6048]~P34(x60481,x60482,x60484)+~P34(x60481,x60482,x60483)+P34(x60481,x60482,f333(f333(f142(x60481),x60483),x60484)) % 173.51/173.28 [6061]P36(x60611,x60612,x60613)+~P36(x60611,x60612,f333(f333(f159(x60611),x60614),x60613))+P106(f333(x60612,x60614)) % 173.51/173.28 [6062]P38(x60621,x60622,x60623)+~P38(x60621,x60622,f333(f333(f159(x60621),x60624),x60623))+P106(f333(x60622,x60624)) % 173.51/173.28 [6073]E(x60731,x60732)+~P106(f333(f333(f202(x60733),x60734),x60732))+~P106(f333(f333(f202(x60733),x60734),x60731)) % 173.51/173.28 [6140]P36(x61401,x61402,x61403)+P36(x61401,x61402,x61404)+~P36(x61401,x61402,f333(f333(f142(x61401),x61404),x61403)) % 173.51/173.28 [6159]~P72(x61591)+E(f333(f333(f6(a910,x61591),x61592),f333(f308(a910,x61593),f333(a123,x61594))),f2(x61591))+~P106(f333(f333(f247(a910),x61594),x61593)) % 173.51/173.28 [6164]~P65(x61641)+~E(f51(x61641,x61642,x61643),f51(x61641,x61644,x61643))+E(f51(x61641,f333(f86(x61641),x61642),x61643),f51(x61641,f333(f86(x61641),x61644),x61643)) % 173.51/173.28 [6231]P106(f333(x62311,x62312))+~E(f333(f144(x62313,x62311),x62314),x62314)+~P106(f333(f333(f335(x62313),x62312),f333(f180(x62313),x62314))) % 173.51/173.28 [6250]~E(f333(f333(f87(a910),x62503),x62502),f333(f333(f87(a910),x62501),x62504))+~P106(f333(f333(f247(a910),x62503),x62504))+P106(f333(f333(f247(a910),x62501),x62502)) % 173.51/173.28 [6256]P36(x62561,x62562,x62563)+~P106(f333(x62562,x62564))+~P106(f333(f333(f335(x62561),x62564),f333(f180(x62561),x62563))) % 173.51/173.28 [6294]~P34(x62943,x62941,x62944)+P106(f333(x62941,x62942))+~P106(f333(f333(f335(x62943),x62942),f333(f180(x62943),x62944))) % 173.51/173.28 [6296]~E(f333(f144(x62961,x62962),x62963),f124(x62961))+~P106(f333(x62962,x62964))+~P106(f333(f333(f335(x62961),x62964),f333(f180(x62961),x62963))) % 173.51/173.28 [6297]~E(f185(x62973,x62971,x62974),x62974)+P106(f333(x62971,x62972))+~P106(f333(f333(f335(x62973),x62972),f333(f180(x62973),x62974))) % 173.51/173.28 [6323]~E(x63234,f196(f917(x63232,a905)))+~E(x63233,f196(f917(x63231,a905)))+E(f319(x63231,x63232,x63233,x63234),f196(f917(f918(x63231,x63232),a905))) % 173.51/173.28 [6468]P106(f333(x64681,x64682))+~P106(f333(f168(x64683,x64681),x64684))+~P106(f333(f333(f335(x64683),x64682),f333(f180(x64683),x64684))) % 173.51/173.28 [6740]~P72(x67401)+E(f333(f333(f6(a910,x67401),x67402),f309(a910,x67403,f333(a123,x67404))),f2(x67401))+~P106(f333(f333(f247(a910),f333(a123,x67404)),x67403)) % 173.51/173.28 [6877]~P110(x68771)+E(f333(f333(f23(f917(x68771,a905)),f333(f308(x68771,x68772),x68773)),f333(f308(x68771,x68772),x68774)),f333(f308(x68771,x68774),x68773))+~P106(f333(f333(f246(x68771),x68772),x68774)) % 173.51/173.28 [6948]~E(x69483,x69484)+E(x69481,f2(a910))+P106(f333(f333(f335(x69482),x69483),f333(f180(x69482),f177(x69482,x69481,x69484)))) % 173.51/173.28 [7225]~P106(f333(f333(f335(f911(x72251)),x72254),f169(x72251,x72253)))+P106(f333(f333(f335(x72251),x72252),x72253))+~P106(f333(f333(f335(x72251),x72252),f333(f180(x72251),x72254))) % 173.51/173.28 [7232]~P40(x72321,x72322)+P106(f333(f333(f335(x72321),f670(x72322,x72321,x72323)),x72323))+~P106(f333(f333(f335(x72321),x72324),x72323)) % 173.51/173.28 [7287]~P72(x72871)+E(f333(f333(f333(f71(x72871,x72872,f87(x72871)),x72873),f2(x72871)),x72874),f333(f333(f6(x72872,x72871),x72873),x72874))+~P106(f333(f67(x72872),x72874)) % 173.51/173.28 [7289]~P78(x72891)+E(f333(f333(f333(f71(x72891,x72892,f88(x72891)),x72893),f85(x72891)),x72894),f333(f333(f9(x72892,x72891),x72893),x72894))+~P106(f333(f67(x72892),x72894)) % 173.51/173.28 [7318]P27(x73181,x73182,x73183,x73184)+~E(f333(f41(x73182),f333(f316(x73181,x73182,x73183),x73184)),f333(f41(x73181),x73184))+~P106(f333(f67(x73181),x73184)) % 173.51/173.28 [7507]~P72(x75071)+E(f333(f333(f87(x75071),f333(x75072,x75073)),f333(f333(f6(a910,x75071),x75072),f311(a910,x75073,x75074))),f333(f333(f6(a910,x75071),x75072),f309(a910,x75073,x75074)))+~P106(f333(f333(f246(a910),x75073),x75074)) % 173.51/173.28 [7517]~P72(x75171)+~P27(x75172,x75171,x75173,x75174)+E(f333(f333(f6(x75171,x75171),f33(x75171)),f333(f316(x75172,x75171,x75173),x75174)),f333(f333(f6(x75172,x75171),x75173),x75174)) % 173.51/173.28 [7518]~P78(x75181)+~P27(x75182,x75181,x75183,x75184)+E(f333(f333(f9(x75181,x75181),f33(x75181)),f333(f316(x75182,x75181,x75183),x75184)),f333(f333(f9(x75182,x75181),x75183),x75184)) % 173.51/173.28 [7567]E(f333(f41(f918(x75671,x75672)),f319(x75671,x75672,x75673,x75674)),f333(f333(f87(a910),f333(f41(x75671),x75673)),f333(f41(x75672),x75674)))+~P106(f333(f67(x75672),x75674))+~P106(f333(f67(x75671),x75673)) % 173.51/173.28 [7648]E(x76481,x76482)+P106(f333(f333(f335(x76483),x76481),f333(f180(x76483),f178(x76483,x76482,x76484))))+~P106(f333(f333(f335(x76483),x76481),f333(f180(x76483),x76484))) % 173.51/173.28 [7876]~P72(x78761)+E(f333(f333(f87(x78761),f333(f333(f6(a910,x78761),x78762),f333(f308(a910,x78763),x78764))),f333(x78762,x78764)),f333(f333(f6(a910,x78761),x78762),f333(f308(a910,x78763),f333(a123,x78764))))+P106(f333(f333(f247(a910),x78764),x78763)) % 173.51/173.28 [7930]~P27(x79301,x79302,x79303,f254(f917(x79301,a905)))+~P106(f333(f67(x79302),x79304))+P106(f333(f67(x79301),f333(f317(x79301,x79302,x79303),x79304))) % 173.51/173.28 [8045]P106(f333(f333(f335(f911(x80451)),f333(f333(f159(x80451),x80452),x80453)),f169(x80451,x80454)))+~P106(f333(f333(f335(f911(x80451)),x80453),f169(x80451,x80454)))+~P106(f333(f333(f335(x80451),x80452),x80454)) % 173.51/173.28 [8135]~E(f333(f316(x81353,x81351,x81354),f254(f917(x81353,a905))),f254(f917(x81351,a905)))+P106(f333(f67(x81351),x81352))+~P106(f333(f67(x81353),f333(f317(x81353,x81351,x81354),x81352))) % 173.51/173.28 [8231]~P27(x82311,x82313,x82314,x82312)+P106(f333(f67(x82311),x82312))+~P106(f333(f67(x82313),f333(f316(x82311,x82313,x82314),x82312))) % 173.51/173.28 [8251]~E(x82512,x82513)+P106(f333(f333(f335(f916(x82511,x82511)),f333(f333(f265(x82511,x82511),x82512),x82513)),f253(x82511,x82514)))+~P106(f333(f333(f335(x82511),x82512),x82514)) % 173.51/173.28 [8287]~P72(x82871)+E(f333(f333(f87(x82871),f333(f333(f6(a910,x82871),x82872),f309(a910,x82873,x82874))),f333(x82872,f333(a123,x82874))),f333(f333(f6(a910,x82871),x82872),f309(a910,x82873,f333(a123,x82874))))+P106(f333(f333(f247(a910),f333(a123,x82874)),x82873)) % 173.51/173.28 [8348]P106(f333(x83481,x83482))+~P106(f333(x83481,f333(f333(f172(x83483),x83484),f709(x83481,x83484,x83483))))+~P106(f333(f333(f335(x83483),x83482),f333(f180(x83483),x83484))) % 173.51/173.28 [8489]~P106(f333(f333(f335(x84891),x84892),f322(x84891,x84894)))+P106(f333(f333(f335(f911(x84891)),f333(f333(f159(x84891),x84892),x84893)),f322(f911(x84891),f165(x84891,x84894))))+~P106(f333(f333(f335(f911(x84891)),x84893),f322(f911(x84891),f165(x84891,x84894)))) % 173.51/173.28 [8504]~P27(x85042,x85043,x85044,f673(x85044,x85043,x85042,x85041))+P27(x85042,x85043,x85044,f44(f917(x85042,a905),x85041))+E(x85041,f196(f917(f917(x85042,a905),a905))) % 173.51/173.28 [8786]E(x87861,x87862)+~P106(f333(f333(f335(f916(x87863,x87863)),f333(f333(f265(x87863,x87863),x87861),x87862)),f313(x87863,x87864)))+P106(f333(f333(f335(x87863),x87861),f333(f263(x87863,x87863),x87864))) % 173.51/173.28 [9070]E(x90701,f2(a910))+P106(f333(x90702,x90703))+P106(f333(f333(f335(x90704),f817(x90702,x90703,x90701,x90704)),f333(f180(x90704),f177(x90704,x90701,x90703)))) % 173.51/173.28 [9082]E(x90821,f2(a910))+~P106(f333(x90823,x90824))+P106(f333(f333(f335(x90822),f816(x90823,x90824,x90821,x90822)),f333(f180(x90822),f177(x90822,x90821,x90824)))) % 173.51/173.28 [9085]~P28(x90851,x90852,x90853,f254(f917(x90851,a905)),f254(f917(x90852,a905)))+~P106(f333(f67(x90852),x90854))+P106(f333(f67(x90851),f333(f317(x90851,x90852,x90853),x90854))) % 173.51/173.28 [9090]P27(x90902,x90903,x90904,f44(f917(x90902,a905),x90901))+E(x90901,f196(f917(f917(x90902,a905),a905)))+P106(f333(f333(f335(f917(x90902,a905)),f673(x90904,x90903,x90902,x90901)),x90901)) % 173.51/173.28 [9142]~P27(x91421,x91422,x91423,f254(f917(x91421,a905)))+~E(f333(x91423,f333(x91424,f877(x91424,x91423,x91422,x91421))),f877(x91424,x91423,x91422,x91421))+E(f99(x91421,x91422,f254(f917(x91421,a905)),x91423),x91424) % 173.51/173.28 [9214]~P28(x92143,x92141,x92144,f254(f917(x92143,a905)),f254(f917(x92141,a905)))+P106(f333(f67(x92141),x92142))+~P106(f333(f67(x92143),f333(f317(x92143,x92141,x92144),x92142))) % 173.51/173.28 [9231]P106(f333(f67(x92311),x92312))+~P106(f333(f67(x92314),f333(f316(x92311,x92314,x92313),x92312)))+P106(f333(f333(f335(x92311),f476(x92313,x92314,x92312,x92311)),x92312)) % 173.51/173.28 [9327]~P8(x93272)+E(f333(f333(f70(x93271,x93272,f333(f333(f8(x93272,f917(x93272,x93272),x93271),f121(x93272)),x93273)),f196(x93272)),x93274),f333(f333(f45(x93271,x93272),x93274),x93273))+~P106(f333(f67(x93271),x93274)) % 173.51/173.28 [9328]~P8(x93282)+E(f333(f333(f70(x93281,x93282,f333(f333(f8(x93282,f917(x93282,x93282),x93281),f112(x93282)),x93283)),f254(x93282)),x93284),f333(f333(f46(x93281,x93282),x93284),x93283))+~P106(f333(f67(x93281),x93284)) % 173.51/173.28 [9413]P106(f333(x94131,x94132))+~P106(f333(x94131,f333(f333(f172(x94133),x94134),f744(x94132,x94131,x94134,x94133))))+~P106(f333(f333(f335(x94133),x94132),f333(f180(x94133),x94134))) % 173.51/173.28 [9433]E(x94331,x94332)+~P106(f333(f333(f335(f916(x94333,x94333)),f333(f333(f265(x94333,x94333),x94331),x94332)),f313(x94333,x94334)))+P106(f333(f333(f335(f916(x94333,x94333)),f333(f333(f265(x94333,x94333),x94331),x94332)),f333(f333(f295(x94333,x94333,x94333),x94334),f313(x94333,x94334)))) % 173.51/173.28 [9488]~E(f333(f197(f911(x94881)),x94882),f333(f197(f911(x94881)),x94883))+~P106(f333(f333(f335(f916(f911(x94881),f911(x94881))),f333(f333(f265(f911(x94881),f911(x94881)),x94882),x94883)),f155(x94881,x94884)))+P106(f333(f333(f335(f916(f911(x94881),f911(x94881))),f333(f333(f265(f911(x94881),f911(x94881)),x94882),x94883)),f153(x94881,x94884))) % 173.51/173.28 [9734]P34(x97341,f333(f333(f18(x97341,a905,a905),f333(f333(f8(a905,f917(a905,a905),x97341),a332),f333(f333(f8(a905,a905,x97341),a328),x97342))),f333(a330,x97343)),x97344)+~P106(f333(x97342,x97343))+~P38(x97341,x97342,f333(f333(f159(x97341),x97343),x97344)) % 173.51/173.28 [9900]~P34(x99001,f333(f333(f18(x99001,a905,a905),f333(f333(f8(a905,f917(a905,a905),x99001),a332),f333(f333(f8(a905,a905,x99001),a328),x99002))),f333(a330,x99003)),x99004)+~P106(f333(x99002,x99003))+P38(x99001,x99002,f333(f333(f159(x99001),x99003),x99004)) % 173.51/173.28 [9904]~P38(x99041,x99042,x99044)+~P34(x99041,f333(f333(f18(x99041,a905,a905),f333(f333(f8(a905,f917(a905,a905),x99041),a332),f333(f333(f8(a905,a905,x99041),a328),x99042))),f333(a330,x99043)),x99044)+P38(x99041,x99042,f333(f333(f159(x99041),x99043),x99044)) % 173.51/173.28 [9939]~P6(x99391)+E(f333(f333(f6(a910,x99391),f333(f333(f18(a910,x99391,x99391),f333(f333(f8(x99391,f917(x99391,x99391),a910),f23(x99391)),x99392)),f333(f333(f8(a910,x99391,a910),x99392),f333(f333(f7(a910,a910,a910),f87(a910)),f85(a910))))),f309(a910,x99393,x99394)),f2(x99391))+P106(f333(f333(f246(a910),x99393),x99394)) % 173.51/173.28 [10174]~P40(x101742,x101744)+~P27(x101742,x101741,x101743,f254(f917(x101742,a905)))+P40(x101741,f333(f316(f916(x101742,x101742),f916(x101741,x101741),f270(x101742,x101741,x101742,x101741,x101743,x101743)),x101744)) % 173.51/173.28 [10352]~E(f333(f197(f911(x103521)),x103523),f333(f197(f911(x103521)),x103522))+P106(f333(f333(f335(f916(f911(x103521),f911(x103521))),f333(f333(f265(f911(x103521),f911(x103521)),x103522),x103523)),f166(x103521,x103524)))+~P106(f333(f333(f269(x103521,x103521,a905),f333(f333(f7(x103521,f917(f916(x103521,x103521),a905),f917(x103521,a905)),f333(f333(f8(f917(x103521,f917(f917(f916(x103521,x103521),a905),a905)),f917(f917(f916(x103521,x103521),a905),f917(x103521,a905)),x103521),f7(x103521,f917(f916(x103521,x103521),a905),a905)),f333(f333(f8(f917(x103521,f916(x103521,x103521)),f917(x103521,f917(f917(f916(x103521,x103521),a905),a905)),x103521),f333(f8(f916(x103521,x103521),f917(f917(f916(x103521,x103521),a905),a905),x103521),f335(f916(x103521,x103521)))),f265(x103521,x103521)))),x103524)),f711(x103524,x103523,x103522,x103521))) % 173.51/173.28 [6122]~E(x61224,x61222)+P106(f333(x61221,x61222))+P106(f333(f333(f202(f30(x61221,x61223)),x61222),x61224)) % 173.51/173.28 [6214]~P64(x62141)+~E(x62142,f2(x62141))+E(f333(f333(f42(x62141),f333(f333(f88(x62141),x62142),x62143)),f333(f333(f88(x62141),x62142),x62144)),f2(x62141)) % 173.51/173.28 [6253]E(x62531,f124(x62532))+E(x62533,f333(f333(f23(a910),f333(f197(f911(x62532)),x62531)),f85(a910)))+E(f152(x62532,f333(f333(f167(x62532,x62531),x62533),x62534)),f152(x62532,x62531)) % 173.51/173.28 [6285]E(x62851,x62852)+P106(f333(x62853,x62852))+~P106(f333(f333(f333(f315(x62854),x62851),x62853),x62852)) % 173.51/173.28 [6301]~P72(x63011)+~P106(f333(f145(x63012),x63014))+E(f333(f173(x63011),f333(f333(f162(x63012,x63011),x63013),x63014)),f333(f333(f6(x63012,x63011),x63013),f333(f180(x63012),x63014))) % 173.51/173.28 [6316]~P78(x63162)+~P106(f333(f67(x63161),x63164))+E(f333(f333(f9(x63161,x63162),f333(f16(x63162,x63161),x63163)),x63164),f333(f333(f256(x63162),x63163),f333(f41(x63161),x63164))) % 173.51/173.28 [6369]~P67(x63692)+E(x63691,f2(x63692))+E(f333(f333(f296(x63692),f333(f333(f88(x63692),x63693),x63691)),f333(f333(f88(x63692),x63694),x63691)),f333(f333(f296(x63692),x63693),x63694)) % 173.51/173.28 [6370]~P67(x63702)+E(x63701,f2(x63702))+E(f333(f333(f296(x63702),f333(f333(f88(x63702),x63701),x63703)),f333(f333(f88(x63702),x63701),x63704)),f333(f333(f296(x63702),x63703),x63704)) % 173.51/173.28 [6371]~P64(x63712)+E(x63711,f2(x63712))+E(f333(f333(f42(x63712),f333(f333(f88(x63712),x63713),x63711)),f333(f333(f88(x63712),x63714),x63711)),f333(f333(f42(x63712),x63713),x63714)) % 173.51/173.28 [6373]~P64(x63732)+E(x63731,f2(x63732))+E(f333(f333(f42(x63732),f333(f333(f88(x63732),x63731),x63733)),f333(f333(f88(x63732),x63731),x63734)),f333(f333(f42(x63732),x63733),x63734)) % 173.51/173.28 [6438]P106(f333(x64381,x64382))+~E(x64383,f333(f333(f87(a910),x64384),x64382))+~P106(f333(x64381,f333(f333(f23(a910),x64383),x64384))) % 173.51/173.28 [6520]P31(x65201,x65202,x65203)+P32(x65201,f525(x65203,x65202,x65201),x65204)+~P106(f333(f333(f335(f909(x65201)),x65204),x65202)) % 173.51/173.28 [6522]~P106(f333(x65222,x65223))+~P106(f333(f168(x65221,x65222),x65224))+P106(f333(f168(x65221,x65222),f333(f333(f159(x65221),x65223),x65224))) % 173.51/173.28 [6564]E(x65641,f124(x65642))+~E(x65643,f333(f333(f23(a910),f333(f197(f911(x65642)),x65641)),f85(a910)))+E(f152(x65642,f333(f333(f167(x65642,x65641),x65643),x65644)),x65644) % 173.51/173.28 [6587]~P101(x65871)+~P106(f333(f333(f246(x65871),x65872),x65874))+P106(f333(f333(f246(x65871),x65872),f333(f333(f121(x65871),x65873),x65874))) % 173.51/173.28 [6588]~P101(x65881)+~P106(f333(f333(f246(x65881),x65882),x65883))+P106(f333(f333(f246(x65881),x65882),f333(f333(f121(x65881),x65883),x65884))) % 173.51/173.28 [6590]~P110(x65901)+~P106(f333(f333(f246(x65901),x65902),x65904))+P106(f333(f333(f246(x65901),x65902),f333(f333(f245(x65901),x65903),x65904))) % 173.51/173.28 [6592]~P110(x65921)+~P106(f333(f333(f246(x65921),x65922),x65923))+P106(f333(f333(f246(x65921),x65922),f333(f333(f245(x65921),x65923),x65924))) % 173.51/173.28 [6593]~P101(x65931)+~P106(f333(f333(f247(x65931),x65932),x65934))+P106(f333(f333(f247(x65931),x65932),f333(f333(f121(x65931),x65933),x65934))) % 173.51/173.28 [6594]~P101(x65941)+~P106(f333(f333(f247(x65941),x65942),x65943))+P106(f333(f333(f247(x65941),x65942),f333(f333(f121(x65941),x65943),x65944))) % 173.51/173.28 [6596]~P110(x65961)+~P106(f333(f333(f247(x65961),x65962),x65964))+P106(f333(f333(f247(x65961),x65962),f333(f333(f245(x65961),x65963),x65964))) % 173.51/173.28 [6598]~P110(x65981)+~P106(f333(f333(f247(x65981),x65982),x65983))+P106(f333(f333(f247(x65981),x65982),f333(f333(f245(x65981),x65983),x65984))) % 173.51/173.28 [6685]~E(f333(f333(f172(x66851),x66852),x66853),x66854)+E(f333(f333(f167(x66851,x66852),x66853),x66854),x66852)+~P106(f333(f333(f247(a910),x66853),f333(f197(f911(x66851)),x66852))) % 173.51/173.28 [6703]E(x67031,x67032)+P106(f333(x67033,x67031))+~P106(f333(f333(f202(f30(x67033,x67034)),x67031),x67032)) % 173.51/173.28 [6726]P106(f333(x67261,x67262))+~P106(f333(x67263,x67262))+~P106(f333(f333(f246(f917(x67264,a905)),x67263),x67261)) % 173.51/173.28 [6758]~E(f333(f333(f167(x67581,x67582),x67583),x67584),x67582)+E(f333(f333(f172(x67581),x67582),x67583),x67584)+~P106(f333(f333(f247(a910),x67583),f333(f197(f911(x67581)),x67582))) % 173.51/173.28 [6772]~P106(f333(f168(x67721,x67722),x67724))+~P106(f333(f168(x67721,x67722),x67723))+P106(f333(f168(x67721,x67722),f333(f333(f142(x67721),x67723),x67724))) % 173.51/173.28 [6866]P32(x68661,x68662,x68663)+~P32(x68661,f333(a123,x68662),f631(x68662,x68664,x68661))+~P106(f333(f333(f335(f909(x68661)),x68663),x68664)) % 173.51/173.28 [6873]E(x68731,f196(f917(x68732,a905)))+E(x68733,f196(f917(x68734,a905)))+~E(f333(f333(f267(x68734,x68732),x68733),f333(f16(f917(x68732,a905),x68734),x68731)),f196(f917(f916(x68734,x68732),a905))) % 173.51/173.28 [6893]E(x68931,x68932)+P106(f333(f333(f335(x68933),x68931),x68934))+~P106(f333(f333(f335(x68933),x68931),f333(f333(f315(x68933),x68932),x68934))) % 173.51/173.28 [6910]~P102(x69101)+P106(f333(f333(f246(x69101),x69102),x69103))+~P106(f333(f333(f246(x69101),x69102),f333(f333(f112(x69101),x69104),x69103))) % 173.51/173.28 [6912]~P102(x69121)+P106(f333(f333(f246(x69121),x69122),x69123))+~P106(f333(f333(f246(x69121),x69122),f333(f333(f112(x69121),x69123),x69124))) % 173.51/173.28 [6914]~P110(x69141)+P106(f333(f333(f246(x69141),x69142),x69143))+~P106(f333(f333(f246(x69141),x69142),f333(f333(f244(x69141),x69144),x69143))) % 173.51/173.28 [6916]~P110(x69161)+P106(f333(f333(f246(x69161),x69162),x69163))+~P106(f333(f333(f246(x69161),x69162),f333(f333(f244(x69161),x69163),x69164))) % 173.51/173.28 [6917]~P110(x69171)+P106(f333(f333(f247(x69171),x69172),x69173))+~P106(f333(f333(f247(x69171),x69172),f333(f333(f244(x69171),x69174),x69173))) % 173.51/173.28 [6918]~P110(x69181)+P106(f333(f333(f247(x69181),x69182),x69183))+~P106(f333(f333(f247(x69181),x69182),f333(f333(f244(x69181),x69183),x69184))) % 173.51/173.28 [6939]~E(f333(f333(f172(x69391),x69393),x69394),x69392)+P106(f333(f333(f335(x69391),x69392),f333(f180(x69391),x69393)))+~P106(f333(f333(f247(a910),x69394),f333(f197(f911(x69391)),x69393))) % 173.51/173.28 [6949]~P110(x69491)+~P16(x69491,f333(f333(f159(x69491),x69492),f333(f333(f159(x69491),x69493),x69494)))+P106(f333(f333(f246(x69491),x69492),x69493)) % 173.51/173.28 [7090]~P34(x70902,x70901,x70903)+P106(f333(x70901,f333(f333(f172(x70902),x70903),x70904)))+~P106(f333(f333(f247(a910),x70904),f333(f197(f911(x70902)),x70903))) % 173.51/173.28 [7108]E(x71081,f2(a1))+E(f333(f333(f42(a1),x71082),x71081),x71083)+~P106(f333(f55(x71082,x71081),f333(f333(f265(a1,a1),x71083),x71084))) % 173.51/173.28 [7129]E(f51(a1,x71292,x71291),x71293)+E(x71291,f2(a1))+~P106(f333(f55(x71292,x71291),f333(f333(f265(a1,a1),x71294),x71293))) % 173.51/173.28 [7249]P106(f333(f333(f335(x72491),x72492),x72493))+~P106(f333(f333(f335(x72491),x72492),x72494))+~P106(f333(f333(f247(f917(x72491,a905)),x72494),x72493)) % 173.51/173.28 [7250]P106(f333(f333(f335(x72501),x72502),x72503))+~P106(f333(f333(f335(x72501),x72502),x72504))+~P106(f333(f333(f246(f917(x72501,a905)),x72504),x72503)) % 173.51/173.28 [7361]P36(x73611,x73612,x73613)+~P106(f333(x73612,f333(f333(f172(x73611),x73613),x73614)))+~P106(f333(f333(f247(a910),x73614),f333(f197(f911(x73611)),x73613))) % 173.51/173.28 [7474]~P111(x74742)+~P106(f333(f333(f247(f917(x74741,x74742)),x74743),x74744))+P106(f333(f333(f246(f917(x74741,x74742)),x74743),x74744)) % 173.51/173.28 [7556]~P26(x75561,x75562,x75564)+P26(x75561,x75562,f333(f333(f315(f909(x75561)),x75563),x75564))+~P26(x75561,x75562,f333(f333(f315(f909(x75561)),x75563),f196(f917(f909(x75561),a905)))) % 173.51/173.28 [7599]~P106(f333(f333(f335(x75991),x75992),x75994))+P106(f333(f333(f335(x75991),x75992),f43(f917(x75991,a905),x75993)))+~P106(f333(f333(f335(f917(x75991,a905)),x75994),x75993)) % 173.51/173.28 [7609]P32(x76091,x76092,x76093)+P106(f333(f333(f335(f909(x76091)),f631(x76092,x76094,x76091)),x76094))+~P106(f333(f333(f335(f909(x76091)),x76093),x76094)) % 173.51/173.28 [7628]~P86(x76281)+~P106(f333(f333(f246(x76281),x76283),x76284))+P106(f333(f333(f246(x76281),f333(f333(f87(x76281),x76282),x76283)),f333(f333(f87(x76281),x76282),x76284))) % 173.51/173.28 [7629]~P89(x76291)+~P106(f333(f333(f246(x76291),x76293),x76294))+P106(f333(f333(f246(x76291),f333(f333(f87(x76291),x76292),x76293)),f333(f333(f87(x76291),x76292),x76294))) % 173.51/173.28 [7630]~P86(x76301)+~P106(f333(f333(f246(x76301),x76302),x76304))+P106(f333(f333(f246(x76301),f333(f333(f87(x76301),x76302),x76303)),f333(f333(f87(x76301),x76304),x76303))) % 173.51/173.28 [7631]~P89(x76311)+~P106(f333(f333(f246(x76311),x76312),x76314))+P106(f333(f333(f246(x76311),f333(f333(f87(x76311),x76312),x76313)),f333(f333(f87(x76311),x76314),x76313))) % 173.51/173.28 [7632]~P88(x76321)+~P106(f333(f333(f247(x76321),x76323),x76324))+P106(f333(f333(f247(x76321),f333(f333(f87(x76321),x76322),x76323)),f333(f333(f87(x76321),x76322),x76324))) % 173.51/173.28 [7633]~P89(x76331)+~P106(f333(f333(f247(x76331),x76333),x76334))+P106(f333(f333(f247(x76331),f333(f333(f87(x76331),x76332),x76333)),f333(f333(f87(x76331),x76332),x76334))) % 173.51/173.28 [7634]~P88(x76341)+~P106(f333(f333(f247(x76341),x76342),x76344))+P106(f333(f333(f247(x76341),f333(f333(f87(x76341),x76342),x76343)),f333(f333(f87(x76341),x76344),x76343))) % 173.51/173.28 [7635]~P89(x76351)+~P106(f333(f333(f247(x76351),x76352),x76354))+P106(f333(f333(f247(x76351),f333(f333(f87(x76351),x76352),x76353)),f333(f333(f87(x76351),x76354),x76353))) % 173.51/173.28 [7642]~P113(x76421)+~P96(x76421)+E(f333(f333(f23(x76421),f333(f333(f88(x76421),x76422),f333(f114(x76421),x76423))),f333(f333(f88(x76421),x76424),f333(f114(x76421),x76423))),f333(f333(f88(x76421),f333(f333(f23(x76421),x76422),x76424)),f333(f114(x76421),x76423))) % 173.51/173.28 [7643]~P142(x76431)+~P96(x76431)+E(f333(f333(f87(x76431),f333(f333(f88(x76431),x76432),f333(f114(x76431),x76433))),f333(f333(f88(x76431),x76434),f333(f114(x76431),x76433))),f333(f333(f88(x76431),f333(f333(f87(x76431),x76432),x76434)),f333(f114(x76431),x76433))) % 173.51/173.28 [7679]~P72(x76791)+E(f333(f333(f87(x76791),f333(x76792,x76793)),f333(f333(f6(a910,x76791),x76792),f309(a910,f333(a123,x76793),x76794))),f333(f333(f6(a910,x76791),x76792),f309(a910,x76793,x76794)))+~P106(f333(f333(f246(a910),x76793),x76794)) % 173.51/173.28 [7691]~P27(x76912,x76911,x76913,f333(f180(x76912),x76914))+~P106(f333(f145(x76912),x76914))+P106(f333(f145(x76911),f333(f333(f162(x76912,x76911),x76913),x76914))) % 173.51/173.28 [7738]~P106(f333(f333(f246(a910),x77382),x77384))+~P106(f333(f333(f246(a910),x77381),x77383))+P106(f333(f333(f246(a910),f333(f333(f87(a910),x77381),x77382)),f333(f333(f87(a910),x77383),x77384))) % 173.51/173.28 [7739]~P106(f333(f333(f246(a910),x77392),x77394))+~P106(f333(f333(f246(a910),x77391),x77393))+P106(f333(f333(f246(a910),f333(f333(f88(a910),x77391),x77392)),f333(f333(f88(a910),x77393),x77394))) % 173.51/173.28 [7742]~P106(f333(f333(f247(a910),x77422),x77424))+~P106(f333(f333(f247(a910),x77421),x77423))+P106(f333(f333(f247(a910),f333(f333(f87(a910),x77421),x77422)),f333(f333(f87(a910),x77423),x77424))) % 173.51/173.28 [7743]~P106(f333(f333(f246(a1),x77432),x77434))+~P106(f333(f333(f247(a1),x77431),x77433))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x77431),x77432)),f333(f333(f87(a1),x77433),x77434))) % 173.51/173.28 [7790]P106(f333(f333(f335(x77901),x77902),x77903))+~P106(f333(f333(f335(x77901),x77902),f44(f917(x77901,a905),x77904)))+~P106(f333(f333(f335(f917(x77901,a905)),x77903),x77904)) % 173.51/173.28 [7806]~P106(f333(x78061,f704(x78061,x78063,x78062)))+P106(f333(x78061,f333(f333(f172(x78062),x78063),x78064)))+~P106(f333(f333(f247(a910),x78064),f333(f197(f911(x78062)),x78063))) % 173.51/173.28 [7813]P106(f333(x78131,x78132))+~P106(f333(f333(f335(x78134),x78132),f333(f180(x78134),x78133)))+P106(f333(f333(f247(a910),f709(x78131,x78133,x78134)),f333(f197(f911(x78134)),x78133))) % 173.51/173.28 [7830]~P106(f333(f333(f202(x78302),x78303),x78304))+~P106(f333(f333(f202(f30(x78301,x78302)),x78304),x78303))+P106(f333(f333(f202(f30(x78301,x78302)),x78303),x78303)) % 173.51/173.28 [7861]~P111(x78611)+~P106(f333(f333(f247(f917(x78612,x78611)),x78614),x78613))+~P106(f333(f333(f246(f917(x78612,x78611)),x78613),x78614)) % 173.51/173.28 [7907]~P106(f333(x79074,x79072))+~P106(f333(f333(f335(x79071),x79072),x79073))+P106(f333(f333(f335(x79071),x79072),f333(f333(f112(f917(x79071,a905)),x79073),f333(f252(x79071),x79074)))) % 173.51/173.28 [8052]~P106(f333(f333(f335(x80521),x80523),x80524))+~P106(f333(f333(f247(f917(x80521,a905)),x80522),x80524))+P106(f333(f333(f247(f917(x80521,a905)),x80522),f333(f333(f315(x80521),x80523),x80524))) % 173.51/173.28 [8054]E(f333(f333(f112(f917(x80541,a905)),x80542),x80543),f196(f917(x80541,a905)))+~E(f333(f333(f112(f917(x80541,a905)),f43(f917(x80541,a905),x80544)),x80543),f196(f917(x80541,a905)))+~P106(f333(f333(f335(f917(x80541,a905)),x80542),x80544)) % 173.51/173.28 [8131]P106(f333(f333(f335(x81311),x81312),x81313))+~P106(f333(f333(f246(f917(x81311,a905)),x81313),f333(f333(f315(x81311),x81312),x81314)))+P106(f333(f333(f246(f917(x81311,a905)),x81313),x81314)) % 173.51/173.28 [8151]P106(f333(f333(f335(x81512),f704(x81511,x81513,x81512)),f333(f180(x81512),x81513)))+P106(f333(x81511,f333(f333(f172(x81512),x81513),x81514)))+~P106(f333(f333(f247(a910),x81514),f333(f197(f911(x81512)),x81513))) % 173.51/173.28 [8159]~P106(f333(f333(f246(f917(x81591,a905)),x81592),x81594))+P106(f333(f333(f246(f917(x81591,a905)),x81592),x81593))+~P106(f333(f333(f246(f917(x81591,a905)),x81594),x81593)) % 173.51/173.28 [8160]~P106(f333(f333(f247(f917(x81601,a905)),x81602),x81604))+~P106(f333(f333(f246(f917(x81601,a905)),x81604),x81603))+P106(f333(f333(f247(f917(x81601,a905)),x81602),x81603)) % 173.51/173.28 [8161]~P106(f333(f333(f246(f917(x81611,a905)),x81612),x81614))+~P106(f333(f333(f247(f917(x81611,a905)),x81614),x81613))+P106(f333(f333(f247(f917(x81611,a905)),x81612),x81613)) % 173.51/173.28 [8162]~P106(f333(f333(f247(f917(x81621,a905)),x81622),x81624))+P106(f333(f333(f247(f917(x81621,a905)),x81622),x81623))+~P106(f333(f333(f247(f917(x81621,a905)),x81624),x81623)) % 173.51/173.28 [8205]~P106(f333(f333(f335(x82051),x82054),x82053))+~P106(f333(f333(f247(f917(x82051,a905)),x82052),f333(f333(f315(x82051),x82054),x82053)))+P106(f333(f333(f247(f917(x82051,a905)),x82052),x82053)) % 173.51/173.28 [8217]~P89(x82171)+P106(f333(f333(f246(x82171),x82172),x82173))+~P106(f333(f333(f246(x82171),f333(f333(f87(x82171),x82174),x82172)),f333(f333(f87(x82171),x82174),x82173))) % 173.51/173.28 [8219]~P89(x82191)+P106(f333(f333(f246(x82191),x82192),x82193))+~P106(f333(f333(f246(x82191),f333(f333(f87(x82191),x82192),x82194)),f333(f333(f87(x82191),x82193),x82194))) % 173.51/173.28 [8221]~P89(x82211)+P106(f333(f333(f247(x82211),x82212),x82213))+~P106(f333(f333(f247(x82211),f333(f333(f87(x82211),x82214),x82212)),f333(f333(f87(x82211),x82214),x82213))) % 173.51/173.28 [8223]~P89(x82231)+P106(f333(f333(f247(x82231),x82232),x82233))+~P106(f333(f333(f247(x82231),f333(f333(f87(x82231),x82232),x82234)),f333(f333(f87(x82231),x82233),x82234))) % 173.51/173.28 [8270]P106(f333(x82701,x82702))+~E(f333(f333(f146(x82703),f333(f197(f911(x82703)),f185(x82703,x82701,x82704))),x82704),f124(x82703))+~P106(f333(f333(f335(x82703),x82702),f333(f180(x82703),x82704))) % 173.51/173.28 [8391]P106(f333(x83911,x83912))+~P106(f333(f333(f335(x83913),x83912),f333(f180(x83913),x83914)))+P106(f333(f333(f247(a910),f333(f197(f911(x83913)),f333(f144(x83913,x83911),x83914))),f333(f197(f911(x83913)),x83914))) % 173.51/173.28 [8521]E(x85211,x85212)+P106(f333(f333(f202(x85213),x85211),f373(x85212,x85211,x85213,x85214)))+~P106(f333(f333(f202(f30(x85214,x85213)),x85211),x85212)) % 173.51/173.28 [8522]E(x85221,x85222)+P106(f333(f333(f202(x85223),x85221),f407(x85222,x85221,x85223,x85224)))+~P106(f333(f333(f202(f30(x85224,x85223)),x85221),x85222)) % 173.51/173.28 [8551]~P106(f333(x85514,x85512))+P106(f333(f333(f202(x85511),x85512),f373(x85513,x85512,x85511,x85514)))+~P106(f333(f333(f202(f30(x85514,x85511)),x85512),x85513)) % 173.51/173.28 [8552]~P106(f333(x85524,x85522))+P106(f333(f333(f202(x85521),x85522),f407(x85523,x85522,x85521,x85524)))+~P106(f333(f333(f202(f30(x85524,x85521)),x85522),x85523)) % 173.51/173.28 [8891]~P106(f333(x88911,f788(x88911,x88913,x88912,x88914)))+P106(f333(x88911,f333(f333(f172(x88912),x88913),x88914)))+~P106(f333(f333(f247(a910),x88914),f333(f197(f911(x88912)),x88913))) % 173.51/173.28 [8915]~P27(x89154,x89153,x89151,f254(f917(x89154,a905)))+E(f333(x89151,f826(x89152,x89151,x89153,x89154)),x89152)+~P106(f333(f333(f335(x89153),x89152),f333(f316(x89154,x89153,x89151),f254(f917(x89154,a905))))) % 173.51/173.28 [8983]E(f185(x89831,x89832,x89833),f333(f333(f183(x89831),x89834),x89833))+P106(f333(f333(f247(a910),f770(x89832,x89833,x89831,x89834)),x89834))+P106(f333(f333(f247(a910),x89834),f333(f197(f911(x89831)),x89833))) % 173.51/173.28 [8986]E(f185(x89861,x89862,x89863),f333(f333(f183(x89861),x89864),x89863))+P106(f333(f333(f247(a910),f770(x89862,x89863,x89861,x89864)),x89864))+P106(f333(x89862,f333(f333(f172(x89861),x89863),x89864))) % 173.51/173.28 [9021]P106(f333(x90211,x90212))+~P106(f333(f333(f335(x90214),x90212),f333(f180(x90214),x90213)))+P106(f333(f333(f247(a910),f744(x90212,x90211,x90213,x90214)),f333(f197(f911(x90214)),x90213))) % 173.51/173.28 [9024]E(f185(x90241,x90242,x90243),f333(f333(f183(x90241),x90244),x90243))+P106(f333(f333(f247(a910),x90244),f333(f197(f911(x90241)),x90243)))+P106(f333(f333(f247(a910),f770(x90242,x90243,x90241,x90244)),f333(f197(f911(x90241)),x90243))) % 173.51/173.28 [9031]E(f185(x90311,x90312,x90313),f333(f333(f183(x90311),x90314),x90313))+P106(f333(x90312,f333(f333(f172(x90311),x90313),x90314)))+P106(f333(f333(f247(a910),f770(x90312,x90313,x90311,x90314)),f333(f197(f911(x90311)),x90313))) % 173.51/173.28 [9060]~P119(x90604)+P106(f333(f333(f335(x90601),f693(x90602,x90603,x90601,x90604)),x90603))+P106(f333(f333(f247(x90604),f2(x90604)),f333(f333(f9(x90601,x90604),x90602),x90603))) % 173.51/173.28 [9061]~P119(x90614)+P106(f333(f333(f335(x90611),f695(x90612,x90613,x90611,x90614)),x90613))+P106(f333(f333(f246(x90614),f2(x90614)),f333(f333(f9(x90611,x90614),x90612),x90613))) % 173.51/173.28 [9092]~P106(f333(f67(x90921),x90924))+P106(f333(f333(f335(x90921),f563(x90922,x90923,x90924,x90921)),x90924))+P106(f333(f67(f916(x90921,x90923)),f333(f333(f267(x90921,x90923),x90924),x90922))) % 173.51/173.28 [9128]P106(f333(f333(f335(x91282),f788(x91281,x91283,x91282,x91284)),f333(f180(x91282),x91283)))+P106(f333(x91281,f333(f333(f172(x91282),x91283),x91284)))+~P106(f333(f333(f247(a910),x91284),f333(f197(f911(x91282)),x91283))) % 173.51/173.28 [9144]E(x91441,x91442)+P106(f333(f333(f202(f30(x91443,x91444)),f373(x91441,x91442,x91444,x91443)),x91441))+~P106(f333(f333(f202(f30(x91443,x91444)),x91442),x91441)) % 173.51/173.28 [9145]E(x91451,x91452)+P106(f333(f333(f202(f30(x91453,x91454)),f407(x91451,x91452,x91454,x91453)),x91451))+~P106(f333(f333(f202(f30(x91453,x91454)),x91452),x91451)) % 173.51/173.28 [9165]~P106(f333(x91651,x91654))+P106(f333(f333(f202(f30(x91651,x91652)),f373(x91653,x91654,x91652,x91651)),x91653))+~P106(f333(f333(f202(f30(x91651,x91652)),x91654),x91653)) % 173.51/173.28 [9166]~P106(f333(x91661,x91664))+P106(f333(f333(f202(f30(x91661,x91662)),f407(x91663,x91664,x91662,x91661)),x91663))+~P106(f333(f333(f202(f30(x91661,x91662)),x91664),x91663)) % 173.51/173.28 [9263]P106(f333(f333(f246(a910),x92634),f333(f197(f911(x92632)),f185(x92632,x92633,x92631))))+P106(f333(f333(f247(a910),f771(x92631,x92632,x92633,x92634)),x92634))+~P106(f333(f333(f246(a910),x92634),f333(f197(f911(x92632)),x92631))) % 173.51/173.28 [9417]E(f185(x94171,x94172,x94173),f333(f333(f183(x94171),x94174),x94173))+~P106(f333(x94172,f333(f333(f172(x94171),x94173),f770(x94172,x94173,x94171,x94174))))+P106(f333(f333(f247(a910),x94174),f333(f197(f911(x94171)),x94173))) % 173.51/173.28 [9423]E(f185(x94231,x94232,x94233),f333(f333(f183(x94231),x94234),x94233))+~P106(f333(x94232,f333(f333(f172(x94231),x94233),f770(x94232,x94233,x94231,x94234))))+P106(f333(x94232,f333(f333(f172(x94231),x94233),x94234))) % 173.51/173.28 [9427]~P106(f333(f67(x94271),x94273))+~P106(f333(f67(x94272),f333(x94274,f563(x94274,x94272,x94273,x94271))))+P106(f333(f67(f916(x94271,x94272)),f333(f333(f267(x94271,x94272),x94273),x94274))) % 173.51/173.28 [9435]~P119(x94351)+~P106(f333(f333(f246(x94351),f2(x94351)),f333(x94353,f695(x94353,x94354,x94352,x94351))))+P106(f333(f333(f246(x94351),f2(x94351)),f333(f333(f9(x94352,x94351),x94353),x94354))) % 173.51/173.28 [9436]~P119(x94361)+~P106(f333(f333(f247(x94361),f2(x94361)),f333(x94363,f693(x94363,x94364,x94362,x94361))))+P106(f333(f333(f247(x94361),f2(x94361)),f333(f333(f9(x94362,x94361),x94363),x94364))) % 173.51/173.28 [9444]~E(f333(f197(f911(x94444)),x94442),f333(f197(f911(x94444)),x94443))+P106(f333(f333(f335(f916(f911(x94444),f911(x94444))),f333(f333(f265(f911(x94444),f911(x94444)),x94443),x94442)),f166(x94444,x94441)))+P106(f333(f333(f247(a910),f696(x94441,x94442,x94443,x94444)),f333(f197(f911(x94444)),x94443))) % 173.51/173.28 [9501]~P106(f333(x95013,f333(f333(f172(x95012),x95014),f771(x95014,x95012,x95013,x95011))))+P106(f333(f333(f246(a910),x95011),f333(f197(f911(x95012)),f185(x95012,x95013,x95014))))+~P106(f333(f333(f246(a910),x95011),f333(f197(f911(x95012)),x95014))) % 173.51/173.28 [9581]E(f333(f333(f183(x95811),f707(x95812,x95813,x95814,x95811)),x95813),f333(f333(f183(x95811),f707(x95812,x95813,x95814,x95811)),x95814))+~P106(f333(f333(f335(f916(f911(x95811),f911(x95811))),f333(f333(f265(f911(x95811),f911(x95811)),x95814),x95813)),f155(x95811,x95812)))+P106(f333(f333(f247(a910),f333(f197(f911(x95811)),x95814)),f333(f197(f911(x95811)),x95813))) % 173.51/173.28 [9638]~P106(f333(f333(f247(a910),f2(a910)),x96383))+~P106(f333(f333(f247(a910),x96384),x96381))+P106(f333(f333(f247(a910),f333(f333(f87(a910),f333(f333(f88(a910),x96381),f51(a910,x96382,x96383))),x96384)),f333(f333(f88(a910),x96381),x96383))) % 173.51/173.28 [9841]~P111(x98412)+~P106(f333(f333(f246(x98412),f333(x98413,f863(x98414,x98413,x98411,x98412))),f333(x98414,f863(x98414,x98413,x98411,x98412))))+P106(f333(f333(f246(f917(x98411,x98412)),x98413),x98414)) % 173.51/173.28 [9943]~P6(x99431)+E(f333(f333(f6(a910,x99431),f333(f333(f18(a910,x99431,x99431),f333(f333(f8(x99431,f917(x99431,x99431),a910),f23(x99431)),x99432)),f333(f333(f8(a910,x99431,a910),x99432),f333(f333(f7(a910,a910,a910),f87(a910)),f85(a910))))),f309(a910,x99433,x99434)),f333(f333(f23(x99431),f333(x99432,x99433)),f333(x99432,f333(f333(f87(a910),x99434),f85(a910)))))+~P106(f333(f333(f246(a910),x99433),x99434)) % 173.51/173.28 [6943]E(f333(f333(f142(x69431),x69432),x69433),x69434)+~E(x69433,f333(f333(f146(x69431),f333(f197(f911(x69431)),x69432)),x69434))+~E(f333(f333(f183(x69431),f333(f197(f911(x69431)),x69432)),x69434),x69432) % 173.51/173.28 [6996]~P68(x69962)+E(x69961,f2(x69962))+E(f333(f333(f296(x69962),f333(f333(f256(x69962),x69963),x69964)),f333(f333(f256(x69962),x69961),x69964)),f333(f333(f256(x69962),f333(f333(f296(x69962),x69963),x69961)),x69964)) % 173.51/173.28 [7147]~P102(x71471)+~P106(f333(f333(f246(x71471),x71473),x71474))+P106(f333(f333(f246(x71471),f333(f333(f112(x71471),x71472),x71473)),x71474)) % 173.51/173.28 [7148]~P102(x71481)+~P106(f333(f333(f246(x71481),x71482),x71484))+P106(f333(f333(f246(x71481),f333(f333(f112(x71481),x71482),x71483)),x71484)) % 173.51/173.28 [7150]~P110(x71501)+~P106(f333(f333(f246(x71501),x71503),x71504))+P106(f333(f333(f246(x71501),f333(f333(f244(x71501),x71502),x71503)),x71504)) % 173.51/173.28 [7152]~P110(x71521)+~P106(f333(f333(f246(x71521),x71522),x71524))+P106(f333(f333(f246(x71521),f333(f333(f244(x71521),x71522),x71523)),x71524)) % 173.51/173.28 [7153]~P102(x71531)+~P106(f333(f333(f247(x71531),x71533),x71534))+P106(f333(f333(f247(x71531),f333(f333(f112(x71531),x71532),x71533)),x71534)) % 173.51/173.28 [7154]~P102(x71541)+~P106(f333(f333(f247(x71541),x71542),x71544))+P106(f333(f333(f247(x71541),f333(f333(f112(x71541),x71542),x71543)),x71544)) % 173.51/173.28 [7156]~P110(x71561)+~P106(f333(f333(f247(x71561),x71563),x71564))+P106(f333(f333(f247(x71561),f333(f333(f244(x71561),x71562),x71563)),x71564)) % 173.51/173.28 [7158]~P110(x71581)+~P106(f333(f333(f247(x71581),x71582),x71584))+P106(f333(f333(f247(x71581),f333(f333(f244(x71581),x71582),x71583)),x71584)) % 173.51/173.28 [7181]~P106(f333(x71813,x71814))+~P106(f333(x71812,x71814))+P106(f333(f333(f333(f112(f917(x71811,a905)),x71812),x71813),x71814)) % 173.51/173.28 [7304]P26(x73041,x73042,x73043)+~P26(x73041,x73044,x73043)+~P106(f333(f333(f246(f917(f909(x73041),a905)),x73044),x73042)) % 173.51/173.28 [7305]P26(x73051,x73052,x73053)+~P26(x73051,x73052,x73054)+~P106(f333(f333(f246(f917(f909(x73051),a905)),x73053),x73054)) % 173.51/173.28 [7669]~P72(x76691)+E(f333(f333(f87(x76691),f333(x76692,x76693)),f333(f333(f6(a910,x76691),x76692),f333(f308(a910,f333(a123,x76693)),x76694))),f333(f333(f6(a910,x76691),x76692),f333(f308(a910,x76693),x76694)))+~P106(f333(f333(f247(a910),x76693),x76694)) % 173.51/173.28 [7687]E(x76871,x76872)+P106(f333(f333(f180(x76873),x76874),x76872))+~P106(f333(f333(f180(x76873),f333(f333(f159(x76873),x76871),x76874)),x76872)) % 173.51/173.28 [7699]~P101(x76991)+P106(f333(f333(f246(x76991),x76992),x76993))+~P106(f333(f333(f246(x76991),f333(f333(f121(x76991),x76994),x76992)),x76993)) % 173.51/173.28 [7701]~P101(x77011)+P106(f333(f333(f246(x77011),x77012),x77013))+~P106(f333(f333(f246(x77011),f333(f333(f121(x77011),x77012),x77014)),x77013)) % 173.51/173.28 [7703]~P110(x77031)+P106(f333(f333(f246(x77031),x77032),x77033))+~P106(f333(f333(f246(x77031),f333(f333(f245(x77031),x77034),x77032)),x77033)) % 173.51/173.28 [7705]~P110(x77051)+P106(f333(f333(f246(x77051),x77052),x77053))+~P106(f333(f333(f246(x77051),f333(f333(f245(x77051),x77052),x77054)),x77053)) % 173.51/173.28 [7706]~P110(x77061)+P106(f333(f333(f247(x77061),x77062),x77063))+~P106(f333(f333(f247(x77061),f333(f333(f245(x77061),x77064),x77062)),x77063)) % 173.51/173.28 [7707]~P110(x77071)+P106(f333(f333(f247(x77071),x77072),x77073))+~P106(f333(f333(f247(x77071),f333(f333(f245(x77071),x77072),x77074)),x77073)) % 173.51/173.28 [7782]~P106(f333(f333(f335(x77821),x77822),x77824))+P106(f333(f333(f335(x77821),x77822),x77823))+P106(f333(f333(f335(x77821),x77822),f333(f333(f23(f917(x77821,a905)),x77824),x77823))) % 173.51/173.28 [7868]P106(f333(x78681,x78682))+P106(f333(x78683,x78682))+~P106(f333(f333(f333(f121(f917(x78684,a905)),x78683),x78681),x78682)) % 173.51/173.28 [7879]~P106(f333(f333(f335(x78791),x78792),x78794))+~P106(f333(f333(f335(x78791),x78792),x78793))+P106(f333(f333(f335(x78791),x78792),f333(f333(f112(f917(x78791,a905)),x78793),x78794))) % 173.51/173.28 [7931]~P101(x79311)+~P106(f333(f67(x79311),x79314))+E(f333(f333(f70(x79311,x79311,f121(x79311)),x79312),f333(f333(f315(x79311),x79313),x79314)),f333(f333(f121(x79311),x79313),f333(f333(f70(x79311,x79311,f121(x79311)),x79312),x79314))) % 173.51/173.28 [7932]~P102(x79321)+~P106(f333(f67(x79321),x79324))+E(f333(f333(f70(x79321,x79321,f112(x79321)),x79322),f333(f333(f315(x79321),x79323),x79324)),f333(f333(f112(x79321),x79323),f333(f333(f70(x79321,x79321,f112(x79321)),x79322),x79324))) % 173.51/173.28 [7933]~P110(x79331)+~P106(f333(f67(x79331),x79334))+E(f333(f333(f70(x79331,x79331,f244(x79331)),x79332),f333(f333(f315(x79331),x79333),x79334)),f333(f333(f244(x79331),x79333),f333(f333(f70(x79331,x79331,f244(x79331)),x79332),x79334))) % 173.51/173.28 [7934]~P110(x79341)+~P106(f333(f67(x79341),x79344))+E(f333(f333(f70(x79341,x79341,f245(x79341)),x79342),f333(f333(f315(x79341),x79343),x79344)),f333(f333(f245(x79341),x79343),f333(f333(f70(x79341,x79341,f245(x79341)),x79342),x79344))) % 173.51/173.28 [7935]~P113(x79351)+~P96(x79351)+E(f333(f333(f23(x79351),f333(f333(f88(x79351),f333(f114(x79351),x79352)),x79353)),f333(f333(f88(x79351),f333(f114(x79351),x79352)),x79354)),f333(f333(f88(x79351),f333(f114(x79351),x79352)),f333(f333(f23(x79351),x79353),x79354))) % 173.51/173.28 [7936]~P142(x79361)+~P96(x79361)+E(f333(f333(f87(x79361),f333(f333(f88(x79361),f333(f114(x79361),x79362)),x79363)),f333(f333(f88(x79361),f333(f114(x79361),x79362)),x79364)),f333(f333(f88(x79361),f333(f114(x79361),x79362)),f333(f333(f87(x79361),x79363),x79364))) % 173.51/173.28 [8050]E(x80501,x80502)+P106(f333(f333(f335(x80503),x80501),f333(f180(x80503),x80504)))+~P106(f333(f333(f335(x80503),x80501),f333(f180(x80503),f333(f333(f159(x80503),x80502),x80504)))) % 173.51/173.28 [8229]P58(x82291,x82292,x82293)+~P58(x82291,x82292,x82294)+~P106(f333(f333(f246(f917(f916(x82291,x82292),a905)),x82293),x82294)) % 173.51/173.28 [8272]P106(f333(f333(f335(x82721),x82722),x82723))+P106(f333(f333(f335(x82721),x82722),x82724))+~P106(f333(f333(f335(x82721),x82722),f333(f333(f121(f917(x82721,a905)),x82724),x82723))) % 173.51/173.28 [8283]~P56(x82831,x82834,x82833)+~P106(f333(f333(f335(x82831),x82832),x82834))+P106(f333(f333(f335(f916(x82831,x82831)),f333(f333(f265(x82831,x82831),x82832),x82832)),x82833)) % 173.51/173.28 [8295]~P106(f333(f67(x82952),x82954))+~P106(f333(f67(x82951),x82953))+P106(f333(f67(f916(x82951,x82952)),f333(f333(f267(x82951,x82952),x82953),f333(f16(f917(x82952,a905),x82951),x82954)))) % 173.51/173.28 [8296]~P106(f333(f333(f335(x82961),x82962),x82964))+~P106(f333(f333(f246(f917(x82961,a905)),x82963),x82964))+P106(f333(f333(f246(f917(x82961,a905)),f333(f333(f315(x82961),x82962),x82963)),x82964)) % 173.51/173.28 [8303]~P107(x83032)+~P78(x83032)+E(f333(f333(f9(x83031,x83032),f333(f333(f8(a910,x83032,x83031),f111(x83032)),x83033)),x83034),f333(f111(x83032),f333(f333(f9(x83031,a910),x83033),x83034))) % 173.51/173.28 [8304]~P139(x83042)+~P78(x83042)+E(f333(f333(f9(x83041,x83042),f333(f333(f8(a1,x83042,x83041),f113(x83042)),x83043)),x83044),f333(f113(x83042),f333(f333(f9(x83041,a1),x83043),x83044))) % 173.51/173.28 [8328]E(f333(f333(f23(f917(x83281,a905)),x83282),f333(f333(f23(f917(x83281,a905)),x83283),x83284)),x83284)+~P106(f333(f333(f246(f917(x83281,a905)),x83282),x83283))+~P106(f333(f333(f246(f917(x83281,a905)),x83284),x83282)) % 173.51/173.28 [8427]~P106(f333(f67(x84271),x84274))+E(f333(f333(f23(a910),f333(f333(f6(x84271,a910),x84272),x84273)),f333(f333(f6(x84271,a910),x84272),x84274)),f333(f333(f6(x84271,a910),x84272),f333(f333(f23(f917(x84271,a905)),x84273),x84274)))+~P106(f333(f333(f246(f917(x84271,a905)),x84274),x84273)) % 173.51/173.28 [8585]~P11(x85851,x85854,x85853)+~P106(f333(f333(f335(x85851),x85852),x85854))+P106(f333(f333(f335(x85851),x85852),f333(f292(x85851,x85851,x85853),f333(f333(f315(x85851),x85852),f196(f917(x85851,a905)))))) % 173.51/173.28 [8651]~P106(f333(f333(f246(f917(x86511,a905)),x86512),x86513))+~P106(f333(f333(f246(f917(x86511,a905)),x86512),x86514))+P106(f333(f333(f246(f917(x86511,a905)),x86512),f333(f333(f112(f917(x86511,a905)),x86513),x86514))) % 173.51/173.28 [8752]E(x87521,f196(f917(x87522,a905)))+P106(f333(f67(x87523),x87524))+~P106(f333(f67(f916(x87523,x87522)),f333(f333(f267(x87523,x87522),x87524),f333(f16(f917(x87522,a905),x87523),x87521)))) % 173.51/173.28 [8753]E(x87531,f196(f917(x87532,a905)))+P106(f333(f67(x87533),x87534))+~P106(f333(f67(f916(x87532,x87533)),f333(f333(f267(x87532,x87533),x87531),f333(f16(f917(x87533,a905),x87532),x87534)))) % 173.51/173.28 [8827]P106(f333(f333(f335(x88271),x88272),f322(x88271,x88273)))+~P106(f333(f333(f335(x88271),x88274),f322(x88271,x88273)))+~P106(f333(f333(f335(f916(x88271,x88271)),f333(f333(f265(x88271,x88271),x88272),x88274)),x88273)) % 173.51/173.28 [8883]~P40(x88831,x88834)+P106(f333(f333(f335(f916(x88831,x88831)),f333(f333(f265(x88831,x88831),x88833),x88832)),f313(x88831,x88834)))+P40(x88831,f333(f333(f315(f916(x88831,x88831)),f333(f333(f265(x88831,x88831),x88832),x88833)),x88834)) % 173.51/173.28 [8884]~P61(x88841,x88844)+P106(f333(f333(f335(f916(x88841,x88841)),f333(f333(f265(x88841,x88841),x88843),x88842)),f313(x88841,x88844)))+P61(x88841,f333(f333(f315(f916(x88841,x88841)),f333(f333(f265(x88841,x88841),x88842),x88843)),x88844)) % 173.51/173.28 [8966]~E(x89662,x89663)+~P106(f333(f333(f335(x89661),x89662),f333(f180(x89661),x89664)))+P106(f333(f333(f335(f916(x89661,x89661)),f333(f333(f265(x89661,x89661),x89662),x89663)),f333(f180(f916(x89661,x89661)),f333(f333(f189(x89661,x89661),x89664),x89664)))) % 173.51/173.28 [9059]~E(x90593,x90594)+P106(f333(f333(f269(x90591,x90591,a905),a330),x90592))+~P106(f333(f333(f335(f916(x90591,x90591)),x90592),f333(f180(f916(x90591,x90591)),f333(f333(f189(x90591,x90591),x90593),x90594)))) % 173.51/173.28 [9083]~P106(f333(x90834,x90832))+P106(f333(f333(f333(f333(a204,x90831),x90832),x90833),f440(x90833,x90832,x90831,x90834)))+~P106(f333(f333(f333(f333(a204,f30(x90834,x90831)),x90832),x90833),x90832)) % 173.51/173.28 [9110]P106(f333(f333(f335(f916(f911(x91101),f911(x91101))),f333(f333(f265(f911(x91101),f911(x91101)),x91102),x91103)),f155(x91101,x91104)))+~E(f333(f333(f183(x91101),f333(f197(f911(x91101)),x91102)),x91103),x91102)+~P106(f333(f333(f247(a910),f333(f197(f911(x91101)),x91102)),f333(f197(f911(x91101)),x91103))) % 173.51/173.28 [9113]~P55(x91131,x91134)+~P106(f333(f333(f335(f916(x91131,x91131)),f333(f333(f265(x91131,x91131),x91133),x91132)),x91134))+P106(f333(f333(f335(f916(x91131,x91131)),f333(f333(f265(x91131,x91131),x91132),x91133)),x91134)) % 173.51/173.28 [9212]~P106(f333(f67(x92121),x92124))+P106(f333(f333(f335(x92121),f479(x92122,x92123,x92124,x92121)),x92124))+P106(f333(f67(x92123),f333(f333(f45(x92121,f917(x92123,a905)),x92124),x92122))) % 173.51/173.28 [9213]~P106(f333(f67(x92131),x92134))+P106(f333(f333(f335(x92131),f494(x92132,x92133,x92134,x92131)),x92134))+P106(f333(f67(x92133),f333(f333(f45(x92131,f917(x92133,a905)),x92134),x92132))) % 173.51/173.28 [9299]P106(f333(f333(f335(f916(x92991,x92991)),x92992),f333(f333(f295(x92991,x92991,x92991),x92993),f313(x92991,x92993))))+~P106(f333(f333(f247(a910),f2(a910)),x92994))+~P106(f333(f333(f335(f916(x92991,x92991)),x92992),f333(f333(f191(f916(x92991,x92991),a905),x92994),x92993))) % 173.51/173.28 [9307]~P40(x93071,x93072)+~P106(f333(f333(f335(f916(x93071,x93071)),f333(f333(f265(x93071,x93071),x93074),x93073)),x93072))+~P106(f333(f333(f335(f916(x93071,x93071)),f333(f333(f265(x93071,x93071),x93073),x93074)),x93072)) % 173.51/173.28 [9434]~P106(f333(f67(x94341),x94344))+E(f333(f333(f6(x94341,a910),f333(f333(f8(f917(x94342,a905),a910,x94341),f41(x94342)),x94343)),x94344),f333(f41(f916(x94341,x94342)),f333(f333(f267(x94341,x94342),x94344),x94343)))+P106(f333(f333(f335(x94341),f564(x94343,x94342,x94344,x94341)),x94344)) % 173.51/173.28 [9438]~P106(f333(f145(x94381),x94382))+P106(f333(f145(x94381),f333(f333(f167(x94381,x94382),x94383),x94384)))+P106(f333(f333(f335(x94381),x94384),f333(f333(f23(f917(x94381,a905)),f333(f180(x94381),x94382)),f333(f333(f315(x94381),f333(f333(f172(x94381),x94382),x94383)),f196(f917(x94381,a905)))))) % 173.51/173.28 [9458]~P106(f333(f67(x94582),x94583))+~P106(f333(f67(x94581),f333(x94584,f479(x94584,x94581,x94583,x94582))))+P106(f333(f67(x94581),f333(f333(f45(x94582,f917(x94581,a905)),x94583),x94584))) % 173.51/173.28 [9459]~P106(f333(f67(x94592),x94593))+~P106(f333(f67(x94591),f333(x94594,f494(x94594,x94591,x94593,x94592))))+P106(f333(f67(x94591),f333(f333(f45(x94592,f917(x94591,a905)),x94593),x94594))) % 173.51/173.28 [9539]~P106(f333(f333(f335(f916(x95391,x95391)),x95392),f333(f333(f295(x95391,x95391,x95391),x95394),f313(x95391,x95394))))+P106(f333(f333(f335(f916(x95391,x95391)),x95392),f333(f333(f295(x95391,x95391,x95391),x95393),f313(x95391,x95393))))+~P106(f333(f333(f246(f917(f916(x95391,x95391),a905)),x95394),x95393)) % 173.51/173.28 [9547]E(f333(f333(f183(x95471),f707(x95474,x95473,x95472,x95471)),x95473),f333(f333(f183(x95471),f707(x95474,x95473,x95472,x95471)),x95472))+~P106(f333(f333(f335(f916(f911(x95471),f911(x95471))),f333(f333(f265(f911(x95471),f911(x95471)),x95472),x95473)),f155(x95471,x95474)))+E(f333(f333(f183(x95471),f333(f197(f911(x95471)),x95472)),x95473),x95472) % 173.51/173.28 [9563]~P106(f333(f67(x95631),x95634))+E(f333(f333(f6(x95631,a910),f333(f333(f8(f917(x95632,a905),a910,x95631),f41(x95632)),x95633)),x95634),f333(f41(f916(x95631,x95632)),f333(f333(f267(x95631,x95632),x95634),x95633)))+~P106(f333(f67(x95632),f333(x95633,f564(x95633,x95632,x95634,x95631)))) % 173.51/173.28 [9568]~E(f333(f197(f911(x95681)),x95683),f333(f197(f911(x95681)),x95682))+P106(f333(f333(f335(f916(f911(x95681),f911(x95681))),f333(f333(f265(f911(x95681),f911(x95681)),x95682),x95683)),f166(x95681,x95684)))+P106(f333(f333(f335(f916(x95681,x95681)),f711(x95684,x95683,x95682,x95681)),f333(f180(f916(x95681,x95681)),f333(f333(f189(x95681,x95681),x95682),x95683)))) % 173.51/173.28 [9650]~P106(f333(f333(f335(f916(f911(x96501),f911(x96501))),f333(f333(f265(f911(x96501),f911(x96501)),x96502),x96503)),f155(x96501,x96504)))+E(f333(f333(f183(x96501),f333(f197(f911(x96501)),x96502)),x96503),x96502)+P106(f333(f333(f247(a910),f707(x96504,x96503,x96502,x96501)),f333(f333(f244(a910),f333(f197(f911(x96501)),x96502)),f333(f197(f911(x96501)),x96503)))) % 173.51/173.28 [9668]~P106(f333(x96681,x96684))+P106(f333(f333(f333(f333(a204,f30(x96681,x96682)),f440(x96683,x96684,x96682,x96681)),x96683),x96684))+~P106(f333(f333(f333(f333(a204,f30(x96681,x96682)),x96684),x96683),x96684)) % 173.51/173.28 [9675]~P106(f333(f333(f335(f916(f911(x96751),f911(x96751))),f333(f333(f265(f911(x96751),f911(x96751)),x96752),x96753)),f155(x96751,x96754)))+P106(f333(f333(f247(a910),f333(f197(f911(x96751)),x96752)),f333(f197(f911(x96751)),x96753)))+P106(f333(f333(f247(a910),f707(x96754,x96753,x96752,x96751)),f333(f333(f244(a910),f333(f197(f911(x96751)),x96752)),f333(f197(f911(x96751)),x96753)))) % 173.51/173.28 [10092]~P106(f333(f333(f335(f916(f911(x100921),f911(x100921))),f333(f333(f265(f911(x100921),f911(x100921)),x100922),x100923)),f155(x100921,x100924)))+E(f333(f333(f183(x100921),f333(f197(f911(x100921)),x100922)),x100923),x100922)+P106(f333(f333(f335(f916(x100921,x100921)),f333(f333(f265(x100921,x100921),f333(f333(f172(x100921),x100922),f707(x100924,x100923,x100922,x100921))),f333(f333(f172(x100921),x100923),f707(x100924,x100923,x100922,x100921)))),x100924)) % 173.51/173.28 [10093]~P106(f333(f333(f335(f916(f911(x100931),f911(x100931))),f333(f333(f265(f911(x100931),f911(x100931)),x100932),x100933)),f155(x100931,x100934)))+P106(f333(f333(f247(a910),f333(f197(f911(x100931)),x100932)),f333(f197(f911(x100931)),x100933)))+P106(f333(f333(f335(f916(x100931,x100931)),f333(f333(f265(x100931,x100931),f333(f333(f172(x100931),x100932),f707(x100934,x100933,x100932,x100931))),f333(f333(f172(x100931),x100933),f707(x100934,x100933,x100932,x100931)))),x100934)) % 173.51/173.28 [10151]~E(f333(f197(f911(x101511)),x101512),f333(f197(f911(x101511)),x101513))+P106(f333(f333(f335(f916(f911(x101511),f911(x101511))),f333(f333(f265(f911(x101511),f911(x101511)),x101512),x101513)),f166(x101511,x101514)))+~P106(f333(f333(f335(f916(x101511,x101511)),f333(f333(f265(x101511,x101511),f333(f333(f172(x101511),x101512),f696(x101514,x101513,x101512,x101511))),f333(f333(f172(x101511),x101513),f696(x101514,x101513,x101512,x101511)))),x101514)) % 173.51/173.28 [10291]~P72(x102911)+~P106(f333(f67(x102912),x102914))+E(f333(f173(x102911),f333(f333(f162(x102912,x102911),x102913),f97(f911(x102912),f333(f333(f18(f911(x102912),a905,a905),f333(f333(f8(a905,f917(a905,a905),f911(x102912)),a331),f333(f333(f7(f911(x102912),f917(x102912,a905),a905),f333(f333(f8(f917(x102912,a905),f917(f917(x102912,a905),a905),f911(x102912)),a330),f180(x102912))),x102914))),f145(x102912))))),f243(x102912,x102911,x102913,x102914)) % 173.51/173.28 [7519]~P67(x75192)+E(x75191,f2(x75192))+E(f333(f333(f296(x75192),f333(f333(f87(x75192),x75193),f333(f333(f88(x75192),x75194),x75191))),x75191),f333(f333(f87(x75192),x75194),f333(f333(f296(x75192),x75193),x75191))) % 173.51/173.28 [7520]~P64(x75202)+E(x75201,f2(x75202))+E(f333(f333(f42(x75202),f333(f333(f87(x75202),x75203),f333(f333(f88(x75202),x75204),x75201))),x75201),f333(f333(f87(x75202),x75204),f333(f333(f42(x75202),x75203),x75201))) % 173.51/173.28 [7521]~P64(x75212)+E(x75211,f2(x75212))+E(f333(f333(f42(x75212),f333(f333(f87(x75212),x75213),f333(f333(f88(x75212),x75211),x75214))),x75211),f333(f333(f87(x75212),x75214),f333(f333(f42(x75212),x75213),x75211))) % 173.51/173.28 [7746]~P68(x77462)+E(x77461,f2(x77462))+E(f333(f333(f296(x77462),f333(f333(f23(x77462),x77463),f333(f333(f88(x77462),x77461),x77464))),x77461),f333(f333(f23(x77462),f333(f333(f296(x77462),x77463),x77461)),x77464)) % 173.51/173.28 [7747]~P67(x77472)+E(x77471,f2(x77472))+E(f333(f333(f296(x77472),f333(f333(f87(x77472),x77473),f333(f333(f88(x77472),x77474),x77471))),x77471),f333(f333(f87(x77472),f333(f333(f296(x77472),x77473),x77471)),x77474)) % 173.51/173.28 [7748]~P68(x77482)+E(x77481,f2(x77482))+E(f333(f333(f296(x77482),f333(f333(f87(x77482),x77483),f333(f333(f88(x77482),x77481),x77484))),x77481),f333(f333(f87(x77482),f333(f333(f296(x77482),x77483),x77481)),x77484)) % 173.51/173.28 [8458]~P106(f333(f168(x84581,x84583),x84584))+~P106(f333(f168(x84581,x84582),x84584))+P106(f333(f168(x84581,f333(f333(f112(f917(x84581,a905)),x84582),x84583)),x84584)) % 173.51/173.28 [8842]~E(f333(f333(f295(x88421,x88421,x88421),x88422),x88424),f196(f917(f916(x88421,x88421),a905)))+~E(f333(f333(f295(x88421,x88421,x88421),x88422),x88423),f196(f917(f916(x88421,x88421),a905)))+E(f333(f333(f295(x88421,x88421,x88421),x88422),f333(f333(f121(f917(f916(x88421,x88421),a905)),x88423),x88424)),f196(f917(f916(x88421,x88421),a905))) % 173.51/173.28 [8967]~P106(f333(f333(f246(f917(x89671,a905)),x89673),x89674))+~P106(f333(f333(f246(f917(x89671,a905)),x89672),x89674))+P106(f333(f333(f246(f917(x89671,a905)),f333(f333(f121(f917(x89671,a905)),x89672),x89673)),x89674)) % 173.51/173.28 [9360]~P106(f333(f67(x93601),x93604))+~P106(f333(f67(x93601),x93603))+E(f333(f333(f23(a910),f333(f333(f87(a910),f333(f333(f6(x93601,a910),x93602),x93603)),f333(f333(f6(x93601,a910),x93602),x93604))),f333(f333(f6(x93601,a910),x93602),f333(f333(f112(f917(x93601,a905)),x93603),x93604))),f333(f333(f6(x93601,a910),x93602),f333(f333(f121(f917(x93601,a905)),x93603),x93604))) % 173.51/173.28 [9455]~P106(f333(f333(f335(x94551),x94553),x94552))+~P106(f333(f333(f246(f917(x94551,a905)),x94552),f333(f333(f315(x94551),x94553),x94554)))+P106(f333(f333(f246(f917(x94551,a905)),f333(f333(f23(f917(x94551,a905)),x94552),f333(f333(f315(x94551),x94553),f196(f917(x94551,a905))))),x94554)) % 173.51/173.28 [9624]~P106(f333(f333(f335(x96241),x96243),x96242))+P106(f333(f333(f246(f917(x96241,a905)),x96242),f333(f333(f315(x96241),x96243),x96244)))+~P106(f333(f333(f246(f917(x96241,a905)),f333(f333(f23(f917(x96241,a905)),x96242),f333(f333(f315(x96241),x96243),f196(f917(x96241,a905))))),x96244)) % 173.51/173.28 [9723]~P106(f333(f333(f246(a910),x97231),x97233))+~P106(f333(f333(f247(a910),x97232),x97234))+P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),f333(f333(f265(a910,a910),x97231),x97232)),f333(f333(f265(a910,a910),x97233),x97234))),a39)) % 173.51/173.28 [9724]~P106(f333(f333(f246(a910),x97242),x97244))+~P106(f333(f333(f246(a910),x97241),x97243))+P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),f333(f333(f265(a910,a910),x97241),x97242)),f333(f333(f265(a910,a910),x97243),x97244))),a77)) % 173.51/173.28 [10015]~P106(f333(f333(f335(f911(x100151)),x100154),f169(x100151,x100153)))+~P106(f333(f333(f335(f911(x100151)),x100154),f169(x100151,x100152)))+P106(f333(f168(x100151,f333(f333(f112(f917(x100151,a905)),f333(f333(f7(x100151,f917(x100151,a905),a905),f335(x100151)),x100152)),f333(f333(f7(x100151,f917(x100151,a905),a905),f335(x100151)),x100153))),x100154)) % 173.51/173.28 [10117]~P27(x101171,f917(f917(x101171,a905),a905),f333(f333(f7(x101171,f917(f916(x101171,x101171),a905),f917(f917(x101171,a905),a905)),f333(f333(f8(f917(x101171,a905),f917(f917(f916(x101171,x101171),a905),f917(f917(x101171,a905),a905)),x101171),f66(x101171)),f333(f333(f7(x101171,f917(x101171,a905),f917(x101171,a905)),f315(x101171)),f196(f917(x101171,a905))))),x101173),x101172)+~P106(f333(f333(f335(x101171),x101174),x101172))+E(f333(f333(f23(f917(f917(x101171,a905),a905)),f333(f333(f66(x101171),x101172),x101173)),f333(f333(f66(x101171),f333(f333(f315(x101171),x101174),f196(f917(x101171,a905)))),x101173)),f333(f333(f66(x101171),f333(f333(f23(f917(x101171,a905)),x101172),f333(f333(f315(x101171),x101174),f196(f917(x101171,a905))))),x101173)) % 173.51/173.28 [10252]~P56(x102521,x102522,x102524)+~P106(f333(f333(f335(f916(x102521,x102521)),x102523),x102524))+P106(f333(f333(f269(x102521,x102521,a905),f333(f333(f7(x102521,f917(x102521,a905),f917(x102521,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x102521,a905),f917(x102521,a905)),x102521),f8(a905,a905,x102521)),f333(f333(f8(a905,f917(a905,a905),x102521),a331),f333(f333(f7(x102521,f917(x102521,a905),a905),f335(x102521)),x102522)))),f333(f333(f7(x102521,f917(x102521,a905),a905),f335(x102521)),x102522))),x102523)) % 173.51/173.28 [10264]P106(f333(f67(x102641),x102642))+~P106(f333(f67(x102643),f333(f316(x102641,x102643,x102644),x102642)))+~P106(f333(f67(x102641),f333(f252(x102641),f333(f333(f18(x102641,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102641),a331),f333(f333(f7(x102641,f917(x102641,a905),a905),f335(x102641)),x102642))),f333(f333(f7(x102641,x102643,a905),f333(f333(f8(x102643,f917(x102643,a905),x102641),a330),x102644)),f333(x102644,f476(x102644,x102643,x102642,x102641))))))) % 173.51/173.28 [8212]~P68(x82122)+E(x82121,f2(x82122))+E(f333(f333(f296(x82122),f333(f333(f23(x82122),f333(f333(f88(x82122),x82121),x82123)),x82124)),x82121),f333(f333(f23(x82122),x82123),f333(f333(f296(x82122),x82124),x82121))) % 173.51/173.28 [8213]~P68(x82132)+E(x82131,f2(x82132))+E(f333(f333(f296(x82132),f333(f333(f87(x82132),f333(f333(f88(x82132),x82131),x82133)),x82134)),x82131),f333(f333(f87(x82132),x82133),f333(f333(f296(x82132),x82134),x82131))) % 173.51/173.28 [9143]~E(f333(f333(f295(x91431,x91431,x91431),x91433),x91434),f196(f917(f916(x91431,x91431),a905)))+~E(f333(f333(f295(x91431,x91431,x91431),x91432),x91434),f196(f917(f916(x91431,x91431),a905)))+E(f333(f333(f295(x91431,x91431,x91431),f333(f333(f121(f917(f916(x91431,x91431),a905)),x91432),x91433)),x91434),f196(f917(f916(x91431,x91431),a905))) % 173.51/173.28 [9934]~P106(f333(f168(x99341,x99343),x99344))+~P106(f333(f168(x99341,x99342),x99344))+P106(f333(f168(x99341,f333(f333(f18(x99341,a905,a905),f333(f333(f8(a905,f917(a905,a905),x99341),a331),x99342)),x99343)),x99344)) % 173.51/173.28 [10189]P106(f333(x101891,f887(x101892,x101893,x101891,x101894)))+~P106(f333(f67(x101894),f333(f252(x101894),x101891)))+P106(f333(f67(x101893),f333(f252(x101893),f333(f333(f8(f917(x101894,a905),a905,x101893),f94(x101894)),f333(f333(f8(f917(x101894,a905),f917(x101894,a905),x101893),f333(f18(x101894,a905,a905),f333(f333(f8(a905,f917(a905,a905),x101894),a331),x101891))),x101892))))) % 173.51/173.28 [10207]~P106(f333(f67(x102072),f333(f252(x102072),x102073)))+~P106(f333(f67(x102071),f333(f252(x102071),f333(f333(f7(x102071,x102072,a905),x102074),f887(x102074,x102071,x102073,x102072)))))+P106(f333(f67(x102071),f333(f252(x102071),f333(f333(f8(f917(x102072,a905),a905,x102071),f94(x102072)),f333(f333(f8(f917(x102072,a905),f917(x102072,a905),x102071),f333(f18(x102072,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102072),a331),x102073))),x102074))))) % 173.51/173.28 [10273]~P106(f333(f67(x102731),x102734))+P106(f333(f333(f335(x102731),f840(x102732,x102733,x102734,x102731)),x102734))+P106(f333(f67(x102733),f333(f252(x102733),f333(f333(f8(f917(x102731,a905),a905,x102733),f94(x102731)),f333(f333(f8(f917(x102731,a905),f917(x102731,a905),x102733),f333(f18(x102731,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102731),a331),f333(f333(f7(x102731,f917(x102731,a905),a905),f335(x102731)),x102734)))),x102732))))) % 173.51/173.28 [10280]~P106(f333(f67(x102802),x102803))+~P106(f333(f67(x102801),f333(f252(x102801),f333(f333(f7(x102801,x102802,a905),x102804),f840(x102804,x102801,x102803,x102802)))))+P106(f333(f67(x102801),f333(f252(x102801),f333(f333(f8(f917(x102802,a905),a905,x102801),f94(x102802)),f333(f333(f8(f917(x102802,a905),f917(x102802,a905),x102801),f333(f18(x102802,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102802),a331),f333(f333(f7(x102802,f917(x102802,a905),a905),f335(x102802)),x102803)))),x102804))))) % 173.51/173.28 [5179]~E(x51792,x51794)+E(f177(x51791,x51792,x51793),f177(x51791,x51794,x51795))+~E(x51792,f2(a910)) % 173.51/173.28 [5432]E(x54321,x54322)+~E(f177(x54324,x54323,x54321),f177(x54324,x54325,x54322))+E(x54323,f2(a910)) % 173.51/173.28 [6664]E(x66641,x66642)+~E(f333(x66643,x66641),f333(x66643,x66642))+~P27(x66644,x66645,x66643,f254(f917(x66644,a905))) % 173.51/173.28 [7551]E(x75511,x75512)+~P27(x75513,x75514,x75515,f254(f917(x75513,a905)))+~E(f333(f316(x75513,x75514,x75515),x75511),f333(f316(x75513,x75514,x75515),x75512)) % 173.51/173.28 [7799]P27(x77992,x77993,f859(x77994,x77993,x77992,x77991),x77991)+~E(f333(f316(x77993,x77992,x77995),x77994),x77991)+E(x77991,f196(f917(x77992,a905))) % 173.51/173.28 [8340]~P106(f333(f333(x83403,x83402),x83405))+~P106(f333(f333(x83403,x83404),x83402))+P106(f333(f333(f335(x83401),x83402),f302(x83401,x83403,x83404,x83405))) % 173.51/173.28 [8341]~P106(f333(f333(x83413,x83412),x83415))+~P106(f333(f333(x83413,x83414),x83412))+P106(f333(f333(f335(x83411),x83412),f305(x83411,x83413,x83414,x83415))) % 173.51/173.28 [8659]~P27(x86591,x86592,x86593,x86594)+P28(x86591,x86592,x86593,x86594,x86595)+~E(f333(f316(x86591,x86592,x86593),x86594),x86595) % 173.51/173.28 [8792]~P28(x87921,x87923,x87924,x87922,x87925)+~P106(f333(f67(x87923),x87925))+P106(f333(f67(x87921),x87922)) % 173.51/173.28 [8793]~P28(x87933,x87931,x87934,x87935,x87932)+~P106(f333(f67(x87933),x87935))+P106(f333(f67(x87931),x87932)) % 173.51/173.28 [8924]~P27(x89241,x89243,x89245,f254(f917(x89241,a905)))+~P27(x89243,x89242,x89244,f254(f917(x89243,a905)))+P27(x89241,x89242,f333(f79(x89243,x89242,x89241,x89244),x89245),f254(f917(x89241,a905))) % 173.51/173.28 [9516]P106(f333(f333(f335(f916(x95161,x95161)),f333(f333(f265(x95161,x95161),x95162),x95163)),f313(x95161,x95164)))+~P106(f333(f333(f335(f916(x95161,x95161)),f333(f333(f265(x95161,x95161),x95162),x95165)),f313(x95161,x95164)))+~P106(f333(f333(f335(f916(x95161,x95161)),f333(f333(f265(x95161,x95161),x95165),x95163)),f313(x95161,x95164))) % 173.51/173.28 [9554]~P110(x95542)+~P106(f333(f145(x95541),x95545))+P106(f333(f145(x95541),f157(x95541,x95542,x95543,x95544,x95545))) % 173.51/173.28 [5503]~E(x55032,f124(x55031))+E(f333(f333(f142(x55031),x55032),x55033),f333(f333(f159(x55031),x55034),x55035))+~E(x55033,f333(f333(f159(x55031),x55034),x55035)) % 173.51/173.28 [5504]~E(x55042,f124(x55041))+E(f333(f333(f142(x55041),x55042),x55043),f333(f333(f159(x55041),x55044),x55045))+~E(f333(f333(f159(x55041),x55044),x55045),x55043) % 173.51/173.28 [6621]~E(f333(f197(f911(x66211)),x66215),f333(f197(f911(x66212)),x66214))+E(f333(f333(f162(f916(x66211,x66212),x66212),f268(x66211,x66212)),x66213),x66214)+~E(f333(f333(f189(x66211,x66212),x66215),x66214),x66213) % 173.51/173.28 [6622]~E(f333(f197(f911(x66221)),x66224),f333(f197(f911(x66222)),x66225))+E(f333(f333(f162(f916(x66221,x66222),x66221),f264(x66221,x66222)),x66223),x66224)+~E(f333(f333(f189(x66221,x66222),x66224),x66225),x66223) % 173.51/173.28 [7091]~P110(x70911)+~P16(x70911,f333(f333(f162(x70912,x70911),x70913),x70915))+P16(x70911,f333(f333(f162(x70912,x70911),x70913),f333(f144(x70912,x70914),x70915))) % 173.51/173.28 [7136]~P106(f333(x71363,x71365))+~P106(f333(f333(x71362,x71364),x71365))+P106(f333(f333(f103(x71361,x71362,x71363),x71364),x71365)) % 173.51/173.28 [7233]~P110(x72331)+P16(x72331,f333(f333(f162(x72332,x72331),x72333),f178(x72332,x72334,x72335)))+~P16(x72331,f333(f333(f162(x72332,x72331),x72333),x72335)) % 173.51/173.28 [7256]~P58(x72563,x72562,x72565)+~P58(x72561,x72563,x72564)+P58(x72561,x72562,f333(f333(f295(x72561,x72563,x72562),x72564),x72565)) % 173.51/173.28 [7351]E(x73511,x73512)+~P27(x73513,x73514,x73515,f254(f917(x73513,a905)))+~E(f333(f333(f162(x73513,x73514),x73515),x73511),f333(f333(f162(x73513,x73514),x73515),x73512)) % 173.51/173.28 [7505]~P106(f333(f333(f246(a910),x75051),f333(x75053,x75055)))+P106(f333(f333(f246(a910),x75051),f163(x75052,x75053,x75054)))+~P106(f333(f333(f335(x75052),x75055),f333(f180(x75052),x75054))) % 173.51/173.28 [7506]~P106(f333(f333(f247(a910),x75061),f333(x75063,x75065)))+P106(f333(f333(f247(a910),x75061),f163(x75062,x75063,x75064)))+~P106(f333(f333(f335(x75062),x75065),f333(f180(x75062),x75064))) % 173.51/173.28 [7900]P106(f333(x79001,x79002))+~P106(f333(x79001,x79003))+~P106(f333(f333(f335(x79004),x79002),f333(f180(x79004),f177(x79004,x79005,x79003)))) % 173.51/173.28 [7901]P106(f333(x79011,x79012))+~P106(f333(x79011,x79013))+~P106(f333(f333(f335(x79014),x79013),f333(f180(x79014),f177(x79014,x79015,x79012)))) % 173.51/173.28 [7906]~P112(x79061)+P106(f333(f333(f246(f917(x79061,a905)),f309(x79061,x79062,x79063)),f309(x79061,x79064,x79065)))+P106(f333(f333(f246(x79061),x79062),x79063)) % 173.51/173.28 [7929]~P8(x79291)+P106(f333(f333(f246(x79291),f333(f333(f46(x79292,x79291),x79293),x79294)),f333(x79294,x79295)))+~P106(f333(f333(f335(x79292),x79295),x79293)) % 173.51/173.28 [7996]~P27(x79961,x79962,x79964,x79963)+E(f333(f84(x79961,x79962,x79963,x79964),f333(x79964,x79965)),x79965)+~P106(f333(f333(f335(x79961),x79965),x79963)) % 173.51/173.28 [7997]~P27(x79971,x79972,x79974,x79973)+E(f333(f99(x79971,x79972,x79973,x79974),f333(x79974,x79975)),x79975)+~P106(f333(f333(f335(x79971),x79975),x79973)) % 173.51/173.28 [8200]~P106(f333(x82001,x82005))+P106(f333(x82001,f705(x82001,x82002,x82003,x82004)))+~P106(f333(f333(f335(x82004),x82005),x82003)) % 173.51/173.28 [8201]~P106(f333(x82011,x82015))+P106(f333(x82011,f705(x82011,x82012,x82013,x82014)))+~P106(f333(f333(f335(x82014),x82015),x82012)) % 173.51/173.28 [8293]P106(f333(f67(x82931),x82932))+~P106(f333(f67(x82933),x82934))+~P106(f333(f333(f246(f917(x82931,a905)),x82932),f333(f316(x82933,x82931,x82935),x82934))) % 173.51/173.28 [8462]E(x84621,x84622)+~P27(x84623,x84624,x84625,f333(f333(f121(f917(x84623,a905)),f333(f180(x84623),x84621)),f333(f180(x84623),x84622)))+~E(f333(f333(f162(x84623,x84624),x84625),x84621),f333(f333(f162(x84623,x84624),x84625),x84622)) % 173.51/173.28 [8514]~P112(x85141)+~P106(f333(f333(f247(f917(x85141,a905)),f309(x85141,x85144,x85145)),f309(x85141,x85142,x85143)))+P106(f333(f333(f246(x85141),x85142),x85143)) % 173.51/173.28 [8584]~P27(x85841,x85844,x85845,f254(f917(x85841,a905)))+~P106(f333(f333(f335(x85844),f333(x85845,x85842)),f333(f316(x85841,x85844,x85845),x85843)))+P106(f333(f333(f335(x85841),x85842),x85843)) % 173.51/173.28 [8665]P106(f333(x86651,x86652))+~P106(f333(x86651,f651(x86651,x86653,x86654,x86655)))+~P106(f333(f333(f335(x86655),x86652),x86654)) % 173.51/173.28 [8666]P106(f333(x86661,x86662))+~P106(f333(x86661,f651(x86661,x86663,x86664,x86665)))+~P106(f333(f333(f335(x86665),x86662),x86663)) % 173.51/173.28 [8964]~P27(x89642,x89643,x89641,x89644)+E(f333(x89641,f333(f84(x89642,x89643,x89644,x89641),x89645)),x89645)+~P106(f333(f333(f335(x89643),x89645),f333(f316(x89642,x89643,x89641),x89644))) % 173.51/173.28 [9075]E(x90751,f124(x90752))+E(f333(f333(f159(x90752),x90753),f724(x90754,x90753,x90755,x90751,x90752)),x90751)+~E(f333(f333(f142(x90752),x90751),x90755),f333(f333(f159(x90752),x90753),x90754)) % 173.51/173.28 [9076]E(x90761,f124(x90762))+E(f333(f333(f159(x90762),x90763),f725(x90764,x90761,x90765,x90763,x90762)),x90761)+~E(f333(f333(f142(x90762),x90761),x90764),f333(f333(f159(x90762),x90763),x90765)) % 173.51/173.28 [9096]E(f333(f333(f159(x90962),x90963),f724(x90964,x90963,x90961,x90965,x90962)),x90965)+~E(f333(f333(f142(x90962),x90965),x90961),f333(f333(f159(x90962),x90963),x90964))+E(x90961,f333(f333(f159(x90962),x90963),x90964)) % 173.51/173.28 [9097]E(f333(f333(f159(x90971),x90972),f725(x90974,x90975,x90973,x90972,x90971)),x90975)+~E(f333(f333(f142(x90971),x90975),x90974),f333(f333(f159(x90971),x90972),x90973))+E(f333(f333(f159(x90971),x90972),x90973),x90974) % 173.51/173.28 [9183]~E(f333(f316(x91833,x91832,x91834),f254(f917(x91833,a905))),f254(f917(x91832,a905)))+~E(f333(f316(x91831,x91833,x91835),f254(f917(x91831,a905))),f254(f917(x91833,a905)))+E(f333(f316(x91831,x91832,f333(f79(x91833,x91832,x91831,x91834),x91835)),f254(f917(x91831,a905))),f254(f917(x91832,a905))) % 173.51/173.28 [9560]E(x95601,f124(x95602))+~E(f333(f333(f142(x95602),x95601),x95603),f333(f333(f159(x95602),x95605),x95604))+E(f333(f333(f142(x95602),f725(x95603,x95601,x95604,x95605,x95602)),x95603),x95604) % 173.51/173.28 [9561]E(x95611,f124(x95612))+~E(f333(f333(f142(x95612),x95611),x95615),f333(f333(f159(x95612),x95614),x95613))+E(f333(f333(f142(x95612),f724(x95613,x95614,x95615,x95611,x95612)),x95615),x95613) % 173.51/173.28 [9569]E(f333(f333(f142(x95692),f724(x95694,x95693,x95691,x95695,x95692)),x95691),x95694)+~E(f333(f333(f142(x95692),x95695),x95691),f333(f333(f159(x95692),x95693),x95694))+E(x95691,f333(f333(f159(x95692),x95693),x95694)) % 173.51/173.28 [9570]~E(f333(f333(f142(x95701),x95705),x95704),f333(f333(f159(x95701),x95702),x95703))+E(f333(f333(f142(x95701),f725(x95704,x95705,x95703,x95702,x95701)),x95704),x95703)+E(f333(f333(f159(x95701),x95702),x95703),x95704) % 173.51/173.28 [9571]E(f333(f333(f142(x95711),x95715),f728(x95713,x95712,x95714,x95715,x95711)),x95712)+E(f333(f333(f142(x95711),x95712),f727(x95713,x95712,x95714,x95715,x95711)),x95715)+~E(f333(f333(f142(x95711),x95715),x95714),f333(f333(f142(x95711),x95712),x95713)) % 173.51/173.28 [9607]~P110(x96071)+P16(x96071,f333(f333(f162(x96072,x96071),x96073),f157(x96072,x96071,x96073,x96074,x96075)))+~P16(x96071,f333(f333(f162(x96072,x96071),x96073),x96075)) % 173.51/173.28 [9621]~P62(x96215,x96211,x96214,x96213)+P106(f333(f333(x96211,x96212),f588(x96213,x96214,x96211,x96215,x96212)))+~P106(f333(f333(f335(x96215),x96212),x96214)) % 173.51/173.28 [9622]~P62(x96225,x96221,x96224,x96223)+P106(f333(f333(x96221,x96222),f844(x96223,x96224,x96221,x96225,x96222)))+~P106(f333(f333(f335(x96225),x96222),x96224)) % 173.51/173.28 [9735]~P106(f333(f333(f335(f916(x97351,x97351)),f333(f333(f265(x97351,x97351),x97355),x97353)),f313(x97351,x97354)))+P106(f333(f333(f335(f916(x97351,x97351)),f333(f333(f265(x97351,x97351),x97352),x97353)),f333(f333(f295(x97351,x97351,x97351),x97354),f313(x97351,x97354))))+~P106(f333(f333(f335(f916(x97351,x97351)),f333(f333(f265(x97351,x97351),x97352),x97355)),f333(f333(f295(x97351,x97351,x97351),x97354),f313(x97351,x97354)))) % 173.51/173.28 [9736]~P106(f333(f333(f335(f916(x97361,x97361)),f333(f333(f265(x97361,x97361),x97362),x97365)),f313(x97361,x97364)))+P106(f333(f333(f335(f916(x97361,x97361)),f333(f333(f265(x97361,x97361),x97362),x97363)),f333(f333(f295(x97361,x97361,x97361),x97364),f313(x97361,x97364))))+~P106(f333(f333(f335(f916(x97361,x97361)),f333(f333(f265(x97361,x97361),x97365),x97363)),f333(f333(f295(x97361,x97361,x97361),x97364),f313(x97361,x97364)))) % 173.51/173.28 [9738]P106(f333(f333(f335(f916(f911(x97381),f911(x97381))),f333(f333(f265(f911(x97381),f911(x97381)),x97382),x97383)),f166(x97381,f313(x97381,x97384))))+~P106(f333(f333(f335(f916(f911(x97381),f911(x97381))),f333(f333(f265(f911(x97381),f911(x97381)),x97382),x97385)),f166(x97381,f313(x97381,x97384))))+~P106(f333(f333(f335(f916(f911(x97381),f911(x97381))),f333(f333(f265(f911(x97381),f911(x97381)),x97385),x97383)),f166(x97381,f313(x97381,x97384)))) % 173.51/173.28 [9743]E(f333(f333(f142(x97431),x97432),f727(x97433,x97432,x97434,x97435,x97431)),x97435)+E(f333(f333(f142(x97431),f728(x97433,x97432,x97434,x97435,x97431)),x97433),x97434)+~E(f333(f333(f142(x97431),x97432),x97433),f333(f333(f142(x97431),x97435),x97434)) % 173.51/173.28 [9744]E(f333(f333(f142(x97441),x97442),f728(x97443,x97444,x97445,x97442,x97441)),x97444)+E(f333(f333(f142(x97441),f727(x97443,x97444,x97445,x97442,x97441)),x97445),x97443)+~E(f333(f333(f142(x97441),x97442),x97445),f333(f333(f142(x97441),x97444),x97443)) % 173.51/173.28 [9799]P106(f333(f333(f335(f916(x97991,x97991)),f333(f333(f265(x97991,x97991),x97992),x97993)),f333(f333(f295(x97991,x97991,x97991),x97994),f313(x97991,x97994))))+~P106(f333(f333(f335(f916(x97991,x97991)),f333(f333(f265(x97991,x97991),x97992),x97995)),f333(f333(f295(x97991,x97991,x97991),x97994),f313(x97991,x97994))))+~P106(f333(f333(f335(f916(x97991,x97991)),f333(f333(f265(x97991,x97991),x97995),x97993)),f333(f333(f295(x97991,x97991,x97991),x97994),f313(x97991,x97994)))) % 173.51/173.28 [9826]P37(x98261,x98262,x98263,x98264,x98265)+~E(f333(f197(f911(x98261)),x98264),f333(f197(f911(x98262)),x98265))+~P106(f333(f333(f269(x98261,x98262,a905),x98263),f745(x98265,x98264,x98263,x98262,x98261))) % 173.51/173.28 [9827]P37(x98271,x98272,x98273,x98274,x98275)+~E(f333(f197(f911(x98271)),x98274),f333(f197(f911(x98272)),x98275))+~P106(f333(f333(f269(x98271,x98272,a905),x98273),f746(x98273,x98275,x98274,x98272,x98271))) % 173.51/173.28 [9832]E(f333(f333(f142(x98321),f727(x98322,x98323,x98324,x98325,x98321)),x98324),x98322)+~E(f333(f333(f142(x98321),x98323),x98322),f333(f333(f142(x98321),x98325),x98324))+E(f333(f333(f142(x98321),f728(x98322,x98323,x98324,x98325,x98321)),x98322),x98324) % 173.51/173.28 [9847]~P110(x98472)+E(f333(f333(f156(x98471,x98472,x98473),x98474),x98475),f333(f333(f159(x98471),x98474),x98475))+P106(f333(f333(f335(x98471),f792(x98474,x98473,x98475,x98471,x98472)),f333(f180(x98471),x98475))) % 173.51/173.28 [9851]~P62(x98511,x98514,x98513,x98512)+~P106(f333(f333(f335(x98511),x98515),x98513))+P106(f333(f333(f335(x98511),f588(x98512,x98513,x98514,x98511,x98515)),x98512)) % 173.51/173.28 [9852]~P62(x98521,x98524,x98523,x98522)+~P106(f333(f333(f335(x98521),x98525),x98523))+P106(f333(f333(f335(x98521),f844(x98522,x98523,x98524,x98521,x98525)),x98522)) % 173.51/173.28 [9966]~P106(f333(f333(f335(f916(f917(x99661,a905),f917(x99661,a905))),f333(f333(f265(f917(x99661,a905),f917(x99661,a905)),x99664),x99663)),f324(x99661,x99662)))+~P106(f333(f333(f335(x99661),x99665),x99664))+P106(f333(f333(f335(x99661),f649(x99662,x99663,x99664,x99661,x99665)),x99663)) % 173.51/173.28 [9977]~P110(x99772)+E(f333(f333(f156(x99771,x99772,x99773),x99774),x99775),f333(f333(f159(x99771),x99774),x99775))+~P106(f333(f333(f246(x99772),f333(x99773,x99774)),f333(x99773,f792(x99774,x99773,x99775,x99771,x99772)))) % 173.51/173.28 [10023]~P27(x100233,x100234,x100235,f254(f917(x100233,a905)))+P106(f333(x100231,x100232))+~P106(f333(x100231,f333(f99(x100233,x100234,f254(f917(x100233,a905)),x100235),f873(x100232,x100231,x100235,x100234,x100233)))) % 173.51/173.28 [10169]P37(x101691,x101692,x101693,x101694,x101695)+~E(f333(f197(f911(x101691)),x101694),f333(f197(f911(x101692)),x101695))+~P106(f333(f333(x101693,f333(f333(f172(x101691),x101694),f747(x101695,x101694,x101693,x101692,x101691))),f333(f333(f172(x101692),x101695),f747(x101695,x101694,x101693,x101692,x101691)))) % 173.51/173.28 [10170]P37(x101701,x101702,x101703,x101704,x101705)+~E(f333(f197(f911(x101701)),x101704),f333(f197(f911(x101702)),x101705))+~P106(f333(f333(x101703,f333(f333(f172(x101701),x101704),f781(x101703,x101705,x101702,x101704,x101701))),f333(f333(f172(x101702),x101705),f781(x101703,x101705,x101702,x101704,x101701)))) % 173.51/173.28 [6694]~P19(x66942,x66945,x66941)+~P106(f333(f67(x66942),x66944))+E(f333(x66941,f333(f333(f315(x66942),x66943),x66944)),f333(f333(f70(x66942,x66942,x66945),x66943),x66944)) % 173.51/173.28 [6695]~E(x66953,x66954)+~E(x66952,x66955)+E(f333(f333(f315(x66951),x66952),f333(f333(f315(x66951),x66953),f196(f917(x66951,a905)))),f333(f333(f315(x66951),x66954),f333(f333(f315(x66951),x66955),f196(f917(x66951,a905))))) % 173.51/173.28 [6707]P106(f333(x67072,x67075))+E(f185(x67071,x67072,f333(f333(f142(x67071),x67073),x67074)),f185(x67071,x67072,x67073))+~P106(f333(f333(f335(x67071),x67075),f333(f180(x67071),x67073))) % 173.51/173.28 [6743]E(f333(x67431,x67432),f196(f917(x67433,a905)))+~E(f333(f333(f45(x67434,f917(x67433,a905)),x67435),x67431),f196(f917(x67433,a905)))+~P106(f333(f333(f335(x67434),x67432),x67435)) % 173.51/173.28 [6744]E(f333(x67441,x67442),f254(f917(x67443,a905)))+~E(f333(f333(f46(x67444,f917(x67443,a905)),x67445),x67441),f254(f917(x67443,a905)))+~P106(f333(f333(f335(x67444),x67442),x67445)) % 173.51/173.28 [7041]~P106(f333(f333(f202(x70411),x70413),x70415))+~P106(f333(f333(f202(x70412),x70415),x70414))+P106(f333(f333(f202(f31(x70411,x70412)),x70413),x70414)) % 173.51/173.28 [7243]~E(x72432,x72434)+~P144(x72431)+E(f333(f333(f87(x72431),f333(f333(f88(x72431),x72432),x72433)),f333(f333(f88(x72431),x72434),x72435)),f333(f333(f87(x72431),f333(f333(f88(x72431),x72432),x72435)),f333(f333(f88(x72431),x72434),x72433))) % 173.51/173.28 [7303]~P8(x73031)+~P106(f333(f333(f335(x73034),x73033),x73035))+P106(f333(f333(f246(x73031),f333(x73032,x73033)),f333(f333(f45(x73034,x73031),x73035),x73032))) % 173.51/173.28 [7356]~P111(x73561)+P106(f333(f333(f246(x73561),f333(x73562,x73563)),f333(x73564,x73563)))+~P106(f333(f333(f246(f917(x73565,x73561)),x73562),x73564)) % 173.51/173.28 [7475]E(x74751,x74752)+E(x74753,x74751)+~E(f333(f333(f315(x74754),x74751),f333(f333(f315(x74754),x74755),f196(f917(x74754,a905)))),f333(f333(f315(x74754),x74752),f333(f333(f315(x74754),x74753),f196(f917(x74754,a905))))) % 173.51/173.28 [7476]E(x74761,x74762)+E(x74763,x74761)+~E(f333(f333(f315(x74764),x74763),f333(f333(f315(x74764),x74762),f196(f917(x74764,a905)))),f333(f333(f315(x74764),x74765),f333(f333(f315(x74764),x74761),f196(f917(x74764,a905))))) % 173.51/173.28 [7477]E(x74771,x74772)+E(x74771,x74773)+~E(f333(f333(f315(x74774),x74773),f333(f333(f315(x74774),x74772),f196(f917(x74774,a905)))),f333(f333(f315(x74774),x74775),f333(f333(f315(x74774),x74771),f196(f917(x74774,a905))))) % 173.51/173.28 [7478]E(x74781,x74782)+E(x74781,x74783)+~E(f333(f333(f315(x74784),x74781),f333(f333(f315(x74784),x74785),f196(f917(x74784,a905)))),f333(f333(f315(x74784),x74782),f333(f333(f315(x74784),x74783),f196(f917(x74784,a905))))) % 173.51/173.28 [8006]P27(x80061,x80062,x80063,x80064)+~P27(x80061,x80062,x80063,x80065)+~P106(f333(f333(f246(f917(x80061,a905)),x80064),x80065)) % 173.51/173.28 [8013]~P106(f333(f333(f246(a910),x80135),x80133))+~P106(f333(f333(f333(f333(a204,x80131),x80132),x80135),x80134))+P106(f333(f333(f333(f333(a204,x80131),x80132),x80133),x80134)) % 173.51/173.28 [8036]~E(f333(x80363,x80365),x80364)+~P27(x80361,x80362,x80363,f254(f917(x80361,a905)))+E(f333(f99(x80361,x80362,f254(f917(x80361,a905)),x80363),x80364),x80365) % 173.51/173.28 [8110]P106(f333(x81101,x81102))+~P106(f333(f333(f202(x81104),x81102),x81105))+P106(f333(f333(f202(f28(x81101,x81103,x81104)),x81102),x81105)) % 173.51/173.28 [8138]~P106(f333(x81381,x81384))+~P106(f333(f333(f202(x81382),x81384),x81385))+P106(f333(f333(f202(f28(x81381,x81382,x81383)),x81384),x81385)) % 173.51/173.28 [8189]E(x81891,x81892)+~E(f333(f316(x81893,x81894,x81895),x81891),f333(f316(x81893,x81894,x81895),x81892))+~P27(x81893,x81894,x81895,f333(f333(f121(f917(x81893,a905)),x81891),x81892)) % 173.51/173.28 [8262]P106(f333(x82622,x82624))+E(f333(f333(f146(x82621),f333(f197(f911(x82621)),f185(x82621,x82622,x82623))),x82623),f333(f333(f159(x82621),x82624),x82625))+~E(f333(f333(f142(x82621),f185(x82621,x82622,x82623)),f333(f333(f159(x82621),x82624),x82625)),x82623) % 173.51/173.28 [8291]~P27(x82911,x82912,x82913,x82915)+~P27(x82911,x82912,x82913,x82914)+P27(x82911,x82912,x82913,f333(f333(f112(f917(x82911,a905)),x82914),x82915)) % 173.51/173.28 [8401]~P72(x84011)+E(f333(f333(f87(x84011),f333(x84012,x84013)),f333(f173(x84011),f333(f333(f162(x84014,x84011),x84012),f178(x84014,x84013,x84015)))),f333(f173(x84011),f333(f333(f162(x84014,x84011),x84012),x84015)))+~P106(f333(f333(f335(x84014),x84013),f333(f180(x84014),x84015))) % 173.51/173.28 [8488]~P110(x84881)+~P16(x84881,f333(f333(f162(x84882,x84881),x84883),x84885))+P16(x84881,f333(f333(f162(x84882,x84881),x84883),f333(f333(f156(x84882,x84881,x84883),x84884),x84885))) % 173.51/173.28 [8569]P106(f333(x85691,x85692))+P106(f333(f333(f202(x85693),x85692),x85694))+~P106(f333(f333(f202(f28(x85691,x85695,x85693)),x85692),x85694)) % 173.51/173.28 [8580]~P8(x85801)+P106(f333(f333(f246(x85801),f333(f333(f45(x85802,x85801),x85803),x85804)),f333(f333(f45(x85802,x85801),x85805),x85804)))+~P106(f333(f333(f246(f917(x85802,a905)),x85803),x85805)) % 173.51/173.28 [8581]~P8(x85811)+P106(f333(f333(f246(x85811),f333(f333(f46(x85812,x85811),x85813),x85814)),f333(f333(f46(x85812,x85811),x85815),x85814)))+~P106(f333(f333(f246(f917(x85812,a905)),x85815),x85813)) % 173.51/173.28 [8590]~P106(f333(x85904,x85902))+P106(f333(f333(f202(x85901),x85902),x85903))+~P106(f333(f333(f202(f28(x85904,x85901,x85905)),x85902),x85903)) % 173.51/173.28 [8617]~P110(x86173)+P106(f333(f145(x86171),x86172))+~P106(f333(f145(x86171),f333(f333(f156(x86171,x86173,x86174),x86175),x86172))) % 173.51/173.28 [8627]P106(f333(f333(f202(x86271),x86272),x86273))+P106(f333(f333(f202(x86274),x86272),x86273))+~P106(f333(f333(f202(f28(x86275,x86271,x86274)),x86272),x86273)) % 173.51/173.28 [8765]~P110(x87651)+~P106(f333(f333(f335(x87652),x87653),f333(f180(x87652),x87654)))+~P106(f333(f145(x87652),f333(f333(f156(x87652,x87651,x87655),x87653),x87654))) % 173.51/173.28 [8854]~P110(x88541)+P16(x88541,f333(f333(f162(x88542,x88541),x88543),x88544))+~P16(x88541,f333(f333(f162(x88542,x88541),x88543),f333(f333(f156(x88542,x88541,x88543),x88545),x88544))) % 173.51/173.28 [8899]~P27(x88992,x88991,x88994,x88993)+E(f333(f316(x88991,x88992,f99(x88992,x88991,x88993,x88994)),f333(f316(x88992,x88991,x88994),x88995)),x88995)+~P106(f333(f333(f246(f917(x88992,a905)),x88995),x88993)) % 173.51/173.28 [8952]~P110(x89522)+E(f333(f333(f156(x89521,x89522,x89523),x89524),x89525),f157(x89521,x89522,x89523,x89524,x89525))+P106(f333(f333(f335(x89522),f333(x89523,x89524)),f333(f316(x89521,x89522,x89523),f333(f180(x89521),x89525)))) % 173.51/173.28 [9034]~P110(x90342)+E(f157(x90341,x90342,x90343,x90344,x90345),x90345)+~P106(f333(f333(f335(x90342),f333(x90343,x90344)),f333(f316(x90341,x90342,x90343),f333(f180(x90341),x90345)))) % 173.51/173.28 [9052]~P27(x90522,x90521,x90523,x90525)+P106(f333(f333(f247(f917(x90521,a905)),f333(f316(x90522,x90521,x90523),x90524)),f333(f316(x90522,x90521,x90523),x90525)))+~P106(f333(f333(f247(f917(x90522,a905)),x90524),x90525)) % 173.51/173.28 [9224]~P27(x92241,x92242,x92243,f254(f917(x92241,a905)))+~P106(f333(f333(f246(f917(x92242,a905)),x92244),f333(f316(x92241,x92242,x92243),x92245)))+P106(f333(f333(f246(f917(x92241,a905)),f333(f317(x92241,x92242,x92243),x92244)),x92245)) % 173.51/173.28 [9248]~E(f333(f316(x92483,x92481,x92484),f254(f917(x92483,a905))),f254(f917(x92481,a905)))+P106(f333(f333(f246(f917(x92481,a905)),x92482),f333(f316(x92483,x92481,x92484),x92485)))+~P106(f333(f333(f246(f917(x92483,a905)),f333(f317(x92483,x92481,x92484),x92482)),x92485)) % 173.51/173.28 [9353]~P27(x93531,x93534,x93535,f254(f917(x93531,a905)))+~P106(f333(f333(f246(f917(x93534,a905)),f333(f316(x93531,x93534,x93535),x93532)),f333(f316(x93531,x93534,x93535),x93533)))+P106(f333(f333(f246(f917(x93531,a905)),x93532),x93533)) % 173.51/173.28 [9484]~P82(x94841)+~E(f333(x94843,f766(x94843,x94844,x94845,x94842,x94841)),f2(x94841))+E(f333(f173(x94841),f333(f333(f162(x94842,x94841),x94843),f333(f144(x94842,x94844),x94845))),f333(f173(x94841),f333(f333(f162(x94842,x94841),x94843),x94845))) % 173.51/173.28 [9511]~P28(x95111,x95112,x95113,f254(f917(x95111,a905)),f254(f917(x95112,a905)))+~P106(f333(f333(f246(f917(x95112,a905)),x95114),f333(f316(x95111,x95112,x95113),x95115)))+P106(f333(f333(f246(f917(x95111,a905)),f333(f317(x95111,x95112,x95113),x95114)),x95115)) % 173.51/173.28 [9540]~P28(x95403,x95401,x95404,f254(f917(x95403,a905)),f254(f917(x95401,a905)))+P106(f333(f333(f246(f917(x95401,a905)),x95402),f333(f316(x95403,x95401,x95404),x95405)))+~P106(f333(f333(f246(f917(x95403,a905)),f333(f317(x95403,x95401,x95404),x95402)),x95405)) % 173.51/173.28 [9667]~P18(x96671,x96672,x96673)+~P106(f333(f67(x96671),x96675))+P106(f333(f72(x96671,x96672,x96673,x96674,x96675),f333(f333(f70(x96671,x96672,x96673),x96674),x96675))) % 173.51/173.28 [9756]~P28(x97562,x97561,x97564,f254(f917(x97562,a905)),f254(f917(x97561,a905)))+~P28(x97561,x97563,x97565,f254(f917(x97561,a905)),f254(f917(x97563,a905)))+E(f333(f79(x97561,x97562,x97563,f99(x97562,x97561,f254(f917(x97562,a905)),x97564)),f99(x97561,x97563,f254(f917(x97561,a905)),x97565)),f99(x97562,x97563,f254(f917(x97562,a905)),f333(f79(x97561,x97563,x97562,x97565),x97564))) % 173.51/173.28 [9757]P106(f333(x97571,f866(x97572,x97571,x97573,x97574,x97575)))+~P106(f333(f333(f246(f917(x97575,a905)),x97574),x97573))+P106(f333(f333(f246(f917(x97575,a905)),f333(f333(f112(f917(x97575,a905)),x97574),f333(f252(x97575),x97571))),f333(f333(f112(f917(x97575,a905)),x97573),f333(f252(x97575),x97572)))) % 173.51/173.28 [9771]~P82(x97711)+~P106(f333(x97714,f766(x97713,x97714,x97715,x97712,x97711)))+E(f333(f173(x97711),f333(f333(f162(x97712,x97711),x97713),f333(f144(x97712,x97714),x97715))),f333(f173(x97711),f333(f333(f162(x97712,x97711),x97713),x97715))) % 173.51/173.28 [9849]~P8(x98495)+P106(f333(f333(f335(x98491),f656(x98492,x98493,x98491,x98494,x98495)),x98493))+P106(f333(f333(f246(x98495),x98494),f333(f333(f46(x98491,x98495),x98493),x98492))) % 173.51/173.28 [9853]~P82(x98531)+E(f333(f173(x98531),f333(f333(f162(x98532,x98531),x98533),f333(f144(x98532,x98534),x98535))),f333(f173(x98531),f333(f333(f162(x98532,x98531),x98533),x98535)))+P106(f333(f333(f335(x98532),f766(x98533,x98534,x98535,x98532,x98531)),f333(f180(x98532),x98535))) % 173.51/173.28 [9863]~P106(f333(x98635,f866(x98635,x98633,x98634,x98632,x98631)))+~P106(f333(f333(f246(f917(x98631,a905)),x98632),x98634))+P106(f333(f333(f246(f917(x98631,a905)),f333(f333(f112(f917(x98631,a905)),x98632),f333(f252(x98631),x98633))),f333(f333(f112(f917(x98631,a905)),x98634),f333(f252(x98631),x98635)))) % 173.51/173.28 [9878]~P27(x98785,x98783,x98784,f254(f917(x98785,a905)))+P106(f333(x98781,x98782))+P106(f333(f333(f335(x98783),f873(x98782,x98781,x98784,x98783,x98785)),f333(f316(x98785,x98783,x98784),f254(f917(x98785,a905))))) % 173.51/173.28 [9901]P37(x99011,x99012,x99013,x99014,x99015)+~E(f333(f197(f911(x99012)),x99015),f333(f197(f911(x99011)),x99014))+P106(f333(f333(f247(a910),f747(x99015,x99014,x99013,x99012,x99011)),f333(f197(f911(x99011)),x99014))) % 173.51/173.28 [9902]P37(x99021,x99022,x99023,x99024,x99025)+~E(f333(f197(f911(x99022)),x99025),f333(f197(f911(x99021)),x99024))+P106(f333(f333(f247(a910),f781(x99023,x99025,x99022,x99024,x99021)),f333(f197(f911(x99021)),x99024))) % 173.51/173.28 [9935]P106(f333(f333(f335(x99351),f866(x99352,x99353,x99354,x99355,x99351)),x99355))+~P106(f333(f333(f246(f917(x99351,a905)),x99355),x99354))+P106(f333(f333(f246(f917(x99351,a905)),f333(f333(f112(f917(x99351,a905)),x99355),f333(f252(x99351),x99353))),f333(f333(f112(f917(x99351,a905)),x99354),f333(f252(x99351),x99352)))) % 173.51/173.28 [9978]~P8(x99781)+~P106(f333(f333(f246(x99781),x99782),f333(x99785,f656(x99785,x99784,x99783,x99782,x99781))))+P106(f333(f333(f246(x99781),x99782),f333(f333(f46(x99783,x99781),x99784),x99785))) % 173.51/173.28 [10013]~P78(x100131)+~P106(f333(f67(x100132),x100135))+E(f333(f333(f333(f71(x100131,x100132,f88(x100131)),f333(f333(f18(x100132,x100131,x100131),f333(f333(f8(x100131,f917(x100131,x100131),x100132),f88(x100131)),x100133)),x100134)),f85(x100131)),x100135),f333(f333(f88(x100131),f333(f333(f333(f71(x100131,x100132,f88(x100131)),x100133),f85(x100131)),x100135)),f333(f333(f333(f71(x100131,x100132,f88(x100131)),x100134),f85(x100131)),x100135))) % 173.51/173.28 [10073]~P106(f333(f333(f335(f916(f917(x100731,a905),f917(x100731,a905))),f333(f333(f265(f917(x100731,a905),f917(x100731,a905)),x100735),x100734)),f324(x100731,x100733)))+~P106(f333(f333(f335(x100731),x100732),x100735))+P106(f333(f333(f335(f916(x100731,x100731)),f333(f333(f265(x100731,x100731),x100732),f649(x100733,x100734,x100735,x100731,x100732))),x100733)) % 173.51/173.28 [10204]~P106(f333(f333(f335(f916(f911(x102041),f911(x102041))),f333(f333(f265(f911(x102041),f911(x102041)),f333(f333(f142(x102041),x102045),x102042)),f333(f333(f142(x102041),x102045),x102043))),f155(x102041,x102044)))+P106(f333(f333(f335(f916(f911(x102041),f911(x102041))),f333(f333(f265(f911(x102041),f911(x102041)),x102042),x102043)),f155(x102041,x102044)))+P106(f333(f333(f335(f916(x102041,x102041)),f333(f333(f265(x102041,x102041),f733(x102044,x102043,x102042,x102045,x102041)),f733(x102044,x102043,x102042,x102045,x102041))),x102044)) % 173.51/173.28 [7359]~E(x73593,x73595)+E(f333(f333(f172(x73591),f333(f333(f167(x73591,x73592),x73593),x73594)),x73595),x73594)+~P106(f333(f333(f247(a910),x73593),f333(f197(f911(x73591)),x73592))) % 173.51/173.28 [7470]~E(f333(f333(f142(x74701),x74702),x74704),f333(f333(f142(x74701),x74703),x74705))+E(f333(f333(f183(x74701),f333(f197(f911(x74701)),x74702)),x74703),x74702)+P106(f333(f333(f246(a910),f333(f197(f911(x74701)),x74703)),f333(f197(f911(x74701)),x74702))) % 173.51/173.28 [7487]~E(x74875,x74872)+P106(f333(x74871,x74872))+P106(f333(f333(f333(f333(a204,f30(x74871,x74873)),x74872),x74874),x74875)) % 173.51/173.28 [7967]~E(f333(f333(f142(x79671),x79672),x79674),f333(f333(f142(x79671),x79673),x79675))+E(f333(f333(f183(x79671),f333(f197(f911(x79671)),x79672)),x79673),x79672)+~P106(f333(f333(f246(a910),f333(f197(f911(x79671)),x79672)),f333(f197(f911(x79671)),x79673))) % 173.51/173.28 [7991]~P106(f333(f67(x79911),f333(x79914,x79915)))+~P106(f333(f333(f335(x79912),x79915),x79913))+P106(f333(f67(x79911),f333(f333(f46(x79912,f917(x79911,a905)),x79913),x79914))) % 173.51/173.28 [8173]~P56(x81731,x81733,x81735)+~P56(x81731,x81732,x81734)+P56(x81731,f333(f333(f121(f917(x81731,a905)),x81732),x81733),f333(f333(f121(f917(f916(x81731,x81731),a905)),x81734),x81735)) % 173.51/173.28 [8174]~P56(x81741,x81743,x81745)+~P56(x81741,x81742,x81744)+P56(x81741,f333(f333(f112(f917(x81741,a905)),x81742),x81743),f333(f333(f112(f917(f916(x81741,x81741),a905)),x81744),x81745)) % 173.51/173.28 [8257]E(x82571,x82572)+P106(f333(x82573,x82571))+~P106(f333(f333(f333(f333(a204,f30(x82573,x82574)),x82571),x82575),x82572)) % 173.51/173.28 [8530]E(f333(f333(f265(x85301,x85302),f333(f333(f172(x85301),x85303),x85304)),f333(f333(f172(x85302),x85305),x85304)),f333(f333(f172(f916(x85301,x85302)),f333(f333(f189(x85301,x85302),x85303),x85305)),x85304))+~P106(f333(f333(f247(a910),x85304),f333(f197(f911(x85301)),x85303)))+~P106(f333(f333(f247(a910),x85304),f333(f197(f911(x85302)),x85305))) % 173.51/173.28 [8693]~P56(x86931,x86933,x86934)+P106(f333(f333(f335(x86931),x86932),x86933))+~P106(f333(f333(f335(f916(x86931,x86931)),f333(f333(f265(x86931,x86931),x86935),x86932)),x86934)) % 173.51/173.28 [8694]~P56(x86941,x86943,x86944)+P106(f333(f333(f335(x86941),x86942),x86943))+~P106(f333(f333(f335(f916(x86941,x86941)),f333(f333(f265(x86941,x86941),x86942),x86945)),x86944)) % 173.51/173.28 [8695]~P11(x86951,x86953,x86954)+P106(f333(f333(f335(x86951),x86952),x86953))+~P106(f333(f333(f335(f916(x86951,x86951)),f333(f333(f265(x86951,x86951),x86955),x86952)),x86954)) % 173.51/173.28 [8696]~P11(x86961,x86963,x86964)+P106(f333(f333(f335(x86961),x86962),x86963))+~P106(f333(f333(f335(f916(x86961,x86961)),f333(f333(f265(x86961,x86961),x86962),x86965)),x86964)) % 173.51/173.28 [8976]~P11(x89761,x89765,x89762)+E(f333(f292(x89761,x89761,x89762),f333(f333(f315(x89761),x89763),f196(f917(x89761,a905)))),f333(f292(x89761,x89761,x89762),f333(f333(f315(x89761),x89764),f196(f917(x89761,a905)))))+~P106(f333(f333(f335(f916(x89761,x89761)),f333(f333(f265(x89761,x89761),x89763),x89764)),x89762)) % 173.51/173.28 [9066]~P106(f333(f333(f333(f333(a204,x90662),x90663),x90664),x90665))+~P106(f333(f333(f333(f333(a204,f30(x90661,x90662)),x90665),x90664),x90663))+P106(f333(f333(f333(f333(a204,f30(x90661,x90662)),x90663),x90664),x90663)) % 173.51/173.28 [9180]P106(f333(x91801,x91802))+~P106(f333(f333(f335(x91803),x91802),x91805))+P106(f333(f333(f335(x91803),f651(x91801,x91804,x91805,x91803)),f333(f333(f121(f917(x91803,a905)),x91805),x91804))) % 173.51/173.28 [9181]P106(f333(x91811,x91812))+~P106(f333(f333(f335(x91813),x91812),x91814))+P106(f333(f333(f335(x91813),f651(x91811,x91814,x91815,x91813)),f333(f333(f121(f917(x91813,a905)),x91815),x91814))) % 173.51/173.28 [9189]~P106(f333(x91892,x91895))+~P106(f333(f333(f335(x91891),x91895),x91894))+P106(f333(f333(f335(x91891),f705(x91892,x91893,x91894,x91891)),f333(f333(f121(f917(x91891,a905)),x91894),x91893))) % 173.51/173.28 [9190]~P106(f333(x91902,x91905))+~P106(f333(f333(f335(x91901),x91905),x91903))+P106(f333(f333(f335(x91901),f705(x91902,x91903,x91904,x91901)),f333(f333(f121(f917(x91901,a905)),x91904),x91903))) % 173.51/173.28 [9205]~P106(f333(f333(f246(f917(x92051,a905)),x92053),x92055))+~P106(f333(f333(f246(f917(x92051,a905)),x92052),x92054))+P106(f333(f333(f246(f917(x92051,a905)),f333(f333(f121(f917(x92051,a905)),x92052),x92053)),f333(f333(f121(f917(x92051,a905)),x92054),x92055))) % 173.51/173.28 [9206]~P106(f333(f333(f246(f917(x92061,a905)),x92063),x92065))+~P106(f333(f333(f246(f917(x92061,a905)),x92062),x92064))+P106(f333(f333(f246(f917(x92061,a905)),f333(f333(f112(f917(x92061,a905)),x92062),x92063)),f333(f333(f112(f917(x92061,a905)),x92064),x92065))) % 173.51/173.28 [9207]~P106(f333(f333(f246(f917(x92071,a905)),x92075),x92073))+~P106(f333(f333(f246(f917(x92071,a905)),x92072),x92074))+P106(f333(f333(f246(f917(x92071,a905)),f333(f333(f23(f917(x92071,a905)),x92072),x92073)),f333(f333(f23(f917(x92071,a905)),x92074),x92075))) % 173.51/173.28 [9302]P106(f333(f333(f335(f916(x93021,x93021)),f333(f333(f265(x93021,x93021),x93022),x93023)),f327(x93021,x93024,x93025)))+~P106(f333(f333(f246(a910),f333(x93024,x93022)),f333(x93024,x93023)))+~P106(f333(f333(f335(f916(x93021,x93021)),f333(f333(f265(x93021,x93021),x93022),x93023)),x93025)) % 173.51/173.28 [9494]P106(f333(f333(f335(f916(x94941,x94941)),f333(f333(f265(x94941,x94941),x94942),x94943)),f313(x94941,x94944)))+~P106(f333(f333(f335(f916(x94941,x94941)),f333(f333(f265(x94941,x94941),x94942),x94945)),f313(x94941,x94944)))+~P106(f333(f333(f335(f916(x94941,x94941)),f333(f333(f265(x94941,x94941),x94945),x94943)),x94944)) % 173.51/173.28 [9495]P106(f333(f333(f335(f916(x94951,x94951)),f333(f333(f265(x94951,x94951),x94952),x94953)),f313(x94951,x94954)))+~P106(f333(f333(f335(f916(x94951,x94951)),f333(f333(f265(x94951,x94951),x94955),x94953)),f313(x94951,x94954)))+~P106(f333(f333(f335(f916(x94951,x94951)),f333(f333(f265(x94951,x94951),x94952),x94955)),x94954)) % 173.51/173.28 [9594]E(x95941,x95942)+E(f333(a123,f575(x95943,x95944,x95941,x95942,x95945)),x95944)+~P106(f333(f333(f335(f916(x95945,x95945)),f333(f333(f265(x95945,x95945),x95942),x95941)),f333(f333(f191(f916(x95945,x95945),a905),x95944),x95943))) % 173.51/173.28 [9595]E(x95951,x95952)+E(f333(a123,f577(x95953,x95954,x95951,x95952,x95955)),x95954)+~P106(f333(f333(f335(f916(x95955,x95955)),f333(f333(f265(x95955,x95955),x95952),x95951)),f333(f333(f191(f916(x95955,x95955),a905),x95954),x95953))) % 173.51/173.28 [9596]E(x95961,f2(a910))+E(f333(a123,f575(x95962,x95961,x95963,x95964,x95965)),x95961)+~P106(f333(f333(f335(f916(x95965,x95965)),f333(f333(f265(x95965,x95965),x95964),x95963)),f333(f333(f191(f916(x95965,x95965),a905),x95961),x95962))) % 173.51/173.28 [9597]E(x95971,f2(a910))+E(f333(a123,f577(x95972,x95971,x95973,x95974,x95975)),x95971)+~P106(f333(f333(f335(f916(x95975,x95975)),f333(f333(f265(x95975,x95975),x95974),x95973)),f333(f333(f191(f916(x95975,x95975),a905),x95971),x95972))) % 173.51/173.28 [9618]P106(f333(f333(f335(f916(x96181,x96181)),f333(f333(f265(x96181,x96181),x96182),x96183)),f333(f333(f295(x96181,x96181,x96181),x96184),f313(x96181,x96184))))+~P106(f333(f333(f335(f916(x96181,x96181)),f333(f333(f265(x96181,x96181),x96182),x96185)),x96184))+~P106(f333(f333(f335(f916(x96181,x96181)),f333(f333(f265(x96181,x96181),x96185),x96183)),x96184)) % 173.51/173.28 [9625]~P106(f333(f333(f335(f916(x96251,x96251)),f333(f333(f265(x96251,x96251),x96252),x96255)),f313(x96251,x96254)))+P106(f333(f333(f335(f916(x96251,x96251)),f333(f333(f265(x96251,x96251),x96252),x96253)),f333(f333(f295(x96251,x96251,x96251),x96254),f313(x96251,x96254))))+~P106(f333(f333(f335(f916(x96251,x96251)),f333(f333(f265(x96251,x96251),x96255),x96253)),x96254)) % 173.51/173.28 [9661]~P11(x96611,x96615,x96612)+~P106(f333(f333(f335(f916(x96611,x96611)),f333(f333(f265(x96611,x96611),x96613),x96614)),x96612))+P106(f333(f333(f246(f917(x96611,a905)),f333(f292(x96611,x96611,x96612),f333(f333(f315(x96611),x96613),f196(f917(x96611,a905))))),f333(f292(x96611,x96611,x96612),f333(f333(f315(x96611),x96614),f196(f917(x96611,a905)))))) % 173.51/173.28 [9689]E(x96891,x96892)+P106(f333(f333(f333(f333(a204,x96893),x96891),x96894),f431(x96892,x96894,x96891,x96893,x96895)))+~P106(f333(f333(f333(f333(a204,f30(x96895,x96893)),x96891),x96894),x96892)) % 173.51/173.28 [9690]E(x96901,x96902)+P106(f333(f333(f333(f333(a204,x96903),x96901),x96904),f508(x96902,x96904,x96901,x96903,x96905)))+~P106(f333(f333(f333(f333(a204,f30(x96905,x96903)),x96901),x96904),x96902)) % 173.51/173.28 [9695]~P106(f333(x96955,x96952))+P106(f333(f333(f333(f333(a204,x96951),x96952),x96953),f431(x96954,x96953,x96952,x96951,x96955)))+~P106(f333(f333(f333(f333(a204,f30(x96955,x96951)),x96952),x96953),x96954)) % 173.51/173.28 [9696]~P106(f333(x96965,x96962))+P106(f333(f333(f333(f333(a204,x96961),x96962),x96963),f508(x96964,x96963,x96962,x96961,x96965)))+~P106(f333(f333(f333(f333(a204,f30(x96965,x96961)),x96962),x96963),x96964)) % 173.51/173.28 [9728]P106(f333(f333(f335(f916(x97281,x97281)),f333(f333(f265(x97281,x97281),x97282),x97283)),f333(f333(f295(x97281,x97281,x97281),x97284),f313(x97281,x97284))))+~P106(f333(f333(f335(f916(x97281,x97281)),f333(f333(f265(x97281,x97281),x97282),x97285)),f333(f333(f295(x97281,x97281,x97281),x97284),f313(x97281,x97284))))+~P106(f333(f333(f335(f916(x97281,x97281)),f333(f333(f265(x97281,x97281),x97285),x97283)),x97284)) % 173.51/173.28 [9729]P106(f333(f333(f335(f916(x97291,x97291)),f333(f333(f265(x97291,x97291),x97292),x97293)),f333(f333(f295(x97291,x97291,x97291),x97294),f313(x97291,x97294))))+~P106(f333(f333(f335(f916(x97291,x97291)),f333(f333(f265(x97291,x97291),x97295),x97293)),f333(f333(f295(x97291,x97291,x97291),x97294),f313(x97291,x97294))))+~P106(f333(f333(f335(f916(x97291,x97291)),f333(f333(f265(x97291,x97291),x97292),x97295)),x97294)) % 173.51/173.28 [9781]~P106(f333(f72(x97811,x97811,x97814,x97812,x97813),x97815))+P106(f333(f333(f335(x97811),x97812),x97813))+P106(f333(f68(x97811,x97814,f333(f333(f315(x97811),x97812),x97813)),x97815)) % 173.51/173.28 [9819]~E(f333(f316(x98193,x98192,x98195),x98194),x98191)+E(x98191,f196(f917(x98192,a905)))+P106(f333(f333(f246(f917(x98193,a905)),f333(f316(x98192,x98193,f859(x98194,x98193,x98192,x98191)),x98191)),x98194)) % 173.51/173.28 [9866]~P8(x98665)+P106(f333(f333(f335(x98661),f486(x98662,x98663,x98664,x98661,x98665)),x98664))+P106(f333(f333(f246(x98665),f333(f333(f45(x98661,x98665),x98664),x98663)),x98662)) % 173.51/173.28 [9922]P37(x99221,x99222,x99223,x99224,x99225)+~E(f333(f197(f911(x99221)),x99224),f333(f197(f911(x99222)),x99225))+P106(f333(f333(f335(f916(x99221,x99222)),f745(x99225,x99224,x99223,x99222,x99221)),f333(f180(f916(x99221,x99222)),f333(f333(f189(x99221,x99222),x99224),x99225)))) % 173.51/173.28 [9923]P37(x99231,x99232,x99233,x99234,x99235)+~E(f333(f197(f911(x99231)),x99234),f333(f197(f911(x99232)),x99235))+P106(f333(f333(f335(f916(x99231,x99232)),f746(x99233,x99235,x99234,x99232,x99231)),f333(f180(f916(x99231,x99232)),f333(f333(f189(x99231,x99232),x99234),x99235)))) % 173.51/173.28 [10044]E(x100441,x100442)+P106(f333(f333(f333(f333(a204,f30(x100443,x100444)),f431(x100441,x100445,x100442,x100444,x100443)),x100445),x100441))+~P106(f333(f333(f333(f333(a204,f30(x100443,x100444)),x100442),x100445),x100441)) % 173.51/173.28 [10045]E(x100451,x100452)+P106(f333(f333(f333(f333(a204,f30(x100453,x100454)),f508(x100451,x100455,x100452,x100454,x100453)),x100455),x100451))+~P106(f333(f333(f333(f333(a204,f30(x100453,x100454)),x100452),x100455),x100451)) % 173.51/173.28 [10047]~P106(f333(x100471,x100475))+P106(f333(f333(f333(f333(a204,f30(x100471,x100472)),f431(x100473,x100474,x100475,x100472,x100471)),x100474),x100473))+~P106(f333(f333(f333(f333(a204,f30(x100471,x100472)),x100475),x100474),x100473)) % 173.51/173.28 [10048]~P106(f333(x100481,x100485))+P106(f333(f333(f333(f333(a204,f30(x100481,x100482)),f508(x100483,x100484,x100485,x100482,x100481)),x100484),x100483))+~P106(f333(f333(f333(f333(a204,f30(x100481,x100482)),x100485),x100484),x100483)) % 173.51/173.28 [10052]E(x100521,x100522)+P106(f333(f333(f335(f916(x100523,x100523)),f333(f333(f265(x100523,x100523),x100521),f576(x100524,x100525,x100522,x100521,x100523))),x100524))+~P106(f333(f333(f335(f916(x100523,x100523)),f333(f333(f265(x100523,x100523),x100521),x100522)),f333(f333(f191(f916(x100523,x100523),a905),x100525),x100524))) % 173.51/173.28 [10053]E(x100531,f2(a910))+P106(f333(f333(f335(f916(x100532,x100532)),f333(f333(f265(x100532,x100532),x100533),f576(x100534,x100531,x100535,x100533,x100532))),x100534))+~P106(f333(f333(f335(f916(x100532,x100532)),f333(f333(f265(x100532,x100532),x100533),x100535)),f333(f333(f191(f916(x100532,x100532),a905),x100531),x100534))) % 173.51/173.28 [10096]~P8(x100961)+~P106(f333(f333(f246(x100961),f333(x100964,f486(x100965,x100964,x100963,x100962,x100961))),x100965))+P106(f333(f333(f246(x100961),f333(f333(f45(x100962,x100961),x100963),x100964)),x100965)) % 173.51/173.28 [10138]E(x101381,x101382)+P106(f333(f333(f335(f916(x101383,x101383)),f333(f333(f265(x101383,x101383),f578(x101384,x101385,x101381,x101382,x101383)),x101381)),x101384))+~P106(f333(f333(f335(f916(x101383,x101383)),f333(f333(f265(x101383,x101383),x101382),x101381)),f333(f333(f191(f916(x101383,x101383),a905),x101385),x101384))) % 173.51/173.28 [10139]E(x101391,f2(a910))+P106(f333(f333(f335(f916(x101392,x101392)),f333(f333(f265(x101392,x101392),f578(x101393,x101391,x101394,x101395,x101392)),x101394)),x101393))+~P106(f333(f333(f335(f916(x101392,x101392)),f333(f333(f265(x101392,x101392),x101395),x101394)),f333(f333(f191(f916(x101392,x101392),a905),x101391),x101393))) % 173.51/173.28 [10143]E(x101431,x101432)+P106(f333(f333(f335(f916(x101433,x101433)),f333(f333(f265(x101433,x101433),x101431),f578(x101434,x101435,x101432,x101431,x101433))),f333(f333(f191(f916(x101433,x101433),a905),f577(x101434,x101435,x101432,x101431,x101433)),x101434)))+~P106(f333(f333(f335(f916(x101433,x101433)),f333(f333(f265(x101433,x101433),x101431),x101432)),f333(f333(f191(f916(x101433,x101433),a905),x101435),x101434))) % 173.51/173.28 [10144]E(x101441,f2(a910))+P106(f333(f333(f335(f916(x101442,x101442)),f333(f333(f265(x101442,x101442),x101443),f578(x101444,x101441,x101445,x101443,x101442))),f333(f333(f191(f916(x101442,x101442),a905),f577(x101444,x101441,x101445,x101443,x101442)),x101444)))+~P106(f333(f333(f335(f916(x101442,x101442)),f333(f333(f265(x101442,x101442),x101443),x101445)),f333(f333(f191(f916(x101442,x101442),a905),x101441),x101444))) % 173.51/173.28 [10195]E(x101951,x101952)+P106(f333(f333(f335(f916(x101953,x101953)),f333(f333(f265(x101953,x101953),f576(x101954,x101955,x101951,x101952,x101953)),x101951)),f333(f333(f191(f916(x101953,x101953),a905),f575(x101954,x101955,x101951,x101952,x101953)),x101954)))+~P106(f333(f333(f335(f916(x101953,x101953)),f333(f333(f265(x101953,x101953),x101952),x101951)),f333(f333(f191(f916(x101953,x101953),a905),x101955),x101954))) % 173.51/173.28 [10196]E(x101961,f2(a910))+P106(f333(f333(f335(f916(x101962,x101962)),f333(f333(f265(x101962,x101962),f576(x101963,x101961,x101964,x101965,x101962)),x101964)),f333(f333(f191(f916(x101962,x101962),a905),f575(x101963,x101961,x101964,x101965,x101962)),x101963)))+~P106(f333(f333(f335(f916(x101962,x101962)),f333(f333(f265(x101962,x101962),x101965),x101964)),f333(f333(f191(f916(x101962,x101962),a905),x101961),x101963))) % 173.51/173.28 [10230]~P72(x102302)+~P106(f333(f67(x102301),x102305))+E(f333(f333(f6(x102301,x102302),f333(f333(f7(x102301,x102302,x102302),f333(f333(f18(x102301,x102302,f917(x102302,x102302)),f333(f333(f8(a905,f917(x102302,f917(x102302,x102302)),x102301),f107(x102302)),f333(f333(f7(x102301,f917(x102301,a905),a905),f335(x102301)),x102303))),x102304)),f2(x102302))),x102305),f333(f333(f6(x102301,x102302),x102304),f333(f333(f112(f917(x102301,a905)),x102305),x102303))) % 173.51/173.28 [8762]~P72(x87621)+~P106(f333(f67(x87624),x87625))+E(f333(f333(f87(x87621),f333(x87622,x87623)),f333(f333(f6(x87624,x87621),x87622),f333(f333(f23(f917(x87624,a905)),x87625),f333(f333(f315(x87624),x87623),f196(f917(x87624,a905)))))),f333(f333(f6(x87624,x87621),x87622),f333(f333(f315(x87624),x87623),x87625))) % 173.51/173.28 [8763]~P78(x87631)+~P106(f333(f67(x87634),x87635))+E(f333(f333(f88(x87631),f333(x87632,x87633)),f333(f333(f9(x87634,x87631),x87632),f333(f333(f23(f917(x87634,a905)),x87635),f333(f333(f315(x87634),x87633),f196(f917(x87634,a905)))))),f333(f333(f9(x87634,x87631),x87632),f333(f333(f315(x87634),x87633),x87635))) % 173.51/173.28 [9105]~P110(x91052)+~P16(x91052,f333(f176(x91052),f333(f333(f162(x91051,x91052),x91054),x91055)))+E(f333(f144(x91051,f333(f333(f8(x91052,a905,x91051),f333(f247(x91052),x91053)),x91054)),x91055),f185(x91051,f333(f333(f8(x91052,a905,x91051),f333(f247(x91052),x91053)),x91054),x91055)) % 173.51/173.28 [9132]~P72(x91321)+E(f333(f333(f87(x91321),f333(f333(f6(a910,x91321),x91322),f309(a910,x91323,x91324))),f333(f333(f6(a910,x91321),x91322),f309(a910,f333(f333(f87(a910),x91324),f85(a910)),f333(f333(f87(a910),x91324),x91325)))),f333(f333(f6(a910,x91321),x91322),f309(a910,x91323,f333(f333(f87(a910),x91324),x91325))))+~P106(f333(f333(f246(a910),x91323),f333(f333(f87(a910),x91324),f85(a910)))) % 173.51/173.28 [9133]~P106(f333(f333(f335(x91331),x91334),x91335))+~P106(f333(f333(f246(f917(x91331,a905)),f333(f180(x91331),x91332)),x91335))+P106(f333(f333(f246(f917(x91331,a905)),f333(f180(x91331),f333(f333(f167(x91331,x91332),x91333),x91334))),x91335)) % 173.51/173.28 [9361]~P8(x93612)+~P106(f333(f67(x93611),x93615))+E(f333(f333(f70(x93611,x93612,f333(f333(f8(x93612,f917(x93612,x93612),x93611),f121(x93612)),x93613)),x93614),x93615),f333(f333(f121(x93612),x93614),f333(f333(f45(x93611,x93612),x93615),x93613))) % 173.51/173.28 [9362]~P8(x93622)+~P106(f333(f67(x93621),x93625))+E(f333(f333(f70(x93621,x93622,f333(f333(f8(x93622,f917(x93622,x93622),x93621),f112(x93622)),x93623)),x93624),x93625),f333(f333(f112(x93622),x93624),f333(f333(f46(x93621,x93622),x93625),x93623))) % 173.51/173.28 [9415]E(f333(x94151,x94152),f333(x94151,x94153))+P106(f333(f333(f247(a910),f333(x94151,x94152)),f333(x94151,x94153)))+~P106(f333(f333(f335(f916(x94154,x94154)),f333(f333(f265(x94154,x94154),x94152),x94153)),f161(x94154,f333(f333(f159(f917(x94154,a910)),x94151),x94155)))) % 173.51/173.28 [9447]~E(f333(x94474,x94472),f333(x94474,x94473))+~P106(f333(f333(f335(f916(x94471,x94471)),f333(f333(f265(x94471,x94471),x94472),x94473)),f161(x94471,x94475)))+P106(f333(f333(f335(f916(x94471,x94471)),f333(f333(f265(x94471,x94471),x94472),x94473)),f161(x94471,f333(f333(f159(f917(x94471,a910)),x94474),x94475)))) % 173.51/173.28 [9471]~P27(x94711,x94712,x94713,x94715)+P27(x94711,x94712,x94713,f333(f333(f315(x94711),x94714),x94715))+P106(f333(f333(f335(x94712),f333(x94713,x94714)),f333(f316(x94711,x94712,x94713),f333(f333(f23(f917(x94711,a905)),x94715),f333(f333(f315(x94711),x94714),f196(f917(x94711,a905))))))) % 173.51/173.28 [9475]P106(f333(x94752,x94755))+~P106(f333(f333(f335(x94751),x94755),f333(f180(x94751),x94753)))+E(f333(f333(f146(x94751),f333(f197(f911(x94751)),f185(x94751,x94752,f333(f333(f142(x94751),x94753),x94754)))),f333(f333(f142(x94751),x94753),x94754)),f333(f333(f142(x94751),f333(f333(f146(x94751),f333(f197(f911(x94751)),f185(x94751,x94752,x94753))),x94753)),x94754)) % 173.51/173.28 [9480]~P106(f333(f333(f335(f916(x94801,x94801)),f333(f333(f265(x94801,x94801),x94802),x94803)),f161(x94801,x94805)))+~P106(f333(f333(f246(a910),f333(x94804,x94802)),f333(x94804,x94803)))+P106(f333(f333(f335(f916(x94801,x94801)),f333(f333(f265(x94801,x94801),x94802),x94803)),f161(x94801,f333(f333(f159(f917(x94801,a910)),x94804),x94805)))) % 173.51/173.28 [9545]P106(f333(f333(f335(f916(x95454,x95454)),f333(f333(f265(x95454,x95454),x95452),x95453)),f161(x95454,x95455)))+P106(f333(f333(f247(a910),f333(x95451,x95452)),f333(x95451,x95453)))+~P106(f333(f333(f335(f916(x95454,x95454)),f333(f333(f265(x95454,x95454),x95452),x95453)),f161(x95454,f333(f333(f159(f917(x95454,a910)),x95451),x95455)))) % 173.51/173.28 [9699]~P106(f333(f333(f335(f916(f911(x96991),f911(x96991))),f333(f333(f265(f911(x96991),f911(x96991)),x96992),x96994)),f166(x96991,x96995)))+~P106(f333(f333(f247(a910),x96993),f333(f197(f911(x96991)),x96992)))+P106(f333(f333(f335(f916(x96991,x96991)),f333(f333(f265(x96991,x96991),f333(f333(f172(x96991),x96992),x96993)),f333(f333(f172(x96991),x96994),x96993))),x96995)) % 173.51/173.28 [9944]E(x99441,f2(a1))+~P106(f333(f55(x99443,x99441),f333(f333(f265(a1,a1),x99444),x99445)))+P106(f333(f55(f333(f333(f88(a1),x99442),x99443),x99441),f333(f333(f265(a1,a1),f333(f333(f87(a1),f333(f333(f88(a1),x99442),x99444)),f333(f333(f42(a1),f333(f333(f88(a1),x99442),x99445)),x99441))),f51(a1,f333(f333(f88(a1),x99442),x99445),x99441)))) % 173.51/173.28 [9945]~P106(f333(f333(f247(a910),f2(a910)),x99453))+~P106(f333(f54(x99452,x99453),f333(f333(f265(a910,a910),x99454),x99455)))+P106(f333(f54(f333(f333(f88(a910),x99451),x99452),x99453),f333(f333(f265(a910,a910),f333(f333(f87(a910),f333(f333(f88(a910),x99451),x99454)),f333(f333(f42(a910),f333(f333(f88(a910),x99451),x99455)),x99453))),f51(a910,f333(f333(f88(a910),x99451),x99455),x99453)))) % 173.51/173.28 [10253]~P72(x102532)+~P106(f333(f67(x102531),x102534))+E(f333(f333(f6(x102531,x102532),x102533),f333(f252(x102531),f333(f333(f18(x102531,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102531),a331),f333(f333(f7(x102531,f917(x102531,a905),a905),f335(x102531)),x102534))),f333(f333(f7(x102531,f917(x102531,a905),a905),f335(x102531)),x102535)))),f333(f333(f6(x102531,x102532),f333(f333(f7(x102531,x102532,x102532),f333(f333(f18(x102531,x102532,f917(x102532,x102532)),f333(f333(f8(a905,f917(x102532,f917(x102532,x102532)),x102531),f107(x102532)),f333(f333(f7(x102531,f917(x102531,a905),a905),f335(x102531)),x102535))),x102533)),f2(x102532))),x102534)) % 173.51/173.28 [8379]~E(f333(f333(f142(x83791),x83792),x83795),f333(f333(f142(x83791),x83793),x83794))+E(f333(f333(f142(x83791),f333(f333(f146(x83791),f333(f197(f911(x83791)),x83792)),x83793)),x83794),x83795)+P106(f333(f333(f246(a910),f333(f197(f911(x83791)),x83793)),f333(f197(f911(x83791)),x83792))) % 173.51/173.28 [8583]~E(f333(f333(f142(x85832),x85833),x85831),f333(f333(f142(x85832),x85834),x85835))+E(x85831,f333(f333(f142(x85832),f333(f333(f146(x85832),f333(f197(f911(x85832)),x85833)),x85834)),x85835))+~P106(f333(f333(f246(a910),f333(f197(f911(x85832)),x85833)),f333(f197(f911(x85832)),x85834))) % 173.51/173.28 [8676]~E(f333(f333(f87(a910),f333(f333(f88(a910),x86763),x86764)),x86761),f333(f333(f87(a910),f333(f333(f88(a910),x86762),x86764)),x86765))+~P106(f333(f333(f246(a910),x86763),x86762))+E(x86761,f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x86762),x86763)),x86764)),x86765)) % 173.51/173.28 [8677]~E(f333(f333(f87(a910),f333(f333(f88(a910),x86771),x86773)),x86774),f333(f333(f87(a910),f333(f333(f88(a910),x86772),x86773)),x86775))+~P106(f333(f333(f246(a910),x86772),x86771))+E(f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x86771),x86772)),x86773)),x86774),x86775) % 173.51/173.28 [8845]E(f333(f333(f87(a910),f333(f333(f88(a910),x88451),x88452)),x88453),f333(f333(f87(a910),f333(f333(f88(a910),x88454),x88452)),x88455))+~P106(f333(f333(f246(a910),x88454),x88451))+~E(x88455,f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x88451),x88454)),x88452)),x88453)) % 173.51/173.28 [8846]E(f333(f333(f87(a910),f333(f333(f88(a910),x88461),x88462)),x88463),f333(f333(f87(a910),f333(f333(f88(a910),x88464),x88462)),x88465))+~P106(f333(f333(f246(a910),x88464),x88461))+~E(f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x88461),x88464)),x88462)),x88463),x88465) % 173.51/173.28 [9755]~P67(x97552)+~P106(f333(f67(x97551),x97555))+E(f333(f333(f9(x97551,x97552),f333(f333(f18(x97551,x97552,x97552),f333(f333(f8(x97552,f917(x97552,x97552),x97551),f296(x97552)),x97553)),x97554)),x97555),f333(f333(f296(x97552),f333(f333(f9(x97551,x97552),x97553),x97555)),f333(f333(f9(x97551,x97552),x97554),x97555))) % 173.51/173.28 [9884]~E(f624(x98845,x98844,x98843,x98842,x98841),f625(x98845,x98844,x98843,x98842,x98841))+P106(f333(f333(f335(f916(x98841,x98841)),f333(f333(f265(x98841,x98841),x98842),x98843)),f313(x98841,x98844)))+~P106(f333(f333(f335(f916(x98841,x98841)),f333(f333(f265(x98841,x98841),x98842),x98843)),f313(x98841,f333(f333(f121(f917(f916(x98841,x98841),a905)),x98844),x98845)))) % 173.51/173.28 [9885]~E(f634(x98855,x98854,x98853,x98852,x98851),f635(x98855,x98854,x98853,x98852,x98851))+P106(f333(f333(f335(f916(x98851,x98851)),f333(f333(f265(x98851,x98851),x98852),x98853)),f313(x98851,x98854)))+~P106(f333(f333(f335(f916(x98851,x98851)),f333(f333(f265(x98851,x98851),x98852),x98853)),f313(x98851,f333(f333(f121(f917(f916(x98851,x98851),a905)),x98854),x98855)))) % 173.51/173.28 [10084]P106(f333(f333(f335(f916(x100841,x100841)),f333(f333(f265(x100841,x100841),x100842),f635(x100845,x100844,x100843,x100842,x100841))),f313(x100841,x100844)))+P106(f333(f333(f335(f916(x100841,x100841)),f333(f333(f265(x100841,x100841),x100842),x100843)),f313(x100841,x100844)))+~P106(f333(f333(f335(f916(x100841,x100841)),f333(f333(f265(x100841,x100841),x100842),x100843)),f313(x100841,f333(f333(f121(f917(f916(x100841,x100841),a905)),x100844),x100845)))) % 173.51/173.28 [10165]P106(f333(f333(f335(f916(x101651,x101651)),f333(f333(f265(x101651,x101651),f625(x101655,x101654,x101653,x101652,x101651)),x101653)),f313(x101651,x101654)))+P106(f333(f333(f335(f916(x101651,x101651)),f333(f333(f265(x101651,x101651),x101652),x101653)),f313(x101651,x101654)))+~P106(f333(f333(f335(f916(x101651,x101651)),f333(f333(f265(x101651,x101651),x101652),x101653)),f313(x101651,f333(f333(f121(f917(f916(x101651,x101651),a905)),x101654),x101655)))) % 173.51/173.28 [10202]P106(f333(f333(f335(f916(x102021,x102021)),f333(f333(f265(x102021,x102021),x102022),x102023)),f313(x102021,x102024)))+P106(f333(f333(f335(f916(x102021,x102021)),f333(f333(f265(x102021,x102021),f624(x102025,x102024,x102023,x102022,x102021)),f625(x102025,x102024,x102023,x102022,x102021))),x102025))+~P106(f333(f333(f335(f916(x102021,x102021)),f333(f333(f265(x102021,x102021),x102022),x102023)),f313(x102021,f333(f333(f121(f917(f916(x102021,x102021),a905)),x102024),x102025)))) % 173.51/173.28 [10203]P106(f333(f333(f335(f916(x102031,x102031)),f333(f333(f265(x102031,x102031),x102032),x102033)),f313(x102031,x102034)))+P106(f333(f333(f335(f916(x102031,x102031)),f333(f333(f265(x102031,x102031),f635(x102035,x102034,x102033,x102032,x102031)),f634(x102035,x102034,x102033,x102032,x102031))),x102035))+~P106(f333(f333(f335(f916(x102031,x102031)),f333(f333(f265(x102031,x102031),x102032),x102033)),f313(x102031,f333(f333(f121(f917(f916(x102031,x102031),a905)),x102034),x102035)))) % 173.51/173.28 [10338]~P106(f333(f333(f335(f916(f911(x103381),f911(x103381))),f333(f333(f265(f911(x103381),f911(x103381)),x103384),x103385)),f166(x103381,x103382)))+~P106(f333(f333(f335(f916(x103381,x103381)),x103383),f333(f180(f916(x103381,x103381)),f333(f333(f189(x103381,x103381),x103384),x103385))))+P106(f333(f333(f269(x103381,x103381,a905),f333(f333(f7(x103381,f917(f916(x103381,x103381),a905),f917(x103381,a905)),f333(f333(f8(f917(x103381,f917(f917(f916(x103381,x103381),a905),a905)),f917(f917(f916(x103381,x103381),a905),f917(x103381,a905)),x103381),f7(x103381,f917(f916(x103381,x103381),a905),a905)),f333(f333(f8(f917(x103381,f916(x103381,x103381)),f917(x103381,f917(f917(f916(x103381,x103381),a905),a905)),x103381),f333(f8(f916(x103381,x103381),f917(f917(f916(x103381,x103381),a905),a905),x103381),f335(f916(x103381,x103381)))),f265(x103381,x103381)))),x103382)),x103383)) % 173.51/173.28 [9785]~P106(f333(f333(f246(a910),x97853),x97852))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),f333(f333(f88(a910),x97853),x97854)),x97851)),f333(f333(f87(a910),f333(f333(f88(a910),x97852),x97854)),x97855)))+P106(f333(f333(f246(a910),x97851),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x97852),x97853)),x97854)),x97855))) % 173.51/173.28 [9786]~P106(f333(f333(f246(a910),x97863),x97862))+~P106(f333(f333(f247(a910),f333(f333(f87(a910),f333(f333(f88(a910),x97863),x97864)),x97861)),f333(f333(f87(a910),f333(f333(f88(a910),x97862),x97864)),x97865)))+P106(f333(f333(f247(a910),x97861),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x97862),x97863)),x97864)),x97865))) % 173.51/173.28 [9803]~P106(f333(f333(f246(a910),x98031),x98034))+P106(f333(f333(f246(a910),f333(f333(f87(a910),f333(f333(f88(a910),x98031),x98032)),x98033)),f333(f333(f87(a910),f333(f333(f88(a910),x98034),x98032)),x98035)))+~P106(f333(f333(f246(a910),x98033),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x98034),x98031)),x98032)),x98035))) % 173.51/173.28 [9804]~P106(f333(f333(f246(a910),x98041),x98044))+P106(f333(f333(f247(a910),f333(f333(f87(a910),f333(f333(f88(a910),x98041),x98042)),x98043)),f333(f333(f87(a910),f333(f333(f88(a910),x98044),x98042)),x98045)))+~P106(f333(f333(f247(a910),x98043),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x98044),x98041)),x98042)),x98045))) % 173.51/173.28 [9920]~P106(f333(f333(f246(a910),x99202),x99201))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),f333(f333(f88(a910),x99201),x99203)),x99204)),f333(f333(f87(a910),f333(f333(f88(a910),x99202),x99203)),x99205)))+P106(f333(f333(f246(a910),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x99201),x99202)),x99203)),x99204)),x99205)) % 173.51/173.28 [9921]~P106(f333(f333(f246(a910),x99212),x99211))+~P106(f333(f333(f247(a910),f333(f333(f87(a910),f333(f333(f88(a910),x99211),x99213)),x99214)),f333(f333(f87(a910),f333(f333(f88(a910),x99212),x99213)),x99215)))+P106(f333(f333(f247(a910),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x99211),x99212)),x99213)),x99214)),x99215)) % 173.51/173.28 [9963]~P106(f333(f333(f246(a910),x99634),x99631))+P106(f333(f333(f246(a910),f333(f333(f87(a910),f333(f333(f88(a910),x99631),x99632)),x99633)),f333(f333(f87(a910),f333(f333(f88(a910),x99634),x99632)),x99635)))+~P106(f333(f333(f246(a910),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x99631),x99634)),x99632)),x99633)),x99635)) % 173.51/173.28 [9964]~P106(f333(f333(f246(a910),x99644),x99641))+P106(f333(f333(f247(a910),f333(f333(f87(a910),f333(f333(f88(a910),x99641),x99642)),x99643)),f333(f333(f87(a910),f333(f333(f88(a910),x99644),x99642)),x99645)))+~P106(f333(f333(f247(a910),f333(f333(f87(a910),f333(f333(f88(a910),f333(f333(f23(a910),x99641),x99644)),x99642)),x99643)),x99645)) % 173.51/173.28 [10190]~P14(x101901,x101902,x101905,x101903)+~P106(f333(f333(f335(f916(x101901,x101901)),x101904),x101905))+P106(f333(f333(f269(x101901,x101901,a905),f333(f333(f7(x101901,f917(x101901,x101902),f917(x101901,a905)),f333(f333(f8(f917(x101902,a905),f917(f917(x101901,x101902),f917(x101901,a905)),x101901),f8(x101902,a905,x101901)),f333(f333(f8(x101902,f917(x101902,a905),x101901),a330),x101903))),x101903)),x101904)) % 173.51/173.28 [8542]~P21(x85426,x85421,x85422,x85424)+E(f333(f79(x85421,x85421,x85421,f333(x85422,x85423)),f333(x85424,x85425)),f333(f79(x85421,x85421,x85421,f333(x85424,x85425)),f333(x85422,x85423)))+~P106(f333(f67(x85426),x85425)) % 173.51/173.28 [8988]~P27(x89881,x89883,x89885,x89886)+~P27(x89883,x89882,x89884,f333(f316(x89881,x89883,x89885),x89886))+P27(x89881,x89882,f333(f79(x89883,x89882,x89881,x89884),x89885),x89886) % 173.51/173.28 [9578]~P106(f333(f333(x95783,x95782),x95786))+~P106(f333(f333(x95784,x95785),x95782))+P106(f333(f333(f335(x95781),x95782),f306(x95781,x95783,x95784,x95785,x95786))) % 173.51/173.28 [9579]~P106(f333(f333(x95794,x95792),x95796))+~P106(f333(f333(x95793,x95795),x95792))+P106(f333(f333(f335(x95791),x95792),f303(x95791,x95793,x95794,x95795,x95796))) % 173.51/173.28 [9700]E(x97001,x97002)+E(x97003,x97004)+~P106(f333(f333(f335(f916(f911(x97005),f911(x97005))),f333(f333(f265(f911(x97005),f911(x97005)),f333(f333(f159(x97005),x97003),x97001)),f333(f333(f159(x97005),x97004),x97002))),f165(x97005,x97006))) % 173.51/173.28 [9710]~E(x97102,x97104)+P106(f333(f333(f335(f916(f911(x97101),f911(x97101))),f333(f333(f265(f911(x97101),f911(x97101)),f333(f333(f159(x97101),x97102),x97103)),f333(f333(f159(x97101),x97104),x97105))),f153(x97101,x97106)))+~P106(f333(f333(f335(f916(f911(x97101),f911(x97101))),f333(f333(f265(f911(x97101),f911(x97101)),x97103),x97105)),f153(x97101,x97106))) % 173.51/173.28 [9711]~E(x97112,x97114)+P106(f333(f333(f335(f916(f911(x97111),f911(x97111))),f333(f333(f265(f911(x97111),f911(x97111)),f333(f333(f159(x97111),x97112),x97113)),f333(f333(f159(x97111),x97114),x97115))),f155(x97111,x97116)))+~P106(f333(f333(f335(f916(f911(x97111),f911(x97111))),f333(f333(f265(f911(x97111),f911(x97111)),x97113),x97115)),f155(x97111,x97116))) % 173.51/173.28 [9712]~E(x97122,x97124)+P106(f333(f333(f335(f916(f911(x97121),f911(x97121))),f333(f333(f265(f911(x97121),f911(x97121)),f333(f333(f159(x97121),x97122),x97123)),f333(f333(f159(x97121),x97124),x97125))),f165(x97121,x97126)))+~P106(f333(f333(f335(f916(f911(x97121),f911(x97121))),f333(f333(f265(f911(x97121),f911(x97121)),x97123),x97125)),f165(x97121,x97126))) % 173.51/173.28 [9713]~E(x97132,x97134)+P106(f333(f333(f335(f916(f911(x97131),f911(x97131))),f333(f333(f265(f911(x97131),f911(x97131)),f333(f333(f142(x97131),x97132),x97133)),f333(f333(f142(x97131),x97134),x97135))),f165(x97131,x97136)))+~P106(f333(f333(f335(f916(f911(x97131),f911(x97131))),f333(f333(f265(f911(x97131),f911(x97131)),x97133),x97135)),f165(x97131,x97136))) % 173.51/173.28 [9714]~E(x97143,x97145)+P106(f333(f333(f335(f916(f911(x97141),f911(x97141))),f333(f333(f265(f911(x97141),f911(x97141)),f333(f333(f142(x97141),x97142),x97143)),f333(f333(f142(x97141),x97144),x97145))),f165(x97141,x97146)))+~P106(f333(f333(f335(f916(f911(x97141),f911(x97141))),f333(f333(f265(f911(x97141),f911(x97141)),x97142),x97144)),f165(x97141,x97146))) % 173.51/173.28 [9772]E(x97721,x97722)+P106(f333(f333(f335(f916(f911(x97723),f911(x97723))),f333(f333(f265(f911(x97723),f911(x97723)),x97721),x97722)),f165(x97723,x97724)))+~P106(f333(f333(f335(f916(f911(x97723),f911(x97723))),f333(f333(f265(f911(x97723),f911(x97723)),f333(f333(f159(x97723),x97725),x97721)),f333(f333(f159(x97723),x97726),x97722))),f165(x97723,x97724))) % 173.51/173.28 [9924]~E(x99243,x99245)+P106(f333(f333(f335(f916(f911(x99241),f911(x99241))),f333(f333(f265(f911(x99241),f911(x99241)),f333(f333(f142(x99241),x99242),f333(f333(f159(x99241),x99243),f124(x99241)))),f333(f333(f142(x99241),x99244),f333(f333(f159(x99241),x99245),f124(x99241))))),f165(x99241,x99246)))+~P106(f333(f333(f335(f916(f911(x99241),f911(x99241))),f333(f333(f265(f911(x99241),f911(x99241)),x99242),x99244)),f165(x99241,x99246))) % 173.51/173.28 [9967]E(x99671,x99672)+E(x99673,x99674)+~P106(f333(f333(f335(f916(f911(x99675),f911(x99675))),f333(f333(f265(f911(x99675),f911(x99675)),f333(f333(f142(x99675),x99673),f333(f333(f159(x99675),x99671),f124(x99675)))),f333(f333(f142(x99675),x99674),f333(f333(f159(x99675),x99672),f124(x99675))))),f165(x99675,x99676))) % 173.51/173.28 [9992]E(x99921,x99922)+~P106(f333(f333(f335(f916(f911(x99923),f911(x99923))),f333(f333(f265(f911(x99923),f911(x99923)),f333(f333(f142(x99923),x99921),f333(f333(f159(x99923),x99925),f124(x99923)))),f333(f333(f142(x99923),x99922),f333(f333(f159(x99923),x99926),f124(x99923))))),f165(x99923,x99924)))+P106(f333(f333(f335(f916(f911(x99923),f911(x99923))),f333(f333(f265(f911(x99923),f911(x99923)),x99921),x99922)),f165(x99923,x99924))) % 173.51/173.28 [10029]~P106(f333(f333(f335(f916(f917(x100291,a905),f917(x100291,a905))),f333(f333(f265(f917(x100291,a905),f917(x100291,a905)),x100292),x100294)),f324(x100291,x100296)))+~P106(f333(f333(f335(f916(f917(x100291,a905),f917(x100291,a905))),f333(f333(f265(f917(x100291,a905),f917(x100291,a905)),x100293),x100295)),f324(x100291,x100296)))+P106(f333(f333(f335(f916(f917(x100291,a905),f917(x100291,a905))),f333(f333(f265(f917(x100291,a905),f917(x100291,a905)),f333(f333(f121(f917(x100291,a905)),x100292),x100293)),f333(f333(f121(f917(x100291,a905)),x100294),x100295))),f324(x100291,x100296))) % 173.51/173.28 [5798]~E(f333(f333(f142(x57981),x57986),x57983),x57985)+E(f333(f333(f142(x57981),x57982),x57983),f333(f333(f159(x57981),x57984),x57985))+~E(x57982,f333(f333(f159(x57981),x57984),x57986)) % 173.51/173.28 [5799]~E(f333(f333(f142(x57991),x57996),x57993),x57995)+E(f333(f333(f142(x57991),x57992),x57993),f333(f333(f142(x57991),x57994),x57995))+~E(x57992,f333(f333(f142(x57991),x57994),x57996)) % 173.51/173.28 [5801]E(f333(f333(f142(x58011),x58012),x58013),f333(f333(f159(x58011),x58014),x58015))+~E(f333(f333(f159(x58011),x58014),x58016),x58012)+~E(x58015,f333(f333(f142(x58011),x58016),x58013)) % 173.51/173.28 [5803]~E(f333(f333(f142(x58031),x58032),x58036),x58034)+E(f333(f333(f142(x58031),x58032),x58033),f333(f333(f142(x58031),x58034),x58035))+~E(x58033,f333(f333(f142(x58031),x58036),x58035)) % 173.51/173.28 [6925]E(f333(x69251,x69252),f333(x69253,x69252))+~E(f333(f333(f162(x69254,x69255),x69251),x69256),f333(f333(f162(x69254,x69255),x69253),x69256))+~P106(f333(f333(f335(x69254),x69252),f333(f180(x69254),x69256))) % 173.51/173.28 [7306]~P21(x73064,x73065,x73066,x73061)+E(f333(f333(x73061,x73062),x73063),f333(f333(f70(x73064,x73065,x73066),x73063),x73062))+~P106(f333(f67(x73064),x73062)) % 173.51/173.28 [7376]~E(x73762,f333(x73764,x73766))+~P106(f333(f333(f335(x73763),x73766),x73765))+P106(f333(f333(f335(x73761),x73762),f333(f316(x73763,x73761,x73764),x73765))) % 173.51/173.28 [7377]~E(f333(x73774,x73772),x73776)+~P106(f333(f333(f335(x73773),x73776),x73775))+P106(f333(f333(f335(x73771),x73772),f333(f317(x73771,x73773,x73774),x73775))) % 173.51/173.28 [7822]~P35(x78221,x78222,x78224,x78226)+P35(x78221,x78222,f333(f333(f159(x78221),x78223),x78224),f333(f333(f159(x78221),x78225),x78226))+~P106(f333(f333(x78222,x78223),x78225)) % 173.51/173.28 [8855]~P60(x88554,x88555,x88551,x88552,x88556)+E(f333(x88551,f333(x88552,x88553)),x88553)+~P106(f333(f333(f335(x88555),x88553),x88556)) % 173.51/173.28 [9371]~P28(x93712,x93711,x93715,x93714,x93713)+E(f333(f99(x93711,x93712,x93713,f99(x93712,x93711,x93714,x93715)),x93716),f333(x93715,x93716))+~P106(f333(f333(f335(x93712),x93716),x93714)) % 173.51/173.28 [9380]~P27(x93801,x93802,x93803,x93806)+P27(x93801,x93802,f81(x93801,x93802,x93803,x93804,x93805),x93806)+P106(f333(f333(f335(x93802),x93805),f333(f316(x93801,x93802,x93803),x93806))) % 173.51/173.28 [9702]E(x97021,x97022)+E(f333(f197(f911(x97023)),x97024),f333(f197(f911(x97023)),x97025))+~P106(f333(f333(f335(f916(f911(x97023),f911(x97023))),f333(f333(f265(f911(x97023),f911(x97023)),f333(f333(f159(x97023),x97021),x97024)),f333(f333(f159(x97023),x97022),x97025))),f153(x97023,x97026))) % 173.51/173.28 [9767]~P18(x97671,x97672,x97673)+E(f333(f333(f70(x97671,x97672,x97673),x97674),x97675),x97676)+~P106(f333(f72(x97671,x97672,x97673,x97674,x97675),x97676)) % 173.51/173.28 [9776]E(f333(f197(f911(x97761)),x97762),f333(f197(f911(x97761)),x97763))+P106(f333(f333(f335(f916(f911(x97761),f911(x97761))),f333(f333(f265(f911(x97761),f911(x97761)),x97762),x97763)),f153(x97761,x97764)))+~P106(f333(f333(f335(f916(f911(x97761),f911(x97761))),f333(f333(f265(f911(x97761),f911(x97761)),f333(f333(f159(x97761),x97765),x97762)),f333(f333(f159(x97761),x97766),x97763))),f153(x97761,x97764))) % 173.51/173.28 [9797]~P106(f333(f333(f335(f916(x97971,x97971)),f333(f333(f265(x97971,x97971),x97972),x97974)),f313(x97971,x97976)))+P106(f333(f333(f335(f916(f911(x97971),f911(x97971))),f333(f333(f265(f911(x97971),f911(x97971)),f333(f333(f159(x97971),x97972),x97973)),f333(f333(f159(x97971),x97974),x97975))),f313(f911(x97971),f165(x97971,x97976))))+~P106(f333(f333(f335(f916(f911(x97971),f911(x97971))),f333(f333(f265(f911(x97971),f911(x97971)),x97973),x97975)),f313(f911(x97971),f165(x97971,x97976)))) % 173.51/173.28 [9973]~P106(f333(x99732,x99736))+~E(f333(f144(x99731,x99732),x99733),f333(f333(f159(x99731),x99734),x99735))+~P106(f333(f333(f335(x99731),x99736),f333(f180(x99731),f793(x99735,x99734,x99733,x99732,x99731)))) % 173.51/173.28 [9974]~P106(f333(x99744,x99746))+~E(f333(f333(f159(x99741),x99742),x99743),f333(f144(x99741,x99744),x99745))+~P106(f333(f333(f335(x99741),x99746),f333(f180(x99741),f791(x99745,x99744,x99743,x99742,x99741)))) % 173.51/173.28 [10284]~P72(x102842)+E(f333(f333(f6(x102841,x102842),f333(f333(f8(f917(x102843,a905),x102842,x102841),f333(f6(x102843,x102842),x102844)),f333(f333(f8(f917(x102843,a905),f917(x102843,a905),x102841),f252(x102843)),f333(f333(f8(f917(x102843,a905),f917(x102843,a905),x102841),f333(f18(x102843,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102843),a331),f333(f333(f7(x102843,f917(x102843,a905),a905),f335(x102843)),x102845)))),f333(f7(x102843,x102841,a905),f333(f333(f8(x102841,f917(x102841,a905),x102843),a330),x102846)))))),f333(f316(x102843,x102841,x102846),x102845)),f333(f333(f6(x102843,x102842),x102844),x102845))+~P106(f333(f67(x102843),x102845)) % 173.51/173.28 [6981]~P110(x69813)+P106(f333(x69812,x69815))+E(f333(f144(x69811,x69812),f333(f333(f156(x69811,x69813,x69814),x69815),x69816)),f333(f144(x69811,x69812),x69816)) % 173.51/173.28 [6983]P106(f333(x69831,x69832))+~E(f174(x69833,x69831,x69834),f333(f333(f265(f911(x69833),f911(x69833)),x69835),x69836))+~P106(f333(f333(f335(x69833),x69832),f333(f180(x69833),x69835))) % 173.51/173.28 [7026]~P106(f333(x70262,x70266))+~E(f174(x70261,x70262,x70263),f333(f333(f265(f911(x70261),f911(x70261)),x70264),x70265))+~P106(f333(f333(f335(x70261),x70266),f333(f180(x70261),x70265))) % 173.51/173.28 [7686]~P17(x76861,x76862,x76863)+~P106(f333(f67(x76861),x76866))+E(f333(f333(f70(x76861,x76862,x76863),x76864),f333(f333(f315(x76861),x76865),x76866)),f333(f333(f70(x76861,x76862,x76863),f333(f333(x76863,x76865),x76864)),x76866)) % 173.51/173.28 [7737]~P110(x77372)+~P106(f333(f333(f246(x77372),f333(x77373,x77374)),f333(x77373,x77375)))+E(f333(f333(f156(x77371,x77372,x77373),x77374),f333(f333(f159(x77371),x77375),x77376)),f333(f333(f159(x77371),x77374),f333(f333(f159(x77371),x77375),x77376))) % 173.51/173.28 [7851]E(x78511,x78512)+~E(f333(f333(f267(x78513,x78514),x78511),f333(f16(f917(x78514,a905),x78513),x78515)),f333(f333(f267(x78513,x78514),x78512),f333(f16(f917(x78514,a905),x78513),x78515)))+~P106(f333(f333(f335(x78514),x78516),x78515)) % 173.51/173.28 [7919]~P17(x79191,x79192,x79193)+~P106(f333(f67(x79191),x79196))+E(f333(f333(f70(x79191,x79192,x79193),x79194),f333(f333(f315(x79191),x79195),x79196)),f333(f333(x79193,x79195),f333(f333(f70(x79191,x79192,x79193),x79194),x79196))) % 173.51/173.28 [8037]~P18(x80371,x80372,x80373)+~P106(f333(f67(x80371),x80376))+E(f333(f333(f70(x80371,x80372,x80373),f333(f333(x80373,x80374),x80375)),x80376),f333(f333(x80373,x80374),f333(f333(f70(x80371,x80372,x80373),x80375),x80376))) % 173.51/173.28 [8106]~P22(x81062,x81065,x81066,x81061)+~P106(f333(f67(x81062),x81064))+E(f333(x81061,f333(f333(f315(x81062),x81063),x81064)),f333(f79(x81065,x81065,x81065,f333(x81061,x81064)),f333(x81066,x81063))) % 173.51/173.28 [8144]~P110(x81442)+P106(f333(f333(f246(x81442),f333(x81443,x81444)),f333(x81443,x81445)))+E(f333(f333(f156(x81441,x81442,x81443),x81444),f333(f333(f159(x81441),x81445),x81446)),f333(f333(f159(x81441),x81445),f333(f333(f156(x81441,x81442,x81443),x81444),x81446))) % 173.51/173.28 [8284]~E(f333(f197(f911(x82841)),x82845),f333(f197(f911(x82842)),x82846))+~E(f333(f197(f911(x82841)),x82843),f333(f197(f911(x82842)),x82844))+E(f333(f333(f142(f916(x82841,x82842)),f333(f333(f189(x82841,x82842),x82843),x82844)),f333(f333(f189(x82841,x82842),x82845),x82846)),f333(f333(f189(x82841,x82842),f333(f333(f142(x82841),x82843),x82845)),f333(f333(f142(x82842),x82844),x82846))) % 173.51/173.28 [8397]~E(x83972,f333(f316(x83973,x83971,x83974),x83976))+P106(f333(f333(f246(f917(x83971,a905)),x83972),f333(f316(x83973,x83971,x83974),x83975)))+~P106(f333(f333(f246(f917(x83973,a905)),x83976),x83975)) % 173.51/173.28 [8499]~P110(x84995)+E(f333(x84991,x84992),f333(x84991,x84993))+E(f333(f333(f156(x84994,x84995,x84991),x84992),f333(f333(f156(x84994,x84995,x84991),x84993),x84996)),f333(f333(f156(x84994,x84995,x84991),x84993),f333(f333(f156(x84994,x84995,x84991),x84992),x84996))) % 173.51/173.28 [8685]~P106(f333(f333(f335(x86852),x86854),f333(x86856,x86853)))+~P106(f333(f333(f335(x86851),x86853),x86855))+P106(f333(f333(f335(f916(x86851,x86852)),f333(f333(f265(x86851,x86852),x86853),x86854)),f333(f333(f267(x86851,x86852),x86855),x86856))) % 173.51/173.28 [9178]~P72(x91782)+~P27(x91784,x91781,x91785,x91786)+E(f333(f333(f6(x91781,x91782),x91783),f333(f316(x91784,x91781,x91785),x91786)),f333(f333(f6(x91784,x91782),f333(f79(x91781,x91782,x91784,x91783),x91785)),x91786)) % 173.51/173.28 [9179]~P78(x91792)+~P27(x91794,x91791,x91795,x91796)+E(f333(f333(f9(x91791,x91792),x91793),f333(f316(x91794,x91791,x91795),x91796)),f333(f333(f9(x91794,x91792),f333(f79(x91791,x91792,x91794,x91793),x91795)),x91796)) % 173.51/173.28 [9226]~P37(x92262,x92265,x92261,x92263,x92266)+P106(f333(f333(x92261,f333(f333(f172(x92262),x92263),x92264)),f333(f333(f172(x92265),x92266),x92264)))+~P106(f333(f333(f247(a910),x92264),f333(f197(f911(x92265)),x92266))) % 173.51/173.28 [9227]~P37(x92272,x92275,x92271,x92273,x92276)+P106(f333(f333(x92271,f333(f333(f172(x92272),x92273),x92274)),f333(f333(f172(x92275),x92276),x92274)))+~P106(f333(f333(f247(a910),x92274),f333(f197(f911(x92272)),x92273))) % 173.51/173.28 [9238]~E(f333(f316(x92381,x92382,x92383),x92384),x92386)+E(f333(f316(x92381,x92382,x92383),f333(f316(x92382,x92381,f99(x92381,x92382,x92384,x92383)),x92385)),x92385)+~P106(f333(f333(f246(f917(x92382,a905)),x92385),x92386)) % 173.51/173.28 [9368]~E(f333(f333(f333(a205,x93685),f34(x93681)),f206(x93684,x93681)),f333(f333(f333(a205,x93686),f34(x93681)),f206(x93684,x93681)))+P106(f333(f333(f202(f27(x93681,x93682,x93683)),x93684),f333(f333(f333(a205,x93685),f34(x93681)),f206(x93684,x93681))))+~P106(f333(f333(f202(x93683),f333(f333(f333(a205,x93684),f34(x93681)),f333(x93682,x93684))),x93686)) % 173.51/173.28 [9442]~P21(x94423,x94421,x94426,x94422)+~P106(f333(f67(x94423),x94424))+E(f333(f79(x94421,x94421,x94421,f333(x94422,f333(f333(f23(f917(x94423,a905)),x94424),f333(f333(f315(x94423),x94425),f196(f917(x94423,a905)))))),f333(x94426,x94425)),f333(x94422,f333(f333(f315(x94423),x94425),x94424))) % 173.51/173.28 [10064]~E(f333(f316(x100642,x100644,x100646),f254(f917(x100642,a905))),f254(f917(x100644,a905)))+~E(f333(f316(x100641,x100643,x100645),f254(f917(x100641,a905))),f254(f917(x100643,a905)))+E(f333(f316(f916(x100641,x100642),f916(x100643,x100644),f270(x100641,x100643,x100642,x100644,x100645,x100646)),f254(f917(f916(x100641,x100642),a905))),f254(f917(f916(x100643,x100644),a905))) % 173.51/173.28 [10114]~P27(x101143,x101144,x101145,f333(x101146,f678(x101146,x101145,x101144,x101143,x101142,x101141)))+P27(x101143,x101144,x101145,f333(f333(f46(x101142,f917(x101143,a905)),x101141),x101146))+E(x101141,f196(f917(x101142,a905))) % 173.51/173.28 [10173]P27(x101736,x101735,x101734,f333(f333(f46(x101732,f917(x101736,a905)),x101731),x101733))+E(x101731,f196(f917(x101732,a905)))+P106(f333(f333(f335(x101732),f678(x101733,x101734,x101735,x101736,x101732,x101731)),x101731)) % 173.51/173.28 [10179]P106(f333(f333(f335(x101791),f639(x101792,x101793,x101794,x101795,x101796,x101791)),x101796))+P106(f333(f333(f246(f917(f916(x101791,x101794),a905)),f333(f333(f267(x101791,x101794),x101796),x101793)),f333(f333(f267(x101791,x101794),x101795),x101792)))+~P106(f333(f333(f246(f917(x101791,a905)),x101796),x101795)) % 173.51/173.28 [10216]P26(x102166,x102165,f333(f333(f315(f909(x102166)),f333(f333(f333(f98(x102166),x102161),x102163),x102162)),f196(f917(f909(x102166),a905))))+~P26(x102166,x102165,f333(f333(f315(f909(x102166)),f333(f333(f333(f98(x102166),x102164),x102163),x102162)),f196(f917(f909(x102166),a905))))+P106(f333(f333(x102161,f782(x102161,x102162,x102163,x102164,x102165,x102166)),f864(x102161,x102162,x102163,x102164,x102165,x102166))) % 173.51/173.28 [10217]P26(x102176,x102175,f333(f333(f315(f909(x102176)),f333(f333(f333(f98(x102176),x102174),x102173),x102172)),f196(f917(f909(x102176),a905))))+~P26(x102176,x102175,f333(f333(f315(f909(x102176)),f333(f333(f333(f98(x102176),x102174),x102173),x102171)),f196(f917(f909(x102176),a905))))+P106(f333(f333(x102171,f874(x102172,x102171,x102173,x102174,x102175,x102176)),f888(x102172,x102171,x102173,x102174,x102175,x102176))) % 173.51/173.28 [10256]~P26(x102561,x102562,f333(f333(f315(f909(x102561)),f333(f333(f333(f98(x102561),x102563),x102564),x102566)),f196(f917(f909(x102561),a905))))+P26(x102561,x102562,f333(f333(f315(f909(x102561)),f333(f333(f333(f98(x102561),x102563),x102564),x102565)),f196(f917(f909(x102561),a905))))+~P106(f333(f333(x102565,f874(x102565,x102566,x102564,x102563,x102562,x102561)),f888(x102565,x102566,x102564,x102563,x102562,x102561))) % 173.51/173.28 [10257]~P26(x102571,x102572,f333(f333(f315(f909(x102571)),f333(f333(f333(f98(x102571),x102576),x102574),x102575)),f196(f917(f909(x102571),a905))))+P26(x102571,x102572,f333(f333(f315(f909(x102571)),f333(f333(f333(f98(x102571),x102573),x102574),x102575)),f196(f917(f909(x102571),a905))))+~P106(f333(f333(x102576,f782(x102573,x102575,x102574,x102576,x102572,x102571)),f864(x102573,x102575,x102574,x102576,x102572,x102571))) % 173.51/173.28 [10295]~P106(f333(f333(f246(f917(x102952,a905)),f333(x102954,f639(x102956,x102954,x102952,x102955,x102953,x102951))),f333(x102956,f639(x102956,x102954,x102952,x102955,x102953,x102951))))+~P106(f333(f333(f246(f917(x102951,a905)),x102953),x102955))+P106(f333(f333(f246(f917(f916(x102951,x102952),a905)),f333(f333(f267(x102951,x102952),x102953),x102954)),f333(f333(f267(x102951,x102952),x102955),x102956))) % 173.51/173.28 [7873]~P106(f333(x78731,x78735))+~P106(f333(x78736,x78734))+P106(f333(x78731,f333(f268(x78732,x78733),f333(f333(f265(x78732,x78733),x78734),x78735)))) % 173.51/173.28 [7874]~P106(f333(x78741,x78744))+~P106(f333(x78746,x78745))+P106(f333(x78741,f333(f264(x78742,x78743),f333(f333(f265(x78742,x78743),x78744),x78745)))) % 173.51/173.28 [7924]~P106(f333(f333(x79244,x79246),x79245))+~P106(f333(f333(f335(x79241),x79246),x79243))+P106(f333(f333(f333(f45(x79241,f917(x79242,a905)),x79243),x79244),x79245)) % 173.51/173.28 [8235]~P106(f333(f333(f335(x82351),x82352),f333(x82355,x82356)))+~P106(f333(f333(f335(x82353),x82356),x82354))+P106(f333(f333(f335(x82351),x82352),f333(f333(f45(x82353,f917(x82351,a905)),x82354),x82355))) % 173.51/173.28 [8277]P106(f333(f333(x82771,x82772),x82773))+~P106(f333(f333(x82774,x82772),x82773))+~P106(f333(f333(f246(f917(x82775,f917(x82776,a905))),x82774),x82771)) % 173.51/173.28 [8421]P106(f333(f333(x84211,x84212),x84213))+~P106(f333(f333(f335(x84214),x84212),x84215))+~P106(f333(f333(f333(f46(x84214,f917(x84216,a905)),x84215),x84211),x84213)) % 173.51/173.28 [8559]P106(f333(f333(f335(x85591),x85592),f333(x85593,x85594)))+~P106(f333(f333(f335(x85595),x85594),x85596))+~P106(f333(f333(f335(x85591),x85592),f333(f333(f46(x85595,f917(x85591,a905)),x85596),x85593))) % 173.51/173.28 [8758]~P106(f333(f333(f333(f333(a204,x87581),x87583),x87584),x87586))+~P106(f333(f333(f333(f333(a204,x87582),x87586),x87584),x87585))+P106(f333(f333(f333(f333(a204,f31(x87581,x87582)),x87583),x87584),x87585)) % 173.51/173.28 [8834]~P14(x88344,x88345,x88346,x88341)+E(f333(x88341,x88342),f333(x88341,x88343))+~P106(f333(f333(f335(f916(x88344,x88344)),f333(f333(f265(x88344,x88344),x88342),x88343)),x88346)) % 173.51/173.28 [8868]P106(f333(f333(f246(f917(x88681,a905)),x88682),f333(x88683,x88684)))+~P106(f333(f333(f335(x88685),x88684),x88686))+~P106(f333(f333(f246(f917(x88681,a905)),x88682),f333(f333(f46(x88685,f917(x88681,a905)),x88686),x88683))) % 173.51/173.28 [8901]~P58(x89013,x89014,f333(f293(x89014,x89013),x89015))+E(x89011,f196(f917(x89012,a905)))+E(f333(f333(f46(x89012,f917(x89013,a905)),x89011),f333(f333(f8(f917(x89014,a905),f917(x89013,a905),x89012),f292(x89014,x89013,x89015)),x89016)),f333(f292(x89014,x89013,x89015),f333(f333(f46(x89012,f917(x89014,a905)),x89011),x89016))) % 173.51/173.28 [8979]P106(f333(f333(f335(x89791),x89792),f333(f292(x89793,x89791,x89794),x89795)))+~P106(f333(f333(f335(x89793),x89796),x89795))+~P106(f333(f333(f335(f916(x89793,x89791)),f333(f333(f265(x89793,x89791),x89796),x89792)),x89794)) % 173.51/173.28 [9104]P106(f333(x91041,x91042))+~P106(f333(f333(f333(f333(a204,x91044),x91042),x91045),x91046))+P106(f333(f333(f333(f333(a204,f28(x91041,x91043,x91044)),x91042),x91045),x91046)) % 173.51/173.28 [9123]~P106(f333(x91231,x91234))+~P106(f333(f333(f333(f333(a204,x91232),x91234),x91235),x91236))+P106(f333(f333(f333(f333(a204,f28(x91231,x91232,x91233)),x91234),x91235),x91236)) % 173.51/173.28 [9304]P106(f333(f333(f246(f917(x93041,a905)),f333(f292(x93042,x93041,x93043),x93044)),f333(f292(x93042,x93041,x93045),x93046)))+~P106(f333(f333(f246(f917(x93042,a905)),x93044),x93046))+~P106(f333(f333(f246(f917(f916(x93042,x93041),a905)),x93043),x93045)) % 173.51/173.28 [9391]P106(f333(x93911,x93912))+P106(f333(f333(f333(f333(a204,x93913),x93912),x93914),x93915))+~P106(f333(f333(f333(f333(a204,f28(x93911,x93916,x93913)),x93912),x93914),x93915)) % 173.51/173.28 [9396]~P106(f333(x93965,x93962))+P106(f333(f333(f333(f333(a204,x93961),x93962),x93963),x93964))+~P106(f333(f333(f333(f333(a204,f28(x93965,x93961,x93966)),x93962),x93963),x93964)) % 173.51/173.28 [9450]P106(f333(f333(f333(f333(a204,x94501),x94502),x94503),x94504))+P106(f333(f333(f333(f333(a204,x94505),x94502),x94503),x94504))+~P106(f333(f333(f333(f333(a204,f28(x94506,x94501,x94505)),x94502),x94503),x94504)) % 173.51/173.28 [9496]~P106(f333(f333(f335(x94962),x94966),x94964))+~P106(f333(f333(f246(f917(x94961,a905)),x94963),x94965))+P106(f333(f333(f246(f917(f916(x94961,x94962),a905)),f333(f333(f267(x94961,x94962),x94963),f333(f16(f917(x94962,a905),x94961),x94964))),f333(f333(f267(x94961,x94962),x94965),f333(f16(f917(x94962,a905),x94961),x94964)))) % 173.51/173.28 [9508]~P37(x95081,x95082,x95083,x95085,x95086)+P106(f333(f333(f269(x95081,x95082,a905),x95083),x95084))+~P106(f333(f333(f335(f916(x95081,x95082)),x95084),f333(f180(f916(x95081,x95082)),f333(f333(f189(x95081,x95082),x95085),x95086)))) % 173.51/173.28 [9648]~E(x96483,x96485)+P106(f333(f333(f335(f916(f911(x96481),f911(x96481))),f333(f333(f265(f911(x96481),f911(x96481)),f333(f333(f159(x96481),x96482),x96483)),f333(f333(f159(x96481),x96484),x96485))),f165(x96481,x96486)))+~P106(f333(f333(f335(f916(x96481,x96481)),f333(f333(f265(x96481,x96481),x96482),x96484)),x96486)) % 173.51/173.28 [9654]~E(f333(f197(f911(x96541)),x96543),f333(f197(f911(x96541)),x96545))+P106(f333(f333(f335(f916(f911(x96541),f911(x96541))),f333(f333(f265(f911(x96541),f911(x96541)),f333(f333(f159(x96541),x96542),x96543)),f333(f333(f159(x96541),x96544),x96545))),f153(x96541,x96546)))+~P106(f333(f333(f335(f916(x96541,x96541)),f333(f333(f265(x96541,x96541),x96542),x96544)),x96546)) % 173.51/173.28 [9692]P106(f333(f333(f335(f916(x96921,x96921)),f333(f333(f265(x96921,x96921),x96922),x96923)),f333(f333(f191(f916(x96921,x96921),a905),f333(a123,x96924)),x96925)))+~P106(f333(f333(f335(f916(x96921,x96921)),f333(f333(f265(x96921,x96921),x96926),x96923)),x96925))+~P106(f333(f333(f335(f916(x96921,x96921)),f333(f333(f265(x96921,x96921),x96922),x96926)),f333(f333(f191(f916(x96921,x96921),a905),x96924),x96925))) % 173.51/173.28 [9693]P106(f333(f333(f335(f916(x96931,x96931)),f333(f333(f265(x96931,x96931),x96932),x96933)),f333(f333(f191(f916(x96931,x96931),a905),f333(a123,x96934)),x96935)))+~P106(f333(f333(f335(f916(x96931,x96931)),f333(f333(f265(x96931,x96931),x96932),x96936)),x96935))+~P106(f333(f333(f335(f916(x96931,x96931)),f333(f333(f265(x96931,x96931),x96936),x96933)),f333(f333(f191(f916(x96931,x96931),a905),x96934),x96935))) % 173.51/173.28 [9698]~P106(f333(f333(f335(x96984),x96985),x96986))+P106(f333(f333(f246(f917(x96981,a905)),x96982),x96983))+~P106(f333(f333(f246(f917(f916(x96981,x96984),a905)),f333(f333(f267(x96981,x96984),x96982),f333(f16(f917(x96984,a905),x96981),x96986))),f333(f333(f267(x96981,x96984),x96983),f333(f16(f917(x96984,a905),x96981),x96986)))) % 173.51/173.28 [9745]E(x97451,x97452)+~P106(f333(f333(f335(f916(f911(x97453),f911(x97453))),f333(f333(f265(f911(x97453),f911(x97453)),f333(f333(f159(x97453),x97451),x97455)),f333(f333(f159(x97453),x97452),x97456))),f153(x97453,x97454)))+P106(f333(f333(f335(f916(x97453,x97453)),f333(f333(f265(x97453,x97453),x97451),x97452)),x97454)) % 173.51/173.28 [9746]E(x97461,x97462)+~P106(f333(f333(f335(f916(f911(x97463),f911(x97463))),f333(f333(f265(f911(x97463),f911(x97463)),f333(f333(f159(x97463),x97461),x97465)),f333(f333(f159(x97463),x97462),x97466))),f155(x97463,x97464)))+P106(f333(f333(f335(f916(x97463,x97463)),f333(f333(f265(x97463,x97463),x97461),x97462)),x97464)) % 173.51/173.28 [9747]E(x97471,x97472)+~P106(f333(f333(f335(f916(f911(x97473),f911(x97473))),f333(f333(f265(f911(x97473),f911(x97473)),f333(f333(f159(x97473),x97471),x97475)),f333(f333(f159(x97473),x97472),x97476))),f165(x97473,x97474)))+P106(f333(f333(f335(f916(x97473,x97473)),f333(f333(f265(x97473,x97473),x97471),x97472)),x97474)) % 173.51/173.28 [9784]P106(f333(f333(f335(f916(f911(x97841),f911(x97841))),f333(f333(f265(f911(x97841),f911(x97841)),f333(f333(f159(x97841),x97842),x97843)),f333(f333(f159(x97841),x97844),x97845))),f166(x97841,x97846)))+~P106(f333(f333(f335(f916(f911(x97841),f911(x97841))),f333(f333(f265(f911(x97841),f911(x97841)),x97843),x97845)),f166(x97841,x97846)))+~P106(f333(f333(f335(f916(x97841,x97841)),f333(f333(f265(x97841,x97841),x97842),x97844)),x97846)) % 173.51/173.28 [9801]P106(f333(x98011,x98012))+~P106(f333(x98011,f483(x98011,x98013,x98014,x98015,x98016)))+~P106(f333(f333(f335(x98016),x98012),f333(f333(f45(x98015,f917(x98016,a905)),x98014),x98013))) % 173.51/173.28 [9806]~P106(f333(f333(f335(f916(f911(x98061),f911(x98061))),f333(f333(f265(f911(x98061),f911(x98061)),f333(f333(f159(x98061),x98062),x98065)),f333(f333(f159(x98061),x98063),x98066))),f153(x98061,x98064)))+P106(f333(f333(f335(f916(f911(x98061),f911(x98061))),f333(f333(f265(f911(x98061),f911(x98061)),x98065),x98066)),f153(x98061,x98064)))+P106(f333(f333(f335(f916(x98061,x98061)),f333(f333(f265(x98061,x98061),x98062),x98063)),x98064)) % 173.51/173.28 [9807]~P106(f333(f333(f335(f916(f911(x98071),f911(x98071))),f333(f333(f265(f911(x98071),f911(x98071)),f333(f333(f159(x98071),x98072),x98075)),f333(f333(f159(x98071),x98073),x98076))),f155(x98071,x98074)))+P106(f333(f333(f335(f916(f911(x98071),f911(x98071))),f333(f333(f265(f911(x98071),f911(x98071)),x98075),x98076)),f155(x98071,x98074)))+P106(f333(f333(f335(f916(x98071,x98071)),f333(f333(f265(x98071,x98071),x98072),x98073)),x98074)) % 173.51/173.28 [9808]~P106(f333(f333(f335(f916(f911(x98081),f911(x98081))),f333(f333(f265(f911(x98081),f911(x98081)),f333(f333(f159(x98081),x98082),x98085)),f333(f333(f159(x98081),x98083),x98086))),f165(x98081,x98084)))+P106(f333(f333(f335(f916(f911(x98081),f911(x98081))),f333(f333(f265(f911(x98081),f911(x98081)),x98085),x98086)),f165(x98081,x98084)))+P106(f333(f333(f335(f916(x98081,x98081)),f333(f333(f265(x98081,x98081),x98082),x98083)),x98084)) % 173.51/173.28 [9895]P106(f333(x98951,x98952))+P106(f333(f333(f335(x98953),f484(x98951,x98954,x98955,x98953,x98956)),x98955))+~P106(f333(f333(f335(x98956),x98952),f333(f333(f45(x98953,f917(x98956,a905)),x98955),x98954))) % 173.51/173.28 [9907]~E(x99072,x99074)+P106(f333(f333(f335(f916(f911(x99071),f911(x99071))),f333(f333(f265(f911(x99071),f911(x99071)),f333(f333(f142(x99071),x99072),f333(f333(f159(x99071),x99073),f124(x99071)))),f333(f333(f142(x99071),x99074),f333(f333(f159(x99071),x99075),f124(x99071))))),f165(x99071,x99076)))+~P106(f333(f333(f335(f916(x99071,x99071)),f333(f333(f265(x99071,x99071),x99073),x99075)),x99076)) % 173.51/173.28 [9982]E(x99821,x99822)+~P106(f333(f333(f335(f916(f911(x99823),f911(x99823))),f333(f333(f265(f911(x99823),f911(x99823)),f333(f333(f142(x99823),x99825),f333(f333(f159(x99823),x99821),f124(x99823)))),f333(f333(f142(x99823),x99826),f333(f333(f159(x99823),x99822),f124(x99823))))),f165(x99823,x99824)))+P106(f333(f333(f335(f916(x99823,x99823)),f333(f333(f265(x99823,x99823),x99821),x99822)),x99824)) % 173.51/173.28 [10011]~P106(f333(f333(f335(f916(f911(x100111),f911(x100111))),f333(f333(f265(f911(x100111),f911(x100111)),f333(f333(f142(x100111),x100115),f333(f333(f159(x100111),x100112),f124(x100111)))),f333(f333(f142(x100111),x100116),f333(f333(f159(x100111),x100113),f124(x100111))))),f165(x100111,x100114)))+P106(f333(f333(f335(f916(f911(x100111),f911(x100111))),f333(f333(f265(f911(x100111),f911(x100111)),x100115),x100116)),f165(x100111,x100114)))+P106(f333(f333(f335(f916(x100111,x100111)),f333(f333(f265(x100111,x100111),x100112),x100113)),x100114)) % 173.51/173.28 [10030]P106(f333(x100301,x100302))+P106(f333(f333(f335(x100303),f483(x100301,x100304,x100305,x100306,x100303)),f333(x100304,f484(x100301,x100304,x100305,x100306,x100303))))+~P106(f333(f333(f335(x100303),x100302),f333(f333(f45(x100306,f917(x100303,a905)),x100305),x100304))) % 173.51/173.28 [8999]~P18(x89993,x89994,x89991)+~P106(f333(f67(x89993),x89996))+E(f333(f333(x89991,x89992),f333(f333(f70(x89993,x89994,x89991),x89995),f333(f333(f23(f917(x89993,a905)),x89996),f333(f333(f315(x89993),x89992),f196(f917(x89993,a905)))))),f333(f333(f70(x89993,x89994,x89991),x89995),f333(f333(f315(x89993),x89992),x89996))) % 173.51/173.28 [9313]~P106(f333(f333(f335(x93135),x93133),x93136))+P106(f333(f333(f246(f917(x93131,a905)),f333(x93132,x93133)),x93134))+~P106(f333(f333(f246(f917(x93131,a905)),f333(f333(f45(x93135,f917(x93131,a905)),x93136),x93132)),x93134)) % 173.51/173.28 [9956]~P11(x99561,x99565,x99564)+P106(f333(f333(f335(f916(x99561,x99561)),f333(f333(f265(x99561,x99561),x99562),x99563)),x99564))+~P106(f333(f333(f335(x99561),x99566),f333(f333(f112(f917(x99561,a905)),f333(f292(x99561,x99561,x99564),f333(f333(f315(x99561),x99562),f196(f917(x99561,a905))))),f333(f292(x99561,x99561,x99564),f333(f333(f315(x99561),x99563),f196(f917(x99561,a905))))))) % 173.51/173.28 [8721]~P113(x87212)+~E(f333(f333(f87(x87212),f333(f333(f88(x87212),x87214),x87215)),x87211),f333(f333(f87(x87212),f333(f333(f88(x87212),x87213),x87215)),x87216))+E(x87211,f333(f333(f87(x87212),f333(f333(f88(x87212),f333(f333(f23(x87212),x87213),x87214)),x87215)),x87216)) % 173.51/173.28 [8722]~P113(x87221)+~E(f333(f333(f87(x87221),f333(f333(f88(x87221),x87222),x87224)),x87225),f333(f333(f87(x87221),f333(f333(f88(x87221),x87223),x87224)),x87226))+E(f333(f333(f87(x87221),f333(f333(f88(x87221),f333(f333(f23(x87221),x87222),x87223)),x87224)),x87225),x87226) % 173.51/173.28 [8904]~P113(x89041)+E(f333(f333(f87(x89041),f333(f333(f88(x89041),x89042),x89043)),x89044),f333(f333(f87(x89041),f333(f333(f88(x89041),x89045),x89043)),x89046))+~E(x89046,f333(f333(f87(x89041),f333(f333(f88(x89041),f333(f333(f23(x89041),x89042),x89045)),x89043)),x89044)) % 173.51/173.28 [8905]~P113(x89051)+E(f333(f333(f87(x89051),f333(f333(f88(x89051),x89052),x89053)),x89054),f333(f333(f87(x89051),f333(f333(f88(x89051),x89055),x89053)),x89056))+~E(f333(f333(f87(x89051),f333(f333(f88(x89051),f333(f333(f23(x89051),x89052),x89055)),x89053)),x89054),x89056) % 173.51/173.28 [9250]~P106(f333(f333(x92504,x92505),x92506))+~P106(f333(f333(x92503,x92505),x92506))+P106(f333(f333(f333(f333(f112(f917(x92501,f917(x92502,a905))),x92503),x92504),x92505),x92506)) % 173.51/173.28 [9517]P106(f333(f333(x95171,x95172),x95173))+P106(f333(f333(x95174,x95172),x95173))+~P106(f333(f333(f333(f333(f121(f917(x95175,f917(x95176,a905))),x95174),x95171),x95172),x95173)) % 173.51/173.28 [9821]~P135(x98211)+~P106(f333(f333(f246(x98211),f333(f333(f87(x98211),f333(f333(f88(x98211),x98214),x98215)),x98212)),f333(f333(f87(x98211),f333(f333(f88(x98211),x98213),x98215)),x98216)))+P106(f333(f333(f246(x98211),x98212),f333(f333(f87(x98211),f333(f333(f88(x98211),f333(f333(f23(x98211),x98213),x98214)),x98215)),x98216))) % 173.51/173.28 [9822]~P135(x98221)+~P106(f333(f333(f247(x98221),f333(f333(f87(x98221),f333(f333(f88(x98221),x98224),x98225)),x98222)),f333(f333(f87(x98221),f333(f333(f88(x98221),x98223),x98225)),x98226)))+P106(f333(f333(f247(x98221),x98222),f333(f333(f87(x98221),f333(f333(f88(x98221),f333(f333(f23(x98221),x98223),x98224)),x98225)),x98226))) % 173.51/173.28 [9845]~P135(x98451)+P106(f333(f333(f246(x98451),f333(f333(f87(x98451),f333(f333(f88(x98451),x98452),x98453)),x98454)),f333(f333(f87(x98451),f333(f333(f88(x98451),x98455),x98453)),x98456)))+~P106(f333(f333(f246(x98451),x98454),f333(f333(f87(x98451),f333(f333(f88(x98451),f333(f333(f23(x98451),x98455),x98452)),x98453)),x98456))) % 173.51/173.28 [9846]~P135(x98461)+P106(f333(f333(f247(x98461),f333(f333(f87(x98461),f333(f333(f88(x98461),x98462),x98463)),x98464)),f333(f333(f87(x98461),f333(f333(f88(x98461),x98465),x98463)),x98466)))+~P106(f333(f333(f247(x98461),x98464),f333(f333(f87(x98461),f333(f333(f88(x98461),f333(f333(f23(x98461),x98465),x98462)),x98463)),x98466))) % 173.51/173.28 [9948]~P135(x99481)+~P106(f333(f333(f246(x99481),f333(f333(f87(x99481),f333(f333(f88(x99481),x99482),x99484)),x99485)),f333(f333(f87(x99481),f333(f333(f88(x99481),x99483),x99484)),x99486)))+P106(f333(f333(f246(x99481),f333(f333(f87(x99481),f333(f333(f88(x99481),f333(f333(f23(x99481),x99482),x99483)),x99484)),x99485)),x99486)) % 173.51/173.28 [9949]~P135(x99491)+~P106(f333(f333(f247(x99491),f333(f333(f87(x99491),f333(f333(f88(x99491),x99492),x99494)),x99495)),f333(f333(f87(x99491),f333(f333(f88(x99491),x99493),x99494)),x99496)))+P106(f333(f333(f247(x99491),f333(f333(f87(x99491),f333(f333(f88(x99491),f333(f333(f23(x99491),x99492),x99493)),x99494)),x99495)),x99496)) % 173.51/173.28 [9994]~P135(x99941)+P106(f333(f333(f246(x99941),f333(f333(f87(x99941),f333(f333(f88(x99941),x99942),x99943)),x99944)),f333(f333(f87(x99941),f333(f333(f88(x99941),x99945),x99943)),x99946)))+~P106(f333(f333(f246(x99941),f333(f333(f87(x99941),f333(f333(f88(x99941),f333(f333(f23(x99941),x99942),x99945)),x99943)),x99944)),x99946)) % 173.51/173.28 [9995]~P135(x99951)+P106(f333(f333(f247(x99951),f333(f333(f87(x99951),f333(f333(f88(x99951),x99952),x99953)),x99954)),f333(f333(f87(x99951),f333(f333(f88(x99951),x99955),x99953)),x99956)))+~P106(f333(f333(f247(x99951),f333(f333(f87(x99951),f333(f333(f88(x99951),f333(f333(f23(x99951),x99952),x99955)),x99953)),x99954)),x99956)) % 173.51/173.28 [10166]~P72(x101662)+~P106(f333(f67(x101661),x101666))+E(f333(f333(f6(x101661,x101662),f333(f333(f18(x101661,x101662,x101662),f333(f333(f18(x101661,x101662,f917(x101662,x101662)),f333(f333(f8(a905,f917(x101662,f917(x101662,x101662)),x101661),f107(x101662)),x101663)),x101664)),x101665)),x101666),f333(f333(f87(x101662),f333(f333(f6(x101661,x101662),x101664),f333(f333(f112(f917(x101661,a905)),x101666),f333(f252(x101661),x101663)))),f333(f333(f6(x101661,x101662),x101665),f333(f333(f112(f917(x101661,a905)),x101666),f333(f86(f917(x101661,a905)),f333(f252(x101661),x101663)))))) % 173.51/173.28 [10226]P106(f333(f333(f335(x102262),x102264),x102266))+P106(f333(f333(f335(x102262),x102265),x102266))+E(f333(f317(x102261,x102262,f333(f333(f7(x102261,x102262,x102262),f333(f333(f7(x102261,x102262,f917(x102262,x102262)),f333(f333(f8(a905,f917(x102262,f917(x102262,x102262)),x102261),f107(x102262)),f333(f333(f7(x102261,f917(x102261,a905),a905),f335(x102261)),x102263))),x102264)),x102265)),x102266),f196(f917(x102261,a905))) % 173.51/173.28 [10227]P106(f333(f333(f335(x102272),x102275),x102276))+~P106(f333(f333(f335(x102272),x102274),x102276))+E(f333(f317(x102271,x102272,f333(f333(f7(x102271,x102272,x102272),f333(f333(f7(x102271,x102272,f917(x102272,x102272)),f333(f333(f8(a905,f917(x102272,f917(x102272,x102272)),x102271),f107(x102272)),f333(f333(f7(x102271,f917(x102271,a905),a905),f335(x102271)),x102273))),x102274)),x102275)),x102276),x102273) % 173.51/173.28 [10228]P106(f333(f333(f335(x102282),x102284),x102286))+~P106(f333(f333(f335(x102282),x102285),x102286))+E(f333(f317(x102281,x102282,f333(f333(f7(x102281,x102282,x102282),f333(f333(f7(x102281,x102282,f917(x102282,x102282)),f333(f333(f8(a905,f917(x102282,f917(x102282,x102282)),x102281),f107(x102282)),f333(f333(f7(x102281,f917(x102281,a905),a905),f335(x102281)),x102283))),x102284)),x102285)),x102286),f333(f86(f917(x102281,a905)),x102283)) % 173.51/173.28 [10229]~P106(f333(f333(f335(x102292),x102294),x102296))+~P106(f333(f333(f335(x102292),x102295),x102296))+E(f333(f317(x102291,x102292,f333(f333(f7(x102291,x102292,x102292),f333(f333(f7(x102291,x102292,f917(x102292,x102292)),f333(f333(f8(a905,f917(x102292,f917(x102292,x102292)),x102291),f107(x102292)),f333(f333(f7(x102291,f917(x102291,a905),a905),f335(x102291)),x102293))),x102294)),x102295)),x102296),f254(f917(x102291,a905))) % 173.51/173.28 [8754]E(x87541,x87542)+~P60(x87544,x87545,x87543,x87546,x87547)+~E(f333(x87543,x87541),f333(x87543,x87542)) % 173.51/173.28 [8785]~P13(x87856,x87855,x87857,x87854,x87851)+E(f333(f333(x87851,x87852),x87853),x87854)+P106(f333(f67(x87855),x87853)) % 173.51/173.28 [9678]P45(x96781,x96782,x96783,x96784,x96785,f333(f333(x96783,x96786),x96787))+~E(f333(f333(x96783,x96786),x96787),x96784)+~E(x96785,f196(f917(x96781,a905))) % 173.51/173.28 [9867]~P106(f333(x98676,x98673))+~P106(f333(f333(f335(f916(x98672,x98672)),f333(f333(f265(x98672,x98672),x98674),x98675)),f333(x98677,x98673)))+P106(f333(f333(f335(f916(f916(x98671,x98672),f916(x98671,x98672))),f333(f333(f265(f916(x98671,x98672),f916(x98671,x98672)),f333(f333(f265(x98671,x98672),x98673),x98674)),f333(f333(f265(x98671,x98672),x98673),x98675))),f287(x98671,x98672,x98676,x98677))) % 173.51/173.28 [10286]~P45(x102862,x102867,x102863,x102866,x102861,f333(f333(x102863,x102865),x102864))+E(f333(f333(x102863,f875(x102864,x102865,x102861,x102866,x102863,x102867,x102862)),f876(x102864,x102865,x102861,x102866,x102863,x102867,x102862)),f333(f333(x102863,x102865),x102864))+E(x102861,f196(f917(x102862,a905))) % 173.51/173.28 [10287]~P45(x102877,x102876,x102871,x102874,x102875,f333(f333(x102871,x102872),x102873))+E(f333(f333(x102871,f875(x102873,x102872,x102875,x102874,x102871,x102876,x102877)),f876(x102873,x102872,x102875,x102874,x102871,x102876,x102877)),f333(f333(x102871,x102872),x102873))+E(f333(f333(x102871,x102872),x102873),x102874) % 173.51/173.28 [9347]~P37(x93471,x93472,x93473,x93475,x93477)+P37(x93471,x93472,x93473,f333(f333(f159(x93471),x93474),x93475),f333(f333(f159(x93472),x93476),x93477))+~P106(f333(f333(x93473,x93474),x93476)) % 173.51/173.28 [9363]P37(x93631,x93632,x93633,x93634,x93635)+~P37(x93631,x93632,x93633,f333(f333(f142(x93631),x93636),x93634),f333(f333(f142(x93632),x93637),x93635))+~E(f333(f197(f911(x93631)),x93636),f333(f197(f911(x93632)),x93637)) % 173.51/173.28 [9364]P37(x93641,x93642,x93643,x93644,x93645)+~P37(x93641,x93642,x93643,f333(f333(f142(x93641),x93644),x93646),f333(f333(f142(x93642),x93645),x93647))+~E(f333(f197(f911(x93641)),x93644),f333(f197(f911(x93642)),x93645)) % 173.51/173.28 [9582]~P37(x95821,x95822,x95823,x95825,x95827)+~P37(x95821,x95822,x95823,x95824,x95826)+P37(x95821,x95822,x95823,f333(f333(f142(x95821),x95824),x95825),f333(f333(f142(x95822),x95826),x95827)) % 173.51/173.28 [9941]~P106(f333(f72(x99411,x99414,x99415,x99416,x99413),x99417))+P106(f333(f72(x99411,x99414,x99415,x99416,f333(f333(f315(x99411),x99412),x99413)),f333(f333(x99415,x99412),x99417)))+P106(f333(f333(f335(x99411),x99412),x99413)) % 173.51/173.28 [10310]~P45(x103102,x103107,x103106,x103105,x103101,f333(f333(x103106,x103104),x103103))+E(x103101,f196(f917(x103102,a905)))+P106(f333(f333(f335(x103102),f875(x103103,x103104,x103101,x103105,x103106,x103107,x103102)),x103101)) % 173.51/173.28 [10311]~P45(x103115,x103117,x103111,x103114,x103116,f333(f333(x103111,x103112),x103113))+E(f333(f333(x103111,x103112),x103113),x103114)+P106(f333(f333(f335(x103115),f875(x103113,x103112,x103116,x103114,x103111,x103117,x103115)),x103116)) % 173.51/173.28 [9025]~P23(x90254,x90255,x90256,x90257,x90251)+~P106(f333(f67(x90255),x90253))+E(f333(f333(x90251,x90252),x90253),f333(f333(f333(f71(x90254,x90255,x90256),x90252),x90257),x90253)) % 173.51/173.28 [9026]~P13(x90264,x90265,x90266,x90267,x90261)+~P106(f333(f67(x90265),x90263))+E(f333(f333(x90261,x90262),x90263),f333(f333(f333(f71(x90264,x90265,x90266),x90262),x90267),x90263)) % 173.51/173.28 [9641]~P26(x96411,x96412,f333(f333(f315(f909(x96411)),f333(f333(f333(f98(x96411),x96413),x96414),x96417)),f196(f917(f909(x96411),a905))))+P26(x96411,x96412,f333(f333(f315(f909(x96411)),f333(f333(f333(f98(x96411),x96413),f31(x96414,x96415)),x96416)),f196(f917(f909(x96411),a905))))+~P26(x96411,x96412,f333(f333(f315(f909(x96411)),f333(f333(f333(f98(x96411),x96417),x96415),x96416)),f196(f917(f909(x96411),a905)))) % 173.51/173.28 [9840]~P25(x98403,x98404,x98405,x98407,x98406,x98401)+~P106(f333(f67(x98404),x98402))+E(f333(x98401,x98402),f333(f333(f333(f71(x98403,x98404,x98405),x98406),x98407),x98402)) % 173.51/173.28 [9989]P45(x99891,x99892,x99893,x99894,x99895,f333(f333(x99893,x99896),x99897))+~P45(x99891,x99892,x99893,x99894,f333(f333(f23(f917(x99891,a905)),x99895),f333(f333(f315(x99891),x99896),f196(f917(x99891,a905)))),x99897)+~P106(f333(f333(f335(x99891),x99896),x99895)) % 173.51/173.28 [10258]~P26(x102581,x102582,f333(f333(f315(f909(x102581)),f333(f333(f333(f98(x102581),f103(x102581,x102583,x102584)),x102585),x102587)),f196(f917(f909(x102581),a905))))+P26(x102581,x102582,f333(f333(f315(f909(x102581)),f333(f333(f333(f98(x102581),x102583),f28(x102584,x102585,x102586)),x102587)),f196(f917(f909(x102581),a905))))+~P26(x102581,x102582,f333(f333(f315(f909(x102581)),f333(f333(f333(f98(x102581),f103(x102581,x102583,f333(f79(a905,a905,a906,a328),x102584))),x102586),x102587)),f196(f917(f909(x102581),a905)))) % 173.51/173.28 [10333]P106(f333(f333(x103337,f834(x103334,x103335,x103331,x103336,x103333,x103332,x103337)),f835(x103334,x103335,x103331,x103336,x103333,x103332,x103337)))+~P106(f333(f333(x103337,f333(f268(x103332,x103333),x103336)),f333(f264(x103332,x103333),x103336)))+P106(f333(x103331,f333(f333(f269(x103332,x103333,x103334),x103335),x103336))) % 173.51/173.28 [10334]P26(x103347,x103346,f333(f333(f315(f909(x103347)),f333(f333(f333(f98(x103347),x103341),x103344),x103342)),f196(f917(f909(x103347),a905))))+~P26(x103347,x103346,f333(f333(f315(f909(x103347)),f333(f333(f333(f98(x103347),x103345),x103344),x103343)),f196(f917(f909(x103347),a905))))+P106(f333(f333(x103341,f896(x103342,x103341,x103343,x103344,x103345,x103346,x103347)),f904(x103342,x103341,x103343,x103344,x103345,x103346,x103347))) % 173.51/173.28 [10344]~P45(x103442,x103443,x103444,x103445,x103441,f333(f333(x103444,x103447),x103446))+P45(x103442,x103443,x103444,x103445,f333(f333(f23(f917(x103442,a905)),x103441),f333(f333(f315(x103442),f875(x103446,x103447,x103441,x103445,x103444,x103443,x103442)),f196(f917(x103442,a905)))),f876(x103446,x103447,x103441,x103445,x103444,x103443,x103442))+E(x103441,f196(f917(x103442,a905))) % 173.51/173.28 [10345]~P45(x103455,x103456,x103451,x103454,x103457,f333(f333(x103451,x103452),x103453))+P45(x103455,x103456,x103451,x103454,f333(f333(f23(f917(x103455,a905)),x103457),f333(f333(f315(x103455),f875(x103453,x103452,x103457,x103454,x103451,x103456,x103455)),f196(f917(x103455,a905)))),f876(x103453,x103452,x103457,x103454,x103451,x103456,x103455))+E(f333(f333(x103451,x103452),x103453),x103454) % 173.51/173.28 [10346]~P26(x103461,x103462,f333(f333(f315(f909(x103461)),f333(f333(f333(f98(x103461),x103467),x103464),x103466)),f196(f917(f909(x103461),a905))))+P26(x103461,x103462,f333(f333(f315(f909(x103461)),f333(f333(f333(f98(x103461),x103463),x103464),x103465)),f196(f917(f909(x103461),a905))))+~P106(f333(f333(x103465,f896(x103465,x103463,x103466,x103464,x103467,x103462,x103461)),f352(x103465,x103463,x103466,x103464,x103467,x103462,x103461))) % 173.51/173.28 [10367]~P106(f333(x103671,f333(f333(x103675,f835(x103674,x103675,x103671,x103676,x103673,x103672,x103677)),f834(x103674,x103675,x103671,x103676,x103673,x103672,x103677))))+~P106(f333(f333(x103677,f333(f268(x103672,x103673),x103676)),f333(f264(x103672,x103673),x103676)))+P106(f333(x103671,f333(f333(f269(x103672,x103673,x103674),x103675),x103676))) % 173.51/173.28 [9662]P106(f333(f333(f246(f917(f916(x96621,x96622),a905)),f333(f333(f295(x96621,x96623,x96622),x96624),x96625)),f333(f333(f295(x96621,x96623,x96622),x96626),x96627)))+~P106(f333(f333(f246(f917(f916(x96623,x96622),a905)),x96625),x96627))+~P106(f333(f333(f246(f917(f916(x96621,x96623),a905)),x96624),x96626)) % 173.51/173.28 [9704]~E(f333(f333(f333(a205,x97046),f34(x97041)),f206(x97044,x97041)),f333(f333(f333(a205,x97047),f34(x97041)),f206(x97044,x97041)))+P106(f333(f333(f333(f333(a204,f27(x97041,x97042,x97043)),x97044),x97045),f333(f333(f333(a205,x97046),f34(x97041)),f206(x97044,x97041))))+~P106(f333(f333(f333(f333(a204,x97043),f333(f333(f333(a205,x97044),f34(x97041)),f333(x97042,x97044))),x97045),x97047)) % 173.51/173.28 [10000]~P106(f333(f333(f335(x100001),x100006),x100005))+P106(f333(f72(x100001,x100002,x100003,x100004,x100005),f333(f333(x100003,x100006),x100007)))+~P106(f333(f72(x100001,x100002,x100003,x100004,f333(f333(f23(f917(x100001,a905)),x100005),f333(f333(f315(x100001),x100006),f196(f917(x100001,a905))))),x100007)) % 173.51/173.28 [10402]~P143(x104021)+~P27(f916(x104022,x104023),x104021,f333(f269(x104022,x104023,x104021),f333(f333(f7(x104022,f917(x104023,x104021),f917(x104023,x104021)),f333(f333(f8(f917(x104021,x104021),f917(f917(x104023,x104021),f917(x104023,x104021)),x104022),f8(x104021,x104021,x104023)),f333(f333(f8(x104021,f917(x104021,x104021),x104022),f88(x104021)),x104024))),x104025)),f333(f333(f267(x104022,x104023),x104026),f333(f16(f917(x104023,a905),x104022),x104027)))+E(f333(f333(f6(x104021,x104021),f33(x104021)),f333(f252(x104021),f333(f333(f8(f917(x104022,a905),a905,x104021),f94(x104022)),f333(f333(f8(f917(x104022,f917(x104023,a905)),f917(x104022,a905),x104021),f333(f8(f917(x104023,a905),a905,x104022),f94(x104023))),f333(f333(f7(x104021,f917(x104022,f917(x104023,a905)),f917(x104022,f917(x104023,a905))),f333(f333(f8(f917(x104022,f917(f917(x104023,a905),f917(x104023,a905))),f917(f917(x104022,f917(x104023,a905)),f917(x104022,f917(x104023,a905))),x104021),f18(x104022,f917(x104023,a905),f917(x104023,a905))),f333(f333(f8(f917(x104022,f917(x104023,f917(a905,a905))),f917(x104022,f917(f917(x104023,a905),f917(x104023,a905))),x104021),f333(f8(f917(x104023,f917(a905,a905)),f917(f917(x104023,a905),f917(x104023,a905)),x104022),f18(x104023,a905,a905))),f333(f333(f8(f917(x104022,f917(x104023,a905)),f917(x104022,f917(x104023,f917(a905,a905))),x104021),f333(f8(f917(x104023,a905),f917(x104023,f917(a905,a905)),x104022),f333(f8(a905,f917(a905,a905),x104023),a331))),f333(f333(f7(x104021,f917(x104022,f917(x104023,x104021)),f917(x104022,f917(x104023,a905))),f333(f333(f8(f917(f917(x104023,x104021),f917(x104023,a905)),f917(f917(x104022,f917(x104023,x104021)),f917(x104022,f917(x104023,a905))),x104021),f8(f917(x104023,x104021),f917(x104023,a905),x104022)),f333(f333(f8(f917(x104021,a905),f917(f917(x104023,x104021),f917(x104023,a905)),x104021),f8(x104021,a905,x104023)),a330))),f333(f333(f7(x104022,f917(x104023,x104021),f917(x104023,x104021)),f333(f333(f8(f917(x104021,x104021),f917(f917(x104023,x104021),f917(x104023,x104021)),x104022),f8(x104021,x104021,x104023)),f333(f333(f8(x104021,f917(x104021,x104021),x104022),f88(x104021)),x104024))),x104025)))))),f333(f333(f7(x104022,f917(x104023,a905),f917(x104023,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x104023,a905),f917(x104023,a905)),x104022),f8(a905,a905,x104023)),f333(f333(f8(a905,f917(a905,a905),x104022),a331),f333(f333(f7(x104022,f917(x104022,a905),a905),f335(x104022)),x104026)))),f333(f333(f7(x104023,f917(x104023,a905),a905),f335(x104023)),x104027))))))),f333(f333(f88(x104021),f333(f333(f6(x104022,x104021),x104024),x104026)),f333(f333(f6(x104023,x104021),x104025),x104027))) % 173.51/173.28 [9666]~P28(x96661,x96663,x96665,x96666,x96668)+~P28(x96663,x96662,x96664,x96668,x96667)+P28(x96661,x96662,f333(f79(x96663,x96662,x96661,x96664),x96665),x96666,x96667) % 173.51/173.28 [9703]P28(x97031,x97032,x97033,x97034,x97035)+~P28(x97036,x97031,x97037,x97038,x97034)+~P28(x97036,x97032,f333(f79(x97031,x97032,x97036,x97033),x97037),x97038,x97035) % 173.51/173.28 [9838]~P106(f333(f333(x98384,x98386),x98388))+~P106(f333(f333(x98385,x98388),x98387))+P106(f333(f333(f266(x98381,x98382,x98383,x98384,x98385),x98386),x98387)) % 173.51/173.28 [9419]~P21(x94198,x94191,x94193,x94195)+~P106(f333(f67(x94198),x94196))+E(f333(f79(x94191,x94191,x94192,f333(x94193,x94194)),f333(f79(x94191,x94191,x94192,f333(x94195,x94196)),x94197)),f333(f79(x94191,x94191,x94192,f333(x94195,x94196)),f333(f79(x94191,x94191,x94192,f333(x94193,x94194)),x94197))) % 173.51/173.28 [9828]~P24(x98287,x98282,x98285,x98288,x98286,x98281)+~P106(f333(f67(x98282),x98284))+E(f333(x98281,f333(f333(f315(x98282),x98283),x98284)),f333(f333(x98285,f333(x98286,x98283)),f333(x98281,x98284))) % 173.51/173.28 [9946]~P27(x99462,x99464,x99466,x99468)+~P27(x99461,x99463,x99465,x99467)+P27(f916(x99461,x99462),f916(x99463,x99464),f270(x99461,x99463,x99462,x99464,x99465,x99466),f333(f333(f267(x99461,x99462),x99467),f333(f16(f917(x99462,a905),x99461),x99468))) % 173.51/173.28 [9608]P106(f333(f333(f335(f916(x96081,x96082)),f333(f333(f265(x96081,x96082),x96083),x96084)),f333(f333(f295(x96081,x96085,x96082),x96086),x96087)))+~P106(f333(f333(f335(f916(x96081,x96085)),f333(f333(f265(x96081,x96085),x96083),x96088)),x96086))+~P106(f333(f333(f335(f916(x96085,x96082)),f333(f333(f265(x96085,x96082),x96088),x96084)),x96087)) % 173.51/173.28 [9809]~P106(f333(f333(f246(f917(f916(x98093,x98092),a905)),x98095),f333(f333(f267(x98093,x98092),x98098),f333(f16(f917(x98092,a905),x98093),x98097))))+~P106(f333(f333(f246(f917(f916(x98091,x98093),a905)),x98094),f333(f333(f267(x98091,x98093),x98096),f333(f16(f917(x98093,a905),x98091),x98098))))+P106(f333(f333(f246(f917(f916(x98091,x98092),a905)),f333(f333(f295(x98091,x98093,x98092),x98094),x98095)),f333(f333(f267(x98091,x98092),x98096),f333(f16(f917(x98092,a905),x98091),x98097)))) % 173.51/173.28 [9862]~E(x98623,x98625)+P106(f333(f333(f335(f916(f916(x98621,x98622),f916(x98621,x98622))),f333(f333(f265(f916(x98621,x98622),f916(x98621,x98622)),f333(f333(f265(x98621,x98622),x98623),x98624)),f333(f333(f265(x98621,x98622),x98625),x98626))),f325(x98621,x98622,x98627,x98628)))+~P106(f333(f333(f335(f916(x98622,x98622)),f333(f333(f265(x98622,x98622),x98624),x98626)),x98628)) % 173.51/173.28 [9965]E(x99651,x99652)+~P106(f333(f333(f335(f916(f916(x99653,x99655),f916(x99653,x99655))),f333(f333(f265(f916(x99653,x99655),f916(x99653,x99655)),f333(f333(f265(x99653,x99655),x99651),x99656)),f333(f333(f265(x99653,x99655),x99652),x99657))),f325(x99653,x99655,x99654,x99658)))+P106(f333(f333(f335(f916(x99653,x99653)),f333(f333(f265(x99653,x99653),x99651),x99652)),x99654)) % 173.51/173.28 [9981]~P106(f333(f333(f335(f916(f916(x99811,x99815),f916(x99811,x99815))),f333(f333(f265(f916(x99811,x99815),f916(x99811,x99815)),f333(f333(f265(x99811,x99815),x99812),x99816)),f333(f333(f265(x99811,x99815),x99813),x99817))),f325(x99811,x99815,x99814,x99818)))+P106(f333(f333(f335(f916(x99811,x99811)),f333(f333(f265(x99811,x99811),x99812),x99813)),x99814))+P106(f333(f333(f335(f916(x99815,x99815)),f333(f333(f265(x99815,x99815),x99816),x99817)),x99818)) % 173.51/173.28 [9896]~P25(x98967,x98965,x98961,x98968,x98962,x98964)+~P106(f333(f67(x98965),x98966))+E(f333(f333(x98961,f333(x98962,x98963)),f333(x98964,f333(f333(f23(f917(x98965,a905)),x98966),f333(f333(f315(x98965),x98963),f196(f917(x98965,a905)))))),f333(x98964,f333(f333(f315(x98965),x98963),x98966))) % 173.51/173.28 [9370]~P106(f333(f333(f333(x93705,x93708),x93706),x93707))+~P106(f333(f333(f335(x93701),x93708),x93704))+P106(f333(f333(f333(f333(f45(x93701,f917(x93702,f917(x93703,a905))),x93704),x93705),x93706),x93707)) % 173.51/173.28 [9593]P106(f333(f333(f333(x95931,x95932),x95933),x95934))+~P106(f333(f333(f335(x95935),x95932),x95936))+~P106(f333(f333(f333(f333(f46(x95935,f917(x95937,f917(x95938,a905))),x95936),x95931),x95933),x95934)) % 173.51/173.28 [9802]~P23(x98023,x98022,x98024,x98028,x98021)+~P106(f333(f67(x98022),x98027))+E(f333(f333(x98021,f333(f333(f18(x98022,x98023,x98023),f333(f333(f8(x98023,f917(x98023,x98023),x98022),x98024),x98025)),x98026)),x98027),f333(f333(x98024,f333(f333(x98021,x98025),x98027)),f333(f333(x98021,x98026),x98027))) % 173.51/173.28 [10070]~E(f333(f316(x100702,x100704,x100706),x100708),x1007010)+~E(f333(f316(x100701,x100703,x100705),x100707),x100709)+E(f333(f316(f916(x100701,x100702),f916(x100703,x100704),f270(x100701,x100703,x100702,x100704,x100705,x100706)),f333(f333(f267(x100701,x100702),x100707),f333(f16(f917(x100702,a905),x100701),x100708))),f333(f333(f267(x100703,x100704),x100709),f333(f16(f917(x100704,a905),x100703),x1007010))) % 173.51/173.28 [5026]~P46(x50261,x50262)+~P53(x50261,x50262)+~P54(x50261,x50262)+P10(x50261,x50262) % 173.51/173.28 [4982]~P110(x49822)+~P16(x49822,x49821)+P16(x49822,f125(x49822,x49821))+E(x49821,f124(x49822)) % 173.51/173.28 [4983]~P110(x49832)+~P16(x49832,x49831)+P16(x49832,f754(x49831,x49832))+E(x49831,f124(x49832)) % 173.51/173.28 [5222]~P8(x52222)+E(f10(x52222,x52221),f44(x52222,x52221))+E(x52221,f196(f917(x52222,a905)))+~P106(f333(f67(x52222),x52221)) % 173.51/173.28 [5223]~P8(x52232)+E(f13(x52232,x52231),f43(x52232,x52231))+E(x52231,f196(f917(x52232,a905)))+~P106(f333(f67(x52232),x52231)) % 173.51/173.28 [5380]~P110(x53802)+~P16(x53802,x53801)+E(x53801,f124(x53802))+E(f333(f333(f159(x53802),f773(x53801,x53802)),f754(x53801,x53802)),x53801) % 173.51/173.28 [6169]~P2(x61692)+E(x61691,f196(f917(x61692,a905)))+P106(f333(f333(f246(x61692),f10(x61692,x61691)),f13(x61692,x61691)))+~P106(f333(f67(x61692),x61691)) % 173.51/173.28 [6181]~P43(x61812)+~P43(x61811)+E(x61811,x61812)+~E(f333(f316(a1,a910,a115),x61811),f333(f316(a1,a910,a115),x61812)) % 173.51/173.28 [9228]~P120(x92281)+~P106(f333(f333(f335(x92281),x92282),f120(x92281)))+P106(f333(f333(f247(x92281),f333(f333(f87(x92281),f333(f333(f87(x92281),f85(x92281)),x92282)),x92282)),f2(x92281)))+~P106(f333(f333(f247(x92281),x92282),f2(x92281))) % 173.51/173.28 [9477]~P120(x94771)+~P106(f333(f333(f335(x94771),x94772),f120(x94771)))+~P106(f333(f333(f247(x94771),f333(f333(f87(x94771),f333(f333(f87(x94771),f85(x94771)),x94772)),x94772)),f2(x94771)))+P106(f333(f333(f247(x94771),x94772),f2(x94771))) % 173.51/173.28 [5041]~P143(x50412)+~P115(x50412)+E(x50411,f2(a910))+E(f333(f333(f256(x50412),f2(x50412)),x50411),f2(x50412)) % 173.51/173.28 [5044]~P143(x50441)+~P115(x50441)+~E(x50442,f2(a910))+E(f333(f333(f256(x50441),f2(x50441)),x50442),f85(x50441)) % 173.51/173.28 [5208]~P141(x52082)+E(x52081,f85(x52082))+E(x52081,f333(f86(x52082),f85(x52082)))+~E(f333(f333(f88(x52082),x52081),x52081),f85(x52082)) % 173.51/173.28 [5460]~P91(x54602)+E(x54601,f2(x54602))+E(f89(x54602,x54601),f333(f86(x54602),f85(x54602)))+P106(f333(f333(f247(x54602),f2(x54602)),x54601)) % 173.51/173.28 [5691]~P91(x56912)+E(f89(x56912,x56911),f85(x56912))+E(x56911,f2(x56912))+~P106(f333(f333(f247(x56912),f2(x56912)),x56911)) % 173.51/173.28 [5700]E(x57001,x57002)+~E(f333(f114(a910),x57001),f333(f114(a910),x57002))+P106(f333(a201,f333(f114(a1),x57002)))+P106(f333(a201,f333(f114(a1),x57001))) % 173.51/173.28 [5750]~P94(x57501)+~E(x57502,f2(x57501))+E(f333(f333(f87(x57501),x57502),x57502),f2(x57501))+~P106(f333(f333(f335(x57501),x57502),f120(x57501))) % 173.51/173.28 [5787]E(x57871,f2(a1))+~E(f333(f333(f42(a1),x57872),x57871),f2(a1))+P106(f333(f333(f247(a1),x57871),x57872))+P106(f333(f333(f247(a1),x57872),x57871)) % 173.51/173.28 [5817]E(x58171,f2(a1))+~E(f333(f333(f42(a1),x58172),x58171),f2(a1))+P106(f333(f333(f246(a1),x58172),f2(a1)))+P106(f333(f333(f247(a1),x58172),x58171)) % 173.51/173.28 [5851]E(x58511,f2(a1))+~E(f333(f333(f42(a1),x58512),x58511),f2(a1))+P106(f333(f333(f246(a1),f2(a1)),x58512))+P106(f333(f333(f247(a1),x58511),x58512)) % 173.51/173.28 [5885]~P94(x58852)+E(x58851,f2(x58852))+~E(f333(f333(f87(x58852),x58851),x58851),f2(x58852))+~P106(f333(f333(f335(x58852),x58851),f120(x58852))) % 173.51/173.28 [5946]E(f333(f114(a910),x59461),f333(f114(a910),x59462))+~E(f333(f114(a1),x59462),f2(a1))+P106(f333(a201,f333(f114(a1),x59462)))+~P106(f333(a201,f333(f114(a1),x59461))) % 173.51/173.28 [5974]~E(f333(f114(a910),x59742),f333(f114(a910),x59741))+E(f333(f114(a1),x59741),f2(a1))+P106(f333(a201,f333(f114(a1),x59741)))+~P106(f333(a201,f333(f114(a1),x59742))) % 173.51/173.28 [5983]~P110(x59832)+E(x59831,f196(f917(x59832,a905)))+~P106(f333(f67(x59832),x59831))+P106(f333(f333(f335(x59832),f14(x59832,x59831)),x59831)) % 173.51/173.28 [5984]~P110(x59842)+E(x59841,f196(f917(x59842,a905)))+~P106(f333(f67(x59842),x59841))+P106(f333(f333(f335(x59842),f15(x59842,x59841)),x59841)) % 173.51/173.28 [6147]~P120(x61471)+~P95(x61471)+P106(f333(f333(f246(x61471),f2(x61471)),f333(f114(x61471),x61472)))+~P106(f333(f333(f246(a1),a90),x61472)) % 173.51/173.28 [6148]~P120(x61481)+~P95(x61481)+P106(f333(f333(f247(x61481),f2(x61481)),f333(f114(x61481),x61482)))+~P106(f333(f333(f247(a1),a90),x61482)) % 173.51/173.28 [6168]~P120(x61681)+~P95(x61681)+E(f333(f82(x61681),f333(f114(x61681),x61682)),f333(f114(x61681),x61682))+P106(f333(f333(f247(x61681),f333(f114(x61681),x61682)),f2(x61681))) % 173.51/173.28 [6205]E(x62051,x62052)+~E(f333(a115,x62051),f333(a115,x62052))+~P106(f333(f333(f246(a1),f2(a1)),x62052))+~P106(f333(f333(f246(a1),f2(a1)),x62051)) % 173.51/173.28 [6396]~P95(x63962)+~P120(x63962)+~P106(f333(f333(f246(x63962),f2(x63962)),f333(f114(x63962),x63961)))+P106(f333(f333(f246(a1),a90),x63961)) % 173.51/173.28 [6397]~P95(x63972)+~P120(x63972)+~P106(f333(f333(f247(x63972),f2(x63972)),f333(f114(x63972),x63971)))+P106(f333(f333(f247(a1),a90),x63971)) % 173.51/173.28 [6402]~P120(x64021)+~P95(x64021)+P106(f333(f333(f246(x64021),f333(f114(x64021),x64022)),f2(x64021)))+~P106(f333(f333(f246(a1),x64022),a90)) % 173.51/173.28 [6403]~P120(x64031)+~P95(x64031)+P106(f333(f333(f247(x64031),f333(f114(x64031),x64032)),f2(x64031)))+~P106(f333(f333(f247(a1),x64032),a90)) % 173.51/173.28 [6717]~P95(x67172)+~P120(x67172)+~P106(f333(f333(f246(x67172),f333(f114(x67172),x67171)),f2(x67172)))+P106(f333(f333(f246(a1),x67171),a90)) % 173.51/173.28 [6718]~P95(x67182)+~P120(x67182)+~P106(f333(f333(f247(x67182),f333(f114(x67182),x67181)),f2(x67182)))+P106(f333(f333(f247(a1),x67181),a90)) % 173.51/173.28 [6808]~P120(x68081)+~P95(x68081)+E(f333(f82(x68081),f333(f114(x68081),x68082)),f333(f86(x68081),f333(f114(x68081),x68082)))+~P106(f333(f333(f247(x68081),f333(f114(x68081),x68082)),f2(x68081))) % 173.51/173.28 [6825]E(f333(f114(a910),x68251),f333(f114(a910),x68252))+~E(f333(f114(a1),x68252),f2(a1))+~P106(f333(f333(f246(a1),f333(f114(a1),x68251)),f2(a1)))+~P106(f333(a201,f333(f114(a1),x68251))) % 173.51/173.28 [7693]~P110(x76932)+E(x76931,f196(f917(x76932,a905)))+~P106(f333(f67(x76932),x76931))+P106(f333(f333(f246(x76932),f11(x76932,f244(x76932),x76931)),f12(x76932,f245(x76932),x76931))) % 173.51/173.28 [8012]~P9(x80121)+~P43(x80122)+P106(f333(f333(f335(a1),x80121),x80122))+~P106(f333(f333(f335(a910),f333(a115,x80121)),f333(f316(a1,a910,a115),x80122))) % 173.51/173.28 [5980]~P139(x59802)+E(x59801,f2(a1))+E(f333(f86(x59802),f333(f113(x59802),f333(f86(a1),x59801))),f333(f113(x59802),x59801))+~P106(f333(f333(f247(a1),x59801),f2(a1))) % 173.51/173.28 [6050]~P94(x60501)+~P95(x60501)+~P30(x60501,f333(f114(x60501),x60502))+P30(x60501,f333(f114(x60501),f333(f333(f87(a1),x60502),x60502))) % 173.51/173.28 [6384]~P80(x63842)+E(x63841,f196(f917(x63842,a905)))+E(f15(x63842,f333(f316(x63842,x63842,f86(x63842)),x63841)),f333(f86(x63842),f14(x63842,x63841)))+~P106(f333(f67(x63842),x63841)) % 173.51/173.28 [6385]~P80(x63852)+E(x63851,f196(f917(x63852,a905)))+E(f14(x63852,f333(f316(x63852,x63852,f86(x63852)),x63851)),f333(f86(x63852),f15(x63852,x63851)))+~P106(f333(f67(x63852),x63851)) % 173.51/173.28 [6419]~P94(x64191)+~P95(x64191)+P30(x64191,f333(f114(x64191),x64192))+~P30(x64191,f333(f114(x64191),f333(f333(f87(a1),x64192),x64192))) % 173.51/173.28 [6508]E(x65081,f2(a1))+E(f333(a57,f56(f333(f86(a1),x65081),f333(f86(a1),x65082))),f52(x65081,x65082))+P106(f333(f333(f246(a1),f2(a1)),x65082))+~P106(f333(f333(f246(a1),f2(a1)),x65081)) % 173.51/173.28 [8812]~P43(x88122)+~P43(x88121)+P106(f333(f333(f247(f917(a910,a905)),f333(f316(a1,a910,a115),x88121)),f333(f316(a1,a910,a115),x88122)))+~P106(f333(f333(f247(f917(a1,a905)),x88121),x88122)) % 173.51/173.28 [9045]~E(f776(x90452,x90451),f777(x90452,x90451))+~P106(f333(f145(x90451),f778(x90452,x90451)))+~P106(f333(f145(f911(x90451)),x90452))+P106(f333(f145(x90451),f333(f150(f911(x90451),f911(x90451),f142(x90451),f124(x90451)),x90452))) % 173.51/173.28 [9146]~P43(x91462)+~P43(x91461)+~P106(f333(f333(f246(f917(a910,a905)),f333(f316(a1,a910,a115),x91461)),f333(f316(a1,a910,a115),x91462)))+P106(f333(f333(f246(f917(a1,a905)),x91461),x91462)) % 173.51/173.28 [9147]~P43(x91472)+~P43(x91471)+~P106(f333(f333(f247(f917(a910,a905)),f333(f316(a1,a910,a115),x91471)),f333(f316(a1,a910,a115),x91472)))+P106(f333(f333(f247(f917(a1,a905)),x91471),x91472)) % 173.51/173.28 [9153]~E(f776(x91532,x91531),f777(x91532,x91531))+~P106(f333(f145(f911(x91531)),x91532))+P106(f333(f145(x91531),f333(f150(f911(x91531),f911(x91531),f142(x91531),f124(x91531)),x91532)))+P106(f333(f333(f335(f911(x91531)),f778(x91532,x91531)),f333(f180(f911(x91531)),x91532))) % 173.51/173.28 [9196]~P106(f333(f145(x91961),f778(x91962,x91961)))+~P106(f333(f145(f911(x91961)),x91962))+P106(f333(f145(x91961),f333(f150(f911(x91961),f911(x91961),f142(x91961),f124(x91961)),x91962)))+P106(f333(f333(f335(f911(x91961)),f777(x91962,x91961)),f333(f180(f911(x91961)),x91962))) % 173.51/173.28 [9197]~P106(f333(f145(x91971),f778(x91972,x91971)))+~P106(f333(f145(f911(x91971)),x91972))+P106(f333(f145(x91971),f333(f150(f911(x91971),f911(x91971),f142(x91971),f124(x91971)),x91972)))+P106(f333(f333(f335(f911(x91971)),f776(x91972,x91971)),f333(f180(f911(x91971)),x91972))) % 173.51/173.28 [9275]~P106(f333(f145(f911(x92751)),x92752))+P106(f333(f145(x92751),f333(f150(f911(x92751),f911(x92751),f142(x92751),f124(x92751)),x92752)))+P106(f333(f333(f335(f911(x92751)),f777(x92752,x92751)),f333(f180(f911(x92751)),x92752)))+P106(f333(f333(f335(f911(x92751)),f778(x92752,x92751)),f333(f180(f911(x92751)),x92752))) % 173.51/173.28 [9276]~P106(f333(f145(f911(x92761)),x92762))+P106(f333(f145(x92761),f333(f150(f911(x92761),f911(x92761),f142(x92761),f124(x92761)),x92762)))+P106(f333(f333(f335(f911(x92761)),f776(x92762,x92761)),f333(f180(f911(x92761)),x92762)))+P106(f333(f333(f335(f911(x92761)),f778(x92762,x92761)),f333(f180(f911(x92761)),x92762))) % 173.51/173.28 [9291]~E(f333(f333(f112(f917(x92911,a905)),f333(f180(x92911),f777(x92912,x92911))),f333(f180(x92911),f776(x92912,x92911))),f196(f917(x92911,a905)))+~P106(f333(f145(x92911),f778(x92912,x92911)))+~P106(f333(f145(f911(x92911)),x92912))+P106(f333(f145(x92911),f333(f150(f911(x92911),f911(x92911),f142(x92911),f124(x92911)),x92912))) % 173.51/173.28 [9351]~E(f333(f333(f112(f917(x93511,a905)),f333(f180(x93511),f777(x93512,x93511))),f333(f180(x93511),f776(x93512,x93511))),f196(f917(x93511,a905)))+~P106(f333(f145(f911(x93511)),x93512))+P106(f333(f145(x93511),f333(f150(f911(x93511),f911(x93511),f142(x93511),f124(x93511)),x93512)))+P106(f333(f333(f335(f911(x93511)),f778(x93512,x93511)),f333(f180(f911(x93511)),x93512))) % 173.51/173.28 [9634]E(x96341,f2(a1))+E(x96342,f2(a1))+E(f333(f333(f93(a1,f916(a1,a1)),f333(f333(a229,x96342),x96341)),f333(f333(f18(a1,a1,f916(a1,a1)),f333(f333(f8(a1,f917(a1,f916(a1,a1)),a1),f265(a1,a1)),f333(f42(a1),x96342))),f333(f42(a1),x96341))),f227(x96342,x96341))+P106(f333(f333(f247(a1),x96341),f2(a1))) % 173.51/173.28 [8344]~P95(x83442)+~P120(x83442)+~P106(f333(f333(f246(x83442),f333(f114(x83442),x83441)),f85(x83442)))+P106(f333(f333(f246(a1),x83441),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))) % 173.51/173.28 [8345]~P95(x83452)+~P120(x83452)+~P106(f333(f333(f247(x83452),f333(f114(x83452),x83451)),f85(x83452)))+P106(f333(f333(f247(a1),x83451),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))) % 173.51/173.28 [8629]~P120(x86291)+~P95(x86291)+P106(f333(f333(f246(x86291),f333(f114(x86291),x86292)),f85(x86291)))+~P106(f333(f333(f246(a1),x86292),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))) % 173.51/173.28 [8630]~P120(x86301)+~P95(x86301)+P106(f333(f333(f247(x86301),f333(f114(x86301),x86302)),f85(x86301)))+~P106(f333(f333(f247(a1),x86302),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))) % 173.51/173.28 [8840]~P95(x88402)+~P120(x88402)+~P106(f333(f333(f246(x88402),f85(x88402)),f333(f114(x88402),x88401)))+P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),x88401)) % 173.51/173.28 [8841]~P95(x88412)+~P120(x88412)+~P106(f333(f333(f247(x88412),f85(x88412)),f333(f114(x88412),x88411)))+P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),x88411)) % 173.51/173.28 [9234]~P120(x92341)+~P95(x92341)+P106(f333(f333(f246(x92341),f85(x92341)),f333(f114(x92341),x92342)))+~P106(f333(f333(f246(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),x92342)) % 173.51/173.28 [9235]~P120(x92351)+~P95(x92351)+P106(f333(f333(f247(x92351),f85(x92351)),f333(f114(x92351),x92352)))+~P106(f333(f333(f247(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),x92352)) % 173.51/173.28 [9775]~P141(x97752)+E(x97751,f85(x97752))+E(x97751,f333(f86(x97752),f85(x97752)))+~E(f333(f333(f256(x97752),x97751),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f85(x97752)) % 173.51/173.28 [10042]~P69(x100421)+~P95(x100421)+~P106(f333(f333(f247(x100421),f2(x100421)),x100422))+P106(f333(f333(f247(x100421),f2(x100421)),f333(f333(f296(x100421),x100422),f333(f114(x100421),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.28 [10102]~P69(x101021)+~P95(x101021)+P106(f333(f333(f247(x101021),f2(x101021)),x101022))+~P106(f333(f333(f247(x101021),f2(x101021)),f333(f333(f296(x101021),x101022),f333(f114(x101021),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.28 [10374]~P139(x103742)+E(x103741,f2(a1))+P106(f333(f333(f247(a1),x103741),f2(a1)))+E(f333(f333(f269(a1,a1,x103742),f333(f333(f7(a1,f917(a1,f917(x103742,x103742)),f917(a1,x103742)),f333(f333(f8(f917(f917(x103742,x103742),x103742),f917(f917(a1,f917(x103742,x103742)),f917(a1,x103742)),a1),f8(f917(x103742,x103742),x103742,a1)),f333(f333(f8(x103742,f917(f917(x103742,x103742),x103742),a1),f93(x103742,x103742)),f113(x103742)))),f333(f333(f7(a1,f917(x103742,x103742),f917(x103742,x103742)),f333(f333(f8(f917(x103742,f917(x103742,x103742)),f917(f917(x103742,x103742),f917(x103742,x103742)),a1),f18(x103742,x103742,x103742)),f333(f333(f7(a1,f917(x103742,x103742),f917(x103742,f917(x103742,x103742))),f333(f333(f8(f917(x103742,f917(x103742,x103742)),f917(f917(x103742,x103742),f917(x103742,f917(x103742,x103742))),a1),f8(x103742,f917(x103742,x103742),x103742)),f333(f333(f8(a905,f917(x103742,f917(x103742,x103742)),a1),f107(x103742)),f333(f333(f7(a1,a1,a905),a330),f2(a1))))),f333(f333(f18(x103742,x103742,x103742),f87(x103742)),f5(x103742))))),f333(f333(f7(x103742,x103742,x103742),f333(f333(f8(x103742,f917(x103742,x103742),x103742),f87(x103742)),f333(f333(f18(x103742,x103742,x103742),f87(x103742)),f5(x103742)))),f85(x103742))))),f52(x103741,f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f113(x103742),x103741)) % 173.51/173.28 [5469]~P41(x54691,x54693)+~P55(x54691,x54693)+~P56(x54691,x54692,x54693)+P11(x54691,x54692,x54693) % 173.51/173.28 [5010]~P94(x50103)+~P95(x50103)+E(x50101,x50102)+~E(f333(f114(x50103),x50101),f333(f114(x50103),x50102)) % 173.51/173.28 [6157]~P106(f333(x61571,x61572))+~P106(f333(x61571,x61573))+~P106(f333(f333(f246(a910),x61573),f366(x61572,x61571)))+P106(f333(x61571,f2(a910))) % 173.51/173.28 [6574]P147(x65742,x65743,x65741)+E(x65741,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f850(x65741,x65743,x65742)))+P106(f333(f333(f247(a1),x65741),f2(a1))) % 173.51/173.28 [6575]P146(x65752,x65753,x65751)+E(x65751,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f856(x65751,x65753,x65752)))+P106(f333(f333(f247(a1),x65751),f2(a1))) % 173.51/173.28 [6696]P146(x66961,x66962,x66963)+~P106(f333(x66961,x66962))+P106(f333(f333(f246(a1),f2(a1)),f856(x66963,x66962,x66961)))+P106(f333(f333(f247(a1),x66963),f2(a1))) % 173.51/173.28 [6723]P147(x67231,x67232,x67233)+P106(f333(f333(f246(a1),f2(a1)),f850(x67233,x67232,x67231)))+~P106(f333(x67231,f2(a1)))+P106(f333(f333(f247(a1),x67233),f2(a1))) % 173.51/173.28 [6751]P147(x67512,x67513,x67511)+E(x67511,f2(a1))+~P106(f333(x67512,f851(x67511,x67513,x67512)))+P106(f333(f333(f247(a1),x67511),f2(a1))) % 173.51/173.28 [6752]P146(x67522,x67523,x67521)+E(x67521,f2(a1))+~P106(f333(x67522,f856(x67521,x67523,x67522)))+P106(f333(f333(f247(a1),x67521),f2(a1))) % 173.51/173.28 [6849]~P110(x68491)+~P8(x68491)+~P106(f333(f333(f247(x68491),x68492),f43(x68491,x68493)))+P106(f333(f333(f247(x68491),x68492),f630(x68493,x68492,x68491))) % 173.51/173.28 [6858]P146(x68581,x68582,x68583)+~P106(f333(x68581,x68582))+~P106(f333(x68581,f856(x68583,x68582,x68581)))+P106(f333(f333(f247(a1),x68583),f2(a1))) % 173.51/173.28 [6889]P147(x68891,x68892,x68893)+~P106(f333(x68891,f851(x68893,x68892,x68891)))+~P106(f333(x68891,f2(a1)))+P106(f333(f333(f247(a1),x68893),f2(a1))) % 173.51/173.28 [7137]P147(x71372,x71373,x71371)+E(x71371,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f850(x71371,x71373,x71372)))+P106(f333(f333(f247(a1),x71371),f849(x71371,x71373,x71372))) % 173.51/173.28 [7138]P146(x71382,x71383,x71381)+E(x71381,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f856(x71381,x71383,x71382)))+P106(f333(f333(f247(a1),x71381),f855(x71381,x71383,x71382))) % 173.51/173.28 [7255]P146(x72551,x72552,x72553)+~P106(f333(x72551,x72552))+P106(f333(f333(f246(a1),f2(a1)),f856(x72553,x72552,x72551)))+P106(f333(f333(f247(a1),x72553),f855(x72553,x72552,x72551))) % 173.51/173.28 [7274]P147(x72741,x72742,x72743)+P106(f333(f333(f246(a1),f2(a1)),f850(x72743,x72742,x72741)))+P106(f333(f333(f247(a1),x72743),f849(x72743,x72742,x72741)))+~P106(f333(x72741,f2(a1))) % 173.51/173.28 [7307]P147(x73072,x73073,x73071)+E(x73071,f2(a1))+~P106(f333(x73072,f851(x73071,x73073,x73072)))+P106(f333(f333(f247(a1),x73071),f849(x73071,x73073,x73072))) % 173.51/173.28 [7308]P146(x73082,x73083,x73081)+E(x73081,f2(a1))+~P106(f333(x73082,f856(x73081,x73083,x73082)))+P106(f333(f333(f247(a1),x73081),f855(x73081,x73083,x73082))) % 173.51/173.28 [7352]P147(x73522,x73523,x73521)+E(x73521,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f850(x73521,x73523,x73522)))+~P106(f333(x73522,f854(x73521,x73523,x73522))) % 173.51/173.28 [7353]P146(x73532,x73533,x73531)+E(x73531,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f856(x73531,x73533,x73532)))+~P106(f333(x73532,f855(x73531,x73533,x73532))) % 173.51/173.28 [7445]P146(x74451,x74452,x74453)+~P106(f333(x74451,x74452))+~P106(f333(x74451,f856(x74453,x74452,x74451)))+P106(f333(f333(f247(a1),x74453),f855(x74453,x74452,x74451))) % 173.51/173.28 [7460]P147(x74601,x74602,x74603)+~P106(f333(x74601,f851(x74603,x74602,x74601)))+P106(f333(f333(f247(a1),x74603),f849(x74603,x74602,x74601)))+~P106(f333(x74601,f2(a1))) % 173.51/173.28 [7463]P146(x74631,x74632,x74633)+~P106(f333(x74631,x74632))+P106(f333(f333(f246(a1),f2(a1)),f856(x74633,x74632,x74631)))+~P106(f333(x74631,f855(x74633,x74632,x74631))) % 173.51/173.28 [7481]P147(x74811,x74812,x74813)+P106(f333(f333(f246(a1),f2(a1)),f850(x74813,x74812,x74811)))+~P106(f333(x74811,f854(x74813,x74812,x74811)))+~P106(f333(x74811,f2(a1))) % 173.51/173.28 [7503]P147(x75032,x75033,x75031)+E(x75031,f2(a1))+~P106(f333(x75032,f851(x75031,x75033,x75032)))+~P106(f333(x75032,f854(x75031,x75033,x75032))) % 173.51/173.28 [7504]P146(x75042,x75043,x75041)+E(x75041,f2(a1))+~P106(f333(x75042,f856(x75041,x75043,x75042)))+~P106(f333(x75042,f855(x75041,x75043,x75042))) % 173.51/173.28 [7591]P146(x75911,x75912,x75913)+~P106(f333(x75911,x75912))+~P106(f333(x75911,f856(x75913,x75912,x75911)))+~P106(f333(x75911,f855(x75913,x75912,x75911))) % 173.51/173.28 [7608]P147(x76081,x76082,x76083)+~P106(f333(x76081,f851(x76083,x76082,x76081)))+~P106(f333(x76081,f854(x76083,x76082,x76081)))+~P106(f333(x76081,f2(a1))) % 173.51/173.28 [7652]P147(x76522,x76523,x76521)+E(x76521,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f850(x76521,x76523,x76522)))+P106(f333(f333(f246(a1),f849(x76521,x76523,x76522)),f2(a1))) % 173.51/173.28 [7653]P146(x76532,x76533,x76531)+E(x76531,f2(a1))+P106(f333(f333(f246(a1),f2(a1)),f856(x76531,x76533,x76532)))+P106(f333(f333(f246(a1),f855(x76531,x76533,x76532)),f2(a1))) % 173.51/173.28 [7654]~P139(x76541)+~P106(f333(f333(f335(x76541),x76543),f120(x76541)))+~P106(f333(f333(f335(x76541),x76542),f120(x76541)))+P106(f333(f333(f335(x76541),f333(f333(f23(x76541),x76542),x76543)),f120(x76541))) % 173.51/173.28 [7655]~P139(x76551)+~P106(f333(f333(f335(x76551),x76553),f120(x76551)))+~P106(f333(f333(f335(x76551),x76552),f120(x76551)))+P106(f333(f333(f335(x76551),f333(f333(f87(x76551),x76552),x76553)),f120(x76551))) % 173.51/173.28 [7656]~P107(x76561)+~P106(f333(f333(f335(x76561),x76563),f194(x76561)))+~P106(f333(f333(f335(x76561),x76562),f194(x76561)))+P106(f333(f333(f335(x76561),f333(f333(f87(x76561),x76562),x76563)),f194(x76561))) % 173.51/173.28 [7657]~P139(x76571)+~P106(f333(f333(f335(x76571),x76573),f120(x76571)))+~P106(f333(f333(f335(x76571),x76572),f120(x76571)))+P106(f333(f333(f335(x76571),f333(f333(f88(x76571),x76572),x76573)),f120(x76571))) % 173.51/173.28 [7658]~P107(x76581)+~P106(f333(f333(f335(x76581),x76583),f194(x76581)))+~P106(f333(f333(f335(x76581),x76582),f194(x76581)))+P106(f333(f333(f335(x76581),f333(f333(f88(x76581),x76582),x76583)),f194(x76581))) % 173.51/173.28 [7659]~P90(x76591)+~P106(f333(f333(f246(x76591),x76593),f2(x76591)))+~P106(f333(f333(f246(x76591),x76592),f2(x76591)))+P106(f333(f333(f246(x76591),f333(f333(f87(x76591),x76592),x76593)),f2(x76591))) % 173.51/173.28 [7660]~P90(x76601)+~P106(f333(f333(f246(x76601),x76603),f2(x76601)))+~P106(f333(f333(f247(x76601),x76602),f2(x76601)))+P106(f333(f333(f247(x76601),f333(f333(f87(x76601),x76602),x76603)),f2(x76601))) % 173.51/173.28 [7661]~P90(x76611)+~P106(f333(f333(f246(x76611),x76612),f2(x76611)))+~P106(f333(f333(f247(x76611),x76613),f2(x76611)))+P106(f333(f333(f247(x76611),f333(f333(f87(x76611),x76612),x76613)),f2(x76611))) % 173.51/173.28 [7662]~P90(x76621)+~P106(f333(f333(f247(x76621),x76623),f2(x76621)))+~P106(f333(f333(f247(x76621),x76622),f2(x76621)))+P106(f333(f333(f247(x76621),f333(f333(f87(x76621),x76622),x76623)),f2(x76621))) % 173.51/173.28 [7689]P147(x76893,x76892,x76891)+E(x76891,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x76891),f851(x76891,x76892,x76893))),f850(x76891,x76892,x76893)),x76892)+P106(f333(f333(f247(a1),x76891),f2(a1))) % 173.51/173.28 [7690]P146(x76903,x76902,x76901)+E(x76901,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x76901),f857(x76901,x76902,x76903))),f856(x76901,x76902,x76903)),x76902)+P106(f333(f333(f247(a1),x76901),f2(a1))) % 173.51/173.28 [7771]P146(x77711,x77712,x77713)+~P106(f333(x77711,x77712))+P106(f333(f333(f246(a1),f2(a1)),f856(x77713,x77712,x77711)))+P106(f333(f333(f246(a1),f855(x77713,x77712,x77711)),f2(a1))) % 173.51/173.28 [7800]P147(x78001,x78002,x78003)+P106(f333(f333(f246(a1),f2(a1)),f850(x78003,x78002,x78001)))+~P106(f333(x78001,f2(a1)))+P106(f333(f333(f246(a1),f849(x78003,x78002,x78001)),f2(a1))) % 173.51/173.28 [7811]P146(x78113,x78112,x78111)+~P106(f333(x78113,x78112))+E(f333(f333(f87(a1),f333(f333(f88(a1),x78111),f857(x78111,x78112,x78113))),f856(x78111,x78112,x78113)),x78112)+P106(f333(f333(f247(a1),x78111),f2(a1))) % 173.51/173.28 [7817]P147(x78172,x78173,x78171)+E(x78171,f2(a1))+~P106(f333(x78172,f851(x78171,x78173,x78172)))+P106(f333(f333(f246(a1),f849(x78171,x78173,x78172)),f2(a1))) % 173.51/173.28 [7818]P146(x78182,x78183,x78181)+E(x78181,f2(a1))+~P106(f333(x78182,f856(x78181,x78183,x78182)))+P106(f333(f333(f246(a1),f855(x78181,x78183,x78182)),f2(a1))) % 173.51/173.28 [7823]P147(x78233,x78232,x78231)+E(f333(f333(f87(a1),f333(f333(f88(a1),x78231),f851(x78231,x78232,x78233))),f850(x78231,x78232,x78233)),x78232)+~P106(f333(x78233,f2(a1)))+P106(f333(f333(f247(a1),x78231),f2(a1))) % 173.51/173.28 [7880]P146(x78801,x78802,x78803)+~P106(f333(x78801,x78802))+~P106(f333(x78801,f856(x78803,x78802,x78801)))+P106(f333(f333(f246(a1),f855(x78803,x78802,x78801)),f2(a1))) % 173.51/173.28 [7884]P147(x78841,x78842,x78843)+~P106(f333(x78841,f851(x78843,x78842,x78841)))+~P106(f333(x78841,f2(a1)))+P106(f333(f333(f246(a1),f849(x78843,x78842,x78841)),f2(a1))) % 173.51/173.28 [7954]~P126(x79541)+~P106(f333(f333(f246(x79541),f333(f333(f88(x79541),x79543),x79542)),f2(x79541)))+P106(f333(f333(f246(x79541),x79542),f2(x79541)))+P106(f333(f333(f246(x79541),x79543),f2(x79541))) % 173.51/173.28 [7955]~P69(x79551)+~P106(f333(f333(f246(x79551),f333(f333(f296(x79551),x79553),x79552)),f2(x79551)))+P106(f333(f333(f246(x79551),x79552),f2(x79551)))+P106(f333(f333(f246(x79551),x79553),f2(x79551))) % 173.51/173.28 [7956]~P69(x79561)+~P106(f333(f333(f247(x79561),f333(f333(f296(x79561),x79563),x79562)),f2(x79561)))+P106(f333(f333(f247(x79561),x79562),f2(x79561)))+P106(f333(f333(f247(x79561),x79563),f2(x79561))) % 173.51/173.28 [8069]P147(x80693,x80692,x80691)+E(x80691,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x80691),f851(x80691,x80692,x80693))),f850(x80691,x80692,x80693)),x80692)+P106(f333(f333(f247(a1),x80691),f849(x80691,x80692,x80693))) % 173.51/173.28 [8070]P146(x80703,x80702,x80701)+E(x80701,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x80701),f857(x80701,x80702,x80703))),f856(x80701,x80702,x80703)),x80702)+P106(f333(f333(f247(a1),x80701),f855(x80701,x80702,x80703))) % 173.51/173.28 [8083]P147(x80833,x80832,x80831)+E(x80831,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x80831),f854(x80831,x80832,x80833))),f849(x80831,x80832,x80833)),x80832)+P106(f333(f333(f246(a1),f2(a1)),f850(x80831,x80832,x80833))) % 173.51/173.28 [8084]P146(x80843,x80842,x80841)+E(x80841,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x80841),f858(x80841,x80842,x80843))),f855(x80841,x80842,x80843)),x80842)+P106(f333(f333(f246(a1),f2(a1)),f856(x80841,x80842,x80843))) % 173.51/173.28 [8129]P146(x81293,x81292,x81291)+~P106(f333(x81293,x81292))+E(f333(f333(f87(a1),f333(f333(f88(a1),x81291),f857(x81291,x81292,x81293))),f856(x81291,x81292,x81293)),x81292)+P106(f333(f333(f247(a1),x81291),f855(x81291,x81292,x81293))) % 173.51/173.28 [8141]P147(x81413,x81412,x81411)+E(f333(f333(f87(a1),f333(f333(f88(a1),x81411),f851(x81411,x81412,x81413))),f850(x81411,x81412,x81413)),x81412)+P106(f333(f333(f247(a1),x81411),f849(x81411,x81412,x81413)))+~P106(f333(x81413,f2(a1))) % 173.51/173.28 [8147]P146(x81473,x81472,x81471)+~P106(f333(x81473,x81472))+E(f333(f333(f87(a1),f333(f333(f88(a1),x81471),f858(x81471,x81472,x81473))),f855(x81471,x81472,x81473)),x81472)+P106(f333(f333(f246(a1),f2(a1)),f856(x81471,x81472,x81473))) % 173.51/173.28 [8153]P147(x81533,x81532,x81531)+E(f333(f333(f87(a1),f333(f333(f88(a1),x81531),f854(x81531,x81532,x81533))),f849(x81531,x81532,x81533)),x81532)+P106(f333(f333(f246(a1),f2(a1)),f850(x81531,x81532,x81533)))+~P106(f333(x81533,f2(a1))) % 173.51/173.28 [8164]P147(x81643,x81642,x81641)+E(x81641,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x81641),f851(x81641,x81642,x81643))),f850(x81641,x81642,x81643)),x81642)+~P106(f333(x81643,f854(x81641,x81642,x81643))) % 173.51/173.28 [8165]P146(x81653,x81652,x81651)+E(x81651,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x81651),f857(x81651,x81652,x81653))),f856(x81651,x81652,x81653)),x81652)+~P106(f333(x81653,f855(x81651,x81652,x81653))) % 173.51/173.28 [8166]P147(x81663,x81662,x81661)+E(x81661,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x81661),f854(x81661,x81662,x81663))),f849(x81661,x81662,x81663)),x81662)+~P106(f333(x81663,f851(x81661,x81662,x81663))) % 173.51/173.28 [8167]P146(x81673,x81672,x81671)+E(x81671,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x81671),f858(x81671,x81672,x81673))),f855(x81671,x81672,x81673)),x81672)+~P106(f333(x81673,f856(x81671,x81672,x81673))) % 173.51/173.28 [8227]P146(x82273,x82272,x82271)+~P106(f333(x82273,x82272))+E(f333(f333(f87(a1),f333(f333(f88(a1),x82271),f857(x82271,x82272,x82273))),f856(x82271,x82272,x82273)),x82272)+~P106(f333(x82273,f855(x82271,x82272,x82273))) % 173.51/173.28 [8228]P146(x82283,x82282,x82281)+~P106(f333(x82283,x82282))+E(f333(f333(f87(a1),f333(f333(f88(a1),x82281),f858(x82281,x82282,x82283))),f855(x82281,x82282,x82283)),x82282)+~P106(f333(x82283,f856(x82281,x82282,x82283))) % 173.51/173.28 [8238]P147(x82383,x82382,x82381)+E(f333(f333(f87(a1),f333(f333(f88(a1),x82381),f851(x82381,x82382,x82383))),f850(x82381,x82382,x82383)),x82382)+~P106(f333(x82383,f854(x82381,x82382,x82383)))+~P106(f333(x82383,f2(a1))) % 173.51/173.28 [8239]P147(x82393,x82392,x82391)+E(f333(f333(f87(a1),f333(f333(f88(a1),x82391),f854(x82391,x82392,x82393))),f849(x82391,x82392,x82393)),x82392)+~P106(f333(x82393,f851(x82391,x82392,x82393)))+~P106(f333(x82393,f2(a1))) % 173.51/173.28 [8337]P147(x83373,x83372,x83371)+E(x83371,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x83371),f851(x83371,x83372,x83373))),f850(x83371,x83372,x83373)),x83372)+P106(f333(f333(f246(a1),f849(x83371,x83372,x83373)),f2(a1))) % 173.51/173.28 [8338]P146(x83383,x83382,x83381)+E(x83381,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x83381),f857(x83381,x83382,x83383))),f856(x83381,x83382,x83383)),x83382)+P106(f333(f333(f246(a1),f855(x83381,x83382,x83383)),f2(a1))) % 173.51/173.28 [8378]P146(x83783,x83782,x83781)+~P106(f333(x83783,x83782))+E(f333(f333(f87(a1),f333(f333(f88(a1),x83781),f857(x83781,x83782,x83783))),f856(x83781,x83782,x83783)),x83782)+P106(f333(f333(f246(a1),f855(x83781,x83782,x83783)),f2(a1))) % 173.51/173.28 [8383]P147(x83833,x83832,x83831)+E(f333(f333(f87(a1),f333(f333(f88(a1),x83831),f851(x83831,x83832,x83833))),f850(x83831,x83832,x83833)),x83832)+~P106(f333(x83833,f2(a1)))+P106(f333(f333(f246(a1),f849(x83831,x83832,x83833)),f2(a1))) % 173.51/173.28 [8516]P147(x85163,x85162,x85161)+E(x85161,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x85161),f854(x85161,x85162,x85163))),f849(x85161,x85162,x85163)),x85162)+E(f333(f333(f87(a1),f333(f333(f88(a1),x85161),f851(x85161,x85162,x85163))),f850(x85161,x85162,x85163)),x85162) % 173.51/173.28 [8517]P146(x85173,x85172,x85171)+E(x85171,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x85171),f858(x85171,x85172,x85173))),f855(x85171,x85172,x85173)),x85172)+E(f333(f333(f87(a1),f333(f333(f88(a1),x85171),f857(x85171,x85172,x85173))),f856(x85171,x85172,x85173)),x85172) % 173.51/173.28 [8541]P146(x85413,x85412,x85411)+~P106(f333(x85413,x85412))+E(f333(f333(f87(a1),f333(f333(f88(a1),x85411),f858(x85411,x85412,x85413))),f855(x85411,x85412,x85413)),x85412)+E(f333(f333(f87(a1),f333(f333(f88(a1),x85411),f857(x85411,x85412,x85413))),f856(x85411,x85412,x85413)),x85412) % 173.51/173.28 [8554]P147(x85543,x85542,x85541)+E(f333(f333(f87(a1),f333(f333(f88(a1),x85541),f854(x85541,x85542,x85543))),f849(x85541,x85542,x85543)),x85542)+E(f333(f333(f87(a1),f333(f333(f88(a1),x85541),f851(x85541,x85542,x85543))),f850(x85541,x85542,x85543)),x85542)+~P106(f333(x85543,f2(a1))) % 173.51/173.28 [9243]~P126(x92431)+~E(x92433,f2(x92431))+~E(x92432,f2(x92431))+P106(f333(f333(f246(x92431),f333(f333(f87(x92431),f333(f333(f88(x92431),x92432),x92432)),f333(f333(f88(x92431),x92433),x92433))),f2(x92431))) % 173.51/173.28 [10313]~P120(x103131)+~E(x103133,f2(x103131))+~E(x103132,f2(x103131))+P106(f333(f333(f246(x103131),f333(f333(f87(x103131),f333(f333(f256(x103131),x103132),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x103131),x103133),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))),f2(x103131))) % 173.51/173.28 [4958]~E(x49583,x49581)+~P122(x49582)+E(x49581,f2(x49582))+E(f333(f333(f296(x49582),x49583),x49581),f85(x49582)) % 173.51/173.28 [5011]~P3(x50111)+~E(x50113,f196(x50111))+~E(x50112,f196(x50111))+E(f333(f333(f121(x50111),x50112),x50113),f196(x50111)) % 173.51/173.28 [5012]~P100(x50121)+~E(x50123,f254(x50121))+~E(x50122,f254(x50121))+E(f333(f333(f112(x50121),x50122),x50123),f254(x50121)) % 173.51/173.28 [5105]~P122(x51053)+E(x51051,x51052)+E(x51052,f2(x51053))+~E(f333(f333(f296(x51053),x51051),x51052),f85(x51053)) % 173.51/173.28 [5123]~P128(x51232)+E(x51231,f2(x51232))+E(x51233,f2(x51232))+~E(f333(f333(f88(x51232),x51233),x51231),f2(x51232)) % 173.51/173.28 [5124]~P140(x51242)+E(x51241,f2(x51242))+E(x51243,f2(x51242))+~E(f333(f333(f88(x51242),x51243),x51241),f2(x51242)) % 173.51/173.28 [5496]~P121(x54963)+E(x54961,x54962)+E(x54961,f333(f86(x54963),x54962))+~E(f333(f333(f88(x54963),x54961),x54961),f333(f333(f88(x54963),x54962),x54962)) % 173.51/173.28 [5534]~P84(x55341)+E(f333(f86(x55341),x55342),x55343)+~E(f333(f333(f121(x55341),x55342),x55343),f254(x55341))+~E(f333(f333(f112(x55341),x55342),x55343),f196(x55341)) % 173.51/173.28 [5611]~P120(x56113)+E(x56111,x56112)+P106(f333(f333(f247(x56113),x56112),x56111))+P106(f333(f333(f247(x56113),x56111),x56112)) % 173.51/173.28 [5612]~P110(x56123)+E(x56121,x56122)+P106(f333(f333(f247(x56123),x56122),x56121))+P106(f333(f333(f247(x56123),x56121),x56122)) % 173.51/173.28 [5613]~E(x56132,x56133)+~P110(x56131)+P106(f333(f333(f247(x56131),x56132),x56133))+P106(f333(f333(f246(x56131),x56132),x56133)) % 173.51/173.28 [5867]~P112(x58673)+E(x58671,x58672)+~P106(f333(f333(f246(x58673),x58672),x58671))+P106(f333(f333(f247(x58673),x58672),x58671)) % 173.51/173.28 [5869]~P110(x58693)+E(x58691,x58692)+~P106(f333(f333(f246(x58693),x58691),x58692))+P106(f333(f333(f247(x58693),x58691),x58692)) % 173.51/173.28 [5875]~P112(x58753)+E(x58751,x58752)+~P106(f333(f333(f246(x58753),x58751),x58752))+P106(f333(f333(f247(x58753),x58751),x58752)) % 173.51/173.28 [5977]P146(x59771,x59772,x59773)+~P106(f333(x59771,x59772))+P106(f333(f333(f247(a1),x59773),f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x59773)) % 173.51/173.28 [6024]P147(x60241,x60242,x60243)+~P106(f333(x60241,f2(a1)))+P106(f333(f333(f247(a1),x60243),f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x60243)) % 173.51/173.28 [6028]~P2(x60281)+E(f333(f333(f121(x60281),x60282),f10(x60281,x60283)),x60282)+~P106(f333(f67(x60281),x60283))+~P106(f333(f333(f335(x60281),x60282),x60283)) % 173.51/173.28 [6029]~P2(x60291)+E(f333(f333(f112(x60291),x60292),f13(x60291,x60293)),x60292)+~P106(f333(f67(x60291),x60293))+~P106(f333(f333(f335(x60291),x60292),x60293)) % 173.51/173.28 [6065]~P2(x60651)+E(f333(f333(f121(x60651),x60652),f13(x60651,x60653)),f13(x60651,x60653))+~P106(f333(f67(x60651),x60653))+~P106(f333(f333(f335(x60651),x60652),x60653)) % 173.51/173.28 [6066]~P2(x60661)+E(f333(f333(f112(x60661),x60662),f10(x60661,x60663)),f10(x60661,x60663))+~P106(f333(f67(x60661),x60663))+~P106(f333(f333(f335(x60661),x60662),x60663)) % 173.51/173.28 [6067]~P110(x60671)+E(f333(f333(f244(x60671),x60672),f14(x60671,x60673)),f14(x60671,x60673))+~P106(f333(f67(x60671),x60673))+~P106(f333(f333(f335(x60671),x60672),x60673)) % 173.51/173.28 [6068]~P110(x60681)+E(f333(f333(f245(x60681),x60682),f15(x60681,x60683)),f15(x60681,x60683))+~P106(f333(f67(x60681),x60683))+~P106(f333(f333(f335(x60681),x60682),x60683)) % 173.51/173.28 [6110]E(x61101,x61102)+~P112(x61103)+~P106(f333(f333(f246(x61103),x61102),x61101))+~P106(f333(f333(f246(x61103),x61101),x61102)) % 173.51/173.28 [6251]~P109(x62511)+P106(f333(f333(f247(x62511),x62513),x62512))+~P106(f333(f333(f246(x62511),x62513),x62512))+P106(f333(f333(f246(x62511),x62512),x62513)) % 173.51/173.28 [6276]~P110(x62761)+~P106(f333(f67(x62761),x62763))+P106(f333(f333(f246(x62761),x62762),f15(x62761,x62763)))+~P106(f333(f333(f335(x62761),x62762),x62763)) % 173.51/173.28 [6321]~P110(x63211)+E(f333(f333(f244(x63211),x63212),f12(x63211,f245(x63211),x63213)),x63212)+~P106(f333(f67(x63211),x63213))+~P106(f333(f333(f335(x63211),x63212),x63213)) % 173.51/173.28 [6322]~P110(x63221)+E(f333(f333(f245(x63221),x63222),f11(x63221,f244(x63221),x63223)),x63222)+~P106(f333(f67(x63221),x63223))+~P106(f333(f333(f335(x63221),x63222),x63223)) % 173.51/173.28 [6461]E(x64611,x64612)+~E(f333(f333(f23(a910),x64611),x64613),f333(f333(f23(a910),x64612),x64613))+~P106(f333(f333(f246(a910),x64613),x64611))+~P106(f333(f333(f246(a910),x64613),x64612)) % 173.51/173.28 [6487]~P110(x64871)+~P106(f333(f67(x64871),x64872))+~P106(f333(f333(f335(x64871),x64873),x64872))+P106(f333(f333(f246(x64871),f14(x64871,x64872)),x64873)) % 173.51/173.28 [6552]P147(x65522,x65523,x65521)+E(x65521,f2(a1))+P106(f333(f333(f247(a1),x65521),f849(x65521,x65523,x65522)))+P106(f333(f333(f247(a1),f2(a1)),x65521)) % 173.51/173.28 [6553]P146(x65532,x65533,x65531)+E(x65531,f2(a1))+P106(f333(f333(f247(a1),x65531),f855(x65531,x65533,x65532)))+P106(f333(f333(f247(a1),f2(a1)),x65531)) % 173.51/173.28 [6554]~P110(x65541)+E(f333(f333(f244(x65541),x65542),f11(x65541,f244(x65541),x65543)),f11(x65541,f244(x65541),x65543))+~P106(f333(f67(x65541),x65543))+~P106(f333(f333(f335(x65541),x65542),x65543)) % 173.51/173.28 [6555]~P110(x65551)+E(f333(f333(f245(x65551),x65552),f12(x65551,f245(x65551),x65553)),f12(x65551,f245(x65551),x65553))+~P106(f333(f67(x65551),x65553))+~P106(f333(f333(f335(x65551),x65552),x65553)) % 173.51/173.28 [6561]~P106(f333(x65611,x65612))+P106(f333(x65611,f526(x65612,x65611,x65613)))+P106(f333(x65611,f2(a910)))+~P106(f333(f333(f247(a910),x65612),x65613)) % 173.51/173.28 [6616]~P106(f333(x66161,x66162))+~P106(f333(f67(x66163),x66162))+P106(f333(x66161,f882(x66161,x66162,x66163)))+P106(f333(x66161,f196(f917(x66163,a905)))) % 173.51/173.28 [6629]~P120(x66291)+~P95(x66291)+P106(f333(f333(f246(x66291),f333(f114(x66291),x66292)),f333(f114(x66291),x66293)))+~P106(f333(f333(f246(a1),x66292),x66293)) % 173.51/173.28 [6630]~P120(x66301)+~P95(x66301)+P106(f333(f333(f247(x66301),f333(f114(x66301),x66302)),f333(f114(x66301),x66303)))+~P106(f333(f333(f247(a1),x66302),x66303)) % 173.51/173.28 [6633]~P106(f333(x66331,x66333))+~P106(f333(f67(x66332),x66333))+P106(f333(f67(x66332),f882(x66331,x66333,x66332)))+P106(f333(x66331,f196(f917(x66332,a905)))) % 173.51/173.28 [6666]P146(x66661,x66662,x66663)+~P106(f333(x66661,x66662))+P106(f333(f333(f247(a1),x66663),f855(x66663,x66662,x66661)))+P106(f333(f333(f247(a1),f2(a1)),x66663)) % 173.51/173.28 [6704]P147(x67041,x67042,x67043)+P106(f333(f333(f247(a1),x67043),f849(x67043,x67042,x67041)))+~P106(f333(x67041,f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x67043)) % 173.51/173.28 [6734]~P111(x67341)+~P96(x67341)+E(f333(f333(f244(x67341),f333(f114(x67341),x67342)),f333(f114(x67341),x67343)),f333(f114(x67341),x67343))+P106(f333(f333(f246(x67341),f333(f114(x67341),x67342)),f333(f114(x67341),x67343))) % 173.51/173.28 [6735]~P111(x67351)+~P96(x67351)+E(f333(f333(f245(x67351),f333(f114(x67351),x67352)),f333(f114(x67351),x67353)),f333(f114(x67351),x67352))+P106(f333(f333(f246(x67351),f333(f114(x67351),x67352)),f333(f114(x67351),x67353))) % 173.51/173.28 [6792]P147(x67922,x67923,x67921)+E(x67921,f2(a1))+~P106(f333(x67922,f854(x67921,x67923,x67922)))+P106(f333(f333(f247(a1),f2(a1)),x67921)) % 173.51/173.28 [6793]P146(x67932,x67933,x67931)+E(x67931,f2(a1))+~P106(f333(x67932,f855(x67931,x67933,x67932)))+P106(f333(f333(f247(a1),f2(a1)),x67931)) % 173.51/173.28 [6797]P106(f333(x67971,x67972))+~P106(f333(f67(x67973),x67972))+P106(f333(x67971,f802(x67971,x67972,x67973)))+~P106(f333(x67971,f196(f917(x67973,a905)))) % 173.51/173.28 [6816]P106(f333(x68161,x68162))+P106(f333(f67(x68163),f802(x68161,x68162,x68163)))+~P106(f333(f67(x68163),x68162))+~P106(f333(x68161,f196(f917(x68163,a905)))) % 173.51/173.28 [6878]P146(x68781,x68782,x68783)+~P106(f333(x68781,x68782))+~P106(f333(x68781,f855(x68783,x68782,x68781)))+P106(f333(f333(f247(a1),f2(a1)),x68783)) % 173.51/173.28 [6908]P147(x69081,x69082,x69083)+~P106(f333(x69081,f854(x69083,x69082,x69081)))+~P106(f333(x69081,f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x69083)) % 173.51/173.28 [7012]~P95(x70123)+~P120(x70123)+~P106(f333(f333(f246(x70123),f333(f114(x70123),x70121)),f333(f114(x70123),x70122)))+P106(f333(f333(f246(a1),x70121),x70122)) % 173.51/173.28 [7013]~P95(x70133)+~P120(x70133)+~P106(f333(f333(f247(x70133),f333(f114(x70133),x70131)),f333(f114(x70133),x70132)))+P106(f333(f333(f247(a1),x70131),x70132)) % 173.51/173.28 [7043]~P110(x70431)+~P16(x70431,x70433)+P16(x70431,f333(f333(f159(x70431),x70432),x70433))+~P106(f333(f333(f246(x70431),x70432),f757(x70433,x70432,x70431))) % 173.51/173.28 [7044]~P110(x70441)+~P16(x70441,x70443)+P16(x70441,f333(f333(f159(x70441),x70442),x70443))+~P106(f333(f333(f246(x70441),x70442),f759(x70443,x70442,x70441))) % 173.51/173.28 [7045]~P110(x70451)+~P16(x70451,x70453)+P16(x70451,f333(f333(f159(x70451),x70452),x70453))+~P106(f333(f333(f246(x70451),x70452),f786(x70452,x70453,x70451))) % 173.51/173.28 [7127]P147(x71272,x71273,x71271)+E(x71271,f2(a1))+P106(f333(f333(f247(a1),x71271),f2(a1)))+P106(f333(f333(f247(a1),f850(x71271,x71273,x71272)),x71271)) % 173.51/173.28 [7128]P146(x71282,x71283,x71281)+E(x71281,f2(a1))+P106(f333(f333(f247(a1),x71281),f2(a1)))+P106(f333(f333(f247(a1),f856(x71281,x71283,x71282)),x71281)) % 173.51/173.28 [7166]P147(x71662,x71663,x71661)+E(x71661,f2(a1))+P106(f333(f333(f246(a1),f849(x71661,x71663,x71662)),f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x71661)) % 173.51/173.28 [7167]P146(x71672,x71673,x71671)+E(x71671,f2(a1))+P106(f333(f333(f246(a1),f855(x71671,x71673,x71672)),f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x71671)) % 173.51/173.28 [7192]~P110(x71921)+~P16(x71921,x71923)+E(f333(f333(f156(x71921,x71921,f5(x71921)),x71922),f178(x71921,x71922,x71923)),x71923)+~P106(f333(f333(f335(x71921),x71922),f333(f180(x71921),x71923))) % 173.51/173.28 [7238]P146(x72381,x72382,x72383)+~P106(f333(x72381,x72382))+P106(f333(f333(f247(a1),x72383),f2(a1)))+P106(f333(f333(f247(a1),f856(x72383,x72382,x72381)),x72383)) % 173.51/173.28 [7244]~P111(x72441)+~P96(x72441)+E(f333(f333(f244(x72441),f333(f114(x72441),x72442)),f333(f114(x72441),x72443)),f333(f114(x72441),x72442))+~P106(f333(f333(f246(x72441),f333(f114(x72441),x72442)),f333(f114(x72441),x72443))) % 173.51/173.28 [7245]~P111(x72451)+~P96(x72451)+E(f333(f333(f245(x72451),f333(f114(x72451),x72452)),f333(f114(x72451),x72453)),f333(f114(x72451),x72453))+~P106(f333(f333(f246(x72451),f333(f114(x72451),x72452)),f333(f114(x72451),x72453))) % 173.51/173.28 [7259]P147(x72591,x72592,x72593)+~P106(f333(x72591,f2(a1)))+P106(f333(f333(f247(a1),x72593),f2(a1)))+P106(f333(f333(f247(a1),f850(x72593,x72592,x72591)),x72593)) % 173.51/173.28 [7267]P146(x72671,x72672,x72673)+~P106(f333(x72671,x72672))+P106(f333(f333(f246(a1),f855(x72673,x72672,x72671)),f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x72673)) % 173.51/173.28 [7291]P147(x72911,x72912,x72913)+~P106(f333(x72911,f2(a1)))+P106(f333(f333(f246(a1),f849(x72913,x72912,x72911)),f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x72913)) % 173.51/173.28 [7319]~P106(f333(x73191,x73192))+P106(f333(x73191,f2(a910)))+~P106(f333(f333(f247(a910),x73192),x73193))+P106(f333(f333(f247(a910),f526(x73192,x73191,x73193)),x73193)) % 173.51/173.28 [7336]~P110(x73361)+~P16(x73361,x73363)+P16(x73361,f333(f333(f159(x73361),x73362),x73363))+P106(f333(f333(f335(x73361),f757(x73363,x73362,x73361)),f333(f180(x73361),x73363))) % 173.51/173.28 [7337]~P110(x73371)+~P16(x73371,x73373)+P16(x73371,f333(f333(f159(x73371),x73372),x73373))+P106(f333(f333(f335(x73371),f759(x73373,x73372,x73371)),f333(f180(x73371),x73373))) % 173.51/173.28 [7338]~P110(x73381)+~P16(x73381,x73383)+P16(x73381,f333(f333(f159(x73381),x73382),x73383))+P106(f333(f333(f335(x73381),f786(x73382,x73383,x73381)),f333(f180(x73381),x73383))) % 173.51/173.28 [7449]~P110(x74491)+~P8(x74491)+~P106(f333(f333(f247(x74491),x74493),f43(x74491,x74492)))+P106(f333(f333(f335(x74491),f630(x74492,x74493,x74491)),x74492)) % 173.51/173.28 [7606]~P110(x76061)+~P8(x76061)+~P106(f333(f333(f247(x76061),f44(x76061,x76063)),x76062))+P106(f333(f333(f335(x76061),f663(x76062,x76063,x76061)),x76063)) % 173.51/173.28 [7607]~P110(x76071)+~P8(x76071)+~P106(f333(f333(f247(x76071),f44(x76071,x76073)),x76072))+P106(f333(f333(f247(x76071),f663(x76072,x76073,x76071)),x76072)) % 173.51/173.28 [7620]P147(x76202,x76203,x76201)+E(x76201,f2(a1))+P106(f333(f333(f247(a1),x76201),f849(x76201,x76203,x76202)))+P106(f333(f333(f247(a1),f850(x76201,x76203,x76202)),x76201)) % 173.51/173.28 [7621]P146(x76212,x76213,x76211)+E(x76211,f2(a1))+P106(f333(f333(f247(a1),x76211),f855(x76211,x76213,x76212)))+P106(f333(f333(f247(a1),f856(x76211,x76213,x76212)),x76211)) % 173.51/173.28 [7710]P147(x77103,x77102,x77101)+E(x77101,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x77101),f854(x77101,x77102,x77103))),f849(x77101,x77102,x77103)),x77102)+P106(f333(f333(f247(a1),f2(a1)),x77101)) % 173.51/173.28 [7711]P146(x77113,x77112,x77111)+E(x77111,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x77111),f858(x77111,x77112,x77113))),f855(x77111,x77112,x77113)),x77112)+P106(f333(f333(f247(a1),f2(a1)),x77111)) % 173.51/173.28 [7714]~P134(x77141)+~P106(f333(f333(f246(x77141),x77143),f2(x77141)))+P106(f333(f333(f246(x77141),f333(f333(f88(x77141),x77142),x77143)),f2(x77141)))+~P106(f333(f333(f246(x77141),f2(x77141)),x77142)) % 173.51/173.28 [7716]~P134(x77161)+~P106(f333(f333(f246(x77161),x77162),f2(x77161)))+P106(f333(f333(f246(x77161),f333(f333(f88(x77161),x77162),x77163)),f2(x77161)))+~P106(f333(f333(f246(x77161),f2(x77161)),x77163)) % 173.51/173.28 [7717]~P126(x77171)+~P106(f333(f333(f246(x77171),x77173),f2(x77171)))+P106(f333(f333(f246(x77171),f333(f333(f88(x77171),x77172),x77173)),f2(x77171)))+~P106(f333(f333(f246(x77171),f2(x77171)),x77172)) % 173.51/173.28 [7718]~P126(x77181)+~P106(f333(f333(f246(x77181),x77182),f2(x77181)))+P106(f333(f333(f246(x77181),f333(f333(f88(x77181),x77182),x77183)),f2(x77181)))+~P106(f333(f333(f246(x77181),f2(x77181)),x77183)) % 173.51/173.28 [7719]~P70(x77191)+~P106(f333(f333(f246(x77191),x77192),f2(x77191)))+P106(f333(f333(f246(x77191),f333(f333(f296(x77191),x77192),x77193)),f2(x77191)))+~P106(f333(f333(f247(x77191),f2(x77191)),x77193)) % 173.51/173.28 [7720]~P70(x77201)+~P106(f333(f333(f247(x77201),x77203),f2(x77201)))+P106(f333(f333(f246(x77201),f333(f333(f296(x77201),x77202),x77203)),f2(x77201)))+~P106(f333(f333(f246(x77201),f2(x77201)),x77202)) % 173.51/173.28 [7721]~P69(x77211)+~P106(f333(f333(f246(x77211),x77213),f2(x77211)))+P106(f333(f333(f246(x77211),f333(f333(f296(x77211),x77212),x77213)),f2(x77211)))+~P106(f333(f333(f246(x77211),f2(x77211)),x77212)) % 173.51/173.28 [7722]~P69(x77221)+~P106(f333(f333(f246(x77221),x77222),f2(x77221)))+P106(f333(f333(f246(x77221),f333(f333(f296(x77221),x77222),x77223)),f2(x77221)))+~P106(f333(f333(f246(x77221),f2(x77221)),x77223)) % 173.51/173.28 [7724]~P130(x77241)+~P106(f333(f333(f247(x77241),x77243),f2(x77241)))+P106(f333(f333(f247(x77241),f333(f333(f88(x77241),x77242),x77243)),f2(x77241)))+~P106(f333(f333(f247(x77241),f2(x77241)),x77242)) % 173.51/173.28 [7725]~P130(x77251)+~P106(f333(f333(f247(x77251),x77252),f2(x77251)))+P106(f333(f333(f247(x77251),f333(f333(f88(x77251),x77252),x77253)),f2(x77251)))+~P106(f333(f333(f247(x77251),f2(x77251)),x77253)) % 173.51/173.28 [7726]~P70(x77261)+~P106(f333(f333(f247(x77261),x77263),f2(x77261)))+P106(f333(f333(f247(x77261),f333(f333(f296(x77261),x77262),x77263)),f2(x77261)))+~P106(f333(f333(f247(x77261),f2(x77261)),x77262)) % 173.51/173.28 [7727]~P70(x77271)+~P106(f333(f333(f247(x77271),x77272),f2(x77271)))+P106(f333(f333(f247(x77271),f333(f333(f296(x77271),x77272),x77273)),f2(x77271)))+~P106(f333(f333(f247(x77271),f2(x77271)),x77273)) % 173.51/173.28 [7728]~P69(x77281)+~P106(f333(f333(f247(x77281),x77283),f2(x77281)))+P106(f333(f333(f247(x77281),f333(f333(f296(x77281),x77282),x77283)),f2(x77281)))+~P106(f333(f333(f247(x77281),f2(x77281)),x77282)) % 173.51/173.28 [7729]~P69(x77291)+~P106(f333(f333(f247(x77291),x77292),f2(x77291)))+P106(f333(f333(f247(x77291),f333(f333(f296(x77291),x77292),x77293)),f2(x77291)))+~P106(f333(f333(f247(x77291),f2(x77291)),x77293)) % 173.51/173.28 [7744]P146(x77441,x77442,x77443)+~P106(f333(x77441,x77442))+P106(f333(f333(f247(a1),x77443),f855(x77443,x77442,x77441)))+P106(f333(f333(f247(a1),f856(x77443,x77442,x77441)),x77443)) % 173.51/173.28 [7757]P147(x77571,x77572,x77573)+P106(f333(f333(f247(a1),x77573),f849(x77573,x77572,x77571)))+~P106(f333(x77571,f2(a1)))+P106(f333(f333(f247(a1),f850(x77573,x77572,x77571)),x77573)) % 173.51/173.28 [7807]P147(x78072,x78073,x78071)+E(x78071,f2(a1))+~P106(f333(x78072,f854(x78071,x78073,x78072)))+P106(f333(f333(f247(a1),f850(x78071,x78073,x78072)),x78071)) % 173.51/173.28 [7808]P146(x78082,x78083,x78081)+E(x78081,f2(a1))+~P106(f333(x78082,f855(x78081,x78083,x78082)))+P106(f333(f333(f247(a1),f856(x78081,x78083,x78082)),x78081)) % 173.51/173.28 [7820]P146(x78203,x78202,x78201)+~P106(f333(x78203,x78202))+E(f333(f333(f87(a1),f333(f333(f88(a1),x78201),f858(x78201,x78202,x78203))),f855(x78201,x78202,x78203)),x78202)+P106(f333(f333(f247(a1),f2(a1)),x78201)) % 173.51/173.28 [7836]P147(x78363,x78362,x78361)+E(f333(f333(f87(a1),f333(f333(f88(a1),x78361),f854(x78361,x78362,x78363))),f849(x78361,x78362,x78363)),x78362)+~P106(f333(x78363,f2(a1)))+P106(f333(f333(f247(a1),f2(a1)),x78361)) % 173.51/173.28 [7864]~P106(f333(x78641,x78643))+~P106(f333(f67(x78642),x78643))+P106(f333(f333(f335(x78642),f883(x78641,x78643,x78642)),f882(x78641,x78643,x78642)))+P106(f333(x78641,f196(f917(x78642,a905)))) % 173.51/173.28 [7875]P146(x78751,x78752,x78753)+~P106(f333(x78751,x78752))+~P106(f333(x78751,f855(x78753,x78752,x78751)))+P106(f333(f333(f247(a1),f856(x78753,x78752,x78751)),x78753)) % 173.51/173.28 [7881]P147(x78811,x78812,x78813)+~P106(f333(x78811,f854(x78813,x78812,x78811)))+~P106(f333(x78811,f2(a1)))+P106(f333(f333(f247(a1),f850(x78813,x78812,x78811)),x78813)) % 173.51/173.28 [7985]~P126(x79851)+~P106(f333(f333(f246(x79851),f333(f333(f88(x79851),x79853),x79852)),f2(x79851)))+P106(f333(f333(f246(x79851),x79852),f2(x79851)))+P106(f333(f333(f246(x79851),f2(x79851)),x79852)) % 173.51/173.28 [7986]~P126(x79861)+~P106(f333(f333(f246(x79861),f333(f333(f88(x79861),x79862),x79863)),f2(x79861)))+P106(f333(f333(f246(x79861),x79862),f2(x79861)))+P106(f333(f333(f246(x79861),f2(x79861)),x79862)) % 173.51/173.28 [7987]~P69(x79871)+~P106(f333(f333(f246(x79871),f333(f333(f296(x79871),x79873),x79872)),f2(x79871)))+P106(f333(f333(f246(x79871),x79872),f2(x79871)))+P106(f333(f333(f246(x79871),f2(x79871)),x79872)) % 173.51/173.28 [7988]~P69(x79881)+~P106(f333(f333(f246(x79881),f333(f333(f296(x79881),x79882),x79883)),f2(x79881)))+P106(f333(f333(f246(x79881),x79882),f2(x79881)))+P106(f333(f333(f246(x79881),f2(x79881)),x79882)) % 173.51/173.28 [7989]~P69(x79891)+~P106(f333(f333(f247(x79891),f333(f333(f296(x79891),x79893),x79892)),f2(x79891)))+P106(f333(f333(f247(x79891),x79892),f2(x79891)))+P106(f333(f333(f247(x79891),f2(x79891)),x79892)) % 173.51/173.28 [7990]~P69(x79901)+~P106(f333(f333(f247(x79901),f333(f333(f296(x79901),x79902),x79903)),f2(x79901)))+P106(f333(f333(f247(x79901),x79902),f2(x79901)))+P106(f333(f333(f247(x79901),f2(x79901)),x79902)) % 173.51/173.28 [8014]~P126(x80141)+~P106(f333(f333(f246(x80141),f333(f333(f88(x80141),x80142),x80143)),f2(x80141)))+P106(f333(f333(f246(x80141),f2(x80141)),x80142))+P106(f333(f333(f246(x80141),f2(x80141)),x80143)) % 173.51/173.28 [8015]~P69(x80151)+~P106(f333(f333(f246(x80151),f333(f333(f296(x80151),x80152),x80153)),f2(x80151)))+P106(f333(f333(f246(x80151),f2(x80151)),x80152))+P106(f333(f333(f246(x80151),f2(x80151)),x80153)) % 173.51/173.28 [8016]~P69(x80161)+~P106(f333(f333(f247(x80161),f333(f333(f296(x80161),x80162),x80163)),f2(x80161)))+P106(f333(f333(f247(x80161),f2(x80161)),x80162))+P106(f333(f333(f247(x80161),f2(x80161)),x80163)) % 173.51/173.28 [8038]P147(x80382,x80383,x80381)+E(x80381,f2(a1))+P106(f333(f333(f246(a1),f849(x80381,x80383,x80382)),f2(a1)))+P106(f333(f333(f247(a1),f850(x80381,x80383,x80382)),x80381)) % 173.51/173.28 [8039]P146(x80392,x80393,x80391)+E(x80391,f2(a1))+P106(f333(f333(f246(a1),f855(x80391,x80393,x80392)),f2(a1)))+P106(f333(f333(f247(a1),f856(x80391,x80393,x80392)),x80391)) % 173.51/173.28 [8046]~P119(x80461)+~P106(f333(f333(f247(x80461),x80462),f85(x80461)))+P106(f333(f333(f247(x80461),f333(f333(f256(x80461),x80462),f333(a123,x80463))),f85(x80461)))+~P106(f333(f333(f247(x80461),f2(x80461)),x80462)) % 173.51/173.28 [8100]~P110(x81001)+~E(x81003,f124(x81001))+~P16(x81001,f333(f176(x81001),x81003))+E(f333(f150(x81001,x81001,f333(f7(x81001,x81001,x81001),f245(x81001)),x81002),f333(f176(x81001),x81003)),x81002) % 173.51/173.28 [8103]P146(x81031,x81032,x81033)+~P106(f333(x81031,x81032))+P106(f333(f333(f246(a1),f855(x81033,x81032,x81031)),f2(a1)))+P106(f333(f333(f247(a1),f856(x81033,x81032,x81031)),x81033)) % 173.51/173.28 [8113]P147(x81131,x81132,x81133)+~P106(f333(x81131,f2(a1)))+P106(f333(f333(f246(a1),f849(x81133,x81132,x81131)),f2(a1)))+P106(f333(f333(f247(a1),f850(x81133,x81132,x81131)),x81133)) % 173.51/173.28 [8331]P147(x83313,x83312,x83311)+E(x83311,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x83311),f854(x83311,x83312,x83313))),f849(x83311,x83312,x83313)),x83312)+P106(f333(f333(f247(a1),f850(x83311,x83312,x83313)),x83311)) % 173.51/173.28 [8332]P146(x83323,x83322,x83321)+E(x83321,f2(a1))+E(f333(f333(f87(a1),f333(f333(f88(a1),x83321),f858(x83321,x83322,x83323))),f855(x83321,x83322,x83323)),x83322)+P106(f333(f333(f247(a1),f856(x83321,x83322,x83323)),x83321)) % 173.51/173.28 [8369]P146(x83693,x83692,x83691)+~P106(f333(x83693,x83692))+E(f333(f333(f87(a1),f333(f333(f88(a1),x83691),f858(x83691,x83692,x83693))),f855(x83691,x83692,x83693)),x83692)+P106(f333(f333(f247(a1),f856(x83691,x83692,x83693)),x83691)) % 173.51/173.28 [8370]~P72(x83701)+~P78(x83701)+~P43(x83703)+E(f333(f333(f6(a910,x83701),f333(f333(f8(a1,x83701,a910),x83702),f111(a1))),f333(f316(a1,a910,a115),x83703)),f333(f333(f6(a1,x83701),x83702),x83703)) % 173.51/173.28 [8371]~P72(x83711)+~P78(x83711)+~P43(x83713)+E(f333(f333(f9(a910,x83711),f333(f333(f8(a1,x83711,a910),x83712),f111(a1))),f333(f316(a1,a910,a115),x83713)),f333(f333(f9(a1,x83711),x83712),x83713)) % 173.51/173.28 [8380]P147(x83803,x83802,x83801)+E(f333(f333(f87(a1),f333(f333(f88(a1),x83801),f854(x83801,x83802,x83803))),f849(x83801,x83802,x83803)),x83802)+~P106(f333(x83803,f2(a1)))+P106(f333(f333(f247(a1),f850(x83801,x83802,x83803)),x83801)) % 173.51/173.28 [8403]~E(x84032,f2(a910))+~E(f333(f264(a910,a910),x84033),f2(a910))+~E(x84031,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),x84033)),x84032)),f333(f268(a910,a910),x84033)))+P106(f333(f54(x84031,x84032),x84033)) % 173.51/173.28 [8459]P106(f333(x84591,x84592))+~P106(f333(f333(f335(x84593),f809(x84591,x84592,x84593)),f802(x84591,x84592,x84593)))+~P106(f333(f67(x84593),x84592))+~P106(f333(x84591,f196(f917(x84593,a905)))) % 173.51/173.28 [9106]P106(f333(x91061,x91062))+~P106(f333(f67(x91063),x91062))+~P106(f333(x91061,f333(f333(f315(x91063),f809(x91061,x91062,x91063)),f802(x91061,x91062,x91063))))+~P106(f333(x91061,f196(f917(x91063,a905)))) % 173.51/173.28 [9346]P106(f333(f333(f246(a1),x93461),f2(a1)))+~P106(f333(f333(f247(a1),f333(f333(f87(a1),f333(f333(f88(a1),x93463),x93461)),x93462)),f2(a1)))+~P106(f333(f333(f246(a1),f2(a1)),x93462))+~P106(f333(f333(f247(a1),f2(a1)),x93463)) % 173.51/173.28 [5936]~P2(x59362)+E(x59361,f196(f917(x59362,a905)))+~P106(f333(f67(x59362),x59361))+E(f13(x59362,f333(f333(f315(x59362),x59363),x59361)),f333(f333(f121(x59362),x59363),f13(x59362,x59361))) % 173.51/173.28 [5937]~P2(x59372)+E(x59371,f196(f917(x59372,a905)))+~P106(f333(f67(x59372),x59371))+E(f10(x59372,f333(f333(f315(x59372),x59373),x59371)),f333(f333(f112(x59372),x59373),f10(x59372,x59371))) % 173.51/173.28 [5938]~P110(x59382)+E(x59381,f196(f917(x59382,a905)))+~P106(f333(f67(x59382),x59381))+E(f14(x59382,f333(f333(f315(x59382),x59383),x59381)),f333(f333(f244(x59382),x59383),f14(x59382,x59381))) % 173.51/173.28 [5939]~P110(x59392)+E(x59391,f196(f917(x59392,a905)))+~P106(f333(f67(x59392),x59391))+E(f15(x59392,f333(f333(f315(x59392),x59393),x59391)),f333(f333(f245(x59392),x59393),f15(x59392,x59391))) % 173.51/173.28 [6248]~P126(x62481)+~E(x62483,f2(x62481))+~E(x62482,f2(x62481))+E(f333(f333(f87(x62481),f333(f333(f88(x62481),x62482),x62482)),f333(f333(f88(x62481),x62483),x62483)),f2(x62481)) % 173.51/173.28 [6314]~P97(x63142)+E(x63141,f196(f917(x63142,a905)))+~P106(f333(f67(x63142),x63141))+E(f333(f69(x63142,f88(x63142)),f333(f333(f315(x63142),x63143),x63141)),f333(f333(f88(x63142),x63143),f333(f69(x63142,f88(x63142)),x63141))) % 173.51/173.28 [6439]~P110(x64392)+E(x64391,f196(f917(x64392,a905)))+~P106(f333(f67(x64392),x64391))+E(f11(x64392,f244(x64392),f333(f333(f315(x64392),x64393),x64391)),f333(f333(f244(x64392),x64393),f11(x64392,f244(x64392),x64391))) % 173.51/173.28 [6440]~P110(x64402)+E(x64401,f196(f917(x64402,a905)))+~P106(f333(f67(x64402),x64401))+E(f12(x64402,f245(x64402),f333(f333(f315(x64402),x64403),x64401)),f333(f333(f245(x64402),x64403),f12(x64402,f245(x64402),x64401))) % 173.51/173.28 [6942]~P76(x69421)+~P106(f333(f67(x69421),x69423))+E(f333(f69(x69421,f88(x69421)),f333(f333(f315(x69421),x69422),x69423)),f333(f333(f70(x69421,x69421,f88(x69421)),x69422),x69423))+P106(f333(f333(f335(x69421),x69422),x69423)) % 173.51/173.28 [7020]~E(f333(f333(f87(a1),x70202),f333(f333(f88(a1),x70203),x70201)),x70203)+~P106(f333(f333(f247(a1),f2(a1)),x70203))+P106(f333(f333(f246(a1),f85(a1)),x70201))+~P106(f333(f333(f247(a1),x70202),x70203)) % 173.51/173.28 [7050]~E(f333(f333(f87(a1),x70502),f333(f333(f88(a1),x70503),x70501)),x70503)+P106(f333(f333(f246(a1),x70501),f85(a1)))+~P106(f333(f333(f246(a1),f2(a1)),x70502))+~P106(f333(f333(f247(a1),f2(a1)),x70503)) % 173.51/173.28 [7065]E(x70651,f2(a910))+~P106(f333(f54(x70653,x70651),x70652))+~P106(f333(f333(f247(a910),f2(a910)),x70651))+P106(f333(f333(f247(a910),f333(f268(a910,a910),x70652)),x70651)) % 173.51/173.28 [7095]~P138(x70951)+~P106(f333(f333(f246(x70951),x70952),f2(x70951)))+~P106(f333(f333(f246(x70951),x70953),f2(x70951)))+E(f333(f333(f88(x70951),f333(f82(x70951),x70952)),f333(f82(x70951),x70953)),f333(f82(x70951),f333(f333(f88(x70951),x70952),x70953))) % 173.51/173.28 [7143]~P138(x71431)+~P106(f333(f333(f246(x71431),x71432),f2(x71431)))+E(f333(f333(f88(x71431),f333(f82(x71431),x71432)),f333(f82(x71431),x71433)),f333(f82(x71431),f333(f333(f88(x71431),x71432),x71433)))+~P106(f333(f333(f246(x71431),f2(x71431)),x71433)) % 173.51/173.28 [7144]~P138(x71441)+~P106(f333(f333(f246(x71441),x71443),f2(x71441)))+E(f333(f333(f88(x71441),f333(f82(x71441),x71442)),f333(f82(x71441),x71443)),f333(f82(x71441),f333(f333(f88(x71441),x71442),x71443)))+~P106(f333(f333(f246(x71441),f2(x71441)),x71442)) % 173.51/173.28 [7200]~P138(x72001)+E(f333(f333(f88(x72001),f333(f82(x72001),x72002)),f333(f82(x72001),x72003)),f333(f82(x72001),f333(f333(f88(x72001),x72002),x72003)))+~P106(f333(f333(f246(x72001),f2(x72001)),x72002))+~P106(f333(f333(f246(x72001),f2(x72001)),x72003)) % 173.51/173.28 [7217]~P135(x72171)+~P106(f333(f333(f246(x72171),x72173),f2(x72171)))+~P106(f333(f333(f246(x72171),x72172),f2(x72171)))+P106(f333(f333(f246(x72171),f2(x72171)),f333(f333(f88(x72171),x72172),x72173))) % 173.51/173.28 [7218]~P126(x72181)+~P106(f333(f333(f246(x72181),x72183),f2(x72181)))+~P106(f333(f333(f246(x72181),x72182),f2(x72181)))+P106(f333(f333(f246(x72181),f2(x72181)),f333(f333(f88(x72181),x72182),x72183))) % 173.51/173.28 [7219]~P70(x72191)+~P106(f333(f333(f247(x72191),x72193),f2(x72191)))+~P106(f333(f333(f246(x72191),x72192),f2(x72191)))+P106(f333(f333(f246(x72191),f2(x72191)),f333(f333(f296(x72191),x72192),x72193))) % 173.51/173.28 [7220]~P69(x72201)+~P106(f333(f333(f246(x72201),x72203),f2(x72201)))+~P106(f333(f333(f246(x72201),x72202),f2(x72201)))+P106(f333(f333(f246(x72201),f2(x72201)),f333(f333(f296(x72201),x72202),x72203))) % 173.51/173.28 [7221]~P126(x72211)+~P106(f333(f333(f247(x72211),x72213),f2(x72211)))+~P106(f333(f333(f247(x72211),x72212),f2(x72211)))+P106(f333(f333(f247(x72211),f2(x72211)),f333(f333(f88(x72211),x72212),x72213))) % 173.51/173.28 [7222]~P70(x72221)+~P106(f333(f333(f247(x72221),x72223),f2(x72221)))+~P106(f333(f333(f247(x72221),x72222),f2(x72221)))+P106(f333(f333(f247(x72221),f2(x72221)),f333(f333(f296(x72221),x72222),x72223))) % 173.51/173.28 [7223]~P69(x72231)+~P106(f333(f333(f247(x72231),x72233),f2(x72231)))+~P106(f333(f333(f247(x72231),x72232),f2(x72231)))+P106(f333(f333(f247(x72231),f2(x72231)),f333(f333(f296(x72231),x72232),x72233))) % 173.51/173.28 [7224]~P119(x72241)+~P106(f333(f333(f247(a910),f2(a910)),x72243))+~P106(f333(f333(f247(x72241),f85(x72241)),x72242))+P106(f333(f333(f247(x72241),f85(x72241)),f333(f333(f256(x72241),x72242),x72243))) % 173.51/173.28 [7321]~P134(x73211)+~P106(f333(f333(f246(x73211),f2(x73211)),x73213))+~P106(f333(f333(f246(x73211),f2(x73211)),x73212))+P106(f333(f333(f246(x73211),f2(x73211)),f333(f333(f88(x73211),x73212),x73213))) % 173.51/173.28 [7322]~P135(x73221)+~P106(f333(f333(f246(x73221),f2(x73221)),x73223))+~P106(f333(f333(f246(x73221),f2(x73221)),x73222))+P106(f333(f333(f246(x73221),f2(x73221)),f333(f333(f88(x73221),x73222),x73223))) % 173.51/173.28 [7323]~P126(x73231)+~P106(f333(f333(f246(x73231),f2(x73231)),x73233))+~P106(f333(f333(f246(x73231),f2(x73231)),x73232))+P106(f333(f333(f246(x73231),f2(x73231)),f333(f333(f88(x73231),x73232),x73233))) % 173.51/173.28 [7324]~P70(x73241)+~P106(f333(f333(f247(x73241),f2(x73241)),x73243))+~P106(f333(f333(f246(x73241),f2(x73241)),x73242))+P106(f333(f333(f246(x73241),f2(x73241)),f333(f333(f296(x73241),x73242),x73243))) % 173.51/173.28 [7325]~P69(x73251)+~P106(f333(f333(f246(x73251),f2(x73251)),x73253))+~P106(f333(f333(f246(x73251),f2(x73251)),x73252))+P106(f333(f333(f246(x73251),f2(x73251)),f333(f333(f296(x73251),x73252),x73253))) % 173.51/173.28 [7328]~P90(x73281)+~P106(f333(f333(f247(x73281),f2(x73281)),x73283))+~P106(f333(f333(f247(x73281),f2(x73281)),x73282))+P106(f333(f333(f247(x73281),f2(x73281)),f333(f333(f87(x73281),x73282),x73283))) % 173.51/173.28 [7329]~P130(x73291)+~P106(f333(f333(f247(x73291),f2(x73291)),x73293))+~P106(f333(f333(f247(x73291),f2(x73291)),x73292))+P106(f333(f333(f247(x73291),f2(x73291)),f333(f333(f88(x73291),x73292),x73293))) % 173.51/173.28 [7330]~P70(x73301)+~P106(f333(f333(f247(x73301),f2(x73301)),x73303))+~P106(f333(f333(f247(x73301),f2(x73301)),x73302))+P106(f333(f333(f247(x73301),f2(x73301)),f333(f333(f296(x73301),x73302),x73303))) % 173.51/173.28 [7331]~P69(x73311)+~P106(f333(f333(f247(x73311),f2(x73311)),x73313))+~P106(f333(f333(f247(x73311),f2(x73311)),x73312))+P106(f333(f333(f247(x73311),f2(x73311)),f333(f333(f296(x73311),x73312),x73313))) % 173.51/173.28 [7332]~P119(x73321)+~P106(f333(f333(f247(x73321),f85(x73321)),x73323))+~P106(f333(f333(f247(x73321),f85(x73321)),x73322))+P106(f333(f333(f247(x73321),f85(x73321)),f333(f333(f88(x73321),x73322),x73323))) % 173.51/173.28 [7409]~P2(x74091)+~P106(f333(f67(x74091),x74093))+E(f13(x74091,f333(f333(f315(x74091),x74092),x74093)),x74092)+~E(f333(f333(f23(f917(x74091,a905)),x74093),f333(f333(f315(x74091),x74092),f196(f917(x74091,a905)))),f196(f917(x74091,a905))) % 173.51/173.28 [7410]~P2(x74101)+~P106(f333(f67(x74101),x74103))+E(f10(x74101,f333(f333(f315(x74101),x74102),x74103)),x74102)+~E(f333(f333(f23(f917(x74101,a905)),x74103),f333(f333(f315(x74101),x74102),f196(f917(x74101,a905)))),f196(f917(x74101,a905))) % 173.51/173.28 [7411]~P110(x74111)+~P106(f333(f67(x74111),x74113))+E(f14(x74111,f333(f333(f315(x74111),x74112),x74113)),x74112)+~E(f333(f333(f23(f917(x74111,a905)),x74113),f333(f333(f315(x74111),x74112),f196(f917(x74111,a905)))),f196(f917(x74111,a905))) % 173.51/173.28 [7412]~P110(x74121)+~P106(f333(f67(x74121),x74123))+E(f15(x74121,f333(f333(f315(x74121),x74122),x74123)),x74122)+~E(f333(f333(f23(f917(x74121,a905)),x74123),f333(f333(f315(x74121),x74122),f196(f917(x74121,a905)))),f196(f917(x74121,a905))) % 173.51/173.28 [7414]~P126(x74141)+P106(f333(f333(f246(x74141),x74142),f2(x74141)))+P106(f333(f333(f246(x74141),f2(x74141)),x74143))+~P106(f333(f333(f246(x74141),f2(x74141)),f333(f333(f88(x74141),x74143),x74142))) % 173.51/173.28 [7415]~P126(x74151)+P106(f333(f333(f246(x74151),x74152),f2(x74151)))+P106(f333(f333(f246(x74151),f2(x74151)),x74153))+~P106(f333(f333(f246(x74151),f2(x74151)),f333(f333(f88(x74151),x74152),x74153))) % 173.51/173.28 [7416]~P69(x74161)+P106(f333(f333(f246(x74161),x74162),f2(x74161)))+P106(f333(f333(f246(x74161),f2(x74161)),x74163))+~P106(f333(f333(f246(x74161),f2(x74161)),f333(f333(f296(x74161),x74163),x74162))) % 173.51/173.28 [7417]~P69(x74171)+P106(f333(f333(f246(x74171),x74172),f2(x74171)))+P106(f333(f333(f246(x74171),f2(x74171)),x74173))+~P106(f333(f333(f246(x74171),f2(x74171)),f333(f333(f296(x74171),x74172),x74173))) % 173.51/173.28 [7418]~P126(x74181)+P106(f333(f333(f246(x74181),x74182),f2(x74181)))+P106(f333(f333(f246(x74181),f2(x74181)),x74182))+~P106(f333(f333(f246(x74181),f2(x74181)),f333(f333(f88(x74181),x74183),x74182))) % 173.51/173.28 [7419]~P126(x74191)+P106(f333(f333(f246(x74191),x74192),f2(x74191)))+P106(f333(f333(f246(x74191),f2(x74191)),x74192))+~P106(f333(f333(f246(x74191),f2(x74191)),f333(f333(f88(x74191),x74192),x74193))) % 173.51/173.28 [7420]~P69(x74201)+P106(f333(f333(f246(x74201),x74202),f2(x74201)))+P106(f333(f333(f246(x74201),f2(x74201)),x74202))+~P106(f333(f333(f246(x74201),f2(x74201)),f333(f333(f296(x74201),x74203),x74202))) % 173.51/173.28 [7421]~P69(x74211)+P106(f333(f333(f246(x74211),x74212),f2(x74211)))+P106(f333(f333(f246(x74211),f2(x74211)),x74212))+~P106(f333(f333(f246(x74211),f2(x74211)),f333(f333(f296(x74211),x74212),x74213))) % 173.51/173.28 [7422]~P69(x74221)+P106(f333(f333(f247(x74221),x74222),f2(x74221)))+P106(f333(f333(f247(x74221),f2(x74221)),x74223))+~P106(f333(f333(f247(x74221),f2(x74221)),f333(f333(f296(x74221),x74223),x74222))) % 173.51/173.28 [7423]~P69(x74231)+P106(f333(f333(f247(x74231),x74232),f2(x74231)))+P106(f333(f333(f247(x74231),f2(x74231)),x74233))+~P106(f333(f333(f247(x74231),f2(x74231)),f333(f333(f296(x74231),x74232),x74233))) % 173.51/173.28 [7424]~P69(x74241)+P106(f333(f333(f247(x74241),x74242),f2(x74241)))+P106(f333(f333(f247(x74241),f2(x74241)),x74242))+~P106(f333(f333(f247(x74241),f2(x74241)),f333(f333(f296(x74241),x74243),x74242))) % 173.51/173.28 [7425]~P69(x74251)+P106(f333(f333(f247(x74251),x74252),f2(x74251)))+P106(f333(f333(f247(x74251),f2(x74251)),x74252))+~P106(f333(f333(f247(x74251),f2(x74251)),f333(f333(f296(x74251),x74252),x74253))) % 173.51/173.28 [7511]~E(f333(f333(f112(f917(x75111,a905)),f333(f180(x75111),x75112)),f333(f180(x75111),x75113)),f196(f917(x75111,a905)))+~P106(f333(f145(x75111),x75113))+~P106(f333(f145(x75111),x75112))+P106(f333(f145(x75111),f333(f333(f142(x75111),x75112),x75113))) % 173.51/173.28 [7512]~P110(x75121)+~P106(f333(f67(x75121),x75123))+E(f11(x75121,f244(x75121),f333(f333(f315(x75121),x75122),x75123)),x75122)+~E(f333(f333(f23(f917(x75121,a905)),x75123),f333(f333(f315(x75121),x75122),f196(f917(x75121,a905)))),f196(f917(x75121,a905))) % 173.51/173.28 [7513]~P110(x75131)+~P106(f333(f67(x75131),x75133))+E(f12(x75131,f245(x75131),f333(f333(f315(x75131),x75132),x75133)),x75132)+~E(f333(f333(f23(f917(x75131,a905)),x75133),f333(f333(f315(x75131),x75132),f196(f917(x75131,a905)))),f196(f917(x75131,a905))) % 173.51/173.28 [7527]~P87(x75271)+~P106(f333(f333(f246(x75271),x75272),x75273))+~P106(f333(f333(f246(x75271),f333(f86(x75271),x75272)),x75273))+P106(f333(f333(f246(x75271),f333(f82(x75271),x75272)),x75273)) % 173.51/173.28 [7528]~P120(x75281)+~P106(f333(f333(f247(x75281),x75282),x75283))+~P106(f333(f333(f247(x75281),f333(f86(x75281),x75282)),x75283))+P106(f333(f333(f247(x75281),f333(f82(x75281),x75282)),x75283)) % 173.51/173.28 [7596]~P130(x75961)+P106(f333(f333(f247(x75961),f2(x75961)),x75962))+~P106(f333(f333(f247(x75961),f2(x75961)),x75963))+~P106(f333(f333(f247(x75961),f2(x75961)),f333(f333(f88(x75961),x75963),x75962))) % 173.51/173.28 [7597]~P130(x75971)+P106(f333(f333(f247(x75971),f2(x75971)),x75972))+~P106(f333(f333(f247(x75971),f2(x75971)),x75973))+~P106(f333(f333(f247(x75971),f2(x75971)),f333(f333(f88(x75971),x75972),x75973))) % 173.51/173.28 [7897]E(x78971,x78972)+~P106(f333(f67(x78973),x78971))+~P106(f333(f333(f246(a910),f333(f41(x78973),x78971)),f333(f41(x78973),x78972)))+~P106(f333(f333(f246(f917(x78973,a905)),x78972),x78971)) % 173.51/173.28 [8043]~P106(f333(f333(f247(a1),x80431),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x80432))+~P106(f333(f333(f246(a1),x80432),x80433))+P106(f333(f333(f246(a1),f333(f333(f42(a1),x80431),x80432)),f333(f333(f42(a1),x80431),x80433))) % 173.51/173.28 [8053]~P106(f333(f333(f246(a1),f2(a1)),x80531))+~P106(f333(f333(f247(a1),f2(a1)),x80533))+~P106(f333(f333(f246(a1),x80533),x80532))+P106(f333(f333(f246(a1),f333(f333(f42(a1),x80531),x80532)),f333(f333(f42(a1),x80531),x80533))) % 173.51/173.28 [8194]E(f333(x81941,f456(x81942,x81941,x81943)),x81942)+~P106(f333(f333(f246(a1),x81942),f333(x81941,x81943)))+P106(f333(f333(f247(a910),f457(x81942,x81941,x81943)),x81943))+~P106(f333(f333(f246(a1),f333(x81941,f2(a910))),x81942)) % 173.51/173.28 [8195]E(f333(x81951,f463(x81952,x81951,x81953)),x81952)+~P106(f333(f333(f246(a1),x81952),f333(x81951,x81953)))+P106(f333(f333(f247(a910),f464(x81952,x81951,x81953)),x81953))+~P106(f333(f333(f246(a1),f333(x81951,f2(a910))),x81952)) % 173.51/173.28 [8294]~P106(f333(f67(x82941),x82943))+~P106(f333(f333(f247(a910),f333(f41(x82941),x82942)),f333(f41(x82941),x82943)))+~P106(f333(f333(f246(f917(x82941,a905)),x82942),x82943))+P106(f333(f333(f247(f917(x82941,a905)),x82942),x82943)) % 173.51/173.28 [8321]E(f333(f333(f87(a1),f390(x83213,x83211,x83212)),f391(x83213,x83211,x83212)),x83211)+E(f333(f333(f23(a1),x83211),x83212),x83211)+~P106(f333(f333(f247(a1),f2(a1)),x83212))+~P106(f333(f333(f335(a1),f333(f333(f23(a1),x83211),f85(a1))),x83213)) % 173.51/173.28 [8322]E(f333(f333(f23(a1),f405(x83223,x83221,x83222)),f406(x83223,x83221,x83222)),x83221)+E(f333(f333(f87(a1),x83221),x83222),x83221)+~P106(f333(f333(f247(a1),f2(a1)),x83222))+~P106(f333(f333(f335(a1),f333(f333(f87(a1),x83221),f85(a1))),x83223)) % 173.51/173.28 [8375]~P106(f333(f333(f246(a910),x83753),x83751))+P106(f333(f333(f246(a910),x83751),x83752))+~P106(f333(f333(f246(a910),x83753),x83752))+~P106(f333(f333(f246(a910),f333(f333(f23(a910),x83751),x83753)),f333(f333(f23(a910),x83752),x83753))) % 173.51/173.28 [8376]~P106(f333(f333(f246(a910),x83763),x83761))+P106(f333(f333(f247(a910),x83761),x83762))+~P106(f333(f333(f246(a910),x83763),x83762))+~P106(f333(f333(f247(a910),f333(f333(f23(a910),x83761),x83763)),f333(f333(f23(a910),x83762),x83763))) % 173.51/173.28 [8395]~P110(x83952)+E(x83951,f124(x83952))+~P16(x83952,f333(f176(x83952),x83951))+E(f333(f150(x83952,x83952,f333(f7(x83952,x83952,x83952),f245(x83952)),x83953),f333(f176(x83952),x83951)),f333(f333(f245(x83952),f333(f333(f172(x83952),x83951),f2(a910))),x83953)) % 173.51/173.28 [8464]E(f333(f333(f23(a1),x84641),x84642),x84641)+~P106(f333(f333(f247(a1),f2(a1)),x84642))+P106(f333(f333(f335(a1),f390(x84643,x84641,x84642)),x84643))+~P106(f333(f333(f335(a1),f333(f333(f23(a1),x84641),f85(a1))),x84643)) % 173.51/173.28 [8465]E(f333(f333(f87(a1),x84651),x84652),x84651)+~P106(f333(f333(f247(a1),f2(a1)),x84652))+P106(f333(f333(f335(a1),f405(x84653,x84651,x84652)),x84653))+~P106(f333(f333(f335(a1),f333(f333(f87(a1),x84651),f85(a1))),x84653)) % 173.51/173.28 [8539]~P106(f333(f333(f246(a1),x85391),f333(x85392,x85393)))+P106(f333(f333(f247(a910),f457(x85391,x85392,x85393)),x85393))+P106(f333(f333(f246(a910),f456(x85391,x85392,x85393)),x85393))+~P106(f333(f333(f246(a1),f333(x85392,f2(a910))),x85391)) % 173.51/173.28 [8540]~P106(f333(f333(f246(a1),x85401),f333(x85402,x85403)))+P106(f333(f333(f247(a910),f464(x85401,x85402,x85403)),x85403))+P106(f333(f333(f246(a910),f463(x85401,x85402,x85403)),x85403))+~P106(f333(f333(f246(a1),f333(x85402,f2(a910))),x85401)) % 173.51/173.28 [8620]E(f333(f333(f23(a1),x86201),x86202),x86201)+~P106(f333(f333(f247(a1),f2(a1)),x86202))+P106(f333(f333(f335(a1),f391(x86203,x86201,x86202)),f309(a1,f85(a1),x86202)))+~P106(f333(f333(f335(a1),f333(f333(f23(a1),x86201),f85(a1))),x86203)) % 173.51/173.28 [8621]E(f333(f333(f87(a1),x86211),x86212),x86211)+~P106(f333(f333(f247(a1),f2(a1)),x86212))+P106(f333(f333(f335(a1),f406(x86213,x86211,x86212)),f309(a1,f85(a1),x86212)))+~P106(f333(f333(f335(a1),f333(f333(f87(a1),x86211),f85(a1))),x86213)) % 173.51/173.28 [8755]~P119(x87551)+~P106(f333(f333(f247(x87551),x87552),f85(x87551)))+~P106(f333(f333(f247(x87551),f2(x87551)),x87552))+P106(f333(f333(f247(x87551),f333(f333(f88(x87551),x87552),f333(f333(f256(x87551),x87552),x87553))),f333(f333(f256(x87551),x87552),x87553))) % 173.51/173.28 [8849]~P106(f333(x88491,x88492))+P106(f333(x88491,f2(a910)))+~P106(f333(f333(f247(a910),x88492),x88493))+~P106(f333(x88491,f51(a910,f333(a123,f526(x88492,x88491,x88493)),x88493))) % 173.51/173.28 [9000]E(f553(x90001,x90002,x90003),f2(a910))+P106(f333(f333(x90001,x90003),x90002))+P106(f333(f333(x90001,f553(x90001,x90002,x90003)),f51(a910,f552(x90001,x90002,x90003),f553(x90001,x90002,x90003))))+~P106(f333(f321(f916(a910,a910),a231),f333(f333(f265(a910,a910),x90003),x90002))) % 173.51/173.28 [9039]~P27(x90391,x90391,x90392,x90393)+E(f333(f316(x90391,x90391,x90392),x90393),x90393)+~P106(f333(f67(x90391),x90393))+~P106(f333(f333(f246(f917(x90391,a905)),f333(f316(x90391,x90391,x90392),x90393)),x90393)) % 173.51/173.28 [9272]P106(f333(f333(x92721,x92722),x92723))+P106(f333(f333(f247(a1),f818(x92721,x92723,x92722)),f819(x92721,x92723,x92722)))+P106(f333(f333(x92721,f818(x92721,x92723,x92722)),f333(f333(f87(a1),f819(x92721,x92723,x92722)),f85(a1))))+~P106(f333(f321(f916(a1,a1),a141),f333(f333(f265(a1,a1),x92722),x92723))) % 173.51/173.28 [9290]P106(f333(f333(x92901,x92902),x92903))+~P106(f333(f333(f247(a1),f550(x92901,x92903,x92902)),f2(a1)))+P106(f333(f333(x92901,f333(f86(a1),f549(x92901,x92903,x92902))),f333(f86(a1),f550(x92901,x92903,x92902))))+~P106(f333(f321(f916(a1,a1),a233),f333(f333(f265(a1,a1),x92902),x92903))) % 173.51/173.28 [9483]P106(f333(f333(x94831,x94832),x94833))+P106(f333(f333(x94831,f333(f333(f87(a1),f722(x94831,x94833,x94832)),f85(a1))),f723(x94831,x94833,x94832)))+~P106(f333(f333(f246(a1),f722(x94831,x94833,x94832)),f723(x94831,x94833,x94832)))+~P106(f333(f321(f916(a1,a1),a190),f333(f333(f265(a1,a1),x94832),x94833))) % 173.51/173.28 [9929]~P7(x99292)+~P7(x99291)+~P106(f333(f63(f916(x99291,x99292)),x99293))+P106(f333(f63(x99291),f333(f333(f8(f917(x99292,a905),a905,x99291),f63(x99292)),f333(f333(f8(f917(x99292,f916(x99291,x99292)),f917(x99292,a905),x99291),f333(f8(f916(x99291,x99292),a905,x99292),x99293)),f265(x99291,x99292))))) % 173.51/173.28 [9930]~P7(x99302)+~P7(x99301)+~P106(f333(f62(f916(x99301,x99302)),x99303))+P106(f333(f62(x99301),f333(f333(f8(f917(x99302,a905),a905,x99301),f62(x99302)),f333(f333(f8(f917(x99302,f916(x99301,x99302)),f917(x99302,a905),x99301),f333(f8(f916(x99301,x99302),a905,x99302),x99303)),f265(x99301,x99302))))) % 173.51/173.28 [10021]~P7(x100212)+~P7(x100211)+P106(f333(f63(f916(x100211,x100212)),x100213))+~P106(f333(f63(x100211),f333(f333(f8(f917(x100212,a905),a905,x100211),f63(x100212)),f333(f333(f8(f917(x100212,f916(x100211,x100212)),f917(x100212,a905),x100211),f333(f8(f916(x100211,x100212),a905,x100212),x100213)),f265(x100211,x100212))))) % 173.51/173.28 [10022]~P7(x100222)+~P7(x100221)+P106(f333(f62(f916(x100221,x100222)),x100223))+~P106(f333(f62(x100221),f333(f333(f8(f917(x100222,a905),a905,x100221),f62(x100222)),f333(f333(f8(f917(x100222,f916(x100221,x100222)),f917(x100222,a905),x100221),f333(f8(f916(x100221,x100222),a905,x100222),x100223)),f265(x100221,x100222))))) % 173.51/173.28 [10193]E(f333(x101931,f456(x101932,x101931,x101933)),x101932)+~P106(f333(f333(f246(a1),x101932),f333(x101931,x101933)))+~P106(f333(f333(f246(a1),f333(f82(a1),f333(f333(f23(a1),f333(x101931,f333(f333(f87(a910),f457(x101932,x101931,x101933)),f85(a910)))),f333(x101931,f457(x101932,x101931,x101933))))),f85(a1)))+~P106(f333(f333(f246(a1),f333(x101931,f2(a910))),x101932)) % 173.51/173.28 [10194]E(f333(x101941,f463(x101942,x101941,x101943)),x101942)+~P106(f333(f333(f246(a1),x101942),f333(x101941,x101943)))+~P106(f333(f333(f246(a1),f333(f82(a1),f333(f333(f23(a1),f333(x101941,f333(f333(f87(a910),f464(x101942,x101941,x101943)),f85(a910)))),f333(x101941,f464(x101942,x101941,x101943))))),f85(a1)))+~P106(f333(f333(f246(a1),f333(x101941,f2(a910))),x101942)) % 173.51/173.28 [10197]~P106(f333(f333(f246(a1),x101971),f333(x101972,x101973)))+~P106(f333(f333(f246(a1),f333(f82(a1),f333(f333(f23(a1),f333(x101972,f333(f333(f87(a910),f457(x101971,x101972,x101973)),f85(a910)))),f333(x101972,f457(x101971,x101972,x101973))))),f85(a1)))+P106(f333(f333(f246(a910),f456(x101971,x101972,x101973)),x101973))+~P106(f333(f333(f246(a1),f333(x101972,f2(a910))),x101971)) % 173.51/173.28 [10198]~P106(f333(f333(f246(a1),x101981),f333(x101982,x101983)))+~P106(f333(f333(f246(a1),f333(f82(a1),f333(f333(f23(a1),f333(x101982,f333(f333(f87(a910),f464(x101981,x101982,x101983)),f85(a910)))),f333(x101982,f464(x101981,x101982,x101983))))),f85(a1)))+P106(f333(f333(f246(a910),f463(x101981,x101982,x101983)),x101983))+~P106(f333(f333(f246(a1),f333(x101982,f2(a910))),x101981)) % 173.51/173.28 [10254]E(x102541,x102542)+~E(f333(f150(f911(x102543),f911(x102543),f142(x102543),f124(x102543)),x102541),f333(f150(f911(x102543),f911(x102543),f142(x102543),f124(x102543)),x102542))+~E(f333(f197(f911(f911(x102543))),x102541),f333(f197(f911(f911(x102543))),x102542))+~P106(f333(f333(f269(f911(x102543),f911(x102543),a905),f333(f333(f7(f911(x102543),f917(f911(x102543),a910),f917(f911(x102543),a905)),f333(f333(f8(f917(a910,a905),f917(f917(f911(x102543),a910),f917(f911(x102543),a905)),f911(x102543)),f8(a910,a905,f911(x102543))),f333(f333(f8(a910,f917(a910,a905),f911(x102543)),a330),f197(f911(x102543))))),f197(f911(x102543)))),f749(x102541,x102542,x102543))) % 173.51/173.28 [10255]E(x102551,x102552)+~E(f333(f150(f911(x102553),f911(x102553),f142(x102553),f124(x102553)),x102551),f333(f150(f911(x102553),f911(x102553),f142(x102553),f124(x102553)),x102552))+~E(f333(f197(f911(f911(x102553))),x102551),f333(f197(f911(f911(x102553))),x102552))+~P106(f333(f333(f269(f911(x102553),f911(x102553),a905),f333(f333(f7(f911(x102553),f917(f911(x102553),a910),f917(f911(x102553),a905)),f333(f333(f8(f917(a910,a905),f917(f917(f911(x102553),a910),f917(f911(x102553),a905)),f911(x102553)),f8(a910,a905,f911(x102553))),f333(f333(f8(a910,f917(a910,a905),f911(x102553)),a330),f197(f911(x102553))))),f197(f911(x102553)))),f750(x102552,x102551,x102553))) % 173.51/173.28 [6930]~E(f85(a910),f2(a910))+~P106(f333(f67(x69301),x69303))+~P106(f333(f67(x69301),x69302))+E(f333(f333(f87(a910),f333(f41(x69301),x69302)),f333(f41(x69301),x69303)),f333(f41(x69301),f333(f333(f121(f917(x69301,a905)),x69302),x69303))) % 173.51/173.28 [7339]~P102(x73391)+~P106(f333(f67(x73391),x73392))+~P106(f333(f333(f335(x73391),x73393),x73392))+P106(f333(f333(f246(x73391),f333(f69(x73391,f112(x73391)),x73392)),x73393)) % 173.51/173.28 [7340]~P110(x73401)+~P106(f333(f67(x73401),x73402))+~P106(f333(f333(f335(x73401),x73403),x73402))+P106(f333(f333(f246(x73401),f333(f69(x73401,f244(x73401)),x73402)),x73403)) % 173.51/173.28 [7590]~P106(f333(f67(x75901),x75903))+~P106(f333(f67(x75901),x75902))+~E(f333(f333(f112(f917(x75901,a905)),x75902),x75903),f196(f917(x75901,a905)))+E(f333(f333(f87(a910),f333(f41(x75901),x75902)),f333(f41(x75901),x75903)),f333(f41(x75901),f333(f333(f121(f917(x75901,a905)),x75902),x75903))) % 173.51/173.28 [8381]~P40(x83811,x83813)+~P40(x83811,x83812)+~E(f333(f333(f112(f917(x83811,a905)),f333(f263(x83811,x83811),x83812)),f333(f291(x83811,x83811),x83813)),f196(f917(x83811,a905)))+P40(x83811,f333(f333(f121(f917(f916(x83811,x83811),a905)),x83812),x83813)) % 173.51/173.28 [8476]E(x84761,f333(f333(f42(a910),x84762),x84763))+~P106(f333(f333(f247(a910),f2(a910)),x84763))+~P106(f333(f333(f247(a910),x84762),f333(f333(f88(a910),x84763),f333(a123,x84761))))+~P106(f333(f333(f246(a910),f333(f333(f88(a910),x84763),x84761)),x84762)) % 173.51/173.28 [8618]~P106(f333(f67(x86181),x86182))+~P106(f333(f67(x86181),x86183))+E(f333(f333(f87(a910),f333(f41(x86181),x86182)),f333(f41(x86181),x86183)),f333(f41(x86181),f333(f333(f121(f917(x86181,a905)),x86182),x86183)))+P106(f333(f333(f335(x86181),f357(x86183,x86182,x86181)),f333(f333(f112(f917(x86181,a905)),x86182),x86183))) % 173.51/173.28 [9012]~P126(x90122)+~E(x90121,f2(x90122))+~E(x90123,f2(x90122))+~P106(f333(f333(f247(x90122),f2(x90122)),f333(f333(f87(x90122),f333(f333(f88(x90122),x90123),x90123)),f333(f333(f88(x90122),x90121),x90121)))) % 173.51/173.28 [9562]~P40(x95621,x95623)+~P40(x95621,x95622)+P40(x95621,f333(f333(f121(f917(f916(x95621,x95621),a905)),x95622),x95623))+~P106(f333(f333(f246(f917(f916(x95621,x95621),a905)),f333(f333(f295(x95621,x95621,x95621),x95622),x95623)),x95622)) % 173.51/173.28 [9701]~P106(f333(x97011,x97013))+~P106(f333(f67(x97012),x97013))+P106(f333(x97011,f196(f917(x97012,a905))))+~P106(f333(x97011,f333(f333(f23(f917(x97012,a905)),f882(x97011,x97013,x97012)),f333(f333(f315(x97012),f883(x97011,x97013,x97012)),f196(f917(x97012,a905)))))) % 173.51/173.28 [8796]~P106(f333(f333(f247(a1),f2(a1)),x87963))+P106(f333(f333(f246(a1),f2(a1)),x87961))+~P106(f333(f333(f247(a1),x87962),x87963))+~P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),f333(f333(f88(a1),x87963),x87961)),x87962))) % 173.51/173.28 [8820]~P2(x88201)+~P106(f333(f67(x88201),x88202))+E(f333(f333(f23(f917(x88201,a905)),x88202),f333(f333(f315(x88201),x88203),f196(f917(x88201,a905)))),f196(f917(x88201,a905)))+E(f333(f333(f121(x88201),x88203),f13(x88201,f333(f333(f23(f917(x88201,a905)),x88202),f333(f333(f315(x88201),x88203),f196(f917(x88201,a905)))))),f13(x88201,f333(f333(f315(x88201),x88203),x88202))) % 173.51/173.28 [8821]~P2(x88211)+~P106(f333(f67(x88211),x88212))+E(f333(f333(f23(f917(x88211,a905)),x88212),f333(f333(f315(x88211),x88213),f196(f917(x88211,a905)))),f196(f917(x88211,a905)))+E(f333(f333(f112(x88211),x88213),f10(x88211,f333(f333(f23(f917(x88211,a905)),x88212),f333(f333(f315(x88211),x88213),f196(f917(x88211,a905)))))),f10(x88211,f333(f333(f315(x88211),x88213),x88212))) % 173.51/173.28 [8822]~P110(x88221)+~P106(f333(f67(x88221),x88222))+E(f333(f333(f23(f917(x88221,a905)),x88222),f333(f333(f315(x88221),x88223),f196(f917(x88221,a905)))),f196(f917(x88221,a905)))+E(f333(f333(f244(x88221),x88223),f14(x88221,f333(f333(f23(f917(x88221,a905)),x88222),f333(f333(f315(x88221),x88223),f196(f917(x88221,a905)))))),f14(x88221,f333(f333(f315(x88221),x88223),x88222))) % 173.51/173.28 [8823]~P110(x88231)+~P106(f333(f67(x88231),x88232))+E(f333(f333(f23(f917(x88231,a905)),x88232),f333(f333(f315(x88231),x88233),f196(f917(x88231,a905)))),f196(f917(x88231,a905)))+E(f333(f333(f245(x88231),x88233),f15(x88231,f333(f333(f23(f917(x88231,a905)),x88232),f333(f333(f315(x88231),x88233),f196(f917(x88231,a905)))))),f15(x88231,f333(f333(f315(x88231),x88233),x88232))) % 173.51/173.28 [8894]~P110(x88941)+~P106(f333(f67(x88941),x88942))+E(f333(f333(f23(f917(x88941,a905)),x88942),f333(f333(f315(x88941),x88943),f196(f917(x88941,a905)))),f196(f917(x88941,a905)))+E(f333(f333(f244(x88941),x88943),f11(x88941,f244(x88941),f333(f333(f23(f917(x88941,a905)),x88942),f333(f333(f315(x88941),x88943),f196(f917(x88941,a905)))))),f11(x88941,f244(x88941),f333(f333(f315(x88941),x88943),x88942))) % 173.51/173.28 [8895]~P110(x88951)+~P106(f333(f67(x88951),x88952))+E(f333(f333(f23(f917(x88951,a905)),x88952),f333(f333(f315(x88951),x88953),f196(f917(x88951,a905)))),f196(f917(x88951,a905)))+E(f333(f333(f245(x88951),x88953),f12(x88951,f245(x88951),f333(f333(f23(f917(x88951,a905)),x88952),f333(f333(f315(x88951),x88953),f196(f917(x88951,a905)))))),f12(x88951,f245(x88951),f333(f333(f315(x88951),x88953),x88952))) % 173.51/173.28 [9502]E(x95021,x95022)+~E(f333(f150(f911(x95023),f911(x95023),f142(x95023),f124(x95023)),x95021),f333(f150(f911(x95023),f911(x95023),f142(x95023),f124(x95023)),x95022))+~E(f333(f197(f911(f911(x95023))),x95021),f333(f197(f911(f911(x95023))),x95022))+P106(f333(f333(f335(f916(f911(x95023),f911(x95023))),f749(x95021,x95022,x95023)),f333(f180(f916(f911(x95023),f911(x95023))),f333(f333(f189(f911(x95023),f911(x95023)),x95022),x95021)))) % 173.51/173.28 [9503]E(x95031,x95032)+~E(f333(f150(f911(x95033),f911(x95033),f142(x95033),f124(x95033)),x95031),f333(f150(f911(x95033),f911(x95033),f142(x95033),f124(x95033)),x95032))+~E(f333(f197(f911(f911(x95033))),x95031),f333(f197(f911(f911(x95033))),x95032))+P106(f333(f333(f335(f916(f911(x95033),f911(x95033))),f750(x95032,x95031,x95033)),f333(f180(f916(f911(x95033),f911(x95033))),f333(f333(f189(f911(x95033),f911(x95033)),x95031),x95032)))) % 173.51/173.28 [10354]~P99(x103542)+E(x103541,f196(f917(x103542,a905)))+~P106(f333(f67(x103542),x103541))+E(f10(x103542,f333(f252(x103542),f333(f333(f8(f917(x103542,a905),a905,x103542),f94(x103542)),f333(f333(f7(x103542,f917(x103542,a905),f917(x103542,a905)),f333(f333(f8(f917(x103542,f917(a905,a905)),f917(f917(x103542,a905),f917(x103542,a905)),x103542),f18(x103542,a905,a905)),f333(f333(f8(f917(x103542,a905),f917(x103542,f917(a905,a905)),x103542),f333(f8(a905,f917(a905,a905),x103542),a331)),f333(f333(f7(x103542,f917(x103542,x103542),f917(x103542,a905)),f333(f333(f8(f917(x103542,a905),f917(f917(x103542,x103542),f917(x103542,a905)),x103542),f8(x103542,a905,x103542)),a330)),f333(f121(x103542),x103543))))),f333(f333(f7(x103542,f917(x103542,a905),a905),f335(x103542)),x103541))))),f333(f333(f121(x103542),x103543),f10(x103542,x103541))) % 173.51/173.28 [10355]~P99(x103552)+E(x103551,f196(f917(x103552,a905)))+~P106(f333(f67(x103552),x103551))+E(f13(x103552,f333(f252(x103552),f333(f333(f8(f917(x103552,a905),a905,x103552),f94(x103552)),f333(f333(f7(x103552,f917(x103552,a905),f917(x103552,a905)),f333(f333(f8(f917(x103552,f917(a905,a905)),f917(f917(x103552,a905),f917(x103552,a905)),x103552),f18(x103552,a905,a905)),f333(f333(f8(f917(x103552,a905),f917(x103552,f917(a905,a905)),x103552),f333(f8(a905,f917(a905,a905),x103552),a331)),f333(f333(f7(x103552,f917(x103552,x103552),f917(x103552,a905)),f333(f333(f8(f917(x103552,a905),f917(f917(x103552,x103552),f917(x103552,a905)),x103552),f8(x103552,a905,x103552)),a330)),f333(f112(x103552),x103553))))),f333(f333(f7(x103552,f917(x103552,a905),a905),f335(x103552)),x103551))))),f333(f333(f112(x103552),x103553),f13(x103552,x103551))) % 173.51/173.28 [10356]~P79(x103562)+E(x103561,f196(f917(x103562,a905)))+~P106(f333(f67(x103562),x103561))+E(f14(x103562,f333(f252(x103562),f333(f333(f8(f917(x103562,a905),a905,x103562),f94(x103562)),f333(f333(f7(x103562,f917(x103562,a905),f917(x103562,a905)),f333(f333(f8(f917(x103562,f917(a905,a905)),f917(f917(x103562,a905),f917(x103562,a905)),x103562),f18(x103562,a905,a905)),f333(f333(f8(f917(x103562,a905),f917(x103562,f917(a905,a905)),x103562),f333(f8(a905,f917(a905,a905),x103562),a331)),f333(f333(f7(x103562,f917(x103562,x103562),f917(x103562,a905)),f333(f333(f8(f917(x103562,a905),f917(f917(x103562,x103562),f917(x103562,a905)),x103562),f8(x103562,a905,x103562)),a330)),f333(f87(x103562),x103563))))),f333(f333(f7(x103562,f917(x103562,a905),a905),f335(x103562)),x103561))))),f333(f333(f87(x103562),x103563),f14(x103562,x103561))) % 173.51/173.28 [10357]~P79(x103572)+E(x103571,f196(f917(x103572,a905)))+~P106(f333(f67(x103572),x103571))+E(f15(x103572,f333(f252(x103572),f333(f333(f8(f917(x103572,a905),a905,x103572),f94(x103572)),f333(f333(f7(x103572,f917(x103572,a905),f917(x103572,a905)),f333(f333(f8(f917(x103572,f917(a905,a905)),f917(f917(x103572,a905),f917(x103572,a905)),x103572),f18(x103572,a905,a905)),f333(f333(f8(f917(x103572,a905),f917(x103572,f917(a905,a905)),x103572),f333(f8(a905,f917(a905,a905),x103572),a331)),f333(f333(f7(x103572,f917(x103572,x103572),f917(x103572,a905)),f333(f333(f8(f917(x103572,a905),f917(f917(x103572,x103572),f917(x103572,a905)),x103572),f8(x103572,a905,x103572)),a330)),f333(f87(x103572),x103573))))),f333(f333(f7(x103572,f917(x103572,a905),a905),f335(x103572)),x103571))))),f333(f333(f87(x103572),x103573),f15(x103572,x103571))) % 173.51/173.28 [10358]~P110(x103582)+E(x103581,f196(f917(x103582,a905)))+~P106(f333(f67(x103582),x103581))+E(f12(x103582,f245(x103582),f333(f252(x103582),f333(f333(f8(f917(x103582,a905),a905,x103582),f94(x103582)),f333(f333(f7(x103582,f917(x103582,a905),f917(x103582,a905)),f333(f333(f8(f917(x103582,f917(a905,a905)),f917(f917(x103582,a905),f917(x103582,a905)),x103582),f18(x103582,a905,a905)),f333(f333(f8(f917(x103582,a905),f917(x103582,f917(a905,a905)),x103582),f333(f8(a905,f917(a905,a905),x103582),a331)),f333(f333(f7(x103582,f917(x103582,x103582),f917(x103582,a905)),f333(f333(f8(f917(x103582,a905),f917(f917(x103582,x103582),f917(x103582,a905)),x103582),f8(x103582,a905,x103582)),a330)),f333(f244(x103582),x103583))))),f333(f333(f7(x103582,f917(x103582,a905),a905),f335(x103582)),x103581))))),f333(f333(f244(x103582),x103583),f12(x103582,f245(x103582),x103581))) % 173.51/173.28 [10359]~P110(x103592)+E(x103591,f196(f917(x103592,a905)))+~P106(f333(f67(x103592),x103591))+E(f11(x103592,f244(x103592),f333(f252(x103592),f333(f333(f8(f917(x103592,a905),a905,x103592),f94(x103592)),f333(f333(f7(x103592,f917(x103592,a905),f917(x103592,a905)),f333(f333(f8(f917(x103592,f917(a905,a905)),f917(f917(x103592,a905),f917(x103592,a905)),x103592),f18(x103592,a905,a905)),f333(f333(f8(f917(x103592,a905),f917(x103592,f917(a905,a905)),x103592),f333(f8(a905,f917(a905,a905),x103592),a331)),f333(f333(f7(x103592,f917(x103592,x103592),f917(x103592,a905)),f333(f333(f8(f917(x103592,a905),f917(f917(x103592,x103592),f917(x103592,a905)),x103592),f8(x103592,a905,x103592)),a330)),f333(f245(x103592),x103593))))),f333(f333(f7(x103592,f917(x103592,a905),a905),f335(x103592)),x103591))))),f333(f333(f245(x103592),x103593),f11(x103592,f244(x103592),x103591))) % 173.51/173.28 [10095]~P120(x100951)+~E(x100953,f2(x100951))+~E(x100952,f2(x100951))+E(f333(f333(f87(x100951),f333(f333(f256(x100951),x100952),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x100951),x100953),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f2(x100951)) % 173.51/173.28 [10238]~P119(x102381)+~P106(f333(f333(f246(x102381),f2(x102381)),x102383))+P106(f333(f333(f246(x102381),x102382),x102383))+~P106(f333(f333(f246(x102381),f333(f333(f256(x102381),x102382),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x102381),x102383),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))))) % 173.51/173.28 [10288]~P120(x102882)+~E(x102881,f2(x102882))+~E(x102883,f2(x102882))+~P106(f333(f333(f247(x102882),f2(x102882)),f333(f333(f87(x102882),f333(f333(f256(x102882),x102883),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))),f333(f333(f256(x102882),x102881),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))))) % 173.51/173.28 [8730]P28(x87301,x87302,f345(x87303,x87302,x87304,x87301),x87304,x87303)+~E(f333(f41(x87301),x87304),f333(f41(x87302),x87303))+~P106(f333(f67(x87302),x87303))+~P106(f333(f67(x87301),x87304)) % 173.51/173.28 [9463]E(x94631,x94632)+~E(f706(x94631,x94632,x94634,x94633),f708(x94631,x94632,x94634,x94633))+P106(f333(f333(f335(f916(f911(x94633),f911(x94633))),f333(f333(f265(f911(x94633),f911(x94633)),x94632),x94631)),f155(x94633,x94634)))+P106(f333(f333(f335(f916(f911(x94633),f911(x94633))),f333(f333(f265(f911(x94633),f911(x94633)),x94631),x94632)),f155(x94633,x94634))) % 173.51/173.28 [4996]~P67(x49962)+~E(x49964,f2(x49962))+~E(x49961,f2(x49962))+E(x49961,f333(f333(f296(x49962),x49963),x49964)) % 173.51/173.28 [4997]~P67(x49971)+~E(x49973,f2(x49971))+~E(x49974,f2(x49971))+E(f333(f333(f296(x49971),x49972),x49973),x49974) % 173.51/173.28 [5113]~P67(x51132)+E(x51131,f2(x51132))+~E(x51133,f2(x51132))+~E(x51131,f333(f333(f296(x51132),x51134),x51133)) % 173.51/173.28 [5114]~P67(x51142)+E(x51141,f2(x51142))+~E(x51143,f2(x51142))+~E(f333(f333(f296(x51142),x51144),x51143),x51141) % 173.51/173.28 [5292]~P122(x52922)+E(x52921,f2(x52922))+~E(f333(f333(f296(x52922),x52923),x52921),x52924)+E(x52923,f333(f333(f88(x52922),x52924),x52921)) % 173.51/173.28 [5294]~P122(x52942)+E(x52941,f2(x52942))+~E(f333(f333(f88(x52942),x52943),x52941),x52944)+E(x52943,f333(f333(f296(x52942),x52944),x52941)) % 173.51/173.28 [5295]~P67(x52952)+E(x52951,f2(x52952))+~E(f333(f333(f296(x52952),x52953),x52951),x52954)+E(x52953,f333(f333(f88(x52952),x52954),x52951)) % 173.51/173.28 [5296]~P67(x52962)+E(x52961,f2(x52962))+~E(f333(f333(f88(x52962),x52963),x52961),x52964)+E(x52963,f333(f333(f296(x52962),x52964),x52961)) % 173.51/173.28 [5297]~P122(x52972)+E(x52971,f2(x52972))+~E(x52973,f333(f333(f296(x52972),x52974),x52971))+E(f333(f333(f88(x52972),x52973),x52971),x52974) % 173.51/173.28 [5299]~P122(x52992)+E(x52991,f2(x52992))+~E(x52993,f333(f333(f88(x52992),x52994),x52991))+E(f333(f333(f296(x52992),x52993),x52991),x52994) % 173.51/173.28 [5300]~P67(x53002)+E(x53001,f2(x53002))+~E(x53003,f333(f333(f296(x53002),x53004),x53001))+E(f333(f333(f88(x53002),x53003),x53001),x53004) % 173.51/173.28 [5301]~P67(x53012)+E(x53011,f2(x53012))+~E(x53013,f333(f333(f88(x53012),x53014),x53011))+E(f333(f333(f296(x53012),x53013),x53011),x53014) % 173.51/173.28 [5327]~P67(x53272)+~E(x53271,f2(x53272))+~E(f333(f333(f88(x53272),x53271),x53274),x53273)+E(x53271,f333(f333(f296(x53272),x53273),x53274)) % 173.51/173.28 [5328]~P67(x53281)+~E(x53284,f2(x53281))+~E(x53282,f333(f333(f88(x53281),x53284),x53283))+E(f333(f333(f296(x53281),x53282),x53283),x53284) % 173.51/173.28 [5401]~E(x54013,x54014)+~E(x54012,x54013)+~P112(x54011)+E(f309(x54011,x54012,x54013),f333(f333(f315(x54011),x54014),f196(f917(x54011,a905)))) % 173.51/173.28 [5601]~E(f125(x56012,x56011),x56013)+~E(f152(x56012,x56011),x56014)+E(x56011,f124(x56012))+E(f333(f333(f142(x56012),x56013),f333(f333(f159(x56012),x56014),f124(x56012))),x56011) % 173.51/173.28 [6216]~P119(x62163)+E(x62161,x62162)+~E(f333(f333(f256(x62163),x62164),x62161),f333(f333(f256(x62163),x62164),x62162))+~P106(f333(f333(f247(x62163),f85(x62163)),x62164)) % 173.51/173.28 [6217]E(x62171,x62172)+~E(f333(f333(f315(x62173),x62174),x62171),f333(f333(f315(x62173),x62174),x62172))+P106(f333(f333(f335(x62173),x62174),x62172))+P106(f333(f333(f335(x62173),x62174),x62171)) % 173.51/173.28 [6257]E(f333(x62571,x62572),f2(a910))+~E(f333(f333(f6(x62573,a910),x62571),x62574),f2(a910))+~P106(f333(f67(x62573),x62574))+~P106(f333(f333(f335(x62573),x62572),x62574)) % 173.51/173.28 [6258]E(f333(x62581,x62582),f85(a910))+~E(f333(f333(f9(x62583,a910),x62581),x62584),f85(a910))+~P106(f333(f67(x62583),x62584))+~P106(f333(f333(f335(x62583),x62582),x62584)) % 173.51/173.28 [6472]~P112(x64721)+~P106(f333(f333(f246(x64721),x64724),x64723))+P106(f333(f333(f246(x64721),x64722),x64723))+~P106(f333(f333(f246(x64721),x64722),x64724)) % 173.51/173.28 [6473]~P109(x64731)+~P106(f333(f333(f246(x64731),x64732),x64734))+P106(f333(f333(f246(x64731),x64732),x64733))+~P106(f333(f333(f246(x64731),x64734),x64733)) % 173.51/173.28 [6474]~P112(x64741)+~P106(f333(f333(f247(x64741),x64744),x64743))+P106(f333(f333(f247(x64741),x64742),x64743))+~P106(f333(f333(f246(x64741),x64742),x64744)) % 173.51/173.28 [6475]~P112(x64751)+~P106(f333(f333(f247(x64751),x64752),x64754))+P106(f333(f333(f247(x64751),x64752),x64753))+~P106(f333(f333(f246(x64751),x64754),x64753)) % 173.51/173.28 [6476]~P112(x64761)+~P106(f333(f333(f247(x64761),x64764),x64763))+P106(f333(f333(f247(x64761),x64762),x64763))+~P106(f333(f333(f247(x64761),x64762),x64764)) % 173.51/173.28 [6477]~P109(x64771)+~P106(f333(f333(f247(x64771),x64772),x64774))+P106(f333(f333(f247(x64771),x64772),x64773))+~P106(f333(f333(f246(x64771),x64774),x64773)) % 173.51/173.28 [6478]~P109(x64781)+~P106(f333(f333(f247(x64781),x64784),x64783))+P106(f333(f333(f247(x64781),x64782),x64783))+~P106(f333(f333(f246(x64781),x64782),x64784)) % 173.51/173.28 [6479]~P109(x64791)+~P106(f333(f333(f247(x64791),x64792),x64794))+P106(f333(f333(f247(x64791),x64792),x64793))+~P106(f333(f333(f247(x64791),x64794),x64793)) % 173.51/173.28 [6562]~P38(x65624,x65623,x65622)+E(x65621,f800(x65622,x65623,x65624))+~P106(f333(x65623,x65621))+~P106(f333(f333(f335(x65624),x65621),f333(f180(x65624),x65622))) % 173.51/173.28 [6563]~P38(x65634,x65633,x65632)+E(x65631,f812(x65632,x65633,x65634))+~P106(f333(x65633,x65631))+~P106(f333(f333(f335(x65634),x65631),f333(f180(x65634),x65632))) % 173.51/173.28 [6710]~P8(x67101)+~P106(f333(f333(f246(x67101),x67102),f44(x67101,x67104)))+P106(f333(f333(f246(x67101),x67102),x67103))+~P106(f333(f333(f335(x67101),x67103),x67104)) % 173.51/173.28 [6852]~P110(x68521)+~P16(x68521,f333(f333(f159(x68521),x68522),x68524))+~P106(f333(f333(f335(x68521),x68523),f333(f180(x68521),x68524)))+P106(f333(f333(f246(x68521),x68522),x68523)) % 173.51/173.28 [6940]~P8(x69401)+~P106(f333(f333(f246(x69401),f43(x69401,x69404)),x69403))+P106(f333(f333(f246(x69401),x69402),x69403))+~P106(f333(f333(f335(x69401),x69402),x69404)) % 173.51/173.28 [7342]~P110(x73421)+E(f333(f333(f121(f917(x73421,a905)),f333(f308(x73421,x73422),x73423)),f333(f308(x73421,x73423),x73424)),f333(f308(x73421,x73422),x73424))+~P106(f333(f333(f246(x73421),x73423),x73424))+~P106(f333(f333(f246(x73421),x73422),x73423)) % 173.51/173.28 [7385]P38(x73851,x73852,x73853)+~E(f814(x73853,x73852,x73851,x73854),x73854)+~P106(f333(x73852,x73854))+~P106(f333(f333(f335(x73851),x73854),f333(f180(x73851),x73853))) % 173.51/173.28 [7386]P38(x73861,x73862,x73863)+~E(f822(x73863,x73862,x73861,x73864),x73864)+~P106(f333(x73862,x73864))+~P106(f333(f333(f335(x73861),x73864),f333(f180(x73861),x73863))) % 173.51/173.28 [7459]~P110(x74591)+E(f333(f333(f121(f917(x74591,a905)),f333(f308(x74591,x74592),x74593)),f309(x74591,x74593,x74594)),f309(x74591,x74592,x74594))+~P106(f333(f333(f246(x74591),x74593),x74594))+~P106(f333(f333(f246(x74591),x74592),x74593)) % 173.51/173.28 [7522]~P110(x75221)+E(f333(f333(f121(f917(x75221,a905)),f312(x75221,x75222,x75223)),f333(f308(x75221,x75223),x75224)),f312(x75221,x75222,x75224))+~P106(f333(f333(f246(x75221),x75223),x75224))+~P106(f333(f333(f247(x75221),x75222),x75223)) % 173.51/173.28 [7539]~P110(x75391)+E(f333(f333(f121(f917(x75391,a905)),f309(x75391,x75392,x75393)),f312(x75391,x75393,x75394)),f333(f308(x75391,x75392),x75394))+~P106(f333(f333(f246(x75391),x75392),x75393))+~P106(f333(f333(f247(x75391),x75393),x75394)) % 173.51/173.28 [7570]~P110(x75701)+E(f333(f333(f121(f917(x75701,a905)),f309(x75701,x75702,x75703)),f311(x75701,x75703,x75704)),f309(x75701,x75702,x75704))+~P106(f333(f333(f246(x75701),x75703),x75704))+~P106(f333(f333(f246(x75701),x75702),x75703)) % 173.51/173.28 [7571]~P110(x75711)+E(f333(f333(f121(f917(x75711,a905)),f311(x75711,x75712,x75713)),f311(x75711,x75713,x75714)),f311(x75711,x75712,x75714))+~P106(f333(f333(f246(x75711),x75713),x75714))+~P106(f333(f333(f246(x75711),x75712),x75713)) % 173.51/173.28 [7572]~P110(x75721)+E(f333(f333(f121(f917(x75721,a905)),f311(x75721,x75722,x75723)),f312(x75721,x75723,x75724)),f312(x75721,x75722,x75724))+~P106(f333(f333(f246(x75721),x75722),x75723))+~P106(f333(f333(f247(x75721),x75723),x75724)) % 173.51/173.28 [7573]~P110(x75731)+E(f333(f333(f121(f917(x75731,a905)),f312(x75731,x75732,x75733)),f309(x75731,x75733,x75734)),f311(x75731,x75732,x75734))+~P106(f333(f333(f246(x75731),x75733),x75734))+~P106(f333(f333(f247(x75731),x75732),x75733)) % 173.51/173.28 [8365]P27(x83651,x83652,f347(x83653,x83652,x83654,x83651),x83654)+~P106(f333(f67(x83652),x83653))+~P106(f333(f67(x83651),x83654))+~P106(f333(f333(f246(a910),f333(f41(x83651),x83654)),f333(f41(x83652),x83653))) % 173.51/173.28 [8386]P38(x83861,x83862,x83863)+~P106(f333(x83862,x83864))+P106(f333(x83862,f814(x83863,x83862,x83861,x83864)))+~P106(f333(f333(f335(x83861),x83864),f333(f180(x83861),x83863))) % 173.51/173.28 [8387]P38(x83871,x83872,x83873)+~P106(f333(x83872,x83874))+P106(f333(x83872,f822(x83873,x83872,x83871,x83874)))+~P106(f333(f333(f335(x83871),x83874),f333(f180(x83871),x83873))) % 173.51/173.28 [8442]~P78(x84421)+~E(f333(x84423,f523(x84423,x84424,x84422,x84421)),f85(x84421))+E(f333(f333(f333(f71(x84421,x84422,f88(x84421)),x84423),f85(x84421)),x84424),f85(x84421))+~P106(f333(f67(x84422),x84424)) % 173.51/173.28 [8719]~P119(x87191)+~P106(f333(f333(f246(x87191),f2(x87191)),x87193))+P106(f333(f333(f246(x87191),x87192),x87193))+~P106(f333(f333(f246(x87191),f333(f333(f256(x87191),x87192),f333(a123,x87194))),f333(f333(f256(x87191),x87193),f333(a123,x87194)))) % 173.51/173.28 [9040]P38(x90401,x90402,x90403)+~P106(f333(x90402,x90404))+~P106(f333(f333(f335(x90401),x90404),f333(f180(x90401),x90403)))+P106(f333(f333(f335(x90401),f814(x90403,x90402,x90401,x90404)),f333(f180(x90401),x90403))) % 173.51/173.28 [9041]P38(x90411,x90412,x90413)+~P106(f333(x90412,x90414))+~P106(f333(f333(f335(x90411),x90414),f333(f180(x90411),x90413)))+P106(f333(f333(f335(x90411),f822(x90413,x90412,x90411,x90414)),f333(f180(x90411),x90413))) % 173.51/173.28 [9129]~P78(x91291)+E(f333(f333(f333(f71(x91291,x91292,f88(x91291)),x91293),f85(x91291)),x91294),f85(x91291))+~P106(f333(f67(x91292),x91294))+P106(f333(f333(f335(x91292),f523(x91293,x91294,x91292,x91291)),x91294)) % 173.51/173.28 [9635]~P106(f333(f333(f246(a1),x96354),f2(a1)))+P106(f333(f333(f246(a1),f333(f333(f87(a1),f333(f333(f88(a1),x96351),f51(a1,x96352,x96353))),x96354)),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x96353))+~P106(f333(f333(f247(a1),x96351),x96354)) % 173.51/173.28 [10086]~P106(f333(f67(x100861),x100862))+~P106(f333(f333(f335(x100861),x100864),x100862))+~P106(f333(f333(f335(x100861),x100863),x100862))+P106(f333(f333(f247(a910),f333(f41(x100861),f333(f333(f23(f917(x100861,a905)),f333(f333(f23(f917(x100861,a905)),x100862),f333(f333(f315(x100861),x100863),f196(f917(x100861,a905))))),f333(f333(f315(x100861),x100864),f196(f917(x100861,a905)))))),f333(f41(x100861),x100862))) % 173.51/173.28 [7054]~P102(x70541)+~P106(f333(f333(f246(x70541),x70542),x70544))+~P106(f333(f333(f246(x70541),x70542),x70543))+P106(f333(f333(f246(x70541),x70542),f333(f333(f112(x70541),x70543),x70544))) % 173.51/173.28 [7057]~P110(x70571)+~P106(f333(f333(f246(x70571),x70572),x70574))+~P106(f333(f333(f246(x70571),x70572),x70573))+P106(f333(f333(f246(x70571),x70572),f333(f333(f244(x70571),x70573),x70574))) % 173.51/173.28 [7058]~P110(x70581)+~P106(f333(f333(f247(x70581),x70582),x70584))+~P106(f333(f333(f247(x70581),x70582),x70583))+P106(f333(f333(f247(x70581),x70582),f333(f333(f244(x70581),x70583),x70584))) % 173.51/173.28 [7077]~P68(x70772)+E(x70771,f2(x70772))+E(f333(f333(f296(x70772),f333(f333(f256(x70772),x70771),x70773)),f333(f333(f256(x70772),x70771),x70774)),f333(f333(f256(x70772),x70771),f333(f333(f23(a910),x70773),x70774)))+~P106(f333(f333(f246(a910),x70774),x70773)) % 173.51/173.28 [7121]~P110(x71211)+~P16(x71211,f333(f333(f159(x71211),x71213),x71214))+P16(x71211,f333(f333(f159(x71211),x71212),f333(f333(f159(x71211),x71213),x71214)))+~P106(f333(f333(f246(x71211),x71212),x71213)) % 173.51/173.28 [7159]~P90(x71591)+~P106(f333(f333(f246(x71591),f2(x71591)),x71594))+~P106(f333(f333(f246(x71591),x71592),x71593))+P106(f333(f333(f246(x71591),x71592),f333(f333(f87(x71591),x71593),x71594))) % 173.51/173.28 [7160]~P90(x71601)+~P106(f333(f333(f246(x71601),f2(x71601)),x71603))+~P106(f333(f333(f246(x71601),x71602),x71604))+P106(f333(f333(f246(x71601),x71602),f333(f333(f87(x71601),x71603),x71604))) % 173.51/173.28 [7161]~P90(x71611)+~P106(f333(f333(f246(x71611),x71612),x71614))+~P106(f333(f333(f247(x71611),f2(x71611)),x71613))+P106(f333(f333(f247(x71611),x71612),f333(f333(f87(x71611),x71613),x71614))) % 173.51/173.28 [7162]~P90(x71621)+~P106(f333(f333(f246(x71621),f2(x71621)),x71623))+~P106(f333(f333(f247(x71621),x71622),x71624))+P106(f333(f333(f247(x71621),x71622),f333(f333(f87(x71621),x71623),x71624))) % 173.51/173.28 [7163]~P119(x71631)+~P106(f333(f333(f247(x71631),f2(x71631)),x71633))+~P106(f333(f333(f247(x71631),x71632),x71634))+P106(f333(f333(f247(x71631),x71632),f333(f333(f87(x71631),x71633),x71634))) % 173.51/173.28 [7204]~P110(x72041)+P106(f333(f333(f246(x72041),x72042),x72043))+P106(f333(f333(f246(x72041),x72042),x72044))+~P106(f333(f333(f246(x72041),x72042),f333(f333(f245(x72041),x72044),x72043))) % 173.51/173.28 [7205]~P110(x72051)+P106(f333(f333(f247(x72051),x72052),x72053))+P106(f333(f333(f247(x72051),x72052),x72054))+~P106(f333(f333(f247(x72051),x72052),f333(f333(f245(x72051),x72054),x72053))) % 173.51/173.28 [7495]~P112(x74952)+~P7(x74951)+~P106(f333(f333(f247(f917(x74951,x74952)),x74953),x74954))+P106(f333(f333(f246(f917(x74951,x74952)),x74953),x74954)) % 173.51/173.28 [7857]~P70(x78571)+~P106(f333(f333(f247(x78571),x78574),f2(x78571)))+~P106(f333(f333(f246(x78571),x78573),f333(f333(f296(x78571),x78572),x78574)))+P106(f333(f333(f246(x78571),x78572),f333(f333(f88(x78571),x78573),x78574))) % 173.51/173.28 [7858]~P70(x78581)+~P106(f333(f333(f247(x78581),x78584),f2(x78581)))+~P106(f333(f333(f246(x78581),x78583),f333(f333(f88(x78581),x78582),x78584)))+P106(f333(f333(f246(x78581),x78582),f333(f333(f296(x78581),x78583),x78584))) % 173.51/173.28 [7859]~P70(x78591)+~P106(f333(f333(f247(x78591),x78594),f2(x78591)))+~P106(f333(f333(f247(x78591),x78593),f333(f333(f296(x78591),x78592),x78594)))+P106(f333(f333(f247(x78591),x78592),f333(f333(f88(x78591),x78593),x78594))) % 173.51/173.28 [7860]~P70(x78601)+~P106(f333(f333(f247(x78601),x78604),f2(x78601)))+~P106(f333(f333(f247(x78601),x78603),f333(f333(f88(x78601),x78602),x78604)))+P106(f333(f333(f247(x78601),x78602),f333(f333(f296(x78601),x78603),x78604))) % 173.51/173.28 [7968]~P135(x79681)+~P106(f333(f333(f246(x79681),x79682),f2(x79681)))+~P106(f333(f333(f246(x79681),x79684),x79683))+P106(f333(f333(f246(x79681),f333(f333(f88(x79681),x79682),x79683)),f333(f333(f88(x79681),x79682),x79684))) % 173.51/173.28 [7969]~P126(x79691)+~P106(f333(f333(f247(x79691),x79692),f2(x79691)))+~P106(f333(f333(f246(x79691),x79694),x79693))+P106(f333(f333(f246(x79691),f333(f333(f88(x79691),x79692),x79693)),f333(f333(f88(x79691),x79692),x79694))) % 173.51/173.28 [7970]~P135(x79701)+~P106(f333(f333(f246(x79701),x79703),f2(x79701)))+~P106(f333(f333(f246(x79701),x79704),x79702))+P106(f333(f333(f246(x79701),f333(f333(f88(x79701),x79702),x79703)),f333(f333(f88(x79701),x79704),x79703))) % 173.51/173.28 [7971]~P69(x79711)+~P106(f333(f333(f246(x79711),x79713),f2(x79711)))+~P106(f333(f333(f246(x79711),x79714),x79712))+P106(f333(f333(f246(x79711),f333(f333(f296(x79711),x79712),x79713)),f333(f333(f296(x79711),x79714),x79713))) % 173.51/173.28 [7975]~P126(x79751)+~P106(f333(f333(f247(x79751),x79753),f2(x79751)))+~P106(f333(f333(f247(x79751),x79754),x79752))+P106(f333(f333(f247(x79751),f333(f333(f88(x79751),x79752),x79753)),f333(f333(f88(x79751),x79754),x79753))) % 173.51/173.28 [7976]~P126(x79761)+~P106(f333(f333(f247(x79761),x79762),f2(x79761)))+~P106(f333(f333(f247(x79761),x79764),x79763))+P106(f333(f333(f247(x79761),f333(f333(f88(x79761),x79762),x79763)),f333(f333(f88(x79761),x79762),x79764))) % 173.51/173.28 [7977]~P70(x79771)+~P106(f333(f333(f247(x79771),x79773),f2(x79771)))+~P106(f333(f333(f247(x79771),x79774),x79772))+P106(f333(f333(f247(x79771),f333(f333(f296(x79771),x79772),x79773)),f333(f333(f296(x79771),x79774),x79773))) % 173.51/173.28 [7978]~P119(x79781)+~P106(f333(f333(f247(x79781),f85(x79781)),x79782))+~P106(f333(f333(f246(a910),x79783),x79784))+P106(f333(f333(f246(x79781),f333(f333(f256(x79781),x79782),x79783)),f333(f333(f256(x79781),x79782),x79784))) % 173.51/173.28 [7979]~P119(x79791)+~P106(f333(f333(f246(x79791),f85(x79791)),x79792))+~P106(f333(f333(f246(a910),x79793),x79794))+P106(f333(f333(f246(x79791),f333(f333(f256(x79791),x79792),x79793)),f333(f333(f256(x79791),x79792),x79794))) % 173.51/173.28 [7981]~P119(x79811)+~P106(f333(f333(f247(x79811),f85(x79811)),x79812))+~P106(f333(f333(f247(a910),x79813),x79814))+P106(f333(f333(f247(x79811),f333(f333(f256(x79811),x79812),x79813)),f333(f333(f256(x79811),x79812),x79814))) % 173.51/173.28 [8008]P106(f333(f333(f247(a910),f2(a910)),f333(x80081,x80082)))+~P106(f333(f67(x80083),x80084))+~P106(f333(f333(f335(x80083),x80082),x80084))+~P106(f333(f333(f247(a910),f2(a910)),f333(f333(f9(x80083,a910),x80081),x80084))) % 173.51/173.28 [8017]~P137(x80171)+~P106(f333(f333(f246(x80171),x80173),x80174))+~P106(f333(f333(f246(x80171),f2(x80171)),x80172))+P106(f333(f333(f246(x80171),f333(f333(f88(x80171),x80172),x80173)),f333(f333(f88(x80171),x80172),x80174))) % 173.51/173.28 [8018]~P136(x80181)+~P106(f333(f333(f246(x80181),x80183),x80184))+~P106(f333(f333(f246(x80181),f2(x80181)),x80182))+P106(f333(f333(f246(x80181),f333(f333(f88(x80181),x80182),x80183)),f333(f333(f88(x80181),x80182),x80184))) % 173.51/173.28 [8019]~P126(x80191)+~P106(f333(f333(f247(x80191),f2(x80191)),x80192))+~P106(f333(f333(f246(x80191),x80193),x80194))+P106(f333(f333(f246(x80191),f333(f333(f88(x80191),x80192),x80193)),f333(f333(f88(x80191),x80192),x80194))) % 173.51/173.28 [8020]~P137(x80201)+~P106(f333(f333(f246(x80201),x80202),x80204))+~P106(f333(f333(f246(x80201),f2(x80201)),x80203))+P106(f333(f333(f246(x80201),f333(f333(f88(x80201),x80202),x80203)),f333(f333(f88(x80201),x80204),x80203))) % 173.51/173.28 [8021]~P119(x80211)+~P106(f333(f333(f246(x80211),x80212),x80214))+~P106(f333(f333(f246(x80211),f2(x80211)),x80212))+P106(f333(f333(f246(x80211),f333(f333(f256(x80211),x80212),x80213)),f333(f333(f256(x80211),x80214),x80213))) % 173.51/173.28 [8022]~P69(x80221)+~P106(f333(f333(f246(x80221),x80222),x80224))+~P106(f333(f333(f246(x80221),f2(x80221)),x80223))+P106(f333(f333(f246(x80221),f333(f333(f296(x80221),x80222),x80223)),f333(f333(f296(x80221),x80224),x80223))) % 173.51/173.28 [8024]~P124(x80241)+~P106(f333(f333(f247(x80241),x80243),x80244))+~P106(f333(f333(f247(x80241),f2(x80241)),x80242))+P106(f333(f333(f247(x80241),f333(f333(f88(x80241),x80242),x80243)),f333(f333(f88(x80241),x80242),x80244))) % 173.51/173.28 [8025]~P130(x80251)+~P106(f333(f333(f247(x80251),x80253),x80254))+~P106(f333(f333(f247(x80251),f2(x80251)),x80252))+P106(f333(f333(f247(x80251),f333(f333(f88(x80251),x80252),x80253)),f333(f333(f88(x80251),x80252),x80254))) % 173.51/173.28 [8026]~P126(x80261)+~P106(f333(f333(f247(x80261),x80262),x80264))+~P106(f333(f333(f247(x80261),f2(x80261)),x80263))+P106(f333(f333(f247(x80261),f333(f333(f88(x80261),x80262),x80263)),f333(f333(f88(x80261),x80264),x80263))) % 173.51/173.28 [8027]~P130(x80271)+~P106(f333(f333(f247(x80271),x80272),x80274))+~P106(f333(f333(f247(x80271),f2(x80271)),x80273))+P106(f333(f333(f247(x80271),f333(f333(f88(x80271),x80272),x80273)),f333(f333(f88(x80271),x80274),x80273))) % 173.51/173.28 [8028]~P126(x80281)+~P106(f333(f333(f247(x80281),x80283),x80284))+~P106(f333(f333(f247(x80281),f2(x80281)),x80282))+P106(f333(f333(f247(x80281),f333(f333(f88(x80281),x80282),x80283)),f333(f333(f88(x80281),x80282),x80284))) % 173.51/173.28 [8029]~P70(x80291)+~P106(f333(f333(f247(x80291),x80292),x80294))+~P106(f333(f333(f247(x80291),f2(x80291)),x80293))+P106(f333(f333(f247(x80291),f333(f333(f296(x80291),x80292),x80293)),f333(f333(f296(x80291),x80294),x80293))) % 173.51/173.28 [8071]~P111(x80712)+P106(f333(f333(f247(f917(x80711,x80712)),x80714),x80713))+~P106(f333(f333(f246(f917(x80711,x80712)),x80714),x80713))+P106(f333(f333(f246(f917(x80711,x80712)),x80713),x80714)) % 173.51/173.28 [8115]P106(f333(f333(f335(x81151),x81152),x81153))+P106(f333(f333(f335(x81151),x81152),x81154))+~P106(f333(f333(f246(f917(x81151,a905)),x81154),x81153))+P106(f333(f333(f247(f917(x81151,a905)),x81154),f333(f333(f315(x81151),x81152),x81153))) % 173.51/173.28 [8275]P106(f333(f333(f335(x82751),x82752),x82753))+P106(f333(f333(f335(x82751),x82752),x82754))+~P106(f333(f333(f247(f917(x82751,a905)),x82754),f333(f333(f315(x82751),x82752),x82753)))+P106(f333(f333(f246(f917(x82751,a905)),x82754),x82753)) % 173.51/173.28 [8342]~P126(x83421)+P106(f333(f333(f247(x83421),x83423),x83422))+P106(f333(f333(f247(x83421),x83422),x83423))+~P106(f333(f333(f247(x83421),f333(f333(f88(x83421),x83424),x83422)),f333(f333(f88(x83421),x83424),x83423))) % 173.51/173.28 [8343]~P126(x83431)+P106(f333(f333(f247(x83431),x83433),x83432))+P106(f333(f333(f247(x83431),x83432),x83433))+~P106(f333(f333(f247(x83431),f333(f333(f88(x83431),x83432),x83434)),f333(f333(f88(x83431),x83433),x83434))) % 173.51/173.28 [8354]~P126(x83541)+P106(f333(f333(f247(x83541),x83544),f2(x83541)))+P106(f333(f333(f247(x83541),x83542),x83543))+~P106(f333(f333(f247(x83541),f333(f333(f88(x83541),x83542),x83544)),f333(f333(f88(x83541),x83543),x83544))) % 173.51/173.28 [8355]~P126(x83551)+P106(f333(f333(f247(x83551),x83554),f2(x83551)))+P106(f333(f333(f247(x83551),x83552),x83553))+~P106(f333(f333(f247(x83551),f333(f333(f88(x83551),x83554),x83552)),f333(f333(f88(x83551),x83554),x83553))) % 173.51/173.28 [8359]~P126(x83591)+P106(f333(f333(f247(x83591),x83592),x83593))+P106(f333(f333(f247(x83591),f2(x83591)),x83594))+~P106(f333(f333(f247(x83591),f333(f333(f88(x83591),x83594),x83593)),f333(f333(f88(x83591),x83594),x83592))) % 173.51/173.28 [8360]~P126(x83601)+P106(f333(f333(f247(x83601),x83602),x83603))+P106(f333(f333(f247(x83601),f2(x83601)),x83604))+~P106(f333(f333(f247(x83601),f333(f333(f88(x83601),x83603),x83604)),f333(f333(f88(x83601),x83602),x83604))) % 173.51/173.28 [8373]~P126(x83731)+P106(f333(f333(f247(x83731),x83732),f2(x83731)))+P106(f333(f333(f247(x83731),f2(x83731)),x83732))+~P106(f333(f333(f247(x83731),f333(f333(f88(x83731),x83733),x83732)),f333(f333(f88(x83731),x83734),x83732))) % 173.51/173.28 [8374]~P126(x83741)+P106(f333(f333(f247(x83741),x83742),f2(x83741)))+P106(f333(f333(f247(x83741),f2(x83741)),x83742))+~P106(f333(f333(f247(x83741),f333(f333(f88(x83741),x83742),x83743)),f333(f333(f88(x83741),x83742),x83744))) % 173.51/173.28 [8404]~P126(x84041)+~P106(f333(f333(f247(x84041),x84044),f2(x84041)))+P106(f333(f333(f246(x84041),x84042),x84043))+~P106(f333(f333(f246(x84041),f333(f333(f88(x84041),x84044),x84043)),f333(f333(f88(x84041),x84044),x84042))) % 173.51/173.28 [8405]~P126(x84051)+~P106(f333(f333(f247(x84051),x84054),f2(x84051)))+P106(f333(f333(f247(x84051),x84052),x84053))+~P106(f333(f333(f247(x84051),f333(f333(f88(x84051),x84054),x84053)),f333(f333(f88(x84051),x84054),x84052))) % 173.51/173.28 [8416]~P119(x84163)+~P106(f333(f333(f247(x84163),f85(x84163)),x84164))+P106(f333(f333(f246(a910),x84161),x84162))+~P106(f333(f333(f246(x84163),f333(f333(f256(x84163),x84164),x84161)),f333(f333(f256(x84163),x84164),x84162))) % 173.51/173.28 [8418]~P119(x84183)+~P106(f333(f333(f247(x84183),f85(x84183)),x84184))+P106(f333(f333(f247(a910),x84181),x84182))+~P106(f333(f333(f247(x84183),f333(f333(f256(x84183),x84184),x84181)),f333(f333(f256(x84183),x84184),x84182))) % 173.51/173.28 [8428]~P126(x84281)+P106(f333(f333(f246(x84281),x84282),x84283))+~P106(f333(f333(f247(x84281),f2(x84281)),x84284))+~P106(f333(f333(f246(x84281),f333(f333(f88(x84281),x84284),x84282)),f333(f333(f88(x84281),x84284),x84283))) % 173.51/173.28 [8429]~P130(x84291)+P106(f333(f333(f246(x84291),x84292),x84293))+~P106(f333(f333(f247(x84291),f2(x84291)),x84294))+~P106(f333(f333(f246(x84291),f333(f333(f88(x84291),x84294),x84292)),f333(f333(f88(x84291),x84294),x84293))) % 173.51/173.28 [8430]~P130(x84301)+P106(f333(f333(f246(x84301),x84302),x84303))+~P106(f333(f333(f247(x84301),f2(x84301)),x84304))+~P106(f333(f333(f246(x84301),f333(f333(f88(x84301),x84302),x84304)),f333(f333(f88(x84301),x84303),x84304))) % 173.51/173.28 [8431]~P126(x84311)+P106(f333(f333(f247(x84311),x84312),x84313))+~P106(f333(f333(f247(x84311),f2(x84311)),x84314))+~P106(f333(f333(f247(x84311),f333(f333(f88(x84311),x84314),x84312)),f333(f333(f88(x84311),x84314),x84313))) % 173.51/173.28 [8432]~P130(x84321)+P106(f333(f333(f247(x84321),x84322),x84323))+~P106(f333(f333(f246(x84321),f2(x84321)),x84324))+~P106(f333(f333(f247(x84321),f333(f333(f88(x84321),x84324),x84322)),f333(f333(f88(x84321),x84324),x84323))) % 173.51/173.28 [8433]~P131(x84331)+P106(f333(f333(f247(x84331),x84332),x84333))+~P106(f333(f333(f246(x84331),f2(x84331)),x84334))+~P106(f333(f333(f247(x84331),f333(f333(f88(x84331),x84334),x84332)),f333(f333(f88(x84331),x84334),x84333))) % 173.51/173.28 [8434]~P119(x84341)+~P106(f333(f333(f246(x84341),f2(x84341)),x84343))+P106(f333(f333(f247(x84341),x84342),x84343))+~P106(f333(f333(f247(x84341),f333(f333(f256(x84341),x84342),x84344)),f333(f333(f256(x84341),x84343),x84344))) % 173.51/173.28 [8435]~P130(x84351)+P106(f333(f333(f247(x84351),x84352),x84353))+~P106(f333(f333(f246(x84351),f2(x84351)),x84354))+~P106(f333(f333(f247(x84351),f333(f333(f88(x84351),x84352),x84354)),f333(f333(f88(x84351),x84353),x84354))) % 173.51/173.28 [8436]~P131(x84361)+P106(f333(f333(f247(x84361),x84362),x84363))+~P106(f333(f333(f246(x84361),f2(x84361)),x84364))+~P106(f333(f333(f247(x84361),f333(f333(f88(x84361),x84362),x84364)),f333(f333(f88(x84361),x84363),x84364))) % 173.51/173.28 [8479]P106(f333(f333(f335(x84791),x84792),x84793))+~P106(f333(f333(f246(f917(x84791,a905)),x84793),x84794))+~P106(f333(f333(f247(f917(x84791,a905)),x84793),x84794))+P106(f333(f333(f247(f917(x84791,a905)),x84793),f333(f333(f315(x84791),x84792),x84794))) % 173.51/173.28 [8869]E(f333(f333(f23(a1),f394(x88691,x88692,x88693,x88694)),f395(x88691,x88692,x88693,x88694)),x88694)+~P106(f333(f333(f247(a1),f2(a1)),x88693))+~P106(f333(f333(f246(a1),x88691),x88694))+P106(f333(f333(f246(a1),x88691),f333(f333(f87(a1),x88694),x88693))) % 173.51/173.28 [8870]E(f333(f333(f23(a1),f416(x88701,x88702,x88703,x88704)),f417(x88701,x88702,x88703,x88704)),x88704)+~P106(f333(f333(f247(a1),f2(a1)),x88703))+~P106(f333(f333(f247(a1),x88701),x88704))+P106(f333(f333(f247(a1),x88701),f333(f333(f87(a1),x88704),x88703))) % 173.51/173.28 [9020]~E(f333(f333(f172(x90201),x90203),f715(x90204,x90203,x90201,x90202)),f333(f333(f172(x90201),x90204),f715(x90204,x90203,x90201,x90202)))+E(f333(f333(f183(x90201),x90202),x90203),f333(f333(f183(x90201),x90202),x90204))+~P106(f333(f333(f246(a910),x90202),f333(f197(f911(x90201)),x90203)))+~P106(f333(f333(f246(a910),x90202),f333(f197(f911(x90201)),x90204))) % 173.51/173.28 [9093]~P106(f333(f333(f247(a1),f2(a1)),x90933))+~P106(f333(f333(f246(a1),x90931),x90934))+P106(f333(f333(f335(a1),f394(x90931,x90932,x90933,x90934)),x90932))+P106(f333(f333(f246(a1),x90931),f333(f333(f87(a1),x90934),x90933))) % 173.51/173.28 [9094]~P106(f333(f333(f247(a1),f2(a1)),x90943))+~P106(f333(f333(f247(a1),x90941),x90944))+P106(f333(f333(f335(a1),f416(x90941,x90942,x90943,x90944)),x90942))+P106(f333(f333(f247(a1),x90941),f333(f333(f87(a1),x90944),x90943))) % 173.51/173.28 [9138]~P102(x91381)+~P106(f333(f67(x91381),x91383))+~P106(f333(f333(f335(x91381),x91384),x91383))+P106(f333(f333(f246(x91381),f333(f333(f70(x91381,x91381,f112(x91381)),x91382),x91383)),f333(f333(f112(x91381),x91384),x91382))) % 173.51/173.28 [9139]~P110(x91391)+~P106(f333(f67(x91391),x91393))+~P106(f333(f333(f335(x91391),x91394),x91393))+P106(f333(f333(f246(x91391),f333(f333(f70(x91391,x91391,f244(x91391)),x91392),x91393)),f333(f333(f244(x91391),x91394),x91392))) % 173.51/173.28 [9188]E(f333(f333(f183(x91881),x91882),x91883),f333(f333(f183(x91881),x91882),x91884))+P106(f333(f333(f247(a910),f715(x91883,x91884,x91881,x91882)),x91882))+~P106(f333(f333(f246(a910),x91882),f333(f197(f911(x91881)),x91883)))+~P106(f333(f333(f246(a910),x91882),f333(f197(f911(x91881)),x91884))) % 173.51/173.28 [9193]~P106(f333(f333(f247(a1),f2(a1)),x91933))+~P106(f333(f333(f246(a1),x91931),x91932))+P106(f333(f333(f335(a1),f395(x91931,x91934,x91933,x91932)),f309(a1,f85(a1),x91933)))+P106(f333(f333(f246(a1),x91931),f333(f333(f87(a1),x91932),x91933))) % 173.51/173.28 [9194]~P106(f333(f333(f247(a1),f2(a1)),x91943))+~P106(f333(f333(f247(a1),x91941),x91942))+P106(f333(f333(f335(a1),f417(x91941,x91944,x91943,x91942)),f309(a1,f85(a1),x91943)))+P106(f333(f333(f247(a1),x91941),f333(f333(f87(a1),x91942),x91943))) % 173.51/173.28 [9523]~P110(x95231)+~P106(f333(f67(x95231),x95234))+P106(f333(f333(f335(x95231),f677(x95232,x95233,x95234,x95231)),x95234))+P106(f333(f333(f246(x95231),f333(f333(f70(x95231,x95231,f245(x95231)),x95232),x95234)),f333(f333(f245(x95231),x95233),x95232))) % 173.51/173.28 [9524]~P101(x95241)+~P106(f333(f67(x95241),x95244))+P106(f333(f333(f335(x95241),f681(x95242,x95243,x95244,x95241)),x95244))+P106(f333(f333(f246(x95241),f333(f333(f70(x95241,x95241,f121(x95241)),x95242),x95244)),f333(f333(f121(x95241),x95243),x95242))) % 173.51/173.28 [9652]~P101(x96521)+~P106(f333(f67(x96521),x96523))+~P106(f333(f333(f246(x96521),f681(x96522,x96524,x96523,x96521)),x96524))+P106(f333(f333(f246(x96521),f333(f333(f70(x96521,x96521,f121(x96521)),x96522),x96523)),f333(f333(f121(x96521),x96524),x96522))) % 173.51/173.28 [9653]~P110(x96531)+~P106(f333(f67(x96531),x96533))+~P106(f333(f333(f246(x96531),f677(x96532,x96534,x96533,x96531)),x96534))+P106(f333(f333(f246(x96531),f333(f333(f70(x96531,x96531,f245(x96531)),x96532),x96533)),f333(f333(f245(x96531),x96534),x96532))) % 173.51/173.28 [9655]~P106(f333(f333(f246(a1),f2(a1)),x96554))+~P106(f333(f333(f247(a1),f2(a1)),x96553))+~P106(f333(f333(f247(a1),x96554),x96551))+P106(f333(f333(f247(a1),f333(f333(f87(a1),f333(f333(f88(a1),x96551),f51(a1,x96552,x96553))),x96554)),f333(f333(f88(a1),x96551),x96553))) % 173.51/173.28 [10056]E(x100561,x100562)+P106(f333(f333(f335(f916(f911(x100563),f911(x100563))),f333(f333(f265(f911(x100563),f911(x100563)),x100562),x100561)),f155(x100563,x100564)))+P106(f333(f333(f335(f916(f911(x100563),f911(x100563))),f333(f333(f265(f911(x100563),f911(x100563)),x100561),x100562)),f155(x100563,x100564)))+~P106(f333(f333(f335(f916(x100563,x100563)),f333(f333(f265(x100563,x100563),f706(x100561,x100562,x100564,x100563)),f708(x100561,x100562,x100564,x100563))),x100564)) % 173.51/173.28 [10057]E(x100571,x100572)+P106(f333(f333(f335(f916(f911(x100573),f911(x100573))),f333(f333(f265(f911(x100573),f911(x100573)),x100572),x100571)),f155(x100573,x100574)))+P106(f333(f333(f335(f916(f911(x100573),f911(x100573))),f333(f333(f265(f911(x100573),f911(x100573)),x100571),x100572)),f155(x100573,x100574)))+~P106(f333(f333(f335(f916(x100573,x100573)),f333(f333(f265(x100573,x100573),f708(x100571,x100572,x100574,x100573)),f706(x100571,x100572,x100574,x100573))),x100574)) % 173.51/173.28 [7561]~P101(x75611)+~P106(f333(f333(f246(x75611),x75613),x75614))+~P106(f333(f333(f246(x75611),x75612),x75614))+P106(f333(f333(f246(x75611),f333(f333(f121(x75611),x75612),x75613)),x75614)) % 173.51/173.28 [7564]~P110(x75641)+~P106(f333(f333(f246(x75641),x75643),x75644))+~P106(f333(f333(f246(x75641),x75642),x75644))+P106(f333(f333(f246(x75641),f333(f333(f245(x75641),x75642),x75643)),x75644)) % 173.51/173.28 [7565]~P110(x75651)+~P106(f333(f333(f247(x75651),x75653),x75654))+~P106(f333(f333(f247(x75651),x75652),x75654))+P106(f333(f333(f247(x75651),f333(f333(f245(x75651),x75652),x75653)),x75654)) % 173.51/173.28 [7882]~E(x78821,x78823)+E(f147(a910,f333(f308(a910,x78821),x78822)),f333(f333(f159(a910),x78823),x78824))+~E(f147(a910,f333(f308(a910,f333(f333(f87(a910),x78821),f85(a910))),x78822)),x78824)+~P106(f333(f333(f247(a910),x78821),x78822)) % 173.51/173.28 [7892]~P110(x78921)+P106(f333(f333(f246(x78921),x78922),x78923))+P106(f333(f333(f246(x78921),x78924),x78923))+~P106(f333(f333(f246(x78921),f333(f333(f244(x78921),x78924),x78922)),x78923)) % 173.51/173.28 [7893]~P110(x78931)+P106(f333(f333(f247(x78931),x78932),x78933))+P106(f333(f333(f247(x78931),x78934),x78933))+~P106(f333(f333(f247(x78931),f333(f333(f244(x78931),x78934),x78932)),x78933)) % 173.51/173.28 [8176]~P69(x81761)+~P106(f333(f333(f247(x81761),f2(x81761)),x81763))+~P106(f333(f333(f246(x81761),x81762),f333(f333(f296(x81761),x81764),x81763)))+P106(f333(f333(f246(x81761),f333(f333(f88(x81761),x81762),x81763)),x81764)) % 173.51/173.28 [8177]~P70(x81771)+~P106(f333(f333(f247(x81771),f2(x81771)),x81773))+~P106(f333(f333(f246(x81771),x81772),f333(f333(f296(x81771),x81774),x81773)))+P106(f333(f333(f246(x81771),f333(f333(f88(x81771),x81772),x81773)),x81774)) % 173.51/173.28 [8179]~P69(x81791)+~P106(f333(f333(f247(x81791),f2(x81791)),x81793))+~P106(f333(f333(f246(x81791),x81792),f333(f333(f88(x81791),x81794),x81793)))+P106(f333(f333(f246(x81791),f333(f333(f296(x81791),x81792),x81793)),x81794)) % 173.51/173.28 [8180]~P70(x81801)+~P106(f333(f333(f247(x81801),f2(x81801)),x81803))+~P106(f333(f333(f246(x81801),x81802),f333(f333(f88(x81801),x81804),x81803)))+P106(f333(f333(f246(x81801),f333(f333(f296(x81801),x81802),x81803)),x81804)) % 173.51/173.28 [8181]~P69(x81811)+~P106(f333(f333(f247(x81811),f2(x81811)),x81813))+~P106(f333(f333(f247(x81811),x81812),f333(f333(f296(x81811),x81814),x81813)))+P106(f333(f333(f247(x81811),f333(f333(f88(x81811),x81812),x81813)),x81814)) % 173.51/173.28 [8182]~P70(x81821)+~P106(f333(f333(f247(x81821),f2(x81821)),x81823))+~P106(f333(f333(f247(x81821),x81822),f333(f333(f296(x81821),x81824),x81823)))+P106(f333(f333(f247(x81821),f333(f333(f88(x81821),x81822),x81823)),x81824)) % 173.51/173.28 [8184]~P69(x81841)+~P106(f333(f333(f247(x81841),f2(x81841)),x81843))+~P106(f333(f333(f247(x81841),x81842),f333(f333(f88(x81841),x81844),x81843)))+P106(f333(f333(f247(x81841),f333(f333(f296(x81841),x81842),x81843)),x81844)) % 173.51/173.28 [8185]~P70(x81851)+~P106(f333(f333(f247(x81851),f2(x81851)),x81853))+~P106(f333(f333(f247(x81851),x81852),f333(f333(f88(x81851),x81854),x81853)))+P106(f333(f333(f247(x81851),f333(f333(f296(x81851),x81852),x81853)),x81854)) % 173.51/173.28 [8311]~P69(x83111)+~P106(f333(f333(f247(x83111),f2(x83111)),x83114))+P106(f333(f333(f246(x83111),x83112),f333(f333(f88(x83111),x83113),x83114)))+~P106(f333(f333(f246(x83111),f333(f333(f296(x83111),x83112),x83114)),x83113)) % 173.51/173.28 [8313]~P69(x83131)+~P106(f333(f333(f247(x83131),f2(x83131)),x83134))+P106(f333(f333(f246(x83131),x83132),f333(f333(f296(x83131),x83133),x83134)))+~P106(f333(f333(f246(x83131),f333(f333(f88(x83131),x83132),x83134)),x83133)) % 173.51/173.28 [8314]~P70(x83141)+~P106(f333(f333(f247(x83141),f2(x83141)),x83144))+P106(f333(f333(f246(x83141),x83142),f333(f333(f88(x83141),x83143),x83144)))+~P106(f333(f333(f246(x83141),f333(f333(f296(x83141),x83142),x83144)),x83143)) % 173.51/173.28 [8315]~P70(x83151)+~P106(f333(f333(f247(x83151),f2(x83151)),x83154))+P106(f333(f333(f246(x83151),x83152),f333(f333(f296(x83151),x83153),x83154)))+~P106(f333(f333(f246(x83151),f333(f333(f88(x83151),x83152),x83154)),x83153)) % 173.51/173.28 [8316]~P69(x83161)+~P106(f333(f333(f247(x83161),f2(x83161)),x83164))+P106(f333(f333(f247(x83161),x83162),f333(f333(f88(x83161),x83163),x83164)))+~P106(f333(f333(f247(x83161),f333(f333(f296(x83161),x83162),x83164)),x83163)) % 173.51/173.28 [8318]~P69(x83181)+~P106(f333(f333(f247(x83181),f2(x83181)),x83184))+P106(f333(f333(f247(x83181),x83182),f333(f333(f296(x83181),x83183),x83184)))+~P106(f333(f333(f247(x83181),f333(f333(f88(x83181),x83182),x83184)),x83183)) % 173.51/173.28 [8319]~P70(x83191)+~P106(f333(f333(f247(x83191),f2(x83191)),x83194))+P106(f333(f333(f247(x83191),x83192),f333(f333(f88(x83191),x83193),x83194)))+~P106(f333(f333(f247(x83191),f333(f333(f296(x83191),x83192),x83194)),x83193)) % 173.51/173.28 [8320]~P70(x83201)+~P106(f333(f333(f247(x83201),f2(x83201)),x83204))+P106(f333(f333(f247(x83201),x83202),f333(f333(f296(x83201),x83203),x83204)))+~P106(f333(f333(f247(x83201),f333(f333(f88(x83201),x83202),x83204)),x83203)) % 173.51/173.28 [8482]~P70(x84821)+~P106(f333(f333(f247(x84821),x84823),f2(x84821)))+~P106(f333(f333(f246(x84821),f333(f333(f296(x84821),x84824),x84823)),x84822))+P106(f333(f333(f246(x84821),f333(f333(f88(x84821),x84822),x84823)),x84824)) % 173.51/173.28 [8483]~P70(x84831)+~P106(f333(f333(f247(x84831),x84833),f2(x84831)))+~P106(f333(f333(f246(x84831),f333(f333(f88(x84831),x84834),x84833)),x84832))+P106(f333(f333(f246(x84831),f333(f333(f296(x84831),x84832),x84833)),x84834)) % 173.51/173.28 [8484]~P70(x84841)+~P106(f333(f333(f247(x84841),x84843),f2(x84841)))+~P106(f333(f333(f247(x84841),f333(f333(f296(x84841),x84844),x84843)),x84842))+P106(f333(f333(f247(x84841),f333(f333(f88(x84841),x84842),x84843)),x84844)) % 173.51/173.28 [8485]~P70(x84851)+~P106(f333(f333(f247(x84851),x84853),f2(x84851)))+~P106(f333(f333(f247(x84851),f333(f333(f88(x84851),x84854),x84853)),x84852))+P106(f333(f333(f247(x84851),f333(f333(f296(x84851),x84852),x84853)),x84854)) % 173.51/173.28 [8497]~P106(f333(x84971,x84974))+~P106(f333(f333(f247(a910),x84972),f333(f333(f88(a910),x84973),f333(a123,x84974))))+P106(f333(x84971,f333(f333(f42(a910),x84972),x84973)))+~P106(f333(f333(f246(a910),f333(f333(f88(a910),x84973),x84974)),x84972)) % 173.51/173.28 [8717]~P101(x87171)+~P106(f333(f67(x87171),x87174))+~P106(f333(f333(f335(x87171),x87172),x87174))+P106(f333(f333(f246(x87171),f333(f333(f121(x87171),x87172),x87173)),f333(f333(f70(x87171,x87171,f121(x87171)),x87173),x87174))) % 173.51/173.28 [8718]~P110(x87181)+~P106(f333(f67(x87181),x87184))+~P106(f333(f333(f335(x87181),x87182),x87184))+P106(f333(f333(f246(x87181),f333(f333(f245(x87181),x87182),x87183)),f333(f333(f70(x87181,x87181,f245(x87181)),x87183),x87184))) % 173.51/173.28 [8871]~P106(f333(f67(x88711),x88712))+E(f333(f41(x88711),f333(f333(f23(f917(x88711,a905)),x88712),f333(f333(f315(x88711),x88713),x88714))),f333(f333(f23(a910),f333(f41(x88711),f333(f333(f23(f917(x88711,a905)),x88712),x88714))),f85(a910)))+P106(f333(f333(f335(x88711),x88713),x88714))+~P106(f333(f333(f335(x88711),x88713),x88712)) % 173.51/173.28 [8948]E(f333(f333(f87(a1),f400(x89481,x89482,x89483,x89484)),f401(x89481,x89482,x89483,x89484)),x89484)+~P106(f333(f333(f247(a1),f2(a1)),x89483))+~P106(f333(f333(f246(a1),x89484),x89481))+P106(f333(f333(f246(a1),f333(f333(f23(a1),x89484),x89483)),x89481)) % 173.51/173.28 [8949]E(f333(f333(f87(a1),f418(x89491,x89492,x89493,x89494)),f419(x89491,x89492,x89493,x89494)),x89494)+~P106(f333(f333(f247(a1),f2(a1)),x89493))+~P106(f333(f333(f247(a1),x89494),x89491))+P106(f333(f333(f247(a1),f333(f333(f23(a1),x89494),x89493)),x89491)) % 173.51/173.28 [9173]~P106(f333(f333(f247(a1),f2(a1)),x91733))+~P106(f333(f333(f246(a1),x91734),x91731))+P106(f333(f333(f335(a1),f400(x91731,x91732,x91733,x91734)),x91732))+P106(f333(f333(f246(a1),f333(f333(f23(a1),x91734),x91733)),x91731)) % 173.51/173.28 [9174]~P106(f333(f333(f247(a1),f2(a1)),x91743))+~P106(f333(f333(f247(a1),x91744),x91741))+P106(f333(f333(f335(a1),f418(x91741,x91742,x91743,x91744)),x91742))+P106(f333(f333(f247(a1),f333(f333(f23(a1),x91744),x91743)),x91741)) % 173.51/173.28 [9261]~P106(f333(f333(f247(a1),f2(a1)),x92612))+~P106(f333(f333(f246(a1),x92611),x92613))+P106(f333(f333(f335(a1),f401(x92613,x92614,x92612,x92611)),f309(a1,f85(a1),x92612)))+P106(f333(f333(f246(a1),f333(f333(f23(a1),x92611),x92612)),x92613)) % 173.51/173.28 [9262]~P106(f333(f333(f247(a1),f2(a1)),x92622))+~P106(f333(f333(f247(a1),x92621),x92623))+P106(f333(f333(f335(a1),f419(x92623,x92624,x92622,x92621)),f309(a1,f85(a1),x92622)))+P106(f333(f333(f247(a1),f333(f333(f23(a1),x92621),x92622)),x92623)) % 173.51/173.28 [9280]~P106(f333(f333(f246(a1),f2(a1)),x92804))+~P106(f333(f333(f247(a1),f2(a1)),x92803))+~P106(f333(f333(f247(a1),x92804),x92801))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),f333(f333(f88(a1),x92801),f51(a1,x92802,x92803))),x92804))) % 173.51/173.28 [9309]E(x93091,x93092)+~P42(x93093,x93094)+~P106(f333(f333(f335(f916(x93093,x93093)),f333(f333(f265(x93093,x93093),x93092),x93091)),x93094))+~P106(f333(f333(f335(f916(x93093,x93093)),f333(f333(f265(x93093,x93093),x93091),x93092)),x93094)) % 173.51/173.28 [9342]~P102(x93421)+~P106(f333(f67(x93421),x93424))+~P106(f333(f333(f246(x93421),x93422),f680(x93423,x93422,x93424,x93421)))+P106(f333(f333(f246(x93421),f333(f333(f112(x93421),x93422),x93423)),f333(f333(f70(x93421,x93421,f112(x93421)),x93423),x93424))) % 173.51/173.28 [9343]~P110(x93431)+~P106(f333(f67(x93431),x93434))+~P106(f333(f333(f246(x93431),x93432),f676(x93433,x93432,x93434,x93431)))+P106(f333(f333(f246(x93431),f333(f333(f244(x93431),x93432),x93433)),f333(f333(f70(x93431,x93431,f244(x93431)),x93433),x93434))) % 173.51/173.28 [9357]~P106(f333(f333(f246(a1),x93574),f2(a1)))+~P106(f333(f333(f247(a1),f2(a1)),x93572))+~P106(f333(f333(f247(a1),x93571),x93574))+P106(f333(f333(f247(a1),f333(f333(f88(a1),x93571),x93572)),f333(f333(f87(a1),f333(f333(f88(a1),x93571),f51(a1,x93573,x93572))),x93574))) % 173.51/173.28 [9381]P106(f333(f67(x93811),x93812))+~P106(f333(f67(x93811),x93813))+~P106(f333(f333(f335(f917(x93811,a905)),x93812),f333(f333(f66(x93811),x93813),x93814)))+~P106(f333(f333(f246(f917(f916(x93811,x93811),a905)),x93814),f333(f333(f267(x93811,x93811),x93813),f333(f16(f917(x93811,a905),x93811),x93813)))) % 173.51/173.28 [9411]~P110(x94111)+~P106(f333(f67(x94111),x94114))+P106(f333(f333(f335(x94111),f676(x94112,x94113,x94114,x94111)),x94114))+P106(f333(f333(f246(x94111),f333(f333(f244(x94111),x94113),x94112)),f333(f333(f70(x94111,x94111,f244(x94111)),x94112),x94114))) % 173.51/173.28 [9412]~P102(x94121)+~P106(f333(f67(x94121),x94124))+P106(f333(f333(f335(x94121),f680(x94122,x94123,x94124,x94121)),x94124))+P106(f333(f333(f246(x94121),f333(f333(f112(x94121),x94123),x94122)),f333(f333(f70(x94121,x94121,f112(x94121)),x94122),x94124))) % 173.51/173.28 [9830]~P106(f333(f67(x98302),x98304))+~P106(f333(f67(x98301),x98303))+~P106(f333(f333(f246(a910),f333(f41(x98302),x98304)),f333(f41(x98301),x98303)))+P106(f333(f333(f246(f917(x98301,a905)),f333(f316(x98302,x98301,f347(x98303,x98301,x98304,x98302)),x98304)),x98303)) % 173.51/173.28 [9462]~P106(f333(f333(f335(x94621),x94622),x94624))+P106(f333(f333(f335(x94621),x94622),x94623))+~P106(f333(f333(f247(f917(x94621,a905)),x94624),f333(f333(f315(x94621),x94622),x94623)))+P106(f333(f333(f247(f917(x94621,a905)),f333(f333(f23(f917(x94621,a905)),x94624),f333(f333(f315(x94621),x94622),f196(f917(x94621,a905))))),x94623)) % 173.51/173.28 [9632]~P106(f333(f333(f335(x96321),x96322),x96324))+P106(f333(f333(f335(x96321),x96322),x96323))+P106(f333(f333(f247(f917(x96321,a905)),x96324),f333(f333(f315(x96321),x96322),x96323)))+~P106(f333(f333(f247(f917(x96321,a905)),f333(f333(f23(f917(x96321,a905)),x96324),f333(f333(f315(x96321),x96322),f196(f917(x96321,a905))))),x96323)) % 173.51/173.28 [9658]P106(f333(f333(f335(x96581),x96582),x96583))+~P106(f333(f333(f246(f917(x96581,a905)),x96584),x96583))+P106(f333(f333(f247(f917(x96581,a905)),x96584),f333(f333(f315(x96581),x96582),x96583)))+~P106(f333(f333(f247(f917(x96581,a905)),f333(f333(f23(f917(x96581,a905)),x96584),f333(f333(f315(x96581),x96582),f196(f917(x96581,a905))))),x96583)) % 173.51/173.28 [9663]~P106(f333(f333(f335(x96631),x96633),x96632))+~P106(f333(f333(f247(f917(x96631,a905)),x96632),x96634))+P106(f333(f333(f247(f917(x96631,a905)),x96632),f333(f333(f315(x96631),x96633),x96634)))+~P106(f333(f333(f247(f917(x96631,a905)),f333(f333(f23(f917(x96631,a905)),x96632),f333(f333(f315(x96631),x96633),f196(f917(x96631,a905))))),x96634)) % 173.51/173.28 [9681]~P106(f333(f333(f246(f917(x96811,a905)),x96812),x96814))+~P106(f333(f333(f247(f917(x96811,a905)),x96812),x96814))+P106(f333(f333(f247(f917(x96811,a905)),x96812),f333(f333(f315(x96811),x96813),x96814)))+~P106(f333(f333(f247(f917(x96811,a905)),f333(f333(f23(f917(x96811,a905)),x96812),f333(f333(f315(x96811),x96813),f196(f917(x96811,a905))))),x96814)) % 173.51/173.28 [9733]~P112(x97332)+~P7(x97331)+~P106(f333(f333(f246(f917(x97331,x97332)),x97333),x97334))+P106(f333(f63(x97331),f333(f333(f18(x97331,x97332,a905),f333(f333(f8(x97332,f917(x97332,a905),x97331),f246(x97332)),x97333)),x97334))) % 173.51/173.28 [9877]~P112(x98772)+~P7(x98771)+P106(f333(f333(f246(f917(x98771,x98772)),x98773),x98774))+~P106(f333(f63(x98771),f333(f333(f18(x98771,x98772,a905),f333(f333(f8(x98772,f917(x98772,a905),x98771),f246(x98772)),x98773)),x98774))) % 173.51/173.28 [10043]E(f333(f333(f172(x100431),f333(f333(f172(f911(x100431)),f187(x100431,x100432)),x100433)),x100434),f333(f333(f172(x100431),f333(f333(f172(f911(x100431)),x100432),x100434)),x100433))+~P106(f333(f333(f247(a910),x100433),f333(f197(f911(f911(x100431))),f187(x100431,x100432))))+~P16(a910,f333(f176(a910),f333(f333(f162(f911(x100431),a910),f197(f911(x100431))),x100432)))+~P106(f333(f333(f247(a910),x100434),f333(f197(f911(f911(x100431))),f333(f144(f911(x100431),f333(f333(f8(a910,a905,f911(x100431)),f333(f247(a910),x100433)),f197(f911(x100431)))),x100432)))) % 173.51/173.28 [10068]~P106(f333(f333(f335(f916(a910,a910)),x100684),x100681))+~P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),x100684),x100682)),a39))+~P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x100681),x100683)),a75))+P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x100681),f333(f333(f315(f916(a910,a910)),x100682),x100683))),a75)) % 173.51/173.28 [10069]~P106(f333(f333(f335(f916(a910,a910)),x100694),x100691))+~P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),x100694),x100692)),a77))+~P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x100691),x100693)),a78))+P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x100691),f333(f333(f315(f916(a910,a910)),x100692),x100693))),a78)) % 173.51/173.28 [9955]~P112(x99552)+~P7(x99551)+~P106(f333(f333(f247(f917(x99551,x99552)),x99553),x99554))+P106(f333(f62(x99551),f333(f333(f8(a905,a905,x99551),a328),f333(f333(f18(x99551,x99552,a905),f333(f333(f8(x99552,f917(x99552,a905),x99551),a330),x99553)),x99554)))) % 173.51/173.28 [10082]~P106(f333(f333(f335(f916(a910,a910)),x100824),x100823))+~P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),x100821),x100824)),a39))+~P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x100822),x100823)),a40))+P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),f333(f333(f315(f916(a910,a910)),x100821),x100822)),x100823)),a40)) % 173.51/173.28 [10083]~P106(f333(f333(f335(f916(a910,a910)),x100834),x100833))+~P106(f333(f333(f335(f916(f916(a910,a910),f916(a910,a910))),f333(f333(f265(f916(a910,a910),f916(a910,a910)),x100831),x100834)),a77))+~P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),x100832),x100833)),a76))+P106(f333(f333(f335(f916(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905))),f333(f333(f265(f917(f916(a910,a910),a905),f917(f916(a910,a910),a905)),f333(f333(f315(f916(a910,a910)),x100831),x100832)),x100833)),a76)) % 173.51/173.28 [6166]~P10(x61664,x61661)+~P106(f333(f333(x61661,x61662),x61665))+P106(f333(f333(x61661,x61662),x61663))+~P106(f333(f333(x61661,x61665),x61663)) % 173.51/173.28 [6167]~P53(x61674,x61671)+~P106(f333(f333(x61671,x61672),x61675))+P106(f333(f333(x61671,x61672),x61673))+~P106(f333(f333(x61671,x61675),x61673)) % 173.51/173.28 [9722]~P41(x97221,x97224)+P106(f333(f333(f335(f916(f911(x97221),f911(x97221))),f333(f333(f265(f911(x97221),f911(x97221)),x97222),x97223)),f155(x97221,x97224)))+~P106(f333(f333(f335(f916(f911(x97221),f911(x97221))),f333(f333(f265(f911(x97221),f911(x97221)),x97222),x97225)),f155(x97221,x97224)))+~P106(f333(f333(f335(f916(f911(x97221),f911(x97221))),f333(f333(f265(f911(x97221),f911(x97221)),x97225),x97223)),f155(x97221,x97224))) % 173.51/173.28 [5431]~P6(x54315)+E(x54311,x54312)+~E(x54313,x54314)+~E(f333(f333(f23(x54315),x54313),x54314),f333(f333(f23(x54315),x54311),x54312)) % 173.51/173.28 [6277]~P19(x62775,x62771,x62773)+E(f333(f333(x62771,x62772),f333(x62773,x62774)),f333(x62773,x62774))+~P106(f333(f67(x62775),x62774))+~P106(f333(f333(f335(x62775),x62772),x62774)) % 173.51/173.28 [6463]~P4(x64631)+~E(f333(f333(f23(x64631),x64634),x64635),f333(f333(f23(x64631),x64632),x64633))+~P106(f333(f333(f246(x64631),x64634),x64635))+P106(f333(f333(f246(x64631),x64632),x64633)) % 173.51/173.28 [6465]~P4(x64651)+~E(f333(f333(f23(x64651),x64654),x64655),f333(f333(f23(x64651),x64652),x64653))+~P106(f333(f333(f247(x64651),x64654),x64655))+P106(f333(f333(f247(x64651),x64652),x64653)) % 173.51/173.28 [7427]~E(x74272,f333(f333(f159(x74271),x74274),x74275))+P106(f333(f333(f335(f911(x74271)),x74272),f169(x74271,x74273)))+~P106(f333(f333(f335(f911(x74271)),x74275),f169(x74271,x74273)))+~P106(f333(f333(f335(x74271),x74274),x74273)) % 173.51/173.28 [7831]~E(f333(f197(f911(x78311)),x78313),f333(f197(f911(x78312)),x78314))+~E(f333(f333(f162(f916(x78311,x78312),x78312),f268(x78311,x78312)),x78315),x78314)+~E(f333(f333(f162(f916(x78311,x78312),x78311),f264(x78311,x78312)),x78315),x78313)+E(f333(f333(f189(x78311,x78312),x78313),x78314),x78315) % 173.51/173.28 [8172]~P112(x81721)+P106(f333(f333(f247(f917(x81721,a905)),f309(x81721,x81722,x81723)),f309(x81721,x81724,x81725)))+~P106(f333(f333(f246(x81721),x81724),x81725))+P106(f333(f333(f246(x81721),x81722),x81723)) % 173.51/173.28 [8268]~P112(x82681)+P106(f333(f333(f246(f917(x82681,a905)),f309(x82681,x82682,x82683)),f309(x82681,x82684,x82685)))+~P106(f333(f333(f246(x82681),x82683),x82685))+~P106(f333(f333(f246(x82681),x82684),x82682)) % 173.51/173.28 [8389]~P110(x83891)+P106(f333(f333(f246(x83891),x83892),x83893))+P106(f333(f333(f246(x83891),x83894),x83893))+~P106(f333(f333(f246(f917(x83891,a905)),f333(f308(x83891,x83893),x83892)),f333(f308(x83891,x83894),x83895))) % 173.51/173.28 [8390]~P110(x83901)+P106(f333(f333(f246(x83901),x83902),x83903))+P106(f333(f333(f246(x83901),x83902),x83904))+~P106(f333(f333(f246(f917(x83901,a905)),f333(f308(x83901,x83903),x83902)),f333(f308(x83901,x83905),x83904))) % 173.51/173.28 [8635]~P112(x86351)+~P106(f333(f333(f246(f917(x86351,a905)),f309(x86351,x86354,x86352)),f309(x86351,x86355,x86353)))+P106(f333(f333(f246(x86351),x86352),x86353))+~P106(f333(f333(f246(x86351),x86354),x86352)) % 173.51/173.28 [8636]~P112(x86361)+~P106(f333(f333(f247(f917(x86361,a905)),f309(x86361,x86364,x86362)),f309(x86361,x86365,x86363)))+P106(f333(f333(f246(x86361),x86362),x86363))+~P106(f333(f333(f246(x86361),x86364),x86362)) % 173.51/173.28 [8637]~P112(x86371)+~P106(f333(f333(f246(f917(x86371,a905)),f309(x86371,x86373,x86374)),f309(x86371,x86372,x86375)))+P106(f333(f333(f246(x86371),x86372),x86373))+~P106(f333(f333(f246(x86371),x86373),x86374)) % 173.51/173.28 [8638]~P112(x86381)+~P106(f333(f333(f247(f917(x86381,a905)),f309(x86381,x86383,x86384)),f309(x86381,x86382,x86385)))+P106(f333(f333(f246(x86381),x86382),x86383))+~P106(f333(f333(f246(x86381),x86383),x86384)) % 173.51/173.28 [6165]~P19(x61652,x61655,x61653)+E(x61651,f196(f917(x61652,a905)))+~P106(f333(f67(x61652),x61651))+E(f333(x61653,f333(f333(f315(x61652),x61654),x61651)),f333(f333(x61655,x61654),f333(x61653,x61651))) % 173.51/173.28 [6928]~E(x69281,x69282)+~E(f333(f333(f112(f917(x69283,a905)),x69284),x69285),f196(f917(x69283,a905)))+~P106(f333(f333(f335(x69283),x69282),x69285))+~P106(f333(f333(f335(x69283),x69281),x69284)) % 173.51/173.28 [7006]~P20(x70062,x70065,x70061)+~P106(f333(f67(x70062),x70064))+E(f333(x70061,f333(f333(f315(x70062),x70063),x70064)),f333(f333(f70(x70062,x70062,x70065),x70063),x70064))+P106(f333(f333(f335(x70062),x70063),x70064)) % 173.51/173.28 [7073]~P72(x70732)+~P106(f333(f67(x70731),x70735))+E(f333(f333(f6(x70731,x70732),x70733),f333(f333(f315(x70731),x70734),x70735)),f333(f333(f87(x70732),f333(x70733,x70734)),f333(f333(f6(x70731,x70732),x70733),x70735)))+P106(f333(f333(f335(x70731),x70734),x70735)) % 173.51/173.28 [7075]~P78(x70752)+~P106(f333(f67(x70751),x70755))+E(f333(f333(f9(x70751,x70752),x70753),f333(f333(f315(x70751),x70754),x70755)),f333(f333(f88(x70752),f333(x70753,x70754)),f333(f333(f9(x70751,x70752),x70753),x70755)))+P106(f333(f333(f335(x70751),x70754),x70755)) % 173.51/173.28 [7575]~P20(x75752,x75755,x75751)+~P106(f333(f67(x75752),x75754))+E(f333(x75751,f333(f333(f315(x75752),x75753),x75754)),x75753)+~E(f333(f333(f23(f917(x75752,a905)),x75754),f333(f333(f315(x75752),x75753),f196(f917(x75752,a905)))),f196(f917(x75752,a905))) % 173.51/173.28 [7886]~P106(f333(x78861,x78863))+~P106(f333(f333(f202(x78862),x78863),x78865))+~P106(f333(f333(f202(f30(x78861,x78862)),x78865),x78864))+P106(f333(f333(f202(f30(x78861,x78862)),x78863),x78864)) % 173.51/173.28 [7938]~P101(x79381)+~P106(f333(f333(f246(x79381),x79383),x79385))+~P106(f333(f333(f246(x79381),x79382),x79384))+P106(f333(f333(f246(x79381),f333(f333(f121(x79381),x79382),x79383)),f333(f333(f121(x79381),x79384),x79385))) % 173.51/173.28 [7939]~P102(x79391)+~P106(f333(f333(f246(x79391),x79393),x79395))+~P106(f333(f333(f246(x79391),x79392),x79394))+P106(f333(f333(f246(x79391),f333(f333(f112(x79391),x79392),x79393)),f333(f333(f112(x79391),x79394),x79395))) % 173.51/173.28 [7940]~P86(x79401)+~P106(f333(f333(f246(x79401),x79403),x79405))+~P106(f333(f333(f246(x79401),x79402),x79404))+P106(f333(f333(f246(x79401),f333(f333(f87(x79401),x79402),x79403)),f333(f333(f87(x79401),x79404),x79405))) % 173.51/173.28 [7941]~P110(x79411)+~P106(f333(f333(f246(x79411),x79413),x79415))+~P106(f333(f333(f246(x79411),x79412),x79414))+P106(f333(f333(f246(x79411),f333(f333(f244(x79411),x79412),x79413)),f333(f333(f244(x79411),x79414),x79415))) % 173.51/173.28 [7942]~P110(x79421)+~P106(f333(f333(f246(x79421),x79423),x79425))+~P106(f333(f333(f246(x79421),x79422),x79424))+P106(f333(f333(f246(x79421),f333(f333(f245(x79421),x79422),x79423)),f333(f333(f245(x79421),x79424),x79425))) % 173.51/173.28 [7943]~P88(x79431)+~P106(f333(f333(f246(x79431),x79433),x79435))+~P106(f333(f333(f247(x79431),x79432),x79434))+P106(f333(f333(f247(x79431),f333(f333(f87(x79431),x79432),x79433)),f333(f333(f87(x79431),x79434),x79435))) % 173.51/173.28 [7944]~P88(x79441)+~P106(f333(f333(f246(x79441),x79442),x79444))+~P106(f333(f333(f247(x79441),x79443),x79445))+P106(f333(f333(f247(x79441),f333(f333(f87(x79441),x79442),x79443)),f333(f333(f87(x79441),x79444),x79445))) % 173.51/173.28 [7945]~P88(x79451)+~P106(f333(f333(f247(x79451),x79453),x79455))+~P106(f333(f333(f247(x79451),x79452),x79454))+P106(f333(f333(f247(x79451),f333(f333(f87(x79451),x79452),x79453)),f333(f333(f87(x79451),x79454),x79455))) % 173.51/173.28 [8082]~P144(x80825)+E(x80821,x80822)+E(x80823,x80824)+~E(f333(f333(f87(x80825),f333(f333(f88(x80825),x80823),x80821)),f333(f333(f88(x80825),x80824),x80822)),f333(f333(f87(x80825),f333(f333(f88(x80825),x80823),x80822)),f333(f333(f88(x80825),x80824),x80821))) % 173.51/173.28 [8224]P32(x82241,x82242,x82243)+~P31(x82241,x82244,x82245)+~P32(x82241,x82242,f527(x82245,x82244,x82241,x82242))+~P106(f333(f333(f335(f909(x82241)),x82243),x82245)) % 173.51/173.28 [8289]~P110(x82894)+~P106(f333(f145(x82891),x82893))+P106(f333(f333(f335(x82891),x82892),f333(f180(x82891),x82893)))+P106(f333(f145(x82891),f333(f333(f156(x82891,x82894,x82895),x82892),x82893))) % 173.51/173.28 [8437]~P6(x84371)+E(f333(f333(f23(x84371),f333(f333(f6(a910,x84371),x84372),f333(f308(a910,x84373),x84374))),f333(f333(f6(a910,x84371),x84372),f333(f308(a910,x84373),x84375))),f333(f333(f6(a910,x84371),x84372),f333(f308(a910,x84375),x84374)))+~P106(f333(f333(f246(a910),x84375),x84374))+~P106(f333(f333(f246(a910),x84373),x84375)) % 173.51/173.28 [8438]~P72(x84381)+E(f333(f333(f87(x84381),f333(f333(f6(a910,x84381),x84382),f333(f308(a910,x84383),x84384))),f333(f333(f6(a910,x84381),x84382),f333(f308(a910,x84384),x84385))),f333(f333(f6(a910,x84381),x84382),f333(f308(a910,x84383),x84385)))+~P106(f333(f333(f246(a910),x84384),x84385))+~P106(f333(f333(f246(a910),x84383),x84384)) % 173.51/173.28 [8779]~P68(x87792)+E(x87791,f2(x87792))+E(x87793,f2(x87792))+E(f333(f333(f296(x87792),f333(f333(f23(x87792),f333(f333(f88(x87792),x87794),x87791)),f333(f333(f88(x87792),x87795),x87793))),f333(f333(f88(x87792),x87793),x87791)),f333(f333(f23(x87792),f333(f333(f296(x87792),x87794),x87793)),f333(f333(f296(x87792),x87795),x87791))) % 173.51/173.28 [8780]~P68(x87802)+E(x87801,f2(x87802))+E(x87803,f2(x87802))+E(f333(f333(f296(x87802),f333(f333(f87(x87802),f333(f333(f88(x87802),x87804),x87801)),f333(f333(f88(x87802),x87805),x87803))),f333(f333(f88(x87802),x87803),x87801)),f333(f333(f87(x87802),f333(f333(f296(x87802),x87804),x87803)),f333(f333(f296(x87802),x87805),x87801))) % 173.51/173.28 [8788]~E(x87882,f333(x87883,x87881))+E(x87881,f826(x87882,x87883,x87884,x87885))+~P27(x87885,x87884,x87883,f254(f917(x87885,a905)))+~P106(f333(f333(f335(x87884),x87882),f333(f316(x87885,x87884,x87883),f254(f917(x87885,a905))))) % 173.51/173.28 [9004]~P120(x90041)+~P106(f333(f333(f247(x90041),f333(f82(x90041),x90042)),x90044))+P106(f333(f333(f247(x90041),f333(f333(f88(x90041),f333(f82(x90041),x90042)),f333(f82(x90041),x90043))),f333(f333(f88(x90041),x90044),x90045)))+~P106(f333(f333(f247(x90041),f333(f82(x90041),x90043)),x90045)) % 173.51/173.28 [9022]~P31(x90221,x90225,x90224)+P32(x90221,x90222,x90223)+P106(f333(f333(f335(f909(x90221)),f527(x90224,x90225,x90221,x90222)),x90225))+~P106(f333(f333(f335(f909(x90221)),x90223),x90224)) % 173.51/173.28 [9130]~P27(x91301,x91303,x91305,x91302)+~P106(f333(f67(x91303),x91304))+P106(f333(f333(f246(a910),f333(f41(x91301),x91302)),f333(f41(x91303),x91304)))+~P106(f333(f333(f246(f917(x91303,a905)),f333(f316(x91301,x91303,x91305),x91302)),x91304)) % 173.51/173.28 [9202]~P72(x92022)+~P27(x92021,x92021,x92024,x92025)+~P106(f333(f67(x92021),x92025))+E(f333(f333(f6(x92021,x92022),f333(f79(x92021,x92022,x92021,x92023),x92024)),x92025),f333(f333(f6(x92021,x92022),x92023),f333(f316(x92021,x92021,x92024),x92025))) % 173.51/173.28 [9203]~P78(x92032)+~P27(x92031,x92031,x92034,x92035)+~P106(f333(f67(x92031),x92035))+E(f333(f333(f9(x92031,x92032),f333(f79(x92031,x92032,x92031,x92033),x92034)),x92035),f333(f333(f9(x92031,x92032),x92033),f333(f316(x92031,x92031,x92034),x92035))) % 173.51/173.28 [9322]~P40(x93221,x93222)+~P106(f333(f333(f335(x93221),x93223),x93224))+~P106(f333(f333(f335(x93221),x93225),x93224))+~P106(f333(f333(f335(f916(x93221,x93221)),f333(f333(f265(x93221,x93221),x93225),f670(x93222,x93221,x93224))),x93222)) % 173.51/173.28 [9356]~P27(x93562,x93563,x93565,x93561)+E(x93561,f196(f917(x93562,a905)))+E(f333(f316(x93563,x93562,f861(x93564,x93563,x93562,x93561)),x93564),x93561)+~P106(f333(f333(f246(f917(x93563,a905)),f333(f316(x93562,x93563,x93565),x93561)),x93564)) % 173.51/173.28 [9859]~P110(x98595)+~P8(x98595)+P106(f333(f333(f335(x98591),f485(x98592,x98593,x98591,x98594,x98595)),x98593))+~P106(f333(f333(f247(x98595),x98594),f333(f333(f45(x98591,x98595),x98593),x98592))) % 173.51/173.28 [9864]~P110(x98641)+~P8(x98641)+P106(f333(f333(f247(x98641),x98642),f333(x98643,f485(x98643,x98644,x98645,x98642,x98641))))+~P106(f333(f333(f247(x98641),x98642),f333(f333(f45(x98645,x98641),x98644),x98643))) % 173.51/173.28 [9881]~P72(x98815)+~P86(x98815)+P106(f333(f333(f335(x98811),f878(x98812,x98813,x98814,x98811,x98815)),x98814))+P106(f333(f333(f246(x98815),f333(f333(f6(x98811,x98815),x98813),x98814)),f333(f333(f6(x98811,x98815),x98812),x98814))) % 173.51/173.28 [9942]~P76(x99421)+~P106(f333(f72(x99421,x99421,f88(x99421),x99422,x99423),x99425))+P106(f333(f333(f335(x99421),x99422),x99423))+P106(f333(f72(x99421,x99421,f88(x99421),x99424,f333(f333(f315(x99421),x99422),x99423)),f333(f333(f88(x99421),x99424),x99425))) % 173.51/173.28 [10152]~P72(x101522)+~P106(f333(f67(x101521),x101525))+E(f333(f333(f6(x101521,x101522),f333(f333(f7(x101521,x101522,x101522),f333(f333(f18(x101521,x101522,f917(x101522,x101522)),f333(f333(f8(a905,f917(x101522,f917(x101522,x101522)),x101521),f107(x101522)),f333(a330,x101523))),x101524)),f2(x101522))),x101525),f2(x101522))+P106(f333(f333(f335(x101521),x101523),x101525)) % 173.51/173.28 [10153]~P78(x101532)+~P106(f333(f67(x101531),x101535))+E(f333(f333(f9(x101531,x101532),f333(f333(f7(x101531,x101532,x101532),f333(f333(f18(x101531,x101532,f917(x101532,x101532)),f333(f333(f8(a905,f917(x101532,f917(x101532,x101532)),x101531),f107(x101532)),f333(a330,x101533))),x101534)),f85(x101532))),x101535),f85(x101532))+P106(f333(f333(f335(x101531),x101533),x101535)) % 173.51/173.28 [10154]~P72(x101542)+~P106(f333(f67(x101541),x101545))+E(f333(f333(f6(x101541,x101542),f333(f333(f7(x101541,x101542,x101542),f333(f333(f18(x101541,x101542,f917(x101542,x101542)),f333(f333(f8(a905,f917(x101542,f917(x101542,x101542)),x101541),f107(x101542)),f333(a330,x101543))),x101544)),f2(x101542))),x101545),f333(x101544,x101543))+~P106(f333(f333(f335(x101541),x101543),x101545)) % 173.51/173.28 [10155]~P78(x101552)+~P106(f333(f67(x101551),x101555))+E(f333(f333(f9(x101551,x101552),f333(f333(f7(x101551,x101552,x101552),f333(f333(f18(x101551,x101552,f917(x101552,x101552)),f333(f333(f8(a905,f917(x101552,f917(x101552,x101552)),x101551),f107(x101552)),f333(a330,x101553))),x101554)),f85(x101552))),x101555),f333(x101554,x101553))+~P106(f333(f333(f335(x101551),x101553),x101555)) % 173.51/173.28 [10167]~P72(x101671)+~P86(x101671)+~P106(f333(f333(f246(x101671),f333(x101673,f878(x101675,x101673,x101674,x101672,x101671))),f333(x101675,f878(x101675,x101673,x101674,x101672,x101671))))+P106(f333(f333(f246(x101671),f333(f333(f6(x101672,x101671),x101673),x101674)),f333(f333(f6(x101672,x101671),x101675),x101674))) % 173.51/173.28 [10211]~P72(x102112)+~P106(f333(f67(x102111),x102115))+E(f333(f333(f6(x102111,x102112),f333(f333(f7(x102111,x102112,x102112),f333(f333(f18(x102111,x102112,f917(x102112,x102112)),f333(f333(f8(a905,f917(x102112,f917(x102112,x102112)),x102111),f107(x102112)),f333(f333(f7(x102111,x102111,a905),a330),x102113))),x102114)),f2(x102112))),x102115),f2(x102112))+P106(f333(f333(f335(x102111),x102113),x102115)) % 173.51/173.28 [10212]~P78(x102122)+~P106(f333(f67(x102121),x102125))+E(f333(f333(f9(x102121,x102122),f333(f333(f7(x102121,x102122,x102122),f333(f333(f18(x102121,x102122,f917(x102122,x102122)),f333(f333(f8(a905,f917(x102122,f917(x102122,x102122)),x102121),f107(x102122)),f333(f333(f7(x102121,x102121,a905),a330),x102123))),x102124)),f85(x102122))),x102125),f85(x102122))+P106(f333(f333(f335(x102121),x102123),x102125)) % 173.51/173.28 [10214]~P72(x102142)+~P106(f333(f67(x102141),x102145))+E(f333(f333(f6(x102141,x102142),f333(f333(f7(x102141,x102142,x102142),f333(f333(f18(x102141,x102142,f917(x102142,x102142)),f333(f333(f8(a905,f917(x102142,f917(x102142,x102142)),x102141),f107(x102142)),f333(f333(f7(x102141,x102141,a905),a330),x102143))),x102144)),f2(x102142))),x102145),f333(x102144,x102143))+~P106(f333(f333(f335(x102141),x102143),x102145)) % 173.51/173.28 [10215]~P78(x102152)+~P106(f333(f67(x102151),x102155))+E(f333(f333(f9(x102151,x102152),f333(f333(f7(x102151,x102152,x102152),f333(f333(f18(x102151,x102152,f917(x102152,x102152)),f333(f333(f8(a905,f917(x102152,f917(x102152,x102152)),x102151),f107(x102152)),f333(f333(f7(x102151,x102151,a905),a330),x102153))),x102154)),f85(x102152))),x102155),f333(x102154,x102153))+~P106(f333(f333(f335(x102151),x102153),x102155)) % 173.51/173.28 [7937]~P6(x79372)+~P106(f333(f67(x79371),x79374))+E(f333(f333(f6(x79371,x79372),x79373),f333(f333(f23(f917(x79371,a905)),x79374),f333(f333(f315(x79371),x79375),f196(f917(x79371,a905))))),f333(f333(f6(x79371,x79372),x79373),x79374))+P106(f333(f333(f335(x79371),x79375),x79374)) % 173.51/173.28 [8445]~P113(x84452)+~P106(f333(f67(x84451),x84454))+E(f333(f333(f6(x84451,x84452),x84453),f333(f333(f23(f917(x84451,a905)),x84454),f333(f333(f315(x84451),x84455),f196(f917(x84451,a905))))),f333(f333(f23(x84452),f333(f333(f6(x84451,x84452),x84453),x84454)),f333(x84453,x84455)))+~P106(f333(f333(f335(x84451),x84455),x84454)) % 173.51/173.28 [8446]~P6(x84462)+~P106(f333(f67(x84461),x84464))+E(f333(f333(f6(x84461,x84462),x84463),f333(f333(f23(f917(x84461,a905)),x84464),f333(f333(f315(x84461),x84465),f196(f917(x84461,a905))))),f333(f333(f23(x84462),f333(f333(f6(x84461,x84462),x84463),x84464)),f333(x84463,x84465)))+~P106(f333(f333(f335(x84461),x84465),x84464)) % 173.51/173.28 [8475]~P6(x84751)+~P106(f333(f67(x84752),x84754))+E(f333(f333(f23(x84751),f333(f333(f6(x84752,x84751),x84753),x84754)),f333(f333(f6(x84752,x84751),x84753),x84755)),f333(f333(f6(x84752,x84751),x84753),f333(f333(f23(f917(x84752,a905)),x84754),x84755)))+~P106(f333(f333(f246(f917(x84752,a905)),x84755),x84754)) % 173.51/173.28 [8494]P106(f333(f67(x84941),f333(x84942,x84943)))+~P106(f333(f67(x84944),x84945))+~P106(f333(f333(f335(x84944),x84943),x84945))+~P106(f333(f67(x84941),f333(f333(f45(x84944,f917(x84941,a905)),x84945),x84942))) % 173.51/173.28 [8960]~P11(x89601,x89605,x89604)+~E(f333(f292(x89601,x89601,x89604),f333(f333(f315(x89601),x89602),f196(f917(x89601,a905)))),f333(f292(x89601,x89601,x89604),f333(f333(f315(x89601),x89603),f196(f917(x89601,a905)))))+~P106(f333(f333(f335(x89601),x89603),x89605))+P106(f333(f333(f335(f916(x89601,x89601)),f333(f333(f265(x89601,x89601),x89602),x89603)),x89604)) % 173.51/173.28 [9278]~P106(f333(x92781,x92785))+P106(f333(x92781,f694(x92781,x92782,x92783,x92784)))+P106(f333(x92781,f682(x92781,x92782,x92783,x92784)))+~P106(f333(f333(f335(x92784),x92785),f333(f333(f121(f917(x92784,a905)),x92783),x92782))) % 173.51/173.28 [9467]~P106(f333(x94671,x94675))+P106(f333(x94671,f682(x94671,x94672,x94673,x94674)))+P106(f333(f333(f335(x94674),f694(x94671,x94672,x94673,x94674)),x94672))+~P106(f333(f333(f335(x94674),x94675),f333(f333(f121(f917(x94674,a905)),x94673),x94672))) % 173.51/173.28 [9468]~P106(f333(x94681,x94685))+P106(f333(x94681,f694(x94681,x94682,x94683,x94684)))+P106(f333(f333(f335(x94684),f682(x94681,x94682,x94683,x94684)),x94683))+~P106(f333(f333(f335(x94684),x94685),f333(f333(f121(f917(x94684,a905)),x94683),x94682))) % 173.51/173.28 [9474]P106(f333(x94741,x94742))+~P106(f333(x94741,f674(x94741,x94743,x94744,x94745)))+~P106(f333(x94741,f662(x94741,x94743,x94744,x94745)))+~P106(f333(f333(f335(x94745),x94742),f333(f333(f121(f917(x94745,a905)),x94744),x94743))) % 173.51/173.28 [9479]~P41(x94791,x94794)+~P106(f333(f333(f335(f916(x94791,x94791)),f333(f333(f265(x94791,x94791),x94792),x94795)),x94794))+P106(f333(f333(f335(f916(x94791,x94791)),f333(f333(f265(x94791,x94791),x94792),x94793)),x94794))+~P106(f333(f333(f335(f916(x94791,x94791)),f333(f333(f265(x94791,x94791),x94795),x94793)),x94794)) % 173.51/173.28 [9518]E(x95181,x95182)+~P106(f333(f333(f335(f916(x95183,x95183)),f333(f333(f265(x95183,x95183),x95181),x95182)),f313(x95183,x95185)))+P106(f333(f333(f335(x95183),x95181),x95184))+~P106(f333(f333(f246(f917(f916(x95183,x95183),a905)),x95185),f333(f333(f267(x95183,x95183),x95184),f333(f16(f917(x95183,a905),x95183),x95184)))) % 173.51/173.28 [9536]P106(f333(x95361,x95362))+~P106(f333(x95361,f662(x95361,x95364,x95365,x95363)))+P106(f333(f333(f335(x95363),f674(x95361,x95364,x95365,x95363)),x95364))+~P106(f333(f333(f335(x95363),x95362),f333(f333(f121(f917(x95363,a905)),x95365),x95364))) % 173.51/173.28 [9537]P106(f333(x95371,x95372))+~P106(f333(x95371,f674(x95371,x95374,x95375,x95373)))+P106(f333(f333(f335(x95373),f662(x95371,x95374,x95375,x95373)),x95375))+~P106(f333(f333(f335(x95373),x95372),f333(f333(f121(f917(x95373,a905)),x95375),x95374))) % 173.51/173.28 [9603]P106(f333(x96031,x96032))+P106(f333(f333(f335(x96033),f674(x96031,x96034,x96035,x96033)),x96034))+P106(f333(f333(f335(x96033),f662(x96031,x96034,x96035,x96033)),x96035))+~P106(f333(f333(f335(x96033),x96032),f333(f333(f121(f917(x96033,a905)),x96035),x96034))) % 173.51/173.28 [9605]~P106(f333(x96052,x96055))+P106(f333(f333(f335(x96051),f694(x96052,x96053,x96054,x96051)),x96053))+P106(f333(f333(f335(x96051),f682(x96052,x96053,x96054,x96051)),x96054))+~P106(f333(f333(f335(x96051),x96055),f333(f333(f121(f917(x96051,a905)),x96054),x96053))) % 173.51/173.28 [9765]~P11(x97651,x97655,x97654)+~P106(f333(f333(f335(x97651),x97653),x97655))+P106(f333(f333(f335(f916(x97651,x97651)),f333(f333(f265(x97651,x97651),x97652),x97653)),x97654))+~P106(f333(f333(f246(f917(x97651,a905)),f333(f292(x97651,x97651,x97654),f333(f333(f315(x97651),x97653),f196(f917(x97651,a905))))),f333(f292(x97651,x97651,x97654),f333(f333(f315(x97651),x97652),f196(f917(x97651,a905)))))) % 173.51/173.28 [9892]~P110(x98925)+~P8(x98925)+P106(f333(f333(f335(x98921),f658(x98922,x98923,x98924,x98921,x98925)),x98924))+~P106(f333(f333(f247(x98925),f333(f333(f46(x98921,x98925),x98924),x98923)),x98922)) % 173.51/173.28 [9926]~P86(x99265)+~P82(x99265)+P106(f333(f333(f335(x99261),f742(x99262,x99263,x99264,x99261,x99265)),f333(f180(x99261),x99264)))+P106(f333(f333(f246(x99265),f333(f173(x99265),f333(f333(f162(x99261,x99265),x99263),x99264))),f333(f173(x99265),f333(f333(f162(x99261,x99265),x99262),x99264)))) % 173.51/173.28 [10031]~P110(x100311)+~P8(x100311)+P106(f333(f333(f247(x100311),f333(x100312,f658(x100313,x100312,x100314,x100315,x100311))),x100313))+~P106(f333(f333(f247(x100311),f333(f333(f46(x100315,x100311),x100314),x100312)),x100313)) % 173.51/173.28 [10171]~P86(x101711)+~P82(x101711)+~P106(f333(f333(f246(x101711),f333(x101713,f742(x101715,x101713,x101714,x101712,x101711))),f333(x101715,f742(x101715,x101713,x101714,x101712,x101711))))+P106(f333(f333(f246(x101711),f333(f173(x101711),f333(f333(f162(x101712,x101711),x101713),x101714))),f333(f173(x101711),f333(f333(f162(x101712,x101711),x101715),x101714)))) % 173.51/173.28 [8801]~P72(x88011)+~P106(f333(f67(x88014),x88015))+~P106(f333(f333(f335(x88014),x88013),x88015))+E(f333(f333(f87(x88011),f333(x88012,x88013)),f333(f333(f6(x88014,x88011),x88012),f333(f333(f23(f917(x88014,a905)),x88015),f333(f333(f315(x88014),x88013),f196(f917(x88014,a905)))))),f333(f333(f6(x88014,x88011),x88012),x88015)) % 173.51/173.28 [8802]~P78(x88021)+~P106(f333(f67(x88024),x88025))+~P106(f333(f333(f335(x88024),x88023),x88025))+E(f333(f333(f88(x88021),f333(x88022,x88023)),f333(f333(f9(x88024,x88021),x88022),f333(f333(f23(f917(x88024,a905)),x88025),f333(f333(f315(x88024),x88023),f196(f917(x88024,a905)))))),f333(f333(f9(x88024,x88021),x88022),x88025)) % 173.51/173.28 [8861]~P20(x88611,x88614,x88615)+~P106(f333(f67(x88611),x88612))+E(f333(f333(f23(f917(x88611,a905)),x88612),f333(f333(f315(x88611),x88613),f196(f917(x88611,a905)))),f196(f917(x88611,a905)))+E(f333(f333(x88614,x88613),f333(x88615,f333(f333(f23(f917(x88611,a905)),x88612),f333(f333(f315(x88611),x88613),f196(f917(x88611,a905)))))),f333(x88615,f333(f333(f315(x88611),x88613),x88612))) % 173.51/173.28 [9256]~P72(x92561)+~P106(f333(f67(x92562),x92565))+~P106(f333(f67(x92562),x92564))+E(f333(f333(f87(x92561),f333(f333(f6(x92562,x92561),x92563),f333(f333(f121(f917(x92562,a905)),x92564),x92565))),f333(f333(f6(x92562,x92561),x92563),f333(f333(f112(f917(x92562,a905)),x92564),x92565))),f333(f333(f87(x92561),f333(f333(f6(x92562,x92561),x92563),x92564)),f333(f333(f6(x92562,x92561),x92563),x92565))) % 173.51/173.28 [9258]~P78(x92581)+~P106(f333(f67(x92582),x92585))+~P106(f333(f67(x92582),x92584))+E(f333(f333(f88(x92581),f333(f333(f9(x92582,x92581),x92583),f333(f333(f121(f917(x92582,a905)),x92584),x92585))),f333(f333(f9(x92582,x92581),x92583),f333(f333(f112(f917(x92582,a905)),x92584),x92585))),f333(f333(f88(x92581),f333(f333(f9(x92582,x92581),x92583),x92584)),f333(f333(f9(x92582,x92581),x92583),x92585))) % 173.51/173.28 [9400]~P6(x94001)+~P106(f333(f67(x94002),x94005))+~P106(f333(f67(x94002),x94004))+E(f333(f333(f23(x94001),f333(f333(f87(x94001),f333(f333(f6(x94002,x94001),x94003),x94004)),f333(f333(f6(x94002,x94001),x94003),x94005))),f333(f333(f6(x94002,x94001),x94003),f333(f333(f112(f917(x94002,a905)),x94004),x94005))),f333(f333(f6(x94002,x94001),x94003),f333(f333(f121(f917(x94002,a905)),x94004),x94005))) % 173.51/173.28 [9615]~P27(x96151,x96152,x96153,x96155)+~P27(x96151,x96152,x96153,x96154)+P27(x96151,x96152,x96153,f333(f333(f121(f917(x96151,a905)),x96154),x96155))+~E(f333(f333(f112(f917(x96152,a905)),f333(f316(x96151,x96152,x96153),f333(f333(f23(f917(x96151,a905)),x96154),x96155))),f333(f316(x96151,x96152,x96153),f333(f333(f23(f917(x96151,a905)),x96155),x96154))),f196(f917(x96152,a905))) % 173.51/173.28 [9739]E(x97391,f2(a1))+~P106(f333(f333(f247(a1),f2(a1)),x97393))+~P106(f333(f55(x97392,x97391),f333(f333(f265(a1,a1),x97394),x97395)))+P106(f333(f55(x97392,f333(f333(f88(a1),x97391),x97393)),f333(f333(f265(a1,a1),f333(f333(f42(a1),x97394),x97393)),f333(f333(f87(a1),f333(f333(f88(a1),x97391),f51(a1,x97394,x97393))),x97395)))) % 173.51/173.28 [9748]~P106(f333(f333(f247(a910),f2(a910)),x97483))+~P106(f333(f333(f247(a910),f2(a910)),x97482))+~P106(f333(f54(x97481,x97482),f333(f333(f265(a910,a910),x97484),x97485)))+P106(f333(f54(x97481,f333(f333(f88(a910),x97482),x97483)),f333(f333(f265(a910,a910),f333(f333(f42(a910),x97484),x97483)),f333(f333(f87(a910),f333(f333(f88(a910),x97482),f51(a910,x97484,x97483))),x97485)))) % 173.51/173.28 [9798]~P78(x97981)+~P106(f333(f67(x97982),x97985))+~P106(f333(f67(x97982),x97984))+E(f333(f333(f88(x97981),f333(f333(f333(f71(x97981,x97982,f88(x97981)),x97983),f85(x97981)),f333(f333(f121(f917(x97982,a905)),x97984),x97985))),f333(f333(f333(f71(x97981,x97982,f88(x97981)),x97983),f85(x97981)),f333(f333(f112(f917(x97982,a905)),x97984),x97985))),f333(f333(f88(x97981),f333(f333(f333(f71(x97981,x97982,f88(x97981)),x97983),f85(x97981)),x97984)),f333(f333(f333(f71(x97981,x97982,f88(x97981)),x97983),f85(x97981)),x97985))) % 173.51/173.28 [9800]~E(f333(f333(f183(x98001),x98005),x98002),f333(f333(f183(x98001),x98005),x98003))+P106(f333(f333(f335(f916(f911(x98001),f911(x98001))),f333(f333(f265(f911(x98001),f911(x98001)),x98002),x98003)),f155(x98001,x98004)))+~P106(f333(f333(f247(a910),x98005),f333(f333(f244(a910),f333(f197(f911(x98001)),x98002)),f333(f197(f911(x98001)),x98003))))+~P106(f333(f333(f335(f916(x98001,x98001)),f333(f333(f265(x98001,x98001),f333(f333(f172(x98001),x98002),x98005)),f333(f333(f172(x98001),x98003),x98005))),x98004)) % 173.51/173.28 [9914]~P107(x99145)+~P86(x99145)+P106(f333(f333(f335(x99141),f422(x99142,x99143,x99144,x99141,x99145)),x99144))+P106(f333(f333(f246(x99145),f333(f333(f6(x99141,x99145),x99143),x99144)),f333(f333(f88(x99145),f333(f111(x99145),f333(f41(x99141),x99144))),x99142))) % 173.51/173.28 [10098]~P107(x100981)+~P86(x100981)+~P106(f333(f333(f246(x100981),f333(x100983,f422(x100985,x100983,x100984,x100982,x100981))),x100985))+P106(f333(f333(f246(x100981),f333(f333(f6(x100982,x100981),x100983),x100984)),f333(f333(f88(x100981),f333(f111(x100981),f333(f41(x100982),x100984))),x100985))) % 173.51/173.28 [8830]E(f333(f333(f142(x88301),x88302),x88303),f333(f333(f142(x88301),x88304),x88305))+~E(f333(f333(f183(x88301),f333(f197(f911(x88301)),x88302)),x88304),x88302)+~E(f333(f333(f142(x88301),f333(f333(f146(x88301),f333(f197(f911(x88301)),x88302)),x88304)),x88305),x88303)+P106(f333(f333(f246(a910),f333(f197(f911(x88301)),x88304)),f333(f197(f911(x88301)),x88302))) % 173.51/173.28 [8959]E(f333(f333(f142(x89591),x89592),x89593),f333(f333(f142(x89591),x89594),x89595))+~E(f333(f333(f183(x89591),f333(f197(f911(x89591)),x89592)),x89594),x89592)+~E(x89593,f333(f333(f142(x89591),f333(f333(f146(x89591),f333(f197(f911(x89591)),x89592)),x89594)),x89595))+~P106(f333(f333(f246(a910),f333(f197(f911(x89591)),x89592)),f333(f197(f911(x89591)),x89594))) % 173.51/173.28 [10234]~P106(f333(x102345,x102344))+~P106(f333(f67(x102342),f333(f252(x102342),x102345)))+P106(f333(f67(x102341),f333(f252(x102341),f333(f333(f7(x102341,x102342,a905),x102343),x102344))))+~P106(f333(f67(x102341),f333(f252(x102341),f333(f333(f8(f917(x102342,a905),a905,x102341),f94(x102342)),f333(f333(f8(f917(x102342,a905),f917(x102342,a905),x102341),f333(f18(x102342,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102342),a331),x102345))),x102343))))) % 173.51/173.28 [10297]~P106(f333(f67(x102972),x102975))+~P106(f333(f333(f335(x102972),x102974),x102975))+P106(f333(f67(x102971),f333(f252(x102971),f333(f333(f7(x102971,x102972,a905),x102973),x102974))))+~P106(f333(f67(x102971),f333(f252(x102971),f333(f333(f8(f917(x102972,a905),a905,x102971),f94(x102972)),f333(f333(f8(f917(x102972,a905),f917(x102972,a905),x102971),f333(f18(x102972,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102972),a331),f333(f333(f7(x102972,f917(x102972,a905),a905),f335(x102972)),x102975)))),x102973))))) % 173.51/173.28 [8614]~P21(x86145,x86141,x86146,x86142)+E(f333(f79(x86141,x86141,x86141,f333(x86142,x86143)),f333(x86142,x86144)),f333(f79(x86141,x86141,x86141,f333(x86142,x86144)),f333(x86142,x86143)))+~P106(f333(f67(x86145),x86144))+~P106(f333(f67(x86145),x86143)) % 173.51/173.28 [7992]~P27(x79921,x79922,x79924,x79923)+~E(f333(x79924,x79926),x79925)+E(f333(f84(x79921,x79922,x79923,x79924),x79925),x79926)+~P106(f333(f333(f335(x79921),x79926),x79923)) % 173.51/173.28 [7993]~P27(x79931,x79932,x79934,x79933)+~E(f333(x79934,x79936),x79935)+E(f333(f99(x79931,x79932,x79933,x79934),x79935),x79936)+~P106(f333(f333(f335(x79931),x79936),x79933)) % 173.51/173.28 [8193]~P22(x81936,x81931,x81934,x81932)+E(f333(f79(x81931,x81931,x81931,f333(x81932,x81933)),f333(x81934,x81935)),f333(x81932,x81933))+~P106(f333(f67(x81936),x81933))+~P106(f333(f333(f335(x81936),x81935),x81933)) % 173.51/173.28 [9348]E(x93481,x93482)+~E(f333(f99(x93483,x93484,x93485,x93486),x93481),f333(f99(x93483,x93484,x93485,x93486),x93482))+~P106(f333(f333(f335(x93484),x93482),f333(f316(x93483,x93484,x93486),x93485)))+~P106(f333(f333(f335(x93484),x93481),f333(f316(x93483,x93484,x93486),x93485))) % 173.51/173.28 [9451]~P21(x94513,x94511,x94516,x94512)+E(f333(f79(x94511,x94511,x94511,f333(x94512,f333(f333(f23(f917(x94513,a905)),x94514),f333(f333(f315(x94513),x94515),f196(f917(x94513,a905)))))),f333(x94516,x94515)),f333(x94512,x94514))+~P106(f333(f67(x94513),x94514))+~P106(f333(f333(f335(x94513),x94515),x94514)) % 173.51/173.28 [7078]~P65(x70781)+~E(f51(x70781,x70783,x70784),f51(x70781,x70786,x70784))+~E(f51(x70781,x70782,x70784),f51(x70781,x70785,x70784))+E(f51(x70781,f333(f333(f23(x70781),x70782),x70783),x70784),f51(x70781,f333(f333(f23(x70781),x70785),x70786),x70784)) % 173.51/173.28 [7079]~P64(x70791)+~E(f51(x70791,x70793,x70794),f51(x70791,x70796,x70794))+~E(f51(x70791,x70792,x70794),f51(x70791,x70795,x70794))+E(f51(x70791,f333(f333(f87(x70791),x70792),x70793),x70794),f51(x70791,f333(f333(f87(x70791),x70795),x70796),x70794)) % 173.51/173.28 [7080]~P64(x70801)+~E(f51(x70801,x70803,x70804),f51(x70801,x70806,x70804))+~E(f51(x70801,x70802,x70804),f51(x70801,x70805,x70804))+E(f51(x70801,f333(f333(f88(x70801),x70802),x70803),x70804),f51(x70801,f333(f333(f88(x70801),x70805),x70806),x70804)) % 173.51/173.28 [7887]~P18(x78871,x78872,x78873)+~P106(f333(f67(x78871),x78876))+E(f333(f333(f70(x78871,x78872,x78873),x78874),f333(f333(f315(x78871),x78875),x78876)),f333(f333(f70(x78871,x78872,x78873),f333(f333(x78873,x78875),x78874)),x78876))+P106(f333(f333(f335(x78871),x78875),x78876)) % 173.51/173.28 [7951]~P8(x79511)+P106(f333(f333(f246(x79511),x79512),f333(x79513,x79514)))+~P106(f333(f333(f335(x79515),x79514),x79516))+~P106(f333(f333(f246(x79511),x79512),f333(f333(f46(x79515,x79511),x79516),x79513))) % 173.51/173.28 [8112]~P18(x81121,x81122,x81123)+~P106(f333(f67(x81121),x81126))+E(f333(f333(f70(x81121,x81122,x81123),x81124),f333(f333(f315(x81121),x81125),x81126)),f333(f333(x81123,x81125),f333(f333(f70(x81121,x81122,x81123),x81124),x81126)))+P106(f333(f333(f335(x81121),x81125),x81126)) % 173.51/173.28 [8210]~P110(x82103)+~P106(f333(x82102,x82105))+~P16(x82103,f333(f333(f162(x82101,x82103),x82104),x82106))+E(f333(f144(x82101,x82102),f333(f333(f156(x82101,x82103,x82104),x82105),x82106)),f333(f333(f156(x82101,x82103,x82104),x82105),f333(f144(x82101,x82102),x82106))) % 173.51/173.28 [8232]E(x82321,x82322)+E(x82323,f2(a1))+~P106(f333(f55(x82324,x82323),f333(f333(f265(a1,a1),x82325),x82322)))+~P106(f333(f55(x82324,x82323),f333(f333(f265(a1,a1),x82326),x82321))) % 173.51/173.28 [8233]E(x82331,x82332)+E(x82333,f2(a1))+~P106(f333(f55(x82334,x82333),f333(f333(f265(a1,a1),x82332),x82335)))+~P106(f333(f55(x82334,x82333),f333(f333(f265(a1,a1),x82331),x82336))) % 173.51/173.28 [8252]~P21(x82522,x82525,x82526,x82521)+~P106(f333(f67(x82522),x82524))+E(f333(x82521,f333(f333(f315(x82522),x82523),x82524)),f333(f79(x82525,x82525,x82525,f333(x82521,x82524)),f333(x82526,x82523)))+P106(f333(f333(f335(x82522),x82523),x82524)) % 173.51/173.28 [8478]~P22(x84785,x84781,x84786,x84782)+E(f333(f79(x84781,x84781,x84781,f333(x84782,x84783)),f333(x84782,x84784)),f333(x84782,x84783))+~P106(f333(f67(x84785),x84783))+~P106(f333(f333(f246(f917(x84785,a905)),x84784),x84783)) % 173.51/173.28 [9660]~P27(x96601,x96602,x96604,x96603)+~P106(f333(f333(f335(x96602),x96605),f333(f316(x96601,x96602,x96604),x96603)))+P106(f333(f333(f335(x96601),f333(f84(x96601,x96602,x96603,x96604),x96605)),x96606))+~P106(f333(f333(f246(f917(x96601,a905)),x96603),x96606)) % 173.51/173.28 [10046]~P72(x100462)+~E(f369(x100461,x100463,x100465,x100466,x100464,x100462),f370(x100461,x100463,x100465,x100466,x100464,x100462))+~P106(f333(f67(x100464),x100466))+E(f333(f333(f6(x100461,x100462),x100463),f333(f316(x100464,x100461,x100465),x100466)),f333(f333(f6(x100464,x100462),f333(f79(x100461,x100462,x100464,x100463),x100465)),x100466)) % 173.51/173.28 [10078]~P72(x100786)+E(f333(x100781,f369(x100782,x100783,x100781,x100784,x100785,x100786)),f333(x100781,f370(x100782,x100783,x100781,x100784,x100785,x100786)))+E(f333(f333(f6(x100782,x100786),x100783),f333(f316(x100785,x100782,x100781),x100784)),f333(f333(f6(x100785,x100786),f333(f79(x100782,x100786,x100785,x100783),x100781)),x100784))+~P106(f333(f67(x100785),x100784)) % 173.51/173.28 [10120]~P72(x101202)+~E(f333(x101203,f333(x101205,f370(x101201,x101203,x101205,x101206,x101204,x101202))),f2(x101202))+~P106(f333(f67(x101204),x101206))+E(f333(f333(f6(x101201,x101202),x101203),f333(f316(x101204,x101201,x101205),x101206)),f333(f333(f6(x101204,x101202),f333(f79(x101201,x101202,x101204,x101203),x101205)),x101206)) % 173.51/173.28 [10180]~P72(x101802)+~P106(f333(f67(x101804),x101806))+E(f333(f333(f6(x101801,x101802),x101803),f333(f316(x101804,x101801,x101805),x101806)),f333(f333(f6(x101804,x101802),f333(f79(x101801,x101802,x101804,x101803),x101805)),x101806))+P106(f333(f333(f335(x101804),f370(x101801,x101803,x101805,x101806,x101804,x101802)),x101806)) % 173.51/173.28 [10181]~P72(x101812)+~P106(f333(f67(x101814),x101816))+E(f333(f333(f6(x101811,x101812),x101813),f333(f316(x101814,x101811,x101815),x101816)),f333(f333(f6(x101814,x101812),f333(f79(x101811,x101812,x101814,x101813),x101815)),x101816))+P106(f333(f333(f335(x101814),f369(x101811,x101813,x101815,x101816,x101814,x101812)),x101816)) % 173.51/173.28 [10296]~P78(x102961)+~P106(f333(f67(x102962),x102966))+E(f333(f333(f333(f71(x102961,x102962,f88(x102961)),f333(f333(f18(x102962,f917(x102963,a905),x102961),f333(f333(f7(x102962,x102961,f917(f917(x102963,a905),x102961)),f333(f333(f8(f917(x102963,x102961),f917(x102961,f917(f917(x102963,a905),x102961)),x102962),f71(x102961,x102963,f88(x102961))),x102964)),f85(x102961))),x102965)),f85(x102961)),x102966),f333(f333(f333(f71(x102961,f916(x102962,x102963),f88(x102961)),f333(f269(x102962,x102963,x102961),x102964)),f85(x102961)),f333(f333(f267(x102962,x102963),x102966),x102965)))+P106(f333(f333(f335(x102962),f554(x102964,x102965,x102963,x102966,x102962,x102961)),x102966)) % 173.51/173.28 [10317]~P78(x103171)+~P106(f333(f67(x103172),x103176))+E(f333(f333(f333(f71(x103171,x103172,f88(x103171)),f333(f333(f18(x103172,f917(x103173,a905),x103171),f333(f333(f7(x103172,x103171,f917(f917(x103173,a905),x103171)),f333(f333(f8(f917(x103173,x103171),f917(x103171,f917(f917(x103173,a905),x103171)),x103172),f71(x103171,x103173,f88(x103171))),x103174)),f85(x103171))),x103175)),f85(x103171)),x103176),f333(f333(f333(f71(x103171,f916(x103172,x103173),f88(x103171)),f333(f269(x103172,x103173,x103171),x103174)),f85(x103171)),f333(f333(f267(x103172,x103173),x103176),x103175)))+~P106(f333(f67(x103173),f333(x103175,f554(x103174,x103175,x103173,x103176,x103172,x103171)))) % 173.51/173.28 [8388]~P22(x83882,x83885,x83886,x83881)+~P106(f333(f67(x83882),x83884))+~P106(f333(f67(x83882),x83883))+E(f333(x83881,f333(f333(f121(f917(x83882,a905)),x83883),x83884)),f333(f79(x83885,x83885,x83885,f333(x83881,x83883)),f333(x83881,x83884))) % 173.51/173.28 [8615]~P8(x86151)+P106(f333(f333(f246(x86151),f333(x86152,x86153)),x86154))+~P106(f333(f333(f335(x86155),x86153),x86156))+~P106(f333(f333(f246(x86151),f333(f333(f45(x86155,x86151),x86156),x86152)),x86154)) % 173.51/173.28 [9048]~P27(x90482,x90481,x90483,x90486)+E(f333(f333(f112(f917(x90481,a905)),f333(f316(x90482,x90481,x90483),x90484)),f333(f316(x90482,x90481,x90483),x90485)),f333(f316(x90482,x90481,x90483),f333(f333(f112(f917(x90482,a905)),x90484),x90485)))+~P106(f333(f333(f246(f917(x90482,a905)),x90485),x90486))+~P106(f333(f333(f246(f917(x90482,a905)),x90484),x90486)) % 173.51/173.28 [9049]~P27(x90492,x90491,x90493,x90496)+E(f333(f333(f23(f917(x90491,a905)),f333(f316(x90492,x90491,x90493),x90494)),f333(f316(x90492,x90491,x90493),x90495)),f333(f316(x90492,x90491,x90493),f333(f333(f23(f917(x90492,a905)),x90494),x90495)))+~P106(f333(f333(f246(f917(x90492,a905)),x90495),x90496))+~P106(f333(f333(f246(f917(x90492,a905)),x90494),x90496)) % 173.51/173.28 [9087]~P106(f333(x90871,x90873))+~P106(f333(f333(f333(f333(a204,x90872),x90873),x90874),x90876))+~P106(f333(f333(f333(f333(a204,f30(x90871,x90872)),x90876),x90874),x90875))+P106(f333(f333(f333(f333(a204,f30(x90871,x90872)),x90873),x90874),x90875)) % 173.51/173.28 [9324]E(x93241,x93242)+~P58(x93243,x93244,x93245)+~P106(f333(f333(f335(f916(x93243,x93244)),f333(f333(f265(x93243,x93244),x93246),x93242)),x93245))+~P106(f333(f333(f335(f916(x93243,x93244)),f333(f333(f265(x93243,x93244),x93246),x93241)),x93245)) % 173.51/173.28 [10115]~P76(x101151)+~E(f333(x101153,f529(x101154,x101156,x101153,x101155,x101152,x101151)),f333(x101156,f529(x101154,x101156,x101153,x101155,x101152,x101151)))+~P106(f333(f67(x101152),x101155))+E(f333(f333(f333(f71(x101151,x101152,f88(x101151)),x101153),x101154),x101155),f333(f333(f333(f71(x101151,x101152,f88(x101151)),x101156),x101154),x101155)) % 173.51/173.28 [10177]~P76(x101771)+~P106(f333(f67(x101772),x101775))+E(f333(f333(f333(f71(x101771,x101772,f88(x101771)),x101773),x101774),x101775),f333(f333(f333(f71(x101771,x101772,f88(x101771)),x101776),x101774),x101775))+P106(f333(f333(f335(x101772),f529(x101774,x101773,x101776,x101775,x101772,x101771)),x101775)) % 173.51/173.28 [8844]~P76(x88441)+~P106(f333(f67(x88442),x88446))+P106(f333(f333(f335(x88442),x88445),x88446))+E(f333(f333(f333(f71(x88441,x88442,f88(x88441)),x88443),x88444),f333(f333(f315(x88442),x88445),x88446)),f333(f333(f88(x88441),f333(x88443,x88445)),f333(f333(f333(f71(x88441,x88442,f88(x88441)),x88443),x88444),x88446))) % 173.51/173.28 [8896]~P11(x88961,x88966,x88963)+~P14(x88961,f917(x88962,a905),x88963,x88965)+~P106(f333(f333(f335(x88961),x88964),x88966))+E(f333(f333(f45(x88961,f917(x88962,a905)),f333(f292(x88961,x88961,x88963),f333(f333(f315(x88961),x88964),f196(f917(x88961,a905))))),x88965),f333(x88965,x88964)) % 173.51/173.28 [9023]~P18(x90233,x90234,x90231)+~P106(f333(f67(x90233),x90236))+~P106(f333(f333(f335(x90233),x90232),x90236))+E(f333(f333(x90231,x90232),f333(f333(f70(x90233,x90234,x90231),x90235),f333(f333(f23(f917(x90233,a905)),x90236),f333(f333(f315(x90233),x90232),f196(f917(x90233,a905)))))),f333(f333(f70(x90233,x90234,x90231),x90235),x90236)) % 173.51/173.28 [9334]~P21(x93343,x93341,x93346,x93342)+~P106(f333(f67(x93343),x93345))+~P106(f333(f67(x93343),x93344))+E(f333(f79(x93341,x93341,x93341,f333(x93342,f333(f333(f121(f917(x93343,a905)),x93344),x93345))),f333(x93342,f333(f333(f112(f917(x93343,a905)),x93344),x93345))),f333(f79(x93341,x93341,x93341,f333(x93342,x93344)),f333(x93342,x93345))) % 173.51/173.28 [9685]~E(x96853,f333(f333(f167(x96851,x96852),x96855),x96856))+P106(f333(f333(f335(f916(f911(x96851),f911(x96851))),f333(f333(f265(f911(x96851),f911(x96851)),x96852),x96853)),f165(x96851,x96854)))+~P106(f333(f333(f247(a910),x96855),f333(f197(f911(x96851)),x96852)))+~P106(f333(f333(f335(f916(x96851,x96851)),f333(f333(f265(x96851,x96851),f333(f333(f172(x96851),x96852),x96855)),x96856)),x96854)) % 173.51/173.28 [10191]~P72(x101912)+~P106(f333(f67(x101911),x101916))+P106(f333(f333(f335(x101911),f557(x101914,x101915,x101913,x101916,x101911,x101912)),x101916))+E(f333(f333(f6(x101911,x101912),f333(f333(f18(x101911,f917(x101913,a905),x101912),f333(f333(f8(f917(x101913,x101912),f917(f917(x101913,a905),x101912),x101911),f6(x101913,x101912)),x101914)),x101915)),x101916),f333(f333(f6(f916(x101911,x101913),x101912),f333(f269(x101911,x101913,x101912),x101914)),f333(f333(f267(x101911,x101913),x101916),x101915))) % 173.51/173.28 [10192]~P78(x101922)+~P106(f333(f67(x101921),x101926))+P106(f333(f333(f335(x101921),f558(x101924,x101925,x101923,x101926,x101921,x101922)),x101926))+E(f333(f333(f9(x101921,x101922),f333(f333(f18(x101921,f917(x101923,a905),x101922),f333(f333(f8(f917(x101923,x101922),f917(f917(x101923,a905),x101922),x101921),f9(x101923,x101922)),x101924)),x101925)),x101926),f333(f333(f9(f916(x101921,x101923),x101922),f333(f269(x101921,x101923,x101922),x101924)),f333(f333(f267(x101921,x101923),x101926),x101925))) % 173.51/173.28 [10231]~P72(x102312)+~P106(f333(f67(x102311),x102316))+~P106(f333(f67(x102313),f333(x102315,f557(x102314,x102315,x102313,x102316,x102311,x102312))))+E(f333(f333(f6(x102311,x102312),f333(f333(f18(x102311,f917(x102313,a905),x102312),f333(f333(f8(f917(x102313,x102312),f917(f917(x102313,a905),x102312),x102311),f6(x102313,x102312)),x102314)),x102315)),x102316),f333(f333(f6(f916(x102311,x102313),x102312),f333(f269(x102311,x102313,x102312),x102314)),f333(f333(f267(x102311,x102313),x102316),x102315))) % 173.51/173.28 [10232]~P78(x102322)+~P106(f333(f67(x102321),x102326))+~P106(f333(f67(x102323),f333(x102325,f558(x102324,x102325,x102323,x102326,x102321,x102322))))+E(f333(f333(f9(x102321,x102322),f333(f333(f18(x102321,f917(x102323,a905),x102322),f333(f333(f8(f917(x102323,x102322),f917(f917(x102323,a905),x102322),x102321),f9(x102323,x102322)),x102324)),x102325)),x102326),f333(f333(f9(f916(x102321,x102323),x102322),f333(f269(x102321,x102323,x102322),x102324)),f333(f333(f267(x102321,x102323),x102326),x102325))) % 173.51/173.28 [10213]~P78(x102132)+~P106(f333(f67(x102131),x102136))+P106(f333(f333(f335(x102131),x102133),x102136))+E(f333(f333(f9(x102131,x102132),f333(f333(f7(x102131,x102132,x102132),f333(f333(f18(x102131,x102132,f917(x102132,x102132)),f333(f333(f8(a905,f917(x102132,f917(x102132,x102132)),x102131),f107(x102132)),f333(f333(f7(x102131,x102131,a905),a330),x102133))),x102134)),x102135)),x102136),f333(f333(f256(x102132),x102135),f333(f41(x102131),x102136))) % 173.51/173.28 [10218]~P78(x102182)+~P106(f333(f67(x102181),x102186))+~P106(f333(f333(f335(x102181),x102183),x102186))+E(f333(f333(f9(x102181,x102182),f333(f333(f7(x102181,x102182,x102182),f333(f333(f18(x102181,x102182,f917(x102182,x102182)),f333(f333(f8(a905,f917(x102182,f917(x102182,x102182)),x102181),f107(x102182)),f333(f333(f7(x102181,x102181,a905),a330),x102183))),x102184)),x102185)),x102186),f333(f333(f88(x102182),f333(x102184,x102183)),f333(f333(f256(x102182),x102185),f333(f333(f23(a910),f333(f41(x102181),x102186)),f85(a910))))) % 173.51/173.28 [10289]~P106(f333(f67(x102891),x102895))+~P106(f333(f67(x102892),x102893))+P106(f333(f333(f335(x102892),f376(x102896,x102894,x102893,x102892,x102895,x102891)),x102893))+E(f333(f333(f6(x102891,a910),f333(f333(f8(f917(x102892,a905),a910,x102891),f41(x102892)),f333(f333(f8(f917(x102892,a905),f917(x102892,a905),x102891),f252(x102892)),f333(f333(f8(f917(x102892,a905),f917(x102892,a905),x102891),f333(f18(x102892,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102892),a331),f333(f333(f7(x102892,f917(x102892,a905),a905),f335(x102892)),x102893)))),x102894)))),x102895),f333(f333(f88(a910),x102896),f333(f41(x102892),x102893))) % 173.51/173.28 [10290]~P106(f333(f67(x102901),x102905))+~P106(f333(f67(x102902),x102903))+P106(f333(f333(f335(x102902),f348(x102906,x102904,x102903,x102902,x102905,x102901)),x102903))+E(f333(f333(f6(x102901,a910),f333(f333(f8(f917(x102902,a905),a910,x102901),f41(x102902)),f333(f333(f8(f917(x102902,a905),f917(x102902,a905),x102901),f252(x102902)),f333(f333(f8(f917(x102902,a905),f917(x102902,a905),x102901),f333(f18(x102902,a905,a905),f333(f333(f8(a905,f917(a905,a905),x102902),a331),f333(f333(f7(x102902,f917(x102902,a905),a905),f335(x102902)),x102903)))),x102904)))),x102905),f333(f333(f6(x102902,a910),x102906),x102903)) % 173.51/173.28 [10329]~P106(f333(f67(x103292),x103293))+~P106(f333(f67(x103291),x103295))+~E(f333(f41(x103291),f333(f252(x103291),f333(f333(f18(x103291,a905,a905),f333(f333(f8(a905,f917(a905,a905),x103291),a331),f333(f333(f7(x103291,f917(x103291,a905),a905),f335(x103291)),x103295))),f333(f333(f7(x103291,x103292,a905),x103294),f376(x103296,x103294,x103293,x103292,x103295,x103291))))),x103296)+E(f333(f333(f6(x103291,a910),f333(f333(f8(f917(x103292,a905),a910,x103291),f41(x103292)),f333(f333(f8(f917(x103292,a905),f917(x103292,a905),x103291),f252(x103292)),f333(f333(f8(f917(x103292,a905),f917(x103292,a905),x103291),f333(f18(x103292,a905,a905),f333(f333(f8(a905,f917(a905,a905),x103292),a331),f333(f333(f7(x103292,f917(x103292,a905),a905),f335(x103292)),x103293)))),x103294)))),x103295),f333(f333(f88(a910),x103296),f333(f41(x103292),x103293))) % 173.51/173.28 [10331]~P106(f333(f67(x103312),x103313))+~P106(f333(f67(x103311),x103315))+~E(f333(f41(x103311),f333(f252(x103311),f333(f333(f18(x103311,a905,a905),f333(f333(f8(a905,f917(a905,a905),x103311),a331),f333(f333(f7(x103311,f917(x103311,a905),a905),f335(x103311)),x103315))),f333(f333(f7(x103311,x103312,a905),x103314),f348(x103316,x103314,x103313,x103312,x103315,x103311))))),f333(x103316,f348(x103316,x103314,x103313,x103312,x103315,x103311)))+E(f333(f333(f6(x103311,a910),f333(f333(f8(f917(x103312,a905),a910,x103311),f41(x103312)),f333(f333(f8(f917(x103312,a905),f917(x103312,a905),x103311),f252(x103312)),f333(f333(f8(f917(x103312,a905),f917(x103312,a905),x103311),f333(f18(x103312,a905,a905),f333(f333(f8(a905,f917(a905,a905),x103312),a331),f333(f333(f7(x103312,f917(x103312,a905),a905),f335(x103312)),x103313)))),x103314)))),x103315),f333(f333(f6(x103312,a910),x103316),x103313)) % 173.51/173.28 [9970]E(x99701,x99702)+~P18(x99703,x99704,x99705)+~P106(f333(f72(x99703,x99704,x99705,x99706,x99707),x99702))+~P106(f333(f72(x99703,x99704,x99705,x99706,x99707),x99701)) % 173.51/173.28 [9769]P106(f333(x97691,x97692))+~P106(f333(f333(f335(x97697),x97692),f333(x97696,x97694)))+~P106(f333(x97691,f481(x97691,x97696,x97695,x97693,x97697)))+~P106(f333(f333(f335(x97693),x97694),x97695)) % 173.51/173.28 [10205]~P18(x102057,x102056,x102051)+E(f333(f333(x102051,x102052),f655(x102052,x102053,x102054,x102055,x102051,x102056,x102057)),x102053)+~P106(f333(f72(x102057,x102056,x102051,x102055,x102054),x102053))+~P106(f333(f333(f335(x102057),x102052),x102054)) % 173.51/173.28 [10271]~P18(x102711,x102712,x102713)+~P106(f333(f72(x102711,x102712,x102713,x102714,x102715),x102717))+P106(f333(f72(x102711,x102712,x102713,x102714,f333(f333(f23(f917(x102711,a905)),x102715),f333(f333(f315(x102711),x102716),f196(f917(x102711,a905))))),f655(x102716,x102717,x102715,x102714,x102713,x102712,x102711)))+~P106(f333(f333(f335(x102711),x102716),x102715)) % 173.51/173.28 [9407]P28(x94071,x94072,x94073,x94074,x94075)+~P28(x94071,x94072,x94073,x94076,x94077)+~E(f333(f316(x94071,x94072,x94073),x94074),x94075)+~P106(f333(f333(f246(f917(x94071,a905)),x94074),x94076)) % 173.51/173.28 [9651]~P28(x96511,x96512,x96513,x96515,x96517)+~P28(x96511,x96512,x96513,x96514,x96516)+P28(x96511,x96512,x96513,f333(f333(f121(f917(x96511,a905)),x96514),x96515),f333(f333(f121(f917(x96512,a905)),x96516),x96517))+~E(f333(f333(f112(f917(x96512,a905)),x96516),x96517),f196(f917(x96512,a905))) % 173.51/173.28 [9656]~P76(x96561)+~P27(x96565,x96562,x96566,x96567)+~P106(f333(f67(x96565),x96567))+E(f333(f333(f333(f71(x96561,x96562,f88(x96561)),x96563),x96564),f333(f316(x96565,x96562,x96566),x96567)),f333(f333(f333(f71(x96561,x96565,f88(x96561)),f333(f79(x96562,x96561,x96565,x96563),x96566)),x96564),x96567)) % 173.51/173.28 [9793]~E(f333(f333(f315(x97931),x97935),x97936),f333(f333(f315(x97931),x97932),x97933))+~P106(f333(f72(x97931,x97931,x97934,x97932,x97933),x97937))+P106(f333(f333(f335(x97931),x97932),x97933))+P106(f333(f68(x97931,x97934,f333(f333(f315(x97931),x97935),x97936)),x97937)) % 173.51/173.28 [9876]P106(f333(x98761,x98762))+~P106(f333(f333(f335(x98763),x98762),f333(x98764,x98767)))+~P106(f333(f333(f335(x98766),x98767),x98765))+P106(f333(f333(f335(x98763),f481(x98761,x98764,x98765,x98766,x98763)),f333(f333(f45(x98766,f917(x98763,a905)),x98765),x98764))) % 173.51/173.28 [9893]~P27(x98932,x98931,x98935,x98934)+~P27(x98931,x98933,x98936,f333(f316(x98932,x98931,x98935),x98934))+E(f333(f333(f79(x98931,x98932,x98933,f84(x98932,x98931,x98934,x98935)),f84(x98931,x98933,f333(f316(x98932,x98931,x98935),x98934),x98936)),x98937),f333(f84(x98932,x98933,x98934,f333(f79(x98931,x98933,x98932,x98936),x98935)),x98937))+~P106(f333(f333(f335(x98933),x98937),f333(f316(x98931,x98933,x98936),f333(f316(x98932,x98931,x98935),x98934)))) % 173.51/173.28 [9894]~P27(x98942,x98941,x98945,x98944)+~P27(x98941,x98943,x98946,f333(f316(x98942,x98941,x98945),x98944))+E(f333(f333(f79(x98941,x98942,x98943,f99(x98942,x98941,x98944,x98945)),f99(x98941,x98943,f333(f316(x98942,x98941,x98945),x98944),x98946)),x98947),f333(f99(x98942,x98943,x98944,f333(f79(x98941,x98943,x98942,x98946),x98945)),x98947))+~P106(f333(f333(f335(x98943),x98947),f333(f316(x98941,x98943,x98946),f333(f316(x98942,x98941,x98945),x98944)))) % 173.51/173.28 [10206]~P18(x102067,x102066,x102061)+E(f333(f333(x102061,x102062),f679(x102063,x102064,x102062,x102065,x102061,x102066,x102067)),x102063)+P106(f333(f333(f335(x102067),x102062),x102064))+~P106(f333(f72(x102067,x102066,x102061,x102065,f333(f333(f315(x102067),x102062),x102064)),x102063)) % 173.51/173.28 [10270]~P18(x102701,x102704,x102705)+P106(f333(f72(x102701,x102704,x102705,x102706,x102703),f679(x102707,x102703,x102702,x102706,x102705,x102704,x102701)))+P106(f333(f333(f335(x102701),x102702),x102703))+~P106(f333(f72(x102701,x102704,x102705,x102706,f333(f333(f315(x102701),x102702),x102703)),x102707)) % 173.51/173.28 [9952]E(x99521,f2(a1))+~P106(f333(f55(x99523,x99521),f333(f333(f265(a1,a1),x99525),x99527)))+~P106(f333(f55(x99522,x99521),f333(f333(f265(a1,a1),x99524),x99526)))+P106(f333(f55(f333(f333(f87(a1),x99522),x99523),x99521),f333(f333(f265(a1,a1),f333(f333(f87(a1),f333(f333(f87(a1),x99524),x99525)),f333(f333(f42(a1),f333(f333(f87(a1),x99526),x99527)),x99521))),f51(a1,f333(f333(f87(a1),x99526),x99527),x99521)))) % 173.51/173.28 [9954]~P106(f333(f333(f247(a910),f2(a910)),x99543))+~P106(f333(f54(x99542,x99543),f333(f333(f265(a910,a910),x99545),x99547)))+~P106(f333(f54(x99541,x99543),f333(f333(f265(a910,a910),x99544),x99546)))+P106(f333(f54(f333(f333(f87(a910),x99541),x99542),x99543),f333(f333(f265(a910,a910),f333(f333(f87(a910),f333(f333(f87(a910),x99544),x99545)),f333(f333(f42(a910),f333(f333(f87(a910),x99546),x99547)),x99543))),f51(a910,f333(f333(f87(a910),x99546),x99547),x99543)))) % 173.51/173.28 [10328]~P72(x103282)+~P106(f333(f67(x103283),x103285))+~P106(f333(f67(x103281),x103287))+E(f333(f333(f6(x103281,x103282),f333(f333(f18(x103281,f917(x103283,a905),x103282),f333(f333(f8(f917(x103283,x103282),f917(f917(x103283,a905),x103282),x103281),f6(x103283,x103282)),x103284)),f333(f333(f8(f917(x103283,a905),f917(x103283,a905),x103281),f252(x103283)),f333(f333(f8(f917(x103283,a905),f917(x103283,a905),x103281),f333(f18(x103283,a905,a905),f333(f333(f8(a905,f917(a905,a905),x103283),a331),f333(f333(f7(x103283,f917(x103283,a905),a905),f335(x103283)),x103285)))),x103286)))),x103287),f333(f333(f6(x103283,x103282),f333(f333(f18(x103283,f917(x103281,a905),x103282),f333(f333(f8(f917(x103281,x103282),f917(f917(x103281,a905),x103282),x103283),f6(x103281,x103282)),f333(f7(x103281,x103283,x103282),x103284))),f333(f333(f8(f917(x103281,a905),f917(x103281,a905),x103283),f252(x103281)),f333(f333(f8(f917(x103281,a905),f917(x103281,a905),x103283),f333(f18(x103281,a905,a905),f333(f333(f8(a905,f917(a905,a905),x103281),a331),f333(f333(f7(x103281,f917(x103281,a905),a905),f335(x103281)),x103287)))),f333(f7(x103281,x103283,a905),x103286))))),x103285)) % 173.51/173.28 [9829]~P24(x98297,x98296,x98291,x98298,x98292,x98294)+E(f333(f333(x98291,f333(x98292,x98293)),f333(x98294,x98295)),f333(x98294,x98295))+~P106(f333(f67(x98296),x98295))+~P106(f333(f333(f335(x98296),x98293),x98295)) % 173.51/173.28 [9833]~P15(x98336,x98331,x98332,x98338,x98333,x98334)+~P11(x98336,x98337,x98338)+P14(x98331,x98332,x98333,f333(x98334,x98335))+~P106(f333(f333(f335(x98336),x98335),x98337)) % 173.51/173.28 [8211]~P32(x82118,x82117,f333(f333(f333(f98(x82118),x82114),x82116),x82111))+P106(f333(f333(x82111,x82112),x82113))+~P106(f333(f333(x82114,x82112),x82115))+~P106(f333(f333(f333(f333(a204,x82116),x82115),x82117),x82113)) % 173.51/173.28 [9431]~P21(x94317,x94311,x94318,x94313)+~P106(f333(f67(x94317),x94315))+~P106(f333(f67(x94317),x94314))+E(f333(f79(x94311,x94311,x94312,f333(x94313,x94314)),f333(f79(x94311,x94311,x94312,f333(x94313,x94315)),x94316)),f333(f79(x94311,x94311,x94312,f333(x94313,x94315)),f333(f79(x94311,x94311,x94312,f333(x94313,x94314)),x94316))) % 173.51/173.28 [9440]~P37(x94401,x94402,x94403,x94404,x94407)+P37(x94401,x94402,x94403,f333(f333(f167(x94401,x94404),x94405),x94406),f333(f333(f167(x94402,x94407),x94405),x94408))+~P106(f333(f333(x94403,x94406),x94408))+~P106(f333(f333(f247(a910),x94405),f333(f197(f911(x94401)),x94404))) % 173.51/173.28 [9441]~P37(x94411,x94412,x94413,x94414,x94417)+P37(x94411,x94412,x94413,f333(f333(f167(x94411,x94414),x94415),x94416),f333(f333(f167(x94412,x94417),x94415),x94418))+~P106(f333(f333(x94413,x94416),x94418))+~P106(f333(f333(f247(a910),x94415),f333(f197(f911(x94412)),x94417))) % 173.51/173.28 [9525]~P27(x95252,x95252,x95255,x95256)+~P23(x95253,x95252,x95257,x95258,x95251)+~P106(f333(f67(x95252),x95256))+E(f333(f333(x95251,f333(f79(x95252,x95253,x95252,x95254),x95255)),x95256),f333(f333(x95251,x95254),f333(f316(x95252,x95252,x95255),x95256))) % 173.51/173.28 [9794]P28(x97941,x97942,x97943,x97944,x97945)+~P28(x97942,x97946,x97947,x97945,x97948)+~P28(x97941,x97946,f333(f79(x97942,x97946,x97941,x97947),x97943),x97944,x97948)+~P106(f333(f333(f246(f917(x97942,a905)),f333(f316(x97941,x97942,x97943),x97944)),x97945)) % 173.51/173.28 [9831]~P25(x98317,x98312,x98315,x98318,x98316,x98311)+~P106(f333(f67(x98312),x98314))+E(f333(x98311,f333(f333(f315(x98312),x98313),x98314)),f333(f333(x98315,f333(x98316,x98313)),f333(x98311,x98314)))+P106(f333(f333(f335(x98312),x98313),x98314)) % 173.51/173.28 [9842]~P24(x98426,x98425,x98421,x98427,x98428,x98422)+E(f333(f333(x98421,f333(x98422,x98423)),f333(x98422,x98424)),f333(x98422,x98424))+~P106(f333(f67(x98425),x98424))+~P106(f333(f333(f246(f917(x98425,a905)),x98423),x98424)) % 173.51/173.28 [10325]P26(x103258,x103257,f333(f333(f315(f909(x103258)),f333(f333(f333(f98(x103258),x103254),x103255),x103253)),f196(f917(f909(x103258),a905))))+~P26(x103258,x103257,f333(f333(f315(f909(x103258)),f333(f333(f333(f98(x103258),x103256),x103255),x103251)),f196(f917(f909(x103258),a905))))+~P106(f333(f333(x103256,x103252),f904(x103253,x103254,x103251,x103255,x103256,x103257,x103258)))+P106(f333(f333(x103251,x103252),f352(x103253,x103254,x103251,x103255,x103256,x103257,x103258))) % 173.51/173.28 [9418]P106(f333(f333(f335(f916(f911(x94181),f911(x94181))),f333(f333(f265(f911(x94181),f911(x94181)),x94182),x94183)),f165(x94181,x94184)))+~E(x94183,f333(f333(f142(x94181),x94185),f333(f333(f159(x94181),x94186),x94187)))+~E(x94182,f333(f333(f142(x94181),x94185),f333(f333(f159(x94181),x94188),x94187)))+~P106(f333(f333(f335(f916(x94181,x94181)),f333(f333(f265(x94181,x94181),x94188),x94186)),x94184)) % 173.51/173.28 [9836]~P24(x98366,x98362,x98365,x98367,x98368,x98361)+~P106(f333(f67(x98362),x98364))+~P106(f333(f67(x98362),x98363))+E(f333(x98361,f333(f333(f121(f917(x98362,a905)),x98363),x98364)),f333(f333(x98365,f333(x98361,x98363)),f333(x98361,x98364))) % 173.51/173.28 [10371]~P27(x103714,x103712,x103715,x103718)+E(f333(f333(f46(x103711,f917(x103712,a905)),x103713),f333(f333(f8(f917(x103714,a905),f917(x103712,a905),x103711),f316(x103714,x103712,x103715)),x103716)),f333(f316(x103714,x103712,x103715),f333(f333(f46(x103711,f917(x103714,a905)),x103713),x103716)))+~P106(f333(f333(f335(x103711),x103717),x103713))+P106(f333(f333(f335(x103711),f667(x103717,x103716,x103713,x103711,x103718,x103715,x103712,x103714)),x103713)) % 173.51/173.28 [10393]~P27(x103934,x103932,x103935,x103937)+E(f333(f333(f46(x103931,f917(x103932,a905)),x103933),f333(f333(f8(f917(x103934,a905),f917(x103932,a905),x103931),f316(x103934,x103932,x103935)),x103936)),f333(f316(x103934,x103932,x103935),f333(f333(f46(x103931,f917(x103934,a905)),x103933),x103936)))+~P106(f333(f333(f335(x103931),x103938),x103933))+~P106(f333(f333(f246(f917(x103934,a905)),f333(x103936,f667(x103938,x103936,x103933,x103931,x103937,x103935,x103932,x103934))),x103937)) % 173.51/173.28 [9903]~P25(x99037,x99035,x99031,x99038,x99032,x99034)+~P106(f333(f67(x99035),x99036))+~P106(f333(f333(f335(x99035),x99033),x99036))+E(f333(f333(x99031,f333(x99032,x99033)),f333(x99034,f333(f333(f23(f917(x99035,a905)),x99036),f333(f333(f315(x99035),x99033),f196(f917(x99035,a905)))))),f333(x99034,x99036)) % 173.51/173.28 [9912]~P25(x99126,x99123,x99121,x99127,x99128,x99122)+~P106(f333(f67(x99123),x99125))+~P106(f333(f67(x99123),x99124))+E(f333(f333(x99121,f333(x99122,f333(f333(f121(f917(x99123,a905)),x99124),x99125))),f333(x99122,f333(f333(f112(f917(x99123,a905)),x99124),x99125))),f333(f333(x99121,f333(x99122,x99124)),f333(x99122,x99125))) % 173.51/173.28 [9993]P45(x99931,x99932,x99933,x99934,x99935,f333(f333(x99933,x99936),x99937))+~P45(x99931,x99932,x99933,x99934,f333(f333(f23(f917(x99931,a905)),x99935),f333(f333(f315(x99931),x99938),f196(f917(x99931,a905)))),x99939)+~E(f333(f333(x99933,x99936),x99937),f333(f333(x99933,x99938),x99939))+~P106(f333(f333(f335(x99931),x99938),x99935)) % 173.51/173.28 [10406]P26(x104061,x104062,f333(f333(f315(f909(x104061)),f333(f333(f333(f98(x104061),f333(x104063,f889(x104064,x104065,x104066,x104067,x104063,x104062,x104061,x104068,x104069))),f333(x104067,f889(x104064,x104065,x104066,x104067,x104063,x104062,x104061,x104068,x104069))),f333(x104066,f889(x104064,x104065,x104066,x104067,x104063,x104062,x104061,x104068,x104069)))),f196(f917(f909(x104061),a905))))+~P106(f333(f67(x104069),x104068))+~P26(x104061,x104062,f333(f316(x104069,f909(x104061),f333(f333(f18(x104069,f917(x104061,f917(a906,a905)),f909(x104061)),f333(f333(f18(x104069,a907,f917(f917(x104061,f917(a906,a905)),f909(x104061))),f333(f333(f8(f917(x104061,f917(a906,a905)),f917(a907,f917(f917(x104061,f917(a906,a905)),f909(x104061))),x104069),f98(x104061)),x104063)),x104067)),x104066)),x104068))+P26(x104061,x104062,f333(f316(x104069,f909(x104061),f333(f333(f18(x104069,f917(x104061,f917(a906,a905)),f909(x104061)),f333(f333(f18(x104069,a907,f917(f917(x104061,f917(a906,a905)),f909(x104061))),f333(f333(f8(f917(x104061,f917(a906,a905)),f917(a907,f917(f917(x104061,f917(a906,a905)),f909(x104061))),x104069),f98(x104061)),x104065)),x104067)),x104064)),x104068)) % 173.51/173.28 [10407]~P26(x104071,x104072,f333(f333(f315(f909(x104071)),f333(f333(f333(f98(x104071),f333(x104074,f889(x104076,x104074,x104078,x104075,x104079,x104072,x104071,x104077,x104073))),f333(x104075,f889(x104076,x104074,x104078,x104075,x104079,x104072,x104071,x104077,x104073))),f333(x104076,f889(x104076,x104074,x104078,x104075,x104079,x104072,x104071,x104077,x104073)))),f196(f917(f909(x104071),a905))))+~P106(f333(f67(x104073),x104077))+~P26(x104071,x104072,f333(f316(x104073,f909(x104071),f333(f333(f18(x104073,f917(x104071,f917(a906,a905)),f909(x104071)),f333(f333(f18(x104073,a907,f917(f917(x104071,f917(a906,a905)),f909(x104071))),f333(f333(f8(f917(x104071,f917(a906,a905)),f917(a907,f917(f917(x104071,f917(a906,a905)),f909(x104071))),x104073),f98(x104071)),x104079)),x104075)),x104078)),x104077))+P26(x104071,x104072,f333(f316(x104073,f909(x104071),f333(f333(f18(x104073,f917(x104071,f917(a906,a905)),f909(x104071)),f333(f333(f18(x104073,a907,f917(f917(x104071,f917(a906,a905)),f909(x104071))),f333(f333(f8(f917(x104071,f917(a906,a905)),f917(a907,f917(f917(x104071,f917(a906,a905)),f909(x104071))),x104073),f98(x104071)),x104074)),x104075)),x104076)),x104077)) % 173.51/173.28 [9937]~P15(x99376,x99377,x99378,x99379,x993710,x99371)+E(f333(f333(x99371,x99372),x99373),f333(f333(x99371,x99374),x99375))+~P106(f333(f333(f335(f916(x99377,x99377)),f333(f333(f265(x99377,x99377),x99373),x99375)),x993710))+~P106(f333(f333(f335(f916(x99376,x99376)),f333(f333(f265(x99376,x99376),x99372),x99374)),x99379)) % 173.51/173.28 [9527]~P2(x95272)+E(x95271,f196(f917(x95272,a905)))+~P106(f333(f67(x95272),x95271))+P106(f333(f333(f335(x95272),f13(x95272,x95271)),x95271))+~P106(f333(f333(f335(x95272),f333(f333(f121(x95272),f886(x95271,x95272)),f890(x95271,x95272))),f333(f333(f315(x95272),f886(x95271,x95272)),f333(f333(f315(x95272),f890(x95271,x95272)),f196(f917(x95272,a905)))))) % 173.51/173.28 [9528]~P2(x95282)+E(x95281,f196(f917(x95282,a905)))+~P106(f333(f67(x95282),x95281))+P106(f333(f333(f335(x95282),f10(x95282,x95281)),x95281))+~P106(f333(f333(f335(x95282),f333(f333(f112(x95282),f891(x95281,x95282)),f894(x95281,x95282))),f333(f333(f315(x95282),f891(x95281,x95282)),f333(f333(f315(x95282),f894(x95281,x95282)),f196(f917(x95282,a905)))))) % 173.51/173.28 [9559]~P76(x95592)+E(x95591,f196(f917(x95592,a905)))+~P106(f333(f67(x95592),x95591))+P106(f333(f333(f335(x95592),f333(f69(x95592,f88(x95592)),x95591)),x95591))+~P106(f333(f333(f335(x95592),f333(f333(f88(x95592),f473(x95591,x95592)),f474(x95591,x95592))),f333(f333(f315(x95592),f473(x95591,x95592)),f333(f333(f315(x95592),f474(x95591,x95592)),f196(f917(x95592,a905)))))) % 173.51/173.28 [9565]~P110(x95652)+E(x95651,f196(f917(x95652,a905)))+~P106(f333(f67(x95652),x95651))+P106(f333(f333(f335(x95652),f11(x95652,f244(x95652),x95651)),x95651))+~P106(f333(f333(f335(x95652),f333(f333(f244(x95652),f428(x95651,x95652)),f429(x95651,x95652))),f333(f333(f315(x95652),f428(x95651,x95652)),f333(f333(f315(x95652),f429(x95651,x95652)),f196(f917(x95652,a905)))))) % 173.51/173.28 [9566]~P110(x95662)+E(x95661,f196(f917(x95662,a905)))+~P106(f333(f67(x95662),x95661))+P106(f333(f333(f335(x95662),f12(x95662,f245(x95662),x95661)),x95661))+~P106(f333(f333(f335(x95662),f333(f333(f245(x95662),f432(x95661,x95662)),f433(x95661,x95662))),f333(f333(f315(x95662),f432(x95661,x95662)),f333(f333(f315(x95662),f433(x95661,x95662)),f196(f917(x95662,a905)))))) % 173.51/173.28 [6652]~P90(x66522)+E(x66521,f2(x66522))+~E(f333(f333(f87(x66522),x66523),x66521),f2(x66522))+~P106(f333(f333(f246(x66522),f2(x66522)),x66523))+~P106(f333(f333(f246(x66522),f2(x66522)),x66521)) % 173.51/173.28 [6653]~P90(x66532)+E(x66531,f2(x66532))+~E(f333(f333(f87(x66532),x66531),x66533),f2(x66532))+~P106(f333(f333(f246(x66532),f2(x66532)),x66533))+~P106(f333(f333(f246(x66532),f2(x66532)),x66531)) % 173.51/173.28 [7179]~P110(x71792)+~P16(x71792,x71791)+E(x71791,f124(x71792))+~P106(f333(f333(f335(x71792),x71793),f333(f180(x71792),f754(x71791,x71792))))+P106(f333(f333(f246(x71792),f773(x71791,x71792)),x71793)) % 173.51/173.28 [7347]~P110(x73471)+E(f14(x73471,x73472),x73473)+~P106(f333(f67(x73471),x73472))+~P106(f333(f333(f246(x73471),x73473),f528(x73473,x73472,x73471)))+~P106(f333(f333(f335(x73471),x73473),x73472)) % 173.51/173.28 [7379]~P110(x73791)+~P16(x73791,x73792)+~P16(x73791,x73793)+P16(x73791,f333(f333(f142(x73791),x73792),x73793))+P106(f333(f333(f335(x73791),f760(x73793,x73792,x73791)),f333(f180(x73791),x73792))) % 173.51/173.28 [7380]~P110(x73801)+~P16(x73801,x73802)+~P16(x73801,x73803)+P16(x73801,f333(f333(f142(x73801),x73802),x73803))+P106(f333(f333(f335(x73801),f761(x73803,x73802,x73801)),f333(f180(x73801),x73803))) % 173.51/173.28 [7439]~P110(x74391)+E(f14(x74391,x74392),x74393)+~P106(f333(f67(x74391),x74392))+P106(f333(f333(f335(x74391),f528(x74393,x74392,x74391)),x74392))+~P106(f333(f333(f335(x74391),x74393),x74392)) % 173.51/173.28 [7440]~P110(x74401)+E(f15(x74401,x74402),x74403)+~P106(f333(f67(x74401),x74402))+P106(f333(f333(f335(x74401),f531(x74403,x74402,x74401)),x74402))+~P106(f333(f333(f335(x74401),x74403),x74402)) % 173.51/173.28 [8011]~P110(x80111)+E(f15(x80111,x80112),x80113)+~P106(f333(f67(x80111),x80112))+~P106(f333(f333(f335(x80111),x80113),x80112))+~P106(f333(f333(f246(x80111),f531(x80113,x80112,x80111)),x80113)) % 173.51/173.28 [8334]~P110(x83341)+~P16(x83341,x83342)+~P16(x83341,x83343)+P16(x83341,f333(f333(f142(x83341),x83342),x83343))+~P106(f333(f333(f246(x83341),f760(x83343,x83342,x83341)),f761(x83343,x83342,x83341))) % 173.51/173.28 [9156]~P2(x91562)+E(x91561,f196(f917(x91562,a905)))+~E(f333(f333(f121(x91562),f333(x91563,f884(x91561,x91563,x91562))),f333(x91563,f897(x91561,x91563,x91562))),f333(x91563,f333(f333(f121(x91562),f884(x91561,x91563,x91562)),f897(x91561,x91563,x91562))))+E(f13(x91562,f333(f316(x91562,x91562,x91563),x91561)),f333(x91563,f13(x91562,x91561)))+~P106(f333(f67(x91562),x91561)) % 173.51/173.28 [9157]~P2(x91572)+E(x91571,f196(f917(x91572,a905)))+~E(f333(f333(f112(x91572),f333(x91573,f885(x91571,x91573,x91572))),f333(x91573,f895(x91571,x91573,x91572))),f333(x91573,f333(f333(f112(x91572),f885(x91571,x91573,x91572)),f895(x91571,x91573,x91572))))+E(f10(x91572,f333(f316(x91572,x91572,x91573),x91571)),f333(x91573,f10(x91572,x91571)))+~P106(f333(f67(x91572),x91571)) % 173.51/173.28 [9158]~P110(x91582)+E(x91581,f196(f917(x91582,a905)))+~E(f333(f333(f244(x91582),f333(x91583,f446(x91581,x91583,x91582))),f333(x91583,f447(x91581,x91583,x91582))),f333(x91583,f333(f333(f244(x91582),f446(x91581,x91583,x91582)),f447(x91581,x91583,x91582))))+E(f14(x91582,f333(f316(x91582,x91582,x91583),x91581)),f333(x91583,f14(x91582,x91581)))+~P106(f333(f67(x91582),x91581)) % 173.51/173.28 [9159]~P110(x91592)+E(x91591,f196(f917(x91592,a905)))+~E(f333(f333(f245(x91592),f333(x91593,f424(x91591,x91593,x91592))),f333(x91593,f436(x91591,x91593,x91592))),f333(x91593,f333(f333(f245(x91592),f424(x91591,x91593,x91592)),f436(x91591,x91593,x91592))))+E(f15(x91592,f333(f316(x91592,x91592,x91593),x91591)),f333(x91593,f15(x91592,x91591)))+~P106(f333(f67(x91592),x91591)) % 173.51/173.28 [9229]~P110(x92292)+E(x92291,f196(f917(x92292,a905)))+~E(f333(f333(f244(x92292),f333(x92293,f425(x92291,x92293,x92292))),f333(x92293,f435(x92291,x92293,x92292))),f333(x92293,f333(f333(f244(x92292),f425(x92291,x92293,x92292)),f435(x92291,x92293,x92292))))+E(f11(x92292,f244(x92292),f333(f316(x92292,x92292,x92293),x92291)),f333(x92293,f11(x92292,f244(x92292),x92291)))+~P106(f333(f67(x92292),x92291)) % 173.51/173.28 [9230]~P110(x92302)+E(x92301,f196(f917(x92302,a905)))+~E(f333(f333(f245(x92302),f333(x92303,f426(x92301,x92303,x92302))),f333(x92303,f434(x92301,x92303,x92302))),f333(x92303,f333(f333(f245(x92302),f426(x92301,x92303,x92302)),f434(x92301,x92303,x92302))))+E(f12(x92302,f245(x92302),f333(f316(x92302,x92302,x92303),x92301)),f333(x92303,f12(x92302,f245(x92302),x92301)))+~P106(f333(f67(x92302),x92301)) % 173.51/173.28 [6668]~P76(x66682)+E(x66681,f196(f917(x66682,a905)))+~P106(f333(f67(x66682),x66681))+E(f333(f69(x66682,f88(x66682)),f333(f333(f315(x66682),x66683),x66681)),f333(f333(f88(x66682),x66683),f333(f69(x66682,f88(x66682)),x66681)))+P106(f333(f333(f335(x66682),x66683),x66681)) % 173.51/173.28 [7185]~P2(x71852)+E(f333(f333(f121(x71852),f13(x71852,x71851)),f13(x71852,x71853)),f13(x71852,x71853))+E(x71851,f196(f917(x71852,a905)))+~P106(f333(f67(x71852),x71853))+~P106(f333(f333(f246(f917(x71852,a905)),x71851),x71853)) % 173.51/173.28 [7186]~P2(x71862)+E(f333(f333(f112(x71862),f10(x71862,x71861)),f10(x71862,x71863)),f10(x71862,x71863))+E(x71861,f196(f917(x71862,a905)))+~P106(f333(f67(x71862),x71863))+~P106(f333(f333(f246(f917(x71862,a905)),x71861),x71863)) % 173.51/173.28 [7187]~P110(x71872)+E(f333(f333(f244(x71872),f14(x71872,x71871)),f14(x71872,x71873)),f14(x71872,x71873))+E(x71871,f196(f917(x71872,a905)))+~P106(f333(f67(x71872),x71873))+~P106(f333(f333(f246(f917(x71872,a905)),x71871),x71873)) % 173.51/173.28 [7188]~P110(x71882)+E(f333(f333(f245(x71882),f15(x71882,x71881)),f15(x71882,x71883)),f15(x71882,x71883))+E(x71881,f196(f917(x71882,a905)))+~P106(f333(f67(x71882),x71883))+~P106(f333(f333(f246(f917(x71882,a905)),x71881),x71883)) % 173.51/173.28 [7489]~P110(x74892)+E(x74891,f196(f917(x74892,a905)))+~P106(f333(f67(x74892),x74893))+P106(f333(f333(f246(x74892),f14(x74892,x74893)),f14(x74892,x74891)))+~P106(f333(f333(f246(f917(x74892,a905)),x74891),x74893)) % 173.51/173.28 [7490]~P110(x74902)+E(x74901,f196(f917(x74902,a905)))+~P106(f333(f67(x74902),x74903))+P106(f333(f333(f246(x74902),f15(x74902,x74901)),f15(x74902,x74903)))+~P106(f333(f333(f246(f917(x74902,a905)),x74901),x74903)) % 173.51/173.28 [7543]~P2(x75431)+E(f13(x75431,x75432),x75433)+~P106(f333(f67(x75431),x75432))+~E(f333(f333(f23(f917(x75431,a905)),x75432),f333(f333(f315(x75431),x75433),f196(f917(x75431,a905)))),f196(f917(x75431,a905)))+~P106(f333(f333(f335(x75431),x75433),x75432)) % 173.51/173.28 [7544]~P2(x75441)+E(f10(x75441,x75442),x75443)+~P106(f333(f67(x75441),x75442))+~E(f333(f333(f23(f917(x75441,a905)),x75442),f333(f333(f315(x75441),x75443),f196(f917(x75441,a905)))),f196(f917(x75441,a905)))+~P106(f333(f333(f335(x75441),x75443),x75442)) % 173.51/173.28 [7545]~P110(x75451)+E(f14(x75451,x75452),x75453)+~P106(f333(f67(x75451),x75452))+~E(f333(f333(f23(f917(x75451,a905)),x75452),f333(f333(f315(x75451),x75453),f196(f917(x75451,a905)))),f196(f917(x75451,a905)))+~P106(f333(f333(f335(x75451),x75453),x75452)) % 173.51/173.28 [7546]~P110(x75461)+E(f15(x75461,x75462),x75463)+~P106(f333(f67(x75461),x75462))+~E(f333(f333(f23(f917(x75461,a905)),x75462),f333(f333(f315(x75461),x75463),f196(f917(x75461,a905)))),f196(f917(x75461,a905)))+~P106(f333(f333(f335(x75461),x75463),x75462)) % 173.51/173.28 [7640]~P110(x76401)+E(f11(x76401,f244(x76401),x76402),x76403)+~P106(f333(f67(x76401),x76402))+~E(f333(f333(f23(f917(x76401,a905)),x76402),f333(f333(f315(x76401),x76403),f196(f917(x76401,a905)))),f196(f917(x76401,a905)))+~P106(f333(f333(f335(x76401),x76403),x76402)) % 173.51/173.28 [7641]~P110(x76411)+E(f12(x76411,f245(x76411),x76412),x76413)+~P106(f333(f67(x76411),x76412))+~E(f333(f333(f23(f917(x76411,a905)),x76412),f333(f333(f315(x76411),x76413),f196(f917(x76411,a905)))),f196(f917(x76411,a905)))+~P106(f333(f333(f335(x76411),x76413),x76412)) % 173.51/173.28 [7676]~P102(x76762)+E(x76761,f196(f917(x76762,a905)))+~P106(f333(f67(x76762),x76761))+~P106(f333(f333(f246(x76762),x76763),f455(x76763,x76761,x76762)))+P106(f333(f333(f246(x76762),x76763),f333(f69(x76762,f112(x76762)),x76761))) % 173.51/173.28 [7677]~P110(x76772)+E(x76771,f196(f917(x76772,a905)))+~P106(f333(f67(x76772),x76771))+~P106(f333(f333(f246(x76772),x76773),f466(x76773,x76771,x76772)))+P106(f333(f333(f246(x76772),x76773),f333(f69(x76772,f244(x76772)),x76771))) % 173.51/173.28 [7678]~P110(x76782)+E(x76781,f196(f917(x76782,a905)))+~P106(f333(f67(x76782),x76781))+~P106(f333(f333(f247(x76782),x76783),f468(x76783,x76781,x76782)))+P106(f333(f333(f247(x76782),x76783),f333(f69(x76782,f244(x76782)),x76781))) % 173.51/173.28 [7763]~P102(x77632)+E(x77631,f196(f917(x77632,a905)))+~P106(f333(f67(x77632),x77631))+P106(f333(f333(f335(x77632),f455(x77633,x77631,x77632)),x77631))+P106(f333(f333(f246(x77632),x77633),f333(f69(x77632,f112(x77632)),x77631))) % 173.51/173.28 [7764]~P110(x77642)+E(x77641,f196(f917(x77642,a905)))+~P106(f333(f67(x77642),x77641))+P106(f333(f333(f335(x77642),f466(x77643,x77641,x77642)),x77641))+P106(f333(f333(f246(x77642),x77643),f333(f69(x77642,f244(x77642)),x77641))) % 173.51/173.28 [7765]~P110(x77652)+E(x77651,f196(f917(x77652,a905)))+~P106(f333(f67(x77652),x77651))+P106(f333(f333(f335(x77652),f468(x77653,x77651,x77652)),x77651))+P106(f333(f333(f247(x77652),x77653),f333(f69(x77652,f244(x77652)),x77651))) % 173.51/173.28 [7889]~P110(x78892)+E(x78891,f196(f917(x78892,a905)))+E(f333(f333(f244(x78892),f11(x78892,f244(x78892),x78891)),f11(x78892,f244(x78892),x78893)),f11(x78892,f244(x78892),x78893))+~P106(f333(f67(x78892),x78893))+~P106(f333(f333(f246(f917(x78892,a905)),x78891),x78893)) % 173.51/173.28 [7890]~P110(x78902)+E(x78901,f196(f917(x78902,a905)))+E(f333(f333(f245(x78902),f12(x78902,f245(x78902),x78901)),f12(x78902,f245(x78902),x78903)),f12(x78902,f245(x78902),x78903))+~P106(f333(f67(x78902),x78903))+~P106(f333(f333(f246(f917(x78902,a905)),x78901),x78903)) % 173.51/173.28 [8090]~E(f664(x80901,x80903,x80902),f665(x80901,x80903,x80902))+~E(f333(f41(x80902),f666(x80901,x80903,x80902)),x80901)+E(f333(f333(f88(a910),x80901),f333(f41(f917(x80902,a905)),x80903)),f333(f41(x80902),f43(f917(x80902,a905),x80903)))+~P106(f333(f67(x80902),f43(f917(x80902,a905),x80903)))+~P106(f333(f67(f917(x80902,a905)),x80903)) % 173.51/173.28 [8273]~P110(x82732)+E(x82731,f196(f917(x82732,a905)))+~P106(f333(f67(x82732),x82733))+P106(f333(f333(f246(x82732),f333(f69(x82732,f244(x82732)),x82733)),f333(f69(x82732,f244(x82732)),x82731)))+~P106(f333(f333(f246(f917(x82732,a905)),x82731),x82733)) % 173.51/173.28 [8582]~E(f664(x85821,x85823,x85822),f665(x85821,x85823,x85822))+E(f333(f333(f88(a910),x85821),f333(f41(f917(x85822,a905)),x85823)),f333(f41(x85822),f43(f917(x85822,a905),x85823)))+P106(f333(f333(f335(f917(x85822,a905)),f666(x85821,x85823,x85822)),x85823))+~P106(f333(f67(x85822),f43(f917(x85822,a905),x85823)))+~P106(f333(f67(f917(x85822,a905)),x85823)) % 173.51/173.28 [8611]~E(f333(f41(x86112),f666(x86111,x86113,x86112)),x86111)+E(f333(f333(f88(a910),x86111),f333(f41(f917(x86112,a905)),x86113)),f333(f41(x86112),f43(f917(x86112,a905),x86113)))+P106(f333(f333(f335(f917(x86112,a905)),f665(x86111,x86113,x86112)),x86113))+~P106(f333(f67(x86112),f43(f917(x86112,a905),x86113)))+~P106(f333(f67(f917(x86112,a905)),x86113)) % 173.51/173.28 [8612]~E(f333(f41(x86122),f666(x86121,x86123,x86122)),x86121)+E(f333(f333(f88(a910),x86121),f333(f41(f917(x86122,a905)),x86123)),f333(f41(x86122),f43(f917(x86122,a905),x86123)))+P106(f333(f333(f335(f917(x86122,a905)),f664(x86121,x86123,x86122)),x86123))+~P106(f333(f67(x86122),f43(f917(x86122,a905),x86123)))+~P106(f333(f67(f917(x86122,a905)),x86123)) % 173.51/173.28 [8639]~E(f333(f41(x86392),f666(x86391,x86393,x86392)),x86391)+~E(f333(f333(f112(f917(x86392,a905)),f665(x86391,x86393,x86392)),f664(x86391,x86393,x86392)),f196(f917(x86392,a905)))+E(f333(f333(f88(a910),x86391),f333(f41(f917(x86392,a905)),x86393)),f333(f41(x86392),f43(f917(x86392,a905),x86393)))+~P106(f333(f67(f917(x86392,a905)),x86393))+~P106(f333(f67(x86392),f43(f917(x86392,a905),x86393))) % 173.51/173.28 [8902]E(f333(f333(f88(a910),x89021),f333(f41(f917(x89022,a905)),x89023)),f333(f41(x89022),f43(f917(x89022,a905),x89023)))+P106(f333(f333(f335(f917(x89022,a905)),f666(x89021,x89023,x89022)),x89023))+P106(f333(f333(f335(f917(x89022,a905)),f665(x89021,x89023,x89022)),x89023))+~P106(f333(f67(f917(x89022,a905)),x89023))+~P106(f333(f67(x89022),f43(f917(x89022,a905),x89023))) % 173.51/173.28 [8903]E(f333(f333(f88(a910),x89031),f333(f41(f917(x89032,a905)),x89033)),f333(f41(x89032),f43(f917(x89032,a905),x89033)))+P106(f333(f333(f335(f917(x89032,a905)),f666(x89031,x89033,x89032)),x89033))+P106(f333(f333(f335(f917(x89032,a905)),f664(x89031,x89033,x89032)),x89033))+~P106(f333(f67(f917(x89032,a905)),x89033))+~P106(f333(f67(x89032),f43(f917(x89032,a905),x89033))) % 173.51/173.28 [8929]~E(f333(f333(f112(f917(x89292,a905)),f665(x89291,x89293,x89292)),f664(x89291,x89293,x89292)),f196(f917(x89292,a905)))+E(f333(f333(f88(a910),x89291),f333(f41(f917(x89292,a905)),x89293)),f333(f41(x89292),f43(f917(x89292,a905),x89293)))+~P106(f333(f67(f917(x89292,a905)),x89293))+P106(f333(f333(f335(f917(x89292,a905)),f666(x89291,x89293,x89292)),x89293))+~P106(f333(f67(x89292),f43(f917(x89292,a905),x89293))) % 173.51/173.28 [9204]~P97(x92042)+E(x92041,f196(f917(x92042,a905)))+~E(f333(f333(f88(x92042),f333(x92043,f472(x92041,x92043,x92042))),f333(x92043,f475(x92041,x92043,x92042))),f333(x92043,f333(f333(f88(x92042),f472(x92041,x92043,x92042)),f475(x92041,x92043,x92042))))+~P106(f333(f67(x92042),x92041))+E(f333(f69(x92042,f88(x92042)),f333(f316(x92042,x92042,x92043),x92041)),f333(x92043,f333(f69(x92042,f88(x92042)),x92041))) % 173.51/173.28 [10150]P106(f333(f333(x101501,x101502),x101503))+P106(f333(f333(f247(a1),f546(x101501,x101503,x101502)),f547(x101501,x101503,x101502)))+P106(f333(f333(f246(a1),f547(x101501,x101503,x101502)),f2(a1)))+P106(f333(f333(x101501,f546(x101501,x101503,x101502)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f547(x101501,x101503,x101502))))+~P106(f333(f321(f916(a1,a1),a64),f333(f333(f265(a1,a1),x101502),x101503))) % 173.51/173.28 [10156]P106(f333(f333(x101561,x101562),x101563))+P106(f333(f333(f246(a1),f545(x101561,x101563,x101562)),f2(a1)))+P106(f333(f333(x101561,f539(x101561,x101563,x101562)),f333(f333(f88(a1),f333(f114(a1),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f545(x101561,x101563,x101562))))+P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),f539(x101561,x101563,x101562)),f545(x101561,x101563,x101562))))+~P106(f333(f321(f916(a1,a1),a58),f333(f333(f265(a1,a1),x101562),x101563))) % 173.51/173.28 [8061]~P120(x80611)+~P106(f333(f333(f246(x80611),x80612),f85(x80611)))+~P106(f333(f333(f246(x80611),f2(x80611)),x80612))+~P106(f333(f333(f246(x80611),f2(x80611)),x80613))+P106(f333(f333(f246(x80611),f333(f333(f88(x80611),x80612),x80613)),x80613)) % 173.51/173.28 [8062]~P120(x80621)+~P106(f333(f333(f246(x80621),x80623),f85(x80621)))+~P106(f333(f333(f246(x80621),f2(x80621)),x80623))+~P106(f333(f333(f246(x80621),f2(x80621)),x80622))+P106(f333(f333(f246(x80621),f333(f333(f88(x80621),x80622),x80623)),x80622)) % 173.51/173.28 [8422]~P110(x84222)+E(x84221,f196(f917(x84222,a905)))+~P106(f333(f67(x84222),x84221))+P106(f333(f333(f335(x84222),f467(x84223,x84221,x84222)),x84221))+~P106(f333(f333(f246(x84222),f333(f69(x84222,f244(x84222)),x84221)),x84223)) % 173.51/173.28 [8423]~P110(x84232)+E(x84231,f196(f917(x84232,a905)))+~P106(f333(f67(x84232),x84231))+P106(f333(f333(f335(x84232),f470(x84233,x84231,x84232)),x84231))+~P106(f333(f333(f247(x84232),f333(f69(x84232,f244(x84232)),x84231)),x84233)) % 173.51/173.28 [8424]~P110(x84242)+E(x84241,f196(f917(x84242,a905)))+~P106(f333(f67(x84242),x84241))+P106(f333(f333(f246(x84242),f467(x84243,x84241,x84242)),x84243))+~P106(f333(f333(f246(x84242),f333(f69(x84242,f244(x84242)),x84241)),x84243)) % 173.51/173.28 [8425]~P110(x84252)+E(x84251,f196(f917(x84252,a905)))+~P106(f333(f67(x84252),x84251))+P106(f333(f333(f247(x84252),f470(x84253,x84251,x84252)),x84253))+~P106(f333(f333(f247(x84252),f333(f69(x84252,f244(x84252)),x84251)),x84253)) % 173.51/173.28 [8510]~P106(f333(x85101,x85103))+P106(f333(x85101,f402(x85101,x85102)))+P106(f333(x85101,f392(x85101,x85102)))+~P106(f333(f333(f247(a1),f2(a1)),x85102))+P106(f333(x85101,f333(f333(f23(a1),f392(x85101,x85102)),f333(f333(f88(a1),f403(x85101,x85102)),x85102)))) % 173.51/173.28 [8739]~P106(f333(x87391,x87393))+P106(f333(x87391,f392(x87391,x87392)))+~P106(f333(f333(f247(a1),f2(a1)),x87392))+P106(f333(f333(f335(a1),f402(x87391,x87392)),f309(a1,f85(a1),x87392)))+P106(f333(x87391,f333(f333(f23(a1),f392(x87391,x87392)),f333(f333(f88(a1),f403(x87391,x87392)),x87392)))) % 173.51/173.28 [8951]~P106(f333(x89511,x89513))+~P106(f333(x89511,f392(x89511,x89512)))+P106(f333(x89511,f402(x89511,x89512)))+~P106(f333(f333(f247(a1),f2(a1)),x89512))+~P106(f333(x89511,f333(f333(f23(a1),f392(x89511,x89512)),f333(f333(f88(a1),f403(x89511,x89512)),x89512)))) % 173.51/173.28 [9084]~P106(f333(x90841,x90843))+~P106(f333(x90841,f392(x90841,x90842)))+~P106(f333(f333(f247(a1),f2(a1)),x90842))+P106(f333(f333(f335(a1),f402(x90841,x90842)),f309(a1,f85(a1),x90842)))+~P106(f333(x90841,f333(f333(f23(a1),f392(x90841,x90842)),f333(f333(f88(a1),f403(x90841,x90842)),x90842)))) % 173.51/173.28 [8857]~P2(x88571)+~P106(f333(f67(x88571),x88572))+E(f333(f333(f23(f917(x88571,a905)),x88572),f333(f333(f315(x88571),x88573),f196(f917(x88571,a905)))),f196(f917(x88571,a905)))+~P106(f333(f333(f335(x88571),x88573),x88572))+E(f333(f333(f121(x88571),x88573),f13(x88571,f333(f333(f23(f917(x88571,a905)),x88572),f333(f333(f315(x88571),x88573),f196(f917(x88571,a905)))))),f13(x88571,x88572)) % 173.51/173.28 [8858]~P2(x88581)+~P106(f333(f67(x88581),x88582))+E(f333(f333(f23(f917(x88581,a905)),x88582),f333(f333(f315(x88581),x88583),f196(f917(x88581,a905)))),f196(f917(x88581,a905)))+~P106(f333(f333(f335(x88581),x88583),x88582))+E(f333(f333(f112(x88581),x88583),f10(x88581,f333(f333(f23(f917(x88581,a905)),x88582),f333(f333(f315(x88581),x88583),f196(f917(x88581,a905)))))),f10(x88581,x88582)) % 173.51/173.28 [8859]~P110(x88591)+~P106(f333(f67(x88591),x88592))+E(f333(f333(f23(f917(x88591,a905)),x88592),f333(f333(f315(x88591),x88593),f196(f917(x88591,a905)))),f196(f917(x88591,a905)))+~P106(f333(f333(f335(x88591),x88593),x88592))+E(f333(f333(f244(x88591),x88593),f14(x88591,f333(f333(f23(f917(x88591,a905)),x88592),f333(f333(f315(x88591),x88593),f196(f917(x88591,a905)))))),f14(x88591,x88592)) % 173.51/173.28 [8860]~P110(x88601)+~P106(f333(f67(x88601),x88602))+E(f333(f333(f23(f917(x88601,a905)),x88602),f333(f333(f315(x88601),x88603),f196(f917(x88601,a905)))),f196(f917(x88601,a905)))+~P106(f333(f333(f335(x88601),x88603),x88602))+E(f333(f333(f245(x88601),x88603),f15(x88601,f333(f333(f23(f917(x88601,a905)),x88602),f333(f333(f315(x88601),x88603),f196(f917(x88601,a905)))))),f15(x88601,x88602)) % 173.51/173.28 [8922]~P110(x89221)+~P106(f333(f67(x89221),x89222))+E(f333(f333(f23(f917(x89221,a905)),x89222),f333(f333(f315(x89221),x89223),f196(f917(x89221,a905)))),f196(f917(x89221,a905)))+~P106(f333(f333(f335(x89221),x89223),x89222))+E(f333(f333(f244(x89221),x89223),f11(x89221,f244(x89221),f333(f333(f23(f917(x89221,a905)),x89222),f333(f333(f315(x89221),x89223),f196(f917(x89221,a905)))))),f11(x89221,f244(x89221),x89222)) % 173.51/173.28 [8923]~P110(x89231)+~P106(f333(f67(x89231),x89232))+E(f333(f333(f23(f917(x89231,a905)),x89232),f333(f333(f315(x89231),x89233),f196(f917(x89231,a905)))),f196(f917(x89231,a905)))+~P106(f333(f333(f335(x89231),x89233),x89232))+E(f333(f333(f245(x89231),x89233),f12(x89231,f245(x89231),f333(f333(f23(f917(x89231,a905)),x89232),f333(f333(f315(x89231),x89233),f196(f917(x89231,a905)))))),f12(x89231,f245(x89231),x89232)) % 173.51/173.28 [8938]~P2(x89381)+~P106(f333(f67(x89381),x89383))+~P106(f333(f67(x89381),x89382))+E(f333(f333(f112(f917(x89381,a905)),x89382),x89383),f196(f917(x89381,a905)))+E(f333(f333(f121(x89381),f13(x89381,f333(f333(f121(f917(x89381,a905)),x89382),x89383))),f13(x89381,f333(f333(f112(f917(x89381,a905)),x89382),x89383))),f333(f333(f121(x89381),f13(x89381,x89382)),f13(x89381,x89383))) % 173.51/173.28 [8939]~P2(x89391)+~P106(f333(f67(x89391),x89393))+~P106(f333(f67(x89391),x89392))+E(f333(f333(f112(f917(x89391,a905)),x89392),x89393),f196(f917(x89391,a905)))+E(f333(f333(f112(x89391),f10(x89391,f333(f333(f121(f917(x89391,a905)),x89392),x89393))),f10(x89391,f333(f333(f112(f917(x89391,a905)),x89392),x89393))),f333(f333(f112(x89391),f10(x89391,x89392)),f10(x89391,x89393))) % 173.51/173.28 [8940]~P110(x89401)+~P106(f333(f67(x89401),x89403))+~P106(f333(f67(x89401),x89402))+E(f333(f333(f112(f917(x89401,a905)),x89402),x89403),f196(f917(x89401,a905)))+E(f333(f333(f244(x89401),f14(x89401,f333(f333(f121(f917(x89401,a905)),x89402),x89403))),f14(x89401,f333(f333(f112(f917(x89401,a905)),x89402),x89403))),f333(f333(f244(x89401),f14(x89401,x89402)),f14(x89401,x89403))) % 173.51/173.28 [8941]~P110(x89411)+~P106(f333(f67(x89411),x89413))+~P106(f333(f67(x89411),x89412))+E(f333(f333(f112(f917(x89411,a905)),x89412),x89413),f196(f917(x89411,a905)))+E(f333(f333(f245(x89411),f15(x89411,f333(f333(f121(f917(x89411,a905)),x89412),x89413))),f15(x89411,f333(f333(f112(f917(x89411,a905)),x89412),x89413))),f333(f333(f245(x89411),f15(x89411,x89412)),f15(x89411,x89413))) % 173.51/173.28 [9176]~P110(x91761)+~P106(f333(f67(x91761),x91763))+~P106(f333(f67(x91761),x91762))+E(f333(f333(f112(f917(x91761,a905)),x91762),x91763),f196(f917(x91761,a905)))+E(f333(f333(f244(x91761),f11(x91761,f244(x91761),f333(f333(f121(f917(x91761,a905)),x91762),x91763))),f11(x91761,f244(x91761),f333(f333(f112(f917(x91761,a905)),x91762),x91763))),f333(f333(f244(x91761),f11(x91761,f244(x91761),x91762)),f11(x91761,f244(x91761),x91763))) % 173.51/173.28 [9177]~P110(x91771)+~P106(f333(f67(x91771),x91773))+~P106(f333(f67(x91771),x91772))+E(f333(f333(f112(f917(x91771,a905)),x91772),x91773),f196(f917(x91771,a905)))+E(f333(f333(f245(x91771),f12(x91771,f245(x91771),f333(f333(f121(f917(x91771,a905)),x91772),x91773))),f12(x91771,f245(x91771),f333(f333(f112(f917(x91771,a905)),x91772),x91773))),f333(f333(f245(x91771),f12(x91771,f245(x91771),x91772)),f12(x91771,f245(x91771),x91773))) % 173.51/173.28 [9990]~P119(x99903)+E(x99901,x99902)+~P106(f333(f333(f246(x99903),f2(x99903)),x99902))+~P106(f333(f333(f246(x99903),f2(x99903)),x99901))+~E(f333(f333(f256(x99903),x99901),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)))),f333(f333(f256(x99903),x99902),f333(f114(a910),f333(f333(f87(a1),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108)),f333(f333(f23(a1),f333(f333(f87(a1),a90),a90)),a108))))) % 173.51/173.28 [6467]E(f346(x64671,x64672,x64673),x64674)+E(f333(x64671,x64674),f2(a910))+~E(f333(f333(f6(x64673,a910),x64671),x64672),f85(a910))+~P106(f333(f67(x64673),x64672))+~P106(f333(f333(f335(x64673),x64674),x64672)) % 173.51/173.28 [6530]E(f354(x65301,x65302,x65303),x65304)+E(f333(x65301,x65304),f2(a910))+~E(f333(f333(f6(x65303,a910),x65301),x65302),f333(a123,f2(a910)))+~P106(f333(f67(x65303),x65302))+~P106(f333(f333(f335(x65303),x65304),x65302)) % 173.51/173.28 [6638]~P110(x66381)+~P8(x66381)+P106(f333(f333(f247(x66381),x66382),f43(x66381,x66383)))+~P106(f333(f333(f247(x66381),x66382),x66384))+~P106(f333(f333(f335(x66381),x66384),x66383)) % 173.51/173.28 [6811]~P110(x68111)+~P8(x68111)+~P106(f333(f333(f247(x68111),x68114),x68113))+P106(f333(f333(f247(x68111),f44(x68111,x68112)),x68113))+~P106(f333(f333(f335(x68111),x68114),x68112)) % 173.51/173.28 [7064]~P119(x70643)+E(x70641,x70642)+~E(f333(f333(f256(x70643),x70641),f333(a123,x70644)),f333(f333(f256(x70643),x70642),f333(a123,x70644)))+~P106(f333(f333(f246(x70643),f2(x70643)),x70642))+~P106(f333(f333(f246(x70643),f2(x70643)),x70641)) % 173.51/173.28 [7273]~E(f349(x72732,x72733,x72731,x72734),x72734)+~E(f333(x72732,x72734),f85(a910))+E(f333(f333(f6(x72731,a910),x72732),x72733),f85(a910))+~P106(f333(f67(x72731),x72733))+~P106(f333(f333(f335(x72731),x72734),x72733)) % 173.51/173.28 [7280]~P117(x72804)+~P128(x72804)+E(f333(x72801,f454(x72801,x72802,x72803,x72804)),f2(x72804))+~E(f333(f333(f9(x72803,x72804),x72801),x72802),f2(x72804))+~P106(f333(f67(x72803),x72802)) % 173.51/173.28 [7369]~E(f356(x73692,x73693,x73691,x73694),x73694)+~E(f333(x73692,x73694),f333(a123,f2(a910)))+E(f333(f333(f6(x73691,a910),x73692),x73693),f333(a123,f2(a910)))+~P106(f333(f67(x73691),x73693))+~P106(f333(f333(f335(x73691),x73694),x73693)) % 173.51/173.28 [8102]~E(f333(x81022,x81024),f85(a910))+~E(f333(x81022,f349(x81022,x81023,x81021,x81024)),f2(a910))+E(f333(f333(f6(x81021,a910),x81022),x81023),f85(a910))+~P106(f333(f67(x81021),x81023))+~P106(f333(f333(f335(x81021),x81024),x81023)) % 173.51/173.28 [8146]~E(f333(x81462,x81464),f333(a123,f2(a910)))+~E(f333(x81462,f356(x81462,x81463,x81461,x81464)),f2(a910))+E(f333(f333(f6(x81461,a910),x81462),x81463),f333(a123,f2(a910)))+~P106(f333(f67(x81461),x81463))+~P106(f333(f333(f335(x81461),x81464),x81463)) % 173.51/173.28 [8706]~P110(x87061)+~P16(x87061,x87064)+P16(x87061,x87062)+~E(x87062,f333(f333(f159(x87061),x87063),x87064))+~P106(f333(f333(f246(x87061),x87063),f775(x87062,x87061,x87064,x87063))) % 173.51/173.28 [8743]E(x87431,x87432)+E(f333(f333(f23(a1),f410(x87433,x87432,x87434,x87431)),f411(x87433,x87432,x87434,x87431)),x87431)+~E(f333(f333(f87(a1),x87431),x87434),x87432)+~P106(f333(f333(f247(a1),f2(a1)),x87434))+~P106(f333(f333(f335(a1),x87432),x87433)) % 173.51/173.28 [8744]E(x87441,x87442)+E(f333(f333(f87(a1),f412(x87443,x87442,x87444,x87441)),f413(x87443,x87442,x87444,x87441)),x87441)+~E(f333(f333(f23(a1),x87441),x87444),x87442)+~P106(f333(f333(f247(a1),f2(a1)),x87444))+~P106(f333(f333(f335(a1),x87442),x87443)) % 173.51/173.28 [8936]E(f333(x89361,f652(x89362,x89361,x89363,x89364)),x89362)+P106(f333(f333(f246(a910),x89364),f653(x89362,x89361,x89363,x89364)))+~P106(f333(f333(f246(a1),x89362),f333(x89361,x89363)))+~P106(f333(f333(f247(a910),x89364),x89363))+~P106(f333(f333(f246(a1),f333(x89361,x89364)),x89362)) % 173.51/173.28 [8937]~P110(x89371)+~P16(x89371,x89373)+P16(x89371,x89372)+~E(x89372,f333(f333(f159(x89371),x89374),x89373))+P106(f333(f333(f335(x89371),f775(x89372,x89371,x89373,x89374)),f333(f180(x89371),x89373))) % 173.51/173.28 [8955]~P117(x89554)+~P128(x89554)+~E(f333(f333(f9(x89551,x89554),x89552),x89553),f2(x89554))+~P106(f333(f67(x89551),x89553))+P106(f333(f333(f335(x89551),f454(x89552,x89553,x89551,x89554)),x89553)) % 173.51/173.28 [8993]~E(f333(x89932,x89934),f85(a910))+E(f333(f333(f6(x89931,a910),x89932),x89933),f85(a910))+~P106(f333(f67(x89931),x89933))+~P106(f333(f333(f335(x89931),x89934),x89933))+P106(f333(f333(f335(x89931),f349(x89932,x89933,x89931,x89934)),x89933)) % 173.51/173.28 [9005]E(x90051,x90052)+~E(f333(f333(f23(a1),x90052),x90054),x90051)+~P106(f333(f333(f247(a1),f2(a1)),x90054))+~P106(f333(f333(f335(a1),x90051),x90053))+P106(f333(f333(f335(a1),f412(x90053,x90051,x90054,x90052)),x90053)) % 173.51/173.28 [9006]E(x90061,x90062)+~E(f333(f333(f87(a1),x90062),x90064),x90061)+~P106(f333(f333(f247(a1),f2(a1)),x90064))+~P106(f333(f333(f335(a1),x90061),x90063))+P106(f333(f333(f335(a1),f410(x90063,x90061,x90064,x90062)),x90063)) % 173.51/173.28 [9008]~E(f333(x90082,x90084),f333(a123,f2(a910)))+E(f333(f333(f6(x90081,a910),x90082),x90083),f333(a123,f2(a910)))+~P106(f333(f67(x90081),x90083))+~P106(f333(f333(f335(x90081),x90084),x90083))+P106(f333(f333(f335(x90081),f356(x90082,x90083,x90081,x90084)),x90083)) % 173.51/173.28 [9013]P62(x90132,x90133,x90134,x90131)+E(x90131,f196(f917(x90132,a905)))+~P106(f333(f67(x90132),x90134))+~P106(f333(f67(x90132),x90131))+P106(f333(f333(f335(x90132),f842(x90133,x90131,x90134,x90132)),x90134)) % 173.51/173.28 [9014]P62(x90142,x90143,x90144,x90141)+E(x90141,f196(f917(x90142,a905)))+~P106(f333(f67(x90142),x90144))+~P106(f333(f67(x90142),x90141))+P106(f333(f333(f335(x90142),f587(x90141,x90144,x90143,x90142)),x90144)) % 173.51/173.28 [9015]P62(x90152,x90153,x90154,x90151)+E(x90151,f196(f917(x90152,a905)))+~P106(f333(f67(x90152),x90154))+~P106(f333(f67(x90152),x90151))+P106(f333(f333(f335(x90152),f843(x90151,x90154,x90153,x90152)),x90154)) % 173.51/173.28 [9098]E(x90981,x90982)+~E(f333(f333(f23(a1),x90982),x90984),x90981)+~P106(f333(f333(f247(a1),f2(a1)),x90984))+~P106(f333(f333(f335(a1),x90981),x90983))+P106(f333(f333(f335(a1),f413(x90983,x90981,x90984,x90982)),f309(a1,f85(a1),x90984))) % 173.51/173.28 [9099]E(x90991,x90992)+~E(f333(f333(f87(a1),x90992),x90994),x90991)+~P106(f333(f333(f247(a1),f2(a1)),x90994))+~P106(f333(f333(f335(a1),x90991),x90993))+P106(f333(f333(f335(a1),f411(x90993,x90991,x90994,x90992)),f309(a1,f85(a1),x90994))) % 173.51/173.28 [9182]P106(f333(f333(f246(a910),x91821),f652(x91822,x91823,x91824,x91821)))+~P106(f333(f333(f246(a1),x91822),f333(x91823,x91824)))+P106(f333(f333(f246(a910),x91821),f653(x91822,x91823,x91824,x91821)))+~P106(f333(f333(f247(a910),x91821),x91824))+~P106(f333(f333(f246(a1),f333(x91823,x91821)),x91822)) % 173.51/173.28 [9297]E(f333(x92971,f652(x92972,x92971,x92973,x92974)),x92972)+~P106(f333(f333(f246(a1),x92972),f333(x92971,x92973)))+P106(f333(f333(f247(a910),f653(x92972,x92971,x92973,x92974)),x92973))+~P106(f333(f333(f247(a910),x92974),x92973))+~P106(f333(f333(f246(a1),f333(x92971,x92974)),x92972)) % 173.51/173.28 [9428]~P106(f333(f333(f246(a1),x94282),f333(x94283,x94284)))+P106(f333(f333(f246(a910),x94281),f653(x94282,x94283,x94284,x94281)))+P106(f333(f333(f246(a910),f652(x94282,x94283,x94284,x94281)),x94284))+~P106(f333(f333(f247(a910),x94281),x94284))+~P106(f333(f333(f246(a1),f333(x94283,x94281)),x94282)) % 173.51/173.28 [9429]~P106(f333(f333(f246(a1),x94292),f333(x94293,x94294)))+P106(f333(f333(f246(a910),x94291),f652(x94292,x94293,x94294,x94291)))+P106(f333(f333(f247(a910),f653(x94292,x94293,x94294,x94291)),x94294))+~P106(f333(f333(f247(a910),x94291),x94294))+~P106(f333(f333(f246(a1),f333(x94293,x94291)),x94292)) % 173.51/173.28 [9542]~P106(f333(f333(f246(a1),x95421),f333(x95422,x95423)))+P106(f333(f333(f247(a910),f653(x95421,x95422,x95423,x95424)),x95423))+~P106(f333(f333(f247(a910),x95424),x95423))+~P106(f333(f333(f246(a1),f333(x95422,x95424)),x95421))+P106(f333(f333(f246(a910),f652(x95421,x95422,x95423,x95424)),x95423)) % 173.51/173.28 [9627]E(x96271,f196(f917(x96272,a905)))+~P106(f333(f67(x96272),x96274))+~P106(f333(f67(x96272),x96271))+P106(f333(f333(f335(f916(f917(x96272,a905),f917(x96272,a905))),f333(f333(f265(f917(x96272,a905),f917(x96272,a905)),x96274),x96271)),f324(x96272,x96273)))+P106(f333(f333(f335(x96272),f589(x96273,x96271,x96274,x96272)),x96274)) % 173.51/173.28 [9628]E(x96281,f196(f917(x96282,a905)))+~P106(f333(f67(x96282),x96284))+~P106(f333(f67(x96282),x96281))+P106(f333(f333(f335(f916(f917(x96282,a905),f917(x96282,a905))),f333(f333(f265(f917(x96282,a905),f917(x96282,a905)),x96284),x96281)),f324(x96282,x96283)))+P106(f333(f333(f335(x96282),f648(x96283,x96281,x96284,x96282)),x96284)) % 173.51/173.28 [10298]E(f333(x102981,f652(x102982,x102981,x102983,x102984)),x102982)+~P106(f333(f333(f246(a1),x102982),f333(x102981,x102983)))+~P106(f333(f333(f246(a1),f333(f82(a1),f333(f333(f23(a1),f333(x102981,f333(f333(f87(a910),f653(x102982,x102981,x102983,x102984)),f85(a910)))),f333(x102981,f653(x102982,x102981,x102983,x102984))))),f85(a1)))+~P106(f333(f333(f247(a910),x102984),x102983))+~P106(f333(f333(f246(a1),f333(x102981,x102984)),x102982)) % 173.51/173.28 [10299]~P106(f333(f333(f246(a1),x102992),f333(x102993,x102994)))+P106(f333(f333(f246(a910),x102991),f652(x102992,x102993,x102994,x102991)))+~P106(f333(f333(f246(a1),f333(f82(a1),f333(f333(f23(a1),f333(x102993,f333(f333(f87(a910),f653(x102992,x102993,x102994,x102991)),f85(a910)))),f333(x102993,f653(x102992,x102993,x102994,x102991))))),f85(a1)))+~P106(f333(f333(f247(a910),x102991),x102994))+~P106(f333(f333(f246(a1),f333(x102993,x102991)),x102992)) % 173.51/173.28 [10300]~P106(f333(f333(f246(a1),x103001),f333(x103002,x103003)))+~P106(f333(f333(f246(a1),f333(f82(a1),f333(f333(f23(a1),f333(x103002,f333(f333(f87(a910),f653(x103001,x103002,x103003,x103004)),f85(a910)))),f333(x103002,f653(x103001,x103002,x103003,x103004))))),f85(a1)))+~P106(f333(f333(f247(a910),x103004),x103003))+~P106(f333(f333(f246(a1),f333(x103002,x103004)),x103001))+P106(f333(f333(f246(a910),f652(x103001,x103002,x103003,x103004)),x103003)) % 173.51/173.28 [7333]~P69(x73331)+P106(f333(f333(f247(x73331),x73332),f2(x73331)))+~P106(f333(f333(f246(x73331),x73333),f2(x73331)))+P106(f333(f333(f247(x73331),f2(x73331)),x73332))+P106(f333(f333(f246(x73331),x73333),f333(f333(f296(x73331),x73334),x73332))) % 173.51/173.28 [7334]~P69(x73341)+P106(f333(f333(f247(x73341),x73342),f2(x73341)))+~P106(f333(f333(f247(x73341),x73343),f2(x73341)))+P106(f333(f333(f247(x73341),f2(x73341)),x73342))+P106(f333(f333(f247(x73341),x73343),f333(f333(f296(x73341),x73344),x73342))) % 173.51/173.28 [7581]~P69(x75811)+P106(f333(f333(f246(x75811),x75812),f2(x75811)))+P106(f333(f333(f247(x75811),x75813),f2(x75811)))+P106(f333(f333(f247(x75811),f2(x75811)),x75813))+~P106(f333(f333(f246(x75811),x75812),f333(f333(f296(x75811),x75814),x75813))) % 173.51/173.28 [7582]~P69(x75821)+P106(f333(f333(f247(x75821),x75822),f2(x75821)))+P106(f333(f333(f247(x75821),x75823),f2(x75821)))+P106(f333(f333(f247(x75821),f2(x75821)),x75823))+~P106(f333(f333(f247(x75821),x75822),f333(f333(f296(x75821),x75824),x75823))) % 173.51/173.28 [7697]E(x76971,x76972)+~E(f333(f333(f172(x76973),x76974),x76971),f333(f333(f172(x76973),x76974),x76972))+~P106(f333(f145(x76973),x76974))+~P106(f333(f333(f247(a910),x76972),f333(f197(f911(x76973)),x76974)))+~P106(f333(f333(f247(a910),x76971),f333(f197(f911(x76973)),x76974))) % 173.51/173.28 [8063]~P69(x80631)+~P106(f333(f333(f246(x80631),x80633),f2(x80631)))+P106(f333(f333(f247(x80631),f2(x80631)),x80632))+~P106(f333(f333(f246(x80631),x80634),f333(f333(f88(x80631),x80633),x80632)))+P106(f333(f333(f246(x80631),x80633),f333(f333(f296(x80631),x80634),x80632))) % 173.51/173.28 [8064]~P69(x80641)+~P106(f333(f333(f247(x80641),x80643),f2(x80641)))+P106(f333(f333(f247(x80641),f2(x80641)),x80642))+~P106(f333(f333(f247(x80641),x80644),f333(f333(f88(x80641),x80643),x80642)))+P106(f333(f333(f247(x80641),x80643),f333(f333(f296(x80641),x80644),x80642))) % 173.51/173.28 [8065]~P69(x80651)+~P106(f333(f333(f247(x80651),x80652),f2(x80651)))+P106(f333(f333(f247(x80651),f2(x80651)),x80652))+~P106(f333(f333(f246(x80651),x80654),f333(f333(f88(x80651),x80653),x80652)))+P106(f333(f333(f246(x80651),x80653),f333(f333(f296(x80651),x80654),x80652))) % 173.51/173.28 [8066]~P69(x80661)+~P106(f333(f333(f247(x80661),x80662),f2(x80661)))+P106(f333(f333(f247(x80661),f2(x80661)),x80662))+~P106(f333(f333(f246(x80661),x80664),f333(f333(f296(x80661),x80663),x80662)))+P106(f333(f333(f246(x80661),x80663),f333(f333(f88(x80661),x80664),x80662))) % 173.51/173.28 [8067]~P69(x80671)+~P106(f333(f333(f247(x80671),x80672),f2(x80671)))+P106(f333(f333(f247(x80671),f2(x80671)),x80672))+~P106(f333(f333(f247(x80671),x80674),f333(f333(f88(x80671),x80673),x80672)))+P106(f333(f333(f247(x80671),x80673),f333(f333(f296(x80671),x80674),x80672))) % 173.51/173.28 [8068]~P69(x80681)+~P106(f333(f333(f247(x80681),x80682),f2(x80681)))+P106(f333(f333(f247(x80681),f2(x80681)),x80682))+~P106(f333(f333(f247(x80681),x80684),f333(f333(f296(x80681),x80683),x80682)))+P106(f333(f333(f247(x80681),x80683),f333(f333(f88(x80681),x80684),x80682))) % 173.51/173.28 [8215]~P110(x82151)+~P16(x82151,x82152)+~P106(f333(f333(f246(a910),x82153),x82154))+P106(f333(f333(f246(x82151),f333(f333(f172(x82151),x82152),x82153)),f333(f333(f172(x82151),x82152),x82154)))+~P106(f333(f333(f247(a910),x82154),f333(f197(f911(x82151)),x82152))) % 173.51/173.28 [8264]~P119(x82641)+~P106(f333(f333(f246(x82641),x82642),f85(x82641)))+~P106(f333(f333(f246(x82641),f2(x82641)),x82642))+~P106(f333(f333(f246(a910),x82644),x82643))+P106(f333(f333(f246(x82641),f333(f333(f256(x82641),x82642),x82643)),f333(f333(f256(x82641),x82642),x82644))) % 173.51/173.28 [8265]~P119(x82651)+~P106(f333(f333(f247(x82651),x82652),f85(x82651)))+~P106(f333(f333(f247(x82651),f2(x82651)),x82652))+~P106(f333(f333(f247(a910),x82654),x82653))+P106(f333(f333(f247(x82651),f333(f333(f256(x82651),x82652),x82653)),f333(f333(f256(x82651),x82652),x82654))) % 173.51/173.28 [8266]~P119(x82661)+~P106(f333(f333(f246(x82661),f2(x82661)),x82662))+~P106(f333(f333(f247(a910),f2(a910)),x82663))+~P106(f333(f333(f247(x82661),x82662),x82664))+P106(f333(f333(f247(x82661),f333(f333(f256(x82661),x82662),x82663)),f333(f333(f256(x82661),x82664),x82663))) % 173.51/173.28 [8285]~P110(x82851)+~P16(x82851,f333(f176(x82851),x82852))+~P106(f333(f333(f246(a910),x82854),x82853))+P106(f333(f333(f246(x82851),f333(f333(f172(x82851),x82852),x82853)),f333(f333(f172(x82851),x82852),x82854)))+~P106(f333(f333(f247(a910),x82853),f333(f197(f911(x82851)),x82852))) % 173.51/173.28 [8534]~P69(x85341)+~P106(f333(f333(f246(x85341),x85342),f2(x85341)))+~P106(f333(f333(f246(x85341),x85343),x85344))+~P106(f333(f333(f247(x85341),f2(x85341)),f333(f333(f88(x85341),x85343),x85344)))+P106(f333(f333(f246(x85341),f333(f333(f296(x85341),x85342),x85343)),f333(f333(f296(x85341),x85342),x85344))) % 173.51/173.28 [8535]~P70(x85351)+~P106(f333(f333(f247(x85351),x85352),f2(x85351)))+~P106(f333(f333(f247(x85351),x85353),x85354))+~P106(f333(f333(f247(x85351),f2(x85351)),f333(f333(f88(x85351),x85353),x85354)))+P106(f333(f333(f247(x85351),f333(f333(f296(x85351),x85352),x85353)),f333(f333(f296(x85351),x85352),x85354))) % 173.51/173.28 [8544]~P70(x85441)+~P106(f333(f333(f246(x85441),x85444),x85443))+~P106(f333(f333(f246(x85441),f2(x85441)),x85442))+~P106(f333(f333(f247(x85441),f2(x85441)),f333(f333(f88(x85441),x85443),x85444)))+P106(f333(f333(f246(x85441),f333(f333(f296(x85441),x85442),x85443)),f333(f333(f296(x85441),x85442),x85444))) % 173.51/173.28 [8545]~P70(x85451)+~P106(f333(f333(f247(x85451),x85454),x85453))+~P106(f333(f333(f247(x85451),f2(x85451)),x85452))+~P106(f333(f333(f247(x85451),f2(x85451)),f333(f333(f88(x85451),x85453),x85454)))+P106(f333(f333(f247(x85451),f333(f333(f296(x85451),x85452),x85453)),f333(f333(f296(x85451),x85452),x85454))) % 173.51/173.28 [8655]P106(f333(x86551,x86552))+~P106(f333(f67(x86554),x86552))+P106(f333(x86551,f900(x86551,x86553,x86552,x86554)))+~P106(f333(x86551,f196(f917(x86554,a905))))+~P106(f333(f333(f246(f917(x86554,a905)),x86552),x86553)) % 173.51/173.28 [8664]P106(f333(x86641,x86642))+P106(f333(f67(x86643),f900(x86641,x86644,x86642,x86643)))+~P106(f333(f67(x86643),x86642))+~P106(f333(x86641,f196(f917(x86643,a905))))+~P106(f333(f333(f246(f917(x86643,a905)),x86642),x86644)) % 173.51/173.28 [8931]E(f333(f333(f87(a1),f414(x89311,x89312,x89313,x89314)),f415(x89311,x89312,x89313,x89314)),x89314)+~P106(f333(f333(f247(a1),f2(a1)),x89313))+~P106(f333(f333(f247(a1),x89312),x89314))+~P106(f333(f333(f335(a1),x89312),x89311))+P106(f333(f333(f247(a1),x89312),f333(f333(f23(a1),x89314),x89313))) % 173.51/173.28 [9162]~P106(f333(f333(f247(a1),f2(a1)),x91623))+~P106(f333(f333(f247(a1),x91622),x91624))+~P106(f333(f333(f335(a1),x91622),x91621))+P106(f333(f333(f335(a1),f414(x91621,x91622,x91623,x91624)),x91621))+P106(f333(f333(f247(a1),x91622),f333(f333(f23(a1),x91624),x91623))) % 173.51/173.28 [9175]P106(f333(x91751,x91752))+~P106(f333(f67(x91753),x91752))+P106(f333(f333(f335(x91753),f901(x91751,x91754,x91752,x91753)),x91754))+~P106(f333(x91751,f196(f917(x91753,a905))))+~P106(f333(f333(f246(f917(x91753,a905)),x91752),x91754)) % 173.51/173.28 [9192]E(f333(f333(f87(a1),f396(x91921,x91922,x91923,x91924)),f397(x91921,x91922,x91923,x91924)),x91924)+~P106(f333(f333(f247(a1),f2(a1)),x91923))+~P106(f333(f333(f246(a1),x91922),x91924))+P106(f333(f333(f246(a1),x91922),f333(f333(f23(a1),x91924),x91923)))+~P106(f333(f333(f335(a1),f333(f333(f23(a1),x91922),f85(a1))),x91921)) % 173.51/173.28 [9247]~P106(f333(f333(f247(a1),f2(a1)),x92473))+~P106(f333(f333(f247(a1),x92471),x92472))+~P106(f333(f333(f335(a1),x92471),x92474))+P106(f333(f333(f335(a1),f415(x92474,x92471,x92473,x92472)),f309(a1,f85(a1),x92473)))+P106(f333(f333(f247(a1),x92471),f333(f333(f23(a1),x92472),x92473))) % 173.51/173.28 [9273]~P72(x92732)+~E(f827(x92733,x92734,x92731,x92732),f828(x92733,x92734,x92731,x92732))+~P106(f333(f67(x92731),f829(x92733,x92734,x92731,x92732)))+E(f333(f333(f6(f917(x92731,a905),x92732),f333(f6(x92731,x92732),x92733)),x92734),f333(f333(f6(x92731,x92732),x92733),f43(f917(x92731,a905),x92734)))+~P106(f333(f67(f917(x92731,a905)),x92734)) % 173.51/173.28 [9277]~P72(x92772)+~E(f333(x92773,f830(x92773,x92774,x92771,x92772)),f2(x92772))+~P106(f333(f67(x92771),f829(x92773,x92774,x92771,x92772)))+E(f333(f333(f6(f917(x92771,a905),x92772),f333(f6(x92771,x92772),x92773)),x92774),f333(f333(f6(x92771,x92772),x92773),f43(f917(x92771,a905),x92774)))+~P106(f333(f67(f917(x92771,a905)),x92774)) % 173.51/173.28 [9341]~P106(f333(f333(f247(a1),f2(a1)),x93413))+~P106(f333(f333(f246(a1),x93412),x93414))+P106(f333(f333(f335(a1),f396(x93411,x93412,x93413,x93414)),x93411))+P106(f333(f333(f246(a1),x93412),f333(f333(f23(a1),x93414),x93413)))+~P106(f333(f333(f335(a1),f333(f333(f23(a1),x93412),f85(a1))),x93411)) % 173.51/173.28 [9382]~P106(f333(f333(f247(a1),f2(a1)),x93823))+~P106(f333(f333(f246(a1),x93821),x93822))+P106(f333(f333(f335(a1),f397(x93824,x93821,x93823,x93822)),f309(a1,f85(a1),x93823)))+P106(f333(f333(f246(a1),x93821),f333(f333(f23(a1),x93822),x93823)))+~P106(f333(f333(f335(a1),f333(f333(f23(a1),x93821),f85(a1))),x93824)) % 173.51/173.28 [9409]~P72(x94092)+~E(f827(x94093,x94094,x94091,x94092),f828(x94093,x94094,x94091,x94092))+E(f333(f333(f6(f917(x94091,a905),x94092),f333(f6(x94091,x94092),x94093)),x94094),f333(f333(f6(x94091,x94092),x94093),f43(f917(x94091,a905),x94094)))+P106(f333(f333(f335(f917(x94091,a905)),f829(x94093,x94094,x94091,x94092)),x94094))+~P106(f333(f67(f917(x94091,a905)),x94094)) % 173.51/173.28 [9414]~P72(x94142)+~E(f333(x94143,f830(x94143,x94144,x94141,x94142)),f2(x94142))+E(f333(f333(f6(f917(x94141,a905),x94142),f333(f6(x94141,x94142),x94143)),x94144),f333(f333(f6(x94141,x94142),x94143),f43(f917(x94141,a905),x94144)))+P106(f333(f333(f335(f917(x94141,a905)),f829(x94143,x94144,x94141,x94142)),x94144))+~P106(f333(f67(f917(x94141,a905)),x94144)) % 173.51/173.28 [9519]~P72(x95192)+~P106(f333(f67(x95191),f829(x95193,x95194,x95191,x95192)))+E(f333(f333(f6(f917(x95191,a905),x95192),f333(f6(x95191,x95192),x95193)),x95194),f333(f333(f6(x95191,x95192),x95193),f43(f917(x95191,a905),x95194)))+P106(f333(f333(f335(f917(x95191,a905)),f828(x95193,x95194,x95191,x95192)),x95194))+~P106(f333(f67(f917(x95191,a905)),x95194)) % 173.51/173.28 [9520]~P72(x95202)+~P106(f333(f67(x95201),f829(x95203,x95204,x95201,x95202)))+E(f333(f333(f6(f917(x95201,a905),x95202),f333(f6(x95201,x95202),x95203)),x95204),f333(f333(f6(x95201,x95202),x95203),f43(f917(x95201,a905),x95204)))+P106(f333(f333(f335(f917(x95201,a905)),f827(x95203,x95204,x95201,x95202)),x95204))+~P106(f333(f67(f917(x95201,a905)),x95204)) % 173.51/173.28 [9598]~P72(x95982)+E(f333(f333(f6(f917(x95981,a905),x95982),f333(f6(x95981,x95982),x95983)),x95984),f333(f333(f6(x95981,x95982),x95983),f43(f917(x95981,a905),x95984)))+P106(f333(f333(f335(f917(x95981,a905)),f829(x95983,x95984,x95981,x95982)),x95984))+P106(f333(f333(f335(f917(x95981,a905)),f828(x95983,x95984,x95981,x95982)),x95984))+~P106(f333(f67(f917(x95981,a905)),x95984)) % 173.51/173.28 [9599]~P72(x95992)+E(f333(f333(f6(f917(x95991,a905),x95992),f333(f6(x95991,x95992),x95993)),x95994),f333(f333(f6(x95991,x95992),x95993),f43(f917(x95991,a905),x95994)))+P106(f333(f333(f335(f917(x95991,a905)),f829(x95993,x95994,x95991,x95992)),x95994))+P106(f333(f333(f335(f917(x95991,a905)),f827(x95993,x95994,x95991,x95992)),x95994))+~P106(f333(f67(f917(x95991,a905)),x95994)) % 173.51/173.28 [9616]~P72(x96162)+P106(f333(f333(f335(x96161),f830(x96163,x96164,x96161,x96162)),f828(x96163,x96164,x96161,x96162)))+~P106(f333(f67(x96161),f829(x96163,x96164,x96161,x96162)))+E(f333(f333(f6(f917(x96161,a905),x96162),f333(f6(x96161,x96162),x96163)),x96164),f333(f333(f6(x96161,x96162),x96163),f43(f917(x96161,a905),x96164)))+~P106(f333(f67(f917(x96161,a905)),x96164)) % 173.51/173.28 [9617]~P72(x96172)+P106(f333(f333(f335(x96171),f830(x96173,x96174,x96171,x96172)),f827(x96173,x96174,x96171,x96172)))+~P106(f333(f67(x96171),f829(x96173,x96174,x96171,x96172)))+E(f333(f333(f6(f917(x96171,a905),x96172),f333(f6(x96171,x96172),x96173)),x96174),f333(f333(f6(x96171,x96172),x96173),f43(f917(x96171,a905),x96174)))+~P106(f333(f67(f917(x96171,a905)),x96174)) % 173.51/173.28 [9630]P106(f333(x96301,x96302))+~P106(f333(f333(f335(x96303),f901(x96301,x96304,x96302,x96303)),f900(x96301,x96304,x96302,x96303)))+~P106(f333(f67(x96303),x96302))+~P106(f333(x96301,f196(f917(x96303,a905))))+~P106(f333(f333(f246(f917(x96303,a905)),x96302),x96304)) % 173.51/173.28 [9670]~P72(x96702)+P106(f333(f333(f335(x96701),f830(x96703,x96704,x96701,x96702)),f828(x96703,x96704,x96701,x96702)))+E(f333(f333(f6(f917(x96701,a905),x96702),f333(f6(x96701,x96702),x96703)),x96704),f333(f333(f6(x96701,x96702),x96703),f43(f917(x96701,a905),x96704)))+P106(f333(f333(f335(f917(x96701,a905)),f829(x96703,x96704,x96701,x96702)),x96704))+~P106(f333(f67(f917(x96701,a905)),x96704)) % 173.51/173.28 [9671]~P72(x96712)+P106(f333(f333(f335(x96711),f830(x96713,x96714,x96711,x96712)),f827(x96713,x96714,x96711,x96712)))+E(f333(f333(f6(f917(x96711,a905),x96712),f333(f6(x96711,x96712),x96713)),x96714),f333(f333(f6(x96711,x96712),x96713),f43(f917(x96711,a905),x96714)))+P106(f333(f333(f335(f917(x96711,a905)),f829(x96713,x96714,x96711,x96712)),x96714))+~P106(f333(f67(f917(x96711,a905)),x96714)) % 173.51/173.28 [9856]P106(f333(x98561,x98562))+~P106(f333(f67(x98563),x98562))+~P106(f333(x98561,f333(f333(f315(x98563),f901(x98561,x98564,x98562,x98563)),f900(x98561,x98564,x98562,x98563))))+~P106(f333(x98561,f196(f917(x98563,a905))))+~P106(f333(f333(f246(f917(x98563,a905)),x98562),x98564)) % 173.51/173.28 [7832]~P69(x78321)+P106(f333(f333(f247(x78321),x78322),f2(x78321)))+~P106(f333(f333(f246(x78321),f2(x78321)),x78324))+P106(f333(f333(f247(x78321),f2(x78321)),x78322))+P106(f333(f333(f246(x78321),f333(f333(f296(x78321),x78323),x78322)),x78324)) % 173.51/173.28 [7833]~P69(x78331)+P106(f333(f333(f247(x78331),x78332),f2(x78331)))+P106(f333(f333(f247(x78331),f2(x78331)),x78332))+~P106(f333(f333(f247(x78331),f2(x78331)),x78334))+P106(f333(f333(f247(x78331),f333(f333(f296(x78331),x78333),x78332)),x78334)) % 173.51/173.28 [8118]~P106(f333(f333(f246(a1),x81184),f2(a1)))+~E(x81182,f333(f333(f87(a1),f333(f333(f88(a1),x81181),x81183)),x81184))+P106(f333(f333(f247(a1),f2(a1)),x81181))+~P106(f333(f333(f247(a1),x81181),x81184))+P106(f333(f55(x81182,x81181),f333(f333(f265(a1,a1),x81183),x81184))) % 173.51/173.28 [8155]~P106(f333(x81551,x81554))+P106(f333(x81551,f444(x81552,x81551,x81553)))+~P106(f333(f333(f246(a1),f2(a1)),x81552))+~P106(f333(f333(f247(a1),f2(a1)),x81553))+P106(f333(x81551,f333(f333(f23(a1),x81554),f333(f333(f88(a1),x81552),x81553)))) % 173.51/173.28 [8156]~P106(f333(x81561,x81564))+P106(f333(x81561,f452(x81562,x81561,x81563)))+~P106(f333(f333(f246(a1),f2(a1)),x81562))+~P106(f333(f333(f247(a1),f2(a1)),x81563))+P106(f333(x81561,f333(f333(f87(a1),x81564),f333(f333(f88(a1),x81562),x81563)))) % 173.51/173.28 [8157]~P69(x81571)+P106(f333(f333(f247(x81571),x81572),f2(x81571)))+P106(f333(f333(f247(x81571),f2(x81571)),x81572))+P106(f333(f333(f246(x81571),f2(x81571)),x81573))+~P106(f333(f333(f246(x81571),f333(f333(f296(x81571),x81574),x81572)),x81573)) % 173.51/173.28 [8158]~P69(x81581)+P106(f333(f333(f247(x81581),x81582),f2(x81581)))+P106(f333(f333(f247(x81581),f2(x81581)),x81582))+P106(f333(f333(f247(x81581),f2(x81581)),x81583))+~P106(f333(f333(f247(x81581),f333(f333(f296(x81581),x81584),x81582)),x81583)) % 173.51/173.28 [8209]~E(x82091,f333(f333(f87(a1),f333(f333(f88(a1),x82092),x82093)),x82094))+~P106(f333(f333(f246(a1),f2(a1)),x82094))+~P106(f333(f333(f247(a1),f2(a1)),x82092))+~P106(f333(f333(f247(a1),x82094),x82092))+P106(f333(f55(x82091,x82092),f333(f333(f265(a1,a1),x82093),x82094))) % 173.51/173.28 [8324]~P69(x83241)+P106(f333(f333(f247(x83241),x83242),f2(x83241)))+~P106(f333(f333(f246(x83241),f2(x83241)),x83244))+~P106(f333(f333(f246(x83241),x83243),f333(f333(f88(x83241),x83244),x83242)))+P106(f333(f333(f246(x83241),f333(f333(f296(x83241),x83243),x83242)),x83244)) % 173.51/173.28 [8325]~P69(x83251)+P106(f333(f333(f247(x83251),x83252),f2(x83251)))+~P106(f333(f333(f247(x83251),f2(x83251)),x83254))+~P106(f333(f333(f247(x83251),x83253),f333(f333(f88(x83251),x83254),x83252)))+P106(f333(f333(f247(x83251),f333(f333(f296(x83251),x83253),x83252)),x83254)) % 173.51/173.28 [8412]~P69(x84121)+P106(f333(f333(f247(x84121),x84122),f2(x84121)))+~P106(f333(f333(f246(x84121),x84123),f2(x84121)))+P106(f333(f333(f246(x84121),x84123),f333(f333(f296(x84121),x84124),x84122)))+~P106(f333(f333(f246(x84121),f333(f333(f88(x84121),x84123),x84122)),x84124)) % 173.51/173.28 [8413]~P69(x84131)+P106(f333(f333(f247(x84131),x84132),f2(x84131)))+~P106(f333(f333(f247(x84131),x84133),f2(x84131)))+P106(f333(f333(f247(x84131),x84133),f333(f333(f296(x84131),x84134),x84132)))+~P106(f333(f333(f247(x84131),f333(f333(f88(x84131),x84133),x84132)),x84134)) % 173.51/173.28 [8571]~P69(x85711)+~P106(f333(f333(f247(x85711),x85712),f2(x85711)))+P106(f333(f333(f247(x85711),f2(x85711)),x85712))+~P106(f333(f333(f246(x85711),f333(f333(f296(x85711),x85714),x85712)),x85713))+P106(f333(f333(f246(x85711),f333(f333(f88(x85711),x85713),x85712)),x85714)) % 173.51/173.28 [8572]~P69(x85721)+~P106(f333(f333(f247(x85721),x85722),f2(x85721)))+P106(f333(f333(f247(x85721),f2(x85721)),x85722))+~P106(f333(f333(f246(x85721),f333(f333(f88(x85721),x85724),x85722)),x85723))+P106(f333(f333(f246(x85721),f333(f333(f296(x85721),x85723),x85722)),x85724)) % 173.51/173.28 [8573]~P69(x85731)+~P106(f333(f333(f247(x85731),x85732),f2(x85731)))+P106(f333(f333(f247(x85731),f2(x85731)),x85732))+~P106(f333(f333(f247(x85731),f333(f333(f296(x85731),x85734),x85732)),x85733))+P106(f333(f333(f247(x85731),f333(f333(f88(x85731),x85733),x85732)),x85734)) % 173.51/173.28 [8574]~P69(x85741)+~P106(f333(f333(f247(x85741),x85742),f2(x85741)))+P106(f333(f333(f247(x85741),f2(x85741)),x85742))+~P106(f333(f333(f247(x85741),f333(f333(f88(x85741),x85744),x85742)),x85743))+P106(f333(f333(f247(x85741),f333(f333(f296(x85741),x85743),x85742)),x85744)) % 173.51/173.28 [8593]~P69(x85931)+~P106(f333(f333(f246(x85931),f2(x85931)),x85934))+P106(f333(f333(f247(x85931),f2(x85931)),x85932))+~P106(f333(f333(f246(x85931),f333(f333(f88(x85931),x85934),x85932)),x85933))+P106(f333(f333(f246(x85931),f333(f333(f296(x85931),x85933),x85932)),x85934)) % 173.51/173.28 [8594]~P69(x85941)+~P106(f333(f333(f247(x85941),f2(x85941)),x85944))+P106(f333(f333(f247(x85941),f2(x85941)),x85942))+~P106(f333(f333(f247(x85941),f333(f333(f88(x85941),x85944),x85942)),x85943))+P106(f333(f333(f247(x85941),f333(f333(f296(x85941),x85943),x85942)),x85944)) % 173.51/173.28 [8672]~P69(x86721)+~P106(f333(f333(f247(x86721),x86724),f2(x86721)))+~P106(f333(f333(f246(x86721),x86723),f333(f333(f88(x86721),x86722),x86724)))+P106(f333(f333(f246(x86721),x86722),f333(f333(f296(x86721),x86723),x86724)))+~P106(f333(f333(f246(x86721),f333(f333(f88(x86721),x86722),x86724)),x86723)) % 173.51/173.29 [8673]~P69(x86731)+~P106(f333(f333(f246(x86731),x86732),f2(x86731)))+~P106(f333(f333(f246(x86731),x86733),f333(f333(f88(x86731),x86732),x86734)))+P106(f333(f333(f246(x86731),x86732),f333(f333(f296(x86731),x86733),x86734)))+~P106(f333(f333(f246(x86731),f333(f333(f88(x86731),x86732),x86734)),x86733)) % 173.51/173.29 [8674]~P69(x86741)+~P106(f333(f333(f247(x86741),x86744),f2(x86741)))+~P106(f333(f333(f247(x86741),x86743),f333(f333(f88(x86741),x86742),x86744)))+P106(f333(f333(f247(x86741),x86742),f333(f333(f296(x86741),x86743),x86744)))+~P106(f333(f333(f247(x86741),f333(f333(f88(x86741),x86742),x86744)),x86743)) % 173.51/173.29 [8675]~P69(x86751)+~P106(f333(f333(f247(x86751),x86752),f2(x86751)))+~P106(f333(f333(f247(x86751),x86753),f333(f333(f88(x86751),x86752),x86754)))+P106(f333(f333(f247(x86751),x86752),f333(f333(f296(x86751),x86753),x86754)))+~P106(f333(f333(f247(x86751),f333(f333(f88(x86751),x86752),x86754)),x86753)) % 173.51/173.29 [8797]~P69(x87971)+~P106(f333(f333(f247(x87971),x87973),f2(x87971)))+~P106(f333(f333(f246(x87971),x87972),f333(f333(f88(x87971),x87974),x87973)))+~P106(f333(f333(f246(x87971),f333(f333(f88(x87971),x87974),x87973)),x87972))+P106(f333(f333(f246(x87971),f333(f333(f296(x87971),x87972),x87973)),x87974)) % 173.51/173.29 [8798]~P69(x87981)+~P106(f333(f333(f247(x87981),x87983),f2(x87981)))+~P106(f333(f333(f247(x87981),x87982),f333(f333(f88(x87981),x87984),x87983)))+~P106(f333(f333(f247(x87981),f333(f333(f88(x87981),x87984),x87983)),x87982))+P106(f333(f333(f247(x87981),f333(f333(f296(x87981),x87982),x87983)),x87984)) % 173.51/173.29 [8815]~P69(x88151)+~P106(f333(f333(f246(x88151),f2(x88151)),x88154))+~P106(f333(f333(f246(x88151),x88152),f333(f333(f88(x88151),x88154),x88153)))+~P106(f333(f333(f246(x88151),f333(f333(f88(x88151),x88154),x88153)),x88152))+P106(f333(f333(f246(x88151),f333(f333(f296(x88151),x88152),x88153)),x88154)) % 173.51/173.29 [8816]~P69(x88161)+~P106(f333(f333(f247(x88161),f2(x88161)),x88164))+~P106(f333(f333(f247(x88161),x88162),f333(f333(f88(x88161),x88164),x88163)))+~P106(f333(f333(f247(x88161),f333(f333(f88(x88161),x88164),x88163)),x88162))+P106(f333(f333(f247(x88161),f333(f333(f296(x88161),x88162),x88163)),x88164)) % 173.51/173.29 [8998]E(f333(f333(f23(a1),f408(x89981,x89982,x89983,x89984)),f409(x89981,x89982,x89983,x89984)),x89984)+~P106(f333(f333(f247(a1),f2(a1)),x89983))+~P106(f333(f333(f335(a1),x89982),x89981))+~P106(f333(f333(f247(a1),x89984),x89982))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x89984),x89983)),x89982)) % 173.51/173.29 [9077]~P106(f333(x90771,x90772))+~P106(f333(f333(f246(a1),f2(a1)),x90773))+~P106(f333(f333(f247(a1),f2(a1)),x90774))+~P106(f333(x90771,f333(f333(f23(a1),f444(x90773,x90771,x90774)),x90774)))+P106(f333(x90771,f333(f333(f23(a1),x90772),f333(f333(f88(a1),x90773),x90774)))) % 173.51/173.29 [9078]~P106(f333(x90781,x90782))+~P106(f333(f333(f246(a1),f2(a1)),x90783))+~P106(f333(f333(f247(a1),f2(a1)),x90784))+~P106(f333(x90781,f333(f333(f87(a1),f452(x90783,x90781,x90784)),x90784)))+P106(f333(x90781,f333(f333(f87(a1),x90782),f333(f333(f88(a1),x90783),x90784)))) % 173.51/173.29 [9240]~P106(f333(f333(f247(a1),f2(a1)),x92403))+~P106(f333(f333(f335(a1),x92402),x92401))+~P106(f333(f333(f247(a1),x92404),x92402))+P106(f333(f333(f335(a1),f408(x92401,x92402,x92403,x92404)),x92401))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x92404),x92403)),x92402)) % 173.51/173.29 [9260]E(f333(f333(f23(a1),f398(x92601,x92602,x92603,x92604)),f399(x92601,x92602,x92603,x92604)),x92604)+~P106(f333(f333(f247(a1),f2(a1)),x92603))+~P106(f333(f333(f246(a1),x92604),x92602))+~P106(f333(f333(f335(a1),f333(f333(f87(a1),x92602),f85(a1))),x92601))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x92604),x92603)),x92602)) % 173.51/173.29 [9289]~P106(f333(f333(f247(a1),f2(a1)),x92892))+~P106(f333(f333(f335(a1),x92893),x92894))+~P106(f333(f333(f247(a1),x92891),x92893))+P106(f333(f333(f335(a1),f409(x92894,x92893,x92892,x92891)),f309(a1,f85(a1),x92892)))+P106(f333(f333(f247(a1),f333(f333(f87(a1),x92891),x92892)),x92893)) % 173.51/173.29 [9376]~P106(f333(f333(f247(a1),f2(a1)),x93763))+~P106(f333(f333(f246(a1),x93764),x93762))+P106(f333(f333(f335(a1),f398(x93761,x93762,x93763,x93764)),x93761))+~P106(f333(f333(f335(a1),f333(f333(f87(a1),x93762),f85(a1))),x93761))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x93764),x93763)),x93762)) % 173.51/173.29 [9424]~P106(f333(f333(f247(a1),f2(a1)),x94242))+~P106(f333(f333(f246(a1),x94241),x94243))+P106(f333(f333(f335(a1),f399(x94244,x94243,x94242,x94241)),f309(a1,f85(a1),x94242)))+~P106(f333(f333(f335(a1),f333(f333(f87(a1),x94243),f85(a1))),x94244))+P106(f333(f333(f246(a1),f333(f333(f87(a1),x94241),x94242)),x94243)) % 173.51/173.29 [9732]~P40(x97321,x97323)+~P29(x97321,x97324)+P40(x97321,f333(f333(f121(f917(f916(x97321,x97321),a905)),x97322),x97323))+~P106(f333(f333(f246(f917(f916(x97321,x97321),a905)),x97322),f333(f264(f917(f916(x97321,x97321),a905),f917(f916(x97321,x97321),a905)),x97324)))+~P106(f333(f333(f246(f917(f916(x97321,x97321),a905)),x97323),f333(f268(f917(f916(x97321,x97321),a905),f917(f916(x97321,x97321),a905)),x97324))) % 173.51/173.29 [10119]~P20(x101192,x101194,x101193)+E(x101191,f196(f917(x101192,a905)))+~P106(f333(f67(x101192),x101191))+P106(f333(f333(f335(x101192),f333(x101193,x101191)),x101191))+~P106(f333(f333(f335(x101192),f333(f333(x101194,f892(x101191,x101193,x101194,x101192)),f893(x101191,x101193,x101194,x101192))),f333(f333(f315(x101192),f892(x101191,x101193,x101194,x101192)),f333(f333(f315(x101192),f893(x101191,x101193,x101194,x101192)),f196(f917(x101192,a905)))))) % 173.51/173.29 [10050]~P112(x100502)+~P7(x100501)+~P106(f333(f333(f246(f917(x100501,x100502)),x100503),x100504))+P106(f333(f333(f247(f917(x100501,x100502)),x100503),x100504))+~P106(f333(f62(x100501),f333(f333(f8(a905,a905,x100501),a328),f333(f333(f18(x100501,x100502,a905),f333(f333(f8(x100502,f917(x100502,a905),x100501),a330),x100503)),x100504)))) % 173.51/173.29 [9637]~P58(x96371,x96371,x96374)+P106(f333(f333(f335(f916(x96371,x96371)),f333(f333(f265(x96371,x96371),x96372),x96373)),f313(x96371,x96374)))+P106(f333(f333(f335(f916(x96371,x96371)),f333(f333(f265(x96371,x96371),x96373),x96372)),f313(x96371,x96374)))+~P106(f333(f333(f335(f916(x96371,x96371)),f333(f333(f265(x96371,x96371),x96375),x96372)),f313(x96371,x96374)))+~P106(f333(f333(f335(f916(x96371,x96371)),f333(f333(f265(x96371,x96371),x96375),x96373)),f313(x96371,x96374))) % 173.51/173.29 [5757]E(x57571,f2(a910))+~E(f333(f41(x57572),x57575),x57571)+E(f333(f41(x57572),x57573),f333(a123,x57571))+~E(x57573,f333(f333(f315(x57572),x57574),x57575))+P106(f333(f333(f335(x57572),x57574),x57575)) % 173.51/173.29 [5879]~P68(x58792)+E(x58791,f2(x58792))+E(x58793,f2(x58792))+~E(f333(f333(f296(x58792),x58794),x58793),f333(f333(f296(x58792),x58795),x58791))+E(f333(f333(f88(x58792),x58794),x58791),f333(f333(f88(x58792),x58795),x58793)) % 173.51/173.29 [5880]~P68(x58802)+E(x58801,f2(x58802))+E(x58803,f2(x58802))+~E(f333(f333(f88(x58802),x58804),x58803),f333(f333(f88(x58802),x58805),x58801))+E(f333(f333(f296(x58802),x58804),x58801),f333(f333(f296(x58802),x58805),x58803)) % 173.51/173.29 [5947]~E(f333(f41(x59471),x59475),x59473)+~E(x59475,f196(f917(x59471,a905)))+E(f333(f41(x59471),x59472),f333(a123,x59473))+~E(x59472,f333(f333(f315(x59471),x59474),x59475))+P106(f333(f333(f335(x59471),x59474),x59475)) % 173.51/173.29 [6176]~P117(x61762)+~E(f333(x61763,x61765),f2(x61762))+E(f333(f333(f9(x61761,x61762),x61763),x61764),f2(x61762))+~P106(f333(f67(x61761),x61764))+~P106(f333(f333(f335(x61761),x61765),x61764)) % 173.51/173.29 [6543]~P110(x65433)+E(x65431,x65432)+~E(f333(f308(x65433,x65434),x65431),f333(f308(x65433,x65435),x65432))+~P106(f333(f333(f247(x65433),x65435),x65432))+~P106(f333(f333(f247(x65433),x65434),x65431)) % 173.51/173.29 [6544]~P110(x65443)+E(x65441,x65442)+~E(f333(f308(x65443,x65441),x65444),f333(f308(x65443,x65442),x65445))+~P106(f333(f333(f247(x65443),x65442),x65445))+~P106(f333(f333(f247(x65443),x65441),x65444)) % 173.51/173.29 [7598]~P110(x75981)+~P16(x75981,f333(f333(f142(x75981),x75984),x75985))+~P106(f333(f333(f335(x75981),x75983),f333(f180(x75981),x75985)))+~P106(f333(f333(f335(x75981),x75982),f333(f180(x75981),x75984)))+P106(f333(f333(f246(x75981),x75982),x75983)) % 173.51/173.29 [8708]~P112(x87081)+~P106(f333(f333(f247(f917(x87081,a905)),f309(x87081,x87085,x87082)),f309(x87081,x87084,x87083)))+~P106(f333(f333(f246(x87081),x87085),x87082))+P106(f333(f333(f247(x87081),x87082),x87083))+P106(f333(f333(f247(x87081),x87084),x87085)) % 173.51/173.29 [10162]~P19(x101622,x101625,x101623)+E(x101621,f196(f917(x101622,a905)))+~E(f333(f333(x101625,f333(x101624,f903(x101621,x101624,x101623,x101625,x101622))),f333(x101624,f342(x101621,x101624,x101623,x101625,x101622))),f333(x101624,f333(f333(x101625,f903(x101621,x101624,x101623,x101625,x101622)),f342(x101621,x101624,x101623,x101625,x101622))))+E(f333(x101623,f333(f316(x101622,x101622,x101624),x101621)),f333(x101624,f333(x101623,x101621)))+~P106(f333(f67(x101622),x101621)) % 173.51/173.29 [6540]~P20(x65402,x65405,x65403)+E(x65401,f196(f917(x65402,a905)))+~P106(f333(f67(x65402),x65401))+E(f333(x65403,f333(f333(f315(x65402),x65404),x65401)),f333(f333(x65405,x65404),f333(x65403,x65401)))+P106(f333(f333(f335(x65402),x65404),x65401)) % 173.51/173.29 [7360]~P19(x73602,x73603,x73604)+E(f333(f333(x73603,f333(x73604,x73601)),f333(x73604,x73605)),f333(x73604,x73605))+E(x73601,f196(f917(x73602,a905)))+~P106(f333(f67(x73602),x73605))+~P106(f333(f333(f246(f917(x73602,a905)),x73601),x73605)) % 173.51/173.29 [7730]~P20(x77304,x77305,x77301)+E(f333(x77301,x77302),x77303)+~P106(f333(f67(x77304),x77302))+~E(f333(f333(f23(f917(x77304,a905)),x77302),f333(f333(f315(x77304),x77303),f196(f917(x77304,a905)))),f196(f917(x77304,a905)))+~P106(f333(f333(f335(x77304),x77303),x77302)) % 173.51/173.29 [8679]E(x86791,x86792)+~P11(x86793,x86794,x86795)+E(f333(f333(f112(f917(x86793,a905)),x86791),x86792),f196(f917(x86793,a905)))+~P106(f333(f333(f335(f917(x86793,a905)),x86792),f333(f333(f66(x86793),x86794),x86795)))+~P106(f333(f333(f335(f917(x86793,a905)),x86791),f333(f333(f66(x86793),x86794),x86795))) % 173.51/173.29 [9512]~P72(x95122)+~E(f333(x95123,f374(x95123,x95124,x95125,x95121,x95122)),f2(x95122))+E(f333(f333(f6(x95121,x95122),x95123),x95124),f333(f333(f6(x95121,x95122),x95123),x95125))+~P106(f333(f67(x95121),x95125))+~P106(f333(f333(f246(f917(x95121,a905)),x95124),x95125)) % 173.51/173.29 [9513]~P72(x95132)+~E(f333(x95133,f375(x95133,x95134,x95135,x95131,x95132)),f2(x95132))+E(f333(f333(f6(x95131,x95132),x95133),x95134),f333(f333(f6(x95131,x95132),x95133),x95135))+~P106(f333(f67(x95131),x95135))+~P106(f333(f333(f246(f917(x95131,a905)),x95134),x95135)) % 173.51/173.29 [9514]~P78(x95142)+~E(f333(x95143,f506(x95143,x95144,x95145,x95141,x95142)),f85(x95142))+E(f333(f333(f9(x95141,x95142),x95143),x95144),f333(f333(f9(x95141,x95142),x95143),x95145))+~P106(f333(f67(x95141),x95145))+~P106(f333(f333(f246(f917(x95141,a905)),x95144),x95145)) % 173.51/173.29 [9515]~P78(x95152)+~E(f333(x95153,f510(x95153,x95154,x95155,x95151,x95152)),f85(x95152))+E(f333(f333(f9(x95151,x95152),x95153),x95154),f333(f333(f9(x95151,x95152),x95153),x95155))+~P106(f333(f67(x95151),x95155))+~P106(f333(f333(f246(f917(x95151,a905)),x95154),x95155)) % 173.51/173.29 [9998]~P90(x99981)+~P106(f333(f67(x99982),x99985))+~P106(f333(f333(f246(x99981),f2(x99981)),f333(x99983,f359(x99983,x99984,x99985,x99982,x99981))))+P106(f333(f333(f246(x99981),f333(f333(f6(x99982,x99981),x99983),x99984)),f333(f333(f6(x99982,x99981),x99983),x99985)))+~P106(f333(f333(f246(f917(x99982,a905)),x99984),x99985)) % 173.51/173.29 [7595]E(x75951,f2(a910))+P106(f333(x75952,x75953))+~E(x75954,f333(f333(f87(a910),f333(f333(f88(a910),x75951),x75953)),x75955))+~P106(f333(f333(f247(a910),x75955),x75951))+~P106(f333(x75952,f333(f333(f42(a910),x75954),x75951))) % 173.51/173.29 [7670]E(x76701,f2(a910))+P106(f333(x76702,x76703))+~P106(f333(x76702,f51(a910,x76704,x76701)))+~E(x76704,f333(f333(f87(a910),f333(f333(f88(a910),x76701),x76705)),x76703))+~P106(f333(f333(f247(a910),x76703),x76701)) % 173.51/173.29 [7964]~P68(x79643)+E(f333(x79641,x79642),f2(x79643))+~P106(f333(f67(x79644),x79645))+E(f333(f333(f9(x79644,x79643),x79641),f333(f333(f23(f917(x79644,a905)),x79645),f333(f333(f315(x79644),x79642),f196(f917(x79644,a905))))),f333(f333(f9(x79644,x79643),x79641),x79645))+P106(f333(f333(f335(x79644),x79642),x79645)) % 173.51/173.29 [8366]~P72(x83661)+~P106(f333(f67(x83662),x83665))+~P106(f333(f67(x83662),x83664))+~E(f333(f333(f112(f917(x83662,a905)),x83664),x83665),f196(f917(x83662,a905)))+E(f333(f333(f87(x83661),f333(f333(f6(x83662,x83661),x83663),x83664)),f333(f333(f6(x83662,x83661),x83663),x83665)),f333(f333(f6(x83662,x83661),x83663),f333(f333(f121(f917(x83662,a905)),x83664),x83665))) % 173.51/173.29 [8368]~P78(x83681)+~P106(f333(f67(x83682),x83685))+~P106(f333(f67(x83682),x83684))+~E(f333(f333(f112(f917(x83682,a905)),x83684),x83685),f196(f917(x83682,a905)))+E(f333(f333(f88(x83681),f333(f333(f9(x83682,x83681),x83683),x83684)),f333(f333(f9(x83682,x83681),x83683),x83685)),f333(f333(f9(x83682,x83681),x83683),f333(f333(f121(f917(x83682,a905)),x83684),x83685))) % 173.51/173.29 [8467]~P68(x84673)+E(f333(x84671,x84672),f2(x84673))+~P106(f333(f67(x84674),x84675))+E(f333(f333(f9(x84674,x84673),x84671),f333(f333(f23(f917(x84674,a905)),x84675),f333(f333(f315(x84674),x84672),f196(f917(x84674,a905))))),f333(f333(f296(x84673),f333(f333(f9(x84674,x84673),x84671),x84675)),f333(x84671,x84672)))+~P106(f333(f333(f335(x84674),x84672),x84675)) % 173.51/173.29 [9217]~P11(x92171,x92175,x92174)+~E(f333(f333(f66(x92171),f333(f333(f315(x92171),x92172),f196(f917(x92171,a905)))),x92174),f333(f333(f66(x92171),f333(f333(f315(x92171),x92173),f196(f917(x92171,a905)))),x92174))+~P106(f333(f333(f335(x92171),x92173),x92175))+~P106(f333(f333(f335(x92171),x92172),x92175))+P106(f333(f333(f335(f916(x92171,x92171)),f333(f333(f265(x92171,x92171),x92172),x92173)),x92174)) % 173.51/173.29 [9239]~P11(x92391,x92395,x92393)+E(f333(f333(f66(x92391),f333(f333(f315(x92391),x92392),f196(f917(x92391,a905)))),x92393),f333(f333(f66(x92391),f333(f333(f315(x92391),x92394),f196(f917(x92391,a905)))),x92393))+~P106(f333(f333(f335(x92391),x92394),x92395))+~P106(f333(f333(f335(x92391),x92392),x92395))+~P106(f333(f333(f335(f916(x92391,x92391)),f333(f333(f265(x92391,x92391),x92392),x92394)),x92393)) % 173.51/173.29 [9541]~P78(x95411)+~P106(f333(f67(x95412),x95415))+~P106(f333(f67(x95412),x95414))+~E(f333(f333(f112(f917(x95412,a905)),x95414),x95415),f196(f917(x95412,a905)))+E(f333(f333(f88(x95411),f333(f333(f333(f71(x95411,x95412,f88(x95411)),x95413),f85(x95411)),x95414)),f333(f333(f333(f71(x95411,x95412,f88(x95411)),x95413),f85(x95411)),x95415)),f333(f333(f333(f71(x95411,x95412,f88(x95411)),x95413),f85(x95411)),f333(f333(f121(f917(x95412,a905)),x95414),x95415))) % 173.51/173.29 [9550]~P72(x95501)+~E(f333(x95503,f358(x95503,x95505,x95504,x95502,x95501)),f2(x95501))+~P106(f333(f67(x95502),x95504))+~P106(f333(f67(x95502),x95505))+E(f333(f333(f87(x95501),f333(f333(f6(x95502,x95501),x95503),x95504)),f333(f333(f6(x95502,x95501),x95503),x95505)),f333(f333(f6(x95502,x95501),x95503),f333(f333(f121(f917(x95502,a905)),x95504),x95505))) % 173.51/173.29 [9551]~P72(x95511)+~E(f333(x95513,f360(x95513,x95515,x95514,x95512,x95511)),f2(x95511))+~P106(f333(f67(x95512),x95514))+~P106(f333(f67(x95512),x95515))+E(f333(f333(f87(x95511),f333(f333(f6(x95512,x95511),x95513),x95514)),f333(f333(f6(x95512,x95511),x95513),x95515)),f333(f333(f6(x95512,x95511),x95513),f333(f333(f121(f917(x95512,a905)),x95514),x95515))) % 173.51/173.29 [9552]~P78(x95521)+~E(f333(x95523,f504(x95523,x95525,x95524,x95522,x95521)),f85(x95521))+~P106(f333(f67(x95522),x95524))+~P106(f333(f67(x95522),x95525))+E(f333(f333(f88(x95521),f333(f333(f9(x95522,x95521),x95523),x95524)),f333(f333(f9(x95522,x95521),x95523),x95525)),f333(f333(f9(x95522,x95521),x95523),f333(f333(f121(f917(x95522,a905)),x95524),x95525))) % 173.51/173.29 [9553]~P78(x95531)+~E(f333(x95533,f505(x95533,x95535,x95534,x95532,x95531)),f85(x95531))+~P106(f333(f67(x95532),x95534))+~P106(f333(f67(x95532),x95535))+E(f333(f333(f88(x95531),f333(f333(f9(x95532,x95531),x95533),x95534)),f333(f333(f9(x95532,x95531),x95533),x95535)),f333(f333(f9(x95532,x95531),x95533),f333(f333(f121(f917(x95532,a905)),x95534),x95535))) % 173.51/173.29 [9777]~P78(x97771)+~E(f333(x97773,f377(x97773,x97775,x97774,x97772,x97771)),f85(x97771))+~P106(f333(f67(x97772),x97774))+~P106(f333(f67(x97772),x97775))+E(f333(f333(f88(x97771),f333(f333(f333(f71(x97771,x97772,f88(x97771)),x97773),f85(x97771)),x97774)),f333(f333(f333(f71(x97771,x97772,f88(x97771)),x97773),f85(x97771)),x97775)),f333(f333(f333(f71(x97771,x97772,f88(x97771)),x97773),f85(x97771)),f333(f333(f121(f917(x97772,a905)),x97774),x97775))) % 173.51/173.29 [9886]~P72(x98862)+E(f333(f333(f6(x98861,x98862),x98863),x98864),f333(f333(f6(x98861,x98862),x98863),x98865))+~P106(f333(f67(x98861),x98865))+~P106(f333(f333(f246(f917(x98861,a905)),x98864),x98865))+P106(f333(f333(f335(x98861),f374(x98863,x98864,x98865,x98861,x98862)),f333(f333(f23(f917(x98861,a905)),x98865),x98864))) % 173.51/173.29 [9887]~P72(x98872)+E(f333(f333(f6(x98871,x98872),x98873),x98874),f333(f333(f6(x98871,x98872),x98873),x98875))+~P106(f333(f67(x98871),x98875))+~P106(f333(f333(f246(f917(x98871,a905)),x98874),x98875))+P106(f333(f333(f335(x98871),f375(x98873,x98874,x98875,x98871,x98872)),f333(f333(f23(f917(x98871,a905)),x98875),x98874))) % 173.51/173.29 [9888]~P78(x98882)+E(f333(f333(f9(x98881,x98882),x98883),x98884),f333(f333(f9(x98881,x98882),x98883),x98885))+~P106(f333(f67(x98881),x98885))+~P106(f333(f333(f246(f917(x98881,a905)),x98884),x98885))+P106(f333(f333(f335(x98881),f506(x98883,x98884,x98885,x98881,x98882)),f333(f333(f23(f917(x98881,a905)),x98885),x98884))) % 173.51/173.29 [9889]~P78(x98892)+E(f333(f333(f9(x98891,x98892),x98893),x98894),f333(f333(f9(x98891,x98892),x98893),x98895))+~P106(f333(f67(x98891),x98895))+~P106(f333(f333(f246(f917(x98891,a905)),x98894),x98895))+P106(f333(f333(f335(x98891),f510(x98893,x98894,x98895,x98891,x98892)),f333(f333(f23(f917(x98891,a905)),x98895),x98894))) % 173.51/173.29 [9908]~P72(x99081)+~P106(f333(f67(x99082),x99084))+~P106(f333(f67(x99082),x99085))+E(f333(f333(f87(x99081),f333(f333(f6(x99082,x99081),x99083),x99084)),f333(f333(f6(x99082,x99081),x99083),x99085)),f333(f333(f6(x99082,x99081),x99083),f333(f333(f121(f917(x99082,a905)),x99084),x99085)))+P106(f333(f333(f335(x99082),f358(x99083,x99085,x99084,x99082,x99081)),f333(f333(f112(f917(x99082,a905)),x99084),x99085))) % 173.51/173.29 [9909]~P72(x99091)+~P106(f333(f67(x99092),x99094))+~P106(f333(f67(x99092),x99095))+E(f333(f333(f87(x99091),f333(f333(f6(x99092,x99091),x99093),x99094)),f333(f333(f6(x99092,x99091),x99093),x99095)),f333(f333(f6(x99092,x99091),x99093),f333(f333(f121(f917(x99092,a905)),x99094),x99095)))+P106(f333(f333(f335(x99092),f360(x99093,x99095,x99094,x99092,x99091)),f333(f333(f112(f917(x99092,a905)),x99094),x99095))) % 173.51/173.29 [9910]~P78(x99101)+~P106(f333(f67(x99102),x99104))+~P106(f333(f67(x99102),x99105))+E(f333(f333(f88(x99101),f333(f333(f9(x99102,x99101),x99103),x99104)),f333(f333(f9(x99102,x99101),x99103),x99105)),f333(f333(f9(x99102,x99101),x99103),f333(f333(f121(f917(x99102,a905)),x99104),x99105)))+P106(f333(f333(f335(x99102),f504(x99103,x99105,x99104,x99102,x99101)),f333(f333(f112(f917(x99102,a905)),x99104),x99105))) % 173.51/173.29 [9911]~P78(x99111)+~P106(f333(f67(x99112),x99114))+~P106(f333(f67(x99112),x99115))+E(f333(f333(f88(x99111),f333(f333(f9(x99112,x99111),x99113),x99114)),f333(f333(f9(x99112,x99111),x99113),x99115)),f333(f333(f9(x99112,x99111),x99113),f333(f333(f121(f917(x99112,a905)),x99114),x99115)))+P106(f333(f333(f335(x99112),f505(x99113,x99115,x99114,x99112,x99111)),f333(f333(f112(f917(x99112,a905)),x99114),x99115))) % 173.51/173.29 [9917]~P90(x99175)+~P106(f333(f67(x99171),x99174))+P106(f333(f333(f246(x99175),f333(f333(f6(x99171,x99175),x99172),x99173)),f333(f333(f6(x99171,x99175),x99172),x99174)))+~P106(f333(f333(f246(f917(x99171,a905)),x99173),x99174))+P106(f333(f333(f335(x99171),f359(x99172,x99173,x99174,x99171,x99175)),f333(f333(f23(f917(x99171,a905)),x99174),x99173))) % 173.51/173.29 [9961]~P78(x99611)+~P106(f333(f67(x99612),x99614))+~P106(f333(f67(x99612),x99615))+E(f333(f333(f88(x99611),f333(f333(f333(f71(x99611,x99612,f88(x99611)),x99613),f85(x99611)),x99614)),f333(f333(f333(f71(x99611,x99612,f88(x99611)),x99613),f85(x99611)),x99615)),f333(f333(f333(f71(x99611,x99612,f88(x99611)),x99613),f85(x99611)),f333(f333(f121(f917(x99612,a905)),x99614),x99615)))+P106(f333(f333(f335(x99612),f377(x99613,x99615,x99614,x99612,x99611)),f333(f333(f112(f917(x99612,a905)),x99614),x99615))) % 173.51/173.29 [8887]~P20(x88871,x88874,x88875)+~P106(f333(f67(x88871),x88872))+E(f333(f333(f23(f917(x88871,a905)),x88872),f333(f333(f315(x88871),x88873),f196(f917(x88871,a905)))),f196(f917(x88871,a905)))+~P106(f333(f333(f335(x88871),x88873),x88872))+E(f333(f333(x88874,x88873),f333(x88875,f333(f333(f23(f917(x88871,a905)),x88872),f333(f333(f315(x88871),x88873),f196(f917(x88871,a905)))))),f333(x88875,x88872)) % 173.51/173.29 [8965]~P20(x89651,x89654,x89655)+~P106(f333(f67(x89651),x89653))+~P106(f333(f67(x89651),x89652))+E(f333(f333(f112(f917(x89651,a905)),x89652),x89653),f196(f917(x89651,a905)))+E(f333(f333(x89654,f333(x89655,f333(f333(f121(f917(x89651,a905)),x89652),x89653))),f333(x89655,f333(f333(f112(f917(x89651,a905)),x89652),x89653))),f333(f333(x89654,f333(x89655,x89652)),f333(x89655,x89653))) % 173.51/173.29 [9555]~P106(f333(f333(f246(a1),x95554),f2(a1)))+~P106(f333(f333(f247(a1),x95553),x95555))+P106(f333(f333(f246(a1),x95551),x95552))+~P106(f333(f333(f247(a1),x95553),x95554))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),f333(f333(f88(a1),x95553),x95552)),x95555)),f333(f333(f87(a1),f333(f333(f88(a1),x95553),x95551)),x95554))) % 173.51/173.29 [9557]~P106(f333(f333(f246(a1),f2(a1)),x95575))+P106(f333(f333(f246(a1),x95571),x95572))+~P106(f333(f333(f247(a1),x95573),x95574))+~P106(f333(f333(f247(a1),x95575),x95574))+~P106(f333(f333(f246(a1),f333(f333(f87(a1),f333(f333(f88(a1),x95574),x95571)),x95575)),f333(f333(f87(a1),f333(f333(f88(a1),x95574),x95572)),x95573))) % 173.51/173.29 [9676]~P68(x96765)+E(f333(x96761,f507(x96761,x96762,x96763,x96764,x96765)),f2(x96765))+~P106(f333(f67(x96764),x96763))+~P106(f333(f67(x96764),x96762))+E(f333(f333(f296(x96765),f333(f333(f88(x96765),f333(f333(f9(x96764,x96765),x96761),x96763)),f333(f333(f9(x96764,x96765),x96761),x96762))),f333(f333(f9(x96764,x96765),x96761),f333(f333(f112(f917(x96764,a905)),x96763),x96762))),f333(f333(f9(x96764,x96765),x96761),f333(f333(f121(f917(x96764,a905)),x96763),x96762))) % 173.51/173.29 [9953]~P68(x99531)+~P106(f333(f67(x99532),x99534))+~P106(f333(f67(x99532),x99535))+E(f333(f333(f296(x99531),f333(f333(f88(x99531),f333(f333(f9(x99532,x99531),x99533),x99534)),f333(f333(f9(x99532,x99531),x99533),x99535))),f333(f333(f9(x99532,x99531),x99533),f333(f333(f112(f917(x99532,a905)),x99534),x99535))),f333(f333(f9(x99532,x99531),x99533),f333(f333(f121(f917(x99532,a905)),x99534),x99535)))+P106(f333(f333(f335(x99532),f507(x99533,x99535,x99534,x99532,x99531)),f333(f333(f112(f917(x99532,a905)),x99534),x99535))) % 173.51/173.29 [9259]E(f333(f333(f142(x92591),x92592),x92593),f333(f333(f142(x92591),x92594),x92595))+~E(f333(f333(f183(x92591),f333(f197(f911(x92591)),x92594)),x92592),x92594)+~E(f333(f333(f183(x92591),f333(f197(f911(x92591)),x92592)),x92594),x92592)+~E(x92595,f333(f333(f142(x92591),f333(f333(f146(x92591),f333(f197(f911(x92591)),x92594)),x92592)),x92593))+~E(f333(f333(f142(x92591),f333(f333(f146(x92591),f333(f197(f911(x92591)),x92592)),x92594)),x92595),x92593) % 173.51/173.29 [9674]~P110(x96742)+E(f333(f333(f156(x96741,x96742,x96743),x96744),f178(x96741,x96744,x96745)),x96745)+~P16(x96742,f333(f333(f162(x96741,x96742),x96743),x96745))+~P106(f333(f333(f335(x96741),x96744),f333(f180(x96741),x96745)))+~E(f333(f149(x96741),f333(f144(x96741,f333(f333(f8(x96742,a905,x96741),f333(a330,f333(x96743,x96744))),x96743)),x96745)),x96744) % 173.51/173.29 [10016]~P76(x100161)+~P106(f333(f72(x100161,x100161,f88(x100161),x100162,x100163),x100165))+~P106(f333(f333(f335(x100161),x100164),x100163))+P106(f333(f333(f335(x100161),x100162),x100163))+P106(f333(f72(x100161,x100161,f88(x100161),x100164,f333(f333(f315(x100161),x100162),f333(f333(f23(f917(x100161,a905)),x100163),f333(f333(f315(x100161),x100164),f196(f917(x100161,a905)))))),x100165)) % 173.51/173.29 [7368]E(x73681,x73682)+~P27(x73684,x73685,x73683,x73686)+~E(f333(x73683,x73681),f333(x73683,x73682))+~P106(f333(f333(f335(x73684),x73682),x73686))+~P106(f333(f333(f335(x73684),x73681),x73686)) % 173.51/173.29 [6632]~P144(x66324)+E(x66321,x66322)+~E(x66325,x66326)+E(x66323,f2(x66324))+~E(f333(f333(f87(x66324),x66325),f333(f333(f88(x66324),x66323),x66321)),f333(f333(f87(x66324),x66326),f333(f333(f88(x66324),x66323),x66322))) % 173.51/173.29 [7650]~P110(x76501)+~P8(x76501)+~P106(f333(f333(f247(x76501),x76502),f333(x76505,x76506)))+~P106(f333(f333(f335(x76503),x76506),x76504))+P106(f333(f333(f247(x76501),x76502),f333(f333(f45(x76503,x76501),x76504),x76505))) % 173.51/173.29 [10012]~P27(x100122,x100121,x100123,x100124)+~P27(x100121,x100122,x100126,x100125)+P28(x100121,x100122,f867(x100123,x100124,x100125,x100126,x100122,x100121),x100125,x100124)+~P106(f333(f333(f246(f917(x100122,a905)),f333(f316(x100121,x100122,x100126),x100125)),x100124))+~P106(f333(f333(f246(f917(x100121,a905)),f333(f316(x100122,x100121,x100123),x100124)),x100125)) % 173.51/173.29 [8336]~P110(x83361)+~P8(x83361)+~P106(f333(f333(f247(x83361),f333(x83364,x83366)),x83365))+~P106(f333(f333(f335(x83362),x83366),x83363))+P106(f333(f333(f247(x83361),f333(f333(f46(x83362,x83361),x83363),x83364)),x83365)) % 173.51/173.29 [8600]~P21(x86002,x86005,x86006,x86001)+~P106(f333(f67(x86002),x86004))+~P106(f333(f67(x86002),x86003))+~E(f333(f333(f112(f917(x86002,a905)),x86003),x86004),f196(f917(x86002,a905)))+E(f333(x86001,f333(f333(f121(f917(x86002,a905)),x86003),x86004)),f333(f79(x86005,x86005,x86005,f333(x86001,x86003)),f333(x86001,x86004))) % 173.51/173.29 [8935]E(x89351,x89352)+~P60(x89354,x89355,x89356,x89353,x89357)+~E(f333(x89353,x89351),f333(x89353,x89352))+~P106(f333(f333(f335(x89355),x89352),x89357))+~P106(f333(f333(f335(x89355),x89351),x89357)) % 173.51/173.29 [10262]~P106(f333(x102622,x102624))+~E(x102625,f333(f144(x102621,x102622),x102627))+E(f333(f144(x102621,x102622),x102623),f333(f333(f159(x102621),x102624),x102625))+~E(x102623,f333(f333(f142(x102621),x102626),f333(f333(f159(x102621),x102624),x102627)))+P106(f333(x102622,f795(x102625,x102624,x102623,x102622,x102621,x102626,x102627))) % 173.51/173.29 [10263]~P106(f333(x102634,x102632))+~E(x102633,f333(f144(x102631,x102634),x102637))+E(f333(f333(f159(x102631),x102632),x102633),f333(f144(x102631,x102634),x102635))+~E(x102635,f333(f333(f142(x102631),x102636),f333(f333(f159(x102631),x102632),x102637)))+P106(f333(x102634,f794(x102635,x102634,x102633,x102632,x102631,x102636,x102637))) % 173.51/173.29 [10301]~P106(f333(x103012,x103014))+~E(x103015,f333(f144(x103011,x103012),x103017))+E(f333(f144(x103011,x103012),x103013),f333(f333(f159(x103011),x103014),x103015))+~E(x103013,f333(f333(f142(x103011),x103016),f333(f333(f159(x103011),x103014),x103017)))+P106(f333(f333(f335(x103011),f795(x103015,x103014,x103013,x103012,x103011,x103016,x103017)),f333(f180(x103011),x103016))) % 173.51/173.29 [10302]~P106(f333(x103024,x103022))+~E(x103023,f333(f144(x103021,x103024),x103027))+E(f333(f333(f159(x103021),x103022),x103023),f333(f144(x103021,x103024),x103025))+~E(x103025,f333(f333(f142(x103021),x103026),f333(f333(f159(x103021),x103022),x103027)))+P106(f333(f333(f335(x103021),f794(x103025,x103024,x103023,x103022,x103021,x103026,x103027)),f333(f180(x103021),x103026))) % 173.51/173.29 [10305]~P11(x103051,x103057,x103056)+~P14(x103051,f917(x103055,a905),x103056,x103054)+P106(f333(f333(f335(x103051),f533(x103052,x103053,x103054,x103055,x103056,x103057,x103051)),x103057))+~P106(f333(f333(f335(f917(x103051,a905)),x103053),f333(f333(f66(x103051),x103057),x103056)))+P106(f333(f333(f335(f917(x103055,a905)),f333(f333(f45(x103051,f917(x103055,a905)),x103053),x103054)),x103052)) % 173.51/173.29 [10362]~P11(x103622,x103626,x103627)+~P14(x103622,f917(x103621,a905),x103627,x103624)+~P106(f333(f333(f335(f917(x103622,a905)),x103623),f333(f333(f66(x103622),x103626),x103627)))+~P106(f333(f333(f335(f917(x103621,a905)),f333(x103624,f533(x103625,x103623,x103624,x103621,x103627,x103626,x103622))),x103625))+P106(f333(f333(f335(f917(x103621,a905)),f333(f333(f45(x103622,f917(x103621,a905)),x103623),x103624)),x103625)) % 173.51/173.29 [8509]~P78(x85092)+~P27(x85091,x85095,x85098,x85094)+~E(x85093,f333(f79(x85095,x85092,x85091,x85096),x85098))+~E(x85097,f333(f316(x85091,x85095,x85098),x85094))+E(f333(f333(f9(x85091,x85092),x85093),x85094),f333(f333(f9(x85095,x85092),x85096),x85097)) % 173.51/173.29 [10366]~P78(x103662)+~P27(x103665,x103661,x103668,x103667)+~E(f333(x103666,f509(x103663,x103666,x103664,x103667,x103668,x103661,x103665,x103662)),f333(f333(f79(x103661,x103662,x103665,x103663),x103668),f509(x103663,x103666,x103664,x103667,x103668,x103661,x103665,x103662)))+~E(x103664,f333(f316(x103665,x103661,x103668),x103667))+E(f333(f333(f9(x103661,x103662),x103663),x103664),f333(f333(f9(x103665,x103662),x103666),x103667)) % 173.51/173.29 [10369]~P72(x103692)+~P27(x103691,x103695,x103698,x103694)+~E(x103697,f333(f316(x103691,x103695,x103698),x103694))+E(f333(f333(f6(x103691,x103692),x103693),x103694),f333(f333(f6(x103695,x103692),x103696),x103697))+P106(f333(f333(f335(x103691),f879(x103696,x103693,x103697,x103694,x103698,x103695,x103691,x103692)),x103694)) % 173.51/173.29 [10370]~P78(x103702)+~P27(x103701,x103705,x103708,x103704)+~E(x103707,f333(f316(x103701,x103705,x103708),x103704))+E(f333(f333(f9(x103701,x103702),x103703),x103704),f333(f333(f9(x103705,x103702),x103706),x103707))+P106(f333(f333(f335(x103701),f509(x103706,x103703,x103707,x103704,x103708,x103705,x103701,x103702)),x103704)) % 173.51/173.29 [10376]~P72(x103762)+~P27(x103765,x103761,x103768,x103767)+~E(x103764,f333(f316(x103765,x103761,x103768),x103767))+~E(f333(x103766,f879(x103763,x103766,x103764,x103767,x103768,x103761,x103765,x103762)),f333(x103763,f333(x103768,f879(x103763,x103766,x103764,x103767,x103768,x103761,x103765,x103762))))+E(f333(f333(f6(x103761,x103762),x103763),x103764),f333(f333(f6(x103765,x103762),x103766),x103767)) % 173.51/173.29 [9850]~P25(x98506,x98502,x98505,x98507,x98508,x98501)+~P106(f333(f67(x98502),x98504))+~P106(f333(f67(x98502),x98503))+~E(f333(f333(f112(f917(x98502,a905)),x98503),x98504),f196(f917(x98502,a905)))+E(f333(x98501,f333(f333(f121(f917(x98502,a905)),x98503),x98504)),f333(f333(x98505,f333(x98501,x98503)),f333(x98501,x98504))) % 173.51/173.29 [10249]~P25(x102498,x102492,x102495,x102497,x102496,x102491)+~E(f333(x102496,f478(x102494,x102493,x102491,x102496,x102497,x102495,x102492)),x102497)+~P106(f333(f67(x102492),x102493))+~P106(f333(f67(x102492),x102494))+E(f333(x102491,f333(f333(f121(f917(x102492,a905)),x102493),x102494)),f333(f333(x102495,f333(x102491,x102493)),f333(x102491,x102494))) % 173.51/173.29 [10312]~P25(x103128,x103122,x103125,x103127,x103126,x103121)+~P106(f333(f67(x103122),x103123))+~P106(f333(f67(x103122),x103124))+E(f333(x103121,f333(f333(f121(f917(x103122,a905)),x103123),x103124)),f333(f333(x103125,f333(x103121,x103123)),f333(x103121,x103124)))+P106(f333(f333(f335(x103122),f478(x103124,x103123,x103121,x103126,x103127,x103125,x103122)),f333(f333(f112(f917(x103122,a905)),x103123),x103124))) % 173.51/173.29 [10003]~P11(x100034,x100038,x100035)+~P11(x100031,x100039,x100033)+~P15(x100031,x100034,f917(x100032,a905),x100033,x100035,x100037)+P14(x100031,f917(x100032,a905),x100033,f333(f333(f8(f917(x100034,f917(x100032,a905)),f917(x100032,a905),x100031),f333(f45(x100034,f917(x100032,a905)),f333(f292(x100034,x100034,x100035),f333(f333(f315(x100034),x100036),f196(f917(x100034,a905)))))),x100037))+~P106(f333(f333(f335(x100034),x100036),x100038)) % 173.51/173.29 [5562]~P110(x55623)+~P16(x55623,x55621)+E(x55621,f772(x55622,x55623))+~E(f333(f180(x55623),x55621),x55622)+~P106(f333(f67(x55623),x55622))+~P106(f333(f145(x55623),x55621)) % 173.51/173.29 [5192]~P145(x51922)+~P128(x51922)+~P129(x51922)+~P115(x51922)+E(x51921,f2(x51922))+~E(f333(f333(f256(x51922),x51921),x51923),f2(x51922)) % 173.51/173.29 [5193]~P145(x51932)+~P128(x51932)+~P129(x51932)+~P115(x51932)+~E(x51931,f2(a910))+~E(f333(f333(f256(x51932),x51933),x51931),f2(x51932)) % 173.51/173.29 [6614]~P90(x66141)+~E(x66143,f2(x66141))+~E(x66142,f2(x66141))+E(f333(f333(f87(x66141),x66142),x66143),f2(x66141))+~P106(f333(f333(f246(x66141),f2(x66141)),x66143))+~P106(f333(f333(f246(x66141),f2(x66141)),x66142)) % 173.51/173.29 [9003]~E(f333(f264(a910,a910),x90033),f2(a910))+~E(x90031,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),x90033)),x90032)),f333(f268(a910,a910),x90033)))+P106(f333(f54(x90031,x90032),x90033))+~P106(f333(f333(f246(a910),f333(f268(a910,a910),x90033)),f2(a910)))+P106(f333(f333(f247(a910),f2(a910)),x90032))+~P106(f333(f333(f247(a910),x90032),f333(f268(a910,a910),x90033))) % 173.51/173.29 [9011]E(x90111,f2(a910))+~E(x90112,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),x90113)),x90111)),f333(f268(a910,a910),x90113)))+P106(f333(f54(x90112,x90111),x90113))+~P106(f333(f333(f247(a910),f2(a910)),x90111))+~P106(f333(f333(f246(a910),f2(a910)),f333(f268(a910,a910),x90113)))+~P106(f333(f333(f247(a910),f333(f268(a910,a910),x90113)),x90111)) % 173.51/173.29 [9030]~E(f333(f264(a910,a910),x90303),f2(a910))+~E(x90301,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),x90303)),x90302)),f333(f268(a910,a910),x90303)))+P106(f333(f54(x90301,x90302),x90303))+~P106(f333(f333(f247(a910),f2(a910)),x90302))+~P106(f333(f333(f246(a910),f2(a910)),f333(f268(a910,a910),x90303)))+~P106(f333(f333(f247(a910),f333(f268(a910,a910),x90303)),x90302)) % 173.51/173.29 [6990]~P2(x69902)+E(x69901,f196(f917(x69902,a905)))+E(x69903,f196(f917(x69902,a905)))+~P106(f333(f67(x69902),x69901))+~P106(f333(f67(x69902),x69903))+E(f13(x69902,f333(f333(f121(f917(x69902,a905)),x69903),x69901)),f333(f333(f121(x69902),f13(x69902,x69903)),f13(x69902,x69901))) % 173.51/173.29 [6991]~P2(x69912)+E(x69911,f196(f917(x69912,a905)))+E(x69913,f196(f917(x69912,a905)))+~P106(f333(f67(x69912),x69911))+~P106(f333(f67(x69912),x69913))+E(f10(x69912,f333(f333(f121(f917(x69912,a905)),x69913),x69911)),f333(f333(f112(x69912),f10(x69912,x69913)),f10(x69912,x69911))) % 173.51/173.29 [6992]~P110(x69922)+E(x69921,f196(f917(x69922,a905)))+E(x69923,f196(f917(x69922,a905)))+~P106(f333(f67(x69922),x69921))+~P106(f333(f67(x69922),x69923))+E(f14(x69922,f333(f333(f121(f917(x69922,a905)),x69923),x69921)),f333(f333(f244(x69922),f14(x69922,x69923)),f14(x69922,x69921))) % 173.51/173.29 [6993]~P110(x69932)+E(x69931,f196(f917(x69932,a905)))+E(x69933,f196(f917(x69932,a905)))+~P106(f333(f67(x69932),x69931))+~P106(f333(f67(x69932),x69933))+E(f15(x69932,f333(f333(f121(f917(x69932,a905)),x69933),x69931)),f333(f333(f245(x69932),f15(x69932,x69933)),f15(x69932,x69931))) % 173.51/173.29 [7627]~P97(x76272)+E(x76271,f196(f917(x76272,a905)))+E(x76273,f196(f917(x76272,a905)))+~P106(f333(f67(x76272),x76271))+~P106(f333(f67(x76272),x76273))+E(f333(f333(f88(x76272),f333(f69(x76272,f88(x76272)),x76273)),f333(f69(x76272,f88(x76272)),x76271)),f333(f69(x76272,f88(x76272)),f333(f333(f121(f917(x76272,a905)),x76273),x76271))) % 173.51/173.29 [7783]~P110(x77832)+E(x77831,f196(f917(x77832,a905)))+E(x77833,f196(f917(x77832,a905)))+~P106(f333(f67(x77832),x77831))+~P106(f333(f67(x77832),x77833))+E(f333(f333(f244(x77832),f11(x77832,f244(x77832),x77833)),f11(x77832,f244(x77832),x77831)),f11(x77832,f244(x77832),f333(f333(f121(f917(x77832,a905)),x77833),x77831))) % 173.51/173.29 [7784]~P110(x77842)+E(x77841,f196(f917(x77842,a905)))+E(x77843,f196(f917(x77842,a905)))+~P106(f333(f67(x77842),x77841))+~P106(f333(f67(x77842),x77843))+E(f333(f333(f245(x77842),f12(x77842,f245(x77842),x77843)),f12(x77842,f245(x77842),x77841)),f12(x77842,f245(x77842),f333(f333(f121(f917(x77842,a905)),x77843),x77841))) % 173.51/173.29 [8837]~P106(f333(x88371,x88373))+P106(f333(x88371,f404(x88371,x88372)))+P106(f333(x88371,f392(x88371,x88372)))+~P106(f333(f333(f247(a1),f2(a1)),x88372))+~P106(f333(f333(f335(a1),x88373),f309(a1,f85(a1),x88372)))+P106(f333(x88371,f333(f333(f23(a1),f392(x88371,x88372)),f333(f333(f88(a1),f403(x88371,x88372)),x88372)))) % 173.51/173.29 [9155]~P106(f333(x91551,x91553))+~P106(f333(x91551,f392(x91551,x91552)))+P106(f333(x91551,f404(x91551,x91552)))+~P106(f333(f333(f247(a1),f2(a1)),x91552))+~P106(f333(f333(f335(a1),x91553),f309(a1,f85(a1),x91552)))+~P106(f333(x91551,f333(f333(f23(a1),f392(x91551,x91552)),f333(f333(f88(a1),f403(x91551,x91552)),x91552)))) % 173.51/173.29 [10397]~P99(x103972)+E(x103971,f196(f917(x103972,a905)))+E(x103973,f196(f917(x103972,a905)))+~P106(f333(f67(x103972),x103971))+~P106(f333(f67(x103972),x103973))+E(f10(x103972,f333(f252(x103972),f333(f333(f8(f917(x103972,a905),a905,x103972),f94(x103972)),f333(f333(f8(f917(x103972,f917(x103972,a905)),f917(x103972,a905),x103972),f333(f8(f917(x103972,a905),a905,x103972),f94(x103972))),f333(f333(f7(x103972,f917(x103972,f917(x103972,a905)),f917(x103972,f917(x103972,a905))),f333(f333(f8(f917(x103972,f917(f917(x103972,a905),f917(x103972,a905))),f917(f917(x103972,f917(x103972,a905)),f917(x103972,f917(x103972,a905))),x103972),f18(x103972,f917(x103972,a905),f917(x103972,a905))),f333(f333(f8(f917(x103972,f917(x103972,f917(a905,a905))),f917(x103972,f917(f917(x103972,a905),f917(x103972,a905))),x103972),f333(f8(f917(x103972,f917(a905,a905)),f917(f917(x103972,a905),f917(x103972,a905)),x103972),f18(x103972,a905,a905))),f333(f333(f8(f917(x103972,f917(x103972,a905)),f917(x103972,f917(x103972,f917(a905,a905))),x103972),f333(f8(f917(x103972,a905),f917(x103972,f917(a905,a905)),x103972),f333(f8(a905,f917(a905,a905),x103972),a331))),f333(f333(f7(x103972,f917(x103972,f917(x103972,x103972)),f917(x103972,f917(x103972,a905))),f333(f333(f8(f917(f917(x103972,x103972),f917(x103972,a905)),f917(f917(x103972,f917(x103972,x103972)),f917(x103972,f917(x103972,a905))),x103972),f8(f917(x103972,x103972),f917(x103972,a905),x103972)),f333(f333(f8(f917(x103972,a905),f917(f917(x103972,x103972),f917(x103972,a905)),x103972),f8(x103972,a905,x103972)),a330))),f121(x103972)))))),f333(f333(f7(x103972,f917(x103972,a905),f917(x103972,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x103972,a905),f917(x103972,a905)),x103972),f8(a905,a905,x103972)),f333(f333(f8(a905,f917(a905,a905),x103972),a331),f333(f333(f7(x103972,f917(x103972,a905),a905),f335(x103972)),x103973)))),f333(f333(f7(x103972,f917(x103972,a905),a905),f335(x103972)),x103971))))))),f333(f333(f121(x103972),f10(x103972,x103973)),f10(x103972,x103971))) % 173.51/173.29 [10398]~P99(x103982)+E(x103981,f196(f917(x103982,a905)))+E(x103983,f196(f917(x103982,a905)))+~P106(f333(f67(x103982),x103981))+~P106(f333(f67(x103982),x103983))+E(f13(x103982,f333(f252(x103982),f333(f333(f8(f917(x103982,a905),a905,x103982),f94(x103982)),f333(f333(f8(f917(x103982,f917(x103982,a905)),f917(x103982,a905),x103982),f333(f8(f917(x103982,a905),a905,x103982),f94(x103982))),f333(f333(f7(x103982,f917(x103982,f917(x103982,a905)),f917(x103982,f917(x103982,a905))),f333(f333(f8(f917(x103982,f917(f917(x103982,a905),f917(x103982,a905))),f917(f917(x103982,f917(x103982,a905)),f917(x103982,f917(x103982,a905))),x103982),f18(x103982,f917(x103982,a905),f917(x103982,a905))),f333(f333(f8(f917(x103982,f917(x103982,f917(a905,a905))),f917(x103982,f917(f917(x103982,a905),f917(x103982,a905))),x103982),f333(f8(f917(x103982,f917(a905,a905)),f917(f917(x103982,a905),f917(x103982,a905)),x103982),f18(x103982,a905,a905))),f333(f333(f8(f917(x103982,f917(x103982,a905)),f917(x103982,f917(x103982,f917(a905,a905))),x103982),f333(f8(f917(x103982,a905),f917(x103982,f917(a905,a905)),x103982),f333(f8(a905,f917(a905,a905),x103982),a331))),f333(f333(f7(x103982,f917(x103982,f917(x103982,x103982)),f917(x103982,f917(x103982,a905))),f333(f333(f8(f917(f917(x103982,x103982),f917(x103982,a905)),f917(f917(x103982,f917(x103982,x103982)),f917(x103982,f917(x103982,a905))),x103982),f8(f917(x103982,x103982),f917(x103982,a905),x103982)),f333(f333(f8(f917(x103982,a905),f917(f917(x103982,x103982),f917(x103982,a905)),x103982),f8(x103982,a905,x103982)),a330))),f112(x103982)))))),f333(f333(f7(x103982,f917(x103982,a905),f917(x103982,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x103982,a905),f917(x103982,a905)),x103982),f8(a905,a905,x103982)),f333(f333(f8(a905,f917(a905,a905),x103982),a331),f333(f333(f7(x103982,f917(x103982,a905),a905),f335(x103982)),x103983)))),f333(f333(f7(x103982,f917(x103982,a905),a905),f335(x103982)),x103981))))))),f333(f333(f112(x103982),f13(x103982,x103983)),f13(x103982,x103981))) % 173.51/173.29 [10399]~P110(x103992)+E(x103991,f196(f917(x103992,a905)))+E(x103993,f196(f917(x103992,a905)))+~P106(f333(f67(x103992),x103991))+~P106(f333(f67(x103992),x103993))+E(f12(x103992,f245(x103992),f333(f252(x103992),f333(f333(f8(f917(x103992,a905),a905,x103992),f94(x103992)),f333(f333(f8(f917(x103992,f917(x103992,a905)),f917(x103992,a905),x103992),f333(f8(f917(x103992,a905),a905,x103992),f94(x103992))),f333(f333(f7(x103992,f917(x103992,f917(x103992,a905)),f917(x103992,f917(x103992,a905))),f333(f333(f8(f917(x103992,f917(f917(x103992,a905),f917(x103992,a905))),f917(f917(x103992,f917(x103992,a905)),f917(x103992,f917(x103992,a905))),x103992),f18(x103992,f917(x103992,a905),f917(x103992,a905))),f333(f333(f8(f917(x103992,f917(x103992,f917(a905,a905))),f917(x103992,f917(f917(x103992,a905),f917(x103992,a905))),x103992),f333(f8(f917(x103992,f917(a905,a905)),f917(f917(x103992,a905),f917(x103992,a905)),x103992),f18(x103992,a905,a905))),f333(f333(f8(f917(x103992,f917(x103992,a905)),f917(x103992,f917(x103992,f917(a905,a905))),x103992),f333(f8(f917(x103992,a905),f917(x103992,f917(a905,a905)),x103992),f333(f8(a905,f917(a905,a905),x103992),a331))),f333(f333(f7(x103992,f917(x103992,f917(x103992,x103992)),f917(x103992,f917(x103992,a905))),f333(f333(f8(f917(f917(x103992,x103992),f917(x103992,a905)),f917(f917(x103992,f917(x103992,x103992)),f917(x103992,f917(x103992,a905))),x103992),f8(f917(x103992,x103992),f917(x103992,a905),x103992)),f333(f333(f8(f917(x103992,a905),f917(f917(x103992,x103992),f917(x103992,a905)),x103992),f8(x103992,a905,x103992)),a330))),f244(x103992)))))),f333(f333(f7(x103992,f917(x103992,a905),f917(x103992,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x103992,a905),f917(x103992,a905)),x103992),f8(a905,a905,x103992)),f333(f333(f8(a905,f917(a905,a905),x103992),a331),f333(f333(f7(x103992,f917(x103992,a905),a905),f335(x103992)),x103993)))),f333(f333(f7(x103992,f917(x103992,a905),a905),f335(x103992)),x103991))))))),f333(f333(f244(x103992),f12(x103992,f245(x103992),x103993)),f12(x103992,f245(x103992),x103991))) % 173.51/173.29 [10400]~P110(x104002)+E(x104001,f196(f917(x104002,a905)))+E(x104003,f196(f917(x104002,a905)))+~P106(f333(f67(x104002),x104001))+~P106(f333(f67(x104002),x104003))+E(f11(x104002,f244(x104002),f333(f252(x104002),f333(f333(f8(f917(x104002,a905),a905,x104002),f94(x104002)),f333(f333(f8(f917(x104002,f917(x104002,a905)),f917(x104002,a905),x104002),f333(f8(f917(x104002,a905),a905,x104002),f94(x104002))),f333(f333(f7(x104002,f917(x104002,f917(x104002,a905)),f917(x104002,f917(x104002,a905))),f333(f333(f8(f917(x104002,f917(f917(x104002,a905),f917(x104002,a905))),f917(f917(x104002,f917(x104002,a905)),f917(x104002,f917(x104002,a905))),x104002),f18(x104002,f917(x104002,a905),f917(x104002,a905))),f333(f333(f8(f917(x104002,f917(x104002,f917(a905,a905))),f917(x104002,f917(f917(x104002,a905),f917(x104002,a905))),x104002),f333(f8(f917(x104002,f917(a905,a905)),f917(f917(x104002,a905),f917(x104002,a905)),x104002),f18(x104002,a905,a905))),f333(f333(f8(f917(x104002,f917(x104002,a905)),f917(x104002,f917(x104002,f917(a905,a905))),x104002),f333(f8(f917(x104002,a905),f917(x104002,f917(a905,a905)),x104002),f333(f8(a905,f917(a905,a905),x104002),a331))),f333(f333(f7(x104002,f917(x104002,f917(x104002,x104002)),f917(x104002,f917(x104002,a905))),f333(f333(f8(f917(f917(x104002,x104002),f917(x104002,a905)),f917(f917(x104002,f917(x104002,x104002)),f917(x104002,f917(x104002,a905))),x104002),f8(f917(x104002,x104002),f917(x104002,a905),x104002)),f333(f333(f8(f917(x104002,a905),f917(f917(x104002,x104002),f917(x104002,a905)),x104002),f8(x104002,a905,x104002)),a330))),f245(x104002)))))),f333(f333(f7(x104002,f917(x104002,a905),f917(x104002,a905)),f333(f333(f8(f917(a905,a905),f917(f917(x104002,a905),f917(x104002,a905)),x104002),f8(a905,a905,x104002)),f333(f333(f8(a905,f917(a905,a905),x104002),a331),f333(f333(f7(x104002,f917(x104002,a905),a905),f335(x104002)),x104003)))),f333(f333(f7(x104002,f917(x104002,a905),a905),f335(x104002)),x104001))))))),f333(f333(f245(x104002),f11(x104002,f244(x104002),x104003)),f11(x104002,f244(x104002),x104001))) % 173.51/173.29 [7316]~P119(x73163)+E(x73161,x73162)+~E(f333(f333(f256(x73163),x73161),x73164),f333(f333(f256(x73163),x73162),x73164))+~P106(f333(f333(f246(x73163),f2(x73163)),x73162))+~P106(f333(f333(f246(x73163),f2(x73163)),x73161))+~P106(f333(f333(f247(a910),f2(a910)),x73164)) % 173.51/173.29 [7587]~P102(x75872)+E(x75871,f196(f917(x75872,a905)))+~P106(f333(f67(x75872),x75871))+~P106(f333(f333(f335(x75872),x75874),x75871))+P106(f333(f333(f246(x75872),x75873),x75874))+~P106(f333(f333(f246(x75872),x75873),f333(f69(x75872,f112(x75872)),x75871))) % 173.51/173.29 [7588]~P110(x75882)+E(x75881,f196(f917(x75882,a905)))+~P106(f333(f67(x75882),x75881))+~P106(f333(f333(f335(x75882),x75884),x75881))+P106(f333(f333(f246(x75882),x75883),x75884))+~P106(f333(f333(f246(x75882),x75883),f333(f69(x75882,f244(x75882)),x75881))) % 173.51/173.29 [7589]~P110(x75892)+E(x75891,f196(f917(x75892,a905)))+~P106(f333(f67(x75892),x75891))+~P106(f333(f333(f335(x75892),x75894),x75891))+P106(f333(f333(f247(x75892),x75893),x75894))+~P106(f333(f333(f247(x75892),x75893),f333(f69(x75892,f244(x75892)),x75891))) % 173.51/173.29 [7493]E(x74931,f2(a1))+E(f333(f333(f42(a1),x74932),x74931),x74933)+~P106(f333(f333(f246(a1),x74934),f2(a1)))+~E(x74932,f333(f333(f87(a1),f333(f333(f88(a1),x74931),x74933)),x74934))+P106(f333(f333(f247(a1),f2(a1)),x74931))+~P106(f333(f333(f247(a1),x74931),x74934)) % 173.51/173.29 [7508]E(f51(a1,x75082,x75081),x75083)+E(x75081,f2(a1))+~P106(f333(f333(f246(a1),x75083),f2(a1)))+~E(x75082,f333(f333(f87(a1),f333(f333(f88(a1),x75081),x75084)),x75083))+P106(f333(f333(f247(a1),f2(a1)),x75081))+~P106(f333(f333(f247(a1),x75081),x75083)) % 173.51/173.29 [7626]E(x76261,f2(a1))+E(f333(f333(f42(a1),x76262),x76261),x76263)+~E(x76262,f333(f333(f87(a1),f333(f333(f88(a1),x76261),x76263)),x76264))+~P106(f333(f333(f246(a1),f2(a1)),x76264))+~P106(f333(f333(f247(a1),f2(a1)),x76261))+~P106(f333(f333(f247(a1),x76264),x76261)) % 173.51/173.29 [7646]E(f51(a1,x76462,x76461),x76463)+E(x76461,f2(a1))+~E(x76462,f333(f333(f87(a1),f333(f333(f88(a1),x76461),x76464)),x76463))+~P106(f333(f333(f246(a1),f2(a1)),x76463))+~P106(f333(f333(f247(a1),f2(a1)),x76461))+~P106(f333(f333(f247(a1),x76463),x76461)) % 173.51/173.29 [7787]~P110(x77872)+E(x77871,f196(f917(x77872,a905)))+~P106(f333(f67(x77872),x77871))+~P106(f333(f333(f246(x77872),x77874),x77873))+~P106(f333(f333(f335(x77872),x77874),x77871))+P106(f333(f333(f246(x77872),f333(f69(x77872,f244(x77872)),x77871)),x77873)) % 173.51/173.29 [7788]~P110(x77882)+E(x77881,f196(f917(x77882,a905)))+~P106(f333(f67(x77882),x77881))+~P106(f333(f333(f247(x77882),x77884),x77883))+~P106(f333(f333(f335(x77882),x77884),x77881))+P106(f333(f333(f247(x77882),f333(f69(x77882,f244(x77882)),x77881)),x77883)) % 173.51/173.29 [8361]~P106(f333(f333(f246(a1),x83614),f2(a1)))+~E(x83611,f333(f333(f87(a1),f333(f333(f88(a1),x83612),x83613)),x83614))+~P106(f333(f333(f246(a1),f2(a1)),x83614))+~P106(f333(f333(f247(a1),x83614),x83612))+~P106(f333(f333(f247(a1),x83612),x83614))+P106(f333(f55(x83611,x83612),f333(f333(f265(a1,a1),x83613),x83614))) % 173.51/173.29 [8531]~P112(x85311)+P106(f333(f333(f247(f917(x85311,a905)),f309(x85311,x85312,x85313)),f309(x85311,x85314,x85315)))+~P106(f333(f333(f246(x85311),x85314),x85312))+~P106(f333(f333(f246(x85311),x85314),x85315))+~P106(f333(f333(f246(x85311),x85313),x85315))+~P106(f333(f333(f247(x85311),x85313),x85315)) % 173.51/173.29 [8532]~P112(x85321)+P106(f333(f333(f247(f917(x85321,a905)),f309(x85321,x85322,x85323)),f309(x85321,x85324,x85325)))+~P106(f333(f333(f246(x85321),x85323),x85325))+~P106(f333(f333(f246(x85321),x85324),x85325))+~P106(f333(f333(f246(x85321),x85324),x85322))+~P106(f333(f333(f247(x85321),x85324),x85322)) % 173.51/173.29 [9420]P62(x94202,x94203,x94204,x94201)+E(x94201,f196(f917(x94202,a905)))+~P106(f333(f67(x94202),x94204))+~P106(f333(f67(x94202),x94201))+~P106(f333(f333(x94203,f587(x94201,x94204,x94203,x94202)),x94205))+~P106(f333(f333(f335(x94202),x94205),x94201)) % 173.51/173.29 [9421]P62(x94212,x94213,x94214,x94211)+E(x94211,f196(f917(x94212,a905)))+~P106(f333(f67(x94212),x94214))+~P106(f333(f67(x94212),x94211))+~P106(f333(f333(x94213,f842(x94213,x94211,x94214,x94212)),x94215))+~P106(f333(f333(f335(x94212),x94215),x94211)) % 173.51/173.29 [9422]P62(x94222,x94223,x94224,x94221)+E(x94221,f196(f917(x94222,a905)))+~P106(f333(f67(x94222),x94224))+~P106(f333(f67(x94222),x94221))+~P106(f333(f333(x94223,f843(x94221,x94224,x94223,x94222)),x94225))+~P106(f333(f333(f335(x94222),x94225),x94221)) % 173.51/173.29 [9574]~E(x95743,x95745)+~P72(x95741)+~P78(x95741)+~P43(x95743)+E(f333(f333(f6(a1,x95741),x95742),x95743),f333(f333(f6(a1,x95741),x95744),x95745))+P106(f333(f333(f246(a1),f2(a1)),f458(x95742,x95744,x95743,x95745,x95741))) % 173.51/173.29 [9575]~E(x95753,x95755)+~P72(x95751)+~P78(x95751)+~P43(x95753)+E(f333(f333(f9(a1,x95751),x95752),x95753),f333(f333(f9(a1,x95751),x95754),x95755))+P106(f333(f333(f246(a1),f2(a1)),f514(x95752,x95754,x95753,x95755,x95751))) % 173.51/173.29 [9759]~E(x97595,x97593)+~P72(x97591)+~P78(x97591)+~P43(x97595)+~E(f333(x97592,f458(x97594,x97592,x97595,x97593,x97591)),f333(x97594,f458(x97594,x97592,x97595,x97593,x97591)))+E(f333(f333(f6(a1,x97591),x97592),x97593),f333(f333(f6(a1,x97591),x97594),x97595)) % 173.51/173.29 [9760]~E(x97605,x97603)+~P72(x97601)+~P78(x97601)+~P43(x97605)+~E(f333(x97602,f514(x97604,x97602,x97605,x97603,x97601)),f333(x97604,f514(x97604,x97602,x97605,x97603,x97601)))+E(f333(f333(f9(a1,x97601),x97602),x97603),f333(f333(f9(a1,x97601),x97604),x97605)) % 173.51/173.29 [9848]~P4(x98483)+E(f333(x98481,x98482),f2(x98483))+~E(f333(f333(f6(x98484,x98483),x98481),x98485),f2(x98483))+~P106(f333(f67(x98484),x98485))+P106(f333(f333(f335(x98484),f367(x98482,x98481,x98485,x98484,x98483)),x98485))+~P106(f333(f333(f335(x98484),x98482),x98485)) % 173.51/173.29 [9976]~P4(x99763)+E(f333(x99761,x99762),f2(x99763))+~E(f333(f333(f6(x99764,x99763),x99761),x99765),f2(x99763))+~P106(f333(f67(x99764),x99765))+~P106(f333(f333(f335(x99764),x99762),x99765))+~P106(f333(f333(f246(x99763),f2(x99763)),f333(x99761,f367(x99762,x99761,x99765,x99764,x99763)))) % 173.51/173.29 [8447]~P137(x84471)+~P106(f333(f333(f246(x84471),x84473),x84475))+~P106(f333(f333(f246(x84471),x84472),x84474))+~P106(f333(f333(f246(x84471),f2(x84471)),x84473))+~P106(f333(f333(f246(x84471),f2(x84471)),x84474))+P106(f333(f333(f246(x84471),f333(f333(f88(x84471),x84472),x84473)),f333(f333(f88(x84471),x84474),x84475))) % 173.51/173.29 [8448]~P137(x84481)+~P106(f333(f333(f246(x84481),x84483),x84485))+~P106(f333(f333(f246(x84481),x84482),x84484))+~P106(f333(f333(f246(x84481),f2(x84481)),x84483))+~P106(f333(f333(f246(x84481),f2(x84481)),x84482))+P106(f333(f333(f246(x84481),f333(f333(f88(x84481),x84482),x84483)),f333(f333(f88(x84481),x84484),x84485))) % 173.51/173.29 [8449]~P70(x84491)+~P106(f333(f333(f247(x84491),f2(x84491)),x84495))+~P106(f333(f333(f246(x84491),x84495),x84493))+~P106(f333(f333(f246(x84491),x84492),x84494))+~P106(f333(f333(f246(x84491),f2(x84491)),x84492))+P106(f333(f333(f246(x84491),f333(f333(f296(x84491),x84492),x84493)),f333(f333(f296(x84491),x84494),x84495))) % 173.51/173.29 [8450]~P130(x84501)+~P106(f333(f333(f246(x84501),x84503),x84505))+~P106(f333(f333(f246(x84501),f2(x84501)),x84502))+~P106(f333(f333(f247(x84501),x84502),x84504))+~P106(f333(f333(f247(x84501),f2(x84501)),x84503))+P106(f333(f333(f247(x84501),f333(f333(f88(x84501),x84502),x84503)),f333(f333(f88(x84501),x84504),x84505))) % 173.51/173.29 [8451]~P130(x84511)+~P106(f333(f333(f246(x84511),x84512),x84514))+~P106(f333(f333(f246(x84511),f2(x84511)),x84513))+~P106(f333(f333(f247(x84511),x84513),x84515))+~P106(f333(f333(f247(x84511),f2(x84511)),x84512))+P106(f333(f333(f247(x84511),f333(f333(f88(x84511),x84512),x84513)),f333(f333(f88(x84511),x84514),x84515))) % 173.51/173.29 [8452]~P130(x84521)+~P106(f333(f333(f246(x84521),f2(x84521)),x84523))+~P106(f333(f333(f246(x84521),f2(x84521)),x84522))+~P106(f333(f333(f247(x84521),x84523),x84525))+~P106(f333(f333(f247(x84521),x84522),x84524))+P106(f333(f333(f247(x84521),f333(f333(f88(x84521),x84522),x84523)),f333(f333(f88(x84521),x84524),x84525))) % 173.51/173.29 [8453]~P130(x84531)+~P106(f333(f333(f246(x84531),f2(x84531)),x84533))+~P106(f333(f333(f247(x84531),x84533),x84535))+~P106(f333(f333(f247(x84531),x84532),x84534))+~P106(f333(f333(f247(x84531),f2(x84531)),x84534))+P106(f333(f333(f247(x84531),f333(f333(f88(x84531),x84532),x84533)),f333(f333(f88(x84531),x84534),x84535))) % 173.51/173.29 [8454]~P70(x84541)+~P106(f333(f333(f246(x84541),x84545),x84543))+~P106(f333(f333(f246(x84541),f2(x84541)),x84542))+~P106(f333(f333(f247(x84541),x84542),x84544))+~P106(f333(f333(f247(x84541),f2(x84541)),x84545))+P106(f333(f333(f247(x84541),f333(f333(f296(x84541),x84542),x84543)),f333(f333(f296(x84541),x84544),x84545))) % 173.51/173.29 [8455]~P70(x84551)+~P106(f333(f333(f246(x84551),x84552),x84554))+~P106(f333(f333(f247(x84551),x84555),x84553))+~P106(f333(f333(f247(x84551),f2(x84551)),x84555))+~P106(f333(f333(f247(x84551),f2(x84551)),x84552))+P106(f333(f333(f247(x84551),f333(f333(f296(x84551),x84552),x84553)),f333(f333(f296(x84551),x84554),x84555))) % 173.51/173.29 [9890]~P72(x98905)+~P88(x98905)+E(x98901,f196(f917(x98902,a905)))+~P106(f333(f67(x98902),x98901))+P106(f333(f333(f335(x98902),f902(x98903,x98904,x98901,x98902,x98905)),x98901))+P106(f333(f333(f247(x98905),f333(f333(f6(x98902,x98905),x98904),x98901)),f333(f333(f6(x98902,x98905),x98903),x98901))) % 173.51/173.29 [9999]~P72(x99991)+~P86(x99991)+~P106(f333(f67(x99992),x99995))+~P106(f333(f333(f246(x99991),f2(x99991)),f333(x99993,f368(x99993,x99994,x99995,x99992,x99991))))+P106(f333(f333(f246(x99991),f333(f333(f6(x99992,x99991),x99993),x99994)),f333(f333(f6(x99992,x99991),x99993),x99995)))+~P106(f333(f333(f246(f917(x99992,a905)),x99994),x99995)) % 173.51/173.29 [10168]~P72(x101683)+~P88(x101683)+E(x101681,f196(f917(x101682,a905)))+~P106(f333(f67(x101682),x101681))+~P106(f333(f333(f247(x101683),f333(x101684,f902(x101685,x101684,x101681,x101682,x101683))),f333(x101685,f902(x101685,x101684,x101681,x101682,x101683))))+P106(f333(f333(f247(x101683),f333(f333(f6(x101682,x101683),x101684),x101681)),f333(f333(f6(x101682,x101683),x101685),x101681))) % 173.51/173.29 [7173]~P19(x71732,x71735,x71734)+E(x71731,f196(f917(x71732,a905)))+E(x71733,f196(f917(x71732,a905)))+~P106(f333(f67(x71732),x71731))+~P106(f333(f67(x71732),x71733))+E(f333(x71734,f333(f333(f121(f917(x71732,a905)),x71733),x71731)),f333(f333(x71735,f333(x71734,x71733)),f333(x71734,x71731))) % 173.51/173.29 [7754]~P147(x77541,x77543,x77544)+P106(f333(x77541,x77542))+~P106(f333(f333(f247(a1),x77544),f2(a1)))+~P106(f333(f333(f246(a1),x77545),f2(a1)))+~E(x77543,f333(f333(f87(a1),f333(f333(f88(a1),x77544),x77542)),x77545))+~P106(f333(f333(f247(a1),x77544),x77545)) % 173.51/173.29 [7755]~P146(x77551,x77553,x77554)+P106(f333(x77551,x77552))+~P106(f333(f333(f247(a1),x77554),f2(a1)))+~P106(f333(f333(f246(a1),x77552),f2(a1)))+~E(x77553,f333(f333(f87(a1),f333(f333(f88(a1),x77554),x77555)),x77552))+~P106(f333(f333(f247(a1),x77554),x77552)) % 173.51/173.29 [7796]~P147(x77961,x77963,x77964)+P106(f333(x77961,x77962))+~E(x77963,f333(f333(f87(a1),f333(f333(f88(a1),x77964),x77962)),x77965))+~P106(f333(f333(f246(a1),f2(a1)),x77965))+~P106(f333(f333(f247(a1),f2(a1)),x77964))+~P106(f333(f333(f247(a1),x77965),x77964)) % 173.51/173.29 [7797]~P146(x77971,x77973,x77974)+P106(f333(x77971,x77972))+~E(x77973,f333(f333(f87(a1),f333(f333(f88(a1),x77974),x77975)),x77972))+~P106(f333(f333(f246(a1),f2(a1)),x77972))+~P106(f333(f333(f247(a1),f2(a1)),x77974))+~P106(f333(f333(f247(a1),x77972),x77974)) % 173.51/173.29 [8749]P106(f333(f333(x87491,x87492),x87493))+~P106(f333(f333(x87491,f333(f333(f42(a1),x87494),x87495)),f51(a1,x87494,x87495)))+~P106(f333(f333(f247(a1),x87495),f2(a1)))+~P106(f333(f333(f246(a1),x87493),f2(a1)))+~E(x87494,f333(f333(f87(a1),f333(f333(f88(a1),x87495),x87492)),x87493))+~P106(f333(f333(f247(a1),x87495),x87493)) % 173.51/173.29 [8760]P106(f333(f333(x87601,x87602),x87603))+~P106(f333(f333(x87601,f333(f333(f42(a1),x87604),x87605)),f51(a1,x87604,x87605)))+~E(x87604,f333(f333(f87(a1),f333(f333(f88(a1),x87605),x87602)),x87603))+~P106(f333(f333(f246(a1),f2(a1)),x87603))+~P106(f333(f333(f247(a1),f2(a1)),x87605))+~P106(f333(f333(f247(a1),x87603),x87605)) % 173.51/173.29 [9019]E(x90191,x90192)+~P59(x90193,x90195,x90194)+~P106(f333(f333(f335(x90193),x90192),x90195))+~P106(f333(f333(f335(x90193),x90191),x90195))+P106(f333(f333(f335(f916(x90193,x90193)),f333(f333(f265(x90193,x90193),x90191),x90192)),x90194))+P106(f333(f333(f335(f916(x90193,x90193)),f333(f333(f265(x90193,x90193),x90192),x90191)),x90194)) % 173.51/173.29 [9918]~P72(x99185)+~P86(x99185)+~P106(f333(f67(x99181),x99184))+P106(f333(f333(f246(x99185),f333(f333(f6(x99181,x99185),x99182),x99183)),f333(f333(f6(x99181,x99185),x99182),x99184)))+~P106(f333(f333(f246(f917(x99181,a905)),x99183),x99184))+P106(f333(f333(f335(x99181),f368(x99182,x99183,x99184,x99181,x99185)),f333(f333(f23(f917(x99181,a905)),x99184),x99183))) % 173.51/173.29 [10007]E(x100071,f196(f917(x100072,a905)))+~P106(f333(f67(x100072),x100073))+~P106(f333(f67(x100072),x100071))+P106(f333(f333(f335(f916(f917(x100072,a905),f917(x100072,a905))),f333(f333(f265(f917(x100072,a905),f917(x100072,a905)),x100073),x100071)),f324(x100072,x100074)))+~P106(f333(f333(f335(x100072),x100075),x100071))+~P106(f333(f333(f335(f916(x100072,x100072)),f333(f333(f265(x100072,x100072),f589(x100074,x100071,x100073,x100072)),x100075)),x100074)) % 173.51/173.29 [10008]E(x100081,f196(f917(x100082,a905)))+~P106(f333(f67(x100082),x100083))+~P106(f333(f67(x100082),x100081))+P106(f333(f333(f335(f916(f917(x100082,a905),f917(x100082,a905))),f333(f333(f265(f917(x100082,a905),f917(x100082,a905)),x100083),x100081)),f324(x100082,x100084)))+~P106(f333(f333(f335(x100082),x100085),x100081))+~P106(f333(f333(f335(f916(x100082,x100082)),f333(f333(f265(x100082,x100082),f648(x100084,x100081,x100083,x100082)),x100085)),x100084)) % 173.51/173.29 [10172]~P4(x101721)+~E(f333(f333(f6(x101725,x101721),x101722),x101726),x101724)+~P106(f333(f67(x101725),x101726))+P106(f333(f333(f335(x101725),f371(x101723,x101724,x101722,x101726,x101725,x101721)),x101726))+P106(f333(f333(f246(x101721),f333(x101722,x101723)),x101724))+~P106(f333(f333(f335(x101725),x101723),x101726)) % 173.51/173.29 [10219]~P4(x102191)+~E(f333(f333(f6(x102195,x102191),x102192),x102196),x102194)+~P106(f333(f67(x102195),x102196))+~P106(f333(f333(f335(x102195),x102193),x102196))+~P106(f333(f333(f246(x102191),f2(x102191)),f333(x102192,f371(x102193,x102194,x102192,x102196,x102195,x102191))))+P106(f333(f333(f246(x102191),f333(x102192,x102193)),x102194)) % 173.51/173.29 [10348]~E(x103485,x103488)+~E(x103484,x103487)+~P111(x103481)+~P72(x103482)+E(f333(f333(f6(x103481,x103482),x103483),f333(f308(x103481,x103484),x103485)),f333(f333(f6(x103481,x103482),x103486),f333(f308(x103481,x103487),x103488)))+P106(f333(f333(f246(x103481),x103484),f654(x103483,x103486,x103485,x103488,x103484,x103487,x103481,x103482))) % 173.51/173.29 [10365]~E(x103657,x103654)+~E(x103658,x103655)+~P111(x103651)+~P72(x103652)+~E(f333(x103653,f654(x103656,x103653,x103658,x103655,x103657,x103654,x103651,x103652)),f333(x103656,f654(x103656,x103653,x103658,x103655,x103657,x103654,x103651,x103652)))+E(f333(f333(f6(x103651,x103652),x103653),f333(f308(x103651,x103654),x103655)),f333(f333(f6(x103651,x103652),x103656),f333(f308(x103651,x103657),x103658))) % 173.51/173.29 [10368]~E(x103684,x103687)+~E(x103685,x103688)+~P111(x103681)+~P72(x103682)+E(f333(f333(f6(x103681,x103682),x103683),f333(f308(x103681,x103684),x103685)),f333(f333(f6(x103681,x103682),x103686),f333(f308(x103681,x103687),x103688)))+P106(f333(f333(f247(x103681),f654(x103683,x103686,x103685,x103688,x103684,x103687,x103681,x103682)),x103685)) % 173.51/173.29 [10014]~P11(x100145,x100149,x100146)+~P11(x100141,x1001410,x100143)+~P15(x100141,x100145,f917(x100142,a905),x100143,x100146,x100148)+~P106(f333(f333(f335(x100145),x100147),x100149))+~P106(f333(f333(f335(x100141),x100144),x1001410))+E(f333(f333(f45(x100141,f917(x100142,a905)),f333(f292(x100141,x100141,x100143),f333(f333(f315(x100141),x100144),f196(f917(x100141,a905))))),f333(f333(f8(f917(x100145,f917(x100142,a905)),f917(x100142,a905),x100141),f333(f45(x100145,f917(x100142,a905)),f333(f292(x100145,x100145,x100146),f333(f333(f315(x100145),x100147),f196(f917(x100145,a905)))))),x100148)),f333(f333(x100148,x100144),x100147)) % 173.51/173.29 [5730]~P110(x57303)+~P16(x57303,x57302)+~P16(x57303,x57301)+E(x57301,x57302)+~E(f333(f180(x57303),x57301),f333(f180(x57303),x57302))+~P106(f333(f145(x57303),x57302))+~P106(f333(f145(x57303),x57301)) % 173.51/173.29 [5073]~P145(x50732)+~P128(x50732)+~P129(x50732)+~P115(x50732)+~E(x50733,f2(x50732))+E(x50731,f2(a910))+E(f333(f333(f256(x50732),x50733),x50731),f2(x50732)) % 173.51/173.29 [9295]E(x92951,f2(a910))+~E(x92952,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),x92953)),x92951)),f333(f268(a910,a910),x92953)))+P106(f333(f54(x92952,x92951),x92953))+~P106(f333(f333(f246(a910),f333(f268(a910,a910),x92953)),f2(a910)))+~P106(f333(f333(f246(a910),f2(a910)),f333(f268(a910,a910),x92953)))+~P106(f333(f333(f247(a910),x92951),f333(f268(a910,a910),x92953)))+~P106(f333(f333(f247(a910),f333(f268(a910,a910),x92953)),x92951)) % 173.51/173.29 [9303]~E(f333(f264(a910,a910),x93033),f2(a910))+~E(x93031,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),x93033)),x93032)),f333(f268(a910,a910),x93033)))+P106(f333(f54(x93031,x93032),x93033))+~P106(f333(f333(f246(a910),f333(f268(a910,a910),x93033)),f2(a910)))+~P106(f333(f333(f246(a910),f2(a910)),f333(f268(a910,a910),x93033)))+~P106(f333(f333(f247(a910),x93032),f333(f268(a910,a910),x93033)))+~P106(f333(f333(f247(a910),f333(f268(a910,a910),x93033)),x93032)) % 173.51/173.29 [8114]~P76(x81142)+E(x81141,f196(f917(x81142,a905)))+E(x81143,f196(f917(x81142,a905)))+~P106(f333(f67(x81142),x81141))+~P106(f333(f67(x81142),x81143))+~E(f333(f333(f112(f917(x81142,a905)),x81143),x81141),f196(f917(x81142,a905)))+E(f333(f333(f88(x81142),f333(f69(x81142,f88(x81142)),x81143)),f333(f69(x81142,f88(x81142)),x81141)),f333(f69(x81142,f88(x81142)),f333(f333(f121(f917(x81142,a905)),x81143),x81141))) % 173.51/173.29 [7895]E(x78951,f2(a1))+E(f333(f333(f42(a1),x78952),x78951),x78953)+~P106(f333(f333(f246(a1),x78954),f2(a1)))+~E(x78952,f333(f333(f87(a1),f333(f333(f88(a1),x78951),x78953)),x78954))+~P106(f333(f333(f246(a1),f2(a1)),x78954))+~P106(f333(f333(f247(a1),x78954),x78951))+~P106(f333(f333(f247(a1),x78951),x78954)) % 173.51/173.29 [7903]E(f51(a1,x79032,x79031),x79033)+E(x79031,f2(a1))+~P106(f333(f333(f246(a1),x79033),f2(a1)))+~E(x79032,f333(f333(f87(a1),f333(f333(f88(a1),x79031),x79034)),x79033))+~P106(f333(f333(f246(a1),f2(a1)),x79033))+~P106(f333(f333(f247(a1),x79033),x79031))+~P106(f333(f333(f247(a1),x79031),x79033)) % 173.51/173.29 [7805]~P20(x78052,x78055,x78054)+E(x78051,f196(f917(x78052,a905)))+E(x78053,f196(f917(x78052,a905)))+~P106(f333(f67(x78052),x78051))+~P106(f333(f67(x78052),x78053))+~E(f333(f333(f112(f917(x78052,a905)),x78053),x78051),f196(f917(x78052,a905)))+E(f333(x78054,f333(f333(f121(f917(x78052,a905)),x78053),x78051)),f333(f333(x78055,f333(x78054,x78053)),f333(x78054,x78051))) % 173.51/173.29 [9546]~P27(x95463,x95461,x95465,x95464)+~P27(x95461,x95463,x95466,x95462)+E(f333(f41(x95461),x95462),f333(f41(x95463),x95464))+~P106(f333(f67(x95463),x95464))+~P106(f333(f67(x95461),x95462))+~P106(f333(f333(f246(f917(x95463,a905)),f333(f316(x95461,x95463,x95466),x95462)),x95464))+~P106(f333(f333(f246(f917(x95461,a905)),f333(f316(x95463,x95461,x95465),x95464)),x95462)) % 173.51/173.29 [9490]~P106(f333(f333(f247(a1),f333(f333(f87(a1),f333(f333(f88(a1),x94905),x94901)),x94906)),f2(a1)))+~E(f333(f333(f87(a1),f333(f333(f88(a1),x94903),x94902)),x94904),f333(f333(f87(a1),f333(f333(f88(a1),x94905),x94901)),x94906))+~P106(f333(f333(f246(a1),f2(a1)),x94906))+~P106(f333(f333(f247(a1),f2(a1)),x94905))+~P106(f333(f333(f246(a1),x94905),x94903))+~P106(f333(f333(f247(a1),x94904),x94903))+P106(f333(f333(f246(a1),x94901),x94902)) % 173.51/173.29 [9246]~E(f333(f333(f87(a1),f333(f333(f88(a1),x92463),x92461)),x92464),f333(f333(f87(a1),f333(f333(f88(a1),x92465),x92462)),x92466))+~P106(f333(f333(f246(a1),f2(a1)),x92464))+~P106(f333(f333(f247(a1),f2(a1)),x92465))+~P106(f333(f333(f246(a1),x92465),x92463))+~P106(f333(f333(f247(a1),x92466),x92465))+P106(f333(f333(f246(a1),x92461),x92462))+~P106(f333(f333(f246(a1),f2(a1)),f333(f333(f87(a1),f333(f333(f88(a1),x92465),x92462)),x92466))) % 173.51/173.29 [9425]~P132(x94251)+~E(f333(f333(f87(x94251),x94252),x94254),f85(x94251))+~P106(f333(f333(f246(x94251),x94255),x94256))+~P106(f333(f333(f246(x94251),x94253),x94256))+~P106(f333(f333(f246(x94251),f2(x94251)),x94254))+~P106(f333(f333(f246(x94251),f2(x94251)),x94252))+P106(f333(f333(f246(x94251),f333(f333(f87(x94251),f333(f333(f88(x94251),x94252),x94253)),f333(f333(f88(x94251),x94254),x94255))),x94256)) % 173.51/173.29 [9426]~P133(x94261)+~E(f333(f333(f87(x94261),x94262),x94264),f85(x94261))+~P106(f333(f333(f246(x94261),f2(x94261)),x94264))+~P106(f333(f333(f246(x94261),f2(x94261)),x94262))+~P106(f333(f333(f247(x94261),x94265),x94266))+~P106(f333(f333(f247(x94261),x94263),x94266))+P106(f333(f333(f247(x94261),f333(f333(f87(x94261),f333(f333(f88(x94261),x94262),x94263)),f333(f333(f88(x94261),x94264),x94265))),x94266)) % 173.51/173.29 [10265]~P11(x102657,x102656,x102655)+E(x102651,x102652)+~P14(x102657,f917(x102654,a905),x102655,x102653)+E(f333(x102653,f543(x102651,x102652,x102653,x102654,x102655,x102656,x102657)),f333(x102653,f544(x102651,x102652,x102653,x102654,x102655,x102656,x102657)))+~E(f333(f333(f45(x102657,f917(x102654,a905)),x102651),x102653),f333(f333(f45(x102657,f917(x102654,a905)),x102652),x102653))+~P106(f333(f333(f335(f917(x102657,a905)),x102652),f333(f333(f66(x102657),x102656),x102655)))+~P106(f333(f333(f335(f917(x102657,a905)),x102651),f333(f333(f66(x102657),x102656),x102655))) % 173.51/173.29 [10303]~P11(x103033,x103037,x103036)+E(x103031,x103032)+~P14(x103033,f917(x103035,a905),x103036,x103034)+~E(f333(f333(f45(x103033,f917(x103035,a905)),x103031),x103034),f333(f333(f45(x103033,f917(x103035,a905)),x103032),x103034))+P106(f333(f333(f335(x103033),f544(x103031,x103032,x103034,x103035,x103036,x103037,x103033)),x103037))+~P106(f333(f333(f335(f917(x103033,a905)),x103032),f333(f333(f66(x103033),x103037),x103036)))+~P106(f333(f333(f335(f917(x103033,a905)),x103031),f333(f333(f66(x103033),x103037),x103036))) % 173.51/173.29 [10304]~P11(x103043,x103047,x103046)+E(x103041,x103042)+~P14(x103043,f917(x103045,a905),x103046,x103044)+~E(f333(f333(f45(x103043,f917(x103045,a905)),x103041),x103044),f333(f333(f45(x103043,f917(x103045,a905)),x103042),x103044))+P106(f333(f333(f335(x103043),f543(x103041,x103042,x103044,x103045,x103046,x103047,x103043)),x103047))+~P106(f333(f333(f335(f917(x103043,a905)),x103042),f333(f333(f66(x103043),x103047),x103046)))+~P106(f333(f333(f335(f917(x103043,a905)),x103041),f333(f333(f66(x103043),x103047),x103046))) % 173.51/173.29 [10383]E(x103831,x103832)+~P11(x103833,x103836,x103837)+~P14(x103833,f917(x103834,a905),x103837,x103835)+~E(f333(f333(f45(x103833,f917(x103834,a905)),x103831),x103835),f333(f333(f45(x103833,f917(x103834,a905)),x103832),x103835))+~P106(f333(f333(f335(f916(x103833,x103833)),f333(f333(f265(x103833,x103833),f544(x103831,x103832,x103835,x103834,x103837,x103836,x103833)),f543(x103831,x103832,x103835,x103834,x103837,x103836,x103833))),x103837))+~P106(f333(f333(f335(f917(x103833,a905)),x103832),f333(f333(f66(x103833),x103836),x103837)))+~P106(f333(f333(f335(f917(x103833,a905)),x103831),f333(f333(f66(x103833),x103836),x103837))) % 173.51/173.29 [9245]~P11(x92451,x92457,x92454)+~E(x92455,x92456)+~P106(f333(f333(f335(x92451),x92453),x92456))+~P106(f333(f333(f335(x92451),x92452),x92455))+~P106(f333(f333(f335(f917(x92451,a905)),x92456),f333(f333(f66(x92451),x92457),x92454)))+~P106(f333(f333(f335(f917(x92451,a905)),x92455),f333(f333(f66(x92451),x92457),x92454)))+P106(f333(f333(f335(f916(x92451,x92451)),f333(f333(f265(x92451,x92451),x92452),x92453)),x92454)) % 173.51/173.29 [9379]E(x93791,x93792)+~P11(x93793,x93794,x93795)+~P106(f333(f333(f335(x93793),x93796),x93792))+~P106(f333(f333(f335(x93793),x93797),x93791))+~P106(f333(f333(f335(f917(x93793,a905)),x93792),f333(f333(f66(x93793),x93794),x93795)))+~P106(f333(f333(f335(f917(x93793,a905)),x93791),f333(f333(f66(x93793),x93794),x93795)))+~P106(f333(f333(f335(f916(x93793,x93793)),f333(f333(f265(x93793,x93793),x93797),x93796)),x93795)) % 173.51/173.29 [10404]~P11(x104049,x104048,x104047)+~P11(x104041,x1040411,x1040410)+~P15(x104041,x104049,f917(x104046,a905),x1040410,x104047,x104045)+P106(f333(f333(f335(x104041),f534(x104042,x104043,x104044,x104045,x104046,x104047,x104048,x104049,x1040410,x1040411,x104041)),x1040411))+~P106(f333(f333(f335(f917(x104049,a905)),x104043),f333(f333(f66(x104049),x104048),x104047)))+~P106(f333(f333(f335(f917(x104041,a905)),x104044),f333(f333(f66(x104041),x1040411),x1040410)))+P106(f333(f333(f335(f917(x104046,a905)),f333(f333(f45(x104041,f917(x104046,a905)),x104044),f333(f333(f8(f917(x104049,f917(x104046,a905)),f917(x104046,a905),x104041),f333(f45(x104049,f917(x104046,a905)),x104043)),x104045))),x104042)) % 173.51/173.29 [10405]~P11(x1040511,x1040510,x104059)+~P11(x104051,x104058,x104057)+~P15(x1040511,x104051,f917(x104056,a905),x104059,x104057,x104055)+P106(f333(f333(f335(x104051),f535(x104052,x104053,x104054,x104055,x104056,x104057,x104058,x104051,x104059,x1040510,x1040511)),x104058))+~P106(f333(f333(f335(f917(x1040511,a905)),x104054),f333(f333(f66(x1040511),x1040510),x104059)))+~P106(f333(f333(f335(f917(x104051,a905)),x104053),f333(f333(f66(x104051),x104058),x104057)))+P106(f333(f333(f335(f917(x104056,a905)),f333(f333(f45(x1040511,f917(x104056,a905)),x104054),f333(f333(f8(f917(x104051,f917(x104056,a905)),f917(x104056,a905),x1040511),f333(f45(x104051,f917(x104056,a905)),x104053)),x104055))),x104052)) % 173.51/173.29 [10408]~P11(x104082,x104088,x104089)+~P11(x104084,x1040810,x1040811)+~P15(x104082,x104084,f917(x104081,a905),x104089,x1040811,x104086)+~P106(f333(f333(f335(f917(x104082,a905)),x104083),f333(f333(f66(x104082),x104088),x104089)))+~P106(f333(f333(f335(f917(x104084,a905)),x104085),f333(f333(f66(x104084),x1040810),x1040811)))+~P106(f333(f333(f335(f917(x104081,a905)),f333(f333(x104086,f534(x104087,x104085,x104083,x104086,x104081,x1040811,x1040810,x104084,x104089,x104088,x104082)),f535(x104087,x104085,x104083,x104086,x104081,x1040811,x1040810,x104084,x104089,x104088,x104082))),x104087))+P106(f333(f333(f335(f917(x104081,a905)),f333(f333(f45(x104082,f917(x104081,a905)),x104083),f333(f333(f8(f917(x104084,f917(x104081,a905)),f917(x104081,a905),x104082),f333(f45(x104084,f917(x104081,a905)),x104085)),x104086))),x104087)) % 173.51/173.29 [9281]E(x92811,x92812)+~P110(x92814)+~P27(x92813,x92814,x92815,f333(f333(f121(f917(x92813,a905)),f333(f180(x92813),x92811)),f333(f180(x92813),x92812)))+~E(f333(f180(x92813),x92811),f333(f180(x92813),x92812))+~P16(x92814,f333(f333(f162(x92813,x92814),x92815),x92812))+~P16(x92814,f333(f333(f162(x92813,x92814),x92815),x92811))+~P106(f333(f145(x92814),f333(f333(f162(x92813,x92814),x92815),x92812)))+~P106(f333(f145(x92814),f333(f333(f162(x92813,x92814),x92815),x92811))) % 173.51/173.29 %EqnAxiom % 173.51/173.29 [1]E(x11,x11) % 173.51/173.29 [2]E(x22,x21)+~E(x21,x22) % 173.51/173.29 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 173.51/173.29 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 173.51/173.29 [5]~E(x51,x52)+E(f111(x51),f111(x52)) % 173.51/173.29 [6]~E(x61,x62)+E(f23(x61),f23(x62)) % 173.51/173.29 [7]~E(x71,x72)+E(f196(x71),f196(x72)) % 173.51/173.29 [8]~E(x81,x82)+E(f333(x81,x83),f333(x82,x83)) % 173.51/173.29 [9]~E(x91,x92)+E(f333(x93,x91),f333(x93,x92)) % 173.51/173.29 [10]~E(x101,x102)+E(f29(x101),f29(x102)) % 173.51/173.29 [11]~E(x111,x112)+E(f917(x111,x113),f917(x112,x113)) % 173.51/173.29 [12]~E(x121,x122)+E(f917(x123,x121),f917(x123,x122)) % 173.51/173.29 [13]~E(x131,x132)+E(f112(x131),f112(x132)) % 173.51/173.29 [14]~E(x141,x142)+E(f244(x141),f244(x142)) % 173.51/173.29 [15]~E(x151,x152)+E(f121(x151),f121(x152)) % 173.51/173.29 [16]~E(x161,x162)+E(f245(x161),f245(x162)) % 173.51/173.29 [17]~E(x171,x172)+E(f113(x171),f113(x172)) % 173.51/173.29 [18]~E(x181,x182)+E(f33(x181),f33(x182)) % 173.51/173.29 [19]~E(x191,x192)+E(f91(x191),f91(x192)) % 173.51/173.29 [20]~E(x201,x202)+E(f335(x201),f335(x202)) % 173.51/173.29 [21]~E(x211,x212)+E(f247(x211),f247(x212)) % 173.51/173.29 [22]~E(x221,x222)+E(f535(x221,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f535(x222,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212)) % 173.51/173.29 [23]~E(x231,x232)+E(f535(x233,x231,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f535(x233,x232,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 173.51/173.29 [24]~E(x241,x242)+E(f535(x243,x244,x241,x245,x246,x247,x248,x249,x2410,x2411,x2412),f535(x243,x244,x242,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 173.51/173.29 [25]~E(x251,x252)+E(f535(x253,x254,x255,x251,x256,x257,x258,x259,x2510,x2511,x2512),f535(x253,x254,x255,x252,x256,x257,x258,x259,x2510,x2511,x2512)) % 173.51/173.29 [26]~E(x261,x262)+E(f535(x263,x264,x265,x266,x261,x267,x268,x269,x2610,x2611,x2612),f535(x263,x264,x265,x266,x262,x267,x268,x269,x2610,x2611,x2612)) % 173.51/173.29 [27]~E(x271,x272)+E(f535(x273,x274,x275,x276,x277,x271,x278,x279,x2710,x2711,x2712),f535(x273,x274,x275,x276,x277,x272,x278,x279,x2710,x2711,x2712)) % 173.51/173.29 [28]~E(x281,x282)+E(f535(x283,x284,x285,x286,x287,x288,x281,x289,x2810,x2811,x2812),f535(x283,x284,x285,x286,x287,x288,x282,x289,x2810,x2811,x2812)) % 173.51/173.29 [29]~E(x291,x292)+E(f535(x293,x294,x295,x296,x297,x298,x299,x291,x2910,x2911,x2912),f535(x293,x294,x295,x296,x297,x298,x299,x292,x2910,x2911,x2912)) % 173.51/173.29 [30]~E(x301,x302)+E(f535(x303,x304,x305,x306,x307,x308,x309,x3010,x301,x3011,x3012),f535(x303,x304,x305,x306,x307,x308,x309,x3010,x302,x3011,x3012)) % 173.51/173.29 [31]~E(x311,x312)+E(f535(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x311,x3112),f535(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x312,x3112)) % 173.51/173.29 [32]~E(x321,x322)+E(f535(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x321),f535(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x322)) % 173.51/173.29 [33]~E(x331,x332)+E(f252(x331),f252(x332)) % 173.51/173.29 [34]~E(x341,x342)+E(f85(x341),f85(x342)) % 173.51/173.29 [35]~E(x351,x352)+E(f534(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f534(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512)) % 173.51/173.29 [36]~E(x361,x362)+E(f534(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f534(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 173.51/173.29 [37]~E(x371,x372)+E(f534(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f534(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 173.51/173.29 [38]~E(x381,x382)+E(f534(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f534(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812)) % 173.51/173.29 [39]~E(x391,x392)+E(f534(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f534(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912)) % 173.51/173.29 [40]~E(x401,x402)+E(f534(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f534(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012)) % 173.51/173.29 [41]~E(x411,x412)+E(f534(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f534(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112)) % 173.51/173.29 [42]~E(x421,x422)+E(f534(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f534(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212)) % 173.51/173.29 [43]~E(x431,x432)+E(f534(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f534(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312)) % 173.51/173.29 [44]~E(x441,x442)+E(f534(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f534(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412)) % 173.51/173.29 [45]~E(x451,x452)+E(f534(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f534(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452)) % 173.51/173.29 [46]~E(x461,x462)+E(f4(x461),f4(x462)) % 173.51/173.29 [47]~E(x471,x472)+E(f124(x471),f124(x472)) % 173.51/173.29 [48]~E(x481,x482)+E(f41(x481),f41(x482)) % 173.51/173.29 [49]~E(x491,x492)+E(f122(x491),f122(x492)) % 173.51/173.29 [50]~E(x501,x502)+E(f8(x501,x503,x504),f8(x502,x503,x504)) % 173.51/173.29 [51]~E(x511,x512)+E(f8(x513,x511,x514),f8(x513,x512,x514)) % 173.51/173.29 [52]~E(x521,x522)+E(f8(x523,x524,x521),f8(x523,x524,x522)) % 173.51/173.29 [53]~E(x531,x532)+E(f909(x531),f909(x532)) % 173.51/173.29 [54]~E(x541,x542)+E(f914(x541),f914(x542)) % 173.51/173.29 [55]~E(x551,x552)+E(f911(x551),f911(x552)) % 173.51/173.29 [56]~E(x561,x562)+E(f912(x561),f912(x562)) % 173.51/173.29 [57]~E(x571,x572)+E(f34(x571),f34(x572)) % 173.51/173.29 [58]~E(x581,x582)+E(f36(x581),f36(x582)) % 173.51/173.29 [59]~E(x591,x592)+E(f254(x591),f254(x592)) % 173.51/173.29 [60]~E(x601,x602)+E(f35(x601),f35(x602)) % 173.51/173.29 [61]~E(x611,x612)+E(f87(x611),f87(x612)) % 173.51/173.29 [62]~E(x621,x622)+E(f45(x621,x623),f45(x622,x623)) % 173.51/173.29 [63]~E(x631,x632)+E(f45(x633,x631),f45(x633,x632)) % 173.51/173.29 [64]~E(x641,x642)+E(f86(x641),f86(x642)) % 173.51/173.29 [65]~E(x651,x652)+E(f6(x651,x653),f6(x652,x653)) % 173.51/173.29 [66]~E(x661,x662)+E(f6(x663,x661),f6(x663,x662)) % 173.51/173.29 [67]~E(x671,x672)+E(f197(x671),f197(x672)) % 173.51/173.29 [68]~E(x681,x682)+E(f916(x681,x683),f916(x682,x683)) % 173.51/173.29 [69]~E(x691,x692)+E(f916(x693,x691),f916(x693,x692)) % 173.51/173.29 [70]~E(x701,x702)+E(f114(x701),f114(x702)) % 173.51/173.29 [71]~E(x711,x712)+E(f67(x711),f67(x712)) % 173.51/173.29 [72]~E(x721,x722)+E(f66(x721),f66(x722)) % 173.51/173.29 [73]~E(x731,x732)+E(f172(x731),f172(x732)) % 173.51/173.29 [74]~E(x741,x742)+E(f53(x741,x743),f53(x742,x743)) % 173.51/173.29 [75]~E(x751,x752)+E(f53(x753,x751),f53(x753,x752)) % 173.51/173.29 [76]~E(x761,x762)+E(f630(x761,x763,x764),f630(x762,x763,x764)) % 173.51/173.29 [77]~E(x771,x772)+E(f630(x773,x771,x774),f630(x773,x772,x774)) % 173.51/173.29 [78]~E(x781,x782)+E(f630(x783,x784,x781),f630(x783,x784,x782)) % 173.51/173.29 [79]~E(x791,x792)+E(f18(x791,x793,x794),f18(x792,x793,x794)) % 173.51/173.29 [80]~E(x801,x802)+E(f18(x803,x801,x804),f18(x803,x802,x804)) % 173.51/173.29 [81]~E(x811,x812)+E(f18(x813,x814,x811),f18(x813,x814,x812)) % 173.51/173.29 [82]~E(x821,x822)+E(f279(x821,x823),f279(x822,x823)) % 173.51/173.29 [83]~E(x831,x832)+E(f279(x833,x831),f279(x833,x832)) % 173.51/173.29 [84]~E(x841,x842)+E(f136(x841,x843,x844),f136(x842,x843,x844)) % 173.51/173.29 [85]~E(x851,x852)+E(f136(x853,x851,x854),f136(x853,x852,x854)) % 173.51/173.29 [86]~E(x861,x862)+E(f136(x863,x864,x861),f136(x863,x864,x862)) % 173.51/173.29 [87]~E(x871,x872)+E(f5(x871),f5(x872)) % 173.51/173.29 [88]~E(x881,x882)+E(f145(x881),f145(x882)) % 173.51/173.29 [89]~E(x891,x892)+E(f246(x891),f246(x892)) % 173.51/173.29 [90]~E(x901,x902)+E(f128(x901,x903,x904),f128(x902,x903,x904)) % 173.51/173.29 [91]~E(x911,x912)+E(f128(x913,x911,x914),f128(x913,x912,x914)) % 173.51/173.29 [92]~E(x921,x922)+E(f128(x923,x924,x921),f128(x923,x924,x922)) % 173.51/173.29 [93]~E(x931,x932)+E(f176(x931),f176(x932)) % 173.51/173.29 [94]~E(x941,x942)+E(f88(x941),f88(x942)) % 173.51/173.29 [95]~E(x951,x952)+E(f235(x951,x953,x954,x955,x956),f235(x952,x953,x954,x955,x956)) % 173.51/173.29 [96]~E(x961,x962)+E(f235(x963,x961,x964,x965,x966),f235(x963,x962,x964,x965,x966)) % 173.51/173.29 [97]~E(x971,x972)+E(f235(x973,x974,x971,x975,x976),f235(x973,x974,x972,x975,x976)) % 173.51/173.29 [98]~E(x981,x982)+E(f235(x983,x984,x985,x981,x986),f235(x983,x984,x985,x982,x986)) % 173.51/173.29 [99]~E(x991,x992)+E(f235(x993,x994,x995,x996,x991),f235(x993,x994,x995,x996,x992)) % 173.51/173.29 [100]~E(x1001,x1002)+E(f44(x1001,x1003),f44(x1002,x1003)) % 173.51/173.29 [101]~E(x1011,x1012)+E(f44(x1013,x1011),f44(x1013,x1012)) % 173.51/173.29 [102]~E(x1021,x1022)+E(f260(x1021,x1023),f260(x1022,x1023)) % 173.51/173.29 [103]~E(x1031,x1032)+E(f260(x1033,x1031),f260(x1033,x1032)) % 173.51/173.29 [104]~E(x1041,x1042)+E(f315(x1041),f315(x1042)) % 173.51/173.29 [105]~E(x1051,x1052)+E(f79(x1051,x1053,x1054,x1055),f79(x1052,x1053,x1054,x1055)) % 173.51/173.29 [106]~E(x1061,x1062)+E(f79(x1063,x1061,x1064,x1065),f79(x1063,x1062,x1064,x1065)) % 173.51/173.29 [107]~E(x1071,x1072)+E(f79(x1073,x1074,x1071,x1075),f79(x1073,x1074,x1072,x1075)) % 173.51/173.29 [108]~E(x1081,x1082)+E(f79(x1083,x1084,x1085,x1081),f79(x1083,x1084,x1085,x1082)) % 173.51/173.29 [109]~E(x1091,x1092)+E(f265(x1091,x1093),f265(x1092,x1093)) % 173.51/173.29 [110]~E(x1101,x1102)+E(f265(x1103,x1101),f265(x1103,x1102)) % 173.51/173.29 [111]~E(x1111,x1112)+E(f146(x1111),f146(x1112)) % 173.51/173.29 [112]~E(x1121,x1122)+E(f159(x1121),f159(x1122)) % 173.51/173.29 [113]~E(x1131,x1132)+E(f15(x1131,x1133),f15(x1132,x1133)) % 173.51/173.29 [114]~E(x1141,x1142)+E(f15(x1143,x1141),f15(x1143,x1142)) % 173.51/173.29 [115]~E(x1151,x1152)+E(f165(x1151,x1153),f165(x1152,x1153)) % 173.51/173.29 [116]~E(x1161,x1162)+E(f165(x1163,x1161),f165(x1163,x1162)) % 173.51/173.29 [117]~E(x1171,x1172)+E(f70(x1171,x1173,x1174),f70(x1172,x1173,x1174)) % 173.51/173.29 [118]~E(x1181,x1182)+E(f70(x1183,x1181,x1184),f70(x1183,x1182,x1184)) % 173.51/173.29 [119]~E(x1191,x1192)+E(f70(x1193,x1194,x1191),f70(x1193,x1194,x1192)) % 173.51/173.29 [120]~E(x1201,x1202)+E(f296(x1201),f296(x1202)) % 173.51/173.29 [121]~E(x1211,x1212)+E(f107(x1211),f107(x1212)) % 173.51/173.29 [122]~E(x1221,x1222)+E(f55(x1221,x1223),f55(x1222,x1223)) % 173.51/173.29 [123]~E(x1231,x1232)+E(f55(x1233,x1231),f55(x1233,x1232)) % 173.51/173.29 [124]~E(x1241,x1242)+E(f7(x1241,x1243,x1244),f7(x1242,x1243,x1244)) % 173.51/173.29 [125]~E(x1251,x1252)+E(f7(x1253,x1251,x1254),f7(x1253,x1252,x1254)) % 173.51/173.29 [126]~E(x1261,x1262)+E(f7(x1263,x1264,x1261),f7(x1263,x1264,x1262)) % 173.51/173.29 [127]~E(x1271,x1272)+E(f142(x1271),f142(x1272)) % 173.51/173.29 [128]~E(x1281,x1282)+E(f849(x1281,x1283,x1284),f849(x1282,x1283,x1284)) % 173.51/173.29 [129]~E(x1291,x1292)+E(f849(x1293,x1291,x1294),f849(x1293,x1292,x1294)) % 173.51/173.29 [130]~E(x1301,x1302)+E(f849(x1303,x1304,x1301),f849(x1303,x1304,x1302)) % 173.51/173.29 [131]~E(x1311,x1312)+E(f13(x1311,x1313),f13(x1312,x1313)) % 173.51/173.29 [132]~E(x1321,x1322)+E(f13(x1323,x1321),f13(x1323,x1322)) % 173.51/173.29 [133]~E(x1331,x1332)+E(f256(x1331),f256(x1332)) % 173.51/173.29 [134]~E(x1341,x1342)+E(f177(x1341,x1343,x1344),f177(x1342,x1343,x1344)) % 173.51/173.29 [135]~E(x1351,x1352)+E(f177(x1353,x1351,x1354),f177(x1353,x1352,x1354)) % 173.51/173.29 [136]~E(x1361,x1362)+E(f177(x1363,x1364,x1361),f177(x1363,x1364,x1362)) % 173.51/173.29 [137]~E(x1371,x1372)+E(f185(x1371,x1373,x1374),f185(x1372,x1373,x1374)) % 173.51/173.29 [138]~E(x1381,x1382)+E(f185(x1383,x1381,x1384),f185(x1383,x1382,x1384)) % 173.51/173.29 [139]~E(x1391,x1392)+E(f185(x1393,x1394,x1391),f185(x1393,x1394,x1392)) % 173.51/173.29 [140]~E(x1401,x1402)+E(f12(x1401,x1403,x1404),f12(x1402,x1403,x1404)) % 173.51/173.29 [141]~E(x1411,x1412)+E(f12(x1413,x1411,x1414),f12(x1413,x1412,x1414)) % 173.51/173.29 [142]~E(x1421,x1422)+E(f12(x1423,x1424,x1421),f12(x1423,x1424,x1422)) % 173.51/173.29 [143]~E(x1431,x1432)+E(f876(x1431,x1433,x1434,x1435,x1436,x1437,x1438),f876(x1432,x1433,x1434,x1435,x1436,x1437,x1438)) % 173.51/173.29 [144]~E(x1441,x1442)+E(f876(x1443,x1441,x1444,x1445,x1446,x1447,x1448),f876(x1443,x1442,x1444,x1445,x1446,x1447,x1448)) % 173.51/173.29 [145]~E(x1451,x1452)+E(f876(x1453,x1454,x1451,x1455,x1456,x1457,x1458),f876(x1453,x1454,x1452,x1455,x1456,x1457,x1458)) % 173.51/173.29 [146]~E(x1461,x1462)+E(f876(x1463,x1464,x1465,x1461,x1466,x1467,x1468),f876(x1463,x1464,x1465,x1462,x1466,x1467,x1468)) % 173.51/173.29 [147]~E(x1471,x1472)+E(f876(x1473,x1474,x1475,x1476,x1471,x1477,x1478),f876(x1473,x1474,x1475,x1476,x1472,x1477,x1478)) % 173.51/173.29 [148]~E(x1481,x1482)+E(f876(x1483,x1484,x1485,x1486,x1487,x1481,x1488),f876(x1483,x1484,x1485,x1486,x1487,x1482,x1488)) % 173.51/173.29 [149]~E(x1491,x1492)+E(f876(x1493,x1494,x1495,x1496,x1497,x1498,x1491),f876(x1493,x1494,x1495,x1496,x1497,x1498,x1492)) % 173.51/173.29 [150]~E(x1501,x1502)+E(f743(x1501,x1503),f743(x1502,x1503)) % 173.51/173.29 [151]~E(x1511,x1512)+E(f743(x1513,x1511),f743(x1513,x1512)) % 173.51/173.29 [152]~E(x1521,x1522)+E(f9(x1521,x1523),f9(x1522,x1523)) % 173.51/173.29 [153]~E(x1531,x1532)+E(f9(x1533,x1531),f9(x1533,x1532)) % 173.51/173.29 [154]~E(x1541,x1542)+E(f10(x1541,x1543),f10(x1542,x1543)) % 173.51/173.29 [155]~E(x1551,x1552)+E(f10(x1553,x1551),f10(x1553,x1552)) % 173.51/173.29 [156]~E(x1561,x1562)+E(f116(x1561),f116(x1562)) % 173.51/173.29 [157]~E(x1571,x1572)+E(f117(x1571),f117(x1572)) % 173.51/173.29 [158]~E(x1581,x1582)+E(f334(x1581),f334(x1582)) % 173.51/173.29 [159]~E(x1591,x1592)+E(f81(x1591,x1593,x1594,x1595,x1596),f81(x1592,x1593,x1594,x1595,x1596)) % 173.51/173.29 [160]~E(x1601,x1602)+E(f81(x1603,x1601,x1604,x1605,x1606),f81(x1603,x1602,x1604,x1605,x1606)) % 173.51/173.29 [161]~E(x1611,x1612)+E(f81(x1613,x1614,x1611,x1615,x1616),f81(x1613,x1614,x1612,x1615,x1616)) % 173.51/173.29 [162]~E(x1621,x1622)+E(f81(x1623,x1624,x1625,x1621,x1626),f81(x1623,x1624,x1625,x1622,x1626)) % 173.51/173.29 [163]~E(x1631,x1632)+E(f81(x1633,x1634,x1635,x1636,x1631),f81(x1633,x1634,x1635,x1636,x1632)) % 173.51/173.29 [164]~E(x1641,x1642)+E(f147(x1641,x1643),f147(x1642,x1643)) % 173.51/173.29 [165]~E(x1651,x1652)+E(f147(x1653,x1651),f147(x1653,x1652)) % 173.51/173.29 [166]~E(x1661,x1662)+E(f82(x1661),f82(x1662)) % 173.51/173.29 [167]~E(x1671,x1672)+E(f392(x1671,x1673),f392(x1672,x1673)) % 173.51/173.29 [168]~E(x1681,x1682)+E(f392(x1683,x1681),f392(x1683,x1682)) % 173.51/173.29 [169]~E(x1691,x1692)+E(f51(x1691,x1693,x1694),f51(x1692,x1693,x1694)) % 173.51/173.29 [170]~E(x1701,x1702)+E(f51(x1703,x1701,x1704),f51(x1703,x1702,x1704)) % 173.51/173.29 [171]~E(x1711,x1712)+E(f51(x1713,x1714,x1711),f51(x1713,x1714,x1712)) % 173.51/173.29 [172]~E(x1721,x1722)+E(f308(x1721,x1723),f308(x1722,x1723)) % 173.51/173.29 [173]~E(x1731,x1732)+E(f308(x1733,x1731),f308(x1733,x1732)) % 173.51/173.29 [174]~E(x1741,x1742)+E(f292(x1741,x1743,x1744),f292(x1742,x1743,x1744)) % 173.51/173.29 [175]~E(x1751,x1752)+E(f292(x1753,x1751,x1754),f292(x1753,x1752,x1754)) % 173.51/173.29 [176]~E(x1761,x1762)+E(f292(x1763,x1764,x1761),f292(x1763,x1764,x1762)) % 173.51/173.29 [177]~E(x1771,x1772)+E(f295(x1771,x1773,x1774),f295(x1772,x1773,x1774)) % 173.51/173.29 [178]~E(x1781,x1782)+E(f295(x1783,x1781,x1784),f295(x1783,x1782,x1784)) % 173.51/173.29 [179]~E(x1791,x1792)+E(f295(x1793,x1794,x1791),f295(x1793,x1794,x1792)) % 173.51/173.29 [180]~E(x1801,x1802)+E(f300(x1801,x1803,x1804),f300(x1802,x1803,x1804)) % 173.51/173.29 [181]~E(x1811,x1812)+E(f300(x1813,x1811,x1814),f300(x1813,x1812,x1814)) % 173.51/173.29 [182]~E(x1821,x1822)+E(f300(x1823,x1824,x1821),f300(x1823,x1824,x1822)) % 173.51/173.29 [183]~E(x1831,x1832)+E(f152(x1831,x1833),f152(x1832,x1833)) % 173.51/173.29 [184]~E(x1841,x1842)+E(f152(x1843,x1841),f152(x1843,x1842)) % 173.51/173.29 [185]~E(x1851,x1852)+E(f46(x1851,x1853),f46(x1852,x1853)) % 173.51/173.29 [186]~E(x1861,x1862)+E(f46(x1863,x1861),f46(x1863,x1862)) % 173.51/173.29 [187]~E(x1871,x1872)+E(f310(x1871),f310(x1872)) % 173.51/173.29 [188]~E(x1881,x1882)+E(f98(x1881),f98(x1882)) % 173.51/173.29 [189]~E(x1891,x1892)+E(f144(x1891,x1893),f144(x1892,x1893)) % 173.51/173.29 [190]~E(x1901,x1902)+E(f144(x1903,x1901),f144(x1903,x1902)) % 173.51/173.29 [191]~E(x1911,x1912)+E(f778(x1911,x1913),f778(x1912,x1913)) % 173.51/173.29 [192]~E(x1921,x1922)+E(f778(x1923,x1921),f778(x1923,x1922)) % 173.51/173.29 [193]~E(x1931,x1932)+E(f269(x1931,x1933,x1934),f269(x1932,x1933,x1934)) % 173.51/173.29 [194]~E(x1941,x1942)+E(f269(x1943,x1941,x1944),f269(x1943,x1942,x1944)) % 173.51/173.29 [195]~E(x1951,x1952)+E(f269(x1953,x1954,x1951),f269(x1953,x1954,x1952)) % 173.51/173.29 [196]~E(x1961,x1962)+E(f857(x1961,x1963,x1964),f857(x1962,x1963,x1964)) % 173.51/173.29 [197]~E(x1971,x1972)+E(f857(x1973,x1971,x1974),f857(x1973,x1972,x1974)) % 173.51/173.29 [198]~E(x1981,x1982)+E(f857(x1983,x1984,x1981),f857(x1983,x1984,x1982)) % 173.51/173.29 [199]~E(x1991,x1992)+E(f270(x1991,x1993,x1994,x1995,x1996,x1997),f270(x1992,x1993,x1994,x1995,x1996,x1997)) % 173.51/173.29 [200]~E(x2001,x2002)+E(f270(x2003,x2001,x2004,x2005,x2006,x2007),f270(x2003,x2002,x2004,x2005,x2006,x2007)) % 173.51/173.29 [201]~E(x2011,x2012)+E(f270(x2013,x2014,x2011,x2015,x2016,x2017),f270(x2013,x2014,x2012,x2015,x2016,x2017)) % 173.51/173.29 [202]~E(x2021,x2022)+E(f270(x2023,x2024,x2025,x2021,x2026,x2027),f270(x2023,x2024,x2025,x2022,x2026,x2027)) % 173.51/173.29 [203]~E(x2031,x2032)+E(f270(x2033,x2034,x2035,x2036,x2031,x2037),f270(x2033,x2034,x2035,x2036,x2032,x2037)) % 173.51/173.29 [204]~E(x2041,x2042)+E(f270(x2043,x2044,x2045,x2046,x2047,x2041),f270(x2043,x2044,x2045,x2046,x2047,x2042)) % 173.51/173.29 [205]~E(x2051,x2052)+E(f173(x2051),f173(x2052)) % 173.51/173.29 [206]~E(x2061,x2062)+E(f264(x2061,x2063),f264(x2062,x2063)) % 173.51/173.29 [207]~E(x2071,x2072)+E(f264(x2073,x2071),f264(x2073,x2072)) % 173.51/173.29 [208]~E(x2081,x2082)+E(f150(x2081,x2083,x2084,x2085),f150(x2082,x2083,x2084,x2085)) % 173.51/173.29 [209]~E(x2091,x2092)+E(f150(x2093,x2091,x2094,x2095),f150(x2093,x2092,x2094,x2095)) % 173.51/173.29 [210]~E(x2101,x2102)+E(f150(x2103,x2104,x2101,x2105),f150(x2103,x2104,x2102,x2105)) % 173.51/173.29 [211]~E(x2111,x2112)+E(f150(x2113,x2114,x2115,x2111),f150(x2113,x2114,x2115,x2112)) % 173.51/173.29 [212]~E(x2121,x2122)+E(f267(x2121,x2123),f267(x2122,x2123)) % 173.51/173.29 [213]~E(x2131,x2132)+E(f267(x2133,x2131),f267(x2133,x2132)) % 173.51/173.29 [214]~E(x2141,x2142)+E(f856(x2141,x2143,x2144),f856(x2142,x2143,x2144)) % 173.51/173.29 [215]~E(x2151,x2152)+E(f856(x2153,x2151,x2154),f856(x2153,x2152,x2154)) % 173.51/173.29 [216]~E(x2161,x2162)+E(f856(x2163,x2164,x2161),f856(x2163,x2164,x2162)) % 173.51/173.29 [217]~E(x2171,x2172)+E(f180(x2171),f180(x2172)) % 173.51/173.29 [218]~E(x2181,x2182)+E(f27(x2181,x2183,x2184),f27(x2182,x2183,x2184)) % 173.51/173.29 [219]~E(x2191,x2192)+E(f27(x2193,x2191,x2194),f27(x2193,x2192,x2194)) % 173.51/173.29 [220]~E(x2201,x2202)+E(f27(x2203,x2204,x2201),f27(x2203,x2204,x2202)) % 173.51/173.29 [221]~E(x2211,x2212)+E(f774(x2211,x2213,x2214),f774(x2212,x2213,x2214)) % 173.51/173.29 [222]~E(x2221,x2222)+E(f774(x2223,x2221,x2224),f774(x2223,x2222,x2224)) % 173.51/173.29 [223]~E(x2231,x2232)+E(f774(x2233,x2234,x2231),f774(x2233,x2234,x2232)) % 173.51/173.29 [224]~E(x2241,x2242)+E(f657(x2241,x2243,x2244,x2245,x2246),f657(x2242,x2243,x2244,x2245,x2246)) % 173.51/173.29 [225]~E(x2251,x2252)+E(f657(x2253,x2251,x2254,x2255,x2256),f657(x2253,x2252,x2254,x2255,x2256)) % 173.51/173.29 [226]~E(x2261,x2262)+E(f657(x2263,x2264,x2261,x2265,x2266),f657(x2263,x2264,x2262,x2265,x2266)) % 173.51/173.29 [227]~E(x2271,x2272)+E(f657(x2273,x2274,x2275,x2271,x2276),f657(x2273,x2274,x2275,x2272,x2276)) % 173.51/173.29 [228]~E(x2281,x2282)+E(f657(x2283,x2284,x2285,x2286,x2281),f657(x2283,x2284,x2285,x2286,x2282)) % 173.51/173.29 [229]~E(x2291,x2292)+E(f30(x2291,x2293),f30(x2292,x2293)) % 173.51/173.29 [230]~E(x2301,x2302)+E(f30(x2303,x2301),f30(x2303,x2302)) % 173.51/173.29 [231]~E(x2311,x2312)+E(f263(x2311,x2313),f263(x2312,x2313)) % 173.51/173.29 [232]~E(x2321,x2322)+E(f263(x2323,x2321),f263(x2323,x2322)) % 173.51/173.29 [233]~E(x2331,x2332)+E(f380(x2331,x2333),f380(x2332,x2333)) % 173.51/173.29 [234]~E(x2341,x2342)+E(f380(x2343,x2341),f380(x2343,x2342)) % 173.51/173.29 [235]~E(x2351,x2352)+E(f162(x2351,x2353),f162(x2352,x2353)) % 173.51/173.29 [236]~E(x2361,x2362)+E(f162(x2363,x2361),f162(x2363,x2362)) % 173.51/173.29 [237]~E(x2371,x2372)+E(f322(x2371,x2373),f322(x2372,x2373)) % 173.51/173.29 [238]~E(x2381,x2382)+E(f322(x2383,x2381),f322(x2383,x2382)) % 173.51/173.29 [239]~E(x2391,x2392)+E(f167(x2391,x2393),f167(x2392,x2393)) % 173.51/173.29 [240]~E(x2401,x2402)+E(f167(x2403,x2401),f167(x2403,x2402)) % 173.51/173.29 [241]~E(x2411,x2412)+E(f316(x2411,x2413,x2414),f316(x2412,x2413,x2414)) % 173.51/173.29 [242]~E(x2421,x2422)+E(f316(x2423,x2421,x2424),f316(x2423,x2422,x2424)) % 173.51/173.29 [243]~E(x2431,x2432)+E(f316(x2433,x2434,x2431),f316(x2433,x2434,x2432)) % 173.51/173.29 [244]~E(x2441,x2442)+E(f189(x2441,x2443),f189(x2442,x2443)) % 173.51/173.29 [245]~E(x2451,x2452)+E(f189(x2453,x2451),f189(x2453,x2452)) % 173.51/173.29 [246]~E(x2461,x2462)+E(f402(x2461,x2463),f402(x2462,x2463)) % 173.51/173.29 [247]~E(x2471,x2472)+E(f402(x2473,x2471),f402(x2473,x2472)) % 173.51/173.29 [248]~E(x2481,x2482)+E(f160(x2481,x2483),f160(x2482,x2483)) % 173.51/173.29 [249]~E(x2491,x2492)+E(f160(x2493,x2491),f160(x2493,x2492)) % 173.51/173.29 [250]~E(x2501,x2502)+E(f289(x2501),f289(x2502)) % 173.51/173.29 [251]~E(x2511,x2512)+E(f651(x2511,x2513,x2514,x2515),f651(x2512,x2513,x2514,x2515)) % 173.51/173.29 [252]~E(x2521,x2522)+E(f651(x2523,x2521,x2524,x2525),f651(x2523,x2522,x2524,x2525)) % 173.51/173.29 [253]~E(x2531,x2532)+E(f651(x2533,x2534,x2531,x2535),f651(x2533,x2534,x2532,x2535)) % 173.51/173.29 [254]~E(x2541,x2542)+E(f651(x2543,x2544,x2545,x2541),f651(x2543,x2544,x2545,x2542)) % 173.51/173.29 [255]~E(x2551,x2552)+E(f42(x2551),f42(x2552)) % 173.51/173.29 [256]~E(x2561,x2562)+E(f313(x2561,x2563),f313(x2562,x2563)) % 173.51/173.29 [257]~E(x2571,x2572)+E(f313(x2573,x2571),f313(x2573,x2572)) % 173.51/173.29 [258]~E(x2581,x2582)+E(f125(x2581,x2583),f125(x2582,x2583)) % 173.51/173.29 [259]~E(x2591,x2592)+E(f125(x2593,x2591),f125(x2593,x2592)) % 173.51/173.29 [260]~E(x2601,x2602)+E(f224(x2601),f224(x2602)) % 173.51/173.29 [261]~E(x2611,x2612)+E(f326(x2611,x2613),f326(x2612,x2613)) % 173.51/173.29 [262]~E(x2621,x2622)+E(f326(x2623,x2621),f326(x2623,x2622)) % 173.51/173.29 [263]~E(x2631,x2632)+E(f268(x2631,x2633),f268(x2632,x2633)) % 173.51/173.29 [264]~E(x2641,x2642)+E(f268(x2643,x2641),f268(x2643,x2642)) % 173.51/173.29 [265]~E(x2651,x2652)+E(f314(x2651),f314(x2652)) % 173.51/173.29 [266]~E(x2661,x2662)+E(f199(x2661),f199(x2662)) % 173.51/173.29 [267]~E(x2671,x2672)+E(f712(x2671,x2673),f712(x2672,x2673)) % 173.51/173.29 [268]~E(x2681,x2682)+E(f712(x2683,x2681),f712(x2683,x2682)) % 173.51/173.29 [269]~E(x2691,x2692)+E(f126(x2691),f126(x2692)) % 173.51/173.29 [270]~E(x2701,x2702)+E(f93(x2701,x2703),f93(x2702,x2703)) % 173.51/173.29 [271]~E(x2711,x2712)+E(f93(x2713,x2711),f93(x2713,x2712)) % 173.51/173.29 [272]~E(x2721,x2722)+E(f735(x2721,x2723,x2724),f735(x2722,x2723,x2724)) % 173.51/173.29 [273]~E(x2731,x2732)+E(f735(x2733,x2731,x2734),f735(x2733,x2732,x2734)) % 173.51/173.29 [274]~E(x2741,x2742)+E(f735(x2743,x2744,x2741),f735(x2743,x2744,x2742)) % 173.51/173.29 [275]~E(x2751,x2752)+E(f166(x2751,x2753),f166(x2752,x2753)) % 173.51/173.29 [276]~E(x2761,x2762)+E(f166(x2763,x2761),f166(x2763,x2762)) % 173.51/173.29 [277]~E(x2771,x2772)+E(f508(x2771,x2773,x2774,x2775,x2776),f508(x2772,x2773,x2774,x2775,x2776)) % 173.51/173.29 [278]~E(x2781,x2782)+E(f508(x2783,x2781,x2784,x2785,x2786),f508(x2783,x2782,x2784,x2785,x2786)) % 173.51/173.29 [279]~E(x2791,x2792)+E(f508(x2793,x2794,x2791,x2795,x2796),f508(x2793,x2794,x2792,x2795,x2796)) % 173.51/173.29 [280]~E(x2801,x2802)+E(f508(x2803,x2804,x2805,x2801,x2806),f508(x2803,x2804,x2805,x2802,x2806)) % 173.51/173.29 [281]~E(x2811,x2812)+E(f508(x2813,x2814,x2815,x2816,x2811),f508(x2813,x2814,x2815,x2816,x2812)) % 173.51/173.29 [282]~E(x2821,x2822)+E(f293(x2821,x2823),f293(x2822,x2823)) % 173.51/173.29 [283]~E(x2831,x2832)+E(f293(x2833,x2831),f293(x2833,x2832)) % 173.51/173.29 [284]~E(x2841,x2842)+E(f69(x2841,x2843),f69(x2842,x2843)) % 173.51/173.29 [285]~E(x2851,x2852)+E(f69(x2853,x2851),f69(x2853,x2852)) % 173.51/173.29 [286]~E(x2861,x2862)+E(f541(x2861,x2863,x2864),f541(x2862,x2863,x2864)) % 173.51/173.29 [287]~E(x2871,x2872)+E(f541(x2873,x2871,x2874),f541(x2873,x2872,x2874)) % 173.51/173.29 [288]~E(x2881,x2882)+E(f541(x2883,x2884,x2881),f541(x2883,x2884,x2882)) % 173.51/173.29 [289]~E(x2891,x2892)+E(f43(x2891,x2893),f43(x2892,x2893)) % 173.51/173.29 [290]~E(x2901,x2902)+E(f43(x2903,x2901),f43(x2903,x2902)) % 173.51/173.29 [291]~E(x2911,x2912)+E(f187(x2911,x2913),f187(x2912,x2913)) % 173.51/173.29 [292]~E(x2921,x2922)+E(f187(x2923,x2921),f187(x2923,x2922)) % 173.51/173.29 [293]~E(x2931,x2932)+E(f918(x2931,x2933),f918(x2932,x2933)) % 173.51/173.29 [294]~E(x2941,x2942)+E(f918(x2943,x2941),f918(x2943,x2942)) % 173.51/173.29 [295]~E(x2951,x2952)+E(f915(x2951,x2953),f915(x2952,x2953)) % 173.51/173.29 [296]~E(x2961,x2962)+E(f915(x2963,x2961),f915(x2963,x2962)) % 173.51/173.29 [297]~E(x2971,x2972)+E(f175(x2971),f175(x2972)) % 173.51/173.29 [298]~E(x2981,x2982)+E(f186(x2981,x2983),f186(x2982,x2983)) % 173.51/173.29 [299]~E(x2991,x2992)+E(f186(x2993,x2991),f186(x2993,x2992)) % 173.51/173.29 [300]~E(x3001,x3002)+E(f524(x3001,x3003,x3004,x3005),f524(x3002,x3003,x3004,x3005)) % 173.51/173.29 [301]~E(x3011,x3012)+E(f524(x3013,x3011,x3014,x3015),f524(x3013,x3012,x3014,x3015)) % 173.51/173.29 [302]~E(x3021,x3022)+E(f524(x3023,x3024,x3021,x3025),f524(x3023,x3024,x3022,x3025)) % 173.51/173.29 [303]~E(x3031,x3032)+E(f524(x3033,x3034,x3035,x3031),f524(x3033,x3034,x3035,x3032)) % 173.51/173.29 [304]~E(x3041,x3042)+E(f191(x3041,x3043),f191(x3042,x3043)) % 173.51/173.29 [305]~E(x3051,x3052)+E(f191(x3053,x3051),f191(x3053,x3052)) % 173.51/173.29 [306]~E(x3061,x3062)+E(f179(x3061),f179(x3062)) % 173.51/173.29 [307]~E(x3071,x3072)+E(f512(x3071,x3073,x3074),f512(x3072,x3073,x3074)) % 173.51/173.29 [308]~E(x3081,x3082)+E(f512(x3083,x3081,x3084),f512(x3083,x3082,x3084)) % 173.51/173.29 [309]~E(x3091,x3092)+E(f512(x3093,x3094,x3091),f512(x3093,x3094,x3092)) % 173.51/173.29 [310]~E(x3101,x3102)+E(f672(x3101,x3103,x3104),f672(x3102,x3103,x3104)) % 173.51/173.29 [311]~E(x3111,x3112)+E(f672(x3113,x3111,x3114),f672(x3113,x3112,x3114)) % 173.51/173.29 [312]~E(x3121,x3122)+E(f672(x3123,x3124,x3121),f672(x3123,x3124,x3122)) % 173.51/173.29 [313]~E(x3131,x3132)+E(f156(x3131,x3133,x3134),f156(x3132,x3133,x3134)) % 173.51/173.29 [314]~E(x3141,x3142)+E(f156(x3143,x3141,x3144),f156(x3143,x3142,x3144)) % 173.51/173.29 [315]~E(x3151,x3152)+E(f156(x3153,x3154,x3151),f156(x3153,x3154,x3152)) % 173.51/173.29 [316]~E(x3161,x3162)+E(f321(x3161,x3163),f321(x3162,x3163)) % 173.51/173.29 [317]~E(x3171,x3172)+E(f321(x3173,x3171),f321(x3173,x3172)) % 173.51/173.29 [318]~E(x3181,x3182)+E(f353(x3181,x3183,x3184),f353(x3182,x3183,x3184)) % 173.51/173.29 [319]~E(x3191,x3192)+E(f353(x3193,x3191,x3194),f353(x3193,x3192,x3194)) % 173.51/173.29 [320]~E(x3201,x3202)+E(f353(x3203,x3204,x3201),f353(x3203,x3204,x3202)) % 173.51/173.29 [321]~E(x3211,x3212)+E(f120(x3211),f120(x3212)) % 173.51/173.29 [322]~E(x3221,x3222)+E(f722(x3221,x3223,x3224),f722(x3222,x3223,x3224)) % 173.51/173.29 [323]~E(x3231,x3232)+E(f722(x3233,x3231,x3234),f722(x3233,x3232,x3234)) % 173.51/173.29 [324]~E(x3241,x3242)+E(f722(x3243,x3244,x3241),f722(x3243,x3244,x3242)) % 173.51/173.29 [325]~E(x3251,x3252)+E(f851(x3251,x3253,x3254),f851(x3252,x3253,x3254)) % 173.51/173.29 [326]~E(x3261,x3262)+E(f851(x3263,x3261,x3264),f851(x3263,x3262,x3264)) % 173.51/173.29 [327]~E(x3271,x3272)+E(f851(x3273,x3274,x3271),f851(x3273,x3274,x3272)) % 173.51/173.29 [328]~E(x3281,x3282)+E(f26(x3281,x3283),f26(x3282,x3283)) % 173.51/173.29 [329]~E(x3291,x3292)+E(f26(x3293,x3291),f26(x3293,x3292)) % 173.51/173.29 [330]~E(x3301,x3302)+E(f168(x3301,x3303),f168(x3302,x3303)) % 173.51/173.29 [331]~E(x3311,x3312)+E(f168(x3313,x3311),f168(x3313,x3312)) % 173.51/173.29 [332]~E(x3321,x3322)+E(f99(x3321,x3323,x3324,x3325),f99(x3322,x3323,x3324,x3325)) % 173.51/173.29 [333]~E(x3331,x3332)+E(f99(x3333,x3331,x3334,x3335),f99(x3333,x3332,x3334,x3335)) % 173.51/173.29 [334]~E(x3341,x3342)+E(f99(x3343,x3344,x3341,x3345),f99(x3343,x3344,x3342,x3345)) % 173.51/173.29 [335]~E(x3351,x3352)+E(f99(x3353,x3354,x3355,x3351),f99(x3353,x3354,x3355,x3352)) % 173.51/173.29 [336]~E(x3361,x3362)+E(f667(x3361,x3363,x3364,x3365,x3366,x3367,x3368,x3369),f667(x3362,x3363,x3364,x3365,x3366,x3367,x3368,x3369)) % 173.51/173.29 [337]~E(x3371,x3372)+E(f667(x3373,x3371,x3374,x3375,x3376,x3377,x3378,x3379),f667(x3373,x3372,x3374,x3375,x3376,x3377,x3378,x3379)) % 173.51/173.29 [338]~E(x3381,x3382)+E(f667(x3383,x3384,x3381,x3385,x3386,x3387,x3388,x3389),f667(x3383,x3384,x3382,x3385,x3386,x3387,x3388,x3389)) % 173.51/173.29 [339]~E(x3391,x3392)+E(f667(x3393,x3394,x3395,x3391,x3396,x3397,x3398,x3399),f667(x3393,x3394,x3395,x3392,x3396,x3397,x3398,x3399)) % 173.51/173.29 [340]~E(x3401,x3402)+E(f667(x3403,x3404,x3405,x3406,x3401,x3407,x3408,x3409),f667(x3403,x3404,x3405,x3406,x3402,x3407,x3408,x3409)) % 173.51/173.29 [341]~E(x3411,x3412)+E(f667(x3413,x3414,x3415,x3416,x3417,x3411,x3418,x3419),f667(x3413,x3414,x3415,x3416,x3417,x3412,x3418,x3419)) % 173.51/173.29 [342]~E(x3421,x3422)+E(f667(x3423,x3424,x3425,x3426,x3427,x3428,x3421,x3429),f667(x3423,x3424,x3425,x3426,x3427,x3428,x3422,x3429)) % 173.51/173.29 [343]~E(x3431,x3432)+E(f667(x3433,x3434,x3435,x3436,x3437,x3438,x3439,x3431),f667(x3433,x3434,x3435,x3436,x3437,x3438,x3439,x3432)) % 173.51/173.29 [344]~E(x3441,x3442)+E(f311(x3441,x3443,x3444),f311(x3442,x3443,x3444)) % 173.51/173.29 [345]~E(x3451,x3452)+E(f311(x3453,x3451,x3454),f311(x3453,x3452,x3454)) % 173.51/173.29 [346]~E(x3461,x3462)+E(f311(x3463,x3464,x3461),f311(x3463,x3464,x3462)) % 173.51/173.29 [347]~E(x3471,x3472)+E(f832(x3471,x3473,x3474,x3475,x3476,x3477,x3478),f832(x3472,x3473,x3474,x3475,x3476,x3477,x3478)) % 173.51/173.29 [348]~E(x3481,x3482)+E(f832(x3483,x3481,x3484,x3485,x3486,x3487,x3488),f832(x3483,x3482,x3484,x3485,x3486,x3487,x3488)) % 173.51/173.29 [349]~E(x3491,x3492)+E(f832(x3493,x3494,x3491,x3495,x3496,x3497,x3498),f832(x3493,x3494,x3492,x3495,x3496,x3497,x3498)) % 173.51/173.29 [350]~E(x3501,x3502)+E(f832(x3503,x3504,x3505,x3501,x3506,x3507,x3508),f832(x3503,x3504,x3505,x3502,x3506,x3507,x3508)) % 173.51/173.29 [351]~E(x3511,x3512)+E(f832(x3513,x3514,x3515,x3516,x3511,x3517,x3518),f832(x3513,x3514,x3515,x3516,x3512,x3517,x3518)) % 173.51/173.29 [352]~E(x3521,x3522)+E(f832(x3523,x3524,x3525,x3526,x3527,x3521,x3528),f832(x3523,x3524,x3525,x3526,x3527,x3522,x3528)) % 173.51/173.29 [353]~E(x3531,x3532)+E(f832(x3533,x3534,x3535,x3536,x3537,x3538,x3531),f832(x3533,x3534,x3535,x3536,x3537,x3538,x3532)) % 173.51/173.29 [354]~E(x3541,x3542)+E(f309(x3541,x3543,x3544),f309(x3542,x3543,x3544)) % 173.51/173.29 [355]~E(x3551,x3552)+E(f309(x3553,x3551,x3554),f309(x3553,x3552,x3554)) % 173.51/173.29 [356]~E(x3561,x3562)+E(f309(x3563,x3564,x3561),f309(x3563,x3564,x3562)) % 173.51/173.29 [357]~E(x3571,x3572)+E(f324(x3571,x3573),f324(x3572,x3573)) % 173.51/173.29 [358]~E(x3581,x3582)+E(f324(x3583,x3581),f324(x3583,x3582)) % 173.51/173.29 [359]~E(x3591,x3592)+E(f16(x3591,x3593),f16(x3592,x3593)) % 173.51/173.29 [360]~E(x3601,x3602)+E(f16(x3603,x3601),f16(x3603,x3602)) % 173.51/173.29 [361]~E(x3611,x3612)+E(f648(x3611,x3613,x3614,x3615),f648(x3612,x3613,x3614,x3615)) % 173.51/173.29 [362]~E(x3621,x3622)+E(f648(x3623,x3621,x3624,x3625),f648(x3623,x3622,x3624,x3625)) % 173.51/173.29 [363]~E(x3631,x3632)+E(f648(x3633,x3634,x3631,x3635),f648(x3633,x3634,x3632,x3635)) % 173.51/173.29 [364]~E(x3641,x3642)+E(f648(x3643,x3644,x3645,x3641),f648(x3643,x3644,x3645,x3642)) % 173.51/173.29 [365]~E(x3651,x3652)+E(f484(x3651,x3653,x3654,x3655,x3656),f484(x3652,x3653,x3654,x3655,x3656)) % 173.51/173.29 [366]~E(x3661,x3662)+E(f484(x3663,x3661,x3664,x3665,x3666),f484(x3663,x3662,x3664,x3665,x3666)) % 173.51/173.29 [367]~E(x3671,x3672)+E(f484(x3673,x3674,x3671,x3675,x3676),f484(x3673,x3674,x3672,x3675,x3676)) % 173.51/173.29 [368]~E(x3681,x3682)+E(f484(x3683,x3684,x3685,x3681,x3686),f484(x3683,x3684,x3685,x3682,x3686)) % 173.51/173.29 [369]~E(x3691,x3692)+E(f484(x3693,x3694,x3695,x3696,x3691),f484(x3693,x3694,x3695,x3696,x3692)) % 173.51/173.29 [370]~E(x3701,x3702)+E(f759(x3701,x3703,x3704),f759(x3702,x3703,x3704)) % 173.51/173.29 [371]~E(x3711,x3712)+E(f759(x3713,x3711,x3714),f759(x3713,x3712,x3714)) % 173.51/173.29 [372]~E(x3721,x3722)+E(f759(x3723,x3724,x3721),f759(x3723,x3724,x3722)) % 173.51/173.29 [373]~E(x3731,x3732)+E(f464(x3731,x3733,x3734),f464(x3732,x3733,x3734)) % 173.51/173.29 [374]~E(x3741,x3742)+E(f464(x3743,x3741,x3744),f464(x3743,x3742,x3744)) % 173.51/173.29 [375]~E(x3751,x3752)+E(f464(x3753,x3754,x3751),f464(x3753,x3754,x3752)) % 173.51/173.29 [376]~E(x3761,x3762)+E(f183(x3761),f183(x3762)) % 173.51/173.29 [377]~E(x3771,x3772)+E(f52(x3771,x3773),f52(x3772,x3773)) % 173.51/173.29 [378]~E(x3781,x3782)+E(f52(x3783,x3781),f52(x3783,x3782)) % 173.51/173.29 [379]~E(x3791,x3792)+E(f568(x3791),f568(x3792)) % 173.51/173.29 [380]~E(x3801,x3802)+E(f850(x3801,x3803,x3804),f850(x3802,x3803,x3804)) % 173.51/173.29 [381]~E(x3811,x3812)+E(f850(x3813,x3811,x3814),f850(x3813,x3812,x3814)) % 173.51/173.29 [382]~E(x3821,x3822)+E(f850(x3823,x3824,x3821),f850(x3823,x3824,x3822)) % 173.51/173.29 [383]~E(x3831,x3832)+E(f855(x3831,x3833,x3834),f855(x3832,x3833,x3834)) % 173.51/173.29 [384]~E(x3841,x3842)+E(f855(x3843,x3841,x3844),f855(x3843,x3842,x3844)) % 173.51/173.29 [385]~E(x3851,x3852)+E(f855(x3853,x3854,x3851),f855(x3853,x3854,x3852)) % 173.51/173.29 [386]~E(x3861,x3862)+E(f509(x3861,x3863,x3864,x3865,x3866,x3867,x3868,x3869),f509(x3862,x3863,x3864,x3865,x3866,x3867,x3868,x3869)) % 173.51/173.29 [387]~E(x3871,x3872)+E(f509(x3873,x3871,x3874,x3875,x3876,x3877,x3878,x3879),f509(x3873,x3872,x3874,x3875,x3876,x3877,x3878,x3879)) % 173.51/173.29 [388]~E(x3881,x3882)+E(f509(x3883,x3884,x3881,x3885,x3886,x3887,x3888,x3889),f509(x3883,x3884,x3882,x3885,x3886,x3887,x3888,x3889)) % 173.51/173.29 [389]~E(x3891,x3892)+E(f509(x3893,x3894,x3895,x3891,x3896,x3897,x3898,x3899),f509(x3893,x3894,x3895,x3892,x3896,x3897,x3898,x3899)) % 173.51/173.29 [390]~E(x3901,x3902)+E(f509(x3903,x3904,x3905,x3906,x3901,x3907,x3908,x3909),f509(x3903,x3904,x3905,x3906,x3902,x3907,x3908,x3909)) % 173.51/173.29 [391]~E(x3911,x3912)+E(f509(x3913,x3914,x3915,x3916,x3917,x3911,x3918,x3919),f509(x3913,x3914,x3915,x3916,x3917,x3912,x3918,x3919)) % 173.51/173.29 [392]~E(x3921,x3922)+E(f509(x3923,x3924,x3925,x3926,x3927,x3928,x3921,x3929),f509(x3923,x3924,x3925,x3926,x3927,x3928,x3922,x3929)) % 173.51/173.29 [393]~E(x3931,x3932)+E(f509(x3933,x3934,x3935,x3936,x3937,x3938,x3939,x3931),f509(x3933,x3934,x3935,x3936,x3937,x3938,x3939,x3932)) % 173.51/173.29 [394]~E(x3941,x3942)+E(f291(x3941,x3943),f291(x3942,x3943)) % 173.51/173.29 [395]~E(x3951,x3952)+E(f291(x3953,x3951),f291(x3953,x3952)) % 173.51/173.29 [396]~E(x3961,x3962)+E(f811(x3961,x3963,x3964),f811(x3962,x3963,x3964)) % 173.51/173.29 [397]~E(x3971,x3972)+E(f811(x3973,x3971,x3974),f811(x3973,x3972,x3974)) % 173.51/173.29 [398]~E(x3981,x3982)+E(f811(x3983,x3984,x3981),f811(x3983,x3984,x3982)) % 173.51/173.29 [399]~E(x3991,x3992)+E(f158(x3991,x3993,x3994,x3995),f158(x3992,x3993,x3994,x3995)) % 173.51/173.29 [400]~E(x4001,x4002)+E(f158(x4003,x4001,x4004,x4005),f158(x4003,x4002,x4004,x4005)) % 173.51/173.29 [401]~E(x4011,x4012)+E(f158(x4013,x4014,x4011,x4015),f158(x4013,x4014,x4012,x4015)) % 173.51/173.29 [402]~E(x4021,x4022)+E(f158(x4023,x4024,x4025,x4021),f158(x4023,x4024,x4025,x4022)) % 173.51/173.29 [403]~E(x4031,x4032)+E(f827(x4031,x4033,x4034,x4035),f827(x4032,x4033,x4034,x4035)) % 173.51/173.29 [404]~E(x4041,x4042)+E(f827(x4043,x4041,x4044,x4045),f827(x4043,x4042,x4044,x4045)) % 173.51/173.29 [405]~E(x4051,x4052)+E(f827(x4053,x4054,x4051,x4055),f827(x4053,x4054,x4052,x4055)) % 173.51/173.29 [406]~E(x4061,x4062)+E(f827(x4063,x4064,x4065,x4061),f827(x4063,x4064,x4065,x4062)) % 173.51/173.29 [407]~E(x4071,x4072)+E(f727(x4071,x4073,x4074,x4075,x4076),f727(x4072,x4073,x4074,x4075,x4076)) % 173.51/173.29 [408]~E(x4081,x4082)+E(f727(x4083,x4081,x4084,x4085,x4086),f727(x4083,x4082,x4084,x4085,x4086)) % 173.51/173.29 [409]~E(x4091,x4092)+E(f727(x4093,x4094,x4091,x4095,x4096),f727(x4093,x4094,x4092,x4095,x4096)) % 173.51/173.29 [410]~E(x4101,x4102)+E(f727(x4103,x4104,x4105,x4101,x4106),f727(x4103,x4104,x4105,x4102,x4106)) % 173.51/173.29 [411]~E(x4111,x4112)+E(f727(x4113,x4114,x4115,x4116,x4111),f727(x4113,x4114,x4115,x4116,x4112)) % 173.51/173.29 [412]~E(x4121,x4122)+E(f319(x4121,x4123,x4124,x4125),f319(x4122,x4123,x4124,x4125)) % 173.51/173.29 [413]~E(x4131,x4132)+E(f319(x4133,x4131,x4134,x4135),f319(x4133,x4132,x4134,x4135)) % 173.51/173.29 [414]~E(x4141,x4142)+E(f319(x4143,x4144,x4141,x4145),f319(x4143,x4144,x4142,x4145)) % 173.51/173.29 [415]~E(x4151,x4152)+E(f319(x4153,x4154,x4155,x4151),f319(x4153,x4154,x4155,x4152)) % 173.51/173.29 [416]~E(x4161,x4162)+E(f730(x4161,x4163,x4164,x4165),f730(x4162,x4163,x4164,x4165)) % 173.51/173.29 [417]~E(x4171,x4172)+E(f730(x4173,x4171,x4174,x4175),f730(x4173,x4172,x4174,x4175)) % 173.51/173.29 [418]~E(x4181,x4182)+E(f730(x4183,x4184,x4181,x4185),f730(x4183,x4184,x4182,x4185)) % 173.51/173.29 [419]~E(x4191,x4192)+E(f730(x4193,x4194,x4195,x4191),f730(x4193,x4194,x4195,x4192)) % 173.51/173.29 [420]~E(x4201,x4202)+E(f92(x4201,x4203),f92(x4202,x4203)) % 173.51/173.29 [421]~E(x4211,x4212)+E(f92(x4213,x4211),f92(x4213,x4212)) % 173.51/173.29 [422]~E(x4221,x4222)+E(f733(x4221,x4223,x4224,x4225,x4226),f733(x4222,x4223,x4224,x4225,x4226)) % 173.51/173.29 [423]~E(x4231,x4232)+E(f733(x4233,x4231,x4234,x4235,x4236),f733(x4233,x4232,x4234,x4235,x4236)) % 173.51/173.29 [424]~E(x4241,x4242)+E(f733(x4243,x4244,x4241,x4245,x4246),f733(x4243,x4244,x4242,x4245,x4246)) % 173.51/173.29 [425]~E(x4251,x4252)+E(f733(x4253,x4254,x4255,x4251,x4256),f733(x4253,x4254,x4255,x4252,x4256)) % 173.51/173.29 [426]~E(x4261,x4262)+E(f733(x4263,x4264,x4265,x4266,x4261),f733(x4263,x4264,x4265,x4266,x4262)) % 173.51/173.29 [427]~E(x4271,x4272)+E(f97(x4271,x4273),f97(x4272,x4273)) % 173.51/173.29 [428]~E(x4281,x4282)+E(f97(x4283,x4281),f97(x4283,x4282)) % 173.51/173.29 [429]~E(x4291,x4292)+E(f54(x4291,x4293),f54(x4292,x4293)) % 173.51/173.29 [430]~E(x4301,x4302)+E(f54(x4303,x4301),f54(x4303,x4302)) % 173.51/173.29 [431]~E(x4311,x4312)+E(f161(x4311,x4313),f161(x4312,x4313)) % 173.51/173.29 [432]~E(x4321,x4322)+E(f161(x4323,x4321),f161(x4323,x4322)) % 173.51/173.29 [433]~E(x4331,x4332)+E(f253(x4331,x4333),f253(x4332,x4333)) % 173.51/173.29 [434]~E(x4341,x4342)+E(f253(x4343,x4341),f253(x4343,x4342)) % 173.51/173.29 [435]~E(x4351,x4352)+E(f153(x4351,x4353),f153(x4352,x4353)) % 173.51/173.29 [436]~E(x4361,x4362)+E(f153(x4363,x4361),f153(x4363,x4362)) % 173.51/173.29 [437]~E(x4371,x4372)+E(f61(x4371,x4373,x4374),f61(x4372,x4373,x4374)) % 173.51/173.29 [438]~E(x4381,x4382)+E(f61(x4383,x4381,x4384),f61(x4383,x4382,x4384)) % 173.51/173.29 [439]~E(x4391,x4392)+E(f61(x4393,x4394,x4391),f61(x4393,x4394,x4392)) % 173.51/173.29 [440]~E(x4401,x4402)+E(f94(x4401),f94(x4402)) % 173.51/173.29 [441]~E(x4411,x4412)+E(f409(x4411,x4413,x4414,x4415),f409(x4412,x4413,x4414,x4415)) % 173.51/173.29 [442]~E(x4421,x4422)+E(f409(x4423,x4421,x4424,x4425),f409(x4423,x4422,x4424,x4425)) % 173.51/173.29 [443]~E(x4431,x4432)+E(f409(x4433,x4434,x4431,x4435),f409(x4433,x4434,x4432,x4435)) % 173.51/173.29 [444]~E(x4441,x4442)+E(f409(x4443,x4444,x4445,x4441),f409(x4443,x4444,x4445,x4442)) % 173.51/173.29 [445]~E(x4451,x4452)+E(f285(x4451),f285(x4452)) % 173.51/173.29 [446]~E(x4461,x4462)+E(f72(x4461,x4463,x4464,x4465,x4466),f72(x4462,x4463,x4464,x4465,x4466)) % 173.51/173.29 [447]~E(x4471,x4472)+E(f72(x4473,x4471,x4474,x4475,x4476),f72(x4473,x4472,x4474,x4475,x4476)) % 173.51/173.29 [448]~E(x4481,x4482)+E(f72(x4483,x4484,x4481,x4485,x4486),f72(x4483,x4484,x4482,x4485,x4486)) % 173.51/173.29 [449]~E(x4491,x4492)+E(f72(x4493,x4494,x4495,x4491,x4496),f72(x4493,x4494,x4495,x4492,x4496)) % 173.51/173.29 [450]~E(x4501,x4502)+E(f72(x4503,x4504,x4505,x4506,x4501),f72(x4503,x4504,x4505,x4506,x4502)) % 173.51/173.29 [451]~E(x4511,x4512)+E(f564(x4511,x4513,x4514,x4515),f564(x4512,x4513,x4514,x4515)) % 173.51/173.29 [452]~E(x4521,x4522)+E(f564(x4523,x4521,x4524,x4525),f564(x4523,x4522,x4524,x4525)) % 173.51/173.29 [453]~E(x4531,x4532)+E(f564(x4533,x4534,x4531,x4535),f564(x4533,x4534,x4532,x4535)) % 173.51/173.29 [454]~E(x4541,x4542)+E(f564(x4543,x4544,x4545,x4541),f564(x4543,x4544,x4545,x4542)) % 173.51/173.29 [455]~E(x4551,x4552)+E(f232(x4551,x4553,x4554,x4555),f232(x4552,x4553,x4554,x4555)) % 173.51/173.29 [456]~E(x4561,x4562)+E(f232(x4563,x4561,x4564,x4565),f232(x4563,x4562,x4564,x4565)) % 173.51/173.29 [457]~E(x4571,x4572)+E(f232(x4573,x4574,x4571,x4575),f232(x4573,x4574,x4572,x4575)) % 173.51/173.29 [458]~E(x4581,x4582)+E(f232(x4583,x4584,x4585,x4581),f232(x4583,x4584,x4585,x4582)) % 173.51/173.29 [459]~E(x4591,x4592)+E(f389(x4591,x4593,x4594),f389(x4592,x4593,x4594)) % 173.51/173.29 [460]~E(x4601,x4602)+E(f389(x4603,x4601,x4604),f389(x4603,x4602,x4604)) % 173.51/173.29 [461]~E(x4611,x4612)+E(f389(x4613,x4614,x4611),f389(x4613,x4614,x4612)) % 173.51/173.29 [462]~E(x4621,x4622)+E(f339(x4621,x4623,x4624),f339(x4622,x4623,x4624)) % 173.51/173.29 [463]~E(x4631,x4632)+E(f339(x4633,x4631,x4634),f339(x4633,x4632,x4634)) % 173.51/173.29 [464]~E(x4641,x4642)+E(f339(x4643,x4644,x4641),f339(x4643,x4644,x4642)) % 173.51/173.29 [465]~E(x4651,x4652)+E(f130(x4651),f130(x4652)) % 173.51/173.29 [466]~E(x4661,x4662)+E(f782(x4661,x4663,x4664,x4665,x4666,x4667),f782(x4662,x4663,x4664,x4665,x4666,x4667)) % 173.51/173.29 [467]~E(x4671,x4672)+E(f782(x4673,x4671,x4674,x4675,x4676,x4677),f782(x4673,x4672,x4674,x4675,x4676,x4677)) % 173.51/173.29 [468]~E(x4681,x4682)+E(f782(x4683,x4684,x4681,x4685,x4686,x4687),f782(x4683,x4684,x4682,x4685,x4686,x4687)) % 173.51/173.29 [469]~E(x4691,x4692)+E(f782(x4693,x4694,x4695,x4691,x4696,x4697),f782(x4693,x4694,x4695,x4692,x4696,x4697)) % 173.51/173.29 [470]~E(x4701,x4702)+E(f782(x4703,x4704,x4705,x4706,x4701,x4707),f782(x4703,x4704,x4705,x4706,x4702,x4707)) % 173.51/173.29 [471]~E(x4711,x4712)+E(f782(x4713,x4714,x4715,x4716,x4717,x4711),f782(x4713,x4714,x4715,x4716,x4717,x4712)) % 173.51/173.29 [472]~E(x4721,x4722)+E(f266(x4721,x4723,x4724,x4725,x4726),f266(x4722,x4723,x4724,x4725,x4726)) % 173.51/173.29 [473]~E(x4731,x4732)+E(f266(x4733,x4731,x4734,x4735,x4736),f266(x4733,x4732,x4734,x4735,x4736)) % 173.51/173.29 [474]~E(x4741,x4742)+E(f266(x4743,x4744,x4741,x4745,x4746),f266(x4743,x4744,x4742,x4745,x4746)) % 173.51/173.29 [475]~E(x4751,x4752)+E(f266(x4753,x4754,x4755,x4751,x4756),f266(x4753,x4754,x4755,x4752,x4756)) % 173.51/173.29 [476]~E(x4761,x4762)+E(f266(x4763,x4764,x4765,x4766,x4761),f266(x4763,x4764,x4765,x4766,x4762)) % 173.51/173.29 [477]~E(x4771,x4772)+E(f668(x4771,x4773,x4774),f668(x4772,x4773,x4774)) % 173.51/173.29 [478]~E(x4781,x4782)+E(f668(x4783,x4781,x4784),f668(x4783,x4782,x4784)) % 173.51/173.29 [479]~E(x4791,x4792)+E(f668(x4793,x4794,x4791),f668(x4793,x4794,x4792)) % 173.51/173.29 [480]~E(x4801,x4802)+E(f589(x4801,x4803,x4804,x4805),f589(x4802,x4803,x4804,x4805)) % 173.51/173.29 [481]~E(x4811,x4812)+E(f589(x4813,x4811,x4814,x4815),f589(x4813,x4812,x4814,x4815)) % 173.51/173.29 [482]~E(x4821,x4822)+E(f589(x4823,x4824,x4821,x4825),f589(x4823,x4824,x4822,x4825)) % 173.51/173.29 [483]~E(x4831,x4832)+E(f589(x4833,x4834,x4835,x4831),f589(x4833,x4834,x4835,x4832)) % 173.51/173.29 [484]~E(x4841,x4842)+E(f662(x4841,x4843,x4844,x4845),f662(x4842,x4843,x4844,x4845)) % 173.51/173.29 [485]~E(x4851,x4852)+E(f662(x4853,x4851,x4854,x4855),f662(x4853,x4852,x4854,x4855)) % 173.51/173.29 [486]~E(x4861,x4862)+E(f662(x4863,x4864,x4861,x4865),f662(x4863,x4864,x4862,x4865)) % 173.51/173.29 [487]~E(x4871,x4872)+E(f662(x4873,x4874,x4875,x4871),f662(x4873,x4874,x4875,x4872)) % 173.51/173.29 [488]~E(x4881,x4882)+E(f694(x4881,x4883,x4884,x4885),f694(x4882,x4883,x4884,x4885)) % 173.51/173.29 [489]~E(x4891,x4892)+E(f694(x4893,x4891,x4894,x4895),f694(x4893,x4892,x4894,x4895)) % 173.51/173.29 [490]~E(x4901,x4902)+E(f694(x4903,x4904,x4901,x4905),f694(x4903,x4904,x4902,x4905)) % 173.51/173.29 [491]~E(x4911,x4912)+E(f694(x4913,x4914,x4915,x4911),f694(x4913,x4914,x4915,x4912)) % 173.51/173.29 [492]~E(x4921,x4922)+E(f14(x4921,x4923),f14(x4922,x4923)) % 173.51/173.29 [493]~E(x4931,x4932)+E(f14(x4933,x4931),f14(x4933,x4932)) % 173.51/173.29 [494]~E(x4941,x4942)+E(f206(x4941,x4943),f206(x4942,x4943)) % 173.51/173.29 [495]~E(x4951,x4952)+E(f206(x4953,x4951),f206(x4953,x4952)) % 173.51/173.29 [496]~E(x4961,x4962)+E(f729(x4961,x4963,x4964,x4965),f729(x4962,x4963,x4964,x4965)) % 173.51/173.29 [497]~E(x4971,x4972)+E(f729(x4973,x4971,x4974,x4975),f729(x4973,x4972,x4974,x4975)) % 173.51/173.29 [498]~E(x4981,x4982)+E(f729(x4983,x4984,x4981,x4985),f729(x4983,x4984,x4982,x4985)) % 173.51/173.29 [499]~E(x4991,x4992)+E(f729(x4993,x4994,x4995,x4991),f729(x4993,x4994,x4995,x4992)) % 173.51/173.29 [500]~E(x5001,x5002)+E(f403(x5001,x5003),f403(x5002,x5003)) % 173.51/173.29 [501]~E(x5011,x5012)+E(f403(x5013,x5011),f403(x5013,x5012)) % 173.51/173.29 [502]~E(x5021,x5022)+E(f810(x5021,x5023,x5024),f810(x5022,x5023,x5024)) % 173.51/173.29 [503]~E(x5031,x5032)+E(f810(x5033,x5031,x5034),f810(x5033,x5032,x5034)) % 173.51/173.29 [504]~E(x5041,x5042)+E(f810(x5043,x5044,x5041),f810(x5043,x5044,x5042)) % 173.51/173.29 [505]~E(x5051,x5052)+E(f317(x5051,x5053,x5054),f317(x5052,x5053,x5054)) % 173.51/173.29 [506]~E(x5061,x5062)+E(f317(x5063,x5061,x5064),f317(x5063,x5062,x5064)) % 173.51/173.29 [507]~E(x5071,x5072)+E(f317(x5073,x5074,x5071),f317(x5073,x5074,x5072)) % 173.51/173.29 [508]~E(x5081,x5082)+E(f169(x5081,x5083),f169(x5082,x5083)) % 173.51/173.29 [509]~E(x5091,x5092)+E(f169(x5093,x5091),f169(x5093,x5092)) % 173.51/173.29 [510]~E(x5101,x5102)+E(f829(x5101,x5103,x5104,x5105),f829(x5102,x5103,x5104,x5105)) % 173.51/173.29 [511]~E(x5111,x5112)+E(f829(x5113,x5111,x5114,x5115),f829(x5113,x5112,x5114,x5115)) % 173.51/173.29 [512]~E(x5121,x5122)+E(f829(x5123,x5124,x5121,x5125),f829(x5123,x5124,x5122,x5125)) % 173.51/173.29 [513]~E(x5131,x5132)+E(f829(x5133,x5134,x5135,x5131),f829(x5133,x5134,x5135,x5132)) % 173.51/173.29 [514]~E(x5141,x5142)+E(f449(x5141,x5143),f449(x5142,x5143)) % 173.51/173.29 [515]~E(x5151,x5152)+E(f449(x5153,x5151),f449(x5153,x5152)) % 173.51/173.29 [516]~E(x5161,x5162)+E(f830(x5161,x5163,x5164,x5165),f830(x5162,x5163,x5164,x5165)) % 173.51/173.29 [517]~E(x5171,x5172)+E(f830(x5173,x5171,x5174,x5175),f830(x5173,x5172,x5174,x5175)) % 173.51/173.29 [518]~E(x5181,x5182)+E(f830(x5183,x5184,x5181,x5185),f830(x5183,x5184,x5182,x5185)) % 173.51/173.29 [519]~E(x5191,x5192)+E(f830(x5193,x5194,x5195,x5191),f830(x5193,x5194,x5195,x5192)) % 173.51/173.29 [520]~E(x5201,x5202)+E(f290(x5201),f290(x5202)) % 173.51/173.29 [521]~E(x5211,x5212)+E(f320(x5211),f320(x5212)) % 173.51/173.29 [522]~E(x5221,x5222)+E(f28(x5221,x5223,x5224),f28(x5222,x5223,x5224)) % 173.51/173.29 [523]~E(x5231,x5232)+E(f28(x5233,x5231,x5234),f28(x5233,x5232,x5234)) % 173.51/173.29 [524]~E(x5241,x5242)+E(f28(x5243,x5244,x5241),f28(x5243,x5244,x5242)) % 173.51/173.29 [525]~E(x5251,x5252)+E(f379(x5251,x5253),f379(x5252,x5253)) % 173.51/173.29 [526]~E(x5261,x5262)+E(f379(x5263,x5261),f379(x5263,x5262)) % 173.51/173.29 [527]~E(x5271,x5272)+E(f182(x5271,x5273,x5274),f182(x5272,x5273,x5274)) % 173.51/173.29 [528]~E(x5281,x5282)+E(f182(x5283,x5281,x5284),f182(x5283,x5282,x5284)) % 173.51/173.29 [529]~E(x5291,x5292)+E(f182(x5293,x5294,x5291),f182(x5293,x5294,x5292)) % 173.51/173.29 [530]~E(x5301,x5302)+E(f49(x5301),f49(x5302)) % 173.51/173.29 [531]~E(x5311,x5312)+E(f669(x5311,x5313,x5314),f669(x5312,x5313,x5314)) % 173.51/173.29 [532]~E(x5321,x5322)+E(f669(x5323,x5321,x5324),f669(x5323,x5322,x5324)) % 173.51/173.29 [533]~E(x5331,x5332)+E(f669(x5333,x5334,x5331),f669(x5333,x5334,x5332)) % 173.51/173.29 [534]~E(x5341,x5342)+E(f567(x5341,x5343,x5344),f567(x5342,x5343,x5344)) % 173.51/173.29 [535]~E(x5351,x5352)+E(f567(x5353,x5351,x5354),f567(x5353,x5352,x5354)) % 173.51/173.29 [536]~E(x5361,x5362)+E(f567(x5363,x5364,x5361),f567(x5363,x5364,x5362)) % 173.51/173.29 [537]~E(x5371,x5372)+E(f443(x5371),f443(x5372)) % 173.51/173.29 [538]~E(x5381,x5382)+E(f550(x5381,x5383,x5384),f550(x5382,x5383,x5384)) % 173.51/173.29 [539]~E(x5391,x5392)+E(f550(x5393,x5391,x5394),f550(x5393,x5392,x5394)) % 173.51/173.29 [540]~E(x5401,x5402)+E(f550(x5403,x5404,x5401),f550(x5403,x5404,x5402)) % 173.51/173.29 [541]~E(x5411,x5412)+E(f294(x5411,x5413),f294(x5412,x5413)) % 173.51/173.29 [542]~E(x5421,x5422)+E(f294(x5423,x5421),f294(x5423,x5422)) % 173.51/173.29 [543]~E(x5431,x5432)+E(f526(x5431,x5433,x5434),f526(x5432,x5433,x5434)) % 173.51/173.29 [544]~E(x5441,x5442)+E(f526(x5443,x5441,x5444),f526(x5443,x5442,x5444)) % 173.51/173.29 [545]~E(x5451,x5452)+E(f526(x5453,x5454,x5451),f526(x5453,x5454,x5452)) % 173.51/173.29 [546]~E(x5461,x5462)+E(f134(x5461),f134(x5462)) % 173.51/173.29 [547]~E(x5471,x5472)+E(f62(x5471),f62(x5472)) % 173.51/173.29 [548]~E(x5481,x5482)+E(f178(x5481,x5483,x5484),f178(x5482,x5483,x5484)) % 173.51/173.29 [549]~E(x5491,x5492)+E(f178(x5493,x5491,x5494),f178(x5493,x5492,x5494)) % 173.51/173.29 [550]~E(x5501,x5502)+E(f178(x5503,x5504,x5501),f178(x5503,x5504,x5502)) % 173.51/173.29 [551]~E(x5511,x5512)+E(f576(x5511,x5513,x5514,x5515,x5516),f576(x5512,x5513,x5514,x5515,x5516)) % 173.51/173.29 [552]~E(x5521,x5522)+E(f576(x5523,x5521,x5524,x5525,x5526),f576(x5523,x5522,x5524,x5525,x5526)) % 173.51/173.29 [553]~E(x5531,x5532)+E(f576(x5533,x5534,x5531,x5535,x5536),f576(x5533,x5534,x5532,x5535,x5536)) % 173.51/173.29 [554]~E(x5541,x5542)+E(f576(x5543,x5544,x5545,x5541,x5546),f576(x5543,x5544,x5545,x5542,x5546)) % 173.51/173.29 [555]~E(x5551,x5552)+E(f576(x5553,x5554,x5555,x5556,x5551),f576(x5553,x5554,x5555,x5556,x5552)) % 173.51/173.29 [556]~E(x5561,x5562)+E(f741(x5561,x5563,x5564,x5565,x5566),f741(x5562,x5563,x5564,x5565,x5566)) % 173.51/173.29 [557]~E(x5571,x5572)+E(f741(x5573,x5571,x5574,x5575,x5576),f741(x5573,x5572,x5574,x5575,x5576)) % 173.51/173.29 [558]~E(x5581,x5582)+E(f741(x5583,x5584,x5581,x5585,x5586),f741(x5583,x5584,x5582,x5585,x5586)) % 173.51/173.29 [559]~E(x5591,x5592)+E(f741(x5593,x5594,x5595,x5591,x5596),f741(x5593,x5594,x5595,x5592,x5596)) % 173.51/173.29 [560]~E(x5601,x5602)+E(f741(x5603,x5604,x5605,x5606,x5601),f741(x5603,x5604,x5605,x5606,x5602)) % 173.51/173.29 [561]~E(x5611,x5612)+E(f864(x5611,x5613,x5614,x5615,x5616,x5617),f864(x5612,x5613,x5614,x5615,x5616,x5617)) % 173.51/173.29 [562]~E(x5621,x5622)+E(f864(x5623,x5621,x5624,x5625,x5626,x5627),f864(x5623,x5622,x5624,x5625,x5626,x5627)) % 173.51/173.29 [563]~E(x5631,x5632)+E(f864(x5633,x5634,x5631,x5635,x5636,x5637),f864(x5633,x5634,x5632,x5635,x5636,x5637)) % 173.51/173.29 [564]~E(x5641,x5642)+E(f864(x5643,x5644,x5645,x5641,x5646,x5647),f864(x5643,x5644,x5645,x5642,x5646,x5647)) % 173.51/173.29 [565]~E(x5651,x5652)+E(f864(x5653,x5654,x5655,x5656,x5651,x5657),f864(x5653,x5654,x5655,x5656,x5652,x5657)) % 173.51/173.29 [566]~E(x5661,x5662)+E(f864(x5663,x5664,x5665,x5666,x5667,x5661),f864(x5663,x5664,x5665,x5666,x5667,x5662)) % 173.51/173.29 [567]~E(x5671,x5672)+E(f273(x5671,x5673,x5674,x5675,x5676),f273(x5672,x5673,x5674,x5675,x5676)) % 173.51/173.29 [568]~E(x5681,x5682)+E(f273(x5683,x5681,x5684,x5685,x5686),f273(x5683,x5682,x5684,x5685,x5686)) % 173.51/173.29 [569]~E(x5691,x5692)+E(f273(x5693,x5694,x5691,x5695,x5696),f273(x5693,x5694,x5692,x5695,x5696)) % 173.51/173.29 [570]~E(x5701,x5702)+E(f273(x5703,x5704,x5705,x5701,x5706),f273(x5703,x5704,x5705,x5702,x5706)) % 173.51/173.29 [571]~E(x5711,x5712)+E(f273(x5713,x5714,x5715,x5716,x5711),f273(x5713,x5714,x5715,x5716,x5712)) % 173.51/173.29 [572]~E(x5721,x5722)+E(f228(x5721,x5723),f228(x5722,x5723)) % 173.51/173.29 [573]~E(x5731,x5732)+E(f228(x5733,x5731),f228(x5733,x5732)) % 173.51/173.29 [574]~E(x5741,x5742)+E(f853(x5741,x5743),f853(x5742,x5743)) % 173.51/173.29 [575]~E(x5751,x5752)+E(f853(x5753,x5751),f853(x5753,x5752)) % 173.51/173.29 [576]~E(x5761,x5762)+E(f465(x5761,x5763,x5764,x5765),f465(x5762,x5763,x5764,x5765)) % 173.51/173.29 [577]~E(x5771,x5772)+E(f465(x5773,x5771,x5774,x5775),f465(x5773,x5772,x5774,x5775)) % 173.51/173.29 [578]~E(x5781,x5782)+E(f465(x5783,x5784,x5781,x5785),f465(x5783,x5784,x5782,x5785)) % 173.51/173.29 [579]~E(x5791,x5792)+E(f465(x5793,x5794,x5795,x5791),f465(x5793,x5794,x5795,x5792)) % 173.51/173.29 [580]~E(x5801,x5802)+E(f255(x5801,x5803,x5804),f255(x5802,x5803,x5804)) % 173.51/173.29 [581]~E(x5811,x5812)+E(f255(x5813,x5811,x5814),f255(x5813,x5812,x5814)) % 173.51/173.29 [582]~E(x5821,x5822)+E(f255(x5823,x5824,x5821),f255(x5823,x5824,x5822)) % 173.51/173.29 [583]~E(x5831,x5832)+E(f715(x5831,x5833,x5834,x5835),f715(x5832,x5833,x5834,x5835)) % 173.51/173.29 [584]~E(x5841,x5842)+E(f715(x5843,x5841,x5844,x5845),f715(x5843,x5842,x5844,x5845)) % 173.51/173.29 [585]~E(x5851,x5852)+E(f715(x5853,x5854,x5851,x5855),f715(x5853,x5854,x5852,x5855)) % 173.51/173.29 [586]~E(x5861,x5862)+E(f715(x5863,x5864,x5865,x5861),f715(x5863,x5864,x5865,x5862)) % 173.51/173.29 [587]~E(x5871,x5872)+E(f548(x5871,x5873,x5874),f548(x5872,x5873,x5874)) % 173.51/173.29 [588]~E(x5881,x5882)+E(f548(x5883,x5881,x5884),f548(x5883,x5882,x5884)) % 173.51/173.29 [589]~E(x5891,x5892)+E(f548(x5893,x5894,x5891),f548(x5893,x5894,x5892)) % 173.51/173.29 [590]~E(x5901,x5902)+E(f621(x5901,x5903,x5904,x5905,x5906),f621(x5902,x5903,x5904,x5905,x5906)) % 173.51/173.29 [591]~E(x5911,x5912)+E(f621(x5913,x5911,x5914,x5915,x5916),f621(x5913,x5912,x5914,x5915,x5916)) % 173.51/173.29 [592]~E(x5921,x5922)+E(f621(x5923,x5924,x5921,x5925,x5926),f621(x5923,x5924,x5922,x5925,x5926)) % 173.51/173.29 [593]~E(x5931,x5932)+E(f621(x5933,x5934,x5935,x5931,x5936),f621(x5933,x5934,x5935,x5932,x5936)) % 173.51/173.29 [594]~E(x5941,x5942)+E(f621(x5943,x5944,x5945,x5946,x5941),f621(x5943,x5944,x5945,x5946,x5942)) % 173.51/173.29 [595]~E(x5951,x5952)+E(f505(x5951,x5953,x5954,x5955,x5956),f505(x5952,x5953,x5954,x5955,x5956)) % 173.51/173.29 [596]~E(x5961,x5962)+E(f505(x5963,x5961,x5964,x5965,x5966),f505(x5963,x5962,x5964,x5965,x5966)) % 173.51/173.29 [597]~E(x5971,x5972)+E(f505(x5973,x5974,x5971,x5975,x5976),f505(x5973,x5974,x5972,x5975,x5976)) % 173.51/173.29 [598]~E(x5981,x5982)+E(f505(x5983,x5984,x5985,x5981,x5986),f505(x5983,x5984,x5985,x5982,x5986)) % 173.51/173.29 [599]~E(x5991,x5992)+E(f505(x5993,x5994,x5995,x5996,x5991),f505(x5993,x5994,x5995,x5996,x5992)) % 173.51/173.29 [600]~E(x6001,x6002)+E(f753(x6001,x6003),f753(x6002,x6003)) % 173.51/173.29 [601]~E(x6011,x6012)+E(f753(x6013,x6011),f753(x6013,x6012)) % 173.51/173.29 [602]~E(x6021,x6022)+E(f32(x6021,x6023,x6024,x6025,x6026,x6027,x6028,x6029,x60210,x60211),f32(x6022,x6023,x6024,x6025,x6026,x6027,x6028,x6029,x60210,x60211)) % 173.51/173.29 [603]~E(x6031,x6032)+E(f32(x6033,x6031,x6034,x6035,x6036,x6037,x6038,x6039,x60310,x60311),f32(x6033,x6032,x6034,x6035,x6036,x6037,x6038,x6039,x60310,x60311)) % 173.51/173.29 [604]~E(x6041,x6042)+E(f32(x6043,x6044,x6041,x6045,x6046,x6047,x6048,x6049,x60410,x60411),f32(x6043,x6044,x6042,x6045,x6046,x6047,x6048,x6049,x60410,x60411)) % 173.51/173.29 [605]~E(x6051,x6052)+E(f32(x6053,x6054,x6055,x6051,x6056,x6057,x6058,x6059,x60510,x60511),f32(x6053,x6054,x6055,x6052,x6056,x6057,x6058,x6059,x60510,x60511)) % 173.51/173.29 [606]~E(x6061,x6062)+E(f32(x6063,x6064,x6065,x6066,x6061,x6067,x6068,x6069,x60610,x60611),f32(x6063,x6064,x6065,x6066,x6062,x6067,x6068,x6069,x60610,x60611)) % 173.51/173.29 [607]~E(x6071,x6072)+E(f32(x6073,x6074,x6075,x6076,x6077,x6071,x6078,x6079,x60710,x60711),f32(x6073,x6074,x6075,x6076,x6077,x6072,x6078,x6079,x60710,x60711)) % 173.51/173.29 [608]~E(x6081,x6082)+E(f32(x6083,x6084,x6085,x6086,x6087,x6088,x6081,x6089,x60810,x60811),f32(x6083,x6084,x6085,x6086,x6087,x6088,x6082,x6089,x60810,x60811)) % 173.51/173.29 [609]~E(x6091,x6092)+E(f32(x6093,x6094,x6095,x6096,x6097,x6098,x6099,x6091,x60910,x60911),f32(x6093,x6094,x6095,x6096,x6097,x6098,x6099,x6092,x60910,x60911)) % 173.51/173.29 [610]~E(x6101,x6102)+E(f32(x6103,x6104,x6105,x6106,x6107,x6108,x6109,x61010,x6101,x61011),f32(x6103,x6104,x6105,x6106,x6107,x6108,x6109,x61010,x6102,x61011)) % 173.51/173.29 [611]~E(x6111,x6112)+E(f32(x6113,x6114,x6115,x6116,x6117,x6118,x6119,x61110,x61111,x6111),f32(x6113,x6114,x6115,x6116,x6117,x6118,x6119,x61110,x61111,x6112)) % 173.51/173.29 [612]~E(x6121,x6122)+E(f73(x6121,x6123,x6124),f73(x6122,x6123,x6124)) % 173.51/173.29 [613]~E(x6131,x6132)+E(f73(x6133,x6131,x6134),f73(x6133,x6132,x6134)) % 173.51/173.29 [614]~E(x6141,x6142)+E(f73(x6143,x6144,x6141),f73(x6143,x6144,x6142)) % 173.51/173.29 [615]~E(x6151,x6152)+E(f155(x6151,x6153),f155(x6152,x6153)) % 173.51/173.29 [616]~E(x6161,x6162)+E(f155(x6163,x6161),f155(x6163,x6162)) % 173.51/173.29 [617]~E(x6171,x6172)+E(f151(x6171,x6173),f151(x6172,x6173)) % 173.51/173.29 [618]~E(x6181,x6182)+E(f151(x6183,x6181),f151(x6183,x6182)) % 173.51/173.29 [619]~E(x6191,x6192)+E(f599(x6191),f599(x6192)) % 173.51/173.29 [620]~E(x6201,x6202)+E(f135(x6201,x6203),f135(x6202,x6203)) % 173.51/173.29 [621]~E(x6211,x6212)+E(f135(x6213,x6211),f135(x6213,x6212)) % 173.51/173.29 [622]~E(x6221,x6222)+E(f679(x6221,x6223,x6224,x6225,x6226,x6227,x6228),f679(x6222,x6223,x6224,x6225,x6226,x6227,x6228)) % 173.51/173.29 [623]~E(x6231,x6232)+E(f679(x6233,x6231,x6234,x6235,x6236,x6237,x6238),f679(x6233,x6232,x6234,x6235,x6236,x6237,x6238)) % 173.51/173.29 [624]~E(x6241,x6242)+E(f679(x6243,x6244,x6241,x6245,x6246,x6247,x6248),f679(x6243,x6244,x6242,x6245,x6246,x6247,x6248)) % 173.51/173.29 [625]~E(x6251,x6252)+E(f679(x6253,x6254,x6255,x6251,x6256,x6257,x6258),f679(x6253,x6254,x6255,x6252,x6256,x6257,x6258)) % 173.51/173.29 [626]~E(x6261,x6262)+E(f679(x6263,x6264,x6265,x6266,x6261,x6267,x6268),f679(x6263,x6264,x6265,x6266,x6262,x6267,x6268)) % 173.51/173.29 [627]~E(x6271,x6272)+E(f679(x6273,x6274,x6275,x6276,x6277,x6271,x6278),f679(x6273,x6274,x6275,x6276,x6277,x6272,x6278)) % 173.51/173.29 [628]~E(x6281,x6282)+E(f679(x6283,x6284,x6285,x6286,x6287,x6288,x6281),f679(x6283,x6284,x6285,x6286,x6287,x6288,x6282)) % 173.51/173.29 [629]~E(x6291,x6292)+E(f882(x6291,x6293,x6294),f882(x6292,x6293,x6294)) % 173.51/173.29 [630]~E(x6301,x6302)+E(f882(x6303,x6301,x6304),f882(x6303,x6302,x6304)) % 173.51/173.29 [631]~E(x6311,x6312)+E(f882(x6313,x6314,x6311),f882(x6313,x6314,x6312)) % 173.51/173.29 [632]~E(x6321,x6322)+E(f635(x6321,x6323,x6324,x6325,x6326),f635(x6322,x6323,x6324,x6325,x6326)) % 173.51/173.29 [633]~E(x6331,x6332)+E(f635(x6333,x6331,x6334,x6335,x6336),f635(x6333,x6332,x6334,x6335,x6336)) % 173.51/173.29 [634]~E(x6341,x6342)+E(f635(x6343,x6344,x6341,x6345,x6346),f635(x6343,x6344,x6342,x6345,x6346)) % 173.51/173.29 [635]~E(x6351,x6352)+E(f635(x6353,x6354,x6355,x6351,x6356),f635(x6353,x6354,x6355,x6352,x6356)) % 173.51/173.29 [636]~E(x6361,x6362)+E(f635(x6363,x6364,x6365,x6366,x6361),f635(x6363,x6364,x6365,x6366,x6362)) % 173.51/173.29 [637]~E(x6371,x6372)+E(f514(x6371,x6373,x6374,x6375,x6376),f514(x6372,x6373,x6374,x6375,x6376)) % 173.51/173.29 [638]~E(x6381,x6382)+E(f514(x6383,x6381,x6384,x6385,x6386),f514(x6383,x6382,x6384,x6385,x6386)) % 173.51/173.29 [639]~E(x6391,x6392)+E(f514(x6393,x6394,x6391,x6395,x6396),f514(x6393,x6394,x6392,x6395,x6396)) % 173.51/173.29 [640]~E(x6401,x6402)+E(f514(x6403,x6404,x6405,x6401,x6406),f514(x6403,x6404,x6405,x6402,x6406)) % 173.51/173.29 [641]~E(x6411,x6412)+E(f514(x6413,x6414,x6415,x6416,x6411),f514(x6413,x6414,x6415,x6416,x6412)) % 173.51/173.29 [642]~E(x6421,x6422)+E(f446(x6421,x6423,x6424),f446(x6422,x6423,x6424)) % 173.51/173.29 [643]~E(x6431,x6432)+E(f446(x6433,x6431,x6434),f446(x6433,x6432,x6434)) % 173.51/173.29 [644]~E(x6441,x6442)+E(f446(x6443,x6444,x6441),f446(x6443,x6444,x6442)) % 173.51/173.29 [645]~E(x6451,x6452)+E(f461(x6451,x6453,x6454,x6455,x6456),f461(x6452,x6453,x6454,x6455,x6456)) % 173.51/173.29 [646]~E(x6461,x6462)+E(f461(x6463,x6461,x6464,x6465,x6466),f461(x6463,x6462,x6464,x6465,x6466)) % 173.51/173.29 [647]~E(x6471,x6472)+E(f461(x6473,x6474,x6471,x6475,x6476),f461(x6473,x6474,x6472,x6475,x6476)) % 173.51/173.29 [648]~E(x6481,x6482)+E(f461(x6483,x6484,x6485,x6481,x6486),f461(x6483,x6484,x6485,x6482,x6486)) % 173.51/173.29 [649]~E(x6491,x6492)+E(f461(x6493,x6494,x6495,x6496,x6491),f461(x6493,x6494,x6495,x6496,x6492)) % 173.51/173.29 [650]~E(x6501,x6502)+E(f11(x6501,x6503,x6504),f11(x6502,x6503,x6504)) % 173.51/173.29 [651]~E(x6511,x6512)+E(f11(x6513,x6511,x6514),f11(x6513,x6512,x6514)) % 173.51/173.29 [652]~E(x6521,x6522)+E(f11(x6523,x6524,x6521),f11(x6523,x6524,x6522)) % 173.51/173.29 [653]~E(x6531,x6532)+E(f517(x6531,x6533,x6534),f517(x6532,x6533,x6534)) % 173.51/173.29 [654]~E(x6541,x6542)+E(f517(x6543,x6541,x6544),f517(x6543,x6542,x6544)) % 173.51/173.29 [655]~E(x6551,x6552)+E(f517(x6553,x6554,x6551),f517(x6553,x6554,x6552)) % 173.51/173.29 [656]~E(x6561,x6562)+E(f37(x6561,x6563,x6564,x6565),f37(x6562,x6563,x6564,x6565)) % 173.51/173.29 [657]~E(x6571,x6572)+E(f37(x6573,x6571,x6574,x6575),f37(x6573,x6572,x6574,x6575)) % 173.51/173.29 [658]~E(x6581,x6582)+E(f37(x6583,x6584,x6581,x6585),f37(x6583,x6584,x6582,x6585)) % 173.51/173.29 [659]~E(x6591,x6592)+E(f37(x6593,x6594,x6595,x6591),f37(x6593,x6594,x6595,x6592)) % 173.51/173.29 [660]~E(x6601,x6602)+E(f893(x6601,x6603,x6604,x6605),f893(x6602,x6603,x6604,x6605)) % 173.51/173.29 [661]~E(x6611,x6612)+E(f893(x6613,x6611,x6614,x6615),f893(x6613,x6612,x6614,x6615)) % 173.51/173.29 [662]~E(x6621,x6622)+E(f893(x6623,x6624,x6621,x6625),f893(x6623,x6624,x6622,x6625)) % 173.51/173.29 [663]~E(x6631,x6632)+E(f893(x6633,x6634,x6635,x6631),f893(x6633,x6634,x6635,x6632)) % 173.51/173.29 [664]~E(x6641,x6642)+E(f710(x6641,x6643,x6644),f710(x6642,x6643,x6644)) % 173.51/173.29 [665]~E(x6651,x6652)+E(f710(x6653,x6651,x6654),f710(x6653,x6652,x6654)) % 173.51/173.29 [666]~E(x6661,x6662)+E(f710(x6663,x6664,x6661),f710(x6663,x6664,x6662)) % 173.51/173.29 [667]~E(x6671,x6672)+E(f736(x6671,x6673,x6674),f736(x6672,x6673,x6674)) % 173.51/173.29 [668]~E(x6681,x6682)+E(f736(x6683,x6681,x6684),f736(x6683,x6682,x6684)) % 173.51/173.29 [669]~E(x6691,x6692)+E(f736(x6693,x6694,x6691),f736(x6693,x6694,x6692)) % 173.51/173.29 [670]~E(x6701,x6702)+E(f382(x6701,x6703),f382(x6702,x6703)) % 173.51/173.29 [671]~E(x6711,x6712)+E(f382(x6713,x6711),f382(x6713,x6712)) % 173.51/173.29 [672]~E(x6721,x6722)+E(f271(x6721,x6723,x6724,x6725),f271(x6722,x6723,x6724,x6725)) % 173.51/173.29 [673]~E(x6731,x6732)+E(f271(x6733,x6731,x6734,x6735),f271(x6733,x6732,x6734,x6735)) % 173.51/173.29 [674]~E(x6741,x6742)+E(f271(x6743,x6744,x6741,x6745),f271(x6743,x6744,x6742,x6745)) % 173.51/173.29 [675]~E(x6751,x6752)+E(f271(x6753,x6754,x6755,x6751),f271(x6753,x6754,x6755,x6752)) % 173.51/173.29 [676]~E(x6761,x6762)+E(f337(x6761,x6763,x6764,x6765),f337(x6762,x6763,x6764,x6765)) % 173.51/173.29 [677]~E(x6771,x6772)+E(f337(x6773,x6771,x6774,x6775),f337(x6773,x6772,x6774,x6775)) % 173.51/173.29 [678]~E(x6781,x6782)+E(f337(x6783,x6784,x6781,x6785),f337(x6783,x6784,x6782,x6785)) % 173.51/173.29 [679]~E(x6791,x6792)+E(f337(x6793,x6794,x6795,x6791),f337(x6793,x6794,x6795,x6792)) % 173.51/173.29 [680]~E(x6801,x6802)+E(f407(x6801,x6803,x6804,x6805),f407(x6802,x6803,x6804,x6805)) % 173.51/173.29 [681]~E(x6811,x6812)+E(f407(x6813,x6811,x6814,x6815),f407(x6813,x6812,x6814,x6815)) % 173.51/173.29 [682]~E(x6821,x6822)+E(f407(x6823,x6824,x6821,x6825),f407(x6823,x6824,x6822,x6825)) % 173.51/173.29 [683]~E(x6831,x6832)+E(f407(x6833,x6834,x6835,x6831),f407(x6833,x6834,x6835,x6832)) % 173.51/173.29 [684]~E(x6841,x6842)+E(f826(x6841,x6843,x6844,x6845),f826(x6842,x6843,x6844,x6845)) % 173.51/173.29 [685]~E(x6851,x6852)+E(f826(x6853,x6851,x6854,x6855),f826(x6853,x6852,x6854,x6855)) % 173.51/173.29 [686]~E(x6861,x6862)+E(f826(x6863,x6864,x6861,x6865),f826(x6863,x6864,x6862,x6865)) % 173.51/173.29 [687]~E(x6871,x6872)+E(f826(x6873,x6874,x6875,x6871),f826(x6873,x6874,x6875,x6872)) % 173.51/173.29 [688]~E(x6881,x6882)+E(f631(x6881,x6883,x6884),f631(x6882,x6883,x6884)) % 173.51/173.29 [689]~E(x6891,x6892)+E(f631(x6893,x6891,x6894),f631(x6893,x6892,x6894)) % 173.51/173.29 [690]~E(x6901,x6902)+E(f631(x6903,x6904,x6901),f631(x6903,x6904,x6902)) % 173.51/173.29 [691]~E(x6911,x6912)+E(f867(x6911,x6913,x6914,x6915,x6916,x6917),f867(x6912,x6913,x6914,x6915,x6916,x6917)) % 173.51/173.29 [692]~E(x6921,x6922)+E(f867(x6923,x6921,x6924,x6925,x6926,x6927),f867(x6923,x6922,x6924,x6925,x6926,x6927)) % 173.51/173.29 [693]~E(x6931,x6932)+E(f867(x6933,x6934,x6931,x6935,x6936,x6937),f867(x6933,x6934,x6932,x6935,x6936,x6937)) % 173.51/173.29 [694]~E(x6941,x6942)+E(f867(x6943,x6944,x6945,x6941,x6946,x6947),f867(x6943,x6944,x6945,x6942,x6946,x6947)) % 173.51/173.29 [695]~E(x6951,x6952)+E(f867(x6953,x6954,x6955,x6956,x6951,x6957),f867(x6953,x6954,x6955,x6956,x6952,x6957)) % 173.51/173.29 [696]~E(x6961,x6962)+E(f867(x6963,x6964,x6965,x6966,x6967,x6961),f867(x6963,x6964,x6965,x6966,x6967,x6962)) % 173.51/173.29 [697]~E(x6971,x6972)+E(f184(x6971,x6973,x6974),f184(x6972,x6973,x6974)) % 173.51/173.29 [698]~E(x6981,x6982)+E(f184(x6983,x6981,x6984),f184(x6983,x6982,x6984)) % 173.51/173.29 [699]~E(x6991,x6992)+E(f184(x6993,x6994,x6991),f184(x6993,x6994,x6992)) % 173.51/173.29 [700]~E(x7001,x7002)+E(f873(x7001,x7003,x7004,x7005,x7006),f873(x7002,x7003,x7004,x7005,x7006)) % 173.51/173.29 [701]~E(x7011,x7012)+E(f873(x7013,x7011,x7014,x7015,x7016),f873(x7013,x7012,x7014,x7015,x7016)) % 173.51/173.29 [702]~E(x7021,x7022)+E(f873(x7023,x7024,x7021,x7025,x7026),f873(x7023,x7024,x7022,x7025,x7026)) % 173.51/173.29 [703]~E(x7031,x7032)+E(f873(x7033,x7034,x7035,x7031,x7036),f873(x7033,x7034,x7035,x7032,x7036)) % 173.51/173.29 [704]~E(x7041,x7042)+E(f873(x7043,x7044,x7045,x7046,x7041),f873(x7043,x7044,x7045,x7046,x7042)) % 173.51/173.29 [705]~E(x7051,x7052)+E(f904(x7051,x7053,x7054,x7055,x7056,x7057,x7058),f904(x7052,x7053,x7054,x7055,x7056,x7057,x7058)) % 173.51/173.29 [706]~E(x7061,x7062)+E(f904(x7063,x7061,x7064,x7065,x7066,x7067,x7068),f904(x7063,x7062,x7064,x7065,x7066,x7067,x7068)) % 173.51/173.29 [707]~E(x7071,x7072)+E(f904(x7073,x7074,x7071,x7075,x7076,x7077,x7078),f904(x7073,x7074,x7072,x7075,x7076,x7077,x7078)) % 173.51/173.29 [708]~E(x7081,x7082)+E(f904(x7083,x7084,x7085,x7081,x7086,x7087,x7088),f904(x7083,x7084,x7085,x7082,x7086,x7087,x7088)) % 173.51/173.29 [709]~E(x7091,x7092)+E(f904(x7093,x7094,x7095,x7096,x7091,x7097,x7098),f904(x7093,x7094,x7095,x7096,x7092,x7097,x7098)) % 173.51/173.29 [710]~E(x7101,x7102)+E(f904(x7103,x7104,x7105,x7106,x7107,x7101,x7108),f904(x7103,x7104,x7105,x7106,x7107,x7102,x7108)) % 173.51/173.29 [711]~E(x7111,x7112)+E(f904(x7113,x7114,x7115,x7116,x7117,x7118,x7111),f904(x7113,x7114,x7115,x7116,x7117,x7118,x7112)) % 173.51/173.29 [712]~E(x7121,x7122)+E(f71(x7121,x7123,x7124),f71(x7122,x7123,x7124)) % 173.51/173.29 [713]~E(x7131,x7132)+E(f71(x7133,x7131,x7134),f71(x7133,x7132,x7134)) % 173.51/173.29 [714]~E(x7141,x7142)+E(f71(x7143,x7144,x7141),f71(x7143,x7144,x7142)) % 173.51/173.29 [715]~E(x7151,x7152)+E(f480(x7151,x7153,x7154,x7155),f480(x7152,x7153,x7154,x7155)) % 173.51/173.29 [716]~E(x7161,x7162)+E(f480(x7163,x7161,x7164,x7165),f480(x7163,x7162,x7164,x7165)) % 173.51/173.29 [717]~E(x7171,x7172)+E(f480(x7173,x7174,x7171,x7175),f480(x7173,x7174,x7172,x7175)) % 173.51/173.29 [718]~E(x7181,x7182)+E(f480(x7183,x7184,x7185,x7181),f480(x7183,x7184,x7185,x7182)) % 173.51/173.29 [719]~E(x7191,x7192)+E(f594(x7191,x7193,x7194,x7195),f594(x7192,x7193,x7194,x7195)) % 173.51/173.29 [720]~E(x7201,x7202)+E(f594(x7203,x7201,x7204,x7205),f594(x7203,x7202,x7204,x7205)) % 173.51/173.29 [721]~E(x7211,x7212)+E(f594(x7213,x7214,x7211,x7215),f594(x7213,x7214,x7212,x7215)) % 173.51/173.29 [722]~E(x7221,x7222)+E(f594(x7223,x7224,x7225,x7221),f594(x7223,x7224,x7225,x7222)) % 173.51/173.29 [723]~E(x7231,x7232)+E(f820(x7231,x7233,x7234,x7235,x7236),f820(x7232,x7233,x7234,x7235,x7236)) % 173.51/173.29 [724]~E(x7241,x7242)+E(f820(x7243,x7241,x7244,x7245,x7246),f820(x7243,x7242,x7244,x7245,x7246)) % 173.51/173.29 [725]~E(x7251,x7252)+E(f820(x7253,x7254,x7251,x7255,x7256),f820(x7253,x7254,x7252,x7255,x7256)) % 173.51/173.29 [726]~E(x7261,x7262)+E(f820(x7263,x7264,x7265,x7261,x7266),f820(x7263,x7264,x7265,x7262,x7266)) % 173.51/173.29 [727]~E(x7271,x7272)+E(f820(x7273,x7274,x7275,x7276,x7271),f820(x7273,x7274,x7275,x7276,x7272)) % 173.51/173.29 [728]~E(x7281,x7282)+E(f307(x7281),f307(x7282)) % 173.51/173.29 [729]~E(x7291,x7292)+E(f349(x7291,x7293,x7294,x7295),f349(x7292,x7293,x7294,x7295)) % 173.51/173.29 [730]~E(x7301,x7302)+E(f349(x7303,x7301,x7304,x7305),f349(x7303,x7302,x7304,x7305)) % 173.51/173.29 [731]~E(x7311,x7312)+E(f349(x7313,x7314,x7311,x7315),f349(x7313,x7314,x7312,x7315)) % 173.51/173.29 [732]~E(x7321,x7322)+E(f349(x7323,x7324,x7325,x7321),f349(x7323,x7324,x7325,x7322)) % 173.51/173.29 [733]~E(x7331,x7332)+E(f809(x7331,x7333,x7334),f809(x7332,x7333,x7334)) % 173.51/173.29 [734]~E(x7341,x7342)+E(f809(x7343,x7341,x7344),f809(x7343,x7342,x7344)) % 173.51/173.29 [735]~E(x7351,x7352)+E(f809(x7353,x7354,x7351),f809(x7353,x7354,x7352)) % 173.51/173.29 [736]~E(x7361,x7362)+E(f747(x7361,x7363,x7364,x7365,x7366),f747(x7362,x7363,x7364,x7365,x7366)) % 173.51/173.29 [737]~E(x7371,x7372)+E(f747(x7373,x7371,x7374,x7375,x7376),f747(x7373,x7372,x7374,x7375,x7376)) % 173.51/173.29 [738]~E(x7381,x7382)+E(f747(x7383,x7384,x7381,x7385,x7386),f747(x7383,x7384,x7382,x7385,x7386)) % 173.51/173.29 [739]~E(x7391,x7392)+E(f747(x7393,x7394,x7395,x7391,x7396),f747(x7393,x7394,x7395,x7392,x7396)) % 173.51/173.29 [740]~E(x7401,x7402)+E(f747(x7403,x7404,x7405,x7406,x7401),f747(x7403,x7404,x7405,x7406,x7402)) % 173.51/173.29 [741]~E(x7411,x7412)+E(f494(x7411,x7413,x7414,x7415),f494(x7412,x7413,x7414,x7415)) % 173.51/173.29 [742]~E(x7421,x7422)+E(f494(x7423,x7421,x7424,x7425),f494(x7423,x7422,x7424,x7425)) % 173.51/173.29 [743]~E(x7431,x7432)+E(f494(x7433,x7434,x7431,x7435),f494(x7433,x7434,x7432,x7435)) % 173.51/173.29 [744]~E(x7441,x7442)+E(f494(x7443,x7444,x7445,x7441),f494(x7443,x7444,x7445,x7442)) % 173.51/173.29 [745]~E(x7451,x7452)+E(f239(x7451,x7453),f239(x7452,x7453)) % 173.51/173.29 [746]~E(x7461,x7462)+E(f239(x7463,x7461),f239(x7463,x7462)) % 173.51/173.29 [747]~E(x7471,x7472)+E(f149(x7471),f149(x7472)) % 173.51/173.29 [748]~E(x7481,x7482)+E(f352(x7481,x7483,x7484,x7485,x7486,x7487,x7488),f352(x7482,x7483,x7484,x7485,x7486,x7487,x7488)) % 173.51/173.29 [749]~E(x7491,x7492)+E(f352(x7493,x7491,x7494,x7495,x7496,x7497,x7498),f352(x7493,x7492,x7494,x7495,x7496,x7497,x7498)) % 173.51/173.29 [750]~E(x7501,x7502)+E(f352(x7503,x7504,x7501,x7505,x7506,x7507,x7508),f352(x7503,x7504,x7502,x7505,x7506,x7507,x7508)) % 173.51/173.29 [751]~E(x7511,x7512)+E(f352(x7513,x7514,x7515,x7511,x7516,x7517,x7518),f352(x7513,x7514,x7515,x7512,x7516,x7517,x7518)) % 173.51/173.29 [752]~E(x7521,x7522)+E(f352(x7523,x7524,x7525,x7526,x7521,x7527,x7528),f352(x7523,x7524,x7525,x7526,x7522,x7527,x7528)) % 173.51/173.29 [753]~E(x7531,x7532)+E(f352(x7533,x7534,x7535,x7536,x7537,x7531,x7538),f352(x7533,x7534,x7535,x7536,x7537,x7532,x7538)) % 173.51/173.29 [754]~E(x7541,x7542)+E(f352(x7543,x7544,x7545,x7546,x7547,x7548,x7541),f352(x7543,x7544,x7545,x7546,x7547,x7548,x7542)) % 173.51/173.29 [755]~E(x7551,x7552)+E(f688(x7551,x7553,x7554,x7555),f688(x7552,x7553,x7554,x7555)) % 173.51/173.29 [756]~E(x7561,x7562)+E(f688(x7563,x7561,x7564,x7565),f688(x7563,x7562,x7564,x7565)) % 173.51/173.29 [757]~E(x7571,x7572)+E(f688(x7573,x7574,x7571,x7575),f688(x7573,x7574,x7572,x7575)) % 173.51/173.29 [758]~E(x7581,x7582)+E(f688(x7583,x7584,x7585,x7581),f688(x7583,x7584,x7585,x7582)) % 173.51/173.29 [759]~E(x7591,x7592)+E(f202(x7591),f202(x7592)) % 173.51/173.29 [760]~E(x7601,x7602)+E(f737(x7601,x7603,x7604),f737(x7602,x7603,x7604)) % 173.51/173.29 [761]~E(x7611,x7612)+E(f737(x7613,x7611,x7614),f737(x7613,x7612,x7614)) % 173.51/173.29 [762]~E(x7621,x7622)+E(f737(x7623,x7624,x7621),f737(x7623,x7624,x7622)) % 173.51/173.29 [763]~E(x7631,x7632)+E(f370(x7631,x7633,x7634,x7635,x7636,x7637),f370(x7632,x7633,x7634,x7635,x7636,x7637)) % 173.51/173.29 [764]~E(x7641,x7642)+E(f370(x7643,x7641,x7644,x7645,x7646,x7647),f370(x7643,x7642,x7644,x7645,x7646,x7647)) % 173.51/173.29 [765]~E(x7651,x7652)+E(f370(x7653,x7654,x7651,x7655,x7656,x7657),f370(x7653,x7654,x7652,x7655,x7656,x7657)) % 173.51/173.29 [766]~E(x7661,x7662)+E(f370(x7663,x7664,x7665,x7661,x7666,x7667),f370(x7663,x7664,x7665,x7662,x7666,x7667)) % 173.51/173.29 [767]~E(x7671,x7672)+E(f370(x7673,x7674,x7675,x7676,x7671,x7677),f370(x7673,x7674,x7675,x7676,x7672,x7677)) % 173.51/173.29 [768]~E(x7681,x7682)+E(f370(x7683,x7684,x7685,x7686,x7687,x7681),f370(x7683,x7684,x7685,x7686,x7687,x7682)) % 173.51/173.29 [769]~E(x7691,x7692)+E(f303(x7691,x7693,x7694,x7695,x7696),f303(x7692,x7693,x7694,x7695,x7696)) % 173.51/173.29 [770]~E(x7701,x7702)+E(f303(x7703,x7701,x7704,x7705,x7706),f303(x7703,x7702,x7704,x7705,x7706)) % 173.51/173.29 [771]~E(x7711,x7712)+E(f303(x7713,x7714,x7711,x7715,x7716),f303(x7713,x7714,x7712,x7715,x7716)) % 173.51/173.29 [772]~E(x7721,x7722)+E(f303(x7723,x7724,x7725,x7721,x7726),f303(x7723,x7724,x7725,x7722,x7726)) % 173.51/173.29 [773]~E(x7731,x7732)+E(f303(x7733,x7734,x7735,x7736,x7731),f303(x7733,x7734,x7735,x7736,x7732)) % 173.51/173.29 [774]~E(x7741,x7742)+E(f95(x7741),f95(x7742)) % 173.51/173.29 [775]~E(x7751,x7752)+E(f562(x7751,x7753,x7754),f562(x7752,x7753,x7754)) % 173.51/173.29 [776]~E(x7761,x7762)+E(f562(x7763,x7761,x7764),f562(x7763,x7762,x7764)) % 173.51/173.29 [777]~E(x7771,x7772)+E(f562(x7773,x7774,x7771),f562(x7773,x7774,x7772)) % 173.51/173.29 [778]~E(x7781,x7782)+E(f89(x7781,x7783),f89(x7782,x7783)) % 173.51/173.29 [779]~E(x7791,x7792)+E(f89(x7793,x7791),f89(x7793,x7792)) % 173.51/173.29 [780]~E(x7801,x7802)+E(f653(x7801,x7803,x7804,x7805),f653(x7802,x7803,x7804,x7805)) % 173.51/173.29 [781]~E(x7811,x7812)+E(f653(x7813,x7811,x7814,x7815),f653(x7813,x7812,x7814,x7815)) % 173.51/173.29 [782]~E(x7821,x7822)+E(f653(x7823,x7824,x7821,x7825),f653(x7823,x7824,x7822,x7825)) % 173.51/173.29 [783]~E(x7831,x7832)+E(f653(x7833,x7834,x7835,x7831),f653(x7833,x7834,x7835,x7832)) % 173.51/173.29 [784]~E(x7841,x7842)+E(f500(x7841,x7843,x7844),f500(x7842,x7843,x7844)) % 173.51/173.29 [785]~E(x7851,x7852)+E(f500(x7853,x7851,x7854),f500(x7853,x7852,x7854)) % 173.51/173.29 [786]~E(x7861,x7862)+E(f500(x7863,x7864,x7861),f500(x7863,x7864,x7862)) % 173.51/173.29 [787]~E(x7871,x7872)+E(f193(x7871,x7873,x7874,x7875),f193(x7872,x7873,x7874,x7875)) % 173.51/173.29 [788]~E(x7881,x7882)+E(f193(x7883,x7881,x7884,x7885),f193(x7883,x7882,x7884,x7885)) % 173.51/173.29 [789]~E(x7891,x7892)+E(f193(x7893,x7894,x7891,x7895),f193(x7893,x7894,x7892,x7895)) % 173.51/173.29 [790]~E(x7901,x7902)+E(f193(x7903,x7904,x7905,x7901),f193(x7903,x7904,x7905,x7902)) % 173.51/173.29 [791]~E(x7911,x7912)+E(f844(x7911,x7913,x7914,x7915,x7916),f844(x7912,x7913,x7914,x7915,x7916)) % 173.51/173.29 [792]~E(x7921,x7922)+E(f844(x7923,x7921,x7924,x7925,x7926),f844(x7923,x7922,x7924,x7925,x7926)) % 173.51/173.29 [793]~E(x7931,x7932)+E(f844(x7933,x7934,x7931,x7935,x7936),f844(x7933,x7934,x7932,x7935,x7936)) % 173.51/173.29 [794]~E(x7941,x7942)+E(f844(x7943,x7944,x7945,x7941,x7946),f844(x7943,x7944,x7945,x7942,x7946)) % 173.51/173.29 [795]~E(x7951,x7952)+E(f844(x7953,x7954,x7955,x7956,x7951),f844(x7953,x7954,x7955,x7956,x7952)) % 173.51/173.29 [796]~E(x7961,x7962)+E(f614(x7961,x7963,x7964,x7965,x7966,x7967),f614(x7962,x7963,x7964,x7965,x7966,x7967)) % 173.51/173.29 [797]~E(x7971,x7972)+E(f614(x7973,x7971,x7974,x7975,x7976,x7977),f614(x7973,x7972,x7974,x7975,x7976,x7977)) % 173.51/173.29 [798]~E(x7981,x7982)+E(f614(x7983,x7984,x7981,x7985,x7986,x7987),f614(x7983,x7984,x7982,x7985,x7986,x7987)) % 173.51/173.29 [799]~E(x7991,x7992)+E(f614(x7993,x7994,x7995,x7991,x7996,x7997),f614(x7993,x7994,x7995,x7992,x7996,x7997)) % 173.51/173.29 [800]~E(x8001,x8002)+E(f614(x8003,x8004,x8005,x8006,x8001,x8007),f614(x8003,x8004,x8005,x8006,x8002,x8007)) % 173.51/173.29 [801]~E(x8011,x8012)+E(f614(x8013,x8014,x8015,x8016,x8017,x8011),f614(x8013,x8014,x8015,x8016,x8017,x8012)) % 173.51/173.29 [802]~E(x8021,x8022)+E(f84(x8021,x8023,x8024,x8025),f84(x8022,x8023,x8024,x8025)) % 173.51/173.29 [803]~E(x8031,x8032)+E(f84(x8033,x8031,x8034,x8035),f84(x8033,x8032,x8034,x8035)) % 173.51/173.29 [804]~E(x8041,x8042)+E(f84(x8043,x8044,x8041,x8045),f84(x8043,x8044,x8042,x8045)) % 173.51/173.29 [805]~E(x8051,x8052)+E(f84(x8053,x8054,x8055,x8051),f84(x8053,x8054,x8055,x8052)) % 173.51/173.29 [806]~E(x8061,x8062)+E(f434(x8061,x8063,x8064),f434(x8062,x8063,x8064)) % 173.51/173.29 [807]~E(x8071,x8072)+E(f434(x8073,x8071,x8074),f434(x8073,x8072,x8074)) % 173.51/173.29 [808]~E(x8081,x8082)+E(f434(x8083,x8084,x8081),f434(x8083,x8084,x8082)) % 173.51/173.29 [809]~E(x8091,x8092)+E(f210(x8091,x8093,x8094,x8095),f210(x8092,x8093,x8094,x8095)) % 173.51/173.29 [810]~E(x8101,x8102)+E(f210(x8103,x8101,x8104,x8105),f210(x8103,x8102,x8104,x8105)) % 173.51/173.29 [811]~E(x8111,x8112)+E(f210(x8113,x8114,x8111,x8115),f210(x8113,x8114,x8112,x8115)) % 173.51/173.29 [812]~E(x8121,x8122)+E(f210(x8123,x8124,x8125,x8121),f210(x8123,x8124,x8125,x8122)) % 173.51/173.29 [813]~E(x8131,x8132)+E(f598(x8131,x8133,x8134,x8135),f598(x8132,x8133,x8134,x8135)) % 173.51/173.29 [814]~E(x8141,x8142)+E(f598(x8143,x8141,x8144,x8145),f598(x8143,x8142,x8144,x8145)) % 173.51/173.29 [815]~E(x8151,x8152)+E(f598(x8153,x8154,x8151,x8155),f598(x8153,x8154,x8152,x8155)) % 173.51/173.29 [816]~E(x8161,x8162)+E(f598(x8163,x8164,x8165,x8161),f598(x8163,x8164,x8165,x8162)) % 173.51/173.29 [817]~E(x8171,x8172)+E(f227(x8171,x8173),f227(x8172,x8173)) % 173.51/173.29 [818]~E(x8181,x8182)+E(f227(x8183,x8181),f227(x8183,x8182)) % 173.51/173.29 [819]~E(x8191,x8192)+E(f719(x8191,x8193),f719(x8192,x8193)) % 173.51/173.29 [820]~E(x8201,x8202)+E(f719(x8203,x8201),f719(x8203,x8202)) % 173.51/173.29 [821]~E(x8211,x8212)+E(f262(x8211,x8213,x8214),f262(x8212,x8213,x8214)) % 173.51/173.29 [822]~E(x8221,x8222)+E(f262(x8223,x8221,x8224),f262(x8223,x8222,x8224)) % 173.51/173.29 [823]~E(x8231,x8232)+E(f262(x8233,x8234,x8231),f262(x8233,x8234,x8232)) % 173.51/173.29 [824]~E(x8241,x8242)+E(f312(x8241,x8243,x8244),f312(x8242,x8243,x8244)) % 173.51/173.29 [825]~E(x8251,x8252)+E(f312(x8253,x8251,x8254),f312(x8253,x8252,x8254)) % 173.51/173.29 [826]~E(x8261,x8262)+E(f312(x8263,x8264,x8261),f312(x8263,x8264,x8262)) % 173.51/173.29 [827]~E(x8271,x8272)+E(f828(x8271,x8273,x8274,x8275),f828(x8272,x8273,x8274,x8275)) % 173.51/173.29 [828]~E(x8281,x8282)+E(f828(x8283,x8281,x8284,x8285),f828(x8283,x8282,x8284,x8285)) % 173.51/173.29 [829]~E(x8291,x8292)+E(f828(x8293,x8294,x8291,x8295),f828(x8293,x8294,x8292,x8295)) % 173.51/173.29 [830]~E(x8301,x8302)+E(f828(x8303,x8304,x8305,x8301),f828(x8303,x8304,x8305,x8302)) % 173.51/173.29 [831]~E(x8311,x8312)+E(f540(x8311,x8313),f540(x8312,x8313)) % 173.51/173.29 [832]~E(x8321,x8322)+E(f540(x8323,x8321),f540(x8323,x8322)) % 173.51/173.29 [833]~E(x8331,x8332)+E(f634(x8331,x8333,x8334,x8335,x8336),f634(x8332,x8333,x8334,x8335,x8336)) % 173.51/173.29 [834]~E(x8341,x8342)+E(f634(x8343,x8341,x8344,x8345,x8346),f634(x8343,x8342,x8344,x8345,x8346)) % 173.51/173.29 [835]~E(x8351,x8352)+E(f634(x8353,x8354,x8351,x8355,x8356),f634(x8353,x8354,x8352,x8355,x8356)) % 173.51/173.29 [836]~E(x8361,x8362)+E(f634(x8363,x8364,x8365,x8361,x8366),f634(x8363,x8364,x8365,x8362,x8366)) % 173.51/173.29 [837]~E(x8371,x8372)+E(f634(x8373,x8374,x8375,x8376,x8371),f634(x8373,x8374,x8375,x8376,x8372)) % 173.51/173.29 [838]~E(x8381,x8382)+E(f369(x8381,x8383,x8384,x8385,x8386,x8387),f369(x8382,x8383,x8384,x8385,x8386,x8387)) % 173.51/173.29 [839]~E(x8391,x8392)+E(f369(x8393,x8391,x8394,x8395,x8396,x8397),f369(x8393,x8392,x8394,x8395,x8396,x8397)) % 173.51/173.29 [840]~E(x8401,x8402)+E(f369(x8403,x8404,x8401,x8405,x8406,x8407),f369(x8403,x8404,x8402,x8405,x8406,x8407)) % 173.51/173.29 [841]~E(x8411,x8412)+E(f369(x8413,x8414,x8415,x8411,x8416,x8417),f369(x8413,x8414,x8415,x8412,x8416,x8417)) % 173.51/173.29 [842]~E(x8421,x8422)+E(f369(x8423,x8424,x8425,x8426,x8421,x8427),f369(x8423,x8424,x8425,x8426,x8422,x8427)) % 173.51/173.29 [843]~E(x8431,x8432)+E(f369(x8433,x8434,x8435,x8436,x8437,x8431),f369(x8433,x8434,x8435,x8436,x8437,x8432)) % 173.51/173.29 [844]~E(x8441,x8442)+E(f770(x8441,x8443,x8444,x8445),f770(x8442,x8443,x8444,x8445)) % 173.51/173.29 [845]~E(x8451,x8452)+E(f770(x8453,x8451,x8454,x8455),f770(x8453,x8452,x8454,x8455)) % 173.51/173.29 [846]~E(x8461,x8462)+E(f770(x8463,x8464,x8461,x8465),f770(x8463,x8464,x8462,x8465)) % 173.51/173.29 [847]~E(x8471,x8472)+E(f770(x8473,x8474,x8475,x8471),f770(x8473,x8474,x8475,x8472)) % 173.51/173.29 [848]~E(x8481,x8482)+E(f457(x8481,x8483,x8484),f457(x8482,x8483,x8484)) % 173.51/173.29 [849]~E(x8491,x8492)+E(f457(x8493,x8491,x8494),f457(x8493,x8492,x8494)) % 173.51/173.29 [850]~E(x8501,x8502)+E(f457(x8503,x8504,x8501),f457(x8503,x8504,x8502)) % 173.51/173.29 [851]~E(x8511,x8512)+E(f675(x8511,x8513,x8514,x8515,x8516),f675(x8512,x8513,x8514,x8515,x8516)) % 173.51/173.29 [852]~E(x8521,x8522)+E(f675(x8523,x8521,x8524,x8525,x8526),f675(x8523,x8522,x8524,x8525,x8526)) % 173.51/173.29 [853]~E(x8531,x8532)+E(f675(x8533,x8534,x8531,x8535,x8536),f675(x8533,x8534,x8532,x8535,x8536)) % 173.51/173.29 [854]~E(x8541,x8542)+E(f675(x8543,x8544,x8545,x8541,x8546),f675(x8543,x8544,x8545,x8542,x8546)) % 173.51/173.29 [855]~E(x8551,x8552)+E(f675(x8553,x8554,x8555,x8556,x8551),f675(x8553,x8554,x8555,x8556,x8552)) % 173.51/173.29 [856]~E(x8561,x8562)+E(f886(x8561,x8563),f886(x8562,x8563)) % 173.51/173.29 [857]~E(x8571,x8572)+E(f886(x8573,x8571),f886(x8573,x8572)) % 173.51/173.29 [858]~E(x8581,x8582)+E(f581(x8581,x8583,x8584,x8585,x8586),f581(x8582,x8583,x8584,x8585,x8586)) % 173.51/173.29 [859]~E(x8591,x8592)+E(f581(x8593,x8591,x8594,x8595,x8596),f581(x8593,x8592,x8594,x8595,x8596)) % 173.51/173.29 [860]~E(x8601,x8602)+E(f581(x8603,x8604,x8601,x8605,x8606),f581(x8603,x8604,x8602,x8605,x8606)) % 173.51/173.29 [861]~E(x8611,x8612)+E(f581(x8613,x8614,x8615,x8611,x8616),f581(x8613,x8614,x8615,x8612,x8616)) % 173.51/173.29 [862]~E(x8621,x8622)+E(f581(x8623,x8624,x8625,x8626,x8621),f581(x8623,x8624,x8625,x8626,x8622)) % 173.51/173.29 [863]~E(x8631,x8632)+E(f31(x8631,x8633),f31(x8632,x8633)) % 173.51/173.29 [864]~E(x8641,x8642)+E(f31(x8643,x8641),f31(x8643,x8642)) % 173.51/173.29 [865]~E(x8651,x8652)+E(f684(x8651,x8653,x8654),f684(x8652,x8653,x8654)) % 173.51/173.29 [866]~E(x8661,x8662)+E(f684(x8663,x8661,x8664),f684(x8663,x8662,x8664)) % 173.51/173.29 [867]~E(x8671,x8672)+E(f684(x8673,x8674,x8671),f684(x8673,x8674,x8672)) % 173.51/173.29 [868]~E(x8681,x8682)+E(f288(x8681),f288(x8682)) % 173.51/173.29 [869]~E(x8691,x8692)+E(f772(x8691,x8693),f772(x8692,x8693)) % 173.51/173.29 [870]~E(x8701,x8702)+E(f772(x8703,x8701),f772(x8703,x8702)) % 173.51/173.29 [871]~E(x8711,x8712)+E(f501(x8711,x8713,x8714),f501(x8712,x8713,x8714)) % 173.51/173.29 [872]~E(x8721,x8722)+E(f501(x8723,x8721,x8724),f501(x8723,x8722,x8724)) % 173.51/173.29 [873]~E(x8731,x8732)+E(f501(x8733,x8734,x8731),f501(x8733,x8734,x8732)) % 173.51/173.29 [874]~E(x8741,x8742)+E(f194(x8741),f194(x8742)) % 173.51/173.29 [875]~E(x8751,x8752)+E(f261(x8751,x8753,x8754),f261(x8752,x8753,x8754)) % 173.51/173.29 [876]~E(x8761,x8762)+E(f261(x8763,x8761,x8764),f261(x8763,x8762,x8764)) % 173.51/173.29 [877]~E(x8771,x8772)+E(f261(x8773,x8774,x8771),f261(x8773,x8774,x8772)) % 173.51/173.29 [878]~E(x8781,x8782)+E(f707(x8781,x8783,x8784,x8785),f707(x8782,x8783,x8784,x8785)) % 173.51/173.29 [879]~E(x8791,x8792)+E(f707(x8793,x8791,x8794,x8795),f707(x8793,x8792,x8794,x8795)) % 173.51/173.29 [880]~E(x8801,x8802)+E(f707(x8803,x8804,x8801,x8805),f707(x8803,x8804,x8802,x8805)) % 173.51/173.29 [881]~E(x8811,x8812)+E(f707(x8813,x8814,x8815,x8811),f707(x8813,x8814,x8815,x8812)) % 173.51/173.29 [882]~E(x8821,x8822)+E(f63(x8821),f63(x8822)) % 173.51/173.29 [883]~E(x8831,x8832)+E(f574(x8831,x8833,x8834),f574(x8832,x8833,x8834)) % 173.51/173.29 [884]~E(x8841,x8842)+E(f574(x8843,x8841,x8844),f574(x8843,x8842,x8844)) % 173.51/173.29 [885]~E(x8851,x8852)+E(f574(x8853,x8854,x8851),f574(x8853,x8854,x8852)) % 173.51/173.29 [886]~E(x8861,x8862)+E(f530(x8861,x8863,x8864),f530(x8862,x8863,x8864)) % 173.51/173.29 [887]~E(x8871,x8872)+E(f530(x8873,x8871,x8874),f530(x8873,x8872,x8874)) % 173.51/173.29 [888]~E(x8881,x8882)+E(f530(x8883,x8884,x8881),f530(x8883,x8884,x8882)) % 173.51/173.29 [889]~E(x8891,x8892)+E(f776(x8891,x8893),f776(x8892,x8893)) % 173.51/173.29 [890]~E(x8901,x8902)+E(f776(x8903,x8901),f776(x8903,x8902)) % 173.51/173.29 [891]~E(x8911,x8912)+E(f83(x8911,x8913,x8914,x8915,x8916),f83(x8912,x8913,x8914,x8915,x8916)) % 173.51/173.29 [892]~E(x8921,x8922)+E(f83(x8923,x8921,x8924,x8925,x8926),f83(x8923,x8922,x8924,x8925,x8926)) % 173.51/173.29 [893]~E(x8931,x8932)+E(f83(x8933,x8934,x8931,x8935,x8936),f83(x8933,x8934,x8932,x8935,x8936)) % 173.51/173.29 [894]~E(x8941,x8942)+E(f83(x8943,x8944,x8945,x8941,x8946),f83(x8943,x8944,x8945,x8942,x8946)) % 173.51/173.29 [895]~E(x8951,x8952)+E(f83(x8953,x8954,x8955,x8956,x8951),f83(x8953,x8954,x8955,x8956,x8952)) % 173.51/173.29 [896]~E(x8961,x8962)+E(f854(x8961,x8963,x8964),f854(x8962,x8963,x8964)) % 173.51/173.29 [897]~E(x8971,x8972)+E(f854(x8973,x8971,x8974),f854(x8973,x8972,x8974)) % 173.51/173.29 [898]~E(x8981,x8982)+E(f854(x8983,x8984,x8981),f854(x8983,x8984,x8982)) % 173.51/173.29 [899]~E(x8991,x8992)+E(f725(x8991,x8993,x8994,x8995,x8996),f725(x8992,x8993,x8994,x8995,x8996)) % 173.51/173.29 [900]~E(x9001,x9002)+E(f725(x9003,x9001,x9004,x9005,x9006),f725(x9003,x9002,x9004,x9005,x9006)) % 173.51/173.29 [901]~E(x9011,x9012)+E(f725(x9013,x9014,x9011,x9015,x9016),f725(x9013,x9014,x9012,x9015,x9016)) % 173.51/173.29 [902]~E(x9021,x9022)+E(f725(x9023,x9024,x9025,x9021,x9026),f725(x9023,x9024,x9025,x9022,x9026)) % 173.51/173.29 [903]~E(x9031,x9032)+E(f725(x9033,x9034,x9035,x9036,x9031),f725(x9033,x9034,x9035,x9036,x9032)) % 173.51/173.29 [904]~E(x9041,x9042)+E(f845(x9041,x9043),f845(x9042,x9043)) % 173.51/173.29 [905]~E(x9051,x9052)+E(f845(x9053,x9051),f845(x9053,x9052)) % 173.51/173.29 [906]~E(x9061,x9062)+E(f808(x9061,x9063,x9064,x9065),f808(x9062,x9063,x9064,x9065)) % 173.51/173.29 [907]~E(x9071,x9072)+E(f808(x9073,x9071,x9074,x9075),f808(x9073,x9072,x9074,x9075)) % 173.51/173.29 [908]~E(x9081,x9082)+E(f808(x9083,x9084,x9081,x9085),f808(x9083,x9084,x9082,x9085)) % 173.51/173.29 [909]~E(x9091,x9092)+E(f808(x9093,x9094,x9095,x9091),f808(x9093,x9094,x9095,x9092)) % 173.51/173.29 [910]~E(x9101,x9102)+E(f822(x9101,x9103,x9104,x9105),f822(x9102,x9103,x9104,x9105)) % 173.51/173.29 [911]~E(x9111,x9112)+E(f822(x9113,x9111,x9114,x9115),f822(x9113,x9112,x9114,x9115)) % 173.51/173.29 [912]~E(x9121,x9122)+E(f822(x9123,x9124,x9121,x9125),f822(x9123,x9124,x9122,x9125)) % 173.51/173.29 [913]~E(x9131,x9132)+E(f822(x9133,x9134,x9135,x9131),f822(x9133,x9134,x9135,x9132)) % 173.51/173.29 [914]~E(x9141,x9142)+E(f356(x9141,x9143,x9144,x9145),f356(x9142,x9143,x9144,x9145)) % 173.51/173.29 [915]~E(x9151,x9152)+E(f356(x9153,x9151,x9154,x9155),f356(x9153,x9152,x9154,x9155)) % 173.51/173.29 [916]~E(x9161,x9162)+E(f356(x9163,x9164,x9161,x9165),f356(x9163,x9164,x9162,x9165)) % 173.51/173.29 [917]~E(x9171,x9172)+E(f356(x9173,x9174,x9175,x9171),f356(x9173,x9174,x9175,x9172)) % 173.51/173.29 [918]~E(x9181,x9182)+E(f170(x9181,x9183),f170(x9182,x9183)) % 173.51/173.29 [919]~E(x9191,x9192)+E(f170(x9193,x9191),f170(x9193,x9192)) % 173.51/173.29 [920]~E(x9201,x9202)+E(f21(x9201,x9203),f21(x9202,x9203)) % 173.51/173.29 [921]~E(x9211,x9212)+E(f21(x9213,x9211),f21(x9213,x9212)) % 173.51/173.29 [922]~E(x9221,x9222)+E(f654(x9221,x9223,x9224,x9225,x9226,x9227,x9228,x9229),f654(x9222,x9223,x9224,x9225,x9226,x9227,x9228,x9229)) % 173.51/173.29 [923]~E(x9231,x9232)+E(f654(x9233,x9231,x9234,x9235,x9236,x9237,x9238,x9239),f654(x9233,x9232,x9234,x9235,x9236,x9237,x9238,x9239)) % 173.51/173.29 [924]~E(x9241,x9242)+E(f654(x9243,x9244,x9241,x9245,x9246,x9247,x9248,x9249),f654(x9243,x9244,x9242,x9245,x9246,x9247,x9248,x9249)) % 173.51/173.29 [925]~E(x9251,x9252)+E(f654(x9253,x9254,x9255,x9251,x9256,x9257,x9258,x9259),f654(x9253,x9254,x9255,x9252,x9256,x9257,x9258,x9259)) % 173.51/173.29 [926]~E(x9261,x9262)+E(f654(x9263,x9264,x9265,x9266,x9261,x9267,x9268,x9269),f654(x9263,x9264,x9265,x9266,x9262,x9267,x9268,x9269)) % 173.51/173.29 [927]~E(x9271,x9272)+E(f654(x9273,x9274,x9275,x9276,x9277,x9271,x9278,x9279),f654(x9273,x9274,x9275,x9276,x9277,x9272,x9278,x9279)) % 173.51/173.29 [928]~E(x9281,x9282)+E(f654(x9283,x9284,x9285,x9286,x9287,x9288,x9281,x9289),f654(x9283,x9284,x9285,x9286,x9287,x9288,x9282,x9289)) % 173.51/173.29 [929]~E(x9291,x9292)+E(f654(x9293,x9294,x9295,x9296,x9297,x9298,x9299,x9291),f654(x9293,x9294,x9295,x9296,x9297,x9298,x9299,x9292)) % 173.51/173.29 [930]~E(x9301,x9302)+E(f103(x9301,x9303,x9304),f103(x9302,x9303,x9304)) % 173.51/173.29 [931]~E(x9311,x9312)+E(f103(x9313,x9311,x9314),f103(x9313,x9312,x9314)) % 173.51/173.29 [932]~E(x9321,x9322)+E(f103(x9323,x9324,x9321),f103(x9323,x9324,x9322)) % 173.51/173.29 [933]~E(x9331,x9332)+E(f106(x9331,x9333,x9334,x9335),f106(x9332,x9333,x9334,x9335)) % 173.51/173.29 [934]~E(x9341,x9342)+E(f106(x9343,x9341,x9344,x9345),f106(x9343,x9342,x9344,x9345)) % 173.51/173.29 [935]~E(x9351,x9352)+E(f106(x9353,x9354,x9351,x9355),f106(x9353,x9354,x9352,x9355)) % 173.51/173.29 [936]~E(x9361,x9362)+E(f106(x9363,x9364,x9365,x9361),f106(x9363,x9364,x9365,x9362)) % 173.51/173.29 [937]~E(x9371,x9372)+E(f705(x9371,x9373,x9374,x9375),f705(x9372,x9373,x9374,x9375)) % 173.51/173.29 [938]~E(x9381,x9382)+E(f705(x9383,x9381,x9384,x9385),f705(x9383,x9382,x9384,x9385)) % 173.51/173.29 [939]~E(x9391,x9392)+E(f705(x9393,x9394,x9391,x9395),f705(x9393,x9394,x9392,x9395)) % 173.51/173.29 [940]~E(x9401,x9402)+E(f705(x9403,x9404,x9405,x9401),f705(x9403,x9404,x9405,x9402)) % 173.51/173.29 [941]~E(x9411,x9412)+E(f388(x9411,x9413),f388(x9412,x9413)) % 173.51/173.29 [942]~E(x9421,x9422)+E(f388(x9423,x9421),f388(x9423,x9422)) % 173.51/173.29 [943]~E(x9431,x9432)+E(f163(x9431,x9433,x9434),f163(x9432,x9433,x9434)) % 173.51/173.29 [944]~E(x9441,x9442)+E(f163(x9443,x9441,x9444),f163(x9443,x9442,x9444)) % 173.51/173.29 [945]~E(x9451,x9452)+E(f163(x9453,x9454,x9451),f163(x9453,x9454,x9452)) % 173.51/173.29 [946]~E(x9461,x9462)+E(f74(x9461,x9463,x9464),f74(x9462,x9463,x9464)) % 173.51/173.29 [947]~E(x9471,x9472)+E(f74(x9473,x9471,x9474),f74(x9473,x9472,x9474)) % 173.51/173.29 [948]~E(x9481,x9482)+E(f74(x9483,x9484,x9481),f74(x9483,x9484,x9482)) % 173.51/173.29 [949]~E(x9491,x9492)+E(f663(x9491,x9493,x9494),f663(x9492,x9493,x9494)) % 173.51/173.29 [950]~E(x9501,x9502)+E(f663(x9503,x9501,x9504),f663(x9503,x9502,x9504)) % 173.51/173.29 [951]~E(x9511,x9512)+E(f663(x9513,x9514,x9511),f663(x9513,x9514,x9512)) % 173.51/173.29 [952]~E(x9521,x9522)+E(f174(x9521,x9523,x9524),f174(x9522,x9523,x9524)) % 173.51/173.29 [953]~E(x9531,x9532)+E(f174(x9533,x9531,x9534),f174(x9533,x9532,x9534)) % 173.51/173.29 [954]~E(x9541,x9542)+E(f174(x9543,x9544,x9541),f174(x9543,x9544,x9542)) % 173.51/173.29 [955]~E(x9551,x9552)+E(f816(x9551,x9553,x9554,x9555),f816(x9552,x9553,x9554,x9555)) % 173.51/173.29 [956]~E(x9561,x9562)+E(f816(x9563,x9561,x9564,x9565),f816(x9563,x9562,x9564,x9565)) % 173.51/173.29 [957]~E(x9571,x9572)+E(f816(x9573,x9574,x9571,x9575),f816(x9573,x9574,x9572,x9575)) % 173.51/173.29 [958]~E(x9581,x9582)+E(f816(x9583,x9584,x9585,x9581),f816(x9583,x9584,x9585,x9582)) % 173.51/173.29 [959]~E(x9591,x9592)+E(f881(x9591),f881(x9592)) % 173.51/173.29 [960]~E(x9601,x9602)+E(f65(x9601,x9603,x9604,x9605),f65(x9602,x9603,x9604,x9605)) % 173.51/173.29 [961]~E(x9611,x9612)+E(f65(x9613,x9611,x9614,x9615),f65(x9613,x9612,x9614,x9615)) % 173.51/173.29 [962]~E(x9621,x9622)+E(f65(x9623,x9624,x9621,x9625),f65(x9623,x9624,x9622,x9625)) % 173.51/173.29 [963]~E(x9631,x9632)+E(f65(x9633,x9634,x9635,x9631),f65(x9633,x9634,x9635,x9632)) % 173.51/173.29 [964]~E(x9641,x9642)+E(f200(x9641,x9643),f200(x9642,x9643)) % 173.51/173.29 [965]~E(x9651,x9652)+E(f200(x9653,x9651),f200(x9653,x9652)) % 173.51/173.29 [966]~E(x9661,x9662)+E(f863(x9661,x9663,x9664,x9665),f863(x9662,x9663,x9664,x9665)) % 173.51/173.29 [967]~E(x9671,x9672)+E(f863(x9673,x9671,x9674,x9675),f863(x9673,x9672,x9674,x9675)) % 173.51/173.29 [968]~E(x9681,x9682)+E(f863(x9683,x9684,x9681,x9685),f863(x9683,x9684,x9682,x9685)) % 173.51/173.29 [969]~E(x9691,x9692)+E(f863(x9693,x9694,x9695,x9691),f863(x9693,x9694,x9695,x9692)) % 173.51/173.29 [970]~E(x9701,x9702)+E(f131(x9701,x9703),f131(x9702,x9703)) % 173.51/173.29 [971]~E(x9711,x9712)+E(f131(x9713,x9711),f131(x9713,x9712)) % 173.51/173.29 [972]~E(x9721,x9722)+E(f579(x9721,x9723,x9724,x9725,x9726),f579(x9722,x9723,x9724,x9725,x9726)) % 173.51/173.29 [973]~E(x9731,x9732)+E(f579(x9733,x9731,x9734,x9735,x9736),f579(x9733,x9732,x9734,x9735,x9736)) % 173.51/173.29 [974]~E(x9741,x9742)+E(f579(x9743,x9744,x9741,x9745,x9746),f579(x9743,x9744,x9742,x9745,x9746)) % 173.51/173.29 [975]~E(x9751,x9752)+E(f579(x9753,x9754,x9755,x9751,x9756),f579(x9753,x9754,x9755,x9752,x9756)) % 173.51/173.29 [976]~E(x9761,x9762)+E(f579(x9763,x9764,x9765,x9766,x9761),f579(x9763,x9764,x9765,x9766,x9762)) % 173.51/173.29 [977]~E(x9771,x9772)+E(f504(x9771,x9773,x9774,x9775,x9776),f504(x9772,x9773,x9774,x9775,x9776)) % 173.51/173.29 [978]~E(x9781,x9782)+E(f504(x9783,x9781,x9784,x9785,x9786),f504(x9783,x9782,x9784,x9785,x9786)) % 173.51/173.29 [979]~E(x9791,x9792)+E(f504(x9793,x9794,x9791,x9795,x9796),f504(x9793,x9794,x9792,x9795,x9796)) % 173.51/173.29 [980]~E(x9801,x9802)+E(f504(x9803,x9804,x9805,x9801,x9806),f504(x9803,x9804,x9805,x9802,x9806)) % 173.51/173.29 [981]~E(x9811,x9812)+E(f504(x9813,x9814,x9815,x9816,x9811),f504(x9813,x9814,x9815,x9816,x9812)) % 173.51/173.29 [982]~E(x9821,x9822)+E(f664(x9821,x9823,x9824),f664(x9822,x9823,x9824)) % 173.51/173.29 [983]~E(x9831,x9832)+E(f664(x9833,x9831,x9834),f664(x9833,x9832,x9834)) % 173.51/173.29 [984]~E(x9841,x9842)+E(f664(x9843,x9844,x9841),f664(x9843,x9844,x9842)) % 173.51/173.29 [985]~E(x9851,x9852)+E(f807(x9851,x9853,x9854),f807(x9852,x9853,x9854)) % 173.51/173.29 [986]~E(x9861,x9862)+E(f807(x9863,x9861,x9864),f807(x9863,x9862,x9864)) % 173.51/173.29 [987]~E(x9871,x9872)+E(f807(x9873,x9874,x9871),f807(x9873,x9874,x9872)) % 173.51/173.29 [988]~E(x9881,x9882)+E(f879(x9881,x9883,x9884,x9885,x9886,x9887,x9888,x9889),f879(x9882,x9883,x9884,x9885,x9886,x9887,x9888,x9889)) % 173.51/173.29 [989]~E(x9891,x9892)+E(f879(x9893,x9891,x9894,x9895,x9896,x9897,x9898,x9899),f879(x9893,x9892,x9894,x9895,x9896,x9897,x9898,x9899)) % 173.51/173.29 [990]~E(x9901,x9902)+E(f879(x9903,x9904,x9901,x9905,x9906,x9907,x9908,x9909),f879(x9903,x9904,x9902,x9905,x9906,x9907,x9908,x9909)) % 173.51/173.29 [991]~E(x9911,x9912)+E(f879(x9913,x9914,x9915,x9911,x9916,x9917,x9918,x9919),f879(x9913,x9914,x9915,x9912,x9916,x9917,x9918,x9919)) % 173.51/173.29 [992]~E(x9921,x9922)+E(f879(x9923,x9924,x9925,x9926,x9921,x9927,x9928,x9929),f879(x9923,x9924,x9925,x9926,x9922,x9927,x9928,x9929)) % 173.51/173.29 [993]~E(x9931,x9932)+E(f879(x9933,x9934,x9935,x9936,x9937,x9931,x9938,x9939),f879(x9933,x9934,x9935,x9936,x9937,x9932,x9938,x9939)) % 173.51/173.29 [994]~E(x9941,x9942)+E(f879(x9943,x9944,x9945,x9946,x9947,x9948,x9941,x9949),f879(x9943,x9944,x9945,x9946,x9947,x9948,x9942,x9949)) % 173.51/173.29 [995]~E(x9951,x9952)+E(f879(x9953,x9954,x9955,x9956,x9957,x9958,x9959,x9951),f879(x9953,x9954,x9955,x9956,x9957,x9958,x9959,x9952)) % 173.51/173.29 [996]~E(x9961,x9962)+E(f713(x9961,x9963),f713(x9962,x9963)) % 173.51/173.29 [997]~E(x9971,x9972)+E(f713(x9973,x9971),f713(x9973,x9972)) % 173.51/173.29 [998]~E(x9981,x9982)+E(f862(x9981,x9983,x9984,x9985,x9986),f862(x9982,x9983,x9984,x9985,x9986)) % 173.51/173.29 [999]~E(x9991,x9992)+E(f862(x9993,x9991,x9994,x9995,x9996),f862(x9993,x9992,x9994,x9995,x9996)) % 173.51/173.29 [1000]~E(x10001,x10002)+E(f862(x10003,x10004,x10001,x10005,x10006),f862(x10003,x10004,x10002,x10005,x10006)) % 173.51/173.29 [1001]~E(x10011,x10012)+E(f862(x10013,x10014,x10015,x10011,x10016),f862(x10013,x10014,x10015,x10012,x10016)) % 173.51/173.29 [1002]~E(x10021,x10022)+E(f862(x10023,x10024,x10025,x10026,x10021),f862(x10023,x10024,x10025,x10026,x10022)) % 173.51/173.29 [1003]~E(x10031,x10032)+E(f127(x10031,x10033,x10034),f127(x10032,x10033,x10034)) % 173.51/173.29 [1004]~E(x10041,x10042)+E(f127(x10043,x10041,x10044),f127(x10043,x10042,x10044)) % 173.51/173.29 [1005]~E(x10051,x10052)+E(f127(x10053,x10054,x10051),f127(x10053,x10054,x10052)) % 173.51/173.29 [1006]~E(x10061,x10062)+E(f773(x10061,x10063),f773(x10062,x10063)) % 173.51/173.29 [1007]~E(x10071,x10072)+E(f773(x10073,x10071),f773(x10073,x10072)) % 173.51/173.29 [1008]~E(x10081,x10082)+E(f859(x10081,x10083,x10084,x10085),f859(x10082,x10083,x10084,x10085)) % 173.51/173.29 [1009]~E(x10091,x10092)+E(f859(x10093,x10091,x10094,x10095),f859(x10093,x10092,x10094,x10095)) % 173.51/173.29 [1010]~E(x10101,x10102)+E(f859(x10103,x10104,x10101,x10105),f859(x10103,x10104,x10102,x10105)) % 173.51/173.29 [1011]~E(x10111,x10112)+E(f859(x10113,x10114,x10115,x10111),f859(x10113,x10114,x10115,x10112)) % 173.51/173.29 [1012]~E(x10121,x10122)+E(f347(x10121,x10123,x10124,x10125),f347(x10122,x10123,x10124,x10125)) % 173.51/173.29 [1013]~E(x10131,x10132)+E(f347(x10133,x10131,x10134,x10135),f347(x10133,x10132,x10134,x10135)) % 173.51/173.29 [1014]~E(x10141,x10142)+E(f347(x10143,x10144,x10141,x10145),f347(x10143,x10144,x10142,x10145)) % 173.51/173.29 [1015]~E(x10151,x10152)+E(f347(x10153,x10154,x10155,x10151),f347(x10153,x10154,x10155,x10152)) % 173.51/173.29 [1016]~E(x10161,x10162)+E(f625(x10161,x10163,x10164,x10165,x10166),f625(x10162,x10163,x10164,x10165,x10166)) % 173.51/173.29 [1017]~E(x10171,x10172)+E(f625(x10173,x10171,x10174,x10175,x10176),f625(x10173,x10172,x10174,x10175,x10176)) % 173.51/173.29 [1018]~E(x10181,x10182)+E(f625(x10183,x10184,x10181,x10185,x10186),f625(x10183,x10184,x10182,x10185,x10186)) % 173.51/173.29 [1019]~E(x10191,x10192)+E(f625(x10193,x10194,x10195,x10191,x10196),f625(x10193,x10194,x10195,x10192,x10196)) % 173.51/173.29 [1020]~E(x10201,x10202)+E(f625(x10203,x10204,x10205,x10206,x10201),f625(x10203,x10204,x10205,x10206,x10202)) % 173.51/173.29 [1021]~E(x10211,x10212)+E(f363(x10211),f363(x10212)) % 173.51/173.29 [1022]~E(x10221,x10222)+E(f835(x10221,x10223,x10224,x10225,x10226,x10227,x10228),f835(x10222,x10223,x10224,x10225,x10226,x10227,x10228)) % 173.51/173.29 [1023]~E(x10231,x10232)+E(f835(x10233,x10231,x10234,x10235,x10236,x10237,x10238),f835(x10233,x10232,x10234,x10235,x10236,x10237,x10238)) % 173.51/173.29 [1024]~E(x10241,x10242)+E(f835(x10243,x10244,x10241,x10245,x10246,x10247,x10248),f835(x10243,x10244,x10242,x10245,x10246,x10247,x10248)) % 173.51/173.29 [1025]~E(x10251,x10252)+E(f835(x10253,x10254,x10255,x10251,x10256,x10257,x10258),f835(x10253,x10254,x10255,x10252,x10256,x10257,x10258)) % 173.51/173.29 [1026]~E(x10261,x10262)+E(f835(x10263,x10264,x10265,x10266,x10261,x10267,x10268),f835(x10263,x10264,x10265,x10266,x10262,x10267,x10268)) % 173.51/173.29 [1027]~E(x10271,x10272)+E(f835(x10273,x10274,x10275,x10276,x10277,x10271,x10278),f835(x10273,x10274,x10275,x10276,x10277,x10272,x10278)) % 173.51/173.29 [1028]~E(x10281,x10282)+E(f835(x10283,x10284,x10285,x10286,x10287,x10288,x10281),f835(x10283,x10284,x10285,x10286,x10287,x10288,x10282)) % 173.51/173.29 [1029]~E(x10291,x10292)+E(f674(x10291,x10293,x10294,x10295),f674(x10292,x10293,x10294,x10295)) % 173.51/173.29 [1030]~E(x10301,x10302)+E(f674(x10303,x10301,x10304,x10305),f674(x10303,x10302,x10304,x10305)) % 173.51/173.29 [1031]~E(x10311,x10312)+E(f674(x10313,x10314,x10311,x10315),f674(x10313,x10314,x10312,x10315)) % 173.51/173.29 [1032]~E(x10321,x10322)+E(f674(x10323,x10324,x10325,x10321),f674(x10323,x10324,x10325,x10322)) % 173.51/173.29 [1033]~E(x10331,x10332)+E(f60(x10331,x10333),f60(x10332,x10333)) % 173.51/173.29 [1034]~E(x10341,x10342)+E(f60(x10343,x10341),f60(x10343,x10342)) % 173.51/173.29 [1035]~E(x10351,x10352)+E(f301(x10351,x10353,x10354),f301(x10352,x10353,x10354)) % 173.51/173.29 [1036]~E(x10361,x10362)+E(f301(x10363,x10361,x10364),f301(x10363,x10362,x10364)) % 173.51/173.29 [1037]~E(x10371,x10372)+E(f301(x10373,x10374,x10371),f301(x10373,x10374,x10372)) % 173.51/173.29 [1038]~E(x10381,x10382)+E(f706(x10381,x10383,x10384,x10385),f706(x10382,x10383,x10384,x10385)) % 173.51/173.29 [1039]~E(x10391,x10392)+E(f706(x10393,x10391,x10394,x10395),f706(x10393,x10392,x10394,x10395)) % 173.51/173.29 [1040]~E(x10401,x10402)+E(f706(x10403,x10404,x10401,x10405),f706(x10403,x10404,x10402,x10405)) % 173.51/173.29 [1041]~E(x10411,x10412)+E(f706(x10413,x10414,x10415,x10411),f706(x10413,x10414,x10415,x10412)) % 173.51/173.29 [1042]~E(x10421,x10422)+E(f415(x10421,x10423,x10424,x10425),f415(x10422,x10423,x10424,x10425)) % 173.51/173.29 [1043]~E(x10431,x10432)+E(f415(x10433,x10431,x10434,x10435),f415(x10433,x10432,x10434,x10435)) % 173.51/173.29 [1044]~E(x10441,x10442)+E(f415(x10443,x10444,x10441,x10445),f415(x10443,x10444,x10442,x10445)) % 173.51/173.29 [1045]~E(x10451,x10452)+E(f415(x10453,x10454,x10455,x10451),f415(x10453,x10454,x10455,x10452)) % 173.51/173.29 [1046]~E(x10461,x10462)+E(f658(x10461,x10463,x10464,x10465,x10466),f658(x10462,x10463,x10464,x10465,x10466)) % 173.51/173.29 [1047]~E(x10471,x10472)+E(f658(x10473,x10471,x10474,x10475,x10476),f658(x10473,x10472,x10474,x10475,x10476)) % 173.51/173.29 [1048]~E(x10481,x10482)+E(f658(x10483,x10484,x10481,x10485,x10486),f658(x10483,x10484,x10482,x10485,x10486)) % 173.51/173.29 [1049]~E(x10491,x10492)+E(f658(x10493,x10494,x10495,x10491,x10496),f658(x10493,x10494,x10495,x10492,x10496)) % 173.51/173.29 [1050]~E(x10501,x10502)+E(f658(x10503,x10504,x10505,x10506,x10501),f658(x10503,x10504,x10505,x10506,x10502)) % 173.51/173.29 [1051]~E(x10511,x10512)+E(f451(x10511),f451(x10512)) % 173.51/173.29 [1052]~E(x10521,x10522)+E(f883(x10521,x10523,x10524),f883(x10522,x10523,x10524)) % 173.51/173.29 [1053]~E(x10531,x10532)+E(f883(x10533,x10531,x10534),f883(x10533,x10532,x10534)) % 173.51/173.29 [1054]~E(x10541,x10542)+E(f883(x10543,x10544,x10541),f883(x10543,x10544,x10542)) % 173.51/173.29 [1055]~E(x10551,x10552)+E(f757(x10551,x10553,x10554),f757(x10552,x10553,x10554)) % 173.51/173.29 [1056]~E(x10561,x10562)+E(f757(x10563,x10561,x10564),f757(x10563,x10562,x10564)) % 173.51/173.29 [1057]~E(x10571,x10572)+E(f757(x10573,x10574,x10571),f757(x10573,x10574,x10572)) % 173.51/173.29 [1058]~E(x10581,x10582)+E(f687(x10581,x10583),f687(x10582,x10583)) % 173.51/173.29 [1059]~E(x10591,x10592)+E(f687(x10593,x10591),f687(x10593,x10592)) % 173.51/173.29 [1060]~E(x10601,x10602)+E(f305(x10601,x10603,x10604,x10605),f305(x10602,x10603,x10604,x10605)) % 173.51/173.29 [1061]~E(x10611,x10612)+E(f305(x10613,x10611,x10614,x10615),f305(x10613,x10612,x10614,x10615)) % 173.51/173.29 [1062]~E(x10621,x10622)+E(f305(x10623,x10624,x10621,x10625),f305(x10623,x10624,x10622,x10625)) % 173.51/173.29 [1063]~E(x10631,x10632)+E(f305(x10633,x10634,x10635,x10631),f305(x10633,x10634,x10635,x10632)) % 173.51/173.29 [1064]~E(x10641,x10642)+E(f188(x10641),f188(x10642)) % 173.51/173.29 [1065]~E(x10651,x10652)+E(f242(x10651,x10653,x10654),f242(x10652,x10653,x10654)) % 173.51/173.29 [1066]~E(x10661,x10662)+E(f242(x10663,x10661,x10664),f242(x10663,x10662,x10664)) % 173.51/173.29 [1067]~E(x10671,x10672)+E(f242(x10673,x10674,x10671),f242(x10673,x10674,x10672)) % 173.51/173.29 [1068]~E(x10681,x10682)+E(f475(x10681,x10683,x10684),f475(x10682,x10683,x10684)) % 173.51/173.29 [1069]~E(x10691,x10692)+E(f475(x10693,x10691,x10694),f475(x10693,x10692,x10694)) % 173.51/173.29 [1070]~E(x10701,x10702)+E(f475(x10703,x10704,x10701),f475(x10703,x10704,x10702)) % 173.51/173.29 [1071]~E(x10711,x10712)+E(f463(x10711,x10713,x10714),f463(x10712,x10713,x10714)) % 173.51/173.29 [1072]~E(x10721,x10722)+E(f463(x10723,x10721,x10724),f463(x10723,x10722,x10724)) % 173.51/173.29 [1073]~E(x10731,x10732)+E(f463(x10733,x10734,x10731),f463(x10733,x10734,x10732)) % 173.51/173.29 [1074]~E(x10741,x10742)+E(f181(x10741,x10743,x10744),f181(x10742,x10743,x10744)) % 173.51/173.29 [1075]~E(x10751,x10752)+E(f181(x10753,x10751,x10754),f181(x10753,x10752,x10754)) % 173.51/173.29 [1076]~E(x10761,x10762)+E(f181(x10763,x10764,x10761),f181(x10763,x10764,x10762)) % 173.51/173.29 [1077]~E(x10771,x10772)+E(f327(x10771,x10773,x10774),f327(x10772,x10773,x10774)) % 173.51/173.29 [1078]~E(x10781,x10782)+E(f327(x10783,x10781,x10784),f327(x10783,x10782,x10784)) % 173.51/173.29 [1079]~E(x10791,x10792)+E(f327(x10793,x10794,x10791),f327(x10793,x10794,x10792)) % 173.51/173.29 [1080]~E(x10801,x10802)+E(f642(x10801,x10803,x10804),f642(x10802,x10803,x10804)) % 173.51/173.29 [1081]~E(x10811,x10812)+E(f642(x10813,x10811,x10814),f642(x10813,x10812,x10814)) % 173.51/173.29 [1082]~E(x10821,x10822)+E(f642(x10823,x10824,x10821),f642(x10823,x10824,x10822)) % 173.51/173.29 [1083]~E(x10831,x10832)+E(f282(x10831,x10833),f282(x10832,x10833)) % 173.51/173.29 [1084]~E(x10841,x10842)+E(f282(x10843,x10841),f282(x10843,x10842)) % 173.51/173.29 [1085]~E(x10851,x10852)+E(f164(x10851,x10853,x10854,x10855),f164(x10852,x10853,x10854,x10855)) % 173.51/173.29 [1086]~E(x10861,x10862)+E(f164(x10863,x10861,x10864,x10865),f164(x10863,x10862,x10864,x10865)) % 173.51/173.29 [1087]~E(x10871,x10872)+E(f164(x10873,x10874,x10871,x10875),f164(x10873,x10874,x10872,x10875)) % 173.51/173.29 [1088]~E(x10881,x10882)+E(f164(x10883,x10884,x10885,x10881),f164(x10883,x10884,x10885,x10882)) % 173.51/173.29 [1089]~E(x10891,x10892)+E(f561(x10891,x10893,x10894),f561(x10892,x10893,x10894)) % 173.51/173.29 [1090]~E(x10901,x10902)+E(f561(x10903,x10901,x10904),f561(x10903,x10902,x10904)) % 173.51/173.29 [1091]~E(x10911,x10912)+E(f561(x10913,x10914,x10911),f561(x10913,x10914,x10912)) % 173.51/173.29 [1092]~E(x10921,x10922)+E(f604(x10921,x10923),f604(x10922,x10923)) % 173.51/173.29 [1093]~E(x10931,x10932)+E(f604(x10933,x10931),f604(x10933,x10932)) % 173.51/173.29 [1094]~E(x10941,x10942)+E(f490(x10941,x10943),f490(x10942,x10943)) % 173.51/173.29 [1095]~E(x10951,x10952)+E(f490(x10953,x10951),f490(x10953,x10952)) % 173.51/173.29 [1096]~E(x10961,x10962)+E(f711(x10961,x10963,x10964,x10965),f711(x10962,x10963,x10964,x10965)) % 173.51/173.29 [1097]~E(x10971,x10972)+E(f711(x10973,x10971,x10974,x10975),f711(x10973,x10972,x10974,x10975)) % 173.51/173.29 [1098]~E(x10981,x10982)+E(f711(x10983,x10984,x10981,x10985),f711(x10983,x10984,x10982,x10985)) % 173.51/173.29 [1099]~E(x10991,x10992)+E(f711(x10993,x10994,x10995,x10991),f711(x10993,x10994,x10995,x10992)) % 173.51/173.29 [1100]~E(x11001,x11002)+E(f396(x11001,x11003,x11004,x11005),f396(x11002,x11003,x11004,x11005)) % 173.51/173.29 [1101]~E(x11011,x11012)+E(f396(x11013,x11011,x11014,x11015),f396(x11013,x11012,x11014,x11015)) % 173.51/173.29 [1102]~E(x11021,x11022)+E(f396(x11023,x11024,x11021,x11025),f396(x11023,x11024,x11022,x11025)) % 173.51/173.29 [1103]~E(x11031,x11032)+E(f396(x11033,x11034,x11035,x11031),f396(x11033,x11034,x11035,x11032)) % 173.51/173.29 [1104]~E(x11041,x11042)+E(f393(x11041,x11043,x11044,x11045),f393(x11042,x11043,x11044,x11045)) % 173.51/173.29 [1105]~E(x11051,x11052)+E(f393(x11053,x11051,x11054,x11055),f393(x11053,x11052,x11054,x11055)) % 173.51/173.29 [1106]~E(x11061,x11062)+E(f393(x11063,x11064,x11061,x11065),f393(x11063,x11064,x11062,x11065)) % 173.51/173.29 [1107]~E(x11071,x11072)+E(f393(x11073,x11074,x11075,x11071),f393(x11073,x11074,x11075,x11072)) % 173.51/173.29 [1108]~E(x11081,x11082)+E(f812(x11081,x11083,x11084),f812(x11082,x11083,x11084)) % 173.51/173.29 [1109]~E(x11091,x11092)+E(f812(x11093,x11091,x11094),f812(x11093,x11092,x11094)) % 173.51/173.29 [1110]~E(x11101,x11102)+E(f812(x11103,x11104,x11101),f812(x11103,x11104,x11102)) % 173.51/173.29 [1111]~E(x11111,x11112)+E(f373(x11111,x11113,x11114,x11115),f373(x11112,x11113,x11114,x11115)) % 173.51/173.29 [1112]~E(x11121,x11122)+E(f373(x11123,x11121,x11124,x11125),f373(x11123,x11122,x11124,x11125)) % 173.51/173.29 [1113]~E(x11131,x11132)+E(f373(x11133,x11134,x11131,x11135),f373(x11133,x11134,x11132,x11135)) % 173.51/173.29 [1114]~E(x11141,x11142)+E(f373(x11143,x11144,x11145,x11141),f373(x11143,x11144,x11145,x11142)) % 173.51/173.29 [1115]~E(x11151,x11152)+E(f655(x11151,x11153,x11154,x11155,x11156,x11157,x11158),f655(x11152,x11153,x11154,x11155,x11156,x11157,x11158)) % 173.51/173.29 [1116]~E(x11161,x11162)+E(f655(x11163,x11161,x11164,x11165,x11166,x11167,x11168),f655(x11163,x11162,x11164,x11165,x11166,x11167,x11168)) % 173.51/173.29 [1117]~E(x11171,x11172)+E(f655(x11173,x11174,x11171,x11175,x11176,x11177,x11178),f655(x11173,x11174,x11172,x11175,x11176,x11177,x11178)) % 173.51/173.29 [1118]~E(x11181,x11182)+E(f655(x11183,x11184,x11185,x11181,x11186,x11187,x11188),f655(x11183,x11184,x11185,x11182,x11186,x11187,x11188)) % 173.51/173.29 [1119]~E(x11191,x11192)+E(f655(x11193,x11194,x11195,x11196,x11191,x11197,x11198),f655(x11193,x11194,x11195,x11196,x11192,x11197,x11198)) % 173.51/173.29 [1120]~E(x11201,x11202)+E(f655(x11203,x11204,x11205,x11206,x11207,x11201,x11208),f655(x11203,x11204,x11205,x11206,x11207,x11202,x11208)) % 173.51/173.29 [1121]~E(x11211,x11212)+E(f655(x11213,x11214,x11215,x11216,x11217,x11218,x11211),f655(x11213,x11214,x11215,x11216,x11217,x11218,x11212)) % 173.51/173.29 [1122]~E(x11221,x11222)+E(f275(x11221,x11223),f275(x11222,x11223)) % 173.51/173.29 [1123]~E(x11231,x11232)+E(f275(x11233,x11231),f275(x11233,x11232)) % 173.51/173.29 [1124]~E(x11241,x11242)+E(f346(x11241,x11243,x11244),f346(x11242,x11243,x11244)) % 173.51/173.29 [1125]~E(x11251,x11252)+E(f346(x11253,x11251,x11254),f346(x11253,x11252,x11254)) % 173.51/173.29 [1126]~E(x11261,x11262)+E(f346(x11263,x11264,x11261),f346(x11263,x11264,x11262)) % 173.51/173.29 [1127]~E(x11271,x11272)+E(f208(x11271,x11273,x11274,x11275),f208(x11272,x11273,x11274,x11275)) % 173.51/173.29 [1128]~E(x11281,x11282)+E(f208(x11283,x11281,x11284,x11285),f208(x11283,x11282,x11284,x11285)) % 173.51/173.29 [1129]~E(x11291,x11292)+E(f208(x11293,x11294,x11291,x11295),f208(x11293,x11294,x11292,x11295)) % 173.51/173.29 [1130]~E(x11301,x11302)+E(f208(x11303,x11304,x11305,x11301),f208(x11303,x11304,x11305,x11302)) % 173.51/173.29 [1131]~E(x11311,x11312)+E(f361(x11311,x11313,x11314),f361(x11312,x11313,x11314)) % 173.51/173.29 [1132]~E(x11321,x11322)+E(f361(x11323,x11321,x11324),f361(x11323,x11322,x11324)) % 173.51/173.29 [1133]~E(x11331,x11332)+E(f361(x11333,x11334,x11331),f361(x11333,x11334,x11332)) % 173.51/173.29 [1134]~E(x11341,x11342)+E(f824(x11341,x11343,x11344),f824(x11342,x11343,x11344)) % 173.51/173.29 [1135]~E(x11351,x11352)+E(f824(x11353,x11351,x11354),f824(x11353,x11352,x11354)) % 173.51/173.29 [1136]~E(x11361,x11362)+E(f824(x11363,x11364,x11361),f824(x11363,x11364,x11362)) % 173.51/173.29 [1137]~E(x11371,x11372)+E(f230(x11371,x11373),f230(x11372,x11373)) % 173.51/173.29 [1138]~E(x11381,x11382)+E(f230(x11383,x11381),f230(x11383,x11382)) % 173.51/173.29 [1139]~E(x11391,x11392)+E(f748(x11391,x11393),f748(x11392,x11393)) % 173.51/173.29 [1140]~E(x11401,x11402)+E(f748(x11403,x11401),f748(x11403,x11402)) % 173.51/173.29 [1141]~E(x11411,x11412)+E(f348(x11411,x11413,x11414,x11415,x11416,x11417),f348(x11412,x11413,x11414,x11415,x11416,x11417)) % 173.51/173.29 [1142]~E(x11421,x11422)+E(f348(x11423,x11421,x11424,x11425,x11426,x11427),f348(x11423,x11422,x11424,x11425,x11426,x11427)) % 173.51/173.29 [1143]~E(x11431,x11432)+E(f348(x11433,x11434,x11431,x11435,x11436,x11437),f348(x11433,x11434,x11432,x11435,x11436,x11437)) % 173.51/173.29 [1144]~E(x11441,x11442)+E(f348(x11443,x11444,x11445,x11441,x11446,x11447),f348(x11443,x11444,x11445,x11442,x11446,x11447)) % 173.51/173.29 [1145]~E(x11451,x11452)+E(f348(x11453,x11454,x11455,x11456,x11451,x11457),f348(x11453,x11454,x11455,x11456,x11452,x11457)) % 173.51/173.29 [1146]~E(x11461,x11462)+E(f348(x11463,x11464,x11465,x11466,x11467,x11461),f348(x11463,x11464,x11465,x11466,x11467,x11462)) % 173.51/173.29 [1147]~E(x11471,x11472)+E(f137(x11471,x11473),f137(x11472,x11473)) % 173.51/173.29 [1148]~E(x11481,x11482)+E(f137(x11483,x11481),f137(x11483,x11482)) % 173.51/173.29 [1149]~E(x11491,x11492)+E(f553(x11491,x11493,x11494),f553(x11492,x11493,x11494)) % 173.51/173.29 [1150]~E(x11501,x11502)+E(f553(x11503,x11501,x11504),f553(x11503,x11502,x11504)) % 173.51/173.29 [1151]~E(x11511,x11512)+E(f553(x11513,x11514,x11511),f553(x11513,x11514,x11512)) % 173.51/173.29 [1152]~E(x11521,x11522)+E(f248(x11521,x11523),f248(x11522,x11523)) % 173.51/173.29 [1153]~E(x11531,x11532)+E(f248(x11533,x11531),f248(x11533,x11532)) % 173.51/173.29 [1154]~E(x11541,x11542)+E(f751(x11541,x11543,x11544),f751(x11542,x11543,x11544)) % 173.51/173.29 [1155]~E(x11551,x11552)+E(f751(x11553,x11551,x11554),f751(x11553,x11552,x11554)) % 173.51/173.29 [1156]~E(x11561,x11562)+E(f751(x11563,x11564,x11561),f751(x11563,x11564,x11562)) % 173.51/173.29 [1157]~E(x11571,x11572)+E(f522(x11571,x11573,x11574),f522(x11572,x11573,x11574)) % 173.51/173.29 [1158]~E(x11581,x11582)+E(f522(x11583,x11581,x11584),f522(x11583,x11582,x11584)) % 173.51/173.29 [1159]~E(x11591,x11592)+E(f522(x11593,x11594,x11591),f522(x11593,x11594,x11592)) % 173.51/173.29 [1160]~E(x11601,x11602)+E(f686(x11601,x11603,x11604),f686(x11602,x11603,x11604)) % 173.51/173.29 [1161]~E(x11611,x11612)+E(f686(x11613,x11611,x11614),f686(x11613,x11612,x11614)) % 173.51/173.29 [1162]~E(x11621,x11622)+E(f686(x11623,x11624,x11621),f686(x11623,x11624,x11622)) % 173.51/173.29 [1163]~E(x11631,x11632)+E(f779(x11631,x11633,x11634,x11635),f779(x11632,x11633,x11634,x11635)) % 173.51/173.29 [1164]~E(x11641,x11642)+E(f779(x11643,x11641,x11644,x11645),f779(x11643,x11642,x11644,x11645)) % 173.51/173.29 [1165]~E(x11651,x11652)+E(f779(x11653,x11654,x11651,x11655),f779(x11653,x11654,x11652,x11655)) % 173.51/173.29 [1166]~E(x11661,x11662)+E(f779(x11663,x11664,x11665,x11661),f779(x11663,x11664,x11665,x11662)) % 173.51/173.29 [1167]~E(x11671,x11672)+E(f203(x11671,x11673),f203(x11672,x11673)) % 173.51/173.29 [1168]~E(x11681,x11682)+E(f203(x11683,x11681),f203(x11683,x11682)) % 173.51/173.29 [1169]~E(x11691,x11692)+E(f790(x11691,x11693,x11694,x11695,x11696),f790(x11692,x11693,x11694,x11695,x11696)) % 173.51/173.29 [1170]~E(x11701,x11702)+E(f790(x11703,x11701,x11704,x11705,x11706),f790(x11703,x11702,x11704,x11705,x11706)) % 173.51/173.29 [1171]~E(x11711,x11712)+E(f790(x11713,x11714,x11711,x11715,x11716),f790(x11713,x11714,x11712,x11715,x11716)) % 173.51/173.29 [1172]~E(x11721,x11722)+E(f790(x11723,x11724,x11725,x11721,x11726),f790(x11723,x11724,x11725,x11722,x11726)) % 173.51/173.29 [1173]~E(x11731,x11732)+E(f790(x11733,x11734,x11735,x11736,x11731),f790(x11733,x11734,x11735,x11736,x11732)) % 173.51/173.29 [1174]~E(x11741,x11742)+E(f287(x11741,x11743,x11744,x11745),f287(x11742,x11743,x11744,x11745)) % 173.51/173.29 [1175]~E(x11751,x11752)+E(f287(x11753,x11751,x11754,x11755),f287(x11753,x11752,x11754,x11755)) % 173.51/173.29 [1176]~E(x11761,x11762)+E(f287(x11763,x11764,x11761,x11765),f287(x11763,x11764,x11762,x11765)) % 173.51/173.29 [1177]~E(x11771,x11772)+E(f287(x11773,x11774,x11775,x11771),f287(x11773,x11774,x11775,x11772)) % 173.51/173.29 [1178]~E(x11781,x11782)+E(f377(x11781,x11783,x11784,x11785,x11786),f377(x11782,x11783,x11784,x11785,x11786)) % 173.51/173.29 [1179]~E(x11791,x11792)+E(f377(x11793,x11791,x11794,x11795,x11796),f377(x11793,x11792,x11794,x11795,x11796)) % 173.51/173.29 [1180]~E(x11801,x11802)+E(f377(x11803,x11804,x11801,x11805,x11806),f377(x11803,x11804,x11802,x11805,x11806)) % 173.51/173.29 [1181]~E(x11811,x11812)+E(f377(x11813,x11814,x11815,x11811,x11816),f377(x11813,x11814,x11815,x11812,x11816)) % 173.51/173.29 [1182]~E(x11821,x11822)+E(f377(x11823,x11824,x11825,x11826,x11821),f377(x11823,x11824,x11825,x11826,x11822)) % 173.51/173.29 [1183]~E(x11831,x11832)+E(f575(x11831,x11833,x11834,x11835,x11836),f575(x11832,x11833,x11834,x11835,x11836)) % 173.51/173.29 [1184]~E(x11841,x11842)+E(f575(x11843,x11841,x11844,x11845,x11846),f575(x11843,x11842,x11844,x11845,x11846)) % 173.51/173.29 [1185]~E(x11851,x11852)+E(f575(x11853,x11854,x11851,x11855,x11856),f575(x11853,x11854,x11852,x11855,x11856)) % 173.51/173.29 [1186]~E(x11861,x11862)+E(f575(x11863,x11864,x11865,x11861,x11866),f575(x11863,x11864,x11865,x11862,x11866)) % 173.51/173.29 [1187]~E(x11871,x11872)+E(f575(x11873,x11874,x11875,x11876,x11871),f575(x11873,x11874,x11875,x11876,x11872)) % 173.51/173.29 [1188]~E(x11881,x11882)+E(f102(x11881,x11883,x11884,x11885),f102(x11882,x11883,x11884,x11885)) % 173.51/173.29 [1189]~E(x11891,x11892)+E(f102(x11893,x11891,x11894,x11895),f102(x11893,x11892,x11894,x11895)) % 173.51/173.29 [1190]~E(x11901,x11902)+E(f102(x11903,x11904,x11901,x11905),f102(x11903,x11904,x11902,x11905)) % 173.51/173.29 [1191]~E(x11911,x11912)+E(f102(x11913,x11914,x11915,x11911),f102(x11913,x11914,x11915,x11912)) % 173.51/173.29 [1192]~E(x11921,x11922)+E(f140(x11921,x11923),f140(x11922,x11923)) % 173.51/173.29 [1193]~E(x11931,x11932)+E(f140(x11933,x11931),f140(x11933,x11932)) % 173.51/173.29 [1194]~E(x11941,x11942)+E(f171(x11941,x11943,x11944,x11945),f171(x11942,x11943,x11944,x11945)) % 173.51/173.29 [1195]~E(x11951,x11952)+E(f171(x11953,x11951,x11954,x11955),f171(x11953,x11952,x11954,x11955)) % 173.51/173.29 [1196]~E(x11961,x11962)+E(f171(x11963,x11964,x11961,x11965),f171(x11963,x11964,x11962,x11965)) % 173.51/173.29 [1197]~E(x11971,x11972)+E(f171(x11973,x11974,x11975,x11971),f171(x11973,x11974,x11975,x11972)) % 173.51/173.29 [1198]~E(x11981,x11982)+E(f680(x11981,x11983,x11984,x11985),f680(x11982,x11983,x11984,x11985)) % 173.51/173.29 [1199]~E(x11991,x11992)+E(f680(x11993,x11991,x11994,x11995),f680(x11993,x11992,x11994,x11995)) % 173.51/173.29 [1200]~E(x12001,x12002)+E(f680(x12003,x12004,x12001,x12005),f680(x12003,x12004,x12002,x12005)) % 173.51/173.29 [1201]~E(x12011,x12012)+E(f680(x12013,x12014,x12015,x12011),f680(x12013,x12014,x12015,x12012)) % 173.51/173.29 [1202]~E(x12021,x12022)+E(f441(x12021,x12023),f441(x12022,x12023)) % 173.51/173.29 [1203]~E(x12031,x12032)+E(f441(x12033,x12031),f441(x12033,x12032)) % 173.51/173.29 [1204]~E(x12041,x12042)+E(f783(x12041,x12043),f783(x12042,x12043)) % 173.51/173.29 [1205]~E(x12051,x12052)+E(f783(x12053,x12051),f783(x12053,x12052)) % 173.51/173.29 [1206]~E(x12061,x12062)+E(f306(x12061,x12063,x12064,x12065,x12066),f306(x12062,x12063,x12064,x12065,x12066)) % 173.51/173.29 [1207]~E(x12071,x12072)+E(f306(x12073,x12071,x12074,x12075,x12076),f306(x12073,x12072,x12074,x12075,x12076)) % 173.51/173.29 [1208]~E(x12081,x12082)+E(f306(x12083,x12084,x12081,x12085,x12086),f306(x12083,x12084,x12082,x12085,x12086)) % 173.51/173.29 [1209]~E(x12091,x12092)+E(f306(x12093,x12094,x12095,x12091,x12096),f306(x12093,x12094,x12095,x12092,x12096)) % 173.51/173.29 [1210]~E(x12101,x12102)+E(f306(x12103,x12104,x12105,x12106,x12101),f306(x12103,x12104,x12105,x12106,x12102)) % 173.51/173.29 [1211]~E(x12111,x12112)+E(f629(x12111,x12113),f629(x12112,x12113)) % 173.51/173.29 [1212]~E(x12121,x12122)+E(f629(x12123,x12121),f629(x12123,x12122)) % 173.51/173.29 [1213]~E(x12131,x12132)+E(f439(x12131),f439(x12132)) % 173.51/173.29 [1214]~E(x12141,x12142)+E(f385(x12141,x12143),f385(x12142,x12143)) % 173.51/173.29 [1215]~E(x12151,x12152)+E(f385(x12153,x12151),f385(x12153,x12152)) % 173.51/173.29 [1216]~E(x12161,x12162)+E(f157(x12161,x12163,x12164,x12165,x12166),f157(x12162,x12163,x12164,x12165,x12166)) % 173.51/173.29 [1217]~E(x12171,x12172)+E(f157(x12173,x12171,x12174,x12175,x12176),f157(x12173,x12172,x12174,x12175,x12176)) % 173.51/173.29 [1218]~E(x12181,x12182)+E(f157(x12183,x12184,x12181,x12185,x12186),f157(x12183,x12184,x12182,x12185,x12186)) % 173.51/173.29 [1219]~E(x12191,x12192)+E(f157(x12193,x12194,x12195,x12191,x12196),f157(x12193,x12194,x12195,x12192,x12196)) % 173.51/173.29 [1220]~E(x12201,x12202)+E(f157(x12203,x12204,x12205,x12206,x12201),f157(x12203,x12204,x12205,x12206,x12202)) % 173.51/173.29 [1221]~E(x12211,x12212)+E(f889(x12211,x12213,x12214,x12215,x12216,x12217,x12218,x12219,x122110),f889(x12212,x12213,x12214,x12215,x12216,x12217,x12218,x12219,x122110)) % 173.51/173.29 [1222]~E(x12221,x12222)+E(f889(x12223,x12221,x12224,x12225,x12226,x12227,x12228,x12229,x122210),f889(x12223,x12222,x12224,x12225,x12226,x12227,x12228,x12229,x122210)) % 173.51/173.29 [1223]~E(x12231,x12232)+E(f889(x12233,x12234,x12231,x12235,x12236,x12237,x12238,x12239,x122310),f889(x12233,x12234,x12232,x12235,x12236,x12237,x12238,x12239,x122310)) % 173.51/173.29 [1224]~E(x12241,x12242)+E(f889(x12243,x12244,x12245,x12241,x12246,x12247,x12248,x12249,x122410),f889(x12243,x12244,x12245,x12242,x12246,x12247,x12248,x12249,x122410)) % 173.51/173.29 [1225]~E(x12251,x12252)+E(f889(x12253,x12254,x12255,x12256,x12251,x12257,x12258,x12259,x122510),f889(x12253,x12254,x12255,x12256,x12252,x12257,x12258,x12259,x122510)) % 173.51/173.29 [1226]~E(x12261,x12262)+E(f889(x12263,x12264,x12265,x12266,x12267,x12261,x12268,x12269,x122610),f889(x12263,x12264,x12265,x12266,x12267,x12262,x12268,x12269,x122610)) % 173.51/173.29 [1227]~E(x12271,x12272)+E(f889(x12273,x12274,x12275,x12276,x12277,x12278,x12271,x12279,x122710),f889(x12273,x12274,x12275,x12276,x12277,x12278,x12272,x12279,x122710)) % 173.51/173.29 [1228]~E(x12281,x12282)+E(f889(x12283,x12284,x12285,x12286,x12287,x12288,x12289,x12281,x122810),f889(x12283,x12284,x12285,x12286,x12287,x12288,x12289,x12282,x122810)) % 173.51/173.29 [1229]~E(x12291,x12292)+E(f889(x12293,x12294,x12295,x12296,x12297,x12298,x12299,x122910,x12291),f889(x12293,x12294,x12295,x12296,x12297,x12298,x12299,x122910,x12292)) % 173.51/173.29 [1230]~E(x12301,x12302)+E(f148(x12301,x12303,x12304),f148(x12302,x12303,x12304)) % 173.51/173.29 [1231]~E(x12311,x12312)+E(f148(x12313,x12311,x12314),f148(x12313,x12312,x12314)) % 173.51/173.29 [1232]~E(x12321,x12322)+E(f148(x12323,x12324,x12321),f148(x12323,x12324,x12322)) % 173.51/173.29 [1233]~E(x12331,x12332)+E(f101(x12331),f101(x12332)) % 173.51/173.29 [1234]~E(x12341,x12342)+E(f211(x12341,x12343),f211(x12342,x12343)) % 173.51/173.29 [1235]~E(x12351,x12352)+E(f211(x12353,x12351),f211(x12353,x12352)) % 173.51/173.29 [1236]~E(x12361,x12362)+E(f838(x12361,x12363,x12364,x12365,x12366),f838(x12362,x12363,x12364,x12365,x12366)) % 173.51/173.29 [1237]~E(x12371,x12372)+E(f838(x12373,x12371,x12374,x12375,x12376),f838(x12373,x12372,x12374,x12375,x12376)) % 173.51/173.29 [1238]~E(x12381,x12382)+E(f838(x12383,x12384,x12381,x12385,x12386),f838(x12383,x12384,x12382,x12385,x12386)) % 173.51/173.29 [1239]~E(x12391,x12392)+E(f838(x12393,x12394,x12395,x12391,x12396),f838(x12393,x12394,x12395,x12392,x12396)) % 173.51/173.29 [1240]~E(x12401,x12402)+E(f838(x12403,x12404,x12405,x12406,x12401),f838(x12403,x12404,x12405,x12406,x12402)) % 173.51/173.29 [1241]~E(x12411,x12412)+E(f138(x12411),f138(x12412)) % 173.51/173.29 [1242]~E(x12421,x12422)+E(f488(x12421,x12423,x12424,x12425),f488(x12422,x12423,x12424,x12425)) % 173.51/173.29 [1243]~E(x12431,x12432)+E(f488(x12433,x12431,x12434,x12435),f488(x12433,x12432,x12434,x12435)) % 173.51/173.29 [1244]~E(x12441,x12442)+E(f488(x12443,x12444,x12441,x12445),f488(x12443,x12444,x12442,x12445)) % 173.51/173.29 [1245]~E(x12451,x12452)+E(f488(x12453,x12454,x12455,x12451),f488(x12453,x12454,x12455,x12452)) % 173.51/173.29 [1246]~E(x12461,x12462)+E(f427(x12461,x12463),f427(x12462,x12463)) % 173.51/173.29 [1247]~E(x12471,x12472)+E(f427(x12473,x12471),f427(x12473,x12472)) % 173.51/173.29 [1248]~E(x12481,x12482)+E(f513(x12481,x12483,x12484),f513(x12482,x12483,x12484)) % 173.51/173.29 [1249]~E(x12491,x12492)+E(f513(x12493,x12491,x12494),f513(x12493,x12492,x12494)) % 173.51/173.29 [1250]~E(x12501,x12502)+E(f513(x12503,x12504,x12501),f513(x12503,x12504,x12502)) % 173.51/173.29 [1251]~E(x12511,x12512)+E(f897(x12511,x12513,x12514),f897(x12512,x12513,x12514)) % 173.51/173.29 [1252]~E(x12521,x12522)+E(f897(x12523,x12521,x12524),f897(x12523,x12522,x12524)) % 173.51/173.29 [1253]~E(x12531,x12532)+E(f897(x12533,x12534,x12531),f897(x12533,x12534,x12532)) % 173.51/173.29 [1254]~E(x12541,x12542)+E(f345(x12541,x12543,x12544,x12545),f345(x12542,x12543,x12544,x12545)) % 173.51/173.29 [1255]~E(x12551,x12552)+E(f345(x12553,x12551,x12554,x12555),f345(x12553,x12552,x12554,x12555)) % 173.51/173.29 [1256]~E(x12561,x12562)+E(f345(x12563,x12564,x12561,x12565),f345(x12563,x12564,x12562,x12565)) % 173.51/173.29 [1257]~E(x12571,x12572)+E(f345(x12573,x12574,x12575,x12571),f345(x12573,x12574,x12575,x12572)) % 173.51/173.29 [1258]~E(x12581,x12582)+E(f723(x12581,x12583,x12584),f723(x12582,x12583,x12584)) % 173.51/173.29 [1259]~E(x12591,x12592)+E(f723(x12593,x12591,x12594),f723(x12593,x12592,x12594)) % 173.51/173.29 [1260]~E(x12601,x12602)+E(f723(x12603,x12604,x12601),f723(x12603,x12604,x12602)) % 173.51/173.29 [1261]~E(x12611,x12612)+E(f800(x12611,x12613,x12614),f800(x12612,x12613,x12614)) % 173.51/173.29 [1262]~E(x12621,x12622)+E(f800(x12623,x12621,x12624),f800(x12623,x12622,x12624)) % 173.51/173.29 [1263]~E(x12631,x12632)+E(f800(x12633,x12634,x12631),f800(x12633,x12634,x12632)) % 173.51/173.29 [1264]~E(x12641,x12642)+E(f652(x12641,x12643,x12644,x12645),f652(x12642,x12643,x12644,x12645)) % 173.51/173.29 [1265]~E(x12651,x12652)+E(f652(x12653,x12651,x12654,x12655),f652(x12653,x12652,x12654,x12655)) % 173.51/173.29 [1266]~E(x12661,x12662)+E(f652(x12663,x12664,x12661,x12665),f652(x12663,x12664,x12662,x12665)) % 173.51/173.29 [1267]~E(x12671,x12672)+E(f652(x12673,x12674,x12675,x12671),f652(x12673,x12674,x12675,x12672)) % 173.51/173.29 [1268]~E(x12681,x12682)+E(f143(x12681),f143(x12682)) % 173.51/173.29 [1269]~E(x12691,x12692)+E(f903(x12691,x12693,x12694,x12695,x12696),f903(x12692,x12693,x12694,x12695,x12696)) % 173.51/173.29 [1270]~E(x12701,x12702)+E(f903(x12703,x12701,x12704,x12705,x12706),f903(x12703,x12702,x12704,x12705,x12706)) % 173.51/173.29 [1271]~E(x12711,x12712)+E(f903(x12713,x12714,x12711,x12715,x12716),f903(x12713,x12714,x12712,x12715,x12716)) % 173.51/173.29 [1272]~E(x12721,x12722)+E(f903(x12723,x12724,x12725,x12721,x12726),f903(x12723,x12724,x12725,x12722,x12726)) % 173.51/173.29 [1273]~E(x12731,x12732)+E(f903(x12733,x12734,x12735,x12736,x12731),f903(x12733,x12734,x12735,x12736,x12732)) % 173.51/173.29 [1274]~E(x12741,x12742)+E(f902(x12741,x12743,x12744,x12745,x12746),f902(x12742,x12743,x12744,x12745,x12746)) % 173.51/173.29 [1275]~E(x12751,x12752)+E(f902(x12753,x12751,x12754,x12755,x12756),f902(x12753,x12752,x12754,x12755,x12756)) % 173.51/173.29 [1276]~E(x12761,x12762)+E(f902(x12763,x12764,x12761,x12765,x12766),f902(x12763,x12764,x12762,x12765,x12766)) % 173.51/173.29 [1277]~E(x12771,x12772)+E(f902(x12773,x12774,x12775,x12771,x12776),f902(x12773,x12774,x12775,x12772,x12776)) % 173.51/173.29 [1278]~E(x12781,x12782)+E(f902(x12783,x12784,x12785,x12786,x12781),f902(x12783,x12784,x12785,x12786,x12782)) % 173.51/173.29 [1279]~E(x12791,x12792)+E(f815(x12791,x12793,x12794,x12795),f815(x12792,x12793,x12794,x12795)) % 173.51/173.29 [1280]~E(x12801,x12802)+E(f815(x12803,x12801,x12804,x12805),f815(x12803,x12802,x12804,x12805)) % 173.51/173.29 [1281]~E(x12811,x12812)+E(f815(x12813,x12814,x12811,x12815),f815(x12813,x12814,x12812,x12815)) % 173.51/173.29 [1282]~E(x12821,x12822)+E(f815(x12823,x12824,x12825,x12821),f815(x12823,x12824,x12825,x12822)) % 173.51/173.29 [1283]~E(x12831,x12832)+E(f796(x12831,x12833,x12834,x12835,x12836,x12837),f796(x12832,x12833,x12834,x12835,x12836,x12837)) % 173.51/173.29 [1284]~E(x12841,x12842)+E(f796(x12843,x12841,x12844,x12845,x12846,x12847),f796(x12843,x12842,x12844,x12845,x12846,x12847)) % 173.51/173.29 [1285]~E(x12851,x12852)+E(f796(x12853,x12854,x12851,x12855,x12856,x12857),f796(x12853,x12854,x12852,x12855,x12856,x12857)) % 173.51/173.29 [1286]~E(x12861,x12862)+E(f796(x12863,x12864,x12865,x12861,x12866,x12867),f796(x12863,x12864,x12865,x12862,x12866,x12867)) % 173.51/173.29 [1287]~E(x12871,x12872)+E(f796(x12873,x12874,x12875,x12876,x12871,x12877),f796(x12873,x12874,x12875,x12876,x12872,x12877)) % 173.51/173.29 [1288]~E(x12881,x12882)+E(f796(x12883,x12884,x12885,x12886,x12887,x12881),f796(x12883,x12884,x12885,x12886,x12887,x12882)) % 173.51/173.29 [1289]~E(x12891,x12892)+E(f781(x12891,x12893,x12894,x12895,x12896),f781(x12892,x12893,x12894,x12895,x12896)) % 173.51/173.29 [1290]~E(x12901,x12902)+E(f781(x12903,x12901,x12904,x12905,x12906),f781(x12903,x12902,x12904,x12905,x12906)) % 173.51/173.29 [1291]~E(x12911,x12912)+E(f781(x12913,x12914,x12911,x12915,x12916),f781(x12913,x12914,x12912,x12915,x12916)) % 173.51/173.29 [1292]~E(x12921,x12922)+E(f781(x12923,x12924,x12925,x12921,x12926),f781(x12923,x12924,x12925,x12922,x12926)) % 173.51/173.29 [1293]~E(x12931,x12932)+E(f781(x12933,x12934,x12935,x12936,x12931),f781(x12933,x12934,x12935,x12936,x12932)) % 173.51/173.29 [1294]~E(x12941,x12942)+E(f739(x12941,x12943,x12944),f739(x12942,x12943,x12944)) % 173.51/173.29 [1295]~E(x12951,x12952)+E(f739(x12953,x12951,x12954),f739(x12953,x12952,x12954)) % 173.51/173.29 [1296]~E(x12961,x12962)+E(f739(x12963,x12964,x12961),f739(x12963,x12964,x12962)) % 173.51/173.29 [1297]~E(x12971,x12972)+E(f858(x12971,x12973,x12974),f858(x12972,x12973,x12974)) % 173.51/173.29 [1298]~E(x12981,x12982)+E(f858(x12983,x12981,x12984),f858(x12983,x12982,x12984)) % 173.51/173.29 [1299]~E(x12991,x12992)+E(f858(x12993,x12994,x12991),f858(x12993,x12994,x12992)) % 173.51/173.29 [1300]~E(x13001,x13002)+E(f685(x13001,x13003,x13004),f685(x13002,x13003,x13004)) % 173.51/173.29 [1301]~E(x13011,x13012)+E(f685(x13013,x13011,x13014),f685(x13013,x13012,x13014)) % 173.51/173.29 [1302]~E(x13021,x13022)+E(f685(x13023,x13024,x13021),f685(x13023,x13024,x13022)) % 173.51/173.29 [1303]~E(x13031,x13032)+E(f59(x13031,x13033),f59(x13032,x13033)) % 173.51/173.29 [1304]~E(x13041,x13042)+E(f59(x13043,x13041),f59(x13043,x13042)) % 173.51/173.29 [1305]~E(x13051,x13052)+E(f659(x13051,x13053,x13054,x13055,x13056),f659(x13052,x13053,x13054,x13055,x13056)) % 173.51/173.29 [1306]~E(x13061,x13062)+E(f659(x13063,x13061,x13064,x13065,x13066),f659(x13063,x13062,x13064,x13065,x13066)) % 173.51/173.29 [1307]~E(x13071,x13072)+E(f659(x13073,x13074,x13071,x13075,x13076),f659(x13073,x13074,x13072,x13075,x13076)) % 173.51/173.29 [1308]~E(x13081,x13082)+E(f659(x13083,x13084,x13085,x13081,x13086),f659(x13083,x13084,x13085,x13082,x13086)) % 173.51/173.29 [1309]~E(x13091,x13092)+E(f659(x13093,x13094,x13095,x13096,x13091),f659(x13093,x13094,x13095,x13096,x13092)) % 173.51/173.29 [1310]~E(x13101,x13102)+E(f218(x13101,x13103,x13104,x13105),f218(x13102,x13103,x13104,x13105)) % 173.51/173.29 [1311]~E(x13111,x13112)+E(f218(x13113,x13111,x13114,x13115),f218(x13113,x13112,x13114,x13115)) % 173.51/173.29 [1312]~E(x13121,x13122)+E(f218(x13123,x13124,x13121,x13125),f218(x13123,x13124,x13122,x13125)) % 173.51/173.29 [1313]~E(x13131,x13132)+E(f218(x13133,x13134,x13135,x13131),f218(x13133,x13134,x13135,x13132)) % 173.51/173.29 [1314]~E(x13141,x13142)+E(f68(x13141,x13143,x13144),f68(x13142,x13143,x13144)) % 173.51/173.29 [1315]~E(x13151,x13152)+E(f68(x13153,x13151,x13154),f68(x13153,x13152,x13154)) % 173.51/173.29 [1316]~E(x13161,x13162)+E(f68(x13163,x13164,x13161),f68(x13163,x13164,x13162)) % 173.51/173.29 [1317]~E(x13171,x13172)+E(f483(x13171,x13173,x13174,x13175,x13176),f483(x13172,x13173,x13174,x13175,x13176)) % 173.51/173.29 [1318]~E(x13181,x13182)+E(f483(x13183,x13181,x13184,x13185,x13186),f483(x13183,x13182,x13184,x13185,x13186)) % 173.51/173.29 [1319]~E(x13191,x13192)+E(f483(x13193,x13194,x13191,x13195,x13196),f483(x13193,x13194,x13192,x13195,x13196)) % 173.51/173.29 [1320]~E(x13201,x13202)+E(f483(x13203,x13204,x13205,x13201,x13206),f483(x13203,x13204,x13205,x13202,x13206)) % 173.51/173.29 [1321]~E(x13211,x13212)+E(f483(x13213,x13214,x13215,x13216,x13211),f483(x13213,x13214,x13215,x13216,x13212)) % 173.51/173.29 [1322]~E(x13221,x13222)+E(f760(x13221,x13223,x13224),f760(x13222,x13223,x13224)) % 173.51/173.29 [1323]~E(x13231,x13232)+E(f760(x13233,x13231,x13234),f760(x13233,x13232,x13234)) % 173.51/173.29 [1324]~E(x13241,x13242)+E(f760(x13243,x13244,x13241),f760(x13243,x13244,x13242)) % 173.51/173.29 [1325]~E(x13251,x13252)+E(f708(x13251,x13253,x13254,x13255),f708(x13252,x13253,x13254,x13255)) % 173.51/173.29 [1326]~E(x13261,x13262)+E(f708(x13263,x13261,x13264,x13265),f708(x13263,x13262,x13264,x13265)) % 173.51/173.29 [1327]~E(x13271,x13272)+E(f708(x13273,x13274,x13271,x13275),f708(x13273,x13274,x13272,x13275)) % 173.51/173.29 [1328]~E(x13281,x13282)+E(f708(x13283,x13284,x13285,x13281),f708(x13283,x13284,x13285,x13282)) % 173.51/173.29 [1329]~E(x13291,x13292)+E(f527(x13291,x13293,x13294,x13295),f527(x13292,x13293,x13294,x13295)) % 173.51/173.29 [1330]~E(x13301,x13302)+E(f527(x13303,x13301,x13304,x13305),f527(x13303,x13302,x13304,x13305)) % 173.51/173.29 [1331]~E(x13311,x13312)+E(f527(x13313,x13314,x13311,x13315),f527(x13313,x13314,x13312,x13315)) % 173.51/173.29 [1332]~E(x13321,x13322)+E(f527(x13323,x13324,x13325,x13321),f527(x13323,x13324,x13325,x13322)) % 173.51/173.29 [1333]~E(x13331,x13332)+E(f259(x13331,x13333,x13334),f259(x13332,x13333,x13334)) % 173.51/173.29 [1334]~E(x13341,x13342)+E(f259(x13343,x13341,x13344),f259(x13343,x13342,x13344)) % 173.51/173.29 [1335]~E(x13351,x13352)+E(f259(x13353,x13354,x13351),f259(x13353,x13354,x13352)) % 173.51/173.29 [1336]~E(x13361,x13362)+E(f376(x13361,x13363,x13364,x13365,x13366,x13367),f376(x13362,x13363,x13364,x13365,x13366,x13367)) % 173.51/173.29 [1337]~E(x13371,x13372)+E(f376(x13373,x13371,x13374,x13375,x13376,x13377),f376(x13373,x13372,x13374,x13375,x13376,x13377)) % 173.51/173.29 [1338]~E(x13381,x13382)+E(f376(x13383,x13384,x13381,x13385,x13386,x13387),f376(x13383,x13384,x13382,x13385,x13386,x13387)) % 173.51/173.29 [1339]~E(x13391,x13392)+E(f376(x13393,x13394,x13395,x13391,x13396,x13397),f376(x13393,x13394,x13395,x13392,x13396,x13397)) % 173.51/173.29 [1340]~E(x13401,x13402)+E(f376(x13403,x13404,x13405,x13406,x13401,x13407),f376(x13403,x13404,x13405,x13406,x13402,x13407)) % 173.51/173.29 [1341]~E(x13411,x13412)+E(f376(x13413,x13414,x13415,x13416,x13417,x13411),f376(x13413,x13414,x13415,x13416,x13417,x13412)) % 173.51/173.29 [1342]~E(x13421,x13422)+E(f408(x13421,x13423,x13424,x13425),f408(x13422,x13423,x13424,x13425)) % 173.51/173.29 [1343]~E(x13431,x13432)+E(f408(x13433,x13431,x13434,x13435),f408(x13433,x13432,x13434,x13435)) % 173.51/173.29 [1344]~E(x13441,x13442)+E(f408(x13443,x13444,x13441,x13445),f408(x13443,x13444,x13442,x13445)) % 173.51/173.29 [1345]~E(x13451,x13452)+E(f408(x13453,x13454,x13455,x13451),f408(x13453,x13454,x13455,x13452)) % 173.51/173.29 [1346]~E(x13461,x13462)+E(f455(x13461,x13463,x13464),f455(x13462,x13463,x13464)) % 173.51/173.29 [1347]~E(x13471,x13472)+E(f455(x13473,x13471,x13474),f455(x13473,x13472,x13474)) % 173.51/173.29 [1348]~E(x13481,x13482)+E(f455(x13483,x13484,x13481),f455(x13483,x13484,x13482)) % 173.51/173.29 [1349]~E(x13491,x13492)+E(f895(x13491,x13493,x13494),f895(x13492,x13493,x13494)) % 173.51/173.29 [1350]~E(x13501,x13502)+E(f895(x13503,x13501,x13504),f895(x13503,x13502,x13504)) % 173.51/173.29 [1351]~E(x13511,x13512)+E(f895(x13513,x13514,x13511),f895(x13513,x13514,x13512)) % 173.51/173.29 [1352]~E(x13521,x13522)+E(f839(x13521,x13523,x13524),f839(x13522,x13523,x13524)) % 173.51/173.29 [1353]~E(x13531,x13532)+E(f839(x13533,x13531,x13534),f839(x13533,x13532,x13534)) % 173.51/173.29 [1354]~E(x13541,x13542)+E(f839(x13543,x13544,x13541),f839(x13543,x13544,x13542)) % 173.51/173.29 [1355]~E(x13551,x13552)+E(f758(x13551,x13553,x13554),f758(x13552,x13553,x13554)) % 173.51/173.29 [1356]~E(x13561,x13562)+E(f758(x13563,x13561,x13564),f758(x13563,x13562,x13564)) % 173.51/173.29 [1357]~E(x13571,x13572)+E(f758(x13573,x13574,x13571),f758(x13573,x13574,x13572)) % 173.51/173.29 [1358]~E(x13581,x13582)+E(f192(x13581,x13583,x13584),f192(x13582,x13583,x13584)) % 173.51/173.29 [1359]~E(x13591,x13592)+E(f192(x13593,x13591,x13594),f192(x13593,x13592,x13594)) % 173.51/173.29 [1360]~E(x13601,x13602)+E(f192(x13603,x13604,x13601),f192(x13603,x13604,x13602)) % 173.51/173.29 [1361]~E(x13611,x13612)+E(f606(x13611,x13613),f606(x13612,x13613)) % 173.51/173.29 [1362]~E(x13621,x13622)+E(f606(x13623,x13621),f606(x13623,x13622)) % 173.51/173.29 [1363]~E(x13631,x13632)+E(f325(x13631,x13633,x13634,x13635),f325(x13632,x13633,x13634,x13635)) % 173.51/173.29 [1364]~E(x13641,x13642)+E(f325(x13643,x13641,x13644,x13645),f325(x13643,x13642,x13644,x13645)) % 173.51/173.29 [1365]~E(x13651,x13652)+E(f325(x13653,x13654,x13651,x13655),f325(x13653,x13654,x13652,x13655)) % 173.51/173.29 [1366]~E(x13661,x13662)+E(f325(x13663,x13664,x13665,x13661),f325(x13663,x13664,x13665,x13662)) % 173.51/173.29 [1367]~E(x13671,x13672)+E(f900(x13671,x13673,x13674,x13675),f900(x13672,x13673,x13674,x13675)) % 173.51/173.29 [1368]~E(x13681,x13682)+E(f900(x13683,x13681,x13684,x13685),f900(x13683,x13682,x13684,x13685)) % 173.51/173.29 [1369]~E(x13691,x13692)+E(f900(x13693,x13694,x13691,x13695),f900(x13693,x13694,x13692,x13695)) % 173.51/173.29 [1370]~E(x13701,x13702)+E(f900(x13703,x13704,x13705,x13701),f900(x13703,x13704,x13705,x13702)) % 173.51/173.29 [1371]~E(x13711,x13712)+E(f284(x13711,x13713,x13714,x13715),f284(x13712,x13713,x13714,x13715)) % 173.51/173.29 [1372]~E(x13721,x13722)+E(f284(x13723,x13721,x13724,x13725),f284(x13723,x13722,x13724,x13725)) % 173.51/173.29 [1373]~E(x13731,x13732)+E(f284(x13733,x13734,x13731,x13735),f284(x13733,x13734,x13732,x13735)) % 173.51/173.29 [1374]~E(x13741,x13742)+E(f284(x13743,x13744,x13745,x13741),f284(x13743,x13744,x13745,x13742)) % 173.51/173.29 [1375]~E(x13751,x13752)+E(f837(x13751,x13753),f837(x13752,x13753)) % 173.51/173.29 [1376]~E(x13761,x13762)+E(f837(x13763,x13761),f837(x13763,x13762)) % 173.51/173.29 [1377]~E(x13771,x13772)+E(f437(x13771),f437(x13772)) % 173.51/173.29 [1378]~E(x13781,x13782)+E(f299(x13781,x13783,x13784),f299(x13782,x13783,x13784)) % 173.51/173.29 [1379]~E(x13791,x13792)+E(f299(x13793,x13791,x13794),f299(x13793,x13792,x13794)) % 173.51/173.29 [1380]~E(x13801,x13802)+E(f299(x13803,x13804,x13801),f299(x13803,x13804,x13802)) % 173.51/173.29 [1381]~E(x13811,x13812)+E(f632(x13811,x13813,x13814,x13815),f632(x13812,x13813,x13814,x13815)) % 173.51/173.29 [1382]~E(x13821,x13822)+E(f632(x13823,x13821,x13824,x13825),f632(x13823,x13822,x13824,x13825)) % 173.51/173.29 [1383]~E(x13831,x13832)+E(f632(x13833,x13834,x13831,x13835),f632(x13833,x13834,x13832,x13835)) % 173.51/173.29 [1384]~E(x13841,x13842)+E(f632(x13843,x13844,x13845,x13841),f632(x13843,x13844,x13845,x13842)) % 173.51/173.29 [1385]~E(x13851,x13852)+E(f257(x13851,x13853,x13854),f257(x13852,x13853,x13854)) % 173.51/173.29 [1386]~E(x13861,x13862)+E(f257(x13863,x13861,x13864),f257(x13863,x13862,x13864)) % 173.51/173.29 [1387]~E(x13871,x13872)+E(f257(x13873,x13874,x13871),f257(x13873,x13874,x13872)) % 173.51/173.29 [1388]~E(x13881,x13882)+E(f133(x13881),f133(x13882)) % 173.51/173.29 [1389]~E(x13891,x13892)+E(f566(x13891,x13893,x13894),f566(x13892,x13893,x13894)) % 173.51/173.29 [1390]~E(x13901,x13902)+E(f566(x13903,x13901,x13904),f566(x13903,x13902,x13904)) % 173.51/173.29 [1391]~E(x13911,x13912)+E(f566(x13913,x13914,x13911),f566(x13913,x13914,x13912)) % 173.51/173.29 [1392]~E(x13921,x13922)+E(f213(x13921),f213(x13922)) % 173.51/173.29 [1393]~E(x13931,x13932)+E(f608(x13931,x13933,x13934),f608(x13932,x13933,x13934)) % 173.51/173.29 [1394]~E(x13941,x13942)+E(f608(x13943,x13941,x13944),f608(x13943,x13942,x13944)) % 173.51/173.29 [1395]~E(x13951,x13952)+E(f608(x13953,x13954,x13951),f608(x13953,x13954,x13952)) % 173.51/173.29 [1396]~E(x13961,x13962)+E(f799(x13961,x13963,x13964),f799(x13962,x13963,x13964)) % 173.51/173.29 [1397]~E(x13971,x13972)+E(f799(x13973,x13971,x13974),f799(x13973,x13972,x13974)) % 173.51/173.29 [1398]~E(x13981,x13982)+E(f799(x13983,x13984,x13981),f799(x13983,x13984,x13982)) % 173.51/173.29 [1399]~E(x13991,x13992)+E(f777(x13991,x13993),f777(x13992,x13993)) % 173.51/173.29 [1400]~E(x14001,x14002)+E(f777(x14003,x14001),f777(x14003,x14002)) % 173.51/173.29 [1401]~E(x14011,x14012)+E(f278(x14011,x14013),f278(x14012,x14013)) % 173.51/173.29 [1402]~E(x14021,x14022)+E(f278(x14023,x14021),f278(x14023,x14022)) % 173.51/173.29 [1403]~E(x14031,x14032)+E(f453(x14031,x14033,x14034),f453(x14032,x14033,x14034)) % 173.51/173.29 [1404]~E(x14041,x14042)+E(f453(x14043,x14041,x14044),f453(x14043,x14042,x14044)) % 173.51/173.29 [1405]~E(x14051,x14052)+E(f453(x14053,x14054,x14051),f453(x14053,x14054,x14052)) % 173.51/173.29 [1406]~E(x14061,x14062)+E(f511(x14061,x14063,x14064),f511(x14062,x14063,x14064)) % 173.51/173.29 [1407]~E(x14071,x14072)+E(f511(x14073,x14071,x14074),f511(x14073,x14072,x14074)) % 173.51/173.29 [1408]~E(x14081,x14082)+E(f511(x14083,x14084,x14081),f511(x14083,x14084,x14082)) % 173.51/173.29 [1409]~E(x14091,x14092)+E(f226(x14091,x14093),f226(x14092,x14093)) % 173.51/173.29 [1410]~E(x14101,x14102)+E(f226(x14103,x14101),f226(x14103,x14102)) % 173.51/173.29 [1411]~E(x14111,x14112)+E(f570(x14111,x14113,x14114,x14115,x14116,x14117),f570(x14112,x14113,x14114,x14115,x14116,x14117)) % 173.51/173.29 [1412]~E(x14121,x14122)+E(f570(x14123,x14121,x14124,x14125,x14126,x14127),f570(x14123,x14122,x14124,x14125,x14126,x14127)) % 173.51/173.29 [1413]~E(x14131,x14132)+E(f570(x14133,x14134,x14131,x14135,x14136,x14137),f570(x14133,x14134,x14132,x14135,x14136,x14137)) % 173.51/173.29 [1414]~E(x14141,x14142)+E(f570(x14143,x14144,x14145,x14141,x14146,x14147),f570(x14143,x14144,x14145,x14142,x14146,x14147)) % 173.51/173.29 [1415]~E(x14151,x14152)+E(f570(x14153,x14154,x14155,x14156,x14151,x14157),f570(x14153,x14154,x14155,x14156,x14152,x14157)) % 173.51/173.29 [1416]~E(x14161,x14162)+E(f570(x14163,x14164,x14165,x14166,x14167,x14161),f570(x14163,x14164,x14165,x14166,x14167,x14162)) % 173.51/173.29 [1417]~E(x14171,x14172)+E(f129(x14171,x14173,x14174),f129(x14172,x14173,x14174)) % 173.51/173.29 [1418]~E(x14181,x14182)+E(f129(x14183,x14181,x14184),f129(x14183,x14182,x14184)) % 173.51/173.29 [1419]~E(x14191,x14192)+E(f129(x14193,x14194,x14191),f129(x14193,x14194,x14192)) % 173.51/173.29 [1420]~E(x14201,x14202)+E(f503(x14201,x14203,x14204),f503(x14202,x14203,x14204)) % 173.51/173.29 [1421]~E(x14211,x14212)+E(f503(x14213,x14211,x14214),f503(x14213,x14212,x14214)) % 173.51/173.29 [1422]~E(x14221,x14222)+E(f503(x14223,x14224,x14221),f503(x14223,x14224,x14222)) % 173.51/173.29 [1423]~E(x14231,x14232)+E(f546(x14231,x14233,x14234),f546(x14232,x14233,x14234)) % 173.51/173.29 [1424]~E(x14241,x14242)+E(f546(x14243,x14241,x14244),f546(x14243,x14242,x14244)) % 173.51/173.29 [1425]~E(x14251,x14252)+E(f546(x14253,x14254,x14251),f546(x14253,x14254,x14252)) % 173.51/173.29 [1426]~E(x14261,x14262)+E(f894(x14261,x14263),f894(x14262,x14263)) % 173.51/173.29 [1427]~E(x14271,x14272)+E(f894(x14273,x14271),f894(x14273,x14272)) % 173.51/173.29 [1428]~E(x14281,x14282)+E(f803(x14281,x14283,x14284),f803(x14282,x14283,x14284)) % 173.51/173.29 [1429]~E(x14291,x14292)+E(f803(x14293,x14291,x14294),f803(x14293,x14292,x14294)) % 173.51/173.29 [1430]~E(x14301,x14302)+E(f803(x14303,x14304,x14301),f803(x14303,x14304,x14302)) % 173.51/173.29 [1431]~E(x14311,x14312)+E(f495(x14311,x14313,x14314),f495(x14312,x14313,x14314)) % 173.51/173.29 [1432]~E(x14321,x14322)+E(f495(x14323,x14321,x14324),f495(x14323,x14322,x14324)) % 173.51/173.29 [1433]~E(x14331,x14332)+E(f495(x14333,x14334,x14331),f495(x14333,x14334,x14332)) % 173.51/173.29 [1434]~E(x14341,x14342)+E(f56(x14341,x14343),f56(x14342,x14343)) % 173.51/173.29 [1435]~E(x14351,x14352)+E(f56(x14353,x14351),f56(x14353,x14352)) % 173.51/173.29 [1436]~E(x14361,x14362)+E(f414(x14361,x14363,x14364,x14365),f414(x14362,x14363,x14364,x14365)) % 173.51/173.29 [1437]~E(x14371,x14372)+E(f414(x14373,x14371,x14374,x14375),f414(x14373,x14372,x14374,x14375)) % 173.51/173.29 [1438]~E(x14381,x14382)+E(f414(x14383,x14384,x14381,x14385),f414(x14383,x14384,x14382,x14385)) % 173.51/173.29 [1439]~E(x14391,x14392)+E(f414(x14393,x14394,x14395,x14391),f414(x14393,x14394,x14395,x14392)) % 173.51/173.29 [1440]~E(x14401,x14402)+E(f801(x14401,x14403,x14404),f801(x14402,x14403,x14404)) % 173.51/173.29 [1441]~E(x14411,x14412)+E(f801(x14413,x14411,x14414),f801(x14413,x14412,x14414)) % 173.51/173.29 [1442]~E(x14421,x14422)+E(f801(x14423,x14424,x14421),f801(x14423,x14424,x14422)) % 173.51/173.29 [1443]~E(x14431,x14432)+E(f605(x14431),f605(x14432)) % 173.51/173.29 [1444]~E(x14441,x14442)+E(f704(x14441,x14443,x14444),f704(x14442,x14443,x14444)) % 173.51/173.29 [1445]~E(x14451,x14452)+E(f704(x14453,x14451,x14454),f704(x14453,x14452,x14454)) % 173.51/173.29 [1446]~E(x14461,x14462)+E(f704(x14463,x14464,x14461),f704(x14463,x14464,x14462)) % 173.51/173.29 [1447]~E(x14471,x14472)+E(f440(x14471,x14473,x14474,x14475),f440(x14472,x14473,x14474,x14475)) % 173.51/173.29 [1448]~E(x14481,x14482)+E(f440(x14483,x14481,x14484,x14485),f440(x14483,x14482,x14484,x14485)) % 173.51/173.29 [1449]~E(x14491,x14492)+E(f440(x14493,x14494,x14491,x14495),f440(x14493,x14494,x14492,x14495)) % 173.51/173.29 [1450]~E(x14501,x14502)+E(f440(x14503,x14504,x14505,x14501),f440(x14503,x14504,x14505,x14502)) % 173.51/173.29 [1451]~E(x14511,x14512)+E(f421(x14511,x14513),f421(x14512,x14513)) % 173.51/173.29 [1452]~E(x14521,x14522)+E(f421(x14523,x14521),f421(x14523,x14522)) % 173.51/173.29 [1453]~E(x14531,x14532)+E(f578(x14531,x14533,x14534,x14535,x14536),f578(x14532,x14533,x14534,x14535,x14536)) % 173.51/173.29 [1454]~E(x14541,x14542)+E(f578(x14543,x14541,x14544,x14545,x14546),f578(x14543,x14542,x14544,x14545,x14546)) % 173.51/173.29 [1455]~E(x14551,x14552)+E(f578(x14553,x14554,x14551,x14555,x14556),f578(x14553,x14554,x14552,x14555,x14556)) % 173.51/173.29 [1456]~E(x14561,x14562)+E(f578(x14563,x14564,x14565,x14561,x14566),f578(x14563,x14564,x14565,x14562,x14566)) % 173.51/173.29 [1457]~E(x14571,x14572)+E(f578(x14573,x14574,x14575,x14576,x14571),f578(x14573,x14574,x14575,x14576,x14572)) % 173.51/173.29 [1458]~E(x14581,x14582)+E(f422(x14581,x14583,x14584,x14585,x14586),f422(x14582,x14583,x14584,x14585,x14586)) % 173.51/173.29 [1459]~E(x14591,x14592)+E(f422(x14593,x14591,x14594,x14595,x14596),f422(x14593,x14592,x14594,x14595,x14596)) % 173.51/173.29 [1460]~E(x14601,x14602)+E(f422(x14603,x14604,x14601,x14605,x14606),f422(x14603,x14604,x14602,x14605,x14606)) % 173.51/173.29 [1461]~E(x14611,x14612)+E(f422(x14613,x14614,x14615,x14611,x14616),f422(x14613,x14614,x14615,x14612,x14616)) % 173.51/173.29 [1462]~E(x14621,x14622)+E(f422(x14623,x14624,x14625,x14626,x14621),f422(x14623,x14624,x14625,x14626,x14622)) % 173.51/173.29 [1463]~E(x14631,x14632)+E(f556(x14631,x14633,x14634),f556(x14632,x14633,x14634)) % 173.51/173.29 [1464]~E(x14641,x14642)+E(f556(x14643,x14641,x14644),f556(x14643,x14642,x14644)) % 173.51/173.29 [1465]~E(x14651,x14652)+E(f556(x14653,x14654,x14651),f556(x14653,x14654,x14652)) % 173.51/173.29 [1466]~E(x14661,x14662)+E(f823(x14661),f823(x14662)) % 173.51/173.29 [1467]~E(x14671,x14672)+E(f447(x14671,x14673,x14674),f447(x14672,x14673,x14674)) % 173.51/173.29 [1468]~E(x14681,x14682)+E(f447(x14683,x14681,x14684),f447(x14683,x14682,x14684)) % 173.51/173.29 [1469]~E(x14691,x14692)+E(f447(x14693,x14694,x14691),f447(x14693,x14694,x14692)) % 173.51/173.29 [1470]~E(x14701,x14702)+E(f836(x14701,x14703),f836(x14702,x14703)) % 173.51/173.29 [1471]~E(x14711,x14712)+E(f836(x14713,x14711),f836(x14713,x14712)) % 173.51/173.29 [1472]~E(x14721,x14722)+E(f456(x14721,x14723,x14724),f456(x14722,x14723,x14724)) % 173.51/173.29 [1473]~E(x14731,x14732)+E(f456(x14733,x14731,x14734),f456(x14733,x14732,x14734)) % 173.51/173.29 [1474]~E(x14741,x14742)+E(f456(x14743,x14744,x14741),f456(x14743,x14744,x14742)) % 173.51/173.29 [1475]~E(x14751,x14752)+E(f637(x14751,x14753,x14754,x14755,x14756),f637(x14752,x14753,x14754,x14755,x14756)) % 173.51/173.29 [1476]~E(x14761,x14762)+E(f637(x14763,x14761,x14764,x14765,x14766),f637(x14763,x14762,x14764,x14765,x14766)) % 173.51/173.29 [1477]~E(x14771,x14772)+E(f637(x14773,x14774,x14771,x14775,x14776),f637(x14773,x14774,x14772,x14775,x14776)) % 173.51/173.29 [1478]~E(x14781,x14782)+E(f637(x14783,x14784,x14785,x14781,x14786),f637(x14783,x14784,x14785,x14782,x14786)) % 173.51/173.29 [1479]~E(x14791,x14792)+E(f637(x14793,x14794,x14795,x14796,x14791),f637(x14793,x14794,x14795,x14796,x14792)) % 173.51/173.29 [1480]~E(x14801,x14802)+E(f660(x14801,x14803,x14804,x14805,x14806),f660(x14802,x14803,x14804,x14805,x14806)) % 173.51/173.29 [1481]~E(x14811,x14812)+E(f660(x14813,x14811,x14814,x14815,x14816),f660(x14813,x14812,x14814,x14815,x14816)) % 173.51/173.29 [1482]~E(x14821,x14822)+E(f660(x14823,x14824,x14821,x14825,x14826),f660(x14823,x14824,x14822,x14825,x14826)) % 173.51/173.29 [1483]~E(x14831,x14832)+E(f660(x14833,x14834,x14835,x14831,x14836),f660(x14833,x14834,x14835,x14832,x14836)) % 173.51/173.29 [1484]~E(x14841,x14842)+E(f660(x14843,x14844,x14845,x14846,x14841),f660(x14843,x14844,x14845,x14846,x14842)) % 173.51/173.29 [1485]~E(x14851,x14852)+E(f701(x14851,x14853,x14854,x14855,x14856),f701(x14852,x14853,x14854,x14855,x14856)) % 173.51/173.29 [1486]~E(x14861,x14862)+E(f701(x14863,x14861,x14864,x14865,x14866),f701(x14863,x14862,x14864,x14865,x14866)) % 173.51/173.29 [1487]~E(x14871,x14872)+E(f701(x14873,x14874,x14871,x14875,x14876),f701(x14873,x14874,x14872,x14875,x14876)) % 173.51/173.29 [1488]~E(x14881,x14882)+E(f701(x14883,x14884,x14885,x14881,x14886),f701(x14883,x14884,x14885,x14882,x14886)) % 173.51/173.29 [1489]~E(x14891,x14892)+E(f701(x14893,x14894,x14895,x14896,x14891),f701(x14893,x14894,x14895,x14896,x14892)) % 173.51/173.29 [1490]~E(x14901,x14902)+E(f544(x14901,x14903,x14904,x14905,x14906,x14907,x14908),f544(x14902,x14903,x14904,x14905,x14906,x14907,x14908)) % 173.51/173.29 [1491]~E(x14911,x14912)+E(f544(x14913,x14911,x14914,x14915,x14916,x14917,x14918),f544(x14913,x14912,x14914,x14915,x14916,x14917,x14918)) % 173.51/173.29 [1492]~E(x14921,x14922)+E(f544(x14923,x14924,x14921,x14925,x14926,x14927,x14928),f544(x14923,x14924,x14922,x14925,x14926,x14927,x14928)) % 173.51/173.29 [1493]~E(x14931,x14932)+E(f544(x14933,x14934,x14935,x14931,x14936,x14937,x14938),f544(x14933,x14934,x14935,x14932,x14936,x14937,x14938)) % 173.51/173.29 [1494]~E(x14941,x14942)+E(f544(x14943,x14944,x14945,x14946,x14941,x14947,x14948),f544(x14943,x14944,x14945,x14946,x14942,x14947,x14948)) % 173.51/173.29 [1495]~E(x14951,x14952)+E(f544(x14953,x14954,x14955,x14956,x14957,x14951,x14958),f544(x14953,x14954,x14955,x14956,x14957,x14952,x14958)) % 173.51/173.29 [1496]~E(x14961,x14962)+E(f544(x14963,x14964,x14965,x14966,x14967,x14968,x14961),f544(x14963,x14964,x14965,x14966,x14967,x14968,x14962)) % 173.51/173.29 [1497]~E(x14971,x14972)+E(f297(x14971,x14973),f297(x14972,x14973)) % 173.51/173.29 [1498]~E(x14981,x14982)+E(f297(x14983,x14981),f297(x14983,x14982)) % 173.51/173.29 [1499]~E(x14991,x14992)+E(f638(x14991,x14993,x14994,x14995,x14996),f638(x14992,x14993,x14994,x14995,x14996)) % 173.51/173.29 [1500]~E(x15001,x15002)+E(f638(x15003,x15001,x15004,x15005,x15006),f638(x15003,x15002,x15004,x15005,x15006)) % 173.51/173.29 [1501]~E(x15011,x15012)+E(f638(x15013,x15014,x15011,x15015,x15016),f638(x15013,x15014,x15012,x15015,x15016)) % 173.51/173.29 [1502]~E(x15021,x15022)+E(f638(x15023,x15024,x15025,x15021,x15026),f638(x15023,x15024,x15025,x15022,x15026)) % 173.51/173.29 [1503]~E(x15031,x15032)+E(f638(x15033,x15034,x15035,x15036,x15031),f638(x15033,x15034,x15035,x15036,x15032)) % 173.51/173.29 [1504]~E(x15041,x15042)+E(f695(x15041,x15043,x15044,x15045),f695(x15042,x15043,x15044,x15045)) % 173.51/173.29 [1505]~E(x15051,x15052)+E(f695(x15053,x15051,x15054,x15055),f695(x15053,x15052,x15054,x15055)) % 173.51/173.29 [1506]~E(x15061,x15062)+E(f695(x15063,x15064,x15061,x15065),f695(x15063,x15064,x15062,x15065)) % 173.51/173.29 [1507]~E(x15071,x15072)+E(f695(x15073,x15074,x15075,x15071),f695(x15073,x15074,x15075,x15072)) % 173.51/173.29 [1508]~E(x15081,x15082)+E(f466(x15081,x15083,x15084),f466(x15082,x15083,x15084)) % 173.51/173.29 [1509]~E(x15091,x15092)+E(f466(x15093,x15091,x15094),f466(x15093,x15092,x15094)) % 173.51/173.29 [1510]~E(x15101,x15102)+E(f466(x15103,x15104,x15101),f466(x15103,x15104,x15102)) % 173.51/173.29 [1511]~E(x15111,x15112)+E(f650(x15111,x15113,x15114),f650(x15112,x15113,x15114)) % 173.51/173.29 [1512]~E(x15121,x15122)+E(f650(x15123,x15121,x15124),f650(x15123,x15122,x15124)) % 173.51/173.29 [1513]~E(x15131,x15132)+E(f650(x15133,x15134,x15131),f650(x15133,x15134,x15132)) % 173.51/173.29 [1514]~E(x15141,x15142)+E(f410(x15141,x15143,x15144,x15145),f410(x15142,x15143,x15144,x15145)) % 173.51/173.29 [1515]~E(x15151,x15152)+E(f410(x15153,x15151,x15154,x15155),f410(x15153,x15152,x15154,x15155)) % 173.51/173.29 [1516]~E(x15161,x15162)+E(f410(x15163,x15164,x15161,x15165),f410(x15163,x15164,x15162,x15165)) % 173.51/173.29 [1517]~E(x15171,x15172)+E(f410(x15173,x15174,x15175,x15171),f410(x15173,x15174,x15175,x15172)) % 173.51/173.29 [1518]~E(x15181,x15182)+E(f472(x15181,x15183,x15184),f472(x15182,x15183,x15184)) % 173.51/173.29 [1519]~E(x15191,x15192)+E(f472(x15193,x15191,x15194),f472(x15193,x15192,x15194)) % 173.51/173.29 [1520]~E(x15201,x15202)+E(f472(x15203,x15204,x15201),f472(x15203,x15204,x15202)) % 173.51/173.29 [1521]~E(x15211,x15212)+E(f547(x15211,x15213,x15214),f547(x15212,x15213,x15214)) % 173.51/173.29 [1522]~E(x15221,x15222)+E(f547(x15223,x15221,x15224),f547(x15223,x15222,x15224)) % 173.51/173.29 [1523]~E(x15231,x15232)+E(f547(x15233,x15234,x15231),f547(x15233,x15234,x15232)) % 173.51/173.29 [1524]~E(x15241,x15242)+E(f696(x15241,x15243,x15244,x15245),f696(x15242,x15243,x15244,x15245)) % 173.51/173.29 [1525]~E(x15251,x15252)+E(f696(x15253,x15251,x15254,x15255),f696(x15253,x15252,x15254,x15255)) % 173.51/173.29 [1526]~E(x15261,x15262)+E(f696(x15263,x15264,x15261,x15265),f696(x15263,x15264,x15262,x15265)) % 173.51/173.29 [1527]~E(x15271,x15272)+E(f696(x15273,x15274,x15275,x15271),f696(x15273,x15274,x15275,x15272)) % 173.51/173.29 [1528]~E(x15281,x15282)+E(f868(x15281,x15283),f868(x15282,x15283)) % 173.51/173.29 [1529]~E(x15291,x15292)+E(f868(x15293,x15291),f868(x15293,x15292)) % 173.51/173.29 [1530]~E(x15301,x15302)+E(f391(x15301,x15303,x15304),f391(x15302,x15303,x15304)) % 173.51/173.29 [1531]~E(x15311,x15312)+E(f391(x15313,x15311,x15314),f391(x15313,x15312,x15314)) % 173.51/173.29 [1532]~E(x15321,x15322)+E(f391(x15323,x15324,x15321),f391(x15323,x15324,x15322)) % 173.51/173.29 [1533]~E(x15331,x15332)+E(f445(x15331,x15333,x15334),f445(x15332,x15333,x15334)) % 173.51/173.29 [1534]~E(x15341,x15342)+E(f445(x15343,x15341,x15344),f445(x15343,x15342,x15344)) % 173.51/173.29 [1535]~E(x15351,x15352)+E(f445(x15353,x15354,x15351),f445(x15353,x15354,x15352)) % 173.51/173.29 [1536]~E(x15361,x15362)+E(f298(x15361,x15363),f298(x15362,x15363)) % 173.51/173.29 [1537]~E(x15371,x15372)+E(f298(x15373,x15371),f298(x15373,x15372)) % 173.51/173.29 [1538]~E(x15381,x15382)+E(f639(x15381,x15383,x15384,x15385,x15386,x15387),f639(x15382,x15383,x15384,x15385,x15386,x15387)) % 173.51/173.29 [1539]~E(x15391,x15392)+E(f639(x15393,x15391,x15394,x15395,x15396,x15397),f639(x15393,x15392,x15394,x15395,x15396,x15397)) % 173.51/173.29 [1540]~E(x15401,x15402)+E(f639(x15403,x15404,x15401,x15405,x15406,x15407),f639(x15403,x15404,x15402,x15405,x15406,x15407)) % 173.51/173.29 [1541]~E(x15411,x15412)+E(f639(x15413,x15414,x15415,x15411,x15416,x15417),f639(x15413,x15414,x15415,x15412,x15416,x15417)) % 173.51/173.29 [1542]~E(x15421,x15422)+E(f639(x15423,x15424,x15425,x15426,x15421,x15427),f639(x15423,x15424,x15425,x15426,x15422,x15427)) % 173.51/173.29 [1543]~E(x15431,x15432)+E(f639(x15433,x15434,x15435,x15436,x15437,x15431),f639(x15433,x15434,x15435,x15436,x15437,x15432)) % 173.51/173.29 [1544]~E(x15441,x15442)+E(f813(x15441,x15443,x15444),f813(x15442,x15443,x15444)) % 173.51/173.29 [1545]~E(x15451,x15452)+E(f813(x15453,x15451,x15454),f813(x15453,x15452,x15454)) % 173.51/173.29 [1546]~E(x15461,x15462)+E(f813(x15463,x15464,x15461),f813(x15463,x15464,x15462)) % 173.51/173.29 [1547]~E(x15471,x15472)+E(f583(x15471,x15473,x15474,x15475,x15476,x15477,x15478,x15479),f583(x15472,x15473,x15474,x15475,x15476,x15477,x15478,x15479)) % 173.51/173.29 [1548]~E(x15481,x15482)+E(f583(x15483,x15481,x15484,x15485,x15486,x15487,x15488,x15489),f583(x15483,x15482,x15484,x15485,x15486,x15487,x15488,x15489)) % 173.51/173.29 [1549]~E(x15491,x15492)+E(f583(x15493,x15494,x15491,x15495,x15496,x15497,x15498,x15499),f583(x15493,x15494,x15492,x15495,x15496,x15497,x15498,x15499)) % 173.51/173.29 [1550]~E(x15501,x15502)+E(f583(x15503,x15504,x15505,x15501,x15506,x15507,x15508,x15509),f583(x15503,x15504,x15505,x15502,x15506,x15507,x15508,x15509)) % 173.51/173.29 [1551]~E(x15511,x15512)+E(f583(x15513,x15514,x15515,x15516,x15511,x15517,x15518,x15519),f583(x15513,x15514,x15515,x15516,x15512,x15517,x15518,x15519)) % 173.51/173.29 [1552]~E(x15521,x15522)+E(f583(x15523,x15524,x15525,x15526,x15527,x15521,x15528,x15529),f583(x15523,x15524,x15525,x15526,x15527,x15522,x15528,x15529)) % 173.51/173.29 [1553]~E(x15531,x15532)+E(f583(x15533,x15534,x15535,x15536,x15537,x15538,x15531,x15539),f583(x15533,x15534,x15535,x15536,x15537,x15538,x15532,x15539)) % 173.51/173.29 [1554]~E(x15541,x15542)+E(f583(x15543,x15544,x15545,x15546,x15547,x15548,x15549,x15541),f583(x15543,x15544,x15545,x15546,x15547,x15548,x15549,x15542)) % 173.51/173.29 [1555]~E(x15551,x15552)+E(f519(x15551,x15553),f519(x15552,x15553)) % 173.51/173.29 [1556]~E(x15561,x15562)+E(f519(x15563,x15561),f519(x15563,x15562)) % 173.51/173.29 [1557]~E(x15571,x15572)+E(f666(x15571,x15573,x15574),f666(x15572,x15573,x15574)) % 173.51/173.29 [1558]~E(x15581,x15582)+E(f666(x15583,x15581,x15584),f666(x15583,x15582,x15584)) % 173.51/173.29 [1559]~E(x15591,x15592)+E(f666(x15593,x15594,x15591),f666(x15593,x15594,x15592)) % 173.51/173.29 [1560]~E(x15601,x15602)+E(f802(x15601,x15603,x15604),f802(x15602,x15603,x15604)) % 173.51/173.29 [1561]~E(x15611,x15612)+E(f802(x15613,x15611,x15614),f802(x15613,x15612,x15614)) % 173.51/173.29 [1562]~E(x15621,x15622)+E(f802(x15623,x15624,x15621),f802(x15623,x15624,x15622)) % 173.51/173.29 [1563]~E(x15631,x15632)+E(f474(x15631,x15633),f474(x15632,x15633)) % 173.51/173.29 [1564]~E(x15641,x15642)+E(f474(x15643,x15641),f474(x15643,x15642)) % 173.51/173.29 [1565]~E(x15651,x15652)+E(f220(x15651,x15653,x15654,x15655,x15656,x15657,x15658),f220(x15652,x15653,x15654,x15655,x15656,x15657,x15658)) % 173.51/173.29 [1566]~E(x15661,x15662)+E(f220(x15663,x15661,x15664,x15665,x15666,x15667,x15668),f220(x15663,x15662,x15664,x15665,x15666,x15667,x15668)) % 173.51/173.29 [1567]~E(x15671,x15672)+E(f220(x15673,x15674,x15671,x15675,x15676,x15677,x15678),f220(x15673,x15674,x15672,x15675,x15676,x15677,x15678)) % 173.51/173.29 [1568]~E(x15681,x15682)+E(f220(x15683,x15684,x15685,x15681,x15686,x15687,x15688),f220(x15683,x15684,x15685,x15682,x15686,x15687,x15688)) % 173.51/173.29 [1569]~E(x15691,x15692)+E(f220(x15693,x15694,x15695,x15696,x15691,x15697,x15698),f220(x15693,x15694,x15695,x15696,x15692,x15697,x15698)) % 173.51/173.29 [1570]~E(x15701,x15702)+E(f220(x15703,x15704,x15705,x15706,x15707,x15701,x15708),f220(x15703,x15704,x15705,x15706,x15707,x15702,x15708)) % 173.51/173.29 [1571]~E(x15711,x15712)+E(f220(x15713,x15714,x15715,x15716,x15717,x15718,x15711),f220(x15713,x15714,x15715,x15716,x15717,x15718,x15712)) % 173.51/173.29 [1572]~E(x15721,x15722)+E(f645(x15721,x15723,x15724),f645(x15722,x15723,x15724)) % 173.51/173.29 [1573]~E(x15731,x15732)+E(f645(x15733,x15731,x15734),f645(x15733,x15732,x15734)) % 173.51/173.29 [1574]~E(x15741,x15742)+E(f645(x15743,x15744,x15741),f645(x15743,x15744,x15742)) % 173.51/173.29 [1575]~E(x15751,x15752)+E(f394(x15751,x15753,x15754,x15755),f394(x15752,x15753,x15754,x15755)) % 173.51/173.29 [1576]~E(x15761,x15762)+E(f394(x15763,x15761,x15764,x15765),f394(x15763,x15762,x15764,x15765)) % 173.51/173.29 [1577]~E(x15771,x15772)+E(f394(x15773,x15774,x15771,x15775),f394(x15773,x15774,x15772,x15775)) % 173.51/173.29 [1578]~E(x15781,x15782)+E(f394(x15783,x15784,x15785,x15781),f394(x15783,x15784,x15785,x15782)) % 173.51/173.29 [1579]~E(x15791,x15792)+E(f520(x15791,x15793,x15794),f520(x15792,x15793,x15794)) % 173.51/173.29 [1580]~E(x15801,x15802)+E(f520(x15803,x15801,x15804),f520(x15803,x15802,x15804)) % 173.51/173.29 [1581]~E(x15811,x15812)+E(f520(x15813,x15814,x15811),f520(x15813,x15814,x15812)) % 173.51/173.29 [1582]~E(x15821,x15822)+E(f870(x15821),f870(x15822)) % 173.51/173.29 [1583]~E(x15831,x15832)+E(f366(x15831,x15833),f366(x15832,x15833)) % 173.51/173.29 [1584]~E(x15841,x15842)+E(f366(x15843,x15841),f366(x15843,x15842)) % 173.51/173.29 [1585]~E(x15851,x15852)+E(f623(x15851,x15853,x15854),f623(x15852,x15853,x15854)) % 173.51/173.29 [1586]~E(x15861,x15862)+E(f623(x15863,x15861,x15864),f623(x15863,x15862,x15864)) % 173.51/173.29 [1587]~E(x15871,x15872)+E(f623(x15873,x15874,x15871),f623(x15873,x15874,x15872)) % 173.51/173.29 [1588]~E(x15881,x15882)+E(f371(x15881,x15883,x15884,x15885,x15886,x15887),f371(x15882,x15883,x15884,x15885,x15886,x15887)) % 173.51/173.29 [1589]~E(x15891,x15892)+E(f371(x15893,x15891,x15894,x15895,x15896,x15897),f371(x15893,x15892,x15894,x15895,x15896,x15897)) % 173.51/173.29 [1590]~E(x15901,x15902)+E(f371(x15903,x15904,x15901,x15905,x15906,x15907),f371(x15903,x15904,x15902,x15905,x15906,x15907)) % 173.51/173.29 [1591]~E(x15911,x15912)+E(f371(x15913,x15914,x15915,x15911,x15916,x15917),f371(x15913,x15914,x15915,x15912,x15916,x15917)) % 173.51/173.29 [1592]~E(x15921,x15922)+E(f371(x15923,x15924,x15925,x15926,x15921,x15927),f371(x15923,x15924,x15925,x15926,x15922,x15927)) % 173.51/173.29 [1593]~E(x15931,x15932)+E(f371(x15933,x15934,x15935,x15936,x15937,x15931),f371(x15933,x15934,x15935,x15936,x15937,x15932)) % 173.51/173.29 [1594]~E(x15941,x15942)+E(f468(x15941,x15943,x15944),f468(x15942,x15943,x15944)) % 173.51/173.29 [1595]~E(x15951,x15952)+E(f468(x15953,x15951,x15954),f468(x15953,x15952,x15954)) % 173.51/173.29 [1596]~E(x15961,x15962)+E(f468(x15963,x15964,x15961),f468(x15963,x15964,x15962)) % 173.51/173.29 [1597]~E(x15971,x15972)+E(f698(x15971,x15973),f698(x15972,x15973)) % 173.51/173.29 [1598]~E(x15981,x15982)+E(f698(x15983,x15981),f698(x15983,x15982)) % 173.51/173.29 [1599]~E(x15991,x15992)+E(f628(x15991,x15993),f628(x15992,x15993)) % 173.51/173.29 [1600]~E(x16001,x16002)+E(f628(x16003,x16001),f628(x16003,x16002)) % 173.51/173.29 [1601]~E(x16011,x16012)+E(f819(x16011,x16013,x16014),f819(x16012,x16013,x16014)) % 173.51/173.29 [1602]~E(x16021,x16022)+E(f819(x16023,x16021,x16024),f819(x16023,x16022,x16024)) % 173.51/173.29 [1603]~E(x16031,x16032)+E(f819(x16033,x16034,x16031),f819(x16033,x16034,x16032)) % 173.51/173.29 [1604]~E(x16041,x16042)+E(f717(x16041,x16043,x16044,x16045),f717(x16042,x16043,x16044,x16045)) % 173.51/173.29 [1605]~E(x16051,x16052)+E(f717(x16053,x16051,x16054,x16055),f717(x16053,x16052,x16054,x16055)) % 173.51/173.29 [1606]~E(x16061,x16062)+E(f717(x16063,x16064,x16061,x16065),f717(x16063,x16064,x16062,x16065)) % 173.51/173.29 [1607]~E(x16071,x16072)+E(f717(x16073,x16074,x16075,x16071),f717(x16073,x16074,x16075,x16072)) % 173.51/173.29 [1608]~E(x16081,x16082)+E(f521(x16081,x16083,x16084),f521(x16082,x16083,x16084)) % 173.51/173.29 [1609]~E(x16091,x16092)+E(f521(x16093,x16091,x16094),f521(x16093,x16092,x16094)) % 173.51/173.29 [1610]~E(x16101,x16102)+E(f521(x16103,x16104,x16101),f521(x16103,x16104,x16102)) % 173.51/173.29 [1611]~E(x16111,x16112)+E(f395(x16111,x16113,x16114,x16115),f395(x16112,x16113,x16114,x16115)) % 173.51/173.29 [1612]~E(x16121,x16122)+E(f395(x16123,x16121,x16124,x16125),f395(x16123,x16122,x16124,x16125)) % 173.51/173.29 [1613]~E(x16131,x16132)+E(f395(x16133,x16134,x16131,x16135),f395(x16133,x16134,x16132,x16135)) % 173.51/173.29 [1614]~E(x16141,x16142)+E(f395(x16143,x16144,x16145,x16141),f395(x16143,x16144,x16145,x16142)) % 173.51/173.29 [1615]~E(x16151,x16152)+E(f476(x16151,x16153,x16154,x16155),f476(x16152,x16153,x16154,x16155)) % 173.51/173.29 [1616]~E(x16161,x16162)+E(f476(x16163,x16161,x16164,x16165),f476(x16163,x16162,x16164,x16165)) % 173.51/173.29 [1617]~E(x16171,x16172)+E(f476(x16173,x16174,x16171,x16175),f476(x16173,x16174,x16172,x16175)) % 173.51/173.29 [1618]~E(x16181,x16182)+E(f476(x16183,x16184,x16185,x16181),f476(x16183,x16184,x16185,x16182)) % 173.51/173.29 [1619]~E(x16191,x16192)+E(f460(x16191,x16193,x16194,x16195,x16196),f460(x16192,x16193,x16194,x16195,x16196)) % 173.51/173.29 [1620]~E(x16201,x16202)+E(f460(x16203,x16201,x16204,x16205,x16206),f460(x16203,x16202,x16204,x16205,x16206)) % 173.51/173.29 [1621]~E(x16211,x16212)+E(f460(x16213,x16214,x16211,x16215,x16216),f460(x16213,x16214,x16212,x16215,x16216)) % 173.51/173.29 [1622]~E(x16221,x16222)+E(f460(x16223,x16224,x16225,x16221,x16226),f460(x16223,x16224,x16225,x16222,x16226)) % 173.51/173.29 [1623]~E(x16231,x16232)+E(f460(x16233,x16234,x16235,x16236,x16231),f460(x16233,x16234,x16235,x16236,x16232)) % 173.51/173.29 [1624]~E(x16241,x16242)+E(f399(x16241,x16243,x16244,x16245),f399(x16242,x16243,x16244,x16245)) % 173.51/173.29 [1625]~E(x16251,x16252)+E(f399(x16253,x16251,x16254,x16255),f399(x16253,x16252,x16254,x16255)) % 173.51/173.29 [1626]~E(x16261,x16262)+E(f399(x16263,x16264,x16261,x16265),f399(x16263,x16264,x16262,x16265)) % 173.51/173.29 [1627]~E(x16271,x16272)+E(f399(x16273,x16274,x16275,x16271),f399(x16273,x16274,x16275,x16272)) % 173.51/173.29 [1628]~E(x16281,x16282)+E(f560(x16281,x16283,x16284),f560(x16282,x16283,x16284)) % 173.51/173.29 [1629]~E(x16291,x16292)+E(f560(x16293,x16291,x16294),f560(x16293,x16292,x16294)) % 173.51/173.29 [1630]~E(x16301,x16302)+E(f560(x16303,x16304,x16301),f560(x16303,x16304,x16302)) % 173.51/173.29 [1631]~E(x16311,x16312)+E(f436(x16311,x16313,x16314),f436(x16312,x16313,x16314)) % 173.51/173.29 [1632]~E(x16321,x16322)+E(f436(x16323,x16321,x16324),f436(x16323,x16322,x16324)) % 173.51/173.29 [1633]~E(x16331,x16332)+E(f436(x16333,x16334,x16331),f436(x16333,x16334,x16332)) % 173.51/173.29 [1634]~E(x16341,x16342)+E(f821(x16341,x16343,x16344,x16345),f821(x16342,x16343,x16344,x16345)) % 173.51/173.29 [1635]~E(x16351,x16352)+E(f821(x16353,x16351,x16354,x16355),f821(x16353,x16352,x16354,x16355)) % 173.51/173.29 [1636]~E(x16361,x16362)+E(f821(x16363,x16364,x16361,x16365),f821(x16363,x16364,x16362,x16365)) % 173.51/173.29 [1637]~E(x16371,x16372)+E(f821(x16373,x16374,x16375,x16371),f821(x16373,x16374,x16375,x16372)) % 173.51/173.29 [1638]~E(x16381,x16382)+E(f763(x16381,x16383),f763(x16382,x16383)) % 173.51/173.29 [1639]~E(x16391,x16392)+E(f763(x16393,x16391),f763(x16393,x16392)) % 173.51/173.29 [1640]~E(x16401,x16402)+E(f818(x16401,x16403,x16404),f818(x16402,x16403,x16404)) % 173.51/173.29 [1641]~E(x16411,x16412)+E(f818(x16413,x16411,x16414),f818(x16413,x16412,x16414)) % 173.51/173.29 [1642]~E(x16421,x16422)+E(f818(x16423,x16424,x16421),f818(x16423,x16424,x16422)) % 173.51/173.29 [1643]~E(x16431,x16432)+E(f613(x16431,x16433,x16434,x16435,x16436,x16437),f613(x16432,x16433,x16434,x16435,x16436,x16437)) % 173.51/173.29 [1644]~E(x16441,x16442)+E(f613(x16443,x16441,x16444,x16445,x16446,x16447),f613(x16443,x16442,x16444,x16445,x16446,x16447)) % 173.51/173.29 [1645]~E(x16451,x16452)+E(f613(x16453,x16454,x16451,x16455,x16456,x16457),f613(x16453,x16454,x16452,x16455,x16456,x16457)) % 173.51/173.29 [1646]~E(x16461,x16462)+E(f613(x16463,x16464,x16465,x16461,x16466,x16467),f613(x16463,x16464,x16465,x16462,x16466,x16467)) % 173.51/173.29 [1647]~E(x16471,x16472)+E(f613(x16473,x16474,x16475,x16476,x16471,x16477),f613(x16473,x16474,x16475,x16476,x16472,x16477)) % 173.51/173.29 [1648]~E(x16481,x16482)+E(f613(x16483,x16484,x16485,x16486,x16487,x16481),f613(x16483,x16484,x16485,x16486,x16487,x16482)) % 173.51/173.29 [1649]~E(x16491,x16492)+E(f890(x16491,x16493),f890(x16492,x16493)) % 173.51/173.29 [1650]~E(x16501,x16502)+E(f890(x16503,x16501),f890(x16503,x16502)) % 173.51/173.29 [1651]~E(x16511,x16512)+E(f424(x16511,x16513,x16514),f424(x16512,x16513,x16514)) % 173.51/173.29 [1652]~E(x16521,x16522)+E(f424(x16523,x16521,x16524),f424(x16523,x16522,x16524)) % 173.51/173.29 [1653]~E(x16531,x16532)+E(f424(x16533,x16534,x16531),f424(x16533,x16534,x16532)) % 173.51/173.29 [1654]~E(x16541,x16542)+E(f754(x16541,x16543),f754(x16542,x16543)) % 173.51/173.29 [1655]~E(x16551,x16552)+E(f754(x16553,x16551),f754(x16553,x16552)) % 173.51/173.29 [1656]~E(x16561,x16562)+E(f154(x16561,x16563),f154(x16562,x16563)) % 173.51/173.29 [1657]~E(x16571,x16572)+E(f154(x16573,x16571),f154(x16573,x16572)) % 173.51/173.29 [1658]~E(x16581,x16582)+E(f386(x16581,x16583),f386(x16582,x16583)) % 173.51/173.29 [1659]~E(x16591,x16592)+E(f386(x16593,x16591),f386(x16593,x16592)) % 173.51/173.29 [1660]~E(x16601,x16602)+E(f871(x16601,x16603),f871(x16602,x16603)) % 173.51/173.29 [1661]~E(x16611,x16612)+E(f871(x16613,x16611),f871(x16613,x16612)) % 173.51/173.29 [1662]~E(x16621,x16622)+E(f400(x16621,x16623,x16624,x16625),f400(x16622,x16623,x16624,x16625)) % 173.51/173.29 [1663]~E(x16631,x16632)+E(f400(x16633,x16631,x16634,x16635),f400(x16633,x16632,x16634,x16635)) % 173.51/173.29 [1664]~E(x16641,x16642)+E(f400(x16643,x16644,x16641,x16645),f400(x16643,x16644,x16642,x16645)) % 173.51/173.29 [1665]~E(x16651,x16652)+E(f400(x16653,x16654,x16655,x16651),f400(x16653,x16654,x16655,x16652)) % 173.51/173.29 [1666]~E(x16661,x16662)+E(f752(x16661,x16663),f752(x16662,x16663)) % 173.51/173.29 [1667]~E(x16671,x16672)+E(f752(x16673,x16671),f752(x16673,x16672)) % 173.51/173.29 [1668]~E(x16681,x16682)+E(f401(x16681,x16683,x16684,x16685),f401(x16682,x16683,x16684,x16685)) % 173.51/173.29 [1669]~E(x16691,x16692)+E(f401(x16693,x16691,x16694,x16695),f401(x16693,x16692,x16694,x16695)) % 173.51/173.29 [1670]~E(x16701,x16702)+E(f401(x16703,x16704,x16701,x16705),f401(x16703,x16704,x16702,x16705)) % 173.51/173.29 [1671]~E(x16711,x16712)+E(f401(x16713,x16714,x16715,x16711),f401(x16713,x16714,x16715,x16712)) % 173.51/173.29 [1672]~E(x16721,x16722)+E(f318(x16721,x16723),f318(x16722,x16723)) % 173.51/173.29 [1673]~E(x16731,x16732)+E(f318(x16733,x16731),f318(x16733,x16732)) % 173.51/173.29 [1674]~E(x16741,x16742)+E(f17(x16741,x16743,x16744,x16745),f17(x16742,x16743,x16744,x16745)) % 173.51/173.29 [1675]~E(x16751,x16752)+E(f17(x16753,x16751,x16754,x16755),f17(x16753,x16752,x16754,x16755)) % 173.51/173.29 [1676]~E(x16761,x16762)+E(f17(x16763,x16764,x16761,x16765),f17(x16763,x16764,x16762,x16765)) % 173.51/173.29 [1677]~E(x16771,x16772)+E(f17(x16773,x16774,x16775,x16771),f17(x16773,x16774,x16775,x16772)) % 173.51/173.29 [1678]~E(x16781,x16782)+E(f887(x16781,x16783,x16784,x16785),f887(x16782,x16783,x16784,x16785)) % 173.51/173.29 [1679]~E(x16791,x16792)+E(f887(x16793,x16791,x16794,x16795),f887(x16793,x16792,x16794,x16795)) % 173.51/173.29 [1680]~E(x16801,x16802)+E(f887(x16803,x16804,x16801,x16805),f887(x16803,x16804,x16802,x16805)) % 173.51/173.29 [1681]~E(x16811,x16812)+E(f887(x16813,x16814,x16815,x16811),f887(x16813,x16814,x16815,x16812)) % 173.51/173.29 [1682]~E(x16821,x16822)+E(f139(x16821,x16823,x16824,x16825),f139(x16822,x16823,x16824,x16825)) % 173.51/173.29 [1683]~E(x16831,x16832)+E(f139(x16833,x16831,x16834,x16835),f139(x16833,x16832,x16834,x16835)) % 173.51/173.29 [1684]~E(x16841,x16842)+E(f139(x16843,x16844,x16841,x16845),f139(x16843,x16844,x16842,x16845)) % 173.51/173.29 [1685]~E(x16851,x16852)+E(f139(x16853,x16854,x16855,x16851),f139(x16853,x16854,x16855,x16852)) % 173.51/173.29 [1686]~E(x16861,x16862)+E(f479(x16861,x16863,x16864,x16865),f479(x16862,x16863,x16864,x16865)) % 173.51/173.29 [1687]~E(x16871,x16872)+E(f479(x16873,x16871,x16874,x16875),f479(x16873,x16872,x16874,x16875)) % 173.51/173.29 [1688]~E(x16881,x16882)+E(f479(x16883,x16884,x16881,x16885),f479(x16883,x16884,x16882,x16885)) % 173.51/173.29 [1689]~E(x16891,x16892)+E(f479(x16893,x16894,x16895,x16891),f479(x16893,x16894,x16895,x16892)) % 173.51/173.29 [1690]~E(x16901,x16902)+E(f761(x16901,x16903,x16904),f761(x16902,x16903,x16904)) % 173.51/173.29 [1691]~E(x16911,x16912)+E(f761(x16913,x16911,x16914),f761(x16913,x16912,x16914)) % 173.51/173.29 [1692]~E(x16921,x16922)+E(f761(x16923,x16924,x16921),f761(x16923,x16924,x16922)) % 173.51/173.29 [1693]~E(x16931,x16932)+E(f593(x16931,x16933),f593(x16932,x16933)) % 173.51/173.29 [1694]~E(x16941,x16942)+E(f593(x16943,x16941),f593(x16943,x16942)) % 173.51/173.29 [1695]~E(x16951,x16952)+E(f487(x16951,x16953,x16954,x16955,x16956),f487(x16952,x16953,x16954,x16955,x16956)) % 173.51/173.29 [1696]~E(x16961,x16962)+E(f487(x16963,x16961,x16964,x16965,x16966),f487(x16963,x16962,x16964,x16965,x16966)) % 173.51/173.29 [1697]~E(x16971,x16972)+E(f487(x16973,x16974,x16971,x16975,x16976),f487(x16973,x16974,x16972,x16975,x16976)) % 173.51/173.29 [1698]~E(x16981,x16982)+E(f487(x16983,x16984,x16985,x16981,x16986),f487(x16983,x16984,x16985,x16982,x16986)) % 173.51/173.29 [1699]~E(x16991,x16992)+E(f487(x16993,x16994,x16995,x16996,x16991),f487(x16993,x16994,x16995,x16996,x16992)) % 173.51/173.29 [1700]~E(x17001,x17002)+E(f523(x17001,x17003,x17004,x17005),f523(x17002,x17003,x17004,x17005)) % 173.51/173.29 [1701]~E(x17011,x17012)+E(f523(x17013,x17011,x17014,x17015),f523(x17013,x17012,x17014,x17015)) % 173.51/173.29 [1702]~E(x17021,x17022)+E(f523(x17023,x17024,x17021,x17025),f523(x17023,x17024,x17022,x17025)) % 173.51/173.29 [1703]~E(x17031,x17032)+E(f523(x17033,x17034,x17035,x17031),f523(x17033,x17034,x17035,x17032)) % 173.51/173.29 [1704]~E(x17041,x17042)+E(f786(x17041,x17043,x17044),f786(x17042,x17043,x17044)) % 173.51/173.29 [1705]~E(x17051,x17052)+E(f786(x17053,x17051,x17054),f786(x17053,x17052,x17054)) % 173.51/173.29 [1706]~E(x17061,x17062)+E(f786(x17063,x17064,x17061),f786(x17063,x17064,x17062)) % 173.51/173.29 [1707]~E(x17071,x17072)+E(f716(x17071,x17073,x17074,x17075),f716(x17072,x17073,x17074,x17075)) % 173.51/173.29 [1708]~E(x17081,x17082)+E(f716(x17083,x17081,x17084,x17085),f716(x17083,x17082,x17084,x17085)) % 173.51/173.29 [1709]~E(x17091,x17092)+E(f716(x17093,x17094,x17091,x17095),f716(x17093,x17094,x17092,x17095)) % 173.51/173.29 [1710]~E(x17101,x17102)+E(f716(x17103,x17104,x17105,x17101),f716(x17103,x17104,x17105,x17102)) % 173.51/173.29 [1711]~E(x17111,x17112)+E(f792(x17111,x17113,x17114,x17115,x17116),f792(x17112,x17113,x17114,x17115,x17116)) % 173.51/173.29 [1712]~E(x17121,x17122)+E(f792(x17123,x17121,x17124,x17125,x17126),f792(x17123,x17122,x17124,x17125,x17126)) % 173.51/173.29 [1713]~E(x17131,x17132)+E(f792(x17133,x17134,x17131,x17135,x17136),f792(x17133,x17134,x17132,x17135,x17136)) % 173.51/173.29 [1714]~E(x17141,x17142)+E(f792(x17143,x17144,x17145,x17141,x17146),f792(x17143,x17144,x17145,x17142,x17146)) % 173.51/173.29 [1715]~E(x17151,x17152)+E(f792(x17153,x17154,x17155,x17156,x17151),f792(x17153,x17154,x17155,x17156,x17152)) % 173.51/173.29 [1716]~E(x17161,x17162)+E(f219(x17161,x17163,x17164,x17165),f219(x17162,x17163,x17164,x17165)) % 173.51/173.29 [1717]~E(x17171,x17172)+E(f219(x17173,x17171,x17174,x17175),f219(x17173,x17172,x17174,x17175)) % 173.51/173.29 [1718]~E(x17181,x17182)+E(f219(x17183,x17184,x17181,x17185),f219(x17183,x17184,x17182,x17185)) % 173.51/173.29 [1719]~E(x17191,x17192)+E(f219(x17193,x17194,x17195,x17191),f219(x17193,x17194,x17195,x17192)) % 173.51/173.29 [1720]~E(x17201,x17202)+E(f573(x17201,x17203,x17204),f573(x17202,x17203,x17204)) % 173.51/173.29 [1721]~E(x17211,x17212)+E(f573(x17213,x17211,x17214),f573(x17213,x17212,x17214)) % 173.51/173.29 [1722]~E(x17221,x17222)+E(f573(x17223,x17224,x17221),f573(x17223,x17224,x17222)) % 173.51/173.29 [1723]~E(x17231,x17232)+E(f454(x17231,x17233,x17234,x17235),f454(x17232,x17233,x17234,x17235)) % 173.51/173.29 [1724]~E(x17241,x17242)+E(f454(x17243,x17241,x17244,x17245),f454(x17243,x17242,x17244,x17245)) % 173.51/173.29 [1725]~E(x17251,x17252)+E(f454(x17253,x17254,x17251,x17255),f454(x17253,x17254,x17252,x17255)) % 173.51/173.29 [1726]~E(x17261,x17262)+E(f454(x17263,x17264,x17265,x17261),f454(x17263,x17264,x17265,x17262)) % 173.51/173.29 [1727]~E(x17271,x17272)+E(f234(x17271,x17273,x17274),f234(x17272,x17273,x17274)) % 173.51/173.29 [1728]~E(x17281,x17282)+E(f234(x17283,x17281,x17284),f234(x17283,x17282,x17284)) % 173.51/173.29 [1729]~E(x17291,x17292)+E(f234(x17293,x17294,x17291),f234(x17293,x17294,x17292)) % 173.51/173.29 [1730]~E(x17301,x17302)+E(f682(x17301,x17303,x17304,x17305),f682(x17302,x17303,x17304,x17305)) % 173.51/173.29 [1731]~E(x17311,x17312)+E(f682(x17313,x17311,x17314,x17315),f682(x17313,x17312,x17314,x17315)) % 173.51/173.29 [1732]~E(x17321,x17322)+E(f682(x17323,x17324,x17321,x17325),f682(x17323,x17324,x17322,x17325)) % 173.51/173.29 [1733]~E(x17331,x17332)+E(f682(x17333,x17334,x17335,x17331),f682(x17333,x17334,x17335,x17332)) % 173.51/173.29 [1734]~E(x17341,x17342)+E(f565(x17341,x17343,x17344,x17345,x17346),f565(x17342,x17343,x17344,x17345,x17346)) % 173.51/173.29 [1735]~E(x17351,x17352)+E(f565(x17353,x17351,x17354,x17355,x17356),f565(x17353,x17352,x17354,x17355,x17356)) % 173.51/173.29 [1736]~E(x17361,x17362)+E(f565(x17363,x17364,x17361,x17365,x17366),f565(x17363,x17364,x17362,x17365,x17366)) % 173.51/173.29 [1737]~E(x17371,x17372)+E(f565(x17373,x17374,x17375,x17371,x17376),f565(x17373,x17374,x17375,x17372,x17376)) % 173.51/173.29 [1738]~E(x17381,x17382)+E(f565(x17383,x17384,x17385,x17386,x17381),f565(x17383,x17384,x17385,x17386,x17382)) % 173.51/173.29 [1739]~E(x17391,x17392)+E(f732(x17391,x17393,x17394,x17395),f732(x17392,x17393,x17394,x17395)) % 173.51/173.29 [1740]~E(x17401,x17402)+E(f732(x17403,x17401,x17404,x17405),f732(x17403,x17402,x17404,x17405)) % 173.51/173.29 [1741]~E(x17411,x17412)+E(f732(x17413,x17414,x17411,x17415),f732(x17413,x17414,x17412,x17415)) % 173.51/173.29 [1742]~E(x17421,x17422)+E(f732(x17423,x17424,x17425,x17421),f732(x17423,x17424,x17425,x17422)) % 173.51/173.29 [1743]~E(x17431,x17432)+E(f869(x17431,x17433),f869(x17432,x17433)) % 173.51/173.29 [1744]~E(x17441,x17442)+E(f869(x17443,x17441),f869(x17443,x17442)) % 173.51/173.29 [1745]~E(x17451,x17452)+E(f249(x17451,x17453),f249(x17452,x17453)) % 173.51/173.29 [1746]~E(x17461,x17462)+E(f249(x17463,x17461),f249(x17463,x17462)) % 173.51/173.29 [1747]~E(x17471,x17472)+E(f746(x17471,x17473,x17474,x17475,x17476),f746(x17472,x17473,x17474,x17475,x17476)) % 173.51/173.29 [1748]~E(x17481,x17482)+E(f746(x17483,x17481,x17484,x17485,x17486),f746(x17483,x17482,x17484,x17485,x17486)) % 173.51/173.29 [1749]~E(x17491,x17492)+E(f746(x17493,x17494,x17491,x17495,x17496),f746(x17493,x17494,x17492,x17495,x17496)) % 173.51/173.29 [1750]~E(x17501,x17502)+E(f746(x17503,x17504,x17505,x17501,x17506),f746(x17503,x17504,x17505,x17502,x17506)) % 173.51/173.29 [1751]~E(x17511,x17512)+E(f746(x17513,x17514,x17515,x17516,x17511),f746(x17513,x17514,x17515,x17516,x17512)) % 173.51/173.29 [1752]~E(x17521,x17522)+E(f557(x17521,x17523,x17524,x17525,x17526,x17527),f557(x17522,x17523,x17524,x17525,x17526,x17527)) % 173.51/173.29 [1753]~E(x17531,x17532)+E(f557(x17533,x17531,x17534,x17535,x17536,x17537),f557(x17533,x17532,x17534,x17535,x17536,x17537)) % 173.51/173.29 [1754]~E(x17541,x17542)+E(f557(x17543,x17544,x17541,x17545,x17546,x17547),f557(x17543,x17544,x17542,x17545,x17546,x17547)) % 173.51/173.29 [1755]~E(x17551,x17552)+E(f557(x17553,x17554,x17555,x17551,x17556,x17557),f557(x17553,x17554,x17555,x17552,x17556,x17557)) % 173.51/173.29 [1756]~E(x17561,x17562)+E(f557(x17563,x17564,x17565,x17566,x17561,x17567),f557(x17563,x17564,x17565,x17566,x17562,x17567)) % 173.51/173.29 [1757]~E(x17571,x17572)+E(f557(x17573,x17574,x17575,x17576,x17577,x17571),f557(x17573,x17574,x17575,x17576,x17577,x17572)) % 173.51/173.29 [1758]~E(x17581,x17582)+E(f627(x17581,x17583),f627(x17582,x17583)) % 173.51/173.29 [1759]~E(x17591,x17592)+E(f627(x17593,x17591),f627(x17593,x17592)) % 173.51/173.29 [1760]~E(x17601,x17602)+E(f222(x17601,x17603,x17604,x17605),f222(x17602,x17603,x17604,x17605)) % 173.51/173.29 [1761]~E(x17611,x17612)+E(f222(x17613,x17611,x17614,x17615),f222(x17613,x17612,x17614,x17615)) % 173.51/173.29 [1762]~E(x17621,x17622)+E(f222(x17623,x17624,x17621,x17625),f222(x17623,x17624,x17622,x17625)) % 173.51/173.29 [1763]~E(x17631,x17632)+E(f222(x17633,x17634,x17635,x17631),f222(x17633,x17634,x17635,x17632)) % 173.51/173.29 [1764]~E(x17641,x17642)+E(f525(x17641,x17643,x17644),f525(x17642,x17643,x17644)) % 173.51/173.29 [1765]~E(x17651,x17652)+E(f525(x17653,x17651,x17654),f525(x17653,x17652,x17654)) % 173.51/173.29 [1766]~E(x17661,x17662)+E(f525(x17663,x17664,x17661),f525(x17663,x17664,x17662)) % 173.51/173.29 [1767]~E(x17671,x17672)+E(f362(x17671),f362(x17672)) % 173.51/173.29 [1768]~E(x17681,x17682)+E(f241(x17681,x17683,x17684,x17685),f241(x17682,x17683,x17684,x17685)) % 173.51/173.29 [1769]~E(x17691,x17692)+E(f241(x17693,x17691,x17694,x17695),f241(x17693,x17692,x17694,x17695)) % 173.51/173.29 [1770]~E(x17701,x17702)+E(f241(x17703,x17704,x17701,x17705),f241(x17703,x17704,x17702,x17705)) % 173.51/173.29 [1771]~E(x17711,x17712)+E(f241(x17713,x17714,x17715,x17711),f241(x17713,x17714,x17715,x17712)) % 173.51/173.29 [1772]~E(x17721,x17722)+E(f595(x17721,x17723,x17724,x17725),f595(x17722,x17723,x17724,x17725)) % 173.51/173.29 [1773]~E(x17731,x17732)+E(f595(x17733,x17731,x17734,x17735),f595(x17733,x17732,x17734,x17735)) % 173.51/173.29 [1774]~E(x17741,x17742)+E(f595(x17743,x17744,x17741,x17745),f595(x17743,x17744,x17742,x17745)) % 173.51/173.29 [1775]~E(x17751,x17752)+E(f595(x17753,x17754,x17755,x17751),f595(x17753,x17754,x17755,x17752)) % 173.51/173.29 [1776]~E(x17761,x17762)+E(f552(x17761,x17763,x17764),f552(x17762,x17763,x17764)) % 173.51/173.29 [1777]~E(x17771,x17772)+E(f552(x17773,x17771,x17774),f552(x17773,x17772,x17774)) % 173.51/173.29 [1778]~E(x17781,x17782)+E(f552(x17783,x17784,x17781),f552(x17783,x17784,x17782)) % 173.51/173.29 [1779]~E(x17791,x17792)+E(f378(x17791,x17793,x17794),f378(x17792,x17793,x17794)) % 173.51/173.29 [1780]~E(x17801,x17802)+E(f378(x17803,x17801,x17804),f378(x17803,x17802,x17804)) % 173.51/173.29 [1781]~E(x17811,x17812)+E(f378(x17813,x17814,x17811),f378(x17813,x17814,x17812)) % 173.51/173.29 [1782]~E(x17821,x17822)+E(f404(x17821,x17823),f404(x17822,x17823)) % 173.51/173.29 [1783]~E(x17831,x17832)+E(f404(x17833,x17831),f404(x17833,x17832)) % 173.51/173.29 [1784]~E(x17841,x17842)+E(f351(x17841,x17843,x17844),f351(x17842,x17843,x17844)) % 173.51/173.29 [1785]~E(x17851,x17852)+E(f351(x17853,x17851,x17854),f351(x17853,x17852,x17854)) % 173.51/173.29 [1786]~E(x17861,x17862)+E(f351(x17863,x17864,x17861),f351(x17863,x17864,x17862)) % 173.51/173.29 [1787]~E(x17871,x17872)+E(f615(x17871,x17873,x17874,x17875,x17876,x17877),f615(x17872,x17873,x17874,x17875,x17876,x17877)) % 173.51/173.29 [1788]~E(x17881,x17882)+E(f615(x17883,x17881,x17884,x17885,x17886,x17887),f615(x17883,x17882,x17884,x17885,x17886,x17887)) % 173.51/173.29 [1789]~E(x17891,x17892)+E(f615(x17893,x17894,x17891,x17895,x17896,x17897),f615(x17893,x17894,x17892,x17895,x17896,x17897)) % 173.51/173.29 [1790]~E(x17901,x17902)+E(f615(x17903,x17904,x17905,x17901,x17906,x17907),f615(x17903,x17904,x17905,x17902,x17906,x17907)) % 173.51/173.29 [1791]~E(x17911,x17912)+E(f615(x17913,x17914,x17915,x17916,x17911,x17917),f615(x17913,x17914,x17915,x17916,x17912,x17917)) % 173.51/173.29 [1792]~E(x17921,x17922)+E(f615(x17923,x17924,x17925,x17926,x17927,x17921),f615(x17923,x17924,x17925,x17926,x17927,x17922)) % 173.51/173.29 [1793]~E(x17931,x17932)+E(f617(x17931,x17933,x17934),f617(x17932,x17933,x17934)) % 173.51/173.29 [1794]~E(x17941,x17942)+E(f617(x17943,x17941,x17944),f617(x17943,x17942,x17944)) % 173.51/173.29 [1795]~E(x17951,x17952)+E(f617(x17953,x17954,x17951),f617(x17953,x17954,x17952)) % 173.51/173.29 [1796]~E(x17961,x17962)+E(f697(x17961,x17963,x17964,x17965,x17966),f697(x17962,x17963,x17964,x17965,x17966)) % 173.51/173.29 [1797]~E(x17971,x17972)+E(f697(x17973,x17971,x17974,x17975,x17976),f697(x17973,x17972,x17974,x17975,x17976)) % 173.51/173.29 [1798]~E(x17981,x17982)+E(f697(x17983,x17984,x17981,x17985,x17986),f697(x17983,x17984,x17982,x17985,x17986)) % 173.51/173.29 [1799]~E(x17991,x17992)+E(f697(x17993,x17994,x17995,x17991,x17996),f697(x17993,x17994,x17995,x17992,x17996)) % 173.51/173.29 [1800]~E(x18001,x18002)+E(f697(x18003,x18004,x18005,x18006,x18001),f697(x18003,x18004,x18005,x18006,x18002)) % 173.51/173.29 [1801]~E(x18011,x18012)+E(f877(x18011,x18013,x18014,x18015),f877(x18012,x18013,x18014,x18015)) % 173.51/173.29 [1802]~E(x18021,x18022)+E(f877(x18023,x18021,x18024,x18025),f877(x18023,x18022,x18024,x18025)) % 173.51/173.29 [1803]~E(x18031,x18032)+E(f877(x18033,x18034,x18031,x18035),f877(x18033,x18034,x18032,x18035)) % 173.51/173.29 [1804]~E(x18041,x18042)+E(f877(x18043,x18044,x18045,x18041),f877(x18043,x18044,x18045,x18042)) % 173.51/173.29 [1805]~E(x18051,x18052)+E(f354(x18051,x18053,x18054),f354(x18052,x18053,x18054)) % 173.51/173.29 [1806]~E(x18061,x18062)+E(f354(x18063,x18061,x18064),f354(x18063,x18062,x18064)) % 173.51/173.29 [1807]~E(x18071,x18072)+E(f354(x18073,x18074,x18071),f354(x18073,x18074,x18072)) % 173.51/173.29 [1808]~E(x18081,x18082)+E(f586(x18081,x18083,x18084),f586(x18082,x18083,x18084)) % 173.51/173.29 [1809]~E(x18091,x18092)+E(f586(x18093,x18091,x18094),f586(x18093,x18092,x18094)) % 173.51/173.29 [1810]~E(x18101,x18102)+E(f586(x18103,x18104,x18101),f586(x18103,x18104,x18102)) % 173.51/173.29 [1811]~E(x18111,x18112)+E(f420(x18111,x18113),f420(x18112,x18113)) % 173.51/173.29 [1812]~E(x18121,x18122)+E(f420(x18123,x18121),f420(x18123,x18122)) % 173.51/173.29 [1813]~E(x18131,x18132)+E(f880(x18131,x18133),f880(x18132,x18133)) % 173.51/173.29 [1814]~E(x18141,x18142)+E(f880(x18143,x18141),f880(x18143,x18142)) % 173.51/173.29 [1815]~E(x18151,x18152)+E(f375(x18151,x18153,x18154,x18155,x18156),f375(x18152,x18153,x18154,x18155,x18156)) % 173.51/173.29 [1816]~E(x18161,x18162)+E(f375(x18163,x18161,x18164,x18165,x18166),f375(x18163,x18162,x18164,x18165,x18166)) % 173.51/173.29 [1817]~E(x18171,x18172)+E(f375(x18173,x18174,x18171,x18175,x18176),f375(x18173,x18174,x18172,x18175,x18176)) % 173.51/173.29 [1818]~E(x18181,x18182)+E(f375(x18183,x18184,x18185,x18181,x18186),f375(x18183,x18184,x18185,x18182,x18186)) % 173.51/173.29 [1819]~E(x18191,x18192)+E(f375(x18193,x18194,x18195,x18196,x18191),f375(x18193,x18194,x18195,x18196,x18192)) % 173.51/173.29 [1820]~E(x18201,x18202)+E(f769(x18201,x18203,x18204),f769(x18202,x18203,x18204)) % 173.51/173.29 [1821]~E(x18211,x18212)+E(f769(x18213,x18211,x18214),f769(x18213,x18212,x18214)) % 173.51/173.29 [1822]~E(x18221,x18222)+E(f769(x18223,x18224,x18221),f769(x18223,x18224,x18222)) % 173.51/173.29 [1823]~E(x18231,x18232)+E(f596(x18231,x18233),f596(x18232,x18233)) % 173.51/173.29 [1824]~E(x18241,x18242)+E(f596(x18243,x18241),f596(x18243,x18242)) % 173.51/173.29 [1825]~E(x18251,x18252)+E(f543(x18251,x18253,x18254,x18255,x18256,x18257,x18258),f543(x18252,x18253,x18254,x18255,x18256,x18257,x18258)) % 173.51/173.29 [1826]~E(x18261,x18262)+E(f543(x18263,x18261,x18264,x18265,x18266,x18267,x18268),f543(x18263,x18262,x18264,x18265,x18266,x18267,x18268)) % 173.51/173.29 [1827]~E(x18271,x18272)+E(f543(x18273,x18274,x18271,x18275,x18276,x18277,x18278),f543(x18273,x18274,x18272,x18275,x18276,x18277,x18278)) % 173.51/173.29 [1828]~E(x18281,x18282)+E(f543(x18283,x18284,x18285,x18281,x18286,x18287,x18288),f543(x18283,x18284,x18285,x18282,x18286,x18287,x18288)) % 173.51/173.29 [1829]~E(x18291,x18292)+E(f543(x18293,x18294,x18295,x18296,x18291,x18297,x18298),f543(x18293,x18294,x18295,x18296,x18292,x18297,x18298)) % 173.51/173.29 [1830]~E(x18301,x18302)+E(f543(x18303,x18304,x18305,x18306,x18307,x18301,x18308),f543(x18303,x18304,x18305,x18306,x18307,x18302,x18308)) % 173.51/173.29 [1831]~E(x18311,x18312)+E(f543(x18313,x18314,x18315,x18316,x18317,x18318,x18311),f543(x18313,x18314,x18315,x18316,x18317,x18318,x18312)) % 173.51/173.29 [1832]~E(x18321,x18322)+E(f342(x18321,x18323,x18324,x18325,x18326),f342(x18322,x18323,x18324,x18325,x18326)) % 173.51/173.29 [1833]~E(x18331,x18332)+E(f342(x18333,x18331,x18334,x18335,x18336),f342(x18333,x18332,x18334,x18335,x18336)) % 173.51/173.29 [1834]~E(x18341,x18342)+E(f342(x18343,x18344,x18341,x18345,x18346),f342(x18343,x18344,x18342,x18345,x18346)) % 173.51/173.29 [1835]~E(x18351,x18352)+E(f342(x18353,x18354,x18355,x18351,x18356),f342(x18353,x18354,x18355,x18352,x18356)) % 173.51/173.29 [1836]~E(x18361,x18362)+E(f342(x18363,x18364,x18365,x18366,x18361),f342(x18363,x18364,x18365,x18366,x18362)) % 173.51/173.29 [1837]~E(x18371,x18372)+E(f551(x18371,x18373,x18374),f551(x18372,x18373,x18374)) % 173.51/173.29 [1838]~E(x18381,x18382)+E(f551(x18383,x18381,x18384),f551(x18383,x18382,x18384)) % 173.51/173.29 [1839]~E(x18391,x18392)+E(f551(x18393,x18394,x18391),f551(x18393,x18394,x18392)) % 173.51/173.29 [1840]~E(x18401,x18402)+E(f584(x18401,x18403,x18404,x18405,x18406,x18407,x18408,x18409),f584(x18402,x18403,x18404,x18405,x18406,x18407,x18408,x18409)) % 173.51/173.29 [1841]~E(x18411,x18412)+E(f584(x18413,x18411,x18414,x18415,x18416,x18417,x18418,x18419),f584(x18413,x18412,x18414,x18415,x18416,x18417,x18418,x18419)) % 173.51/173.29 [1842]~E(x18421,x18422)+E(f584(x18423,x18424,x18421,x18425,x18426,x18427,x18428,x18429),f584(x18423,x18424,x18422,x18425,x18426,x18427,x18428,x18429)) % 173.51/173.29 [1843]~E(x18431,x18432)+E(f584(x18433,x18434,x18435,x18431,x18436,x18437,x18438,x18439),f584(x18433,x18434,x18435,x18432,x18436,x18437,x18438,x18439)) % 173.51/173.29 [1844]~E(x18441,x18442)+E(f584(x18443,x18444,x18445,x18446,x18441,x18447,x18448,x18449),f584(x18443,x18444,x18445,x18446,x18442,x18447,x18448,x18449)) % 173.51/173.29 [1845]~E(x18451,x18452)+E(f584(x18453,x18454,x18455,x18456,x18457,x18451,x18458,x18459),f584(x18453,x18454,x18455,x18456,x18457,x18452,x18458,x18459)) % 173.51/173.29 [1846]~E(x18461,x18462)+E(f584(x18463,x18464,x18465,x18466,x18467,x18468,x18461,x18469),f584(x18463,x18464,x18465,x18466,x18467,x18468,x18462,x18469)) % 173.51/173.29 [1847]~E(x18471,x18472)+E(f584(x18473,x18474,x18475,x18476,x18477,x18478,x18479,x18471),f584(x18473,x18474,x18475,x18476,x18477,x18478,x18479,x18472)) % 173.51/173.29 [1848]~E(x18481,x18482)+E(f766(x18481,x18483,x18484,x18485,x18486),f766(x18482,x18483,x18484,x18485,x18486)) % 173.51/173.29 [1849]~E(x18491,x18492)+E(f766(x18493,x18491,x18494,x18495,x18496),f766(x18493,x18492,x18494,x18495,x18496)) % 173.51/173.29 [1850]~E(x18501,x18502)+E(f766(x18503,x18504,x18501,x18505,x18506),f766(x18503,x18504,x18502,x18505,x18506)) % 173.51/173.29 [1851]~E(x18511,x18512)+E(f766(x18513,x18514,x18515,x18511,x18516),f766(x18513,x18514,x18515,x18512,x18516)) % 173.51/173.29 [1852]~E(x18521,x18522)+E(f766(x18523,x18524,x18525,x18526,x18521),f766(x18523,x18524,x18525,x18526,x18522)) % 173.51/173.29 [1853]~E(x18531,x18532)+E(f866(x18531,x18533,x18534,x18535,x18536),f866(x18532,x18533,x18534,x18535,x18536)) % 173.51/173.29 [1854]~E(x18541,x18542)+E(f866(x18543,x18541,x18544,x18545,x18546),f866(x18543,x18542,x18544,x18545,x18546)) % 173.51/173.29 [1855]~E(x18551,x18552)+E(f866(x18553,x18554,x18551,x18555,x18556),f866(x18553,x18554,x18552,x18555,x18556)) % 173.51/173.29 [1856]~E(x18561,x18562)+E(f866(x18563,x18564,x18565,x18561,x18566),f866(x18563,x18564,x18565,x18562,x18566)) % 173.51/173.29 [1857]~E(x18571,x18572)+E(f866(x18573,x18574,x18575,x18576,x18571),f866(x18573,x18574,x18575,x18576,x18572)) % 173.51/173.29 [1858]~E(x18581,x18582)+E(f592(x18581,x18583,x18584),f592(x18582,x18583,x18584)) % 173.51/173.29 [1859]~E(x18591,x18592)+E(f592(x18593,x18591,x18594),f592(x18593,x18592,x18594)) % 173.51/173.29 [1860]~E(x18601,x18602)+E(f592(x18603,x18604,x18601),f592(x18603,x18604,x18602)) % 173.51/173.29 [1861]~E(x18611,x18612)+E(f775(x18611,x18613,x18614,x18615),f775(x18612,x18613,x18614,x18615)) % 173.51/173.29 [1862]~E(x18621,x18622)+E(f775(x18623,x18621,x18624,x18625),f775(x18623,x18622,x18624,x18625)) % 173.51/173.29 [1863]~E(x18631,x18632)+E(f775(x18633,x18634,x18631,x18635),f775(x18633,x18634,x18632,x18635)) % 173.51/173.29 [1864]~E(x18641,x18642)+E(f775(x18643,x18644,x18645,x18641),f775(x18643,x18644,x18645,x18642)) % 173.51/173.29 [1865]~E(x18651,x18652)+E(f588(x18651,x18653,x18654,x18655,x18656),f588(x18652,x18653,x18654,x18655,x18656)) % 173.51/173.29 [1866]~E(x18661,x18662)+E(f588(x18663,x18661,x18664,x18665,x18666),f588(x18663,x18662,x18664,x18665,x18666)) % 173.51/173.29 [1867]~E(x18671,x18672)+E(f588(x18673,x18674,x18671,x18675,x18676),f588(x18673,x18674,x18672,x18675,x18676)) % 173.51/173.29 [1868]~E(x18681,x18682)+E(f588(x18683,x18684,x18685,x18681,x18686),f588(x18683,x18684,x18685,x18682,x18686)) % 173.51/173.29 [1869]~E(x18691,x18692)+E(f588(x18693,x18694,x18695,x18696,x18691),f588(x18693,x18694,x18695,x18696,x18692)) % 173.51/173.29 [1870]~E(x18701,x18702)+E(f787(x18701,x18703,x18704,x18705),f787(x18702,x18703,x18704,x18705)) % 173.51/173.29 [1871]~E(x18711,x18712)+E(f787(x18713,x18711,x18714,x18715),f787(x18713,x18712,x18714,x18715)) % 173.51/173.29 [1872]~E(x18721,x18722)+E(f787(x18723,x18724,x18721,x18725),f787(x18723,x18724,x18722,x18725)) % 173.51/173.29 [1873]~E(x18731,x18732)+E(f787(x18733,x18734,x18735,x18731),f787(x18733,x18734,x18735,x18732)) % 173.51/173.29 [1874]~E(x18741,x18742)+E(f580(x18741,x18743,x18744,x18745,x18746),f580(x18742,x18743,x18744,x18745,x18746)) % 173.51/173.29 [1875]~E(x18751,x18752)+E(f580(x18753,x18751,x18754,x18755,x18756),f580(x18753,x18752,x18754,x18755,x18756)) % 173.51/173.29 [1876]~E(x18761,x18762)+E(f580(x18763,x18764,x18761,x18765,x18766),f580(x18763,x18764,x18762,x18765,x18766)) % 173.51/173.29 [1877]~E(x18771,x18772)+E(f580(x18773,x18774,x18775,x18771,x18776),f580(x18773,x18774,x18775,x18772,x18776)) % 173.51/173.29 [1878]~E(x18781,x18782)+E(f580(x18783,x18784,x18785,x18786,x18781),f580(x18783,x18784,x18785,x18786,x18782)) % 173.51/173.29 [1879]~E(x18791,x18792)+E(f381(x18791,x18793),f381(x18792,x18793)) % 173.51/173.29 [1880]~E(x18801,x18802)+E(f381(x18803,x18801),f381(x18803,x18802)) % 173.51/173.29 [1881]~E(x18811,x18812)+E(f587(x18811,x18813,x18814,x18815),f587(x18812,x18813,x18814,x18815)) % 173.51/173.29 [1882]~E(x18821,x18822)+E(f587(x18823,x18821,x18824,x18825),f587(x18823,x18822,x18824,x18825)) % 173.51/173.29 [1883]~E(x18831,x18832)+E(f587(x18833,x18834,x18831,x18835),f587(x18833,x18834,x18832,x18835)) % 173.51/173.29 [1884]~E(x18841,x18842)+E(f587(x18843,x18844,x18845,x18841),f587(x18843,x18844,x18845,x18842)) % 173.51/173.29 [1885]~E(x18851,x18852)+E(f358(x18851,x18853,x18854,x18855,x18856),f358(x18852,x18853,x18854,x18855,x18856)) % 173.51/173.29 [1886]~E(x18861,x18862)+E(f358(x18863,x18861,x18864,x18865,x18866),f358(x18863,x18862,x18864,x18865,x18866)) % 173.51/173.29 [1887]~E(x18871,x18872)+E(f358(x18873,x18874,x18871,x18875,x18876),f358(x18873,x18874,x18872,x18875,x18876)) % 173.51/173.29 [1888]~E(x18881,x18882)+E(f358(x18883,x18884,x18885,x18881,x18886),f358(x18883,x18884,x18885,x18882,x18886)) % 173.51/173.29 [1889]~E(x18891,x18892)+E(f358(x18893,x18894,x18895,x18896,x18891),f358(x18893,x18894,x18895,x18896,x18892)) % 173.51/173.29 [1890]~E(x18901,x18902)+E(f788(x18901,x18903,x18904,x18905),f788(x18902,x18903,x18904,x18905)) % 173.51/173.29 [1891]~E(x18911,x18912)+E(f788(x18913,x18911,x18914,x18915),f788(x18913,x18912,x18914,x18915)) % 173.51/173.29 [1892]~E(x18921,x18922)+E(f788(x18923,x18924,x18921,x18925),f788(x18923,x18924,x18922,x18925)) % 173.51/173.29 [1893]~E(x18931,x18932)+E(f788(x18933,x18934,x18935,x18931),f788(x18933,x18934,x18935,x18932)) % 173.51/173.29 [1894]~E(x18941,x18942)+E(f344(x18941,x18943),f344(x18942,x18943)) % 173.51/173.29 [1895]~E(x18951,x18952)+E(f344(x18953,x18951),f344(x18953,x18952)) % 173.51/173.29 [1896]~E(x18961,x18962)+E(f742(x18961,x18963,x18964,x18965,x18966),f742(x18962,x18963,x18964,x18965,x18966)) % 173.51/173.29 [1897]~E(x18971,x18972)+E(f742(x18973,x18971,x18974,x18975,x18976),f742(x18973,x18972,x18974,x18975,x18976)) % 173.51/173.29 [1898]~E(x18981,x18982)+E(f742(x18983,x18984,x18981,x18985,x18986),f742(x18983,x18984,x18982,x18985,x18986)) % 173.51/173.29 [1899]~E(x18991,x18992)+E(f742(x18993,x18994,x18995,x18991,x18996),f742(x18993,x18994,x18995,x18992,x18996)) % 173.51/173.29 [1900]~E(x19001,x19002)+E(f742(x19003,x19004,x19005,x19006,x19001),f742(x19003,x19004,x19005,x19006,x19002)) % 173.51/173.29 [1901]~E(x19011,x19012)+E(f383(x19011),f383(x19012)) % 173.51/173.29 [1902]~E(x19021,x19022)+E(f236(x19021,x19023,x19024,x19025,x19026),f236(x19022,x19023,x19024,x19025,x19026)) % 173.51/173.29 [1903]~E(x19031,x19032)+E(f236(x19033,x19031,x19034,x19035,x19036),f236(x19033,x19032,x19034,x19035,x19036)) % 173.51/173.29 [1904]~E(x19041,x19042)+E(f236(x19043,x19044,x19041,x19045,x19046),f236(x19043,x19044,x19042,x19045,x19046)) % 173.51/173.29 [1905]~E(x19051,x19052)+E(f236(x19053,x19054,x19055,x19051,x19056),f236(x19053,x19054,x19055,x19052,x19056)) % 173.51/173.29 [1906]~E(x19061,x19062)+E(f236(x19063,x19064,x19065,x19066,x19061),f236(x19063,x19064,x19065,x19066,x19062)) % 173.51/173.29 [1907]~E(x19071,x19072)+E(f559(x19071),f559(x19072)) % 173.51/173.29 [1908]~E(x19081,x19082)+E(f624(x19081,x19083,x19084,x19085,x19086),f624(x19082,x19083,x19084,x19085,x19086)) % 173.51/173.29 [1909]~E(x19091,x19092)+E(f624(x19093,x19091,x19094,x19095,x19096),f624(x19093,x19092,x19094,x19095,x19096)) % 173.51/173.29 [1910]~E(x19101,x19102)+E(f624(x19103,x19104,x19101,x19105,x19106),f624(x19103,x19104,x19102,x19105,x19106)) % 173.51/173.29 [1911]~E(x19111,x19112)+E(f624(x19113,x19114,x19115,x19111,x19116),f624(x19113,x19114,x19115,x19112,x19116)) % 173.51/173.29 [1912]~E(x19121,x19122)+E(f624(x19123,x19124,x19125,x19126,x19121),f624(x19123,x19124,x19125,x19126,x19122)) % 173.51/173.29 [1913]~E(x19131,x19132)+E(f338(x19131),f338(x19132)) % 173.51/173.29 [1914]~E(x19141,x19142)+E(f814(x19141,x19143,x19144,x19145),f814(x19142,x19143,x19144,x19145)) % 173.51/173.29 [1915]~E(x19151,x19152)+E(f814(x19153,x19151,x19154,x19155),f814(x19153,x19152,x19154,x19155)) % 173.51/173.29 [1916]~E(x19161,x19162)+E(f814(x19163,x19164,x19161,x19165),f814(x19163,x19164,x19162,x19165)) % 173.51/173.29 [1917]~E(x19171,x19172)+E(f814(x19173,x19174,x19175,x19171),f814(x19173,x19174,x19175,x19172)) % 173.51/173.29 [1918]~E(x19181,x19182)+E(f555(x19181),f555(x19182)) % 173.51/173.29 [1919]~E(x19191,x19192)+E(f622(x19191,x19193),f622(x19192,x19193)) % 173.51/173.29 [1920]~E(x19201,x19202)+E(f622(x19203,x19201),f622(x19203,x19202)) % 173.51/173.29 [1921]~E(x19211,x19212)+E(f433(x19211,x19213),f433(x19212,x19213)) % 173.51/173.29 [1922]~E(x19221,x19222)+E(f433(x19223,x19221),f433(x19223,x19222)) % 173.51/173.29 [1923]~E(x19231,x19232)+E(f577(x19231,x19233,x19234,x19235,x19236),f577(x19232,x19233,x19234,x19235,x19236)) % 173.51/173.29 [1924]~E(x19241,x19242)+E(f577(x19243,x19241,x19244,x19245,x19246),f577(x19243,x19242,x19244,x19245,x19246)) % 173.51/173.29 [1925]~E(x19251,x19252)+E(f577(x19253,x19254,x19251,x19255,x19256),f577(x19253,x19254,x19252,x19255,x19256)) % 173.51/173.29 [1926]~E(x19261,x19262)+E(f577(x19263,x19264,x19265,x19261,x19266),f577(x19263,x19264,x19265,x19262,x19266)) % 173.51/173.29 [1927]~E(x19271,x19272)+E(f577(x19273,x19274,x19275,x19276,x19271),f577(x19273,x19274,x19275,x19276,x19272)) % 173.51/173.29 [1928]~E(x19281,x19282)+E(f398(x19281,x19283,x19284,x19285),f398(x19282,x19283,x19284,x19285)) % 173.51/173.29 [1929]~E(x19291,x19292)+E(f398(x19293,x19291,x19294,x19295),f398(x19293,x19292,x19294,x19295)) % 173.51/173.29 [1930]~E(x19301,x19302)+E(f398(x19303,x19304,x19301,x19305),f398(x19303,x19304,x19302,x19305)) % 173.51/173.29 [1931]~E(x19311,x19312)+E(f398(x19313,x19314,x19315,x19311),f398(x19313,x19314,x19315,x19312)) % 173.51/173.29 [1932]~E(x19321,x19322)+E(f603(x19321,x19323),f603(x19322,x19323)) % 173.51/173.29 [1933]~E(x19331,x19332)+E(f603(x19333,x19331),f603(x19333,x19332)) % 173.51/173.29 [1934]~E(x19341,x19342)+E(f731(x19341,x19343,x19344,x19345),f731(x19342,x19343,x19344,x19345)) % 173.51/173.29 [1935]~E(x19351,x19352)+E(f731(x19353,x19351,x19354,x19355),f731(x19353,x19352,x19354,x19355)) % 173.51/173.29 [1936]~E(x19361,x19362)+E(f731(x19363,x19364,x19361,x19365),f731(x19363,x19364,x19362,x19365)) % 173.51/173.29 [1937]~E(x19371,x19372)+E(f731(x19373,x19374,x19375,x19371),f731(x19373,x19374,x19375,x19372)) % 173.51/173.29 [1938]~E(x19381,x19382)+E(f214(x19381,x19383),f214(x19382,x19383)) % 173.51/173.29 [1939]~E(x19391,x19392)+E(f214(x19393,x19391),f214(x19393,x19392)) % 173.51/173.29 [1940]~E(x19401,x19402)+E(f872(x19401,x19403,x19404),f872(x19402,x19403,x19404)) % 173.51/173.29 [1941]~E(x19411,x19412)+E(f872(x19413,x19411,x19414),f872(x19413,x19412,x19414)) % 173.51/173.29 [1942]~E(x19421,x19422)+E(f872(x19423,x19424,x19421),f872(x19423,x19424,x19422)) % 173.51/173.29 [1943]~E(x19431,x19432)+E(f537(x19431,x19433,x19434),f537(x19432,x19433,x19434)) % 173.51/173.29 [1944]~E(x19441,x19442)+E(f537(x19443,x19441,x19444),f537(x19443,x19442,x19444)) % 173.51/173.29 [1945]~E(x19451,x19452)+E(f537(x19453,x19454,x19451),f537(x19453,x19454,x19452)) % 173.51/173.29 [1946]~E(x19461,x19462)+E(f502(x19461,x19463,x19464),f502(x19462,x19463,x19464)) % 173.51/173.29 [1947]~E(x19471,x19472)+E(f502(x19473,x19471,x19474),f502(x19473,x19472,x19474)) % 173.51/173.29 [1948]~E(x19481,x19482)+E(f502(x19483,x19484,x19481),f502(x19483,x19484,x19482)) % 173.51/173.29 [1949]~E(x19491,x19492)+E(f656(x19491,x19493,x19494,x19495,x19496),f656(x19492,x19493,x19494,x19495,x19496)) % 173.51/173.29 [1950]~E(x19501,x19502)+E(f656(x19503,x19501,x19504,x19505,x19506),f656(x19503,x19502,x19504,x19505,x19506)) % 173.51/173.29 [1951]~E(x19511,x19512)+E(f656(x19513,x19514,x19511,x19515,x19516),f656(x19513,x19514,x19512,x19515,x19516)) % 173.51/173.29 [1952]~E(x19521,x19522)+E(f656(x19523,x19524,x19525,x19521,x19526),f656(x19523,x19524,x19525,x19522,x19526)) % 173.51/173.29 [1953]~E(x19531,x19532)+E(f656(x19533,x19534,x19535,x19536,x19531),f656(x19533,x19534,x19535,x19536,x19532)) % 173.51/173.29 [1954]~E(x19541,x19542)+E(f374(x19541,x19543,x19544,x19545,x19546),f374(x19542,x19543,x19544,x19545,x19546)) % 173.51/173.29 [1955]~E(x19551,x19552)+E(f374(x19553,x19551,x19554,x19555,x19556),f374(x19553,x19552,x19554,x19555,x19556)) % 173.51/173.29 [1956]~E(x19561,x19562)+E(f374(x19563,x19564,x19561,x19565,x19566),f374(x19563,x19564,x19562,x19565,x19566)) % 173.51/173.29 [1957]~E(x19571,x19572)+E(f374(x19573,x19574,x19575,x19571,x19576),f374(x19573,x19574,x19575,x19572,x19576)) % 173.51/173.29 [1958]~E(x19581,x19582)+E(f374(x19583,x19584,x19585,x19586,x19581),f374(x19583,x19584,x19585,x19586,x19582)) % 173.51/173.29 [1959]~E(x19591,x19592)+E(f539(x19591,x19593,x19594),f539(x19592,x19593,x19594)) % 173.51/173.29 [1960]~E(x19601,x19602)+E(f539(x19603,x19601,x19604),f539(x19603,x19602,x19604)) % 173.51/173.29 [1961]~E(x19611,x19612)+E(f539(x19613,x19614,x19611),f539(x19613,x19614,x19612)) % 173.51/173.29 [1962]~E(x19621,x19622)+E(f738(x19621,x19623,x19624),f738(x19622,x19623,x19624)) % 173.51/173.29 [1963]~E(x19631,x19632)+E(f738(x19633,x19631,x19634),f738(x19633,x19632,x19634)) % 173.51/173.29 [1964]~E(x19641,x19642)+E(f738(x19643,x19644,x19641),f738(x19643,x19644,x19642)) % 173.51/173.29 [1965]~E(x19651,x19652)+E(f619(x19651,x19653,x19654),f619(x19652,x19653,x19654)) % 173.51/173.29 [1966]~E(x19661,x19662)+E(f619(x19663,x19661,x19664),f619(x19663,x19662,x19664)) % 173.51/173.29 [1967]~E(x19671,x19672)+E(f619(x19673,x19674,x19671),f619(x19673,x19674,x19672)) % 173.51/173.29 [1968]~E(x19681,x19682)+E(f384(x19681,x19683,x19684,x19685),f384(x19682,x19683,x19684,x19685)) % 173.51/173.29 [1969]~E(x19691,x19692)+E(f384(x19693,x19691,x19694,x19695),f384(x19693,x19692,x19694,x19695)) % 173.51/173.29 [1970]~E(x19701,x19702)+E(f384(x19703,x19704,x19701,x19705),f384(x19703,x19704,x19702,x19705)) % 173.51/173.29 [1971]~E(x19711,x19712)+E(f384(x19713,x19714,x19715,x19711),f384(x19713,x19714,x19715,x19712)) % 173.51/173.29 [1972]~E(x19721,x19722)+E(f215(x19721,x19723,x19724),f215(x19722,x19723,x19724)) % 173.51/173.29 [1973]~E(x19731,x19732)+E(f215(x19733,x19731,x19734),f215(x19733,x19732,x19734)) % 173.51/173.29 [1974]~E(x19741,x19742)+E(f215(x19743,x19744,x19741),f215(x19743,x19744,x19742)) % 173.51/173.29 [1975]~E(x19751,x19752)+E(f528(x19751,x19753,x19754),f528(x19752,x19753,x19754)) % 173.51/173.29 [1976]~E(x19761,x19762)+E(f528(x19763,x19761,x19764),f528(x19763,x19762,x19764)) % 173.51/173.29 [1977]~E(x19771,x19772)+E(f528(x19773,x19774,x19771),f528(x19773,x19774,x19772)) % 173.51/173.29 [1978]~E(x19781,x19782)+E(f683(x19781,x19783,x19784),f683(x19782,x19783,x19784)) % 173.51/173.29 [1979]~E(x19791,x19792)+E(f683(x19793,x19791,x19794),f683(x19793,x19792,x19794)) % 173.51/173.29 [1980]~E(x19801,x19802)+E(f683(x19803,x19804,x19801),f683(x19803,x19804,x19802)) % 173.51/173.29 [1981]~E(x19811,x19812)+E(f734(x19811,x19813,x19814),f734(x19812,x19813,x19814)) % 173.51/173.29 [1982]~E(x19821,x19822)+E(f734(x19823,x19821,x19824),f734(x19823,x19822,x19824)) % 173.51/173.29 [1983]~E(x19831,x19832)+E(f734(x19833,x19834,x19831),f734(x19833,x19834,x19832)) % 173.51/173.29 [1984]~E(x19841,x19842)+E(f368(x19841,x19843,x19844,x19845,x19846),f368(x19842,x19843,x19844,x19845,x19846)) % 173.51/173.29 [1985]~E(x19851,x19852)+E(f368(x19853,x19851,x19854,x19855,x19856),f368(x19853,x19852,x19854,x19855,x19856)) % 173.51/173.29 [1986]~E(x19861,x19862)+E(f368(x19863,x19864,x19861,x19865,x19866),f368(x19863,x19864,x19862,x19865,x19866)) % 173.51/173.29 [1987]~E(x19871,x19872)+E(f368(x19873,x19874,x19875,x19871,x19876),f368(x19873,x19874,x19875,x19872,x19876)) % 173.51/173.29 [1988]~E(x19881,x19882)+E(f368(x19883,x19884,x19885,x19886,x19881),f368(x19883,x19884,x19885,x19886,x19882)) % 173.51/173.29 [1989]~E(x19891,x19892)+E(f477(x19891,x19893,x19894,x19895),f477(x19892,x19893,x19894,x19895)) % 173.51/173.29 [1990]~E(x19901,x19902)+E(f477(x19903,x19901,x19904,x19905),f477(x19903,x19902,x19904,x19905)) % 173.51/173.29 [1991]~E(x19911,x19912)+E(f477(x19913,x19914,x19911,x19915),f477(x19913,x19914,x19912,x19915)) % 173.51/173.29 [1992]~E(x19921,x19922)+E(f477(x19923,x19924,x19925,x19921),f477(x19923,x19924,x19925,x19922)) % 173.51/173.29 [1993]~E(x19931,x19932)+E(f482(x19931,x19933,x19934,x19935,x19936),f482(x19932,x19933,x19934,x19935,x19936)) % 173.51/173.29 [1994]~E(x19941,x19942)+E(f482(x19943,x19941,x19944,x19945,x19946),f482(x19943,x19942,x19944,x19945,x19946)) % 173.51/173.29 [1995]~E(x19951,x19952)+E(f482(x19953,x19954,x19951,x19955,x19956),f482(x19953,x19954,x19952,x19955,x19956)) % 173.51/173.29 [1996]~E(x19961,x19962)+E(f482(x19963,x19964,x19965,x19961,x19966),f482(x19963,x19964,x19965,x19962,x19966)) % 173.51/173.29 [1997]~E(x19971,x19972)+E(f482(x19973,x19974,x19975,x19976,x19971),f482(x19973,x19974,x19975,x19976,x19972)) % 173.51/173.29 [1998]~E(x19981,x19982)+E(f417(x19981,x19983,x19984,x19985),f417(x19982,x19983,x19984,x19985)) % 173.51/173.29 [1999]~E(x19991,x19992)+E(f417(x19993,x19991,x19994,x19995),f417(x19993,x19992,x19994,x19995)) % 173.51/173.29 [2000]~E(x20001,x20002)+E(f417(x20003,x20004,x20001,x20005),f417(x20003,x20004,x20002,x20005)) % 173.51/173.29 [2001]~E(x20011,x20012)+E(f417(x20013,x20014,x20015,x20011),f417(x20013,x20014,x20015,x20012)) % 173.51/173.29 [2002]~E(x20021,x20022)+E(f276(x20021),f276(x20022)) % 173.51/173.29 [2003]~E(x20031,x20032)+E(f390(x20031,x20033,x20034),f390(x20032,x20033,x20034)) % 173.51/173.29 [2004]~E(x20041,x20042)+E(f390(x20043,x20041,x20044),f390(x20043,x20042,x20044)) % 173.51/173.29 [2005]~E(x20051,x20052)+E(f390(x20053,x20054,x20051),f390(x20053,x20054,x20052)) % 173.51/173.29 [2006]~E(x20061,x20062)+E(f647(x20061,x20063),f647(x20062,x20063)) % 173.51/173.29 [2007]~E(x20071,x20072)+E(f647(x20073,x20071),f647(x20073,x20072)) % 173.51/173.29 [2008]~E(x20081,x20082)+E(f223(x20081,x20083,x20084,x20085,x20086,x20087,x20088),f223(x20082,x20083,x20084,x20085,x20086,x20087,x20088)) % 173.51/173.29 [2009]~E(x20091,x20092)+E(f223(x20093,x20091,x20094,x20095,x20096,x20097,x20098),f223(x20093,x20092,x20094,x20095,x20096,x20097,x20098)) % 173.51/173.29 [2010]~E(x20101,x20102)+E(f223(x20103,x20104,x20101,x20105,x20106,x20107,x20108),f223(x20103,x20104,x20102,x20105,x20106,x20107,x20108)) % 173.51/173.29 [2011]~E(x20111,x20112)+E(f223(x20113,x20114,x20115,x20111,x20116,x20117,x20118),f223(x20113,x20114,x20115,x20112,x20116,x20117,x20118)) % 173.51/173.29 [2012]~E(x20121,x20122)+E(f223(x20123,x20124,x20125,x20126,x20121,x20127,x20128),f223(x20123,x20124,x20125,x20126,x20122,x20127,x20128)) % 173.51/173.29 [2013]~E(x20131,x20132)+E(f223(x20133,x20134,x20135,x20136,x20137,x20131,x20138),f223(x20133,x20134,x20135,x20136,x20137,x20132,x20138)) % 173.51/173.29 [2014]~E(x20141,x20142)+E(f223(x20143,x20144,x20145,x20146,x20147,x20148,x20141),f223(x20143,x20144,x20145,x20146,x20147,x20148,x20142)) % 173.51/173.29 [2015]~E(x20151,x20152)+E(f302(x20151,x20153,x20154,x20155),f302(x20152,x20153,x20154,x20155)) % 173.51/173.29 [2016]~E(x20161,x20162)+E(f302(x20163,x20161,x20164,x20165),f302(x20163,x20162,x20164,x20165)) % 173.51/173.29 [2017]~E(x20171,x20172)+E(f302(x20173,x20174,x20171,x20175),f302(x20173,x20174,x20172,x20175)) % 173.51/173.29 [2018]~E(x20181,x20182)+E(f302(x20183,x20184,x20185,x20181),f302(x20183,x20184,x20185,x20182)) % 173.51/173.29 [2019]~E(x20191,x20192)+E(f875(x20191,x20193,x20194,x20195,x20196,x20197,x20198),f875(x20192,x20193,x20194,x20195,x20196,x20197,x20198)) % 173.51/173.29 [2020]~E(x20201,x20202)+E(f875(x20203,x20201,x20204,x20205,x20206,x20207,x20208),f875(x20203,x20202,x20204,x20205,x20206,x20207,x20208)) % 173.51/173.29 [2021]~E(x20211,x20212)+E(f875(x20213,x20214,x20211,x20215,x20216,x20217,x20218),f875(x20213,x20214,x20212,x20215,x20216,x20217,x20218)) % 173.51/173.29 [2022]~E(x20221,x20222)+E(f875(x20223,x20224,x20225,x20221,x20226,x20227,x20228),f875(x20223,x20224,x20225,x20222,x20226,x20227,x20228)) % 173.51/173.29 [2023]~E(x20231,x20232)+E(f875(x20233,x20234,x20235,x20236,x20231,x20237,x20238),f875(x20233,x20234,x20235,x20236,x20232,x20237,x20238)) % 173.51/173.29 [2024]~E(x20241,x20242)+E(f875(x20243,x20244,x20245,x20246,x20247,x20241,x20248),f875(x20243,x20244,x20245,x20246,x20247,x20242,x20248)) % 173.51/173.29 [2025]~E(x20251,x20252)+E(f875(x20253,x20254,x20255,x20256,x20257,x20258,x20251),f875(x20253,x20254,x20255,x20256,x20257,x20258,x20252)) % 173.51/173.29 [2026]~E(x20261,x20262)+E(f419(x20261,x20263,x20264,x20265),f419(x20262,x20263,x20264,x20265)) % 173.51/173.29 [2027]~E(x20271,x20272)+E(f419(x20273,x20271,x20274,x20275),f419(x20273,x20272,x20274,x20275)) % 173.51/173.29 [2028]~E(x20281,x20282)+E(f419(x20283,x20284,x20281,x20285),f419(x20283,x20284,x20282,x20285)) % 173.51/173.29 [2029]~E(x20291,x20292)+E(f419(x20293,x20294,x20295,x20291),f419(x20293,x20294,x20295,x20292)) % 173.51/173.29 [2030]~E(x20301,x20302)+E(f755(x20301,x20303),f755(x20302,x20303)) % 173.51/173.29 [2031]~E(x20311,x20312)+E(f755(x20313,x20311),f755(x20313,x20312)) % 173.51/173.29 [2032]~E(x20321,x20322)+E(f132(x20321,x20323,x20324,x20325),f132(x20322,x20323,x20324,x20325)) % 173.51/173.29 [2033]~E(x20331,x20332)+E(f132(x20333,x20331,x20334,x20335),f132(x20333,x20332,x20334,x20335)) % 173.51/173.29 [2034]~E(x20341,x20342)+E(f132(x20343,x20344,x20341,x20345),f132(x20343,x20344,x20342,x20345)) % 173.51/173.29 [2035]~E(x20351,x20352)+E(f132(x20353,x20354,x20355,x20351),f132(x20353,x20354,x20355,x20352)) % 173.51/173.29 [2036]~E(x20361,x20362)+E(f538(x20361,x20363),f538(x20362,x20363)) % 173.51/173.29 [2037]~E(x20371,x20372)+E(f538(x20373,x20371),f538(x20373,x20372)) % 173.51/173.29 [2038]~E(x20381,x20382)+E(f341(x20381,x20383),f341(x20382,x20383)) % 173.51/173.29 [2039]~E(x20391,x20392)+E(f341(x20393,x20391),f341(x20393,x20392)) % 173.51/173.29 [2040]~E(x20401,x20402)+E(f372(x20401,x20403),f372(x20402,x20403)) % 173.51/173.29 [2041]~E(x20411,x20412)+E(f372(x20413,x20411),f372(x20413,x20412)) % 173.51/173.29 [2042]~E(x20421,x20422)+E(f343(x20421,x20423),f343(x20422,x20423)) % 173.51/173.29 [2043]~E(x20431,x20432)+E(f343(x20433,x20431),f343(x20433,x20432)) % 173.51/173.29 [2044]~E(x20441,x20442)+E(f724(x20441,x20443,x20444,x20445,x20446),f724(x20442,x20443,x20444,x20445,x20446)) % 173.51/173.29 [2045]~E(x20451,x20452)+E(f724(x20453,x20451,x20454,x20455,x20456),f724(x20453,x20452,x20454,x20455,x20456)) % 173.51/173.29 [2046]~E(x20461,x20462)+E(f724(x20463,x20464,x20461,x20465,x20466),f724(x20463,x20464,x20462,x20465,x20466)) % 173.51/173.29 [2047]~E(x20471,x20472)+E(f724(x20473,x20474,x20475,x20471,x20476),f724(x20473,x20474,x20475,x20472,x20476)) % 173.51/173.29 [2048]~E(x20481,x20482)+E(f724(x20483,x20484,x20485,x20486,x20481),f724(x20483,x20484,x20485,x20486,x20482)) % 173.51/173.29 [2049]~E(x20491,x20492)+E(f691(x20491,x20493,x20494,x20495,x20496,x20497),f691(x20492,x20493,x20494,x20495,x20496,x20497)) % 173.51/173.29 [2050]~E(x20501,x20502)+E(f691(x20503,x20501,x20504,x20505,x20506,x20507),f691(x20503,x20502,x20504,x20505,x20506,x20507)) % 173.51/173.29 [2051]~E(x20511,x20512)+E(f691(x20513,x20514,x20511,x20515,x20516,x20517),f691(x20513,x20514,x20512,x20515,x20516,x20517)) % 173.51/173.29 [2052]~E(x20521,x20522)+E(f691(x20523,x20524,x20525,x20521,x20526,x20527),f691(x20523,x20524,x20525,x20522,x20526,x20527)) % 173.51/173.29 [2053]~E(x20531,x20532)+E(f691(x20533,x20534,x20535,x20536,x20531,x20537),f691(x20533,x20534,x20535,x20536,x20532,x20537)) % 173.51/173.29 [2054]~E(x20541,x20542)+E(f691(x20543,x20544,x20545,x20546,x20547,x20541),f691(x20543,x20544,x20545,x20546,x20547,x20542)) % 173.51/173.29 [2055]~E(x20551,x20552)+E(f610(x20551,x20553,x20554),f610(x20552,x20553,x20554)) % 173.51/173.29 [2056]~E(x20561,x20562)+E(f610(x20563,x20561,x20564),f610(x20563,x20562,x20564)) % 173.51/173.29 [2057]~E(x20571,x20572)+E(f610(x20573,x20574,x20571),f610(x20573,x20574,x20572)) % 173.51/173.29 [2058]~E(x20581,x20582)+E(f841(x20581,x20583,x20584),f841(x20582,x20583,x20584)) % 173.51/173.29 [2059]~E(x20591,x20592)+E(f841(x20593,x20591,x20594),f841(x20593,x20592,x20594)) % 173.51/173.29 [2060]~E(x20601,x20602)+E(f841(x20603,x20604,x20601),f841(x20603,x20604,x20602)) % 173.51/173.29 [2061]~E(x20611,x20612)+E(f497(x20611,x20613,x20614,x20615,x20616),f497(x20612,x20613,x20614,x20615,x20616)) % 173.51/173.29 [2062]~E(x20621,x20622)+E(f497(x20623,x20621,x20624,x20625,x20626),f497(x20623,x20622,x20624,x20625,x20626)) % 173.51/173.29 [2063]~E(x20631,x20632)+E(f497(x20633,x20634,x20631,x20635,x20636),f497(x20633,x20634,x20632,x20635,x20636)) % 173.51/173.29 [2064]~E(x20641,x20642)+E(f497(x20643,x20644,x20645,x20641,x20646),f497(x20643,x20644,x20645,x20642,x20646)) % 173.51/173.29 [2065]~E(x20651,x20652)+E(f497(x20653,x20654,x20655,x20656,x20651),f497(x20653,x20654,x20655,x20656,x20652)) % 173.51/173.29 [2066]~E(x20661,x20662)+E(f749(x20661,x20663,x20664),f749(x20662,x20663,x20664)) % 173.51/173.29 [2067]~E(x20671,x20672)+E(f749(x20673,x20671,x20674),f749(x20673,x20672,x20674)) % 173.51/173.29 [2068]~E(x20681,x20682)+E(f749(x20683,x20684,x20681),f749(x20683,x20684,x20682)) % 173.51/173.29 [2069]~E(x20691,x20692)+E(f481(x20691,x20693,x20694,x20695,x20696),f481(x20692,x20693,x20694,x20695,x20696)) % 173.51/173.29 [2070]~E(x20701,x20702)+E(f481(x20703,x20701,x20704,x20705,x20706),f481(x20703,x20702,x20704,x20705,x20706)) % 173.51/173.29 [2071]~E(x20711,x20712)+E(f481(x20713,x20714,x20711,x20715,x20716),f481(x20713,x20714,x20712,x20715,x20716)) % 173.51/173.29 [2072]~E(x20721,x20722)+E(f481(x20723,x20724,x20725,x20721,x20726),f481(x20723,x20724,x20725,x20722,x20726)) % 173.51/173.29 [2073]~E(x20731,x20732)+E(f481(x20733,x20734,x20735,x20736,x20731),f481(x20733,x20734,x20735,x20736,x20732)) % 173.51/173.29 [2074]~E(x20741,x20742)+E(f542(x20741,x20743,x20744),f542(x20742,x20743,x20744)) % 173.51/173.29 [2075]~E(x20751,x20752)+E(f542(x20753,x20751,x20754),f542(x20753,x20752,x20754)) % 173.51/173.29 [2076]~E(x20761,x20762)+E(f542(x20763,x20764,x20761),f542(x20763,x20764,x20762)) % 173.51/173.29 [2077]~E(x20771,x20772)+E(f554(x20771,x20773,x20774,x20775,x20776,x20777),f554(x20772,x20773,x20774,x20775,x20776,x20777)) % 173.51/173.29 [2078]~E(x20781,x20782)+E(f554(x20783,x20781,x20784,x20785,x20786,x20787),f554(x20783,x20782,x20784,x20785,x20786,x20787)) % 173.51/173.29 [2079]~E(x20791,x20792)+E(f554(x20793,x20794,x20791,x20795,x20796,x20797),f554(x20793,x20794,x20792,x20795,x20796,x20797)) % 173.51/173.29 [2080]~E(x20801,x20802)+E(f554(x20803,x20804,x20805,x20801,x20806,x20807),f554(x20803,x20804,x20805,x20802,x20806,x20807)) % 173.51/173.29 [2081]~E(x20811,x20812)+E(f554(x20813,x20814,x20815,x20816,x20811,x20817),f554(x20813,x20814,x20815,x20816,x20812,x20817)) % 173.51/173.29 [2082]~E(x20821,x20822)+E(f554(x20823,x20824,x20825,x20826,x20827,x20821),f554(x20823,x20824,x20825,x20826,x20827,x20822)) % 173.51/173.29 [2083]~E(x20831,x20832)+E(f281(x20831,x20833,x20834),f281(x20832,x20833,x20834)) % 173.51/173.29 [2084]~E(x20841,x20842)+E(f281(x20843,x20841,x20844),f281(x20843,x20842,x20844)) % 173.51/173.29 [2085]~E(x20851,x20852)+E(f281(x20853,x20854,x20851),f281(x20853,x20854,x20852)) % 173.51/173.29 [2086]~E(x20861,x20862)+E(f529(x20861,x20863,x20864,x20865,x20866,x20867),f529(x20862,x20863,x20864,x20865,x20866,x20867)) % 173.51/173.29 [2087]~E(x20871,x20872)+E(f529(x20873,x20871,x20874,x20875,x20876,x20877),f529(x20873,x20872,x20874,x20875,x20876,x20877)) % 173.51/173.29 [2088]~E(x20881,x20882)+E(f529(x20883,x20884,x20881,x20885,x20886,x20887),f529(x20883,x20884,x20882,x20885,x20886,x20887)) % 173.51/173.29 [2089]~E(x20891,x20892)+E(f529(x20893,x20894,x20895,x20891,x20896,x20897),f529(x20893,x20894,x20895,x20892,x20896,x20897)) % 173.51/173.29 [2090]~E(x20901,x20902)+E(f529(x20903,x20904,x20905,x20906,x20901,x20907),f529(x20903,x20904,x20905,x20906,x20902,x20907)) % 173.51/173.29 [2091]~E(x20911,x20912)+E(f529(x20913,x20914,x20915,x20916,x20917,x20911),f529(x20913,x20914,x20915,x20916,x20917,x20912)) % 173.51/173.29 [2092]~E(x20921,x20922)+E(f798(x20921,x20923,x20924),f798(x20922,x20923,x20924)) % 173.51/173.29 [2093]~E(x20931,x20932)+E(f798(x20933,x20931,x20934),f798(x20933,x20932,x20934)) % 173.51/173.29 [2094]~E(x20941,x20942)+E(f798(x20943,x20944,x20941),f798(x20943,x20944,x20942)) % 173.51/173.29 [2095]~E(x20951,x20952)+E(f473(x20951,x20953),f473(x20952,x20953)) % 173.51/173.29 [2096]~E(x20961,x20962)+E(f473(x20963,x20961),f473(x20963,x20962)) % 173.51/173.29 [2097]~E(x20971,x20972)+E(f238(x20971,x20973,x20974,x20975,x20976),f238(x20972,x20973,x20974,x20975,x20976)) % 173.51/173.29 [2098]~E(x20981,x20982)+E(f238(x20983,x20981,x20984,x20985,x20986),f238(x20983,x20982,x20984,x20985,x20986)) % 173.51/173.29 [2099]~E(x20991,x20992)+E(f238(x20993,x20994,x20991,x20995,x20996),f238(x20993,x20994,x20992,x20995,x20996)) % 173.51/173.29 [2100]~E(x21001,x21002)+E(f238(x21003,x21004,x21005,x21001,x21006),f238(x21003,x21004,x21005,x21002,x21006)) % 173.51/173.29 [2101]~E(x21011,x21012)+E(f238(x21013,x21014,x21015,x21016,x21011),f238(x21013,x21014,x21015,x21016,x21012)) % 173.51/173.29 [2102]~E(x21021,x21022)+E(f397(x21021,x21023,x21024,x21025),f397(x21022,x21023,x21024,x21025)) % 173.51/173.29 [2103]~E(x21031,x21032)+E(f397(x21033,x21031,x21034,x21035),f397(x21033,x21032,x21034,x21035)) % 173.51/173.29 [2104]~E(x21041,x21042)+E(f397(x21043,x21044,x21041,x21045),f397(x21043,x21044,x21042,x21045)) % 173.51/173.29 [2105]~E(x21051,x21052)+E(f397(x21053,x21054,x21055,x21051),f397(x21053,x21054,x21055,x21052)) % 173.51/173.29 [2106]~E(x21061,x21062)+E(f387(x21061),f387(x21062)) % 173.51/173.29 [2107]~E(x21071,x21072)+E(f692(x21071,x21073,x21074,x21075,x21076,x21077),f692(x21072,x21073,x21074,x21075,x21076,x21077)) % 173.51/173.29 [2108]~E(x21081,x21082)+E(f692(x21083,x21081,x21084,x21085,x21086,x21087),f692(x21083,x21082,x21084,x21085,x21086,x21087)) % 173.51/173.29 [2109]~E(x21091,x21092)+E(f692(x21093,x21094,x21091,x21095,x21096,x21097),f692(x21093,x21094,x21092,x21095,x21096,x21097)) % 173.51/173.29 [2110]~E(x21101,x21102)+E(f692(x21103,x21104,x21105,x21101,x21106,x21107),f692(x21103,x21104,x21105,x21102,x21106,x21107)) % 173.51/173.29 [2111]~E(x21111,x21112)+E(f692(x21113,x21114,x21115,x21116,x21111,x21117),f692(x21113,x21114,x21115,x21116,x21112,x21117)) % 173.51/173.29 [2112]~E(x21121,x21122)+E(f692(x21123,x21124,x21125,x21126,x21127,x21121),f692(x21123,x21124,x21125,x21126,x21127,x21122)) % 173.51/173.29 [2113]~E(x21131,x21132)+E(f469(x21131,x21133,x21134,x21135),f469(x21132,x21133,x21134,x21135)) % 173.51/173.29 [2114]~E(x21141,x21142)+E(f469(x21143,x21141,x21144,x21145),f469(x21143,x21142,x21144,x21145)) % 173.51/173.29 [2115]~E(x21151,x21152)+E(f469(x21153,x21154,x21151,x21155),f469(x21153,x21154,x21152,x21155)) % 173.51/173.29 [2116]~E(x21161,x21162)+E(f469(x21163,x21164,x21165,x21161),f469(x21163,x21164,x21165,x21162)) % 173.51/173.29 [2117]~E(x21171,x21172)+E(f768(x21171,x21173,x21174),f768(x21172,x21173,x21174)) % 173.51/173.29 [2118]~E(x21181,x21182)+E(f768(x21183,x21181,x21184),f768(x21183,x21182,x21184)) % 173.51/173.29 [2119]~E(x21191,x21192)+E(f768(x21193,x21194,x21191),f768(x21193,x21194,x21192)) % 173.51/173.29 [2120]~E(x21201,x21202)+E(f756(x21201,x21203),f756(x21202,x21203)) % 173.51/173.29 [2121]~E(x21211,x21212)+E(f756(x21213,x21211),f756(x21213,x21212)) % 173.51/173.29 [2122]~E(x21221,x21222)+E(f793(x21221,x21223,x21224,x21225,x21226),f793(x21222,x21223,x21224,x21225,x21226)) % 173.51/173.29 [2123]~E(x21231,x21232)+E(f793(x21233,x21231,x21234,x21235,x21236),f793(x21233,x21232,x21234,x21235,x21236)) % 173.51/173.29 [2124]~E(x21241,x21242)+E(f793(x21243,x21244,x21241,x21245,x21246),f793(x21243,x21244,x21242,x21245,x21246)) % 173.51/173.29 [2125]~E(x21251,x21252)+E(f793(x21253,x21254,x21255,x21251,x21256),f793(x21253,x21254,x21255,x21252,x21256)) % 173.51/173.29 [2126]~E(x21261,x21262)+E(f793(x21263,x21264,x21265,x21266,x21261),f793(x21263,x21264,x21265,x21266,x21262)) % 173.51/173.29 [2127]~E(x21271,x21272)+E(f665(x21271,x21273,x21274),f665(x21272,x21273,x21274)) % 173.51/173.29 [2128]~E(x21281,x21282)+E(f665(x21283,x21281,x21284),f665(x21283,x21282,x21284)) % 173.51/173.29 [2129]~E(x21291,x21292)+E(f665(x21293,x21294,x21291),f665(x21293,x21294,x21292)) % 173.51/173.29 [2130]~E(x21301,x21302)+E(f492(x21301,x21303,x21304,x21305),f492(x21302,x21303,x21304,x21305)) % 173.51/173.29 [2131]~E(x21311,x21312)+E(f492(x21313,x21311,x21314,x21315),f492(x21313,x21312,x21314,x21315)) % 173.51/173.29 [2132]~E(x21321,x21322)+E(f492(x21323,x21324,x21321,x21325),f492(x21323,x21324,x21322,x21325)) % 173.51/173.29 [2133]~E(x21331,x21332)+E(f492(x21333,x21334,x21335,x21331),f492(x21333,x21334,x21335,x21332)) % 173.51/173.29 [2134]~E(x21341,x21342)+E(f572(x21341),f572(x21342)) % 173.51/173.29 [2135]~E(x21351,x21352)+E(f888(x21351,x21353,x21354,x21355,x21356,x21357),f888(x21352,x21353,x21354,x21355,x21356,x21357)) % 173.51/173.29 [2136]~E(x21361,x21362)+E(f888(x21363,x21361,x21364,x21365,x21366,x21367),f888(x21363,x21362,x21364,x21365,x21366,x21367)) % 173.51/173.29 [2137]~E(x21371,x21372)+E(f888(x21373,x21374,x21371,x21375,x21376,x21377),f888(x21373,x21374,x21372,x21375,x21376,x21377)) % 173.51/173.29 [2138]~E(x21381,x21382)+E(f888(x21383,x21384,x21385,x21381,x21386,x21387),f888(x21383,x21384,x21385,x21382,x21386,x21387)) % 173.51/173.29 [2139]~E(x21391,x21392)+E(f888(x21393,x21394,x21395,x21396,x21391,x21397),f888(x21393,x21394,x21395,x21396,x21392,x21397)) % 173.51/173.29 [2140]~E(x21401,x21402)+E(f888(x21403,x21404,x21405,x21406,x21407,x21401),f888(x21403,x21404,x21405,x21406,x21407,x21402)) % 173.51/173.29 [2141]~E(x21411,x21412)+E(f721(x21411,x21413),f721(x21412,x21413)) % 173.51/173.29 [2142]~E(x21421,x21422)+E(f721(x21423,x21421),f721(x21423,x21422)) % 173.51/173.29 [2143]~E(x21431,x21432)+E(f431(x21431,x21433,x21434,x21435,x21436),f431(x21432,x21433,x21434,x21435,x21436)) % 173.51/173.29 [2144]~E(x21441,x21442)+E(f431(x21443,x21441,x21444,x21445,x21446),f431(x21443,x21442,x21444,x21445,x21446)) % 173.51/173.29 [2145]~E(x21451,x21452)+E(f431(x21453,x21454,x21451,x21455,x21456),f431(x21453,x21454,x21452,x21455,x21456)) % 173.51/173.29 [2146]~E(x21461,x21462)+E(f431(x21463,x21464,x21465,x21461,x21466),f431(x21463,x21464,x21465,x21462,x21466)) % 173.51/173.29 [2147]~E(x21471,x21472)+E(f431(x21473,x21474,x21475,x21476,x21471),f431(x21473,x21474,x21475,x21476,x21472)) % 173.51/173.29 [2148]~E(x21481,x21482)+E(f636(x21481,x21483,x21484,x21485,x21486),f636(x21482,x21483,x21484,x21485,x21486)) % 173.51/173.29 [2149]~E(x21491,x21492)+E(f636(x21493,x21491,x21494,x21495,x21496),f636(x21493,x21492,x21494,x21495,x21496)) % 173.51/173.29 [2150]~E(x21501,x21502)+E(f636(x21503,x21504,x21501,x21505,x21506),f636(x21503,x21504,x21502,x21505,x21506)) % 173.51/173.29 [2151]~E(x21511,x21512)+E(f636(x21513,x21514,x21515,x21511,x21516),f636(x21513,x21514,x21515,x21512,x21516)) % 173.51/173.29 [2152]~E(x21521,x21522)+E(f636(x21523,x21524,x21525,x21526,x21521),f636(x21523,x21524,x21525,x21526,x21522)) % 173.51/173.29 [2153]~E(x21531,x21532)+E(f485(x21531,x21533,x21534,x21535,x21536),f485(x21532,x21533,x21534,x21535,x21536)) % 173.51/173.29 [2154]~E(x21541,x21542)+E(f485(x21543,x21541,x21544,x21545,x21546),f485(x21543,x21542,x21544,x21545,x21546)) % 173.51/173.29 [2155]~E(x21551,x21552)+E(f485(x21553,x21554,x21551,x21555,x21556),f485(x21553,x21554,x21552,x21555,x21556)) % 173.51/173.29 [2156]~E(x21561,x21562)+E(f485(x21563,x21564,x21565,x21561,x21566),f485(x21563,x21564,x21565,x21562,x21566)) % 173.51/173.29 [2157]~E(x21571,x21572)+E(f485(x21573,x21574,x21575,x21576,x21571),f485(x21573,x21574,x21575,x21576,x21572)) % 173.51/173.29 [2158]~E(x21581,x21582)+E(f644(x21581,x21583,x21584,x21585),f644(x21582,x21583,x21584,x21585)) % 173.51/173.29 [2159]~E(x21591,x21592)+E(f644(x21593,x21591,x21594,x21595),f644(x21593,x21592,x21594,x21595)) % 173.51/173.29 [2160]~E(x21601,x21602)+E(f644(x21603,x21604,x21601,x21605),f644(x21603,x21604,x21602,x21605)) % 173.51/173.29 [2161]~E(x21611,x21612)+E(f644(x21613,x21614,x21615,x21611),f644(x21613,x21614,x21615,x21612)) % 173.51/173.29 [2162]~E(x21621,x21622)+E(f762(x21621,x21623,x21624,x21625),f762(x21622,x21623,x21624,x21625)) % 173.51/173.29 [2163]~E(x21631,x21632)+E(f762(x21633,x21631,x21634,x21635),f762(x21633,x21632,x21634,x21635)) % 173.51/173.29 [2164]~E(x21641,x21642)+E(f762(x21643,x21644,x21641,x21645),f762(x21643,x21644,x21642,x21645)) % 173.51/173.29 [2165]~E(x21651,x21652)+E(f762(x21653,x21654,x21655,x21651),f762(x21653,x21654,x21655,x21652)) % 173.51/173.29 [2166]~E(x21661,x21662)+E(f545(x21661,x21663,x21664),f545(x21662,x21663,x21664)) % 173.51/173.29 [2167]~E(x21671,x21672)+E(f545(x21673,x21671,x21674),f545(x21673,x21672,x21674)) % 173.51/173.29 [2168]~E(x21681,x21682)+E(f545(x21683,x21684,x21681),f545(x21683,x21684,x21682)) % 173.51/173.29 [2169]~E(x21691,x21692)+E(f690(x21691,x21693,x21694,x21695,x21696,x21697),f690(x21692,x21693,x21694,x21695,x21696,x21697)) % 173.51/173.29 [2170]~E(x21701,x21702)+E(f690(x21703,x21701,x21704,x21705,x21706,x21707),f690(x21703,x21702,x21704,x21705,x21706,x21707)) % 173.51/173.29 [2171]~E(x21711,x21712)+E(f690(x21713,x21714,x21711,x21715,x21716,x21717),f690(x21713,x21714,x21712,x21715,x21716,x21717)) % 173.51/173.29 [2172]~E(x21721,x21722)+E(f690(x21723,x21724,x21725,x21721,x21726,x21727),f690(x21723,x21724,x21725,x21722,x21726,x21727)) % 173.51/173.29 [2173]~E(x21731,x21732)+E(f690(x21733,x21734,x21735,x21736,x21731,x21737),f690(x21733,x21734,x21735,x21736,x21732,x21737)) % 173.51/173.29 [2174]~E(x21741,x21742)+E(f690(x21743,x21744,x21745,x21746,x21747,x21741),f690(x21743,x21744,x21745,x21746,x21747,x21742)) % 173.51/173.29 [2175]~E(x21751,x21752)+E(f364(x21751),f364(x21752)) % 173.51/173.29 [2176]~E(x21761,x21762)+E(f499(x21761,x21763,x21764),f499(x21762,x21763,x21764)) % 173.51/173.29 [2177]~E(x21771,x21772)+E(f499(x21773,x21771,x21774),f499(x21773,x21772,x21774)) % 173.51/173.29 [2178]~E(x21781,x21782)+E(f499(x21783,x21784,x21781),f499(x21783,x21784,x21782)) % 173.51/173.29 [2179]~E(x21791,x21792)+E(f518(x21791,x21793,x21794),f518(x21792,x21793,x21794)) % 173.51/173.29 [2180]~E(x21801,x21802)+E(f518(x21803,x21801,x21804),f518(x21803,x21802,x21804)) % 173.51/173.29 [2181]~E(x21811,x21812)+E(f518(x21813,x21814,x21811),f518(x21813,x21814,x21812)) % 173.51/173.29 [2182]~E(x21821,x21822)+E(f677(x21821,x21823,x21824,x21825),f677(x21822,x21823,x21824,x21825)) % 173.51/173.29 [2183]~E(x21831,x21832)+E(f677(x21833,x21831,x21834,x21835),f677(x21833,x21832,x21834,x21835)) % 173.51/173.29 [2184]~E(x21841,x21842)+E(f677(x21843,x21844,x21841,x21845),f677(x21843,x21844,x21842,x21845)) % 173.51/173.29 [2185]~E(x21851,x21852)+E(f677(x21853,x21854,x21855,x21851),f677(x21853,x21854,x21855,x21852)) % 173.51/173.29 [2186]~E(x21861,x21862)+E(f780(x21861,x21863,x21864,x21865,x21866,x21867,x21868,x21869),f780(x21862,x21863,x21864,x21865,x21866,x21867,x21868,x21869)) % 173.51/173.29 [2187]~E(x21871,x21872)+E(f780(x21873,x21871,x21874,x21875,x21876,x21877,x21878,x21879),f780(x21873,x21872,x21874,x21875,x21876,x21877,x21878,x21879)) % 173.51/173.29 [2188]~E(x21881,x21882)+E(f780(x21883,x21884,x21881,x21885,x21886,x21887,x21888,x21889),f780(x21883,x21884,x21882,x21885,x21886,x21887,x21888,x21889)) % 173.51/173.29 [2189]~E(x21891,x21892)+E(f780(x21893,x21894,x21895,x21891,x21896,x21897,x21898,x21899),f780(x21893,x21894,x21895,x21892,x21896,x21897,x21898,x21899)) % 173.51/173.29 [2190]~E(x21901,x21902)+E(f780(x21903,x21904,x21905,x21906,x21901,x21907,x21908,x21909),f780(x21903,x21904,x21905,x21906,x21902,x21907,x21908,x21909)) % 173.51/173.29 [2191]~E(x21911,x21912)+E(f780(x21913,x21914,x21915,x21916,x21917,x21911,x21918,x21919),f780(x21913,x21914,x21915,x21916,x21917,x21912,x21918,x21919)) % 173.51/173.29 [2192]~E(x21921,x21922)+E(f780(x21923,x21924,x21925,x21926,x21927,x21928,x21921,x21929),f780(x21923,x21924,x21925,x21926,x21927,x21928,x21922,x21929)) % 173.51/173.29 [2193]~E(x21931,x21932)+E(f780(x21933,x21934,x21935,x21936,x21937,x21938,x21939,x21931),f780(x21933,x21934,x21935,x21936,x21937,x21938,x21939,x21932)) % 173.51/173.29 [2194]~E(x21941,x21942)+E(f471(x21941,x21943),f471(x21942,x21943)) % 173.51/173.29 [2195]~E(x21951,x21952)+E(f471(x21953,x21951),f471(x21953,x21952)) % 173.51/173.29 [2196]~E(x21961,x21962)+E(f493(x21961,x21963,x21964,x21965),f493(x21962,x21963,x21964,x21965)) % 173.51/173.29 [2197]~E(x21971,x21972)+E(f493(x21973,x21971,x21974,x21975),f493(x21973,x21972,x21974,x21975)) % 173.51/173.29 [2198]~E(x21981,x21982)+E(f493(x21983,x21984,x21981,x21985),f493(x21983,x21984,x21982,x21985)) % 173.51/173.29 [2199]~E(x21991,x21992)+E(f493(x21993,x21994,x21995,x21991),f493(x21993,x21994,x21995,x21992)) % 173.51/173.29 [2200]~E(x22001,x22002)+E(f649(x22001,x22003,x22004,x22005,x22006),f649(x22002,x22003,x22004,x22005,x22006)) % 173.51/173.29 [2201]~E(x22011,x22012)+E(f649(x22013,x22011,x22014,x22015,x22016),f649(x22013,x22012,x22014,x22015,x22016)) % 173.51/173.29 [2202]~E(x22021,x22022)+E(f649(x22023,x22024,x22021,x22025,x22026),f649(x22023,x22024,x22022,x22025,x22026)) % 173.51/173.29 [2203]~E(x22031,x22032)+E(f649(x22033,x22034,x22035,x22031,x22036),f649(x22033,x22034,x22035,x22032,x22036)) % 173.51/173.29 [2204]~E(x22041,x22042)+E(f649(x22043,x22044,x22045,x22046,x22041),f649(x22043,x22044,x22045,x22046,x22042)) % 173.51/173.29 [2205]~E(x22051,x22052)+E(f217(x22051),f217(x22052)) % 173.51/173.29 [2206]~E(x22061,x22062)+E(f432(x22061,x22063),f432(x22062,x22063)) % 173.51/173.29 [2207]~E(x22071,x22072)+E(f432(x22073,x22071),f432(x22073,x22072)) % 173.51/173.29 [2208]~E(x22081,x22082)+E(f19(x22081,x22083,x22084,x22085),f19(x22082,x22083,x22084,x22085)) % 173.51/173.29 [2209]~E(x22091,x22092)+E(f19(x22093,x22091,x22094,x22095),f19(x22093,x22092,x22094,x22095)) % 173.51/173.29 [2210]~E(x22101,x22102)+E(f19(x22103,x22104,x22101,x22105),f19(x22103,x22104,x22102,x22105)) % 173.51/173.29 [2211]~E(x22111,x22112)+E(f19(x22113,x22114,x22115,x22111),f19(x22113,x22114,x22115,x22112)) % 173.51/173.29 [2212]~E(x22121,x22122)+E(f901(x22121,x22123,x22124,x22125),f901(x22122,x22123,x22124,x22125)) % 173.51/173.29 [2213]~E(x22131,x22132)+E(f901(x22133,x22131,x22134,x22135),f901(x22133,x22132,x22134,x22135)) % 173.51/173.29 [2214]~E(x22141,x22142)+E(f901(x22143,x22144,x22141,x22145),f901(x22143,x22144,x22142,x22145)) % 173.51/173.29 [2215]~E(x22151,x22152)+E(f901(x22153,x22154,x22155,x22151),f901(x22153,x22154,x22155,x22152)) % 173.51/173.29 [2216]~E(x22161,x22162)+E(f367(x22161,x22163,x22164,x22165,x22166),f367(x22162,x22163,x22164,x22165,x22166)) % 173.51/173.29 [2217]~E(x22171,x22172)+E(f367(x22173,x22171,x22174,x22175,x22176),f367(x22173,x22172,x22174,x22175,x22176)) % 173.51/173.29 [2218]~E(x22181,x22182)+E(f367(x22183,x22184,x22181,x22185,x22186),f367(x22183,x22184,x22182,x22185,x22186)) % 173.51/173.29 [2219]~E(x22191,x22192)+E(f367(x22193,x22194,x22195,x22191,x22196),f367(x22193,x22194,x22195,x22192,x22196)) % 173.51/173.29 [2220]~E(x22201,x22202)+E(f367(x22203,x22204,x22205,x22206,x22201),f367(x22203,x22204,x22205,x22206,x22202)) % 173.51/173.29 [2221]~E(x22211,x22212)+E(f597(x22211,x22213,x22214,x22215),f597(x22212,x22213,x22214,x22215)) % 173.51/173.29 [2222]~E(x22221,x22222)+E(f597(x22223,x22221,x22224,x22225),f597(x22223,x22222,x22224,x22225)) % 173.51/173.29 [2223]~E(x22231,x22232)+E(f597(x22233,x22234,x22231,x22235),f597(x22233,x22234,x22232,x22235)) % 173.51/173.29 [2224]~E(x22241,x22242)+E(f597(x22243,x22244,x22245,x22241),f597(x22243,x22244,x22245,x22242)) % 173.51/173.29 [2225]~E(x22251,x22252)+E(f661(x22251,x22253,x22254,x22255,x22256,x22257,x22258),f661(x22252,x22253,x22254,x22255,x22256,x22257,x22258)) % 173.51/173.29 [2226]~E(x22261,x22262)+E(f661(x22263,x22261,x22264,x22265,x22266,x22267,x22268),f661(x22263,x22262,x22264,x22265,x22266,x22267,x22268)) % 173.51/173.29 [2227]~E(x22271,x22272)+E(f661(x22273,x22274,x22271,x22275,x22276,x22277,x22278),f661(x22273,x22274,x22272,x22275,x22276,x22277,x22278)) % 173.51/173.29 [2228]~E(x22281,x22282)+E(f661(x22283,x22284,x22285,x22281,x22286,x22287,x22288),f661(x22283,x22284,x22285,x22282,x22286,x22287,x22288)) % 173.51/173.29 [2229]~E(x22291,x22292)+E(f661(x22293,x22294,x22295,x22296,x22291,x22297,x22298),f661(x22293,x22294,x22295,x22296,x22292,x22297,x22298)) % 173.51/173.29 [2230]~E(x22301,x22302)+E(f661(x22303,x22304,x22305,x22306,x22307,x22301,x22308),f661(x22303,x22304,x22305,x22306,x22307,x22302,x22308)) % 173.51/173.29 [2231]~E(x22311,x22312)+E(f661(x22313,x22314,x22315,x22316,x22317,x22318,x22311),f661(x22313,x22314,x22315,x22316,x22317,x22318,x22312)) % 173.51/173.29 [2232]~E(x22321,x22322)+E(f258(x22321,x22323,x22324,x22325,x22326,x22327),f258(x22322,x22323,x22324,x22325,x22326,x22327)) % 173.51/173.29 [2233]~E(x22331,x22332)+E(f258(x22333,x22331,x22334,x22335,x22336,x22337),f258(x22333,x22332,x22334,x22335,x22336,x22337)) % 173.51/173.29 [2234]~E(x22341,x22342)+E(f258(x22343,x22344,x22341,x22345,x22346,x22347),f258(x22343,x22344,x22342,x22345,x22346,x22347)) % 173.51/173.29 [2235]~E(x22351,x22352)+E(f258(x22353,x22354,x22355,x22351,x22356,x22357),f258(x22353,x22354,x22355,x22352,x22356,x22357)) % 173.51/173.29 [2236]~E(x22361,x22362)+E(f258(x22363,x22364,x22365,x22366,x22361,x22367),f258(x22363,x22364,x22365,x22366,x22362,x22367)) % 173.51/173.29 [2237]~E(x22371,x22372)+E(f258(x22373,x22374,x22375,x22376,x22377,x22371),f258(x22373,x22374,x22375,x22376,x22377,x22372)) % 173.51/173.29 [2238]~E(x22381,x22382)+E(f676(x22381,x22383,x22384,x22385),f676(x22382,x22383,x22384,x22385)) % 173.51/173.29 [2239]~E(x22391,x22392)+E(f676(x22393,x22391,x22394,x22395),f676(x22393,x22392,x22394,x22395)) % 173.51/173.29 [2240]~E(x22401,x22402)+E(f676(x22403,x22404,x22401,x22405),f676(x22403,x22404,x22402,x22405)) % 173.51/173.29 [2241]~E(x22411,x22412)+E(f676(x22413,x22414,x22415,x22411),f676(x22413,x22414,x22415,x22412)) % 173.51/173.29 [2242]~E(x22421,x22422)+E(f413(x22421,x22423,x22424,x22425),f413(x22422,x22423,x22424,x22425)) % 173.51/173.29 [2243]~E(x22431,x22432)+E(f413(x22433,x22431,x22434,x22435),f413(x22433,x22432,x22434,x22435)) % 173.51/173.29 [2244]~E(x22441,x22442)+E(f413(x22443,x22444,x22441,x22445),f413(x22443,x22444,x22442,x22445)) % 173.51/173.29 [2245]~E(x22451,x22452)+E(f413(x22453,x22454,x22455,x22451),f413(x22453,x22454,x22455,x22452)) % 173.51/173.29 [2246]~E(x22461,x22462)+E(f740(x22461,x22463,x22464),f740(x22462,x22463,x22464)) % 173.51/173.29 [2247]~E(x22471,x22472)+E(f740(x22473,x22471,x22474),f740(x22473,x22472,x22474)) % 173.51/173.29 [2248]~E(x22481,x22482)+E(f740(x22483,x22484,x22481),f740(x22483,x22484,x22482)) % 173.51/173.29 [2249]~E(x22491,x22492)+E(f616(x22491,x22493,x22494),f616(x22492,x22493,x22494)) % 173.59/173.29 [2250]~E(x22501,x22502)+E(f616(x22503,x22501,x22504),f616(x22503,x22502,x22504)) % 173.59/173.29 [2251]~E(x22511,x22512)+E(f616(x22513,x22514,x22511),f616(x22513,x22514,x22512)) % 173.59/173.29 [2252]~E(x22521,x22522)+E(f405(x22521,x22523,x22524),f405(x22522,x22523,x22524)) % 173.59/173.29 [2253]~E(x22531,x22532)+E(f405(x22533,x22531,x22534),f405(x22533,x22532,x22534)) % 173.59/173.29 [2254]~E(x22541,x22542)+E(f405(x22543,x22544,x22541),f405(x22543,x22544,x22542)) % 173.59/173.29 [2255]~E(x22551,x22552)+E(f590(x22551,x22553,x22554,x22555),f590(x22552,x22553,x22554,x22555)) % 173.59/173.29 [2256]~E(x22561,x22562)+E(f590(x22563,x22561,x22564,x22565),f590(x22563,x22562,x22564,x22565)) % 173.59/173.29 [2257]~E(x22571,x22572)+E(f590(x22573,x22574,x22571,x22575),f590(x22573,x22574,x22572,x22575)) % 173.59/173.29 [2258]~E(x22581,x22582)+E(f590(x22583,x22584,x22585,x22581),f590(x22583,x22584,x22585,x22582)) % 173.59/173.29 [2259]~E(x22591,x22592)+E(f600(x22591,x22593),f600(x22592,x22593)) % 173.59/173.29 [2260]~E(x22601,x22602)+E(f600(x22603,x22601),f600(x22603,x22602)) % 173.59/173.29 [2261]~E(x22611,x22612)+E(f709(x22611,x22613,x22614),f709(x22612,x22613,x22614)) % 173.59/173.29 [2262]~E(x22621,x22622)+E(f709(x22623,x22621,x22624),f709(x22623,x22622,x22624)) % 173.59/173.29 [2263]~E(x22631,x22632)+E(f709(x22633,x22634,x22631),f709(x22633,x22634,x22632)) % 173.59/173.29 [2264]~E(x22641,x22642)+E(f671(x22641,x22643,x22644),f671(x22642,x22643,x22644)) % 173.59/173.29 [2265]~E(x22651,x22652)+E(f671(x22653,x22651,x22654),f671(x22653,x22652,x22654)) % 173.59/173.29 [2266]~E(x22661,x22662)+E(f671(x22663,x22664,x22661),f671(x22663,x22664,x22662)) % 173.59/173.29 [2267]~E(x22671,x22672)+E(f602(x22671,x22673,x22674,x22675),f602(x22672,x22673,x22674,x22675)) % 173.59/173.29 [2268]~E(x22681,x22682)+E(f602(x22683,x22681,x22684,x22685),f602(x22683,x22682,x22684,x22685)) % 173.59/173.29 [2269]~E(x22691,x22692)+E(f602(x22693,x22694,x22691,x22695),f602(x22693,x22694,x22692,x22695)) % 173.59/173.29 [2270]~E(x22701,x22702)+E(f602(x22703,x22704,x22705,x22701),f602(x22703,x22704,x22705,x22702)) % 173.59/173.29 [2271]~E(x22711,x22712)+E(f899(x22711,x22713),f899(x22712,x22713)) % 173.59/173.29 [2272]~E(x22721,x22722)+E(f899(x22723,x22721),f899(x22723,x22722)) % 173.59/173.29 [2273]~E(x22731,x22732)+E(f533(x22731,x22733,x22734,x22735,x22736,x22737,x22738),f533(x22732,x22733,x22734,x22735,x22736,x22737,x22738)) % 173.59/173.29 [2274]~E(x22741,x22742)+E(f533(x22743,x22741,x22744,x22745,x22746,x22747,x22748),f533(x22743,x22742,x22744,x22745,x22746,x22747,x22748)) % 173.59/173.29 [2275]~E(x22751,x22752)+E(f533(x22753,x22754,x22751,x22755,x22756,x22757,x22758),f533(x22753,x22754,x22752,x22755,x22756,x22757,x22758)) % 173.59/173.29 [2276]~E(x22761,x22762)+E(f533(x22763,x22764,x22765,x22761,x22766,x22767,x22768),f533(x22763,x22764,x22765,x22762,x22766,x22767,x22768)) % 173.59/173.29 [2277]~E(x22771,x22772)+E(f533(x22773,x22774,x22775,x22776,x22771,x22777,x22778),f533(x22773,x22774,x22775,x22776,x22772,x22777,x22778)) % 173.59/173.29 [2278]~E(x22781,x22782)+E(f533(x22783,x22784,x22785,x22786,x22787,x22781,x22788),f533(x22783,x22784,x22785,x22786,x22787,x22782,x22788)) % 173.59/173.29 [2279]~E(x22791,x22792)+E(f533(x22793,x22794,x22795,x22796,x22797,x22798,x22791),f533(x22793,x22794,x22795,x22796,x22797,x22798,x22792)) % 173.59/173.29 [2280]~E(x22801,x22802)+E(f442(x22801,x22803),f442(x22802,x22803)) % 173.59/173.29 [2281]~E(x22811,x22812)+E(f442(x22813,x22811),f442(x22813,x22812)) % 173.59/173.29 [2282]~E(x22821,x22822)+E(f105(x22821,x22823,x22824,x22825),f105(x22822,x22823,x22824,x22825)) % 173.59/173.29 [2283]~E(x22831,x22832)+E(f105(x22833,x22831,x22834,x22835),f105(x22833,x22832,x22834,x22835)) % 173.59/173.29 [2284]~E(x22841,x22842)+E(f105(x22843,x22844,x22841,x22845),f105(x22843,x22844,x22842,x22845)) % 173.59/173.29 [2285]~E(x22851,x22852)+E(f105(x22853,x22854,x22855,x22851),f105(x22853,x22854,x22855,x22852)) % 173.59/173.29 [2286]~E(x22861,x22862)+E(f601(x22861,x22863,x22864,x22865),f601(x22862,x22863,x22864,x22865)) % 173.59/173.29 [2287]~E(x22871,x22872)+E(f601(x22873,x22871,x22874,x22875),f601(x22873,x22872,x22874,x22875)) % 173.59/173.29 [2288]~E(x22881,x22882)+E(f601(x22883,x22884,x22881,x22885),f601(x22883,x22884,x22882,x22885)) % 173.59/173.29 [2289]~E(x22891,x22892)+E(f601(x22893,x22894,x22895,x22891),f601(x22893,x22894,x22895,x22892)) % 173.59/173.29 [2290]~E(x22901,x22902)+E(f462(x22901,x22903,x22904,x22905,x22906),f462(x22902,x22903,x22904,x22905,x22906)) % 173.59/173.29 [2291]~E(x22911,x22912)+E(f462(x22913,x22911,x22914,x22915,x22916),f462(x22913,x22912,x22914,x22915,x22916)) % 173.59/173.29 [2292]~E(x22921,x22922)+E(f462(x22923,x22924,x22921,x22925,x22926),f462(x22923,x22924,x22922,x22925,x22926)) % 173.59/173.29 [2293]~E(x22931,x22932)+E(f462(x22933,x22934,x22935,x22931,x22936),f462(x22933,x22934,x22935,x22932,x22936)) % 173.59/173.29 [2294]~E(x22941,x22942)+E(f462(x22943,x22944,x22945,x22946,x22941),f462(x22943,x22944,x22945,x22946,x22942)) % 173.59/173.29 [2295]~E(x22951,x22952)+E(f840(x22951,x22953,x22954,x22955),f840(x22952,x22953,x22954,x22955)) % 173.59/173.29 [2296]~E(x22961,x22962)+E(f840(x22963,x22961,x22964,x22965),f840(x22963,x22962,x22964,x22965)) % 173.59/173.29 [2297]~E(x22971,x22972)+E(f840(x22973,x22974,x22971,x22975),f840(x22973,x22974,x22972,x22975)) % 173.59/173.29 [2298]~E(x22981,x22982)+E(f840(x22983,x22984,x22985,x22981),f840(x22983,x22984,x22985,x22982)) % 173.59/173.29 [2299]~E(x22991,x22992)+E(f355(x22991,x22993,x22994),f355(x22992,x22993,x22994)) % 173.59/173.29 [2300]~E(x23001,x23002)+E(f355(x23003,x23001,x23004),f355(x23003,x23002,x23004)) % 173.59/173.29 [2301]~E(x23011,x23012)+E(f355(x23013,x23014,x23011),f355(x23013,x23014,x23012)) % 173.59/173.29 [2302]~E(x23021,x23022)+E(f459(x23021,x23023,x23024,x23025,x23026),f459(x23022,x23023,x23024,x23025,x23026)) % 173.59/173.29 [2303]~E(x23031,x23032)+E(f459(x23033,x23031,x23034,x23035,x23036),f459(x23033,x23032,x23034,x23035,x23036)) % 173.59/173.29 [2304]~E(x23041,x23042)+E(f459(x23043,x23044,x23041,x23045,x23046),f459(x23043,x23044,x23042,x23045,x23046)) % 173.59/173.29 [2305]~E(x23051,x23052)+E(f459(x23053,x23054,x23055,x23051,x23056),f459(x23053,x23054,x23055,x23052,x23056)) % 173.59/173.29 [2306]~E(x23061,x23062)+E(f459(x23063,x23064,x23065,x23066,x23061),f459(x23063,x23064,x23065,x23066,x23062)) % 173.59/173.29 [2307]~E(x23071,x23072)+E(f423(x23071,x23073),f423(x23072,x23073)) % 173.59/173.29 [2308]~E(x23081,x23082)+E(f423(x23083,x23081),f423(x23083,x23082)) % 173.59/173.29 [2309]~E(x23091,x23092)+E(f458(x23091,x23093,x23094,x23095,x23096),f458(x23092,x23093,x23094,x23095,x23096)) % 173.59/173.29 [2310]~E(x23101,x23102)+E(f458(x23103,x23101,x23104,x23105,x23106),f458(x23103,x23102,x23104,x23105,x23106)) % 173.59/173.29 [2311]~E(x23111,x23112)+E(f458(x23113,x23114,x23111,x23115,x23116),f458(x23113,x23114,x23112,x23115,x23116)) % 173.59/173.29 [2312]~E(x23121,x23122)+E(f458(x23123,x23124,x23125,x23121,x23126),f458(x23123,x23124,x23125,x23122,x23126)) % 173.59/173.29 [2313]~E(x23131,x23132)+E(f458(x23133,x23134,x23135,x23136,x23131),f458(x23133,x23134,x23135,x23136,x23132)) % 173.59/173.29 [2314]~E(x23141,x23142)+E(f626(x23141,x23143,x23144,x23145,x23146,x23147),f626(x23142,x23143,x23144,x23145,x23146,x23147)) % 173.59/173.29 [2315]~E(x23151,x23152)+E(f626(x23153,x23151,x23154,x23155,x23156,x23157),f626(x23153,x23152,x23154,x23155,x23156,x23157)) % 173.59/173.29 [2316]~E(x23161,x23162)+E(f626(x23163,x23164,x23161,x23165,x23166,x23167),f626(x23163,x23164,x23162,x23165,x23166,x23167)) % 173.59/173.29 [2317]~E(x23171,x23172)+E(f626(x23173,x23174,x23175,x23171,x23176,x23177),f626(x23173,x23174,x23175,x23172,x23176,x23177)) % 173.59/173.29 [2318]~E(x23181,x23182)+E(f626(x23183,x23184,x23185,x23186,x23181,x23187),f626(x23183,x23184,x23185,x23186,x23182,x23187)) % 173.59/173.29 [2319]~E(x23191,x23192)+E(f626(x23193,x23194,x23195,x23196,x23197,x23191),f626(x23193,x23194,x23195,x23196,x23197,x23192)) % 173.59/173.29 [2320]~E(x23201,x23202)+E(f418(x23201,x23203,x23204,x23205),f418(x23202,x23203,x23204,x23205)) % 173.59/173.29 [2321]~E(x23211,x23212)+E(f418(x23213,x23211,x23214,x23215),f418(x23213,x23212,x23214,x23215)) % 173.59/173.29 [2322]~E(x23221,x23222)+E(f418(x23223,x23224,x23221,x23225),f418(x23223,x23224,x23222,x23225)) % 173.59/173.29 [2323]~E(x23231,x23232)+E(f418(x23233,x23234,x23235,x23231),f418(x23233,x23234,x23235,x23232)) % 173.59/173.29 [2324]~E(x23241,x23242)+E(f728(x23241,x23243,x23244,x23245,x23246),f728(x23242,x23243,x23244,x23245,x23246)) % 173.59/173.29 [2325]~E(x23251,x23252)+E(f728(x23253,x23251,x23254,x23255,x23256),f728(x23253,x23252,x23254,x23255,x23256)) % 173.59/173.29 [2326]~E(x23261,x23262)+E(f728(x23263,x23264,x23261,x23265,x23266),f728(x23263,x23264,x23262,x23265,x23266)) % 173.59/173.29 [2327]~E(x23271,x23272)+E(f728(x23273,x23274,x23275,x23271,x23276),f728(x23273,x23274,x23275,x23272,x23276)) % 173.59/173.29 [2328]~E(x23281,x23282)+E(f728(x23283,x23284,x23285,x23286,x23281),f728(x23283,x23284,x23285,x23286,x23282)) % 173.59/173.29 [2329]~E(x23291,x23292)+E(f80(x23291,x23293),f80(x23292,x23293)) % 173.59/173.29 [2330]~E(x23301,x23302)+E(f80(x23303,x23301),f80(x23303,x23302)) % 173.59/173.29 [2331]~E(x23311,x23312)+E(f767(x23311,x23313),f767(x23312,x23313)) % 173.59/173.29 [2332]~E(x23321,x23322)+E(f767(x23323,x23321),f767(x23323,x23322)) % 173.59/173.29 [2333]~E(x23331,x23332)+E(f789(x23331,x23333,x23334,x23335,x23336),f789(x23332,x23333,x23334,x23335,x23336)) % 173.59/173.29 [2334]~E(x23341,x23342)+E(f789(x23343,x23341,x23344,x23345,x23346),f789(x23343,x23342,x23344,x23345,x23346)) % 173.59/173.29 [2335]~E(x23351,x23352)+E(f789(x23353,x23354,x23351,x23355,x23356),f789(x23353,x23354,x23352,x23355,x23356)) % 173.59/173.29 [2336]~E(x23361,x23362)+E(f789(x23363,x23364,x23365,x23361,x23366),f789(x23363,x23364,x23365,x23362,x23366)) % 173.59/173.29 [2337]~E(x23371,x23372)+E(f789(x23373,x23374,x23375,x23376,x23371),f789(x23373,x23374,x23375,x23376,x23372)) % 173.59/173.29 [2338]~E(x23381,x23382)+E(f340(x23381),f340(x23382)) % 173.59/173.29 [2339]~E(x23391,x23392)+E(f416(x23391,x23393,x23394,x23395),f416(x23392,x23393,x23394,x23395)) % 173.59/173.29 [2340]~E(x23401,x23402)+E(f416(x23403,x23401,x23404,x23405),f416(x23403,x23402,x23404,x23405)) % 173.59/173.29 [2341]~E(x23411,x23412)+E(f416(x23413,x23414,x23411,x23415),f416(x23413,x23414,x23412,x23415)) % 173.59/173.29 [2342]~E(x23421,x23422)+E(f416(x23423,x23424,x23425,x23421),f416(x23423,x23424,x23425,x23422)) % 173.59/173.29 [2343]~E(x23431,x23432)+E(f833(x23431,x23433),f833(x23432,x23433)) % 173.59/173.29 [2344]~E(x23441,x23442)+E(f833(x23443,x23441),f833(x23443,x23442)) % 173.59/173.29 [2345]~E(x23451,x23452)+E(f898(x23451,x23453),f898(x23452,x23453)) % 173.59/173.29 [2346]~E(x23461,x23462)+E(f898(x23463,x23461),f898(x23463,x23462)) % 173.59/173.29 [2347]~E(x23471,x23472)+E(f791(x23471,x23473,x23474,x23475,x23476),f791(x23472,x23473,x23474,x23475,x23476)) % 173.59/173.29 [2348]~E(x23481,x23482)+E(f791(x23483,x23481,x23484,x23485,x23486),f791(x23483,x23482,x23484,x23485,x23486)) % 173.59/173.29 [2349]~E(x23491,x23492)+E(f791(x23493,x23494,x23491,x23495,x23496),f791(x23493,x23494,x23492,x23495,x23496)) % 173.59/173.29 [2350]~E(x23501,x23502)+E(f791(x23503,x23504,x23505,x23501,x23506),f791(x23503,x23504,x23505,x23502,x23506)) % 173.59/173.29 [2351]~E(x23511,x23512)+E(f791(x23513,x23514,x23515,x23516,x23511),f791(x23513,x23514,x23515,x23516,x23512)) % 173.59/173.29 [2352]~E(x23521,x23522)+E(f406(x23521,x23523,x23524),f406(x23522,x23523,x23524)) % 173.59/173.29 [2353]~E(x23531,x23532)+E(f406(x23533,x23531,x23534),f406(x23533,x23532,x23534)) % 173.59/173.29 [2354]~E(x23541,x23542)+E(f406(x23543,x23544,x23541),f406(x23543,x23544,x23542)) % 173.59/173.29 [2355]~E(x23551,x23552)+E(f846(x23551,x23553),f846(x23552,x23553)) % 173.59/173.29 [2356]~E(x23561,x23562)+E(f846(x23563,x23561),f846(x23563,x23562)) % 173.59/173.29 [2357]~E(x23571,x23572)+E(f274(x23571,x23573,x23574),f274(x23572,x23573,x23574)) % 173.59/173.29 [2358]~E(x23581,x23582)+E(f274(x23583,x23581,x23584),f274(x23583,x23582,x23584)) % 173.59/173.29 [2359]~E(x23591,x23592)+E(f274(x23593,x23594,x23591),f274(x23593,x23594,x23592)) % 173.59/173.29 [2360]~E(x23601,x23602)+E(f848(x23601),f848(x23602)) % 173.59/173.29 [2361]~E(x23611,x23612)+E(f720(x23611,x23613),f720(x23612,x23613)) % 173.59/173.29 [2362]~E(x23621,x23622)+E(f720(x23623,x23621),f720(x23623,x23622)) % 173.59/173.29 [2363]~E(x23631,x23632)+E(f726(x23631,x23633),f726(x23632,x23633)) % 173.59/173.29 [2364]~E(x23641,x23642)+E(f726(x23643,x23641),f726(x23643,x23642)) % 173.59/173.29 [2365]~E(x23651,x23652)+E(f411(x23651,x23653,x23654,x23655),f411(x23652,x23653,x23654,x23655)) % 173.59/173.29 [2366]~E(x23661,x23662)+E(f411(x23663,x23661,x23664,x23665),f411(x23663,x23662,x23664,x23665)) % 173.59/173.29 [2367]~E(x23671,x23672)+E(f411(x23673,x23674,x23671,x23675),f411(x23673,x23674,x23672,x23675)) % 173.59/173.29 [2368]~E(x23681,x23682)+E(f411(x23683,x23684,x23685,x23681),f411(x23683,x23684,x23685,x23682)) % 173.59/173.29 [2369]~E(x23691,x23692)+E(f549(x23691,x23693,x23694),f549(x23692,x23693,x23694)) % 173.59/173.29 [2370]~E(x23701,x23702)+E(f549(x23703,x23701,x23704),f549(x23703,x23702,x23704)) % 173.59/173.29 [2371]~E(x23711,x23712)+E(f549(x23713,x23714,x23711),f549(x23713,x23714,x23712)) % 173.59/173.29 [2372]~E(x23721,x23722)+E(f563(x23721,x23723,x23724,x23725),f563(x23722,x23723,x23724,x23725)) % 173.59/173.29 [2373]~E(x23731,x23732)+E(f563(x23733,x23731,x23734,x23735),f563(x23733,x23732,x23734,x23735)) % 173.59/173.29 [2374]~E(x23741,x23742)+E(f563(x23743,x23744,x23741,x23745),f563(x23743,x23744,x23742,x23745)) % 173.59/173.29 [2375]~E(x23751,x23752)+E(f563(x23753,x23754,x23755,x23751),f563(x23753,x23754,x23755,x23752)) % 173.59/173.29 [2376]~E(x23761,x23762)+E(f221(x23761,x23763,x23764,x23765),f221(x23762,x23763,x23764,x23765)) % 173.59/173.29 [2377]~E(x23771,x23772)+E(f221(x23773,x23771,x23774,x23775),f221(x23773,x23772,x23774,x23775)) % 173.59/173.29 [2378]~E(x23781,x23782)+E(f221(x23783,x23784,x23781,x23785),f221(x23783,x23784,x23782,x23785)) % 173.59/173.29 [2379]~E(x23791,x23792)+E(f221(x23793,x23794,x23795,x23791),f221(x23793,x23794,x23795,x23792)) % 173.59/173.29 [2380]~E(x23801,x23802)+E(f805(x23801,x23803,x23804),f805(x23802,x23803,x23804)) % 173.59/173.29 [2381]~E(x23811,x23812)+E(f805(x23813,x23811,x23814),f805(x23813,x23812,x23814)) % 173.59/173.29 [2382]~E(x23821,x23822)+E(f805(x23823,x23824,x23821),f805(x23823,x23824,x23822)) % 173.59/173.29 [2383]~E(x23831,x23832)+E(f360(x23831,x23833,x23834,x23835,x23836),f360(x23832,x23833,x23834,x23835,x23836)) % 173.59/173.29 [2384]~E(x23841,x23842)+E(f360(x23843,x23841,x23844,x23845,x23846),f360(x23843,x23842,x23844,x23845,x23846)) % 173.59/173.29 [2385]~E(x23851,x23852)+E(f360(x23853,x23854,x23851,x23855,x23856),f360(x23853,x23854,x23852,x23855,x23856)) % 173.59/173.29 [2386]~E(x23861,x23862)+E(f360(x23863,x23864,x23865,x23861,x23866),f360(x23863,x23864,x23865,x23862,x23866)) % 173.59/173.29 [2387]~E(x23871,x23872)+E(f360(x23873,x23874,x23875,x23876,x23871),f360(x23873,x23874,x23875,x23876,x23872)) % 173.59/173.29 [2388]~E(x23881,x23882)+E(f435(x23881,x23883,x23884),f435(x23882,x23883,x23884)) % 173.59/173.29 [2389]~E(x23891,x23892)+E(f435(x23893,x23891,x23894),f435(x23893,x23892,x23894)) % 173.59/173.29 [2390]~E(x23901,x23902)+E(f435(x23903,x23904,x23901),f435(x23903,x23904,x23902)) % 173.59/173.29 [2391]~E(x23911,x23912)+E(f47(x23911),f47(x23912)) % 173.59/173.29 [2392]~E(x23921,x23922)+E(f612(x23921,x23923,x23924,x23925,x23926,x23927),f612(x23922,x23923,x23924,x23925,x23926,x23927)) % 173.59/173.29 [2393]~E(x23931,x23932)+E(f612(x23933,x23931,x23934,x23935,x23936,x23937),f612(x23933,x23932,x23934,x23935,x23936,x23937)) % 173.59/173.29 [2394]~E(x23941,x23942)+E(f612(x23943,x23944,x23941,x23945,x23946,x23947),f612(x23943,x23944,x23942,x23945,x23946,x23947)) % 173.59/173.29 [2395]~E(x23951,x23952)+E(f612(x23953,x23954,x23955,x23951,x23956,x23957),f612(x23953,x23954,x23955,x23952,x23956,x23957)) % 173.59/173.29 [2396]~E(x23961,x23962)+E(f612(x23963,x23964,x23965,x23966,x23961,x23967),f612(x23963,x23964,x23965,x23966,x23962,x23967)) % 173.59/173.29 [2397]~E(x23971,x23972)+E(f612(x23973,x23974,x23975,x23976,x23977,x23971),f612(x23973,x23974,x23975,x23976,x23977,x23972)) % 173.59/173.29 [2398]~E(x23981,x23982)+E(f797(x23981,x23983,x23984),f797(x23982,x23983,x23984)) % 173.59/173.29 [2399]~E(x23991,x23992)+E(f797(x23993,x23991,x23994),f797(x23993,x23992,x23994)) % 173.59/173.29 [2400]~E(x24001,x24002)+E(f797(x24003,x24004,x24001),f797(x24003,x24004,x24002)) % 173.59/173.29 [2401]~E(x24011,x24012)+E(f825(x24011,x24013),f825(x24012,x24013)) % 173.59/173.29 [2402]~E(x24021,x24022)+E(f825(x24023,x24021),f825(x24023,x24022)) % 173.59/173.29 [2403]~E(x24031,x24032)+E(f700(x24031,x24033,x24034,x24035,x24036),f700(x24032,x24033,x24034,x24035,x24036)) % 173.59/173.29 [2404]~E(x24041,x24042)+E(f700(x24043,x24041,x24044,x24045,x24046),f700(x24043,x24042,x24044,x24045,x24046)) % 173.59/173.29 [2405]~E(x24051,x24052)+E(f700(x24053,x24054,x24051,x24055,x24056),f700(x24053,x24054,x24052,x24055,x24056)) % 173.59/173.29 [2406]~E(x24061,x24062)+E(f700(x24063,x24064,x24065,x24061,x24066),f700(x24063,x24064,x24065,x24062,x24066)) % 173.59/173.29 [2407]~E(x24071,x24072)+E(f700(x24073,x24074,x24075,x24076,x24071),f700(x24073,x24074,x24075,x24076,x24072)) % 173.59/173.29 [2408]~E(x24081,x24082)+E(f852(x24081,x24083),f852(x24082,x24083)) % 173.59/173.29 [2409]~E(x24091,x24092)+E(f852(x24093,x24091),f852(x24093,x24092)) % 173.59/173.29 [2410]~E(x24101,x24102)+E(f558(x24101,x24103,x24104,x24105,x24106,x24107),f558(x24102,x24103,x24104,x24105,x24106,x24107)) % 173.59/173.29 [2411]~E(x24111,x24112)+E(f558(x24113,x24111,x24114,x24115,x24116,x24117),f558(x24113,x24112,x24114,x24115,x24116,x24117)) % 173.59/173.29 [2412]~E(x24121,x24122)+E(f558(x24123,x24124,x24121,x24125,x24126,x24127),f558(x24123,x24124,x24122,x24125,x24126,x24127)) % 173.59/173.29 [2413]~E(x24131,x24132)+E(f558(x24133,x24134,x24135,x24131,x24136,x24137),f558(x24133,x24134,x24135,x24132,x24136,x24137)) % 173.59/173.29 [2414]~E(x24141,x24142)+E(f558(x24143,x24144,x24145,x24146,x24141,x24147),f558(x24143,x24144,x24145,x24146,x24142,x24147)) % 173.59/173.29 [2415]~E(x24151,x24152)+E(f558(x24153,x24154,x24155,x24156,x24157,x24151),f558(x24153,x24154,x24155,x24156,x24157,x24152)) % 173.59/173.29 [2416]~E(x24161,x24162)+E(f38(x24161,x24163,x24164,x24165),f38(x24162,x24163,x24164,x24165)) % 173.59/173.29 [2417]~E(x24171,x24172)+E(f38(x24173,x24171,x24174,x24175),f38(x24173,x24172,x24174,x24175)) % 173.59/173.29 [2418]~E(x24181,x24182)+E(f38(x24183,x24184,x24181,x24185),f38(x24183,x24184,x24182,x24185)) % 173.59/173.29 [2419]~E(x24191,x24192)+E(f38(x24193,x24194,x24195,x24191),f38(x24193,x24194,x24195,x24192)) % 173.59/173.29 [2420]~E(x24201,x24202)+E(f425(x24201,x24203,x24204),f425(x24202,x24203,x24204)) % 173.59/173.29 [2421]~E(x24211,x24212)+E(f425(x24213,x24211,x24214),f425(x24213,x24212,x24214)) % 173.59/173.29 [2422]~E(x24221,x24222)+E(f425(x24223,x24224,x24221),f425(x24223,x24224,x24222)) % 173.59/173.29 [2423]~E(x24231,x24232)+E(f198(x24231,x24233,x24234,x24235),f198(x24232,x24233,x24234,x24235)) % 173.59/173.29 [2424]~E(x24241,x24242)+E(f198(x24243,x24241,x24244,x24245),f198(x24243,x24242,x24244,x24245)) % 173.59/173.29 [2425]~E(x24251,x24252)+E(f198(x24253,x24254,x24251,x24255),f198(x24253,x24254,x24252,x24255)) % 173.59/173.29 [2426]~E(x24261,x24262)+E(f198(x24263,x24264,x24265,x24261),f198(x24263,x24264,x24265,x24262)) % 173.59/173.29 [2427]~E(x24271,x24272)+E(f350(x24271,x24273,x24274),f350(x24272,x24273,x24274)) % 173.59/173.29 [2428]~E(x24281,x24282)+E(f350(x24283,x24281,x24284),f350(x24283,x24282,x24284)) % 173.59/173.29 [2429]~E(x24291,x24292)+E(f350(x24293,x24294,x24291),f350(x24293,x24294,x24292)) % 173.59/173.29 [2430]~E(x24301,x24302)+E(f444(x24301,x24303,x24304),f444(x24302,x24303,x24304)) % 173.59/173.29 [2431]~E(x24311,x24312)+E(f444(x24313,x24311,x24314),f444(x24313,x24312,x24314)) % 173.59/173.29 [2432]~E(x24321,x24322)+E(f444(x24323,x24324,x24321),f444(x24323,x24324,x24322)) % 173.59/173.29 [2433]~E(x24331,x24332)+E(f834(x24331,x24333,x24334,x24335,x24336,x24337,x24338),f834(x24332,x24333,x24334,x24335,x24336,x24337,x24338)) % 173.59/173.29 [2434]~E(x24341,x24342)+E(f834(x24343,x24341,x24344,x24345,x24346,x24347,x24348),f834(x24343,x24342,x24344,x24345,x24346,x24347,x24348)) % 173.59/173.29 [2435]~E(x24351,x24352)+E(f834(x24353,x24354,x24351,x24355,x24356,x24357,x24358),f834(x24353,x24354,x24352,x24355,x24356,x24357,x24358)) % 173.59/173.29 [2436]~E(x24361,x24362)+E(f834(x24363,x24364,x24365,x24361,x24366,x24367,x24368),f834(x24363,x24364,x24365,x24362,x24366,x24367,x24368)) % 173.59/173.29 [2437]~E(x24371,x24372)+E(f834(x24373,x24374,x24375,x24376,x24371,x24377,x24378),f834(x24373,x24374,x24375,x24376,x24372,x24377,x24378)) % 173.59/173.29 [2438]~E(x24381,x24382)+E(f834(x24383,x24384,x24385,x24386,x24387,x24381,x24388),f834(x24383,x24384,x24385,x24386,x24387,x24382,x24388)) % 173.59/173.29 [2439]~E(x24391,x24392)+E(f834(x24393,x24394,x24395,x24396,x24397,x24398,x24391),f834(x24393,x24394,x24395,x24396,x24397,x24398,x24392)) % 173.59/173.29 [2440]~E(x24401,x24402)+E(f703(x24401,x24403,x24404),f703(x24402,x24403,x24404)) % 173.59/173.29 [2441]~E(x24411,x24412)+E(f703(x24413,x24411,x24414),f703(x24413,x24412,x24414)) % 173.59/173.29 [2442]~E(x24421,x24422)+E(f703(x24423,x24424,x24421),f703(x24423,x24424,x24422)) % 173.59/173.29 [2443]~E(x24431,x24432)+E(f641(x24431,x24433,x24434),f641(x24432,x24433,x24434)) % 173.59/173.29 [2444]~E(x24441,x24442)+E(f641(x24443,x24441,x24444),f641(x24443,x24442,x24444)) % 173.59/173.29 [2445]~E(x24451,x24452)+E(f641(x24453,x24454,x24451),f641(x24453,x24454,x24452)) % 173.59/173.29 [2446]~E(x24461,x24462)+E(f470(x24461,x24463,x24464),f470(x24462,x24463,x24464)) % 173.59/173.29 [2447]~E(x24471,x24472)+E(f470(x24473,x24471,x24474),f470(x24473,x24472,x24474)) % 173.59/173.29 [2448]~E(x24481,x24482)+E(f470(x24483,x24484,x24481),f470(x24483,x24484,x24482)) % 173.59/173.29 [2449]~E(x24491,x24492)+E(f412(x24491,x24493,x24494,x24495),f412(x24492,x24493,x24494,x24495)) % 173.59/173.29 [2450]~E(x24501,x24502)+E(f412(x24503,x24501,x24504,x24505),f412(x24503,x24502,x24504,x24505)) % 173.59/173.29 [2451]~E(x24511,x24512)+E(f412(x24513,x24514,x24511,x24515),f412(x24513,x24514,x24512,x24515)) % 173.59/173.29 [2452]~E(x24521,x24522)+E(f412(x24523,x24524,x24525,x24521),f412(x24523,x24524,x24525,x24522)) % 173.59/173.29 [2453]~E(x24531,x24532)+E(f280(x24531,x24533,x24534,x24535),f280(x24532,x24533,x24534,x24535)) % 173.59/173.29 [2454]~E(x24541,x24542)+E(f280(x24543,x24541,x24544,x24545),f280(x24543,x24542,x24544,x24545)) % 173.59/173.29 [2455]~E(x24551,x24552)+E(f280(x24553,x24554,x24551,x24555),f280(x24553,x24554,x24552,x24555)) % 173.59/173.29 [2456]~E(x24561,x24562)+E(f280(x24563,x24564,x24565,x24561),f280(x24563,x24564,x24565,x24562)) % 173.59/173.29 [2457]~E(x24571,x24572)+E(f681(x24571,x24573,x24574,x24575),f681(x24572,x24573,x24574,x24575)) % 173.59/173.29 [2458]~E(x24581,x24582)+E(f681(x24583,x24581,x24584,x24585),f681(x24583,x24582,x24584,x24585)) % 173.59/173.29 [2459]~E(x24591,x24592)+E(f681(x24593,x24594,x24591,x24595),f681(x24593,x24594,x24592,x24595)) % 173.59/173.29 [2460]~E(x24601,x24602)+E(f681(x24603,x24604,x24605,x24601),f681(x24603,x24604,x24605,x24602)) % 173.59/173.29 [2461]~E(x24611,x24612)+E(f277(x24611,x24613),f277(x24612,x24613)) % 173.59/173.29 [2462]~E(x24621,x24622)+E(f277(x24623,x24621),f277(x24623,x24622)) % 173.59/173.29 [2463]~E(x24631,x24632)+E(f582(x24631,x24633,x24634,x24635,x24636),f582(x24632,x24633,x24634,x24635,x24636)) % 173.59/173.29 [2464]~E(x24641,x24642)+E(f582(x24643,x24641,x24644,x24645,x24646),f582(x24643,x24642,x24644,x24645,x24646)) % 173.59/173.29 [2465]~E(x24651,x24652)+E(f582(x24653,x24654,x24651,x24655,x24656),f582(x24653,x24654,x24652,x24655,x24656)) % 173.59/173.29 [2466]~E(x24661,x24662)+E(f582(x24663,x24664,x24665,x24661,x24666),f582(x24663,x24664,x24665,x24662,x24666)) % 173.59/173.29 [2467]~E(x24671,x24672)+E(f582(x24673,x24674,x24675,x24676,x24671),f582(x24673,x24674,x24675,x24676,x24672)) % 173.59/173.29 [2468]~E(x24681,x24682)+E(f207(x24681,x24683,x24684,x24685),f207(x24682,x24683,x24684,x24685)) % 173.59/173.29 [2469]~E(x24691,x24692)+E(f207(x24693,x24691,x24694,x24695),f207(x24693,x24692,x24694,x24695)) % 173.59/173.29 [2470]~E(x24701,x24702)+E(f207(x24703,x24704,x24701,x24705),f207(x24703,x24704,x24702,x24705)) % 173.59/173.29 [2471]~E(x24711,x24712)+E(f207(x24713,x24714,x24715,x24711),f207(x24713,x24714,x24715,x24712)) % 173.59/173.29 [2472]~E(x24721,x24722)+E(f286(x24721,x24723,x24724,x24725),f286(x24722,x24723,x24724,x24725)) % 173.59/173.29 [2473]~E(x24731,x24732)+E(f286(x24733,x24731,x24734,x24735),f286(x24733,x24732,x24734,x24735)) % 173.59/173.29 [2474]~E(x24741,x24742)+E(f286(x24743,x24744,x24741,x24745),f286(x24743,x24744,x24742,x24745)) % 173.59/173.29 [2475]~E(x24751,x24752)+E(f286(x24753,x24754,x24755,x24751),f286(x24753,x24754,x24755,x24752)) % 173.59/173.29 [2476]~E(x24761,x24762)+E(f764(x24761,x24763,x24764),f764(x24762,x24763,x24764)) % 173.59/173.29 [2477]~E(x24771,x24772)+E(f764(x24773,x24771,x24774),f764(x24773,x24772,x24774)) % 173.59/173.29 [2478]~E(x24781,x24782)+E(f764(x24783,x24784,x24781),f764(x24783,x24784,x24782)) % 173.59/173.29 [2479]~E(x24791,x24792)+E(f765(x24791,x24793,x24794),f765(x24792,x24793,x24794)) % 173.59/173.29 [2480]~E(x24801,x24802)+E(f765(x24803,x24801,x24804),f765(x24803,x24802,x24804)) % 173.59/173.29 [2481]~E(x24811,x24812)+E(f765(x24813,x24814,x24811),f765(x24813,x24814,x24812)) % 173.59/173.29 [2482]~E(x24821,x24822)+E(f212(x24821),f212(x24822)) % 173.59/173.29 [2483]~E(x24831,x24832)+E(f591(x24831,x24833),f591(x24832,x24833)) % 173.59/173.29 [2484]~E(x24841,x24842)+E(f591(x24843,x24841),f591(x24843,x24842)) % 173.59/173.29 [2485]~E(x24851,x24852)+E(f831(x24851,x24853,x24854,x24855,x24856,x24857,x24858),f831(x24852,x24853,x24854,x24855,x24856,x24857,x24858)) % 173.59/173.29 [2486]~E(x24861,x24862)+E(f831(x24863,x24861,x24864,x24865,x24866,x24867,x24868),f831(x24863,x24862,x24864,x24865,x24866,x24867,x24868)) % 173.59/173.29 [2487]~E(x24871,x24872)+E(f831(x24873,x24874,x24871,x24875,x24876,x24877,x24878),f831(x24873,x24874,x24872,x24875,x24876,x24877,x24878)) % 173.59/173.29 [2488]~E(x24881,x24882)+E(f831(x24883,x24884,x24885,x24881,x24886,x24887,x24888),f831(x24883,x24884,x24885,x24882,x24886,x24887,x24888)) % 173.59/173.29 [2489]~E(x24891,x24892)+E(f831(x24893,x24894,x24895,x24896,x24891,x24897,x24898),f831(x24893,x24894,x24895,x24896,x24892,x24897,x24898)) % 173.59/173.29 [2490]~E(x24901,x24902)+E(f831(x24903,x24904,x24905,x24906,x24907,x24901,x24908),f831(x24903,x24904,x24905,x24906,x24907,x24902,x24908)) % 173.59/173.29 [2491]~E(x24911,x24912)+E(f831(x24913,x24914,x24915,x24916,x24917,x24918,x24911),f831(x24913,x24914,x24915,x24916,x24917,x24918,x24912)) % 173.59/173.29 [2492]~E(x24921,x24922)+E(f429(x24921,x24923),f429(x24922,x24923)) % 173.59/173.29 [2493]~E(x24931,x24932)+E(f429(x24933,x24931),f429(x24933,x24932)) % 173.59/173.29 [2494]~E(x24941,x24942)+E(f633(x24941,x24943,x24944,x24945),f633(x24942,x24943,x24944,x24945)) % 173.59/173.29 [2495]~E(x24951,x24952)+E(f633(x24953,x24951,x24954,x24955),f633(x24953,x24952,x24954,x24955)) % 173.59/173.29 [2496]~E(x24961,x24962)+E(f633(x24963,x24964,x24961,x24965),f633(x24963,x24964,x24962,x24965)) % 173.59/173.29 [2497]~E(x24971,x24972)+E(f633(x24973,x24974,x24975,x24971),f633(x24973,x24974,x24975,x24972)) % 173.59/173.29 [2498]~E(x24981,x24982)+E(f507(x24981,x24983,x24984,x24985,x24986),f507(x24982,x24983,x24984,x24985,x24986)) % 173.59/173.29 [2499]~E(x24991,x24992)+E(f507(x24993,x24991,x24994,x24995,x24996),f507(x24993,x24992,x24994,x24995,x24996)) % 173.59/173.29 [2500]~E(x25001,x25002)+E(f507(x25003,x25004,x25001,x25005,x25006),f507(x25003,x25004,x25002,x25005,x25006)) % 173.59/173.29 [2501]~E(x25011,x25012)+E(f507(x25013,x25014,x25015,x25011,x25016),f507(x25013,x25014,x25015,x25012,x25016)) % 173.59/173.29 [2502]~E(x25021,x25022)+E(f507(x25023,x25024,x25025,x25026,x25021),f507(x25023,x25024,x25025,x25026,x25022)) % 173.59/173.29 [2503]~E(x25031,x25032)+E(f426(x25031,x25033,x25034),f426(x25032,x25033,x25034)) % 173.59/173.29 [2504]~E(x25041,x25042)+E(f426(x25043,x25041,x25044),f426(x25043,x25042,x25044)) % 173.59/173.29 [2505]~E(x25051,x25052)+E(f426(x25053,x25054,x25051),f426(x25053,x25054,x25052)) % 173.59/173.29 [2506]~E(x25061,x25062)+E(f365(x25061,x25063),f365(x25062,x25063)) % 173.59/173.29 [2507]~E(x25071,x25072)+E(f365(x25073,x25071),f365(x25073,x25072)) % 173.59/173.29 [2508]~E(x25081,x25082)+E(f428(x25081,x25083),f428(x25082,x25083)) % 173.59/173.29 [2509]~E(x25091,x25092)+E(f428(x25093,x25091),f428(x25093,x25092)) % 173.59/173.29 [2510]~E(x25101,x25102)+E(f467(x25101,x25103,x25104),f467(x25102,x25103,x25104)) % 173.59/173.29 [2511]~E(x25111,x25112)+E(f467(x25113,x25111,x25114),f467(x25113,x25112,x25114)) % 173.59/173.29 [2512]~E(x25121,x25122)+E(f467(x25123,x25124,x25121),f467(x25123,x25124,x25122)) % 173.59/173.29 [2513]~E(x25131,x25132)+E(f489(x25131,x25133),f489(x25132,x25133)) % 173.59/173.29 [2514]~E(x25141,x25142)+E(f489(x25143,x25141),f489(x25143,x25142)) % 173.59/173.29 [2515]~E(x25151,x25152)+E(f817(x25151,x25153,x25154,x25155),f817(x25152,x25153,x25154,x25155)) % 173.59/173.29 [2516]~E(x25161,x25162)+E(f817(x25163,x25161,x25164,x25165),f817(x25163,x25162,x25164,x25165)) % 173.59/173.29 [2517]~E(x25171,x25172)+E(f817(x25173,x25174,x25171,x25175),f817(x25173,x25174,x25172,x25175)) % 173.59/173.29 [2518]~E(x25181,x25182)+E(f817(x25183,x25184,x25185,x25181),f817(x25183,x25184,x25185,x25182)) % 173.59/173.29 [2519]~E(x25191,x25192)+E(f478(x25191,x25193,x25194,x25195,x25196,x25197,x25198),f478(x25192,x25193,x25194,x25195,x25196,x25197,x25198)) % 173.59/173.29 [2520]~E(x25201,x25202)+E(f478(x25203,x25201,x25204,x25205,x25206,x25207,x25208),f478(x25203,x25202,x25204,x25205,x25206,x25207,x25208)) % 173.59/173.29 [2521]~E(x25211,x25212)+E(f478(x25213,x25214,x25211,x25215,x25216,x25217,x25218),f478(x25213,x25214,x25212,x25215,x25216,x25217,x25218)) % 173.59/173.29 [2522]~E(x25221,x25222)+E(f478(x25223,x25224,x25225,x25221,x25226,x25227,x25228),f478(x25223,x25224,x25225,x25222,x25226,x25227,x25228)) % 173.59/173.29 [2523]~E(x25231,x25232)+E(f478(x25233,x25234,x25235,x25236,x25231,x25237,x25238),f478(x25233,x25234,x25235,x25236,x25232,x25237,x25238)) % 173.59/173.29 [2524]~E(x25241,x25242)+E(f478(x25243,x25244,x25245,x25246,x25247,x25241,x25248),f478(x25243,x25244,x25245,x25246,x25247,x25242,x25248)) % 173.59/173.29 [2525]~E(x25251,x25252)+E(f478(x25253,x25254,x25255,x25256,x25257,x25258,x25251),f478(x25253,x25254,x25255,x25256,x25257,x25258,x25252)) % 173.59/173.29 [2526]~E(x25261,x25262)+E(f516(x25261,x25263,x25264),f516(x25262,x25263,x25264)) % 173.59/173.29 [2527]~E(x25271,x25272)+E(f516(x25273,x25271,x25274),f516(x25273,x25272,x25274)) % 173.59/173.29 [2528]~E(x25281,x25282)+E(f516(x25283,x25284,x25281),f516(x25283,x25284,x25282)) % 173.59/173.29 [2529]~E(x25291,x25292)+E(f718(x25291,x25293,x25294,x25295),f718(x25292,x25293,x25294,x25295)) % 173.59/173.29 [2530]~E(x25301,x25302)+E(f718(x25303,x25301,x25304,x25305),f718(x25303,x25302,x25304,x25305)) % 173.59/173.29 [2531]~E(x25311,x25312)+E(f718(x25313,x25314,x25311,x25315),f718(x25313,x25314,x25312,x25315)) % 173.59/173.29 [2532]~E(x25321,x25322)+E(f718(x25323,x25324,x25325,x25321),f718(x25323,x25324,x25325,x25322)) % 173.59/173.29 [2533]~E(x25331,x25332)+E(f536(x25331,x25333,x25334,x25335,x25336),f536(x25332,x25333,x25334,x25335,x25336)) % 173.59/173.29 [2534]~E(x25341,x25342)+E(f536(x25343,x25341,x25344,x25345,x25346),f536(x25343,x25342,x25344,x25345,x25346)) % 173.59/173.29 [2535]~E(x25351,x25352)+E(f536(x25353,x25354,x25351,x25355,x25356),f536(x25353,x25354,x25352,x25355,x25356)) % 173.59/173.29 [2536]~E(x25361,x25362)+E(f536(x25363,x25364,x25365,x25361,x25366),f536(x25363,x25364,x25365,x25362,x25366)) % 173.59/173.29 [2537]~E(x25371,x25372)+E(f536(x25373,x25374,x25375,x25376,x25371),f536(x25373,x25374,x25375,x25376,x25372)) % 173.59/173.29 [2538]~E(x25381,x25382)+E(f510(x25381,x25383,x25384,x25385,x25386),f510(x25382,x25383,x25384,x25385,x25386)) % 173.59/173.29 [2539]~E(x25391,x25392)+E(f510(x25393,x25391,x25394,x25395,x25396),f510(x25393,x25392,x25394,x25395,x25396)) % 173.59/173.29 [2540]~E(x25401,x25402)+E(f510(x25403,x25404,x25401,x25405,x25406),f510(x25403,x25404,x25402,x25405,x25406)) % 173.59/173.29 [2541]~E(x25411,x25412)+E(f510(x25413,x25414,x25415,x25411,x25416),f510(x25413,x25414,x25415,x25412,x25416)) % 173.59/173.29 [2542]~E(x25421,x25422)+E(f510(x25423,x25424,x25425,x25426,x25421),f510(x25423,x25424,x25425,x25426,x25422)) % 173.59/173.29 [2543]~E(x25431,x25432)+E(f304(x25431,x25433,x25434),f304(x25432,x25433,x25434)) % 173.59/173.29 [2544]~E(x25441,x25442)+E(f304(x25443,x25441,x25444),f304(x25443,x25442,x25444)) % 173.59/173.29 [2545]~E(x25451,x25452)+E(f304(x25453,x25454,x25451),f304(x25453,x25454,x25452)) % 173.59/173.29 [2546]~E(x25461,x25462)+E(f896(x25461,x25463,x25464,x25465,x25466,x25467,x25468),f896(x25462,x25463,x25464,x25465,x25466,x25467,x25468)) % 173.59/173.29 [2547]~E(x25471,x25472)+E(f896(x25473,x25471,x25474,x25475,x25476,x25477,x25478),f896(x25473,x25472,x25474,x25475,x25476,x25477,x25478)) % 173.59/173.29 [2548]~E(x25481,x25482)+E(f896(x25483,x25484,x25481,x25485,x25486,x25487,x25488),f896(x25483,x25484,x25482,x25485,x25486,x25487,x25488)) % 173.59/173.29 [2549]~E(x25491,x25492)+E(f896(x25493,x25494,x25495,x25491,x25496,x25497,x25498),f896(x25493,x25494,x25495,x25492,x25496,x25497,x25498)) % 173.59/173.29 [2550]~E(x25501,x25502)+E(f896(x25503,x25504,x25505,x25506,x25501,x25507,x25508),f896(x25503,x25504,x25505,x25506,x25502,x25507,x25508)) % 173.59/173.29 [2551]~E(x25511,x25512)+E(f896(x25513,x25514,x25515,x25516,x25517,x25511,x25518),f896(x25513,x25514,x25515,x25516,x25517,x25512,x25518)) % 173.59/173.29 [2552]~E(x25521,x25522)+E(f896(x25523,x25524,x25525,x25526,x25527,x25528,x25521),f896(x25523,x25524,x25525,x25526,x25527,x25528,x25522)) % 173.59/173.29 [2553]~E(x25531,x25532)+E(f209(x25531,x25533,x25534,x25535),f209(x25532,x25533,x25534,x25535)) % 173.59/173.29 [2554]~E(x25541,x25542)+E(f209(x25543,x25541,x25544,x25545),f209(x25543,x25542,x25544,x25545)) % 173.59/173.29 [2555]~E(x25551,x25552)+E(f209(x25553,x25554,x25551,x25555),f209(x25553,x25554,x25552,x25555)) % 173.59/173.29 [2556]~E(x25561,x25562)+E(f209(x25563,x25564,x25565,x25561),f209(x25563,x25564,x25565,x25562)) % 173.59/173.29 [2557]~E(x25571,x25572)+E(f569(x25571),f569(x25572)) % 173.59/173.29 [2558]~E(x25581,x25582)+E(f643(x25581,x25583,x25584,x25585),f643(x25582,x25583,x25584,x25585)) % 173.59/173.29 [2559]~E(x25591,x25592)+E(f643(x25593,x25591,x25594,x25595),f643(x25593,x25592,x25594,x25595)) % 173.59/173.29 [2560]~E(x25601,x25602)+E(f643(x25603,x25604,x25601,x25605),f643(x25603,x25604,x25602,x25605)) % 173.59/173.29 [2561]~E(x25611,x25612)+E(f643(x25613,x25614,x25615,x25611),f643(x25613,x25614,x25615,x25612)) % 173.59/173.29 [2562]~E(x25621,x25622)+E(f673(x25621,x25623,x25624,x25625),f673(x25622,x25623,x25624,x25625)) % 173.59/173.29 [2563]~E(x25631,x25632)+E(f673(x25633,x25631,x25634,x25635),f673(x25633,x25632,x25634,x25635)) % 173.59/173.29 [2564]~E(x25641,x25642)+E(f673(x25643,x25644,x25641,x25645),f673(x25643,x25644,x25642,x25645)) % 173.59/173.29 [2565]~E(x25651,x25652)+E(f673(x25653,x25654,x25655,x25651),f673(x25653,x25654,x25655,x25652)) % 173.59/173.29 [2566]~E(x25661,x25662)+E(f620(x25661,x25663),f620(x25662,x25663)) % 173.59/173.29 [2567]~E(x25671,x25672)+E(f620(x25673,x25671),f620(x25673,x25672)) % 173.59/173.29 [2568]~E(x25681,x25682)+E(f785(x25681,x25683,x25684),f785(x25682,x25683,x25684)) % 173.59/173.29 [2569]~E(x25691,x25692)+E(f785(x25693,x25691,x25694),f785(x25693,x25692,x25694)) % 173.59/173.29 [2570]~E(x25701,x25702)+E(f785(x25703,x25704,x25701),f785(x25703,x25704,x25702)) % 173.59/173.29 [2571]~E(x25711,x25712)+E(f670(x25711,x25713,x25714),f670(x25712,x25713,x25714)) % 173.59/173.29 [2572]~E(x25721,x25722)+E(f670(x25723,x25721,x25724),f670(x25723,x25722,x25724)) % 173.59/173.29 [2573]~E(x25731,x25732)+E(f670(x25733,x25734,x25731),f670(x25733,x25734,x25732)) % 173.59/173.29 [2574]~E(x25741,x25742)+E(f283(x25741,x25743,x25744,x25745),f283(x25742,x25743,x25744,x25745)) % 173.59/173.29 [2575]~E(x25751,x25752)+E(f283(x25753,x25751,x25754,x25755),f283(x25753,x25752,x25754,x25755)) % 173.59/173.29 [2576]~E(x25761,x25762)+E(f283(x25763,x25764,x25761,x25765),f283(x25763,x25764,x25762,x25765)) % 173.59/173.29 [2577]~E(x25771,x25772)+E(f283(x25773,x25774,x25775,x25771),f283(x25773,x25774,x25775,x25772)) % 173.59/173.29 [2578]~E(x25781,x25782)+E(f794(x25781,x25783,x25784,x25785,x25786,x25787,x25788),f794(x25782,x25783,x25784,x25785,x25786,x25787,x25788)) % 173.59/173.29 [2579]~E(x25791,x25792)+E(f794(x25793,x25791,x25794,x25795,x25796,x25797,x25798),f794(x25793,x25792,x25794,x25795,x25796,x25797,x25798)) % 173.59/173.29 [2580]~E(x25801,x25802)+E(f794(x25803,x25804,x25801,x25805,x25806,x25807,x25808),f794(x25803,x25804,x25802,x25805,x25806,x25807,x25808)) % 173.59/173.29 [2581]~E(x25811,x25812)+E(f794(x25813,x25814,x25815,x25811,x25816,x25817,x25818),f794(x25813,x25814,x25815,x25812,x25816,x25817,x25818)) % 173.59/173.29 [2582]~E(x25821,x25822)+E(f794(x25823,x25824,x25825,x25826,x25821,x25827,x25828),f794(x25823,x25824,x25825,x25826,x25822,x25827,x25828)) % 173.59/173.29 [2583]~E(x25831,x25832)+E(f794(x25833,x25834,x25835,x25836,x25837,x25831,x25838),f794(x25833,x25834,x25835,x25836,x25837,x25832,x25838)) % 173.59/173.29 [2584]~E(x25841,x25842)+E(f794(x25843,x25844,x25845,x25846,x25847,x25848,x25841),f794(x25843,x25844,x25845,x25846,x25847,x25848,x25842)) % 173.59/173.29 [2585]~E(x25851,x25852)+E(f884(x25851,x25853,x25854),f884(x25852,x25853,x25854)) % 173.59/173.29 [2586]~E(x25861,x25862)+E(f884(x25863,x25861,x25864),f884(x25863,x25862,x25864)) % 173.59/173.29 [2587]~E(x25871,x25872)+E(f884(x25873,x25874,x25871),f884(x25873,x25874,x25872)) % 173.59/173.29 [2588]~E(x25881,x25882)+E(f430(x25881,x25883),f430(x25882,x25883)) % 173.59/173.29 [2589]~E(x25891,x25892)+E(f430(x25893,x25891),f430(x25893,x25892)) % 173.59/173.29 [2590]~E(x25901,x25902)+E(f100(x25901,x25903,x25904),f100(x25902,x25903,x25904)) % 173.59/173.29 [2591]~E(x25911,x25912)+E(f100(x25913,x25911,x25914),f100(x25913,x25912,x25914)) % 173.59/173.29 [2592]~E(x25921,x25922)+E(f100(x25923,x25924,x25921),f100(x25923,x25924,x25922)) % 173.59/173.29 [2593]~E(x25931,x25932)+E(f744(x25931,x25933,x25934,x25935),f744(x25932,x25933,x25934,x25935)) % 173.59/173.29 [2594]~E(x25941,x25942)+E(f744(x25943,x25941,x25944,x25945),f744(x25943,x25942,x25944,x25945)) % 173.59/173.29 [2595]~E(x25951,x25952)+E(f744(x25953,x25954,x25951,x25955),f744(x25953,x25954,x25952,x25955)) % 173.59/173.29 [2596]~E(x25961,x25962)+E(f744(x25963,x25964,x25965,x25961),f744(x25963,x25964,x25965,x25962)) % 173.59/173.29 [2597]~E(x25971,x25972)+E(f571(x25971),f571(x25972)) % 173.59/173.29 [2598]~E(x25981,x25982)+E(f843(x25981,x25983,x25984,x25985),f843(x25982,x25983,x25984,x25985)) % 173.59/173.29 [2599]~E(x25991,x25992)+E(f843(x25993,x25991,x25994,x25995),f843(x25993,x25992,x25994,x25995)) % 173.59/173.29 [2600]~E(x26001,x26002)+E(f843(x26003,x26004,x26001,x26005),f843(x26003,x26004,x26002,x26005)) % 173.59/173.29 [2601]~E(x26011,x26012)+E(f843(x26013,x26014,x26015,x26011),f843(x26013,x26014,x26015,x26012)) % 173.59/173.29 [2602]~E(x26021,x26022)+E(f745(x26021,x26023,x26024,x26025,x26026),f745(x26022,x26023,x26024,x26025,x26026)) % 173.59/173.29 [2603]~E(x26031,x26032)+E(f745(x26033,x26031,x26034,x26035,x26036),f745(x26033,x26032,x26034,x26035,x26036)) % 173.59/173.29 [2604]~E(x26041,x26042)+E(f745(x26043,x26044,x26041,x26045,x26046),f745(x26043,x26044,x26042,x26045,x26046)) % 173.59/173.29 [2605]~E(x26051,x26052)+E(f745(x26053,x26054,x26055,x26051,x26056),f745(x26053,x26054,x26055,x26052,x26056)) % 173.59/173.29 [2606]~E(x26061,x26062)+E(f745(x26063,x26064,x26065,x26066,x26061),f745(x26063,x26064,x26065,x26066,x26062)) % 173.59/173.29 [2607]~E(x26071,x26072)+E(f640(x26071,x26073,x26074),f640(x26072,x26073,x26074)) % 173.59/173.29 [2608]~E(x26081,x26082)+E(f640(x26083,x26081,x26084),f640(x26083,x26082,x26084)) % 173.59/173.29 [2609]~E(x26091,x26092)+E(f640(x26093,x26094,x26091),f640(x26093,x26094,x26092)) % 173.59/173.29 [2610]~E(x26101,x26102)+E(f496(x26101,x26103,x26104,x26105),f496(x26102,x26103,x26104,x26105)) % 173.59/173.29 [2611]~E(x26111,x26112)+E(f496(x26113,x26111,x26114,x26115),f496(x26113,x26112,x26114,x26115)) % 173.59/173.29 [2612]~E(x26121,x26122)+E(f496(x26123,x26124,x26121,x26125),f496(x26123,x26124,x26122,x26125)) % 173.59/173.29 [2613]~E(x26131,x26132)+E(f496(x26133,x26134,x26135,x26131),f496(x26133,x26134,x26135,x26132)) % 173.59/173.29 [2614]~E(x26141,x26142)+E(f771(x26141,x26143,x26144,x26145),f771(x26142,x26143,x26144,x26145)) % 173.59/173.29 [2615]~E(x26151,x26152)+E(f771(x26153,x26151,x26154,x26155),f771(x26153,x26152,x26154,x26155)) % 173.59/173.29 [2616]~E(x26161,x26162)+E(f771(x26163,x26164,x26161,x26165),f771(x26163,x26164,x26162,x26165)) % 173.59/173.29 [2617]~E(x26171,x26172)+E(f771(x26173,x26174,x26175,x26171),f771(x26173,x26174,x26175,x26172)) % 173.59/173.29 [2618]~E(x26181,x26182)+E(f678(x26181,x26183,x26184,x26185,x26186,x26187),f678(x26182,x26183,x26184,x26185,x26186,x26187)) % 173.59/173.29 [2619]~E(x26191,x26192)+E(f678(x26193,x26191,x26194,x26195,x26196,x26197),f678(x26193,x26192,x26194,x26195,x26196,x26197)) % 173.59/173.29 [2620]~E(x26201,x26202)+E(f678(x26203,x26204,x26201,x26205,x26206,x26207),f678(x26203,x26204,x26202,x26205,x26206,x26207)) % 173.59/173.29 [2621]~E(x26211,x26212)+E(f678(x26213,x26214,x26215,x26211,x26216,x26217),f678(x26213,x26214,x26215,x26212,x26216,x26217)) % 173.59/173.29 [2622]~E(x26221,x26222)+E(f678(x26223,x26224,x26225,x26226,x26221,x26227),f678(x26223,x26224,x26225,x26226,x26222,x26227)) % 173.59/173.29 [2623]~E(x26231,x26232)+E(f678(x26233,x26234,x26235,x26236,x26237,x26231),f678(x26233,x26234,x26235,x26236,x26237,x26232)) % 173.59/173.29 [2624]~E(x26241,x26242)+E(f450(x26241,x26243),f450(x26242,x26243)) % 173.59/173.29 [2625]~E(x26251,x26252)+E(f450(x26253,x26251),f450(x26253,x26252)) % 173.59/173.29 [2626]~E(x26261,x26262)+E(f448(x26261,x26263,x26264,x26265,x26266),f448(x26262,x26263,x26264,x26265,x26266)) % 173.59/173.29 [2627]~E(x26271,x26272)+E(f448(x26273,x26271,x26274,x26275,x26276),f448(x26273,x26272,x26274,x26275,x26276)) % 173.59/173.29 [2628]~E(x26281,x26282)+E(f448(x26283,x26284,x26281,x26285,x26286),f448(x26283,x26284,x26282,x26285,x26286)) % 173.59/173.29 [2629]~E(x26291,x26292)+E(f448(x26293,x26294,x26295,x26291,x26296),f448(x26293,x26294,x26295,x26292,x26296)) % 173.59/173.29 [2630]~E(x26301,x26302)+E(f448(x26303,x26304,x26305,x26306,x26301),f448(x26303,x26304,x26305,x26306,x26302)) % 173.59/173.29 [2631]~E(x26311,x26312)+E(f750(x26311,x26313,x26314),f750(x26312,x26313,x26314)) % 173.59/173.29 [2632]~E(x26321,x26322)+E(f750(x26323,x26321,x26324),f750(x26323,x26322,x26324)) % 173.59/173.29 [2633]~E(x26331,x26332)+E(f750(x26333,x26334,x26331),f750(x26333,x26334,x26332)) % 173.59/173.29 [2634]~E(x26341,x26342)+E(f611(x26341,x26343,x26344,x26345,x26346),f611(x26342,x26343,x26344,x26345,x26346)) % 173.59/173.29 [2635]~E(x26351,x26352)+E(f611(x26353,x26351,x26354,x26355,x26356),f611(x26353,x26352,x26354,x26355,x26356)) % 173.59/173.29 [2636]~E(x26361,x26362)+E(f611(x26363,x26364,x26361,x26365,x26366),f611(x26363,x26364,x26362,x26365,x26366)) % 173.59/173.29 [2637]~E(x26371,x26372)+E(f611(x26373,x26374,x26375,x26371,x26376),f611(x26373,x26374,x26375,x26372,x26376)) % 173.59/173.29 [2638]~E(x26381,x26382)+E(f611(x26383,x26384,x26385,x26386,x26381),f611(x26383,x26384,x26385,x26386,x26382)) % 173.59/173.29 [2639]~E(x26391,x26392)+E(f885(x26391,x26393,x26394),f885(x26392,x26393,x26394)) % 173.59/173.29 [2640]~E(x26401,x26402)+E(f885(x26403,x26401,x26404),f885(x26403,x26402,x26404)) % 173.59/173.29 [2641]~E(x26411,x26412)+E(f885(x26413,x26414,x26411),f885(x26413,x26414,x26412)) % 173.59/173.29 [2642]~E(x26421,x26422)+E(f498(x26421,x26423,x26424,x26425,x26426,x26427,x26428),f498(x26422,x26423,x26424,x26425,x26426,x26427,x26428)) % 173.59/173.29 [2643]~E(x26431,x26432)+E(f498(x26433,x26431,x26434,x26435,x26436,x26437,x26438),f498(x26433,x26432,x26434,x26435,x26436,x26437,x26438)) % 173.59/173.29 [2644]~E(x26441,x26442)+E(f498(x26443,x26444,x26441,x26445,x26446,x26447,x26448),f498(x26443,x26444,x26442,x26445,x26446,x26447,x26448)) % 173.59/173.29 [2645]~E(x26451,x26452)+E(f498(x26453,x26454,x26455,x26451,x26456,x26457,x26458),f498(x26453,x26454,x26455,x26452,x26456,x26457,x26458)) % 173.59/173.29 [2646]~E(x26461,x26462)+E(f498(x26463,x26464,x26465,x26466,x26461,x26467,x26468),f498(x26463,x26464,x26465,x26466,x26462,x26467,x26468)) % 173.59/173.29 [2647]~E(x26471,x26472)+E(f498(x26473,x26474,x26475,x26476,x26477,x26471,x26478),f498(x26473,x26474,x26475,x26476,x26477,x26472,x26478)) % 173.59/173.29 [2648]~E(x26481,x26482)+E(f498(x26483,x26484,x26485,x26486,x26487,x26488,x26481),f498(x26483,x26484,x26485,x26486,x26487,x26488,x26482)) % 173.59/173.29 [2649]~E(x26491,x26492)+E(f842(x26491,x26493,x26494,x26495),f842(x26492,x26493,x26494,x26495)) % 173.59/173.29 [2650]~E(x26501,x26502)+E(f842(x26503,x26501,x26504,x26505),f842(x26503,x26502,x26504,x26505)) % 173.59/173.29 [2651]~E(x26511,x26512)+E(f842(x26513,x26514,x26511,x26515),f842(x26513,x26514,x26512,x26515)) % 173.59/173.29 [2652]~E(x26521,x26522)+E(f842(x26523,x26524,x26525,x26521),f842(x26523,x26524,x26525,x26522)) % 173.59/173.29 [2653]~E(x26531,x26532)+E(f689(x26531,x26533,x26534,x26535),f689(x26532,x26533,x26534,x26535)) % 173.59/173.29 [2654]~E(x26541,x26542)+E(f689(x26543,x26541,x26544,x26545),f689(x26543,x26542,x26544,x26545)) % 173.59/173.29 [2655]~E(x26551,x26552)+E(f689(x26553,x26554,x26551,x26555),f689(x26553,x26554,x26552,x26555)) % 173.59/173.29 [2656]~E(x26561,x26562)+E(f689(x26563,x26564,x26565,x26561),f689(x26563,x26564,x26565,x26562)) % 173.59/173.29 [2657]~E(x26571,x26572)+E(f702(x26571,x26573,x26574),f702(x26572,x26573,x26574)) % 173.59/173.29 [2658]~E(x26581,x26582)+E(f702(x26583,x26581,x26584),f702(x26583,x26582,x26584)) % 173.59/173.29 [2659]~E(x26591,x26592)+E(f702(x26593,x26594,x26591),f702(x26593,x26594,x26592)) % 173.59/173.29 [2660]~E(x26601,x26602)+E(f784(x26601,x26603,x26604),f784(x26602,x26603,x26604)) % 173.59/173.29 [2661]~E(x26611,x26612)+E(f784(x26613,x26611,x26614),f784(x26613,x26612,x26614)) % 173.59/173.29 [2662]~E(x26621,x26622)+E(f784(x26623,x26624,x26621),f784(x26623,x26624,x26622)) % 173.59/173.29 [2663]~E(x26631,x26632)+E(f860(x26631,x26633,x26634),f860(x26632,x26633,x26634)) % 173.59/173.29 [2664]~E(x26641,x26642)+E(f860(x26643,x26641,x26644),f860(x26643,x26642,x26644)) % 173.59/173.29 [2665]~E(x26651,x26652)+E(f860(x26653,x26654,x26651),f860(x26653,x26654,x26652)) % 173.59/173.29 [2666]~E(x26661,x26662)+E(f892(x26661,x26663,x26664,x26665),f892(x26662,x26663,x26664,x26665)) % 173.59/173.29 [2667]~E(x26671,x26672)+E(f892(x26673,x26671,x26674,x26675),f892(x26673,x26672,x26674,x26675)) % 173.59/173.29 [2668]~E(x26681,x26682)+E(f892(x26683,x26684,x26681,x26685),f892(x26683,x26684,x26682,x26685)) % 173.59/173.29 [2669]~E(x26691,x26692)+E(f892(x26693,x26694,x26695,x26691),f892(x26693,x26694,x26695,x26692)) % 173.59/173.29 [2670]~E(x26701,x26702)+E(f878(x26701,x26703,x26704,x26705,x26706),f878(x26702,x26703,x26704,x26705,x26706)) % 173.59/173.29 [2671]~E(x26711,x26712)+E(f878(x26713,x26711,x26714,x26715,x26716),f878(x26713,x26712,x26714,x26715,x26716)) % 173.59/173.29 [2672]~E(x26721,x26722)+E(f878(x26723,x26724,x26721,x26725,x26726),f878(x26723,x26724,x26722,x26725,x26726)) % 173.59/173.29 [2673]~E(x26731,x26732)+E(f878(x26733,x26734,x26735,x26731,x26736),f878(x26733,x26734,x26735,x26732,x26736)) % 173.59/173.29 [2674]~E(x26741,x26742)+E(f878(x26743,x26744,x26745,x26746,x26741),f878(x26743,x26744,x26745,x26746,x26742)) % 173.59/173.29 [2675]~E(x26751,x26752)+E(f806(x26751,x26753,x26754),f806(x26752,x26753,x26754)) % 173.59/173.29 [2676]~E(x26761,x26762)+E(f806(x26763,x26761,x26764),f806(x26763,x26762,x26764)) % 173.59/173.29 [2677]~E(x26771,x26772)+E(f806(x26773,x26774,x26771),f806(x26773,x26774,x26772)) % 173.59/173.29 [2678]~E(x26781,x26782)+E(f491(x26781,x26783,x26784,x26785,x26786),f491(x26782,x26783,x26784,x26785,x26786)) % 173.59/173.29 [2679]~E(x26791,x26792)+E(f491(x26793,x26791,x26794,x26795,x26796),f491(x26793,x26792,x26794,x26795,x26796)) % 173.59/173.29 [2680]~E(x26801,x26802)+E(f491(x26803,x26804,x26801,x26805,x26806),f491(x26803,x26804,x26802,x26805,x26806)) % 173.59/173.29 [2681]~E(x26811,x26812)+E(f491(x26813,x26814,x26815,x26811,x26816),f491(x26813,x26814,x26815,x26812,x26816)) % 173.59/173.29 [2682]~E(x26821,x26822)+E(f491(x26823,x26824,x26825,x26826,x26821),f491(x26823,x26824,x26825,x26826,x26822)) % 173.59/173.29 [2683]~E(x26831,x26832)+E(f243(x26831,x26833,x26834,x26835),f243(x26832,x26833,x26834,x26835)) % 173.59/173.29 [2684]~E(x26841,x26842)+E(f243(x26843,x26841,x26844,x26845),f243(x26843,x26842,x26844,x26845)) % 173.59/173.29 [2685]~E(x26851,x26852)+E(f243(x26853,x26854,x26851,x26855),f243(x26853,x26854,x26852,x26855)) % 173.59/173.29 [2686]~E(x26861,x26862)+E(f243(x26863,x26864,x26865,x26861),f243(x26863,x26864,x26865,x26862)) % 173.59/173.29 [2687]~E(x26871,x26872)+E(f714(x26871,x26873,x26874,x26875),f714(x26872,x26873,x26874,x26875)) % 173.59/173.29 [2688]~E(x26881,x26882)+E(f714(x26883,x26881,x26884,x26885),f714(x26883,x26882,x26884,x26885)) % 173.59/173.29 [2689]~E(x26891,x26892)+E(f714(x26893,x26894,x26891,x26895),f714(x26893,x26894,x26892,x26895)) % 173.59/173.29 [2690]~E(x26901,x26902)+E(f714(x26903,x26904,x26905,x26901),f714(x26903,x26904,x26905,x26902)) % 173.59/173.29 [2691]~E(x26911,x26912)+E(f359(x26911,x26913,x26914,x26915,x26916),f359(x26912,x26913,x26914,x26915,x26916)) % 173.59/173.29 [2692]~E(x26921,x26922)+E(f359(x26923,x26921,x26924,x26925,x26926),f359(x26923,x26922,x26924,x26925,x26926)) % 173.59/173.29 [2693]~E(x26931,x26932)+E(f359(x26933,x26934,x26931,x26935,x26936),f359(x26933,x26934,x26932,x26935,x26936)) % 173.59/173.29 [2694]~E(x26941,x26942)+E(f359(x26943,x26944,x26945,x26941,x26946),f359(x26943,x26944,x26945,x26942,x26946)) % 173.59/173.29 [2695]~E(x26951,x26952)+E(f359(x26953,x26954,x26955,x26956,x26951),f359(x26953,x26954,x26955,x26956,x26952)) % 173.59/173.29 [2696]~E(x26961,x26962)+E(f874(x26961,x26963,x26964,x26965,x26966,x26967),f874(x26962,x26963,x26964,x26965,x26966,x26967)) % 173.59/173.29 [2697]~E(x26971,x26972)+E(f874(x26973,x26971,x26974,x26975,x26976,x26977),f874(x26973,x26972,x26974,x26975,x26976,x26977)) % 173.59/173.29 [2698]~E(x26981,x26982)+E(f874(x26983,x26984,x26981,x26985,x26986,x26987),f874(x26983,x26984,x26982,x26985,x26986,x26987)) % 173.59/173.29 [2699]~E(x26991,x26992)+E(f874(x26993,x26994,x26995,x26991,x26996,x26997),f874(x26993,x26994,x26995,x26992,x26996,x26997)) % 173.59/173.29 [2700]~E(x27001,x27002)+E(f874(x27003,x27004,x27005,x27006,x27001,x27007),f874(x27003,x27004,x27005,x27006,x27002,x27007)) % 173.59/173.29 [2701]~E(x27011,x27012)+E(f874(x27013,x27014,x27015,x27016,x27017,x27011),f874(x27013,x27014,x27015,x27016,x27017,x27012)) % 173.59/173.29 [2702]~E(x27021,x27022)+E(f216(x27021),f216(x27022)) % 173.59/173.29 [2703]~E(x27031,x27032)+E(f515(x27031,x27033,x27034),f515(x27032,x27033,x27034)) % 173.59/173.29 [2704]~E(x27041,x27042)+E(f515(x27043,x27041,x27044),f515(x27043,x27042,x27044)) % 173.59/173.29 [2705]~E(x27051,x27052)+E(f515(x27053,x27054,x27051),f515(x27053,x27054,x27052)) % 173.59/173.29 [2706]~E(x27061,x27062)+E(f506(x27061,x27063,x27064,x27065,x27066),f506(x27062,x27063,x27064,x27065,x27066)) % 173.59/173.29 [2707]~E(x27071,x27072)+E(f506(x27073,x27071,x27074,x27075,x27076),f506(x27073,x27072,x27074,x27075,x27076)) % 173.59/173.29 [2708]~E(x27081,x27082)+E(f506(x27083,x27084,x27081,x27085,x27086),f506(x27083,x27084,x27082,x27085,x27086)) % 173.59/173.29 [2709]~E(x27091,x27092)+E(f506(x27093,x27094,x27095,x27091,x27096),f506(x27093,x27094,x27095,x27092,x27096)) % 173.59/173.29 [2710]~E(x27101,x27102)+E(f506(x27103,x27104,x27105,x27106,x27101),f506(x27103,x27104,x27105,x27106,x27102)) % 173.59/173.29 [2711]~E(x27111,x27112)+E(f646(x27111,x27113,x27114),f646(x27112,x27113,x27114)) % 173.59/173.29 [2712]~E(x27121,x27122)+E(f646(x27123,x27121,x27124),f646(x27123,x27122,x27124)) % 173.59/173.29 [2713]~E(x27131,x27132)+E(f646(x27133,x27134,x27131),f646(x27133,x27134,x27132)) % 173.59/173.29 [2714]~E(x27141,x27142)+E(f237(x27141,x27143,x27144,x27145,x27146),f237(x27142,x27143,x27144,x27145,x27146)) % 173.59/173.29 [2715]~E(x27151,x27152)+E(f237(x27153,x27151,x27154,x27155,x27156),f237(x27153,x27152,x27154,x27155,x27156)) % 173.59/173.29 [2716]~E(x27161,x27162)+E(f237(x27163,x27164,x27161,x27165,x27166),f237(x27163,x27164,x27162,x27165,x27166)) % 173.59/173.29 [2717]~E(x27171,x27172)+E(f237(x27173,x27174,x27175,x27171,x27176),f237(x27173,x27174,x27175,x27172,x27176)) % 173.59/173.29 [2718]~E(x27181,x27182)+E(f237(x27183,x27184,x27185,x27186,x27181),f237(x27183,x27184,x27185,x27186,x27182)) % 173.59/173.29 [2719]~E(x27191,x27192)+E(f48(x27191),f48(x27192)) % 173.59/173.29 [2720]~E(x27201,x27202)+E(f693(x27201,x27203,x27204,x27205),f693(x27202,x27203,x27204,x27205)) % 173.59/173.29 [2721]~E(x27211,x27212)+E(f693(x27213,x27211,x27214,x27215),f693(x27213,x27212,x27214,x27215)) % 173.59/173.29 [2722]~E(x27221,x27222)+E(f693(x27223,x27224,x27221,x27225),f693(x27223,x27224,x27222,x27225)) % 173.59/173.29 [2723]~E(x27231,x27232)+E(f693(x27233,x27234,x27235,x27231),f693(x27233,x27234,x27235,x27232)) % 173.59/173.29 [2724]~E(x27241,x27242)+E(f891(x27241,x27243),f891(x27242,x27243)) % 173.59/173.29 [2725]~E(x27251,x27252)+E(f891(x27253,x27251),f891(x27253,x27252)) % 173.59/173.29 [2726]~E(x27261,x27262)+E(f104(x27261,x27263,x27264),f104(x27262,x27263,x27264)) % 173.59/173.29 [2727]~E(x27271,x27272)+E(f104(x27273,x27271,x27274),f104(x27273,x27272,x27274)) % 173.59/173.29 [2728]~E(x27281,x27282)+E(f104(x27283,x27284,x27281),f104(x27283,x27284,x27282)) % 173.59/173.29 [2729]~E(x27291,x27292)+E(f585(x27291,x27293),f585(x27292,x27293)) % 173.59/173.29 [2730]~E(x27301,x27302)+E(f585(x27303,x27301),f585(x27303,x27302)) % 173.59/173.29 [2731]~E(x27311,x27312)+E(f452(x27311,x27313,x27314),f452(x27312,x27313,x27314)) % 173.59/173.29 [2732]~E(x27321,x27322)+E(f452(x27323,x27321,x27324),f452(x27323,x27322,x27324)) % 173.59/173.29 [2733]~E(x27331,x27332)+E(f452(x27333,x27334,x27331),f452(x27333,x27334,x27332)) % 173.59/173.29 [2734]~E(x27341,x27342)+E(f795(x27341,x27343,x27344,x27345,x27346,x27347,x27348),f795(x27342,x27343,x27344,x27345,x27346,x27347,x27348)) % 173.59/173.29 [2735]~E(x27351,x27352)+E(f795(x27353,x27351,x27354,x27355,x27356,x27357,x27358),f795(x27353,x27352,x27354,x27355,x27356,x27357,x27358)) % 173.59/173.29 [2736]~E(x27361,x27362)+E(f795(x27363,x27364,x27361,x27365,x27366,x27367,x27368),f795(x27363,x27364,x27362,x27365,x27366,x27367,x27368)) % 173.59/173.29 [2737]~E(x27371,x27372)+E(f795(x27373,x27374,x27375,x27371,x27376,x27377,x27378),f795(x27373,x27374,x27375,x27372,x27376,x27377,x27378)) % 173.59/173.29 [2738]~E(x27381,x27382)+E(f795(x27383,x27384,x27385,x27386,x27381,x27387,x27388),f795(x27383,x27384,x27385,x27386,x27382,x27387,x27388)) % 173.59/173.29 [2739]~E(x27391,x27392)+E(f795(x27393,x27394,x27395,x27396,x27397,x27391,x27398),f795(x27393,x27394,x27395,x27396,x27397,x27392,x27398)) % 173.59/173.29 [2740]~E(x27401,x27402)+E(f795(x27403,x27404,x27405,x27406,x27407,x27408,x27401),f795(x27403,x27404,x27405,x27406,x27407,x27408,x27402)) % 173.59/173.29 [2741]~E(x27411,x27412)+E(f50(x27411),f50(x27412)) % 173.59/173.29 [2742]~E(x27421,x27422)+E(f357(x27421,x27423,x27424),f357(x27422,x27423,x27424)) % 173.59/173.29 [2743]~E(x27431,x27432)+E(f357(x27433,x27431,x27434),f357(x27433,x27432,x27434)) % 173.59/173.29 [2744]~E(x27441,x27442)+E(f357(x27443,x27444,x27441),f357(x27443,x27444,x27442)) % 173.59/173.29 [2745]~E(x27451,x27452)+E(f847(x27451,x27453),f847(x27452,x27453)) % 173.59/173.29 [2746]~E(x27461,x27462)+E(f847(x27463,x27461),f847(x27463,x27462)) % 173.59/173.29 [2747]~E(x27471,x27472)+E(f486(x27471,x27473,x27474,x27475,x27476),f486(x27472,x27473,x27474,x27475,x27476)) % 173.59/173.29 [2748]~E(x27481,x27482)+E(f486(x27483,x27481,x27484,x27485,x27486),f486(x27483,x27482,x27484,x27485,x27486)) % 173.59/173.29 [2749]~E(x27491,x27492)+E(f486(x27493,x27494,x27491,x27495,x27496),f486(x27493,x27494,x27492,x27495,x27496)) % 173.59/173.29 [2750]~E(x27501,x27502)+E(f486(x27503,x27504,x27505,x27501,x27506),f486(x27503,x27504,x27505,x27502,x27506)) % 173.59/173.29 [2751]~E(x27511,x27512)+E(f486(x27513,x27514,x27515,x27516,x27511),f486(x27513,x27514,x27515,x27516,x27512)) % 173.59/173.29 [2752]~E(x27521,x27522)+E(f272(x27521,x27523,x27524,x27525,x27526),f272(x27522,x27523,x27524,x27525,x27526)) % 173.59/173.29 [2753]~E(x27531,x27532)+E(f272(x27533,x27531,x27534,x27535,x27536),f272(x27533,x27532,x27534,x27535,x27536)) % 173.59/173.29 [2754]~E(x27541,x27542)+E(f272(x27543,x27544,x27541,x27545,x27546),f272(x27543,x27544,x27542,x27545,x27546)) % 173.59/173.29 [2755]~E(x27551,x27552)+E(f272(x27553,x27554,x27555,x27551,x27556),f272(x27553,x27554,x27555,x27552,x27556)) % 173.59/173.29 [2756]~E(x27561,x27562)+E(f272(x27563,x27564,x27565,x27566,x27561),f272(x27563,x27564,x27565,x27566,x27562)) % 173.59/173.29 [2757]~E(x27571,x27572)+E(f607(x27571,x27573),f607(x27572,x27573)) % 173.59/173.29 [2758]~E(x27581,x27582)+E(f607(x27583,x27581),f607(x27583,x27582)) % 173.59/173.29 [2759]~E(x27591,x27592)+E(f699(x27591,x27593,x27594,x27595,x27596),f699(x27592,x27593,x27594,x27595,x27596)) % 173.59/173.29 [2760]~E(x27601,x27602)+E(f699(x27603,x27601,x27604,x27605,x27606),f699(x27603,x27602,x27604,x27605,x27606)) % 173.59/173.29 [2761]~E(x27611,x27612)+E(f699(x27613,x27614,x27611,x27615,x27616),f699(x27613,x27614,x27612,x27615,x27616)) % 173.59/173.29 [2762]~E(x27621,x27622)+E(f699(x27623,x27624,x27625,x27621,x27626),f699(x27623,x27624,x27625,x27622,x27626)) % 173.59/173.29 [2763]~E(x27631,x27632)+E(f699(x27633,x27634,x27635,x27636,x27631),f699(x27633,x27634,x27635,x27636,x27632)) % 173.59/173.29 [2764]~E(x27641,x27642)+E(f438(x27641),f438(x27642)) % 173.59/173.29 [2765]~E(x27651,x27652)+E(f531(x27651,x27653,x27654),f531(x27652,x27653,x27654)) % 173.59/173.29 [2766]~E(x27661,x27662)+E(f531(x27663,x27661,x27664),f531(x27663,x27662,x27664)) % 173.59/173.29 [2767]~E(x27671,x27672)+E(f531(x27673,x27674,x27671),f531(x27673,x27674,x27672)) % 173.59/173.29 [2768]~E(x27681,x27682)+E(f861(x27681,x27683,x27684,x27685),f861(x27682,x27683,x27684,x27685)) % 173.59/173.29 [2769]~E(x27691,x27692)+E(f861(x27693,x27691,x27694,x27695),f861(x27693,x27692,x27694,x27695)) % 173.59/173.29 [2770]~E(x27701,x27702)+E(f861(x27703,x27704,x27701,x27705),f861(x27703,x27704,x27702,x27705)) % 173.59/173.29 [2771]~E(x27711,x27712)+E(f861(x27713,x27714,x27715,x27711),f861(x27713,x27714,x27715,x27712)) % 173.59/173.29 [2772]~E(x27721,x27722)+E(f618(x27721,x27723,x27724),f618(x27722,x27723,x27724)) % 173.59/173.29 [2773]~E(x27731,x27732)+E(f618(x27733,x27731,x27734),f618(x27733,x27732,x27734)) % 173.59/173.29 [2774]~E(x27741,x27742)+E(f618(x27743,x27744,x27741),f618(x27743,x27744,x27742)) % 173.59/173.29 [2775]~E(x27751,x27752)+E(f609(x27751,x27753,x27754),f609(x27752,x27753,x27754)) % 173.59/173.29 [2776]~E(x27761,x27762)+E(f609(x27763,x27761,x27764),f609(x27763,x27762,x27764)) % 173.59/173.29 [2777]~E(x27771,x27772)+E(f609(x27773,x27774,x27771),f609(x27773,x27774,x27772)) % 173.59/173.29 [2778]~E(x27781,x27782)+E(f532(x27781,x27783,x27784,x27785),f532(x27782,x27783,x27784,x27785)) % 173.59/173.29 [2779]~E(x27791,x27792)+E(f532(x27793,x27791,x27794,x27795),f532(x27793,x27792,x27794,x27795)) % 173.59/173.29 [2780]~E(x27801,x27802)+E(f532(x27803,x27804,x27801,x27805),f532(x27803,x27804,x27802,x27805)) % 173.59/173.29 [2781]~E(x27811,x27812)+E(f532(x27813,x27814,x27815,x27811),f532(x27813,x27814,x27815,x27812)) % 173.59/173.29 [2782]~E(x27821,x27822)+E(f240(x27821,x27823,x27824),f240(x27822,x27823,x27824)) % 173.59/173.29 [2783]~E(x27831,x27832)+E(f240(x27833,x27831,x27834),f240(x27833,x27832,x27834)) % 173.59/173.29 [2784]~E(x27841,x27842)+E(f240(x27843,x27844,x27841),f240(x27843,x27844,x27842)) % 173.59/173.29 [2785]~E(x27851,x27852)+E(f804(x27851,x27853,x27854),f804(x27852,x27853,x27854)) % 173.59/173.29 [2786]~E(x27861,x27862)+E(f804(x27863,x27861,x27864),f804(x27863,x27862,x27864)) % 173.59/173.29 [2787]~E(x27871,x27872)+E(f804(x27873,x27874,x27871),f804(x27873,x27874,x27872)) % 173.59/173.29 [2788]~E(x27881,x27882)+E(f865(x27881,x27883),f865(x27882,x27883)) % 173.59/173.29 [2789]~E(x27891,x27892)+E(f865(x27893,x27891),f865(x27893,x27892)) % 173.59/173.29 [2790]~P1(x27901)+P1(x27902)+~E(x27901,x27902) % 173.59/173.29 [2791]~P106(x27911)+P106(x27912)+~E(x27911,x27912) % 173.59/173.29 [2792]P26(x27922,x27923,x27924)+~E(x27921,x27922)+~P26(x27921,x27923,x27924) % 173.59/173.29 [2793]P26(x27933,x27932,x27934)+~E(x27931,x27932)+~P26(x27933,x27931,x27934) % 173.59/173.29 [2794]P26(x27943,x27944,x27942)+~E(x27941,x27942)+~P26(x27943,x27944,x27941) % 173.59/173.29 [2795]~P2(x27951)+P2(x27952)+~E(x27951,x27952) % 173.59/173.29 [2796]P61(x27962,x27963)+~E(x27961,x27962)+~P61(x27961,x27963) % 173.59/173.29 [2797]P61(x27973,x27972)+~E(x27971,x27972)+~P61(x27973,x27971) % 173.59/173.29 [2798]P63(x27982,x27983)+~E(x27981,x27982)+~P63(x27981,x27983) % 173.59/173.29 [2799]P63(x27993,x27992)+~E(x27991,x27992)+~P63(x27993,x27991) % 173.59/173.29 [2800]~P3(x28001)+P3(x28002)+~E(x28001,x28002) % 173.59/173.29 [2801]~P101(x28011)+P101(x28012)+~E(x28011,x28012) % 173.59/173.29 [2802]P32(x28022,x28023,x28024)+~E(x28021,x28022)+~P32(x28021,x28023,x28024) % 173.59/173.29 [2803]P32(x28033,x28032,x28034)+~E(x28031,x28032)+~P32(x28033,x28031,x28034) % 173.59/173.29 [2804]P32(x28043,x28044,x28042)+~E(x28041,x28042)+~P32(x28043,x28044,x28041) % 173.59/173.29 [2805]~P119(x28051)+P119(x28052)+~E(x28051,x28052) % 173.59/173.29 [2806]~P102(x28061)+P102(x28062)+~E(x28061,x28062) % 173.59/173.29 [2807]P27(x28072,x28073,x28074,x28075)+~E(x28071,x28072)+~P27(x28071,x28073,x28074,x28075) % 173.59/173.29 [2808]P27(x28083,x28082,x28084,x28085)+~E(x28081,x28082)+~P27(x28083,x28081,x28084,x28085) % 173.59/173.29 [2809]P27(x28093,x28094,x28092,x28095)+~E(x28091,x28092)+~P27(x28093,x28094,x28091,x28095) % 173.59/173.29 [2810]P27(x28103,x28104,x28105,x28102)+~E(x28101,x28102)+~P27(x28103,x28104,x28105,x28101) % 173.59/173.29 [2811]~P8(x28111)+P8(x28112)+~E(x28111,x28112) % 173.59/173.29 [2812]~P99(x28121)+P99(x28122)+~E(x28121,x28122) % 173.59/173.29 [2813]P146(x28132,x28133,x28134)+~E(x28131,x28132)+~P146(x28131,x28133,x28134) % 173.59/173.29 [2814]P146(x28143,x28142,x28144)+~E(x28141,x28142)+~P146(x28143,x28141,x28144) % 173.59/173.29 [2815]P146(x28153,x28154,x28152)+~E(x28151,x28152)+~P146(x28153,x28154,x28151) % 173.59/173.29 [2816]P40(x28162,x28163)+~E(x28161,x28162)+~P40(x28161,x28163) % 173.59/173.29 [2817]P40(x28173,x28172)+~E(x28171,x28172)+~P40(x28173,x28171) % 173.59/173.29 [2818]~P107(x28181)+P107(x28182)+~E(x28181,x28182) % 173.59/173.29 [2819]~P112(x28191)+P112(x28192)+~E(x28191,x28192) % 173.59/173.29 [2820]~P120(x28201)+P120(x28202)+~E(x28201,x28202) % 173.59/173.29 [2821]~P108(x28211)+P108(x28212)+~E(x28211,x28212) % 173.59/173.29 [2822]~P100(x28221)+P100(x28222)+~E(x28221,x28222) % 173.59/173.29 [2823]~P109(x28231)+P109(x28232)+~E(x28231,x28232) % 173.59/173.29 [2824]~P111(x28241)+P111(x28242)+~E(x28241,x28242) % 173.59/173.29 [2825]P46(x28252,x28253)+~E(x28251,x28252)+~P46(x28251,x28253) % 173.59/173.29 [2826]P46(x28263,x28262)+~E(x28261,x28262)+~P46(x28263,x28261) % 173.59/173.29 [2827]P56(x28272,x28273,x28274)+~E(x28271,x28272)+~P56(x28271,x28273,x28274) % 173.59/173.29 [2828]P56(x28283,x28282,x28284)+~E(x28281,x28282)+~P56(x28283,x28281,x28284) % 173.59/173.29 [2829]P56(x28293,x28294,x28292)+~E(x28291,x28292)+~P56(x28293,x28294,x28291) % 173.59/173.29 [2830]~P4(x28301)+P4(x28302)+~E(x28301,x28302) % 173.59/173.29 [2831]~P84(x28311)+P84(x28312)+~E(x28311,x28312) % 173.59/173.29 [2832]~P85(x28321)+P85(x28322)+~E(x28321,x28322) % 173.59/173.29 [2833]~P95(x28331)+P95(x28332)+~E(x28331,x28332) % 173.59/173.29 [2834]~P5(x28341)+P5(x28342)+~E(x28341,x28342) % 173.59/173.29 [2835]~P126(x28351)+P126(x28352)+~E(x28351,x28352) % 173.59/173.29 [2836]~P110(x28361)+P110(x28362)+~E(x28361,x28362) % 173.59/173.29 [2837]~P72(x28371)+P72(x28372)+~E(x28371,x28372) % 173.59/173.29 [2838]P147(x28382,x28383,x28384)+~E(x28381,x28382)+~P147(x28381,x28383,x28384) % 173.59/173.29 [2839]P147(x28393,x28392,x28394)+~E(x28391,x28392)+~P147(x28393,x28391,x28394) % 173.59/173.29 [2840]P147(x28403,x28404,x28402)+~E(x28401,x28402)+~P147(x28403,x28404,x28401) % 173.59/173.29 [2841]P41(x28412,x28413)+~E(x28411,x28412)+~P41(x28411,x28413) % 173.59/173.29 [2842]P41(x28423,x28422)+~E(x28421,x28422)+~P41(x28423,x28421) % 173.59/173.29 [2843]~P64(x28431)+P64(x28432)+~E(x28431,x28432) % 173.59/173.29 [2844]P16(x28442,x28443)+~E(x28441,x28442)+~P16(x28441,x28443) % 173.59/173.29 [2845]P16(x28453,x28452)+~E(x28451,x28452)+~P16(x28453,x28451) % 173.59/173.29 [2846]~P68(x28461)+P68(x28462)+~E(x28461,x28462) % 173.59/173.29 [2847]~P96(x28471)+P96(x28472)+~E(x28471,x28472) % 173.59/173.29 [2848]~P69(x28481)+P69(x28482)+~E(x28481,x28482) % 173.59/173.29 [2849]P38(x28492,x28493,x28494)+~E(x28491,x28492)+~P38(x28491,x28493,x28494) % 173.59/173.29 [2850]P38(x28503,x28502,x28504)+~E(x28501,x28502)+~P38(x28503,x28501,x28504) % 173.59/173.29 [2851]P38(x28513,x28514,x28512)+~E(x28511,x28512)+~P38(x28513,x28514,x28511) % 173.59/173.29 [2852]P20(x28522,x28523,x28524)+~E(x28521,x28522)+~P20(x28521,x28523,x28524) % 173.59/173.29 [2853]P20(x28533,x28532,x28534)+~E(x28531,x28532)+~P20(x28533,x28531,x28534) % 173.59/173.29 [2854]P20(x28543,x28544,x28542)+~E(x28541,x28542)+~P20(x28543,x28544,x28541) % 173.59/173.29 [2855]~P43(x28551)+P43(x28552)+~E(x28551,x28552) % 173.59/173.29 [2856]~P90(x28561)+P90(x28562)+~E(x28561,x28562) % 173.59/173.29 [2857]~P6(x28571)+P6(x28572)+~E(x28571,x28572) % 173.59/173.29 [2858]~P7(x28581)+P7(x28582)+~E(x28581,x28582) % 173.59/173.29 [2859]P47(x28592,x28593)+~E(x28591,x28592)+~P47(x28591,x28593) % 173.59/173.29 [2860]P47(x28603,x28602)+~E(x28601,x28602)+~P47(x28603,x28601) % 173.59/173.29 [2861]~P71(x28611)+P71(x28612)+~E(x28611,x28612) % 173.59/173.29 [2862]~P70(x28621)+P70(x28622)+~E(x28621,x28622) % 173.59/173.29 [2863]~P117(x28631)+P117(x28632)+~E(x28631,x28632) % 173.59/173.29 [2864]~P83(x28641)+P83(x28642)+~E(x28641,x28642) % 173.59/173.29 [2865]~P113(x28651)+P113(x28652)+~E(x28651,x28652) % 173.59/173.29 [2866]~P86(x28661)+P86(x28662)+~E(x28661,x28662) % 173.59/173.29 [2867]P11(x28672,x28673,x28674)+~E(x28671,x28672)+~P11(x28671,x28673,x28674) % 173.59/173.29 [2868]P11(x28683,x28682,x28684)+~E(x28681,x28682)+~P11(x28683,x28681,x28684) % 173.59/173.29 [2869]P11(x28693,x28694,x28692)+~E(x28691,x28692)+~P11(x28693,x28694,x28691) % 173.59/173.29 [2870]P28(x28702,x28703,x28704,x28705,x28706)+~E(x28701,x28702)+~P28(x28701,x28703,x28704,x28705,x28706) % 173.59/173.29 [2871]P28(x28713,x28712,x28714,x28715,x28716)+~E(x28711,x28712)+~P28(x28713,x28711,x28714,x28715,x28716) % 173.59/173.29 [2872]P28(x28723,x28724,x28722,x28725,x28726)+~E(x28721,x28722)+~P28(x28723,x28724,x28721,x28725,x28726) % 173.59/173.29 [2873]P28(x28733,x28734,x28735,x28732,x28736)+~E(x28731,x28732)+~P28(x28733,x28734,x28735,x28731,x28736) % 173.59/173.29 [2874]P28(x28743,x28744,x28745,x28746,x28742)+~E(x28741,x28742)+~P28(x28743,x28744,x28745,x28746,x28741) % 173.59/173.29 [2875]~P66(x28751)+P66(x28752)+~E(x28751,x28752) % 173.59/173.29 [2876]P42(x28762,x28763)+~E(x28761,x28762)+~P42(x28761,x28763) % 173.59/173.29 [2877]P42(x28773,x28772)+~E(x28771,x28772)+~P42(x28773,x28771) % 173.59/173.29 [2878]~P88(x28781)+P88(x28782)+~E(x28781,x28782) % 173.59/173.29 [2879]~P78(x28791)+P78(x28792)+~E(x28791,x28792) % 173.59/173.29 [2880]P29(x28802,x28803)+~E(x28801,x28802)+~P29(x28801,x28803) % 173.59/173.29 [2881]P29(x28813,x28812)+~E(x28811,x28812)+~P29(x28813,x28811) % 173.59/173.29 [2882]~P73(x28821)+P73(x28822)+~E(x28821,x28822) % 173.59/173.29 [2883]P34(x28832,x28833,x28834)+~E(x28831,x28832)+~P34(x28831,x28833,x28834) % 173.59/173.29 [2884]P34(x28843,x28842,x28844)+~E(x28841,x28842)+~P34(x28843,x28841,x28844) % 173.59/173.29 [2885]P34(x28853,x28854,x28852)+~E(x28851,x28852)+~P34(x28853,x28854,x28851) % 173.59/173.29 [2886]P31(x28862,x28863,x28864)+~E(x28861,x28862)+~P31(x28861,x28863,x28864) % 173.59/173.29 [2887]P31(x28873,x28872,x28874)+~E(x28871,x28872)+~P31(x28873,x28871,x28874) % 173.59/173.29 [2888]P31(x28883,x28884,x28882)+~E(x28881,x28882)+~P31(x28883,x28884,x28881) % 173.59/173.29 [2889]~P74(x28891)+P74(x28892)+~E(x28891,x28892) % 173.59/173.29 [2890]P45(x28902,x28903,x28904,x28905,x28906,x28907)+~E(x28901,x28902)+~P45(x28901,x28903,x28904,x28905,x28906,x28907) % 173.59/173.29 [2891]P45(x28913,x28912,x28914,x28915,x28916,x28917)+~E(x28911,x28912)+~P45(x28913,x28911,x28914,x28915,x28916,x28917) % 173.59/173.29 [2892]P45(x28923,x28924,x28922,x28925,x28926,x28927)+~E(x28921,x28922)+~P45(x28923,x28924,x28921,x28925,x28926,x28927) % 173.59/173.29 [2893]P45(x28933,x28934,x28935,x28932,x28936,x28937)+~E(x28931,x28932)+~P45(x28933,x28934,x28935,x28931,x28936,x28937) % 173.59/173.29 [2894]P45(x28943,x28944,x28945,x28946,x28942,x28947)+~E(x28941,x28942)+~P45(x28943,x28944,x28945,x28946,x28941,x28947) % 173.59/173.29 [2895]P45(x28953,x28954,x28955,x28956,x28957,x28952)+~E(x28951,x28952)+~P45(x28953,x28954,x28955,x28956,x28957,x28951) % 173.59/173.29 [2896]~P135(x28961)+P135(x28962)+~E(x28961,x28962) % 173.59/173.29 [2897]~P75(x28971)+P75(x28972)+~E(x28971,x28972) % 173.59/173.29 [2898]~P129(x28981)+P129(x28982)+~E(x28981,x28982) % 173.59/173.29 [2899]~P128(x28991)+P128(x28992)+~E(x28991,x28992) % 173.59/173.29 [2900]~P89(x29001)+P89(x29002)+~E(x29001,x29002) % 173.59/173.29 [2901]P21(x29012,x29013,x29014,x29015)+~E(x29011,x29012)+~P21(x29011,x29013,x29014,x29015) % 173.59/173.29 [2902]P21(x29023,x29022,x29024,x29025)+~E(x29021,x29022)+~P21(x29023,x29021,x29024,x29025) % 173.59/173.29 [2903]P21(x29033,x29034,x29032,x29035)+~E(x29031,x29032)+~P21(x29033,x29034,x29031,x29035) % 173.59/173.29 [2904]P21(x29043,x29044,x29045,x29042)+~E(x29041,x29042)+~P21(x29043,x29044,x29045,x29041) % 173.59/173.29 [2905]P36(x29052,x29053,x29054)+~E(x29051,x29052)+~P36(x29051,x29053,x29054) % 173.59/173.29 [2906]P36(x29063,x29062,x29064)+~E(x29061,x29062)+~P36(x29063,x29061,x29064) % 173.59/173.29 [2907]P36(x29073,x29074,x29072)+~E(x29071,x29072)+~P36(x29073,x29074,x29071) % 173.59/173.29 [2908]~P114(x29081)+P114(x29082)+~E(x29081,x29082) % 173.59/173.29 [2909]~P79(x29091)+P79(x29092)+~E(x29091,x29092) % 173.59/173.29 [2910]~P67(x29101)+P67(x29102)+~E(x29101,x29102) % 173.59/173.29 [2911]~P140(x29111)+P140(x29112)+~E(x29111,x29112) % 173.59/173.29 [2912]P60(x29122,x29123,x29124,x29125,x29126)+~E(x29121,x29122)+~P60(x29121,x29123,x29124,x29125,x29126) % 173.59/173.29 [2913]P60(x29133,x29132,x29134,x29135,x29136)+~E(x29131,x29132)+~P60(x29133,x29131,x29134,x29135,x29136) % 173.59/173.29 [2914]P60(x29143,x29144,x29142,x29145,x29146)+~E(x29141,x29142)+~P60(x29143,x29144,x29141,x29145,x29146) % 173.59/173.29 [2915]P60(x29153,x29154,x29155,x29152,x29156)+~E(x29151,x29152)+~P60(x29153,x29154,x29155,x29151,x29156) % 173.59/173.29 [2916]P60(x29163,x29164,x29165,x29166,x29162)+~E(x29161,x29162)+~P60(x29163,x29164,x29165,x29166,x29161) % 173.59/173.29 [2917]~P9(x29171)+P9(x29172)+~E(x29171,x29172) % 173.59/173.29 [2918]~P139(x29181)+P139(x29182)+~E(x29181,x29182) % 173.59/173.29 [2919]~P144(x29191)+P144(x29192)+~E(x29191,x29192) % 173.59/173.29 [2920]~P115(x29201)+P115(x29202)+~E(x29201,x29202) % 173.59/173.29 [2921]~P81(x29211)+P81(x29212)+~E(x29211,x29212) % 173.59/173.29 [2922]P55(x29222,x29223)+~E(x29221,x29222)+~P55(x29221,x29223) % 173.59/173.29 [2923]P55(x29233,x29232)+~E(x29231,x29232)+~P55(x29233,x29231) % 173.59/173.29 [2924]~P80(x29241)+P80(x29242)+~E(x29241,x29242) % 173.59/173.29 [2925]~P93(x29251)+P93(x29252)+~E(x29251,x29252) % 173.59/173.29 [2926]~P97(x29261)+P97(x29262)+~E(x29261,x29262) % 173.59/173.29 [2927]P17(x29272,x29273,x29274)+~E(x29271,x29272)+~P17(x29271,x29273,x29274) % 173.59/173.29 [2928]P17(x29283,x29282,x29284)+~E(x29281,x29282)+~P17(x29283,x29281,x29284) % 173.59/173.29 [2929]P17(x29293,x29294,x29292)+~E(x29291,x29292)+~P17(x29293,x29294,x29291) % 173.59/173.29 [2930]~P82(x29301)+P82(x29302)+~E(x29301,x29302) % 173.59/173.29 [2931]~P143(x29311)+P143(x29312)+~E(x29311,x29312) % 173.59/173.29 [2932]P30(x29322,x29323)+~E(x29321,x29322)+~P30(x29321,x29323) % 173.59/173.29 [2933]P30(x29333,x29332)+~E(x29331,x29332)+~P30(x29333,x29331) % 173.59/173.29 [2934]~P87(x29341)+P87(x29342)+~E(x29341,x29342) % 173.59/173.29 [2935]P14(x29352,x29353,x29354,x29355)+~E(x29351,x29352)+~P14(x29351,x29353,x29354,x29355) % 173.59/173.29 [2936]P14(x29363,x29362,x29364,x29365)+~E(x29361,x29362)+~P14(x29363,x29361,x29364,x29365) % 173.59/173.29 [2937]P14(x29373,x29374,x29372,x29375)+~E(x29371,x29372)+~P14(x29373,x29374,x29371,x29375) % 173.59/173.29 [2938]P14(x29383,x29384,x29385,x29382)+~E(x29381,x29382)+~P14(x29383,x29384,x29385,x29381) % 173.59/173.29 [2939]~P92(x29391)+P92(x29392)+~E(x29391,x29392) % 173.59/173.29 [2940]~P141(x29401)+P141(x29402)+~E(x29401,x29402) % 173.59/173.29 [2941]~P138(x29411)+P138(x29412)+~E(x29411,x29412) % 173.59/173.29 [2942]P37(x29422,x29423,x29424,x29425,x29426)+~E(x29421,x29422)+~P37(x29421,x29423,x29424,x29425,x29426) % 173.59/173.29 [2943]P37(x29433,x29432,x29434,x29435,x29436)+~E(x29431,x29432)+~P37(x29433,x29431,x29434,x29435,x29436) % 173.59/173.29 [2944]P37(x29443,x29444,x29442,x29445,x29446)+~E(x29441,x29442)+~P37(x29443,x29444,x29441,x29445,x29446) % 173.59/173.29 [2945]P37(x29453,x29454,x29455,x29452,x29456)+~E(x29451,x29452)+~P37(x29453,x29454,x29455,x29451,x29456) % 173.59/173.29 [2946]P37(x29463,x29464,x29465,x29466,x29462)+~E(x29461,x29462)+~P37(x29463,x29464,x29465,x29466,x29461) % 173.59/173.29 [2947]P25(x29472,x29473,x29474,x29475,x29476,x29477)+~E(x29471,x29472)+~P25(x29471,x29473,x29474,x29475,x29476,x29477) % 173.59/173.29 [2948]P25(x29483,x29482,x29484,x29485,x29486,x29487)+~E(x29481,x29482)+~P25(x29483,x29481,x29484,x29485,x29486,x29487) % 173.59/173.29 [2949]P25(x29493,x29494,x29492,x29495,x29496,x29497)+~E(x29491,x29492)+~P25(x29493,x29494,x29491,x29495,x29496,x29497) % 173.59/173.29 [2950]P25(x29503,x29504,x29505,x29502,x29506,x29507)+~E(x29501,x29502)+~P25(x29503,x29504,x29505,x29501,x29506,x29507) % 173.59/173.29 [2951]P25(x29513,x29514,x29515,x29516,x29512,x29517)+~E(x29511,x29512)+~P25(x29513,x29514,x29515,x29516,x29511,x29517) % 173.59/173.29 [2952]P25(x29523,x29524,x29525,x29526,x29527,x29522)+~E(x29521,x29522)+~P25(x29523,x29524,x29525,x29526,x29527,x29521) % 173.59/173.29 [2953]P49(x29532,x29533)+~E(x29531,x29532)+~P49(x29531,x29533) % 173.59/173.29 [2954]P49(x29543,x29542)+~E(x29541,x29542)+~P49(x29543,x29541) % 173.59/173.29 [2955]~P145(x29551)+P145(x29552)+~E(x29551,x29552) % 173.59/173.29 [2956]~P142(x29561)+P142(x29562)+~E(x29561,x29562) % 173.59/173.29 [2957]P15(x29572,x29573,x29574,x29575,x29576,x29577)+~E(x29571,x29572)+~P15(x29571,x29573,x29574,x29575,x29576,x29577) % 173.59/173.29 [2958]P15(x29583,x29582,x29584,x29585,x29586,x29587)+~E(x29581,x29582)+~P15(x29583,x29581,x29584,x29585,x29586,x29587) % 173.59/173.29 [2959]P15(x29593,x29594,x29592,x29595,x29596,x29597)+~E(x29591,x29592)+~P15(x29593,x29594,x29591,x29595,x29596,x29597) % 173.59/173.29 [2960]P15(x29603,x29604,x29605,x29602,x29606,x29607)+~E(x29601,x29602)+~P15(x29603,x29604,x29605,x29601,x29606,x29607) % 173.59/173.29 [2961]P15(x29613,x29614,x29615,x29616,x29612,x29617)+~E(x29611,x29612)+~P15(x29613,x29614,x29615,x29616,x29611,x29617) % 173.59/173.29 [2962]P15(x29623,x29624,x29625,x29626,x29627,x29622)+~E(x29621,x29622)+~P15(x29623,x29624,x29625,x29626,x29627,x29621) % 173.59/173.29 [2963]~P121(x29631)+P121(x29632)+~E(x29631,x29632) % 173.59/173.29 [2964]~P94(x29641)+P94(x29642)+~E(x29641,x29642) % 173.59/173.29 [2965]~P130(x29651)+P130(x29652)+~E(x29651,x29652) % 173.59/173.29 [2966]P35(x29662,x29663,x29664,x29665)+~E(x29661,x29662)+~P35(x29661,x29663,x29664,x29665) % 173.59/173.29 [2967]P35(x29673,x29672,x29674,x29675)+~E(x29671,x29672)+~P35(x29673,x29671,x29674,x29675) % 173.59/173.29 [2968]P35(x29683,x29684,x29682,x29685)+~E(x29681,x29682)+~P35(x29683,x29684,x29681,x29685) % 173.59/173.29 [2969]P35(x29693,x29694,x29695,x29692)+~E(x29691,x29692)+~P35(x29693,x29694,x29695,x29691) % 173.59/173.29 [2970]~P127(x29701)+P127(x29702)+~E(x29701,x29702) % 173.59/173.29 [2971]~P76(x29711)+P76(x29712)+~E(x29711,x29712) % 173.59/173.29 [2972]~P98(x29721)+P98(x29722)+~E(x29721,x29722) % 173.59/173.29 [2973]~P122(x29731)+P122(x29732)+~E(x29731,x29732) % 173.59/173.29 [2974]P18(x29742,x29743,x29744)+~E(x29741,x29742)+~P18(x29741,x29743,x29744) % 173.59/173.29 [2975]P18(x29753,x29752,x29754)+~E(x29751,x29752)+~P18(x29753,x29751,x29754) % 173.59/173.29 [2976]P18(x29763,x29764,x29762)+~E(x29761,x29762)+~P18(x29763,x29764,x29761) % 173.59/173.29 [2977]P13(x29772,x29773,x29774,x29775,x29776)+~E(x29771,x29772)+~P13(x29771,x29773,x29774,x29775,x29776) % 173.59/173.29 [2978]P13(x29783,x29782,x29784,x29785,x29786)+~E(x29781,x29782)+~P13(x29783,x29781,x29784,x29785,x29786) % 173.59/173.29 [2979]P13(x29793,x29794,x29792,x29795,x29796)+~E(x29791,x29792)+~P13(x29793,x29794,x29791,x29795,x29796) % 173.59/173.29 [2980]P13(x29803,x29804,x29805,x29802,x29806)+~E(x29801,x29802)+~P13(x29803,x29804,x29805,x29801,x29806) % 173.59/173.29 [2981]P13(x29813,x29814,x29815,x29816,x29812)+~E(x29811,x29812)+~P13(x29813,x29814,x29815,x29816,x29811) % 173.59/173.29 [2982]P23(x29822,x29823,x29824,x29825,x29826)+~E(x29821,x29822)+~P23(x29821,x29823,x29824,x29825,x29826) % 173.59/173.29 [2983]P23(x29833,x29832,x29834,x29835,x29836)+~E(x29831,x29832)+~P23(x29833,x29831,x29834,x29835,x29836) % 173.59/173.29 [2984]P23(x29843,x29844,x29842,x29845,x29846)+~E(x29841,x29842)+~P23(x29843,x29844,x29841,x29845,x29846) % 173.59/173.29 [2985]P23(x29853,x29854,x29855,x29852,x29856)+~E(x29851,x29852)+~P23(x29853,x29854,x29855,x29851,x29856) % 173.59/173.29 [2986]P23(x29863,x29864,x29865,x29866,x29862)+~E(x29861,x29862)+~P23(x29863,x29864,x29865,x29866,x29861) % 173.59/173.29 [2987]P62(x29872,x29873,x29874,x29875)+~E(x29871,x29872)+~P62(x29871,x29873,x29874,x29875) % 173.59/173.29 [2988]P62(x29883,x29882,x29884,x29885)+~E(x29881,x29882)+~P62(x29883,x29881,x29884,x29885) % 173.59/173.29 [2989]P62(x29893,x29894,x29892,x29895)+~E(x29891,x29892)+~P62(x29893,x29894,x29891,x29895) % 173.59/173.29 [2990]P62(x29903,x29904,x29905,x29902)+~E(x29901,x29902)+~P62(x29903,x29904,x29905,x29901) % 173.59/173.29 [2991]P24(x29912,x29913,x29914,x29915,x29916,x29917)+~E(x29911,x29912)+~P24(x29911,x29913,x29914,x29915,x29916,x29917) % 173.59/173.29 [2992]P24(x29923,x29922,x29924,x29925,x29926,x29927)+~E(x29921,x29922)+~P24(x29923,x29921,x29924,x29925,x29926,x29927) % 173.59/173.29 [2993]P24(x29933,x29934,x29932,x29935,x29936,x29937)+~E(x29931,x29932)+~P24(x29933,x29934,x29931,x29935,x29936,x29937) % 173.59/173.29 [2994]P24(x29943,x29944,x29945,x29942,x29946,x29947)+~E(x29941,x29942)+~P24(x29943,x29944,x29945,x29941,x29946,x29947) % 173.59/173.29 [2995]P24(x29953,x29954,x29955,x29956,x29952,x29957)+~E(x29951,x29952)+~P24(x29953,x29954,x29955,x29956,x29951,x29957) % 173.59/173.29 [2996]P24(x29963,x29964,x29965,x29966,x29967,x29962)+~E(x29961,x29962)+~P24(x29963,x29964,x29965,x29966,x29967,x29961) % 173.59/173.29 [2997]P10(x29972,x29973)+~E(x29971,x29972)+~P10(x29971,x29973) % 173.59/173.29 [2998]P10(x29983,x29982)+~E(x29981,x29982)+~P10(x29983,x29981) % 173.59/173.29 [2999]P59(x29992,x29993,x29994)+~E(x29991,x29992)+~P59(x29991,x29993,x29994) % 173.59/173.29 [3000]P59(x30003,x30002,x30004)+~E(x30001,x30002)+~P59(x30003,x30001,x30004) % 173.59/173.29 [3001]P59(x30013,x30014,x30012)+~E(x30011,x30012)+~P59(x30013,x30014,x30011) % 173.59/173.29 [3002]~P118(x30021)+P118(x30022)+~E(x30021,x30022) % 173.59/173.29 [3003]P53(x30032,x30033)+~E(x30031,x30032)+~P53(x30031,x30033) % 173.59/173.29 [3004]P53(x30043,x30042)+~E(x30041,x30042)+~P53(x30043,x30041) % 173.59/173.29 [3005]~P103(x30051)+P103(x30052)+~E(x30051,x30052) % 173.59/173.29 [3006]~P104(x30061)+P104(x30062)+~E(x30061,x30062) % 173.59/173.29 [3007]~P77(x30071)+P77(x30072)+~E(x30071,x30072) % 173.59/173.29 [3008]P12(x30082,x30083,x30084)+~E(x30081,x30082)+~P12(x30081,x30083,x30084) % 173.59/173.29 [3009]P12(x30093,x30092,x30094)+~E(x30091,x30092)+~P12(x30093,x30091,x30094) % 173.59/173.29 [3010]P12(x30103,x30104,x30102)+~E(x30101,x30102)+~P12(x30103,x30104,x30101) % 173.59/173.29 [3011]P54(x30112,x30113)+~E(x30111,x30112)+~P54(x30111,x30113) % 173.59/173.29 [3012]P54(x30123,x30122)+~E(x30121,x30122)+~P54(x30123,x30121) % 173.59/173.29 [3013]P22(x30132,x30133,x30134,x30135)+~E(x30131,x30132)+~P22(x30131,x30133,x30134,x30135) % 173.59/173.29 [3014]P22(x30143,x30142,x30144,x30145)+~E(x30141,x30142)+~P22(x30143,x30141,x30144,x30145) % 173.59/173.29 [3015]P22(x30153,x30154,x30152,x30155)+~E(x30151,x30152)+~P22(x30153,x30154,x30151,x30155) % 173.59/173.29 [3016]P22(x30163,x30164,x30165,x30162)+~E(x30161,x30162)+~P22(x30163,x30164,x30165,x30161) % 173.59/173.29 [3017]~P48(x30171)+P48(x30172)+~E(x30171,x30172) % 173.59/173.29 [3018]~P137(x30181)+P137(x30182)+~E(x30181,x30182) % 173.59/173.29 [3019]~P39(x30191)+P39(x30192)+~E(x30191,x30192) % 173.59/173.29 [3020]P52(x30202,x30203,x30204,x30205)+~E(x30201,x30202)+~P52(x30201,x30203,x30204,x30205) % 173.59/173.29 [3021]P52(x30213,x30212,x30214,x30215)+~E(x30211,x30212)+~P52(x30213,x30211,x30214,x30215) % 173.59/173.29 [3022]P52(x30223,x30224,x30222,x30225)+~E(x30221,x30222)+~P52(x30223,x30224,x30221,x30225) % 173.59/173.29 [3023]P52(x30233,x30234,x30235,x30232)+~E(x30231,x30232)+~P52(x30233,x30234,x30235,x30231) % 173.59/173.29 [3024]P58(x30242,x30243,x30244)+~E(x30241,x30242)+~P58(x30241,x30243,x30244) % 173.59/173.29 [3025]P58(x30253,x30252,x30254)+~E(x30251,x30252)+~P58(x30253,x30251,x30254) % 173.59/173.29 [3026]P58(x30263,x30264,x30262)+~E(x30261,x30262)+~P58(x30263,x30264,x30261) % 173.59/173.29 [3027]~P134(x30271)+P134(x30272)+~E(x30271,x30272) % 173.59/173.29 [3028]P33(x30282,x30283,x30284)+~E(x30281,x30282)+~P33(x30281,x30283,x30284) % 173.59/173.29 [3029]P33(x30293,x30292,x30294)+~E(x30291,x30292)+~P33(x30293,x30291,x30294) % 173.59/173.29 [3030]P33(x30303,x30304,x30302)+~E(x30301,x30302)+~P33(x30303,x30304,x30301) % 173.59/173.29 [3031]P57(x30312,x30313)+~E(x30311,x30312)+~P57(x30311,x30313) % 173.59/173.29 [3032]P57(x30323,x30322)+~E(x30321,x30322)+~P57(x30323,x30321) % 173.59/173.29 [3033]~P65(x30331)+P65(x30332)+~E(x30331,x30332) % 173.59/173.29 [3034]P19(x30342,x30343,x30344)+~E(x30341,x30342)+~P19(x30341,x30343,x30344) % 173.59/173.29 [3035]P19(x30353,x30352,x30354)+~E(x30351,x30352)+~P19(x30353,x30351,x30354) % 173.59/173.29 [3036]P19(x30363,x30364,x30362)+~E(x30361,x30362)+~P19(x30363,x30364,x30361) % 173.59/173.29 [3037]~P105(x30371)+P105(x30372)+~E(x30371,x30372) % 173.59/173.29 [3038]~P91(x30381)+P91(x30382)+~E(x30381,x30382) % 173.59/173.29 [3039]~P136(x30391)+P136(x30392)+~E(x30391,x30392) % 173.59/173.29 [3040]~P116(x30401)+P116(x30402)+~E(x30401,x30402) % 173.59/173.29 [3041]~P123(x30411)+P123(x30412)+~E(x30411,x30412) % 173.59/173.29 [3042]~P131(x30421)+P131(x30422)+~E(x30421,x30422) % 173.59/173.29 [3043]~P124(x30431)+P124(x30432)+~E(x30431,x30432) % 173.59/173.29 [3044]P51(x30442,x30443,x30444)+~E(x30441,x30442)+~P51(x30441,x30443,x30444) % 173.59/173.29 [3045]P51(x30453,x30452,x30454)+~E(x30451,x30452)+~P51(x30453,x30451,x30454) % 173.59/173.29 [3046]P51(x30463,x30464,x30462)+~E(x30461,x30462)+~P51(x30463,x30464,x30461) % 173.59/173.29 [3047]~P132(x30471)+P132(x30472)+~E(x30471,x30472) % 173.59/173.29 [3048]~P133(x30481)+P133(x30482)+~E(x30481,x30482) % 173.59/173.29 [3049]P50(x30492,x30493,x30494)+~E(x30491,x30492)+~P50(x30491,x30493,x30494) % 173.59/173.29 [3050]P50(x30503,x30502,x30504)+~E(x30501,x30502)+~P50(x30503,x30501,x30504) % 173.59/173.29 [3051]P50(x30513,x30514,x30512)+~E(x30511,x30512)+~P50(x30513,x30514,x30511) % 173.59/173.29 [3052]P44(x30522,x30523,x30524,x30525)+~E(x30521,x30522)+~P44(x30521,x30523,x30524,x30525) % 173.59/173.29 [3053]P44(x30533,x30532,x30534,x30535)+~E(x30531,x30532)+~P44(x30533,x30531,x30534,x30535) % 173.59/173.29 [3054]P44(x30543,x30544,x30542,x30545)+~E(x30541,x30542)+~P44(x30543,x30544,x30541,x30545) % 173.59/173.29 [3055]P44(x30553,x30554,x30555,x30552)+~E(x30551,x30552)+~P44(x30553,x30554,x30555,x30551) % 173.59/173.29 [3056]~P125(x30561)+P125(x30562)+~E(x30561,x30562) % 173.59/173.29 % 173.59/173.29 %------------------------------------------- % 173.59/173.34 cnf(10410,plain, % 173.59/173.34 (E(f32(x104101,x104102,x104103,x104104,x104105,x104106,x104107,x104108,x104109,a25),x104102)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10413,plain, % 173.59/173.34 (~E(f333(a123,x104131),x104131)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10420,plain, % 173.59/173.34 (~E(f333(a123,x104201),x104201)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10427,plain, % 173.59/173.34 (E(f32(x104271,x104272,x104273,x104274,x104275,x104276,x104277,x104278,x104279,a25),x104272)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10434,plain, % 173.59/173.34 (~E(f333(a123,x104341),x104341)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10439,plain, % 173.59/173.34 (~P106(f333(f333(f180(x104391),f124(x104391)),x104392))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10442,plain, % 173.59/173.34 (~P106(f333(f333(f180(x104421),f124(x104421)),x104422))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10445,plain, % 173.59/173.34 (~E(f333(a123,x104451),x104451)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10448,plain, % 173.59/173.34 (~E(f333(a123,x104481),x104481)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10451,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x104511),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(10454,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x104541),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(10471,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x104711)),x104711))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(10474,plain, % 173.59/173.34 (~E(f333(f333(f159(x104741),x104742),x104743),x104743)), % 173.59/173.34 inference(rename_variables,[],[4647])). % 173.59/173.34 cnf(10480,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x104801),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(10483,plain, % 173.59/173.34 (E(f32(x104831,x104832,x104833,x104834,x104835,x104836,x104837,x104838,x104839,a25),x104832)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10486,plain, % 173.59/173.34 (E(f32(x104861,x104862,x104863,x104864,x104865,x104866,x104867,x104868,x104869,a25),x104862)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10493,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x104931),x104932)),x104932))), % 173.59/173.34 inference(rename_variables,[],[4707])). % 173.59/173.34 cnf(10496,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x104961),x104962)),x104962))), % 173.59/173.34 inference(rename_variables,[],[4707])). % 173.59/173.34 cnf(10517,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x105171),x105171))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(10520,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f51(a910,x105201,x105202)),x105201))), % 173.59/173.34 inference(rename_variables,[],[3913])). % 173.59/173.34 cnf(10541,plain, % 173.59/173.34 (E(f333(f41(a910),f333(f289(a910),x105411)),x105411)), % 173.59/173.34 inference(rename_variables,[],[3351])). % 173.59/173.34 cnf(10549,plain, % 173.59/173.34 (~E(f333(a123,x105491),x105491)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10552,plain, % 173.59/173.34 (~E(f333(a123,x105521),x105521)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10555,plain, % 173.59/173.34 (~E(f333(a123,x105551),x105551)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10560,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x105601),f333(a123,x105601)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(10569,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x105691),x105691))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(10576,plain, % 173.59/173.34 (E(f32(x105761,x105762,x105763,x105764,x105765,x105766,x105767,x105768,x105769,a25),x105762)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10579,plain, % 173.59/173.34 (E(f32(x105791,x105792,x105793,x105794,x105795,x105796,x105797,x105798,x105799,a25),x105792)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10602,plain, % 173.59/173.34 (~P106(f333(f333(f180(x106021),f124(x106021)),x106022))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10631,plain, % 173.59/173.34 (~E(f333(f333(f159(x106311),x106312),x106313),x106313)), % 173.59/173.34 inference(rename_variables,[],[4647])). % 173.59/173.34 cnf(10634,plain, % 173.59/173.34 (~E(f333(a123,x106341),f2(a910))), % 173.59/173.34 inference(rename_variables,[],[4634])). % 173.59/173.34 cnf(10645,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x106451),x106451))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(10650,plain, % 173.59/173.34 (~E(f333(a123,x106501),x106501)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10657,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x106571),x106571))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(10670,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x106701),f333(a123,x106701)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(10691,plain, % 173.59/173.34 (~P106(f333(f333(f180(x106911),f124(x106911)),x106912))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10710,plain, % 173.59/173.34 (~P106(f333(f333(f180(x107101),f124(x107101)),x107102))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10717,plain, % 173.59/173.34 (~P106(f333(f333(f180(x107171),f124(x107171)),x107172))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10728,plain, % 173.59/173.34 (~E(f333(a123,x107281),f2(a910))), % 173.59/173.34 inference(rename_variables,[],[4634])). % 173.59/173.34 cnf(10734,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),f2(a910)),f333(a115,f85(a1))))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,4622,10413,10420,10434,10445,10448,10549,10552,10555,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,4236,4712,3371,3821,3524,10560,10670,3439,4687,10451,10454,10480,4700,3896,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,4186,3456,10569,3457,3458,4683,10517,3549,3976,3913,10520,4693,10471,4277,4690,4675,3432,3436,4677,4676,4709,3936,4707,10493,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026])). % 173.59/173.34 cnf(10737,plain, % 173.59/173.34 (~P106(f333(f333(f180(x107371),f124(x107371)),x107372))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10742,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x107421),f333(a123,x107421)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(10745,plain, % 173.59/173.34 (~P106(f333(f333(f180(x107451),f124(x107451)),x107452))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10748,plain, % 173.59/173.34 (~P106(f333(f333(f180(x107481),f124(x107481)),x107482))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10751,plain, % 173.59/173.34 (~P106(f333(f68(x107511,x107512,f196(f917(x107511,a905))),x107513))), % 173.59/173.34 inference(rename_variables,[],[4706])). % 173.59/173.34 cnf(10754,plain, % 173.59/173.34 (~P106(f333(f68(x107541,x107542,f196(f917(x107541,a905))),x107543))), % 173.59/173.34 inference(rename_variables,[],[4706])). % 173.59/173.34 cnf(10757,plain, % 173.59/173.34 (~P106(f333(f333(f196(f917(x107571,f917(x107572,a905))),x107573),x107574))), % 173.59/173.34 inference(rename_variables,[],[4710])). % 173.59/173.34 cnf(10762,plain, % 173.59/173.34 (~P106(f333(f333(f180(x107621),f124(x107621)),x107622))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10773,plain, % 173.59/173.34 (~E(f333(a123,x107731),x107731)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(10791,plain, % 173.59/173.34 (P106(f333(f333(f247(a110),f333(a3,x107911)),f333(a3,f333(a123,x107911))))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,4236,4712,3371,3821,3524,10560,10670,10742,3908,3439,4687,10451,10454,10480,4700,3896,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,4186,3456,10569,3457,3458,4683,10517,3549,3976,3913,10520,4693,10471,4277,4690,4675,3432,3436,4677,4676,4706,10751,4709,4710,3936,4707,10493,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224])). % 173.59/173.34 cnf(10798,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x107981),x107981))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(10801,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x108011),f333(f333(f88(a910),x108011),x108011)))), % 173.59/173.34 inference(rename_variables,[],[3720])). % 173.59/173.34 cnf(10804,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x108041),f333(f333(f88(a910),x108041),x108041)))), % 173.59/173.34 inference(rename_variables,[],[3720])). % 173.59/173.34 cnf(10807,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x108071),f333(a123,f333(f333(f87(a910),x108072),x108071))))), % 173.59/173.34 inference(rename_variables,[],[3906])). % 173.59/173.34 cnf(10812,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x108121),f333(a123,x108121)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(10815,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x108151),f333(a123,x108151)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(10818,plain, % 173.59/173.34 (P106(f333(f333(f335(x108181),x108182),f254(f917(x108181,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(10837,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x108371)),x108371))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(10840,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x108401)),x108401))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(10843,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x108431),x108432)),x108432))), % 173.59/173.34 inference(rename_variables,[],[4707])). % 173.59/173.34 cnf(10846,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x108461),x108462)),x108462))), % 173.59/173.34 inference(rename_variables,[],[4707])). % 173.59/173.34 cnf(10849,plain, % 173.59/173.34 (P106(f333(f254(f917(x108491,a905)),x108492))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(10852,plain, % 173.59/173.34 (E(f333(f41(a910),f333(f289(a910),x108521)),x108521)), % 173.59/173.34 inference(rename_variables,[],[3351])). % 173.59/173.34 cnf(10855,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x108551),f333(a123,x108551)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(10862,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x108621),x108621))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(10867,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x108671),x108671))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(10876,plain, % 173.59/173.34 (E(f32(x108761,x108762,x108763,x108764,x108765,x108766,x108767,x108768,x108769,a25),x108762)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10879,plain, % 173.59/173.34 (P106(f333(f254(f917(x108791,a905)),x108792))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(10882,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x108821))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(10885,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x108851,a905)),f196(f917(x108851,a905))),x108852))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(10888,plain, % 173.59/173.34 (P106(f333(f254(f917(x108881,a905)),x108882))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(10891,plain, % 173.59/173.34 (P106(f333(f254(f917(x108911,a905)),x108912))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(10893,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(f333(f88(a910),f333(a123,x108931)),f333(a123,x108931))),x108931))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,10541,4236,4712,3371,3821,3756,3524,10560,10670,10742,10812,10815,3908,3439,4687,10451,10454,10480,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,4186,3456,10569,10657,10798,3457,3458,10645,4683,10517,3609,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,3477,4277,4690,4675,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,4709,4710,3936,4707,10493,10496,10843,3906,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455])). % 173.59/173.34 cnf(10894,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x108941),f333(f333(f88(a910),x108941),x108941)))), % 173.59/173.34 inference(rename_variables,[],[3720])). % 173.59/173.34 cnf(10898,plain, % 173.59/173.34 (E(f333(f176(x108981),f32(x108982,f333(f333(f142(x108981),f333(f176(x108981),x108983)),f333(f333(f159(x108981),x108984),f124(x108981))),x108985,x108986,x108987,x108988,x108989,x1089810,x1089811,a25)),f333(f333(f159(x108981),x108984),x108983))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,10541,4236,4712,3371,3821,3756,3524,10560,10670,10742,10812,10815,3908,3439,4687,10451,10454,10480,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,4186,3456,10569,10657,10798,3457,3458,10645,4683,10517,3609,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,3477,4277,4690,4675,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,4709,4710,3936,4707,10493,10496,10843,3906,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493])). % 173.59/173.34 cnf(10899,plain, % 173.59/173.34 (E(f32(x108991,x108992,x108993,x108994,x108995,x108996,x108997,x108998,x108999,a25),x108992)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(10903,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,f333(a123,f333(f333(f87(a910),x109031),x109032)))),f333(a123,x109032)))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,10541,4236,4712,3371,3821,3756,3524,10560,10670,10742,10812,10815,10855,3908,3439,4687,10451,10454,10480,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,4186,3456,10569,10657,10798,3457,3458,10645,4683,10517,3609,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,3477,4277,4690,4675,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,4709,4710,3936,4707,10493,10496,10843,3906,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497])). % 173.59/173.34 cnf(10911,plain, % 173.59/173.34 (~P106(f333(f333(f247(a110),f333(a3,x109111)),f333(a3,f2(a910))))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,10541,4236,4712,3371,3821,3756,3524,10560,10670,10742,10812,10815,10855,3908,3439,4687,10451,10454,10480,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,4186,3456,10569,10657,10798,3457,3458,10645,4683,10517,3609,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,4277,4690,4675,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,4709,4710,3936,4707,10493,10496,10843,3906,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502])). % 173.59/173.34 cnf(10936,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x109361),x109361))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(10947,plain, % 173.59/173.34 (~P106(f333(f333(f180(x109471),f124(x109471)),x109472))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(10956,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x109561),f333(a123,x109561)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(10958,plain, % 173.59/173.34 (P106(f333(f333(f247(a1),f333(f333(f23(a1),x109581),f85(a1))),x109581))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,10541,4236,4094,4712,3371,3821,3756,3524,10560,10670,10742,10812,10815,10855,3908,3439,4687,10451,10454,10480,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4186,3456,10569,10657,10798,3457,10936,3458,10645,10867,4683,10517,3609,4696,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,4277,4690,4675,4678,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,4709,4710,3936,4707,10493,10496,10843,3906,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762])). % 173.59/173.34 cnf(10959,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x109591),x109591))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(10964,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x109641),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(10977,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x109771),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(10980,plain, % 173.59/173.34 (~P106(f333(f333(f247(f917(x109801,a905)),x109802),f196(f917(x109801,a905))))), % 173.59/173.34 inference(rename_variables,[],[4704])). % 173.59/173.34 cnf(10983,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x109831),x109831))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(10986,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x109861),x109861))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(11000,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x110001),f333(f333(f23(a910),x110001),x110002)))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,4634,10634,3288,3355,3315,3297,3927,3386,4647,10474,3351,10541,4236,4094,4712,3371,3821,3756,3524,10560,10670,10742,10812,10815,10855,3908,3439,4687,10451,10454,10480,10964,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4198,4186,4704,3456,10569,10657,10798,3457,10936,10983,10986,3458,10645,10867,4683,10517,3609,4696,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,4277,4690,4675,4678,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,4709,4710,3936,4707,10493,10496,10843,3906,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920])). % 173.59/173.34 cnf(11001,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x110011),x110011))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(11010,plain, % 173.59/173.34 (~P106(f333(f333(f335(x110101),x110102),f196(f917(x110101,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11017,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x110171),x110171))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(11020,plain, % 173.59/173.34 (~P106(f333(f333(f335(x110201),x110202),f196(f917(x110201,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11023,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x110231,a905)),f333(f316(x110232,x110231,x110233),f333(f317(x110232,x110231,x110233),x110234))),x110234))), % 173.59/173.34 inference(rename_variables,[],[4333])). % 173.59/173.34 cnf(11030,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x110301,a905)),f333(f180(x110301),f333(f144(x110301,x110302),x110303))),f333(f180(x110301),x110303)))), % 173.59/173.34 inference(rename_variables,[],[4103])). % 173.59/173.34 cnf(11033,plain, % 173.59/173.34 (E(f333(f316(x110331,x110331,f5(x110331)),x110332),x110332)), % 173.59/173.34 inference(rename_variables,[],[3513])). % 173.59/173.34 cnf(11036,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x110361))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(11039,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x110391),x110391))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(11042,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x110421),x110421))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(11051,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x110511),x110511))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(11062,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x110621),f333(f333(f88(a910),x110621),x110621)))), % 173.59/173.34 inference(rename_variables,[],[3720])). % 173.59/173.34 cnf(11068,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x110681),f333(a123,f333(f333(f87(a910),x110682),x110681))))), % 173.59/173.34 inference(rename_variables,[],[3906])). % 173.59/173.34 cnf(11075,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x110751),x110751))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(11078,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x110781),x110781))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(11081,plain, % 173.59/173.34 (~E(f333(a123,x110811),x110811)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11085,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x110851,x110851)),x110852),f313(x110851,f254(f917(f916(x110851,x110851),a905)))))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,4634,10634,3288,3355,3315,3297,3927,3513,3386,4647,10474,3351,10541,4236,4094,4712,3371,3650,3821,3756,3524,10560,10670,10742,10812,10815,10855,10956,3908,3439,4687,10451,10454,10480,10964,10977,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4198,4103,4186,4704,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,4696,11010,11020,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,10882,4277,4690,4675,4678,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,10894,11062,4709,4710,4333,3936,4707,10493,10496,10843,3906,10807,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568])). % 173.59/173.34 cnf(11086,plain, % 173.59/173.34 (P106(f333(f333(f335(x110861),x110862),f254(f917(x110861,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11091,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x110911),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(11106,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x111061))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(11113,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x111131),x111131))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(11122,plain, % 173.59/173.34 (~P106(f333(f333(f335(x111221),x111222),f196(f917(x111221,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11124,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x111241,a905)),f44(f917(x111241,a905),f333(f314(x111241),x111242))),x111242))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,4634,10634,3288,3355,3315,3297,3927,3513,3386,4647,10474,3351,10541,4236,4094,4712,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,3908,3439,4687,10451,10454,10480,10964,10977,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4198,4103,11030,3822,4186,4704,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,4696,11010,11020,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,10894,11062,4709,4710,4333,3936,4707,10493,10496,10843,3906,10807,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896])). % 173.59/173.34 cnf(11130,plain, % 173.59/173.34 (P106(f333(f333(f335(x111301),x111302),f254(f917(x111301,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11133,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x111331),f911(x111331))),f333(f333(f265(f911(x111331),f911(x111331)),x111332),f124(x111331))),f153(x111331,x111333)))), % 173.59/173.34 inference(rename_variables,[],[4712])). % 173.59/173.34 cnf(11139,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(x111391,x111391)),x111392),f253(x111391,f196(f917(x111391,a905)))))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,4634,10634,3288,3355,3315,3297,3927,3513,3386,4647,10474,3351,10541,4236,4094,4712,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,3908,3439,4687,10451,10454,10480,10964,10977,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4198,4103,11030,3822,4186,4704,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,4696,11010,11020,11122,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,10894,11062,4709,4710,4333,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042])). % 173.59/173.34 cnf(11140,plain, % 173.59/173.34 (~P106(f333(f333(f335(x111401),x111402),f196(f917(x111401,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11142,plain, % 173.59/173.34 (~P106(f333(f333(f335(x111421),x111422),f333(f317(x111421,x111423,x111424),f196(f917(x111423,a905)))))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,4634,10634,3288,3355,3315,3297,3927,3513,3386,4647,10474,3351,10541,4236,4094,4712,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,3908,3439,4687,10451,10454,10480,10964,10977,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4198,4103,11030,3822,4186,4704,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,4696,11010,11020,11122,11140,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,3905,3720,10801,10804,10894,11062,4709,4710,4333,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074])). % 173.59/173.34 cnf(11143,plain, % 173.59/173.34 (~P106(f333(f333(f335(x111431),x111432),f196(f917(x111431,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11146,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x111461,a905)),x111462),f333(f333(f315(x111461),x111463),x111462)))), % 173.59/173.34 inference(rename_variables,[],[3903])). % 173.59/173.34 cnf(11149,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x111491),x111491))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(11152,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x111521,a905)),x111522),f333(f333(f315(x111521),x111523),x111522)))), % 173.59/173.34 inference(rename_variables,[],[3903])). % 173.59/173.34 cnf(11155,plain, % 173.59/173.34 (E(f333(f316(x111551,x111551,f5(x111551)),x111552),x111552)), % 173.59/173.34 inference(rename_variables,[],[3513])). % 173.59/173.34 cnf(11157,plain, % 173.59/173.34 (P37(x111571,x111572,x111573,f32(x111574,f124(x111571),x111575,x111576,x111577,x111578,x111579,x1115710,x1115711,a25),f124(x111572))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,10899,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,4634,10634,3288,3355,3315,3297,3927,3513,11033,3386,4647,10474,3351,10541,4236,4094,4712,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,3908,3439,4687,10451,10454,10480,10964,10977,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4198,4103,11030,3822,4186,4704,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,4696,11010,11020,11122,11140,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,3903,11146,3905,3720,10801,10804,10894,11062,4709,4710,4333,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186])). % 173.59/173.34 cnf(11158,plain, % 173.59/173.34 (E(f32(x111581,x111582,x111583,x111584,x111585,x111586,x111587,x111588,x111589,a25),x111582)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11161,plain, % 173.59/173.34 (E(f32(x111611,x111612,x111613,x111614,x111615,x111616,x111617,x111618,x111619,a25),x111612)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11169,plain, % 173.59/173.34 (E(f333(x111691,f860(x111691,x111692,f333(x111691,x111693))),f333(x111691,x111693))), % 173.59/173.34 inference(scs_inference,[],[4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,4634,10634,3288,3355,3315,3297,3927,3513,11033,3386,4647,10474,3351,10541,4236,4094,4712,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,3908,3439,4687,10451,10454,10480,10964,10977,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,4198,4103,11030,3822,4186,4704,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,11130,4696,11010,11020,11122,11140,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,4060,3903,11146,3905,3720,10801,10804,10894,11062,4709,4710,4333,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357])). % 173.59/173.34 cnf(11172,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x111721,a905)),x111722),f333(f333(f315(x111721),x111723),x111722)))), % 173.59/173.34 inference(rename_variables,[],[3903])). % 173.59/173.34 cnf(11185,plain, % 173.59/173.34 (~E(f333(a123,x111851),f2(a910))), % 173.59/173.34 inference(rename_variables,[],[4634])). % 173.59/173.34 cnf(11188,plain, % 173.59/173.34 (~P106(f333(f333(f180(x111881),f124(x111881)),x111882))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(11201,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x112011),f333(a123,x112011)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(11211,plain, % 173.59/173.34 (~E(f333(f316(x112111,f917(x112111,a905),x112112),x112113),f333(f314(x112111),x112113))), % 173.59/173.34 inference(rename_variables,[],[4694])). % 173.59/173.34 cnf(11214,plain, % 173.59/173.34 (~P106(f333(f333(f335(x112141),x112142),f196(f917(x112141,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11217,plain, % 173.59/173.34 (~P106(f333(f333(f335(x112171),x112172),f196(f917(x112171,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11220,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(x112201,x112201)),f333(f333(f265(x112201,x112201),x112202),x112203)),f161(x112201,f124(f917(x112201,a910)))))), % 173.59/173.34 inference(rename_variables,[],[4711])). % 173.59/173.34 cnf(11223,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(x112231,x112231)),f333(f333(f265(x112231,x112231),x112232),x112233)),f161(x112231,f124(f917(x112231,a910)))))), % 173.59/173.34 inference(rename_variables,[],[4711])). % 173.59/173.34 cnf(11228,plain, % 173.59/173.34 (~P106(f333(f333(f335(x112281),x112282),f196(f917(x112281,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11231,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x112311,x112311)),f333(f333(f265(x112311,x112311),x112312),x112312)),f313(x112311,x112313)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(11234,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x112341,a905)),f333(f180(x112341),f184(x112341,x112342,x112343))),f333(f180(x112341),x112342)))), % 173.59/173.34 inference(rename_variables,[],[4152])). % 173.59/173.34 cnf(11237,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x112371,a905)),x112372),f254(f917(x112371,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(11253,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x112531,a905)),f196(f917(x112531,a905))),x112532))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(11264,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x112641),f911(x112641))),f333(f333(f265(f911(x112641),f911(x112641)),x112642),f124(x112641))),f155(x112641,x112643)))), % 173.59/173.34 inference(rename_variables,[],[4713])). % 173.59/173.34 cnf(11275,plain, % 173.59/173.34 (~E(f333(a123,x112751),x112751)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11278,plain, % 173.59/173.34 (~E(f333(a123,x112781),x112781)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11285,plain, % 173.59/173.34 (~E(f333(a123,x112851),f2(a910))), % 173.59/173.34 inference(rename_variables,[],[4634])). % 173.59/173.34 cnf(11290,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x112901,a905)),x112902),x112902))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(11297,plain, % 173.59/173.34 (~E(f333(a123,x112971),x112971)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11300,plain, % 173.59/173.34 (~E(f333(a123,x113001),x113001)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11305,plain, % 173.59/173.34 (P27(x113051,x113051,f5(x113051),x113052)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(11310,plain, % 173.59/173.34 (~E(f333(f316(x113101,f917(x113101,a905),x113102),x113103),f333(f314(x113101),x113103))), % 173.59/173.34 inference(rename_variables,[],[4694])). % 173.59/173.34 cnf(11315,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x113151,a905)),x113152),f254(f917(x113151,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(11331,plain, % 173.59/173.34 (~P106(f333(f333(f335(x113311),x113312),f196(f917(x113311,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11334,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x113341)),x113341))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(11339,plain, % 173.59/173.34 (~P106(f333(f333(f335(x113391),x113392),f196(f917(x113391,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11350,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x113501)),x113501))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(11353,plain, % 173.59/173.34 (~P106(f333(f333(f335(x113531),x113532),f196(f917(x113531,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11366,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x113661,x113661)),f333(f333(f265(x113661,x113661),x113662),x113662)),f313(x113661,x113663)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(11369,plain, % 173.59/173.34 (P106(f333(f333(f335(x113691),x113692),f254(f917(x113691,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11372,plain, % 173.59/173.34 (P106(f333(f333(f335(x113721),x113722),f254(f917(x113721,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11377,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x113771),f911(x113771))),f333(f333(f265(f911(x113771),f911(x113771)),x113772),f124(x113771))),f153(x113771,x113773)))), % 173.59/173.34 inference(rename_variables,[],[4712])). % 173.59/173.34 cnf(11380,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x113801),f911(x113801))),f333(f333(f265(f911(x113801),f911(x113801)),x113802),f124(x113801))),f155(x113801,x113803)))), % 173.59/173.34 inference(rename_variables,[],[4713])). % 173.59/173.34 cnf(11383,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x113831),f911(x113831))),f333(f333(f265(f911(x113831),f911(x113831)),x113832),f124(x113831))),f165(x113831,x113833)))), % 173.59/173.34 inference(rename_variables,[],[4714])). % 173.59/173.34 cnf(11388,plain, % 173.59/173.34 (~P106(f333(f333(f247(f917(x113881,a905)),x113882),f196(f917(x113881,a905))))), % 173.59/173.34 inference(rename_variables,[],[4704])). % 173.59/173.34 cnf(11391,plain, % 173.59/173.34 (~P106(f333(f333(f335(x113911),x113912),f196(f917(x113911,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11397,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x113971,a905)),x113972),f333(f333(f121(f917(x113971,a905)),x113973),f254(f917(x113971,a905)))))), % 173.59/173.34 inference(scs_inference,[],[3690,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,4634,10634,10728,11185,3915,3288,3355,3315,3297,3927,3513,11033,3386,4091,4647,10474,4694,11211,3560,3351,10541,4236,4094,11231,4712,11133,11377,4713,11264,4714,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,3908,3439,4687,10451,10454,10480,10964,10977,11091,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,4198,4103,11030,4152,3822,4186,3839,11237,11315,4704,10980,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,11130,11369,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,11334,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,11220,4060,3903,11146,11152,3752,3905,10885,3720,10801,10804,10894,11062,4709,4710,4333,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271])). % 173.59/173.34 cnf(11398,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x113981,a905)),x113982),f254(f917(x113981,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(11401,plain, % 173.59/173.34 (~P106(f333(f333(f196(f917(x114011,f917(x114012,a905))),x114013),x114014))), % 173.59/173.34 inference(rename_variables,[],[4710])). % 173.59/173.34 cnf(11410,plain, % 173.59/173.34 (~P106(f333(f333(f335(x114101),x114102),f196(f917(x114101,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11413,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(x114131,x114131)),f333(f333(f265(x114131,x114131),x114132),x114133)),f161(x114131,f124(f917(x114131,a910)))))), % 173.59/173.34 inference(rename_variables,[],[4711])). % 173.59/173.34 cnf(11416,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x114161,a905)),x114162),x114162))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(11419,plain, % 173.59/173.34 (~P106(f333(f333(f335(x114191),x114192),f196(f917(x114191,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11421,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x114211,a905)),f333(f292(x114212,x114211,f196(f917(f916(x114212,x114211),a905))),x114213)),x114214))), % 173.59/173.34 inference(scs_inference,[],[3690,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,4634,10634,10728,11185,3915,3288,3355,3315,3297,3927,3513,11033,3386,4091,4647,10474,4694,11211,3560,3351,10541,4236,4094,11231,4712,11133,11377,4713,11264,4714,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,3908,3439,4687,10451,10454,10480,10964,10977,11091,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,4198,4103,11030,4152,3822,4186,3839,11237,11315,4704,10980,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,11130,11369,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,11334,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,11220,11223,4060,3903,11146,11152,3752,11290,3905,10885,11253,3720,10801,10804,10894,11062,4709,4710,10757,4333,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446])). % 173.59/173.34 cnf(11422,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x114221,a905)),f196(f917(x114221,a905))),x114222))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(11425,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x114251,x114251)),f333(f333(f265(x114251,x114251),x114252),x114252)),f313(x114251,x114253)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(11436,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x114361),f911(x114361))),f333(f333(f265(f911(x114361),f911(x114361)),x114362),f124(x114361))),f165(x114361,x114363)))), % 173.59/173.34 inference(rename_variables,[],[4714])). % 173.59/173.34 cnf(11443,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x114431),f911(x114431))),f333(f333(f265(f911(x114431),f911(x114431)),f124(x114431)),x114432)),f153(x114431,x114433)))), % 173.59/173.34 inference(rename_variables,[],[4715])). % 173.59/173.34 cnf(11451,plain, % 173.59/173.34 (P106(f333(f333(f335(x114511),x114512),f254(f917(x114511,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11456,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x114561,a905)),f196(f917(x114561,a905))),x114562))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(11459,plain, % 173.59/173.34 (~P106(f333(f333(f335(x114591),x114592),f196(f917(x114591,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11462,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x114621,a905)),x114622),f254(f917(x114621,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(11467,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x114671,a905)),f196(f917(x114671,a905))),x114672))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(11469,plain, % 173.59/173.34 (~P106(f333(f72(a910,x114691,x114692,x114693,f254(f917(a910,a905))),x114694))), % 173.59/173.34 inference(scs_inference,[],[3690,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,4634,10634,10728,11185,3915,3288,3355,3315,3297,3927,3513,11033,3386,4091,4647,10474,4694,11211,3560,3351,10541,4236,4094,11231,11366,4712,11133,11377,4713,11264,4714,11383,4715,4716,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,3908,3439,4687,10451,10454,10480,10964,10977,11091,4700,3896,3659,4042,3484,3485,3459,4684,4642,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,11130,11369,11372,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,3517,10849,10879,10888,3549,3976,3913,10520,4693,10471,10837,10840,11334,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,11220,11223,4060,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,4710,10757,4333,4240,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752])). % 173.59/173.34 cnf(11480,plain, % 173.59/173.34 (P106(f333(f254(f917(x114801,a905)),x114802))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(11488,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x114881),f911(x114881))),f333(f333(f265(f911(x114881),f911(x114881)),x114882),f124(x114881))),f153(x114881,x114883)))), % 173.59/173.34 inference(rename_variables,[],[4712])). % 173.59/173.34 cnf(11491,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x114911),f911(x114911))),f333(f333(f265(f911(x114911),f911(x114911)),x114912),f124(x114911))),f155(x114911,x114913)))), % 173.59/173.34 inference(rename_variables,[],[4713])). % 173.59/173.34 cnf(11494,plain, % 173.59/173.34 (~E(f333(f333(f159(x114941),x114942),x114943),x114943)), % 173.59/173.34 inference(rename_variables,[],[4647])). % 173.59/173.34 cnf(11497,plain, % 173.59/173.34 (~E(f333(a123,x114971),x114971)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11500,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115001),x115002),f196(f917(x115001,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11505,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115051),x115052),f196(f917(x115051,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11508,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(f911(x115081),f911(x115081))),f333(f333(f265(f911(x115081),f911(x115081)),x115082),x115082)),f166(x115081,f313(x115081,x115083))))), % 173.59/173.34 inference(rename_variables,[],[4229])). % 173.59/173.34 cnf(11511,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x115111),f911(x115111))),f333(f333(f265(f911(x115111),f911(x115111)),x115112),f124(x115111))),f153(x115111,x115113)))), % 173.59/173.34 inference(rename_variables,[],[4712])). % 173.59/173.34 cnf(11521,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115211),x115212),f196(f917(x115211,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11524,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115241),x115242),f196(f917(x115241,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11527,plain, % 173.59/173.34 (P106(f333(f333(f335(x115271),x115272),f254(f917(x115271,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11530,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x115301),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(11535,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(x115351,x115351)),f333(f333(f265(x115351,x115351),x115352),x115353)),f161(x115351,f124(f917(x115351,a910)))))), % 173.59/173.34 inference(rename_variables,[],[4711])). % 173.59/173.34 cnf(11538,plain, % 173.59/173.34 (~E(f333(f316(x115381,f917(x115381,a905),x115382),x115383),f333(f314(x115381),x115383))), % 173.59/173.34 inference(rename_variables,[],[4694])). % 173.59/173.34 cnf(11541,plain, % 173.59/173.34 (~E(f333(f316(x115411,f917(x115411,a905),x115412),x115413),f333(f314(x115411),x115413))), % 173.59/173.34 inference(rename_variables,[],[4694])). % 173.59/173.34 cnf(11543,plain, % 173.59/173.34 (E(f333(f333(f265(a910,a910),f690(f313(a910,a323),a323,a910,f333(f333(f265(a910,a910),x115431),f333(a123,x115431)),a910,a910)),f691(f313(a910,a323),a323,a910,f333(f333(f265(a910,a910),x115431),f333(a123,x115431)),a910,a910)),f333(f333(f265(a910,a910),x115431),f333(a123,x115431)))), % 173.59/173.34 inference(scs_inference,[],[3690,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,4634,10634,10728,11185,3915,3288,3355,3315,3297,3927,3513,11033,3386,4091,4647,10474,10631,4694,11211,11310,11538,3560,3351,10541,4236,4094,11231,11366,4712,11133,11377,11488,4713,11264,11380,4714,11383,4715,11443,4716,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,3908,3439,4687,10451,10454,10480,10964,10977,11091,4700,3896,3659,4042,3484,3485,3459,4684,4642,4229,11508,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,11130,11369,11372,11451,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,3517,10849,10879,10888,10891,3549,3976,3913,10520,4693,10471,10837,10840,11334,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,11220,11223,11413,4060,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,4710,10757,4333,4240,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111])). % 173.59/173.34 cnf(11546,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x115461),f911(x115461))),f333(f333(f265(f911(x115461),f911(x115461)),x115462),f124(x115461))),f153(x115461,x115463)))), % 173.59/173.34 inference(rename_variables,[],[4712])). % 173.59/173.34 cnf(11552,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x115521),f911(x115521))),f333(f333(f265(f911(x115521),f911(x115521)),x115522),f124(x115521))),f153(x115521,x115523)))), % 173.59/173.34 inference(rename_variables,[],[4712])). % 173.59/173.34 cnf(11555,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115551),x115552),f196(f917(x115551,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11558,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115581),x115582),f196(f917(x115581,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11563,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115631),x115632),f196(f917(x115631,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11566,plain, % 173.59/173.34 (~P106(f333(f333(f335(x115661),x115662),f196(f917(x115661,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11569,plain, % 173.59/173.34 (P106(f333(f333(f335(x115691),f333(x115692,x115693)),f333(f316(x115694,x115691,x115692),f254(f917(x115694,a905)))))), % 173.59/173.34 inference(rename_variables,[],[4060])). % 173.59/173.34 cnf(11572,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(x115721,x115721)),f333(f333(f265(x115721,x115721),x115722),x115723)),f161(x115721,f124(f917(x115721,a910)))))), % 173.59/173.34 inference(rename_variables,[],[4711])). % 173.59/173.34 cnf(11574,plain, % 173.59/173.34 (E(x115741,f32(x115742,x115741,x115743,x115744,x115745,x115746,x115747,x115748,x115749,a25))), % 173.59/173.34 inference(scs_inference,[],[3690,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,4634,10634,10728,11185,3915,3288,3355,3315,3297,3927,3513,11033,3386,4091,4647,10474,10631,4694,11211,11310,11538,3560,3351,10541,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,3908,3439,4687,10451,10454,10480,10964,10977,11091,4700,3896,3659,4042,3484,3485,3459,4684,4642,4229,11508,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,11130,11369,11372,11451,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,3517,10849,10879,10888,10891,3549,3976,3913,10520,4693,10471,10837,10840,11334,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,4711,11220,11223,11413,11535,4060,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,4710,10757,4333,4240,3936,4707,10493,10496,10843,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2])). % 173.59/173.34 cnf(11578,plain, % 173.59/173.34 (E(f32(x115781,x115782,x115783,x115784,x115785,x115786,x115787,x115788,x115789,a25),x115782)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11581,plain, % 173.59/173.34 (E(f32(x115811,x115812,x115813,x115814,x115815,x115816,x115817,x115818,x115819,a25),x115812)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11584,plain, % 173.59/173.34 (~E(f333(a123,x115841),x115841)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11591,plain, % 173.59/173.34 (~E(f333(a123,x115911),x115911)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11596,plain, % 173.59/173.34 (E(f32(x115961,x115962,x115963,x115964,x115965,x115966,x115967,x115968,x115969,a25),x115962)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11599,plain, % 173.59/173.34 (E(f32(x115991,x115992,x115993,x115994,x115995,x115996,x115997,x115998,x115999,a25),x115992)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11605,plain, % 173.59/173.34 (~E(f333(a123,x116051),x116051)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11610,plain, % 173.59/173.34 (~E(f333(f333(f87(a1),x116101),x116101),a108)), % 173.59/173.34 inference(rename_variables,[],[4645])). % 173.59/173.34 cnf(11617,plain, % 173.59/173.34 (E(f333(f333(f23(a910),f2(a910)),x116171),f2(a910))), % 173.59/173.34 inference(rename_variables,[],[3372])). % 173.59/173.34 cnf(11620,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x116201),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(11627,plain, % 173.59/173.34 (E(f333(f333(f87(a1),f333(f333(f88(a1),x116271),f333(f333(f42(a1),x116272),x116271))),f51(a1,x116272,x116271)),x116272)), % 173.59/173.34 inference(rename_variables,[],[4007])). % 173.59/173.34 cnf(11637,plain, % 173.59/173.34 (E(f32(x116371,x116372,x116373,x116374,x116375,x116376,x116377,x116378,x116379,a25),x116372)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11644,plain, % 173.59/173.34 (E(f32(x116441,x116442,x116443,x116444,x116445,x116446,x116447,x116448,x116449,a25),x116442)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11647,plain, % 173.59/173.34 (E(f32(x116471,x116472,x116473,x116474,x116475,x116476,x116477,x116478,x116479,a25),x116472)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11650,plain, % 173.59/173.34 (E(f32(x116501,x116502,x116503,x116504,x116505,x116506,x116507,x116508,x116509,a25),x116502)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11653,plain, % 173.59/173.34 (E(f32(x116531,x116532,x116533,x116534,x116535,x116536,x116537,x116538,x116539,a25),x116532)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11656,plain, % 173.59/173.34 (~E(f333(a123,x116561),x116561)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11659,plain, % 173.59/173.34 (~E(f333(a123,x116591),x116591)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11663,plain, % 173.59/173.34 (E(f32(x116631,x116632,x116633,x116634,x116635,x116636,x116637,x116638,x116639,a25),x116632)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11682,plain, % 173.59/173.34 (P106(f333(f254(f917(x116821,a905)),x116822))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(11689,plain, % 173.59/173.34 (~P106(f333(f333(f180(x116891),f124(x116891)),x116892))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(11695,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),f2(a910)),f333(a123,x116951)))), % 173.59/173.34 inference(rename_variables,[],[3536])). % 173.59/173.34 cnf(11696,plain, % 173.59/173.34 (~E(f333(a123,x116961),x116961)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11699,plain, % 173.59/173.34 (P106(f333(f333(f335(x116991),x116992),f254(f917(x116991,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11707,plain, % 173.59/173.34 (E(f32(x117071,x117072,x117073,x117074,x117075,x117076,x117077,x117078,x117079,a25),x117072)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11712,plain, % 173.59/173.34 (~E(f333(a123,x117121),x117121)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11715,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x117151),x117151))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(11722,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x117221),x117221))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(11723,plain, % 173.59/173.34 (E(f32(x117231,x117232,x117233,x117234,x117235,x117236,x117237,x117238,x117239,a25),x117232)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11736,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x117361),x117362)),x117362))), % 173.59/173.34 inference(rename_variables,[],[4707])). % 173.59/173.34 cnf(11739,plain, % 173.59/173.34 (~P106(f333(f333(f247(a1),f333(f111(a1),x117391)),f2(a1)))), % 173.59/173.34 inference(rename_variables,[],[4700])). % 173.59/173.34 cnf(11751,plain, % 173.59/173.34 (~E(f333(f333(f112(a910),f333(a123,x117511)),x117511),f333(a123,x117511))), % 173.59/173.34 inference(scs_inference,[],[3690,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,4634,10634,10728,11185,3064,3068,3071,3076,3083,3093,3101,3102,3105,3107,3108,3120,3139,3140,3150,3157,3161,3163,3219,3247,4618,3915,3288,4007,11627,3355,3315,3297,3927,3513,11033,3386,4091,4647,10474,10631,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,4645,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,3908,3439,3536,4687,10451,10454,10480,10964,10977,11091,11530,11620,4700,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,10862,11715,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,4683,10517,11001,11042,3609,10818,11086,11130,11369,11372,11451,11527,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,3517,10849,10879,10888,10891,11480,3549,3976,3913,10520,4693,10471,10837,10840,11334,11350,3477,10882,11036,4277,4690,3983,4675,4678,3432,3436,4677,4676,4706,10751,10754,4711,11220,11223,11413,11535,4060,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,4710,10757,4333,4240,3936,4707,10493,10496,10843,10846,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509])). % 173.59/173.34 cnf(11758,plain, % 173.59/173.34 (E(f32(x117581,x117582,x117583,x117584,x117585,x117586,x117587,x117588,x117589,a25),x117582)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11763,plain, % 173.59/173.34 (E(f32(x117631,x117632,x117633,x117634,x117635,x117636,x117637,x117638,x117639,a25),x117632)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11766,plain, % 173.59/173.34 (~P106(f333(f333(f247(a1),f333(f111(a1),x117661)),f2(a1)))), % 173.59/173.34 inference(rename_variables,[],[4700])). % 173.59/173.34 cnf(11769,plain, % 173.59/173.34 (E(f32(x117691,x117692,x117693,x117694,x117695,x117696,x117697,x117698,x117699,a25),x117692)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11772,plain, % 173.59/173.34 (~E(f333(a123,x117721),x117721)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11775,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x117751),x117751))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(11782,plain, % 173.59/173.34 (~P106(f333(f333(f180(x117821),f124(x117821)),x117822))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(11803,plain, % 173.59/173.34 (~P106(f333(f333(f247(a1),f333(f111(a1),x118031)),f2(a1)))), % 173.59/173.34 inference(rename_variables,[],[4700])). % 173.59/173.34 cnf(11806,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x118061),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(11807,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x118071),f333(a123,x118071)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(11822,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x118221)),x118221))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(11823,plain, % 173.59/173.34 (~E(f333(a123,x118231),x118231)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11833,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x118331),x118332)),x118331))), % 173.59/173.34 inference(rename_variables,[],[4708])). % 173.59/173.34 cnf(11836,plain, % 173.59/173.34 (~P106(f333(f333(f247(a1),f333(f111(a1),x118361)),f2(a1)))), % 173.59/173.34 inference(rename_variables,[],[4700])). % 173.59/173.34 cnf(11839,plain, % 173.59/173.34 (~E(f333(a123,x118391),x118391)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(11852,plain, % 173.59/173.34 (P106(f333(f333(f335(x118521),x118522),f333(f333(f315(x118521),x118522),x118523)))), % 173.59/173.34 inference(rename_variables,[],[3768])). % 173.59/173.34 cnf(11853,plain, % 173.59/173.34 (~P106(f333(f333(f246(a1),f2(a1)),f333(f86(a1),f333(f111(a1),f333(a123,x118531)))))), % 173.59/173.34 inference(rename_variables,[],[4709])). % 173.59/173.34 cnf(11856,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),f333(f333(f23(a910),x118561),x118562)),f333(a123,x118561)))), % 173.59/173.34 inference(rename_variables,[],[3908])). % 173.59/173.34 cnf(11859,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f51(a910,x118591,x118592)),x118591))), % 173.59/173.34 inference(rename_variables,[],[3913])). % 173.59/173.34 cnf(11863,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x118631))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(11864,plain, % 173.59/173.34 (E(f32(x118641,x118642,x118643,x118644,x118645,x118646,x118647,x118648,x118649,a25),x118642)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11867,plain, % 173.59/173.34 (E(f32(x118671,x118672,x118673,x118674,x118675,x118676,x118677,x118678,x118679,a25),x118672)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11870,plain, % 173.59/173.34 (E(f32(x118701,x118702,x118703,x118704,x118705,x118706,x118707,x118708,x118709,a25),x118702)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11873,plain, % 173.59/173.34 (E(f32(x118731,x118732,x118733,x118734,x118735,x118736,x118737,x118738,x118739,a25),x118732)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11876,plain, % 173.59/173.34 (E(f32(x118761,x118762,x118763,x118764,x118765,x118766,x118767,x118768,x118769,a25),x118762)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11879,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x118791)),x118791))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(11880,plain, % 173.59/173.34 (E(f32(x118801,x118802,x118803,x118804,x118805,x118806,x118807,x118808,x118809,a25),x118802)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11889,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x118891),x118891))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(11890,plain, % 173.59/173.34 (E(f32(x118901,x118902,x118903,x118904,x118905,x118906,x118907,x118908,x118909,a25),x118902)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11893,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f51(a910,x118931,x118932)),x118931))), % 173.59/173.34 inference(rename_variables,[],[3913])). % 173.59/173.34 cnf(11894,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x118941))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(11911,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x119111),x119111))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(11914,plain, % 173.59/173.34 (P106(f333(f333(f335(x119141),f333(x119142,x119143)),f333(f316(x119144,x119141,x119142),f254(f917(x119144,a905)))))), % 173.59/173.34 inference(rename_variables,[],[4060])). % 173.59/173.34 cnf(11915,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x119151)),x119151))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(11918,plain, % 173.59/173.34 (P106(f333(f333(f335(x119181),f333(x119182,x119183)),f333(f316(x119184,x119181,x119182),f254(f917(x119184,a905)))))), % 173.59/173.34 inference(rename_variables,[],[4060])). % 173.59/173.34 cnf(11919,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x119191),x119192)),x119192))), % 173.59/173.34 inference(rename_variables,[],[4707])). % 173.59/173.34 cnf(11924,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x119241),x119242)),x119241))), % 173.59/173.34 inference(rename_variables,[],[4708])). % 173.59/173.34 cnf(11927,plain, % 173.59/173.34 (~P106(f333(f333(f180(x119271),f124(x119271)),x119272))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(11930,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x119301),x119301))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(11936,plain, % 173.59/173.34 (~P38(x119361,x119362,f124(x119361))), % 173.59/173.34 inference(rename_variables,[],[4658])). % 173.59/173.34 cnf(11939,plain, % 173.59/173.34 (P106(f333(f333(f335(x119391),x119392),f254(f917(x119391,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(11940,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x119401)),x119401))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(11943,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x119431),x119431))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(11956,plain, % 173.59/173.34 (~P106(f333(f333(f335(x119561),x119562),f196(f917(x119561,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(11959,plain, % 173.59/173.34 (E(f333(f333(f16(x119591,x119592),x119593),x119594),x119593)), % 173.59/173.34 inference(rename_variables,[],[3446])). % 173.59/173.34 cnf(11962,plain, % 173.59/173.34 (E(f333(f333(f16(x119621,x119622),x119623),x119624),x119623)), % 173.59/173.34 inference(rename_variables,[],[3446])). % 173.59/173.34 cnf(11974,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),f2(a910)),f333(a123,x119741)))), % 173.59/173.34 inference(rename_variables,[],[3536])). % 173.59/173.34 cnf(11976,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),f333(f333(f42(a910),x119761),f32(x119762,f2(a910),x119763,x119764,x119765,x119766,x119767,x119768,x119769,a25))),f2(a910)))), % 173.59/173.34 inference(scs_inference,[],[3690,4657,4658,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3093,3094,3101,3102,3105,3107,3108,3120,3139,3140,3150,3157,3161,3163,3217,3219,3247,4618,4021,3497,3915,3288,4007,11627,3355,3315,3310,3297,3927,3513,11033,3386,4091,4647,10474,10631,3446,11959,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3612,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,4507,4508,4645,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,3908,11856,3439,3536,11695,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,4700,11739,11766,11803,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,11078,3532,4683,10517,11001,11042,11051,11889,3609,10818,11086,11130,11369,11372,11451,11527,11699,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,3517,10849,10879,10888,10891,11480,3556,3549,3976,3913,10520,11859,4693,10471,10837,10840,11334,11350,11822,11879,11915,3477,10882,11036,11106,11863,4277,4690,3983,4675,4678,3432,3436,4677,4676,3768,4706,10751,10754,4711,11220,11223,11413,11535,4060,11569,11914,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,11853,4710,10757,4333,4240,3936,3882,4707,10493,10496,10843,10846,11736,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509,5510,5511,5541,5542,5543,5551,5552,5553,5554,5595,5600,5602,5638,5640,5641,5643,5644,5646,5647,5649,5658,5663,5664,5666,5667,5668,5669,5670,5671,5680,5690,5693,5704,5720,5721,5724,5734,5736,5737,5738,5763,5773,5788,5789,5798,5799,5801,5803,5808,5843,5848,5850,5908,5942,5943,5948,5954,5957,5958,5959,5960,5978,5981,5982,5990,6011,6039,6058,6061,6062,6064,6073,6088,6092,6095,6096,6097,6115,6126,6127,6158,6159,6163,6184,6187,6190])). % 173.59/173.34 cnf(11977,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x119771),x119771))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(11978,plain, % 173.59/173.34 (E(f32(x119781,x119782,x119783,x119784,x119785,x119786,x119787,x119788,x119789,a25),x119782)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(11981,plain, % 173.59/173.34 (P106(f333(f67(x119811),f333(f180(x119811),x119812)))), % 173.59/173.34 inference(rename_variables,[],[3496])). % 173.59/173.34 cnf(11984,plain, % 173.59/173.34 (P106(f333(f67(x119841),f333(f180(x119841),x119842)))), % 173.59/173.34 inference(rename_variables,[],[3496])). % 173.59/173.34 cnf(11987,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),f333(f86(a1),f333(f111(a1),x119871))),f333(f111(a1),x119872)))), % 173.59/173.34 inference(rename_variables,[],[3937])). % 173.59/173.34 cnf(11990,plain, % 173.59/173.34 (~P106(f333(f333(f335(x119901),x119902),f196(f917(x119901,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12004,plain, % 173.59/173.34 (~P106(f333(f333(f335(a910),f2(a910)),f333(f310(a910),x120041)))), % 173.59/173.34 inference(scs_inference,[],[3690,4657,4658,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3093,3094,3097,3101,3102,3105,3107,3108,3120,3139,3140,3150,3157,3161,3163,3217,3219,3220,3247,4618,4021,3497,3915,3288,4007,11627,3355,3315,3310,3297,3927,3513,11033,3386,4091,4647,10474,10631,3446,11959,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3612,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,4507,4508,4645,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,3908,11856,3439,3536,11695,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,4700,11739,11766,11803,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,3496,11981,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,11078,3532,4683,10517,11001,11042,11051,11889,3609,10818,11086,11130,11369,11372,11451,11527,11699,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,3517,10849,10879,10888,10891,11480,3556,3549,3976,3913,10520,11859,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,3477,10882,11036,11106,11863,3937,4277,4690,3983,4675,4678,3432,3436,4677,4676,3768,4706,10751,10754,4711,11220,11223,11413,11535,4060,11569,11914,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,11853,4710,10757,4333,4240,3936,3882,4707,10493,10496,10843,10846,11736,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509,5510,5511,5541,5542,5543,5551,5552,5553,5554,5595,5600,5602,5638,5640,5641,5643,5644,5646,5647,5649,5658,5663,5664,5666,5667,5668,5669,5670,5671,5680,5690,5693,5704,5720,5721,5724,5734,5736,5737,5738,5763,5773,5788,5789,5798,5799,5801,5803,5808,5843,5848,5850,5908,5942,5943,5948,5954,5957,5958,5959,5960,5978,5981,5982,5990,6011,6039,6058,6061,6062,6064,6073,6088,6092,6095,6096,6097,6115,6126,6127,6158,6159,6163,6184,6187,6190,6212,6213,6239,6242,6250,6260,6268,6272,6279,6280,6281])). % 173.59/173.34 cnf(12006,plain, % 173.59/173.34 (~P106(f333(f333(f335(a910),x120061),f333(f289(a910),f2(a910))))), % 173.59/173.34 inference(scs_inference,[],[3690,4657,4658,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3093,3094,3097,3101,3102,3105,3107,3108,3120,3139,3140,3150,3157,3161,3163,3217,3219,3220,3247,4618,4021,3497,3915,3288,4007,11627,3355,3315,3310,3297,3927,3513,11033,3386,4091,4647,10474,10631,3446,11959,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3612,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,4507,4508,4645,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,3908,11856,3439,3536,11695,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,4700,11739,11766,11803,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,3496,11981,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,11078,3532,4683,10517,11001,11042,11051,11889,3609,10818,11086,11130,11369,11372,11451,11527,11699,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,3517,10849,10879,10888,10891,11480,3556,3549,3976,3913,10520,11859,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,3477,10882,11036,11106,11863,3937,4277,4690,3983,4675,4678,3432,3436,4677,4676,3768,4706,10751,10754,4711,11220,11223,11413,11535,4060,11569,11914,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,11853,4710,10757,4333,4240,3936,3882,4707,10493,10496,10843,10846,11736,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509,5510,5511,5541,5542,5543,5551,5552,5553,5554,5595,5600,5602,5638,5640,5641,5643,5644,5646,5647,5649,5658,5663,5664,5666,5667,5668,5669,5670,5671,5680,5690,5693,5704,5720,5721,5724,5734,5736,5737,5738,5763,5773,5788,5789,5798,5799,5801,5803,5808,5843,5848,5850,5908,5942,5943,5948,5954,5957,5958,5959,5960,5978,5981,5982,5990,6011,6039,6058,6061,6062,6064,6073,6088,6092,6095,6096,6097,6115,6126,6127,6158,6159,6163,6184,6187,6190,6212,6213,6239,6242,6250,6260,6268,6272,6279,6280,6281,6282])). % 173.59/173.34 cnf(12009,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x120091),x120091))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(12010,plain, % 173.59/173.34 (E(f32(x120101,x120102,x120103,x120104,x120105,x120106,x120107,x120108,x120109,a25),x120102)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12013,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x120131),x120131))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12022,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x120221),x120221))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12025,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x120251),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12030,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x120301),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12039,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x120391))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(12040,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x120401)),x120401))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(12043,plain, % 173.59/173.34 (~P106(f333(f333(f180(x120431),f124(x120431)),x120432))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(12046,plain, % 173.59/173.34 (~P106(f333(f333(f180(x120461),f124(x120461)),x120462))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(12049,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x120491),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12050,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x120501),f333(a123,x120501)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12066,plain, % 173.59/173.34 (P106(f333(f333(f247(a1),f333(f86(a1),f85(a1))),f2(a1)))), % 173.59/173.34 inference(scs_inference,[],[3690,4657,4658,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3097,3101,3102,3105,3107,3108,3120,3139,3140,3150,3154,3157,3161,3163,3217,3219,3220,3228,3247,4618,4021,3497,3915,3288,4007,11627,3355,3315,3310,3297,3927,3513,11033,3386,4091,4647,10474,10631,3446,11959,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3612,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,4507,4508,4645,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,3908,11856,3439,3536,11695,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,4700,11739,11766,11803,11836,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,3496,11981,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,4198,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,3457,10936,10983,10986,11017,11039,11075,11113,3458,10645,10867,10959,11078,11775,12013,3532,4683,10517,11001,11042,11051,11889,3609,10818,11086,11130,11369,11372,11451,11527,11699,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,3517,10849,10879,10888,10891,11480,3556,3549,3976,3913,10520,11859,11893,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,3477,10882,11036,11106,11863,11894,3937,4277,4690,3983,4675,4678,3432,3436,4677,4676,3768,4706,10751,10754,4711,11220,11223,11413,11535,4060,11569,11914,3903,11146,11152,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,11853,4710,10757,4333,4240,3936,3882,4707,10493,10496,10843,10846,11736,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509,5510,5511,5541,5542,5543,5551,5552,5553,5554,5595,5600,5602,5638,5640,5641,5643,5644,5646,5647,5649,5658,5663,5664,5666,5667,5668,5669,5670,5671,5680,5690,5693,5704,5720,5721,5724,5734,5736,5737,5738,5763,5773,5788,5789,5798,5799,5801,5803,5808,5843,5848,5850,5908,5942,5943,5948,5954,5957,5958,5959,5960,5978,5981,5982,5990,6011,6039,6058,6061,6062,6064,6073,6088,6092,6095,6096,6097,6115,6126,6127,6158,6159,6163,6184,6187,6190,6212,6213,6239,6242,6250,6260,6268,6272,6279,6280,6281,6282,6312,6329,6380,6418,6420,6441,6442,6448,6452,6453,6456,6470,6485,6506,6507,6510,6513,6523,6538,6559,6566,6568,6583,6584])). % 173.59/173.34 cnf(12069,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x120691)),x120691))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(12072,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x120721)),x120721))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(12075,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x120751)),x120751))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(12078,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x120781)),x120781))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(12081,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x120811),x120811))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12084,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x120841),x120841))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12087,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x120871),x120871))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12090,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x120901),x120901))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12108,plain, % 173.59/173.34 (E(f333(f197(f911(x121081)),f177(x121081,x121082,x121083)),x121082)), % 173.59/173.34 inference(rename_variables,[],[3523])). % 173.59/173.34 cnf(12111,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x121111),x121111))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(12114,plain, % 173.59/173.34 (P27(a910,a910,a123,x121141)), % 173.59/173.34 inference(rename_variables,[],[3658])). % 173.59/173.34 cnf(12117,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x121171),x121171))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12128,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x121281),x121281))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12131,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(f916(f911(x121311),f911(x121311)),a905)),f166(x121311,x121312)),f313(f911(x121311),f165(x121311,x121312))))), % 173.59/173.34 inference(rename_variables,[],[4157])). % 173.59/173.34 cnf(12138,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x121381),f333(a123,x121381)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12141,plain, % 173.59/173.34 (P106(f333(f333(f335(f917(x121411,a905)),x121412),f333(f314(x121411),x121412)))), % 173.59/173.34 inference(rename_variables,[],[3822])). % 173.59/173.34 cnf(12142,plain, % 173.59/173.34 (~E(f333(a123,x121421),x121421)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12147,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x121471),x121471))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12152,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x121521),x121521))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12163,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x121631,a905)),x121632),f333(f333(f315(x121631),x121633),x121632)))), % 173.59/173.34 inference(rename_variables,[],[3903])). % 173.59/173.34 cnf(12166,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x121661),x121661))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(12167,plain, % 173.59/173.34 (~E(f333(a123,x121671),x121671)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12178,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x121781),x121781))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12179,plain, % 173.59/173.34 (~E(f333(a123,x121791),x121791)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12182,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x121821),x121821))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12185,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x121851),x121851))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12188,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x121881),x121881))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12191,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x121911),x121911))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12194,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x121941),x121941))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12197,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x121971),x121971))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12200,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122001),x122001))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12201,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x122011),f333(a123,x122011)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12208,plain, % 173.59/173.34 (~E(f333(a123,x122081),x122081)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12213,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122131),x122131))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12214,plain, % 173.59/173.34 (~E(f333(a123,x122141),x122141)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12217,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x122171),x122171))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12234,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x122341),x122341))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12239,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x122391))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(12253,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122531),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12256,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122561),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12259,plain, % 173.59/173.34 (~P106(f333(f333(f335(x122591),x122592),f196(f917(x122591,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12262,plain, % 173.59/173.34 (~P106(f333(f333(f335(x122621),x122622),f196(f917(x122621,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12265,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122651),x122651))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12267,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122671),f333(f333(f112(a910),x122671),x122672)))), % 173.59/173.34 inference(scs_inference,[],[3690,4657,4658,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,11839,12142,12167,12179,12208,3658,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3097,3101,3102,3105,3107,3108,3120,3139,3140,3150,3154,3157,3161,3163,3217,3219,3220,3228,3247,4618,4021,3497,3402,3508,3915,4222,3523,3288,4007,11627,3355,3315,3310,3297,3927,3513,11033,3386,4091,4647,10474,10631,3446,11959,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3612,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,4507,4508,4645,3756,3972,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,12050,12138,3908,11856,3439,3536,11695,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,12049,12253,4700,11739,11766,11803,11836,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,3496,11981,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,4198,4157,4103,11030,4152,3822,4186,3839,11237,11315,11398,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,12009,12111,3457,10936,10983,10986,11017,11039,11075,11113,11149,12182,12185,12188,12191,3458,10645,10867,10959,11078,11775,12013,12022,12117,12128,12147,12152,12194,12217,3532,4683,10517,11001,11042,11051,11889,11911,12081,12084,12087,12090,12178,12197,12200,12213,12265,3609,10818,11086,11130,11369,11372,11451,11527,11699,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,11990,12259,3517,10849,10879,10888,10891,11480,3556,3549,3976,3913,10520,11859,11893,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,12040,12069,12072,12075,12078,3477,10882,11036,11106,11863,11894,12039,3937,4277,4690,3948,3983,4675,4678,3432,3436,4677,4676,3768,4706,10751,10754,4711,11220,11223,11413,11535,4060,11569,11914,3903,11146,11152,11172,3752,11290,3905,10885,11253,11422,11456,3720,10801,10804,10894,11062,4709,11853,4710,10757,4333,4240,3936,3882,4707,10493,10496,10843,10846,11736,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5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% 173.59/173.34 cnf(12268,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122681),x122681))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12271,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122711),x122711))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12274,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x122741),x122741))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12277,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x122771),f333(a123,x122771)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12284,plain, % 173.59/173.34 (P106(f333(f333(f335(f917(x122841,a905)),x122842),f333(f314(x122841),x122842)))), % 173.59/173.34 inference(rename_variables,[],[3822])). % 173.59/173.34 cnf(12289,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x122891,a905)),x122892),f333(f333(f315(x122891),x122893),x122892)))), % 173.59/173.34 inference(rename_variables,[],[3903])). % 173.59/173.34 cnf(12296,plain, % 173.59/173.34 (~P106(f333(f333(f335(x122961),x122962),f196(f917(x122961,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12305,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x123051,a905)),x123052),f254(f917(x123051,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(12306,plain, % 173.59/173.34 (~E(f333(a123,x123061),x123061)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12309,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x123091,a905)),f196(f917(x123091,a905))),x123092))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(12312,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x123121,a905)),f333(f180(x123121),f333(f144(x123121,x123122),x123123))),f333(f180(x123121),x123123)))), % 173.59/173.34 inference(rename_variables,[],[4103])). % 173.59/173.34 cnf(12318,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x123181),f333(a123,x123181)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12327,plain, % 173.59/173.34 (E(f32(x123271,x123272,x123273,x123274,x123275,x123276,x123277,x123278,x123279,a25),x123272)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12338,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x123381)),x123381))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(12339,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x123391),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12342,plain, % 173.59/173.34 (P106(f333(f67(x123421),f196(f917(x123421,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(12343,plain, % 173.59/173.34 (~P106(f333(f333(f335(x123431),x123432),f196(f917(x123431,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12350,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x123501,a905)),f333(f180(x123501),f184(x123501,x123502,x123503))),f333(f180(x123501),x123502)))), % 173.59/173.34 inference(rename_variables,[],[4152])). % 173.59/173.34 cnf(12353,plain, % 173.59/173.34 (P27(x123531,x123531,f5(x123531),x123532)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12360,plain, % 173.59/173.34 (P106(f333(f333(f335(f917(x123601,a905)),x123602),f333(f314(x123601),x123602)))), % 173.59/173.34 inference(rename_variables,[],[3822])). % 173.59/173.34 cnf(12367,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x123671),x123671))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(12370,plain, % 173.59/173.34 (~P106(f333(f333(f335(x123701),x123702),f196(f917(x123701,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12373,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x123731,a905)),x123732),f333(f333(f315(x123731),x123733),x123732)))), % 173.59/173.34 inference(rename_variables,[],[3903])). % 173.59/173.34 cnf(12374,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x123741,a905)),x123742),f254(f917(x123741,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(12381,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x123811),x123811))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12384,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x123841),x123841))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12387,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x123871),x123871))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12390,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x123901),x123901))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12393,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x123931),f333(a123,x123931)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12396,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x123961),f333(a123,x123961)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12399,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x123991,a905)),x123992),x123992))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(12401,plain, % 173.59/173.34 (~P106(f333(f333(f246(a1),f333(f333(f23(a1),a90),a108)),f2(a1)))), % 173.59/173.34 inference(scs_inference,[],[4717,3690,11305,4657,4658,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,12010,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,11839,12142,12167,12179,12208,12214,3658,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3096,3097,3100,3101,3102,3105,3107,3108,3120,3139,3140,3150,3154,3157,3161,3163,3217,3219,3220,3228,3247,4618,4021,3497,3402,3508,3915,4222,3523,3288,4007,11627,3355,3315,3310,3297,3927,3513,11033,3386,4091,4647,10474,10631,3446,11959,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3612,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,3821,4507,4508,4645,3756,4092,3972,3636,3898,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,12050,12138,12201,12277,12318,12393,3908,11856,3439,3536,11695,3717,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,12049,12253,12256,4700,11739,11766,11803,11836,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,3496,11981,11984,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,4198,4157,4103,11030,4152,11234,3822,12141,12284,4186,3839,11237,11315,11398,11462,12305,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,12009,12111,12166,3457,10936,10983,10986,11017,11039,11075,11113,11149,12182,12185,12188,12191,12381,12384,12387,3458,10645,10867,10959,11078,11775,12013,12022,12117,12128,12147,12152,12194,12217,3532,12342,4683,10517,11001,11042,11051,11889,11911,12081,12084,12087,12090,12178,12197,12200,12213,12265,12268,12271,3609,10818,11086,11130,11369,11372,11451,11527,11699,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,11990,12259,12262,12296,12343,3517,10849,10879,10888,10891,11480,3556,3549,3976,3913,10520,11859,11893,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,12040,12069,12072,12075,12078,3477,10882,11036,11106,11863,11894,12039,3937,4277,4690,3948,3983,4675,4678,3432,3436,4677,4676,3768,4706,10751,10754,4711,11220,11223,11413,11535,4060,11569,11914,3903,11146,11152,11172,12163,12289,3752,11290,11416,3905,10885,11253,11422,11456,11467,3720,10801,10804,10894,11062,4709,11853,4710,10757,4333,4240,3936,3882,4707,10493,10496,10843,10846,11736,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9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% 173.59/173.34 cnf(12406,plain, % 173.59/173.34 (P106(f333(f333(f335(f917(x124061,a905)),x124062),f333(f314(x124061),x124062)))), % 173.59/173.34 inference(rename_variables,[],[3822])). % 173.59/173.34 cnf(12415,plain, % 173.59/173.34 (~E(f333(a123,x124151),x124151)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12416,plain, % 173.59/173.34 (E(f333(f316(x124161,x124161,f5(x124161)),x124162),x124162)), % 173.59/173.34 inference(rename_variables,[],[3513])). % 173.59/173.34 cnf(12419,plain, % 173.59/173.34 (P35(x124191,x124192,f124(x124191),f124(x124191))), % 173.59/173.34 inference(rename_variables,[],[3698])). % 173.59/173.34 cnf(12422,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x124221,a905)),f333(f180(x124221),f184(x124221,x124222,x124223))),f333(f180(x124221),x124222)))), % 173.59/173.34 inference(rename_variables,[],[4152])). % 173.59/173.34 cnf(12423,plain, % 173.59/173.34 (P106(f333(f67(x124231),f333(f180(x124231),x124232)))), % 173.59/173.34 inference(rename_variables,[],[3496])). % 173.59/173.34 cnf(12434,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x124341),x124341))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12437,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x124371),x124371))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12442,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x124421))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(12449,plain, % 173.59/173.34 (P16(a910,f333(f176(a910),f333(f333(f162(f911(x124491),a910),f197(f911(x124491))),f187(x124491,x124492))))), % 173.59/173.34 inference(rename_variables,[],[4017])). % 173.59/173.34 cnf(12452,plain, % 173.59/173.34 (P27(x124521,x124521,f5(x124521),x124522)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12455,plain, % 173.59/173.34 (P27(x124551,x124551,f5(x124551),x124552)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12458,plain, % 173.59/173.34 (P106(f333(f333(f335(f911(x124581)),f124(x124581)),f169(x124581,x124582)))), % 173.59/173.34 inference(rename_variables,[],[3650])). % 173.59/173.34 cnf(12461,plain, % 173.59/173.34 (~P106(f333(f333(f196(f917(x124611,f917(x124612,a905))),x124613),x124614))), % 173.59/173.34 inference(rename_variables,[],[4710])). % 173.59/173.34 cnf(12466,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x124661),x124661))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12467,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x124671))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(12470,plain, % 173.59/173.34 (~P106(f333(f333(f196(f917(x124701,f917(x124702,a905))),x124703),x124704))), % 173.59/173.34 inference(rename_variables,[],[4710])). % 173.59/173.34 cnf(12473,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(f916(f911(x124731),f911(x124731)),a905)),f166(x124731,x124732)),f313(f911(x124731),f165(x124731,x124732))))), % 173.59/173.34 inference(rename_variables,[],[4157])). % 173.59/173.34 cnf(12479,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x124791,a905)),f333(f316(x124792,x124791,x124793),f333(f317(x124792,x124791,x124793),x124794))),x124794))), % 173.59/173.34 inference(rename_variables,[],[4333])). % 173.59/173.34 cnf(12482,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x124821,a905)),f333(f180(x124821),f184(x124821,x124822,x124823))),f333(f180(x124821),x124822)))), % 173.59/173.34 inference(rename_variables,[],[4152])). % 173.59/173.34 cnf(12483,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x124831,a905)),f333(f180(x124831),f333(f144(x124831,x124832),x124833))),f333(f180(x124831),x124833)))), % 173.59/173.34 inference(rename_variables,[],[4103])). % 173.59/173.34 cnf(12486,plain, % 173.59/173.34 (~P106(f333(f333(f247(f917(x124861,a905)),x124862),f196(f917(x124861,a905))))), % 173.59/173.34 inference(rename_variables,[],[4704])). % 173.59/173.34 cnf(12494,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x124941,a905)),f333(f316(x124942,x124941,x124943),f333(f317(x124942,x124941,x124943),x124944))),x124944))), % 173.59/173.34 inference(rename_variables,[],[4333])). % 173.59/173.34 cnf(12499,plain, % 173.59/173.34 (P106(f333(f333(f335(f911(x124991)),f124(x124991)),f169(x124991,x124992)))), % 173.59/173.34 inference(rename_variables,[],[3650])). % 173.59/173.34 cnf(12502,plain, % 173.59/173.34 (~P106(f333(f333(f335(f916(f911(x125021),f911(x125021))),f333(f333(f265(f911(x125021),f911(x125021)),x125022),f124(x125021))),f153(x125021,x125023)))), % 173.59/173.34 inference(rename_variables,[],[4712])). % 173.59/173.34 cnf(12505,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x125051),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12507,plain, % 173.59/173.34 (~P106(f333(f67(x125071),f254(f917(x125071,a905))))), % 173.59/173.34 inference(scs_inference,[],[4717,3690,11305,12353,12452,3698,3707,3426,4657,4658,3324,3327,4656,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,12010,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,11839,12142,12167,12179,12208,12214,12306,3658,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3096,3097,3100,3101,3102,3105,3107,3108,3120,3129,3139,3140,3150,3154,3157,3161,3163,3217,3219,3220,3228,3247,4618,4021,3497,3402,3508,3915,4222,3523,3288,4007,11627,3355,3315,3310,3297,3927,3334,3513,11033,11155,3386,4091,4647,10474,10631,3446,11959,4694,11211,11310,11538,11541,3560,3350,3351,10541,10852,3612,3268,3372,11617,4236,4094,11231,11366,11425,4712,11133,11377,11488,11511,11546,11552,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,12458,12499,3821,4507,4508,4645,3756,4092,3972,4017,3636,3898,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,12050,12138,12201,12277,12318,12393,3908,11856,3439,3536,11695,3717,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,12049,12253,12256,12339,4700,11739,11766,11803,11836,3896,3659,4042,3484,3485,3459,4684,4642,3643,4701,4229,11508,3778,3496,11981,11984,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,4198,4157,12131,12473,4103,11030,12312,4152,11234,12350,12422,3822,12141,12284,12360,12406,4186,3839,11237,11315,11398,11462,12305,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,12009,12111,12166,3457,10936,10983,10986,11017,11039,11075,11113,11149,12182,12185,12188,12191,12381,12384,12387,12390,3458,10645,10867,10959,11078,11775,12013,12022,12117,12128,12147,12152,12194,12217,3532,12342,4683,10517,11001,11042,11051,11889,11911,12081,12084,12087,12090,12178,12197,12200,12213,12265,12268,12271,12274,12434,3609,10818,11086,11130,11369,11372,11451,11527,11699,11939,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,11990,12259,12262,12296,12343,3517,10849,10879,10888,10891,11480,3556,3549,3976,3913,10520,11859,11893,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,12040,12069,12072,12075,12078,12338,3477,10882,11036,11106,11863,11894,12039,12239,12442,3937,4277,4690,3948,3983,4675,4678,3432,3436,4677,4676,3768,4706,10751,10754,4711,11220,11223,11413,11535,4060,11569,11914,3903,11146,11152,11172,12163,12289,3752,11290,11416,12399,3905,10885,11253,11422,11456,11467,3720,10801,10804,10894,11062,4709,11853,4710,10757,11401,12461,4333,11023,12479,4240,3936,3882,4707,10493,10496,10843,10846,11736,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,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% 173.59/173.34 cnf(12508,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x125081,a905)),x125082),x125082))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(12511,plain, % 173.59/173.34 (~P106(f333(f333(f335(x125111),x125112),f196(f917(x125111,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12514,plain, % 173.59/173.34 (~P106(f333(f333(f196(f917(x125141,f917(x125142,a905))),x125143),x125144))), % 173.59/173.34 inference(rename_variables,[],[4710])). % 173.59/173.34 cnf(12517,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x125171,a905)),f333(f316(x125172,x125171,x125173),f333(f317(x125172,x125171,x125173),x125174))),x125174))), % 173.59/173.34 inference(rename_variables,[],[4333])). % 173.59/173.34 cnf(12518,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x125181,a905)),x125182),x125182))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(12523,plain, % 173.59/173.34 (E(f32(x125231,x125232,x125233,x125234,x125235,x125236,x125237,x125238,x125239,a25),x125232)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12526,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x125261,a905)),f333(f180(x125261),f184(x125261,x125262,x125263))),f333(f180(x125261),x125262)))), % 173.59/173.34 inference(rename_variables,[],[4152])). % 173.59/173.34 cnf(12527,plain, % 173.59/173.34 (P106(f333(f67(x125271),f333(f180(x125271),x125272)))), % 173.59/173.34 inference(rename_variables,[],[3496])). % 173.59/173.34 cnf(12530,plain, % 173.59/173.34 (P106(f333(f333(f202(a25),x125301),x125301))), % 173.59/173.34 inference(rename_variables,[],[3456])). % 173.59/173.34 cnf(12533,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x125331),x125331))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12536,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x125361),x125361))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12547,plain, % 173.59/173.34 (P27(x125471,x125471,f5(x125471),x125472)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12555,plain, % 173.59/173.34 (~P106(f333(f333(f335(x125551),x125552),f196(f917(x125551,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12558,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x125581,x125581)),f333(f333(f265(x125581,x125581),x125582),x125582)),f313(x125581,x125583)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(12561,plain, % 173.59/173.34 (~P106(f333(f333(f335(x125611),x125612),f196(f917(x125611,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12564,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x125641,x125641)),f333(f333(f265(x125641,x125641),x125642),x125642)),f313(x125641,x125643)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(12574,plain, % 173.59/173.34 (~E(f333(f333(f159(x125741),x125742),x125743),x125743)), % 173.59/173.34 inference(rename_variables,[],[4647])). % 173.59/173.34 cnf(12581,plain, % 173.59/173.34 (P106(f333(f333(f335(x125811),x125812),f254(f917(x125811,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(12582,plain, % 173.59/173.34 (~E(f333(a123,x125821),x125821)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12585,plain, % 173.59/173.34 (P106(f333(f333(f335(f911(x125851)),f124(x125851)),f169(x125851,x125852)))), % 173.59/173.34 inference(rename_variables,[],[3650])). % 173.59/173.34 cnf(12586,plain, % 173.59/173.34 (~E(f333(f333(f159(x125861),x125862),x125863),f124(x125861))), % 173.59/173.34 inference(rename_variables,[],[4654])). % 173.59/173.34 cnf(12589,plain, % 173.59/173.34 (P27(x125891,x125891,f5(x125891),x125892)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12592,plain, % 173.59/173.34 (P106(f333(f333(f335(x125921),f333(x125922,x125923)),f333(f316(x125924,x125921,x125922),f254(f917(x125924,a905)))))), % 173.59/173.34 inference(rename_variables,[],[4060])). % 173.59/173.34 cnf(12593,plain, % 173.59/173.34 (P27(x125931,x125931,f5(x125931),x125932)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12596,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x125961,a905)),f196(f917(x125961,a905))),x125962))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(12597,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x125971,a905)),x125972),x125972))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(12600,plain, % 173.59/173.34 (P106(f333(f333(f335(x126001),f333(x126002,x126003)),f333(f316(x126004,x126001,x126002),f254(f917(x126004,a905)))))), % 173.59/173.34 inference(rename_variables,[],[4060])). % 173.59/173.34 cnf(12601,plain, % 173.59/173.34 (P27(x126011,x126011,f5(x126011),x126012)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12604,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(f911(x126041),f911(x126041))),f333(f333(f265(f911(x126041),f911(x126041)),f124(x126041)),f124(x126041))),f166(x126041,x126042)))), % 173.59/173.34 inference(rename_variables,[],[4236])). % 173.59/173.34 cnf(12607,plain, % 173.59/173.34 (~P106(f333(f333(f180(x126071),f124(x126071)),x126072))), % 173.59/173.34 inference(rename_variables,[],[4692])). % 173.59/173.34 cnf(12608,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x126081),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12614,plain, % 173.59/173.34 (E(f333(f333(f142(x126141),x126142),f124(x126141)),x126142)), % 173.59/173.34 inference(rename_variables,[],[3387])). % 173.59/173.34 cnf(12615,plain, % 173.59/173.34 (~E(f333(f333(f159(x126151),x126152),x126153),x126153)), % 173.59/173.34 inference(rename_variables,[],[4647])). % 173.59/173.34 cnf(12618,plain, % 173.59/173.34 (E(f333(f333(f142(x126181),x126182),f124(x126181)),x126182)), % 173.59/173.34 inference(rename_variables,[],[3387])). % 173.59/173.34 cnf(12619,plain, % 173.59/173.34 (~E(f333(f333(f159(x126191),x126192),x126193),x126193)), % 173.59/173.34 inference(rename_variables,[],[4647])). % 173.59/173.34 cnf(12622,plain, % 173.59/173.34 (E(f333(f333(f142(x126221),x126222),f124(x126221)),x126222)), % 173.59/173.34 inference(rename_variables,[],[3387])). % 173.59/173.34 cnf(12629,plain, % 173.59/173.34 (P55(x126291,f253(x126291,x126292))), % 173.59/173.34 inference(rename_variables,[],[3328])). % 173.59/173.34 cnf(12632,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x126321,a905)),f333(f180(x126321),f333(f144(x126321,x126322),x126323))),f333(f180(x126321),x126323)))), % 173.59/173.34 inference(rename_variables,[],[4103])). % 173.59/173.34 cnf(12633,plain, % 173.59/173.34 (E(f333(f316(x126331,x126331,f5(x126331)),x126332),x126332)), % 173.59/173.34 inference(rename_variables,[],[3513])). % 173.59/173.34 cnf(12638,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x126381,a905)),x126382),f254(f917(x126381,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(12642,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x126421),x126421))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12643,plain, % 173.59/173.34 (~E(f333(a123,x126431),x126431)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(12646,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x126461,a905)),f196(f917(x126461,a905))),x126462))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(12649,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x126491),x126491))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12652,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x126521,a905)),x126522),x126522))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(12657,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x126571,a905)),x126572),f333(f333(f315(x126571),x126573),x126572)))), % 173.59/173.34 inference(rename_variables,[],[3903])). % 173.59/173.34 cnf(12660,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x126601,a905)),x126602),x126602))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(12661,plain, % 173.59/173.34 (~P106(f333(f333(f335(x126611),x126612),f196(f917(x126611,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12664,plain, % 173.59/173.34 (~P106(f333(f333(f335(x126641),x126642),f196(f917(x126641,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12673,plain, % 173.59/173.34 (P27(x126731,x126731,f5(x126731),x126732)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12676,plain, % 173.59/173.34 (E(f333(f197(f911(x126761)),f177(x126761,x126762,x126763)),x126762)), % 173.59/173.34 inference(rename_variables,[],[3523])). % 173.59/173.34 cnf(12679,plain, % 173.59/173.34 (P28(x126791,x126791,f33(x126791),x126792,x126792)), % 173.59/173.34 inference(rename_variables,[],[4118])). % 173.59/173.34 cnf(12682,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x126821),x126821))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12683,plain, % 173.59/173.34 (P106(f333(f254(f917(x126831,a905)),x126832))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(12686,plain, % 173.59/173.34 (~P106(f333(f333(f335(x126861),x126862),f196(f917(x126861,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12689,plain, % 173.59/173.34 (P106(f333(f333(f335(x126891),f333(x126892,x126893)),f333(f316(x126894,x126891,x126892),f254(f917(x126894,a905)))))), % 173.59/173.34 inference(rename_variables,[],[4060])). % 173.59/173.34 cnf(12690,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x126901,x126901)),f333(f333(f265(x126901,x126901),x126902),x126902)),f313(x126901,x126903)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(12693,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x126931,x126931)),f333(f333(f265(x126931,x126931),x126932),x126932)),f313(x126931,x126933)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(12696,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x126961),x126961))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12697,plain, % 173.59/173.34 (P106(f333(f254(f917(x126971,a905)),x126972))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(12700,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x127001,a905)),x127002),f254(f917(x127001,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(12701,plain, % 173.59/173.34 (P28(x127011,x127011,f33(x127011),x127012,x127012)), % 173.59/173.34 inference(rename_variables,[],[4118])). % 173.59/173.34 cnf(12704,plain, % 173.59/173.34 (P106(f333(f67(x127041),f333(f180(x127041),x127042)))), % 173.59/173.34 inference(rename_variables,[],[3496])). % 173.59/173.34 cnf(12714,plain, % 173.59/173.34 (~P106(f333(f333(f196(f917(x127141,f917(x127142,a905))),x127143),x127144))), % 173.59/173.34 inference(rename_variables,[],[4710])). % 173.59/173.34 cnf(12717,plain, % 173.59/173.34 (~P106(f333(f333(f196(f917(x127171,f917(x127172,a905))),x127173),x127174))), % 173.59/173.34 inference(rename_variables,[],[4710])). % 173.59/173.34 cnf(12720,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x127201,a905)),x127202),f254(f917(x127201,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(12723,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(x127231,x127231)),f333(f333(f265(x127231,x127231),x127232),x127232)),f313(x127231,x127233)))), % 173.59/173.34 inference(rename_variables,[],[4094])). % 173.59/173.34 cnf(12726,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),f333(f333(f87(a910),x127261),x127262)),x127262))), % 173.59/173.34 inference(rename_variables,[],[4707])). % 173.59/173.34 cnf(12727,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x127271),f333(a123,x127271)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12730,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x127301,a905)),x127302),f254(f917(x127301,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(12733,plain, % 173.59/173.34 (E(f32(x127331,x127332,x127333,x127334,x127335,x127336,x127337,x127338,x127339,a25),x127332)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12744,plain, % 173.59/173.34 (~P106(f333(f333(f335(x127441),x127442),f196(f917(x127441,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12745,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(f911(x127451),f911(x127451))),f333(f333(f265(f911(x127451),f911(x127451)),f124(x127451)),f124(x127451))),f166(x127451,x127452)))), % 173.59/173.34 inference(rename_variables,[],[4236])). % 173.59/173.34 cnf(12750,plain, % 173.59/173.34 (~P106(f333(f333(f335(x127501),x127502),f196(f917(x127501,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12755,plain, % 173.59/173.34 (P34(x127551,x127552,f124(x127551))), % 173.59/173.34 inference(rename_variables,[],[3392])). % 173.59/173.34 cnf(12758,plain, % 173.59/173.34 (E(f333(f197(f911(x127581)),f177(x127581,x127582,x127583)),x127582)), % 173.59/173.34 inference(rename_variables,[],[3523])). % 173.59/173.34 cnf(12761,plain, % 173.59/173.34 (~P106(f333(f333(f335(x127611),x127612),f196(f917(x127611,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12767,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x127671),x127671))), % 173.59/173.34 inference(rename_variables,[],[4683])). % 173.59/173.34 cnf(12769,plain, % 173.59/173.34 (P106(f333(f333(f335(f916(f911(x127691),f911(x127691))),f333(f333(f265(f911(x127691),f911(x127691)),f177(x127691,f333(f197(f911(x127691)),x127692),x127693)),x127692)),f166(x127691,f254(f917(f916(x127691,x127691),a905)))))), % 173.59/173.34 inference(scs_inference,[],[4717,4118,12679,3690,11305,12353,12452,12455,12547,12589,12593,12601,3698,3707,3426,3392,4657,4658,3324,3327,3328,4656,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,12010,12327,12523,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,11839,12142,12167,12179,12208,12214,12306,12415,12582,3512,3658,12114,4634,10634,10728,11185,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3096,3097,3100,3101,3102,3105,3107,3108,3111,3120,3129,3139,3140,3150,3154,3157,3161,3163,3217,3219,3220,3228,3247,4618,3794,4021,3497,3387,12614,12618,12622,3402,3508,3915,4222,3523,12108,12676,12758,3288,4007,11627,3355,3315,3773,3310,3297,3927,3334,3513,11033,11155,12416,12633,3386,4091,4647,10474,10631,11494,12574,12615,4654,12586,3446,11959,4694,11211,11310,11538,11541,3560,4672,3350,3351,10541,10852,3612,3268,3372,11617,4236,12604,12745,4094,11231,11366,11425,12558,12564,12690,12693,12723,4712,11133,11377,11488,11511,11546,11552,12502,4713,11264,11380,11491,4714,11383,4715,11443,4716,3371,3650,12458,12499,12585,3821,3602,4507,4508,4645,11610,3756,4092,3972,4017,3636,3898,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,12050,12138,12201,12277,12318,12393,12396,3908,11856,3439,3536,11695,3717,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,12049,12253,12256,12339,12505,4700,11739,11766,11803,11836,3896,3659,4042,3484,3485,3459,4684,4642,3847,3643,4701,4229,11508,3778,3496,11981,11984,12423,12527,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,12046,4198,4157,12131,12473,4103,11030,12312,12483,4152,11234,12350,12422,12482,12526,3822,12141,12284,12360,12406,4186,3839,11237,11315,11398,11462,12305,12374,12638,12700,12720,4704,10980,11388,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,12009,12111,12166,12367,3457,10936,10983,10986,11017,11039,11075,11113,11149,12182,12185,12188,12191,12381,12384,12387,12390,12466,12649,3458,10645,10867,10959,11078,11775,12013,12022,12117,12128,12147,12152,12194,12217,3532,12342,4683,10517,11001,11042,11051,11889,11911,12081,12084,12087,12090,12178,12197,12200,12213,12265,12268,12271,12274,12434,12437,12533,12536,12642,12682,3609,10818,11086,11130,11369,11372,11451,11527,11699,11939,12581,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,11990,12259,12262,12296,12343,12370,12511,12555,12561,12661,12664,12686,12744,12750,3517,10849,10879,10888,10891,11480,11682,12683,3556,3549,3976,3913,10520,11859,11893,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,12040,12069,12072,12075,12078,12338,3477,10882,11036,11106,11863,11894,12039,12239,12442,3937,4277,4690,3948,3983,4675,4678,3432,3436,4677,4676,3768,4371,4706,10751,10754,4711,11220,11223,11413,11535,11572,4060,11569,11914,11918,12592,12600,3903,11146,11152,11172,12163,12289,12373,3752,11290,11416,12399,12508,12518,12597,12652,4234,3905,10885,11253,11422,11456,11467,12309,12596,3720,10801,10804,10894,11062,4709,11853,4710,10757,11401,12461,12470,12514,12714,4333,11023,12479,12494,4240,3936,3882,4707,10493,10496,10843,10846,11736,11919,4708,11833,3906,10807,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946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% 173.59/173.34 cnf(12770,plain, % 173.59/173.34 (P106(f333(f333(f335(x127701),x127702),f254(f917(x127701,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(12774,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x127741,a905)),x127742),x127742))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(12777,plain, % 173.59/173.34 (~P106(f333(f333(f335(x127771),x127772),f196(f917(x127771,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(12780,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),f2(a1)),f333(f333(f256(a1),f333(f82(a1),x127801)),x127802)))), % 173.59/173.34 inference(rename_variables,[],[3936])). % 173.59/173.34 cnf(12783,plain, % 173.59/173.34 (E(f32(x127831,x127832,x127833,x127834,x127835,x127836,x127837,x127838,x127839,a25),x127832)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12785,plain, % 173.59/173.34 (E(f32(x127851,x127852,x127853,x127854,x127855,x127856,x127857,x127858,x127859,a25),x127852)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12787,plain, % 173.59/173.34 (P26(x127871,x127872,f196(f917(f909(x127871),a905)))), % 173.59/173.34 inference(rename_variables,[],[3511])). % 173.59/173.34 cnf(12796,plain, % 173.59/173.34 (E(f333(f333(x127961,x127962),f333(f192(x127963,x127964,x127961),x127962)),f333(f192(x127963,x127964,x127961),f333(a123,x127962)))), % 173.59/173.34 inference(rename_variables,[],[3856])). % 173.59/173.34 cnf(12798,plain, % 173.59/173.34 (P27(x127981,x127981,f5(x127981),x127982)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12800,plain, % 173.59/173.34 (P27(x128001,x128001,f5(x128001),x128002)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(12807,plain, % 173.59/173.34 (E(f32(x128071,x128072,x128073,x128074,x128075,x128076,x128077,x128078,x128079,a25),x128072)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12812,plain, % 173.59/173.34 (P40(x128121,f161(x128121,x128122))), % 173.59/173.34 inference(rename_variables,[],[3324])). % 173.59/173.34 cnf(12816,plain, % 173.59/173.34 (E(f32(x128161,x128162,x128163,x128164,x128165,x128166,x128167,x128168,x128169,a25),x128162)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12818,plain, % 173.59/173.34 (E(f32(x128181,x128182,x128183,x128184,x128185,x128186,x128187,x128188,x128189,a25),x128182)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12820,plain, % 173.59/173.34 (P56(x128201,x128202,f253(x128201,x128202))), % 173.59/173.34 inference(rename_variables,[],[3425])). % 173.59/173.34 cnf(12822,plain, % 173.59/173.34 (P56(x128221,x128222,f253(x128221,x128222))), % 173.59/173.34 inference(rename_variables,[],[3425])). % 173.59/173.34 cnf(12824,plain, % 173.59/173.34 (P56(x128241,x128242,f253(x128241,x128242))), % 173.59/173.34 inference(rename_variables,[],[3425])). % 173.59/173.34 cnf(12826,plain, % 173.59/173.34 (E(f32(x128261,x128262,x128263,x128264,x128265,x128266,x128267,x128268,x128269,a25),x128262)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12831,plain, % 173.59/173.34 (P41(x128311,f253(x128311,x128312))), % 173.59/173.34 inference(rename_variables,[],[3325])). % 173.59/173.34 cnf(12841,plain, % 173.59/173.34 (E(f32(x128411,x128412,x128413,x128414,x128415,x128416,x128417,x128418,x128419,a25),x128412)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12843,plain, % 173.59/173.34 (E(f32(x128431,x128432,x128433,x128434,x128435,x128436,x128437,x128438,x128439,a25),x128432)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12845,plain, % 173.59/173.34 (E(f32(x128451,x128452,x128453,x128454,x128455,x128456,x128457,x128458,x128459,a25),x128452)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12849,plain, % 173.59/173.34 (E(f196(f917(f916(x128491,x128491),a905)),f253(x128491,f196(f917(x128491,a905))))), % 173.59/173.34 inference(rename_variables,[],[3527])). % 173.59/173.34 cnf(12851,plain, % 173.59/173.34 (P28(x128511,x128511,f33(x128511),x128512,x128512)), % 173.59/173.34 inference(rename_variables,[],[4118])). % 173.59/173.34 cnf(12853,plain, % 173.59/173.34 (P28(x128531,x128531,f33(x128531),x128532,x128532)), % 173.59/173.34 inference(rename_variables,[],[4118])). % 173.59/173.34 cnf(12855,plain, % 173.59/173.34 (P28(x128551,x128551,f33(x128551),x128552,x128552)), % 173.59/173.34 inference(rename_variables,[],[4118])). % 173.59/173.34 cnf(12859,plain, % 173.59/173.34 (E(f32(x128591,x128592,x128593,x128594,x128595,x128596,x128597,x128598,x128599,a25),x128592)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12869,plain, % 173.59/173.34 (E(f32(x128691,x128692,x128693,x128694,x128695,x128696,x128697,x128698,x128699,a25),x128692)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12871,plain, % 173.59/173.34 (P45(x128711,x128712,x128713,x128714,f196(f917(x128711,a905)),x128714)), % 173.59/173.34 inference(rename_variables,[],[4393])). % 173.59/173.34 cnf(12880,plain, % 173.59/173.34 (E(f32(x128801,x128802,x128803,x128804,x128805,x128806,x128807,x128808,x128809,a25),x128802)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12882,plain, % 173.59/173.34 (P55(x128821,f253(x128821,x128822))), % 173.59/173.34 inference(rename_variables,[],[3328])). % 173.59/173.34 cnf(12887,plain, % 173.59/173.34 (P17(x128871,f917(x128871,a905),f315(x128871))), % 173.59/173.34 inference(rename_variables,[],[3429])). % 173.59/173.34 cnf(12900,plain, % 173.59/173.34 (P35(x129001,x129002,f124(x129001),f124(x129001))), % 173.59/173.34 inference(rename_variables,[],[3698])). % 173.59/173.34 cnf(12901,plain, % 173.59/173.34 (E(f32(x129011,x129012,x129013,x129014,x129015,x129016,x129017,x129018,x129019,a25),x129012)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(12903,plain, % 173.59/173.34 (P35(x129031,x129032,f124(x129031),f124(x129031))), % 173.59/173.34 inference(rename_variables,[],[3698])). % 173.59/173.34 cnf(12909,plain, % 173.59/173.34 (P59(x129091,f196(f917(x129091,a905)),x129092)), % 173.59/173.34 inference(rename_variables,[],[3475])). % 173.59/173.34 cnf(12915,plain, % 173.59/173.34 (P58(x129151,x129151,f253(x129151,x129152))), % 173.59/173.34 inference(rename_variables,[],[3426])). % 173.59/173.34 cnf(12933,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x129331),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12942,plain, % 173.59/173.34 (~P106(f333(f333(f247(a1),f333(f111(a1),x129421)),f333(f86(a1),f333(f111(a1),x129422))))), % 173.59/173.34 inference(rename_variables,[],[4705])). % 173.59/173.34 cnf(12952,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x129521),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12955,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x129551),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12958,plain, % 173.59/173.34 (P106(f333(f67(a910),f311(a910,x129581,x129582)))), % 173.59/173.34 inference(rename_variables,[],[3660])). % 173.59/173.34 cnf(12961,plain, % 173.59/173.34 (P106(f333(f67(a910),f311(a910,x129611,x129612)))), % 173.59/173.34 inference(rename_variables,[],[3660])). % 173.59/173.34 cnf(12964,plain, % 173.59/173.34 (P106(f333(f67(a910),f311(a910,x129641,x129642)))), % 173.59/173.34 inference(rename_variables,[],[3660])). % 173.59/173.34 cnf(12967,plain, % 173.59/173.34 (P106(f333(f67(a910),f311(a910,x129671,x129672)))), % 173.59/173.34 inference(rename_variables,[],[3660])). % 173.59/173.34 cnf(12974,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),f333(f86(a1),f333(f111(a1),x129741))),f333(f111(a1),x129742)))), % 173.59/173.34 inference(rename_variables,[],[3937])). % 173.59/173.34 cnf(12979,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x129791),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(12980,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x129801),x129801))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(12987,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x129871),f333(a123,x129871)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(12994,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x129941),x129941))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(12997,plain, % 173.59/173.34 (P106(f333(f67(a910),f311(a910,x129971,x129972)))), % 173.59/173.34 inference(rename_variables,[],[3660])). % 173.59/173.34 cnf(13000,plain, % 173.59/173.34 (P106(f333(f67(a910),f311(a910,x130001,x130002)))), % 173.59/173.34 inference(rename_variables,[],[3660])). % 173.59/173.34 cnf(13003,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x130031),x130031))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13004,plain, % 173.59/173.34 (~E(f333(a123,x130041),f2(a910))), % 173.59/173.34 inference(rename_variables,[],[4634])). % 173.59/173.34 cnf(13021,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f51(a910,x130211,x130212)),x130211))), % 173.59/173.34 inference(rename_variables,[],[3913])). % 173.59/173.34 cnf(13026,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x130261),f333(a123,x130261)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(13029,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x130291),f333(a123,x130291)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(13030,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x130301),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(13039,plain, % 173.59/173.34 (~P106(f333(f333(f247(a1),f333(f111(a1),x130391)),f2(a1)))), % 173.59/173.34 inference(rename_variables,[],[4700])). % 173.59/173.34 cnf(13040,plain, % 173.59/173.34 (P106(f333(f254(f917(x130401,a905)),x130402))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(13043,plain, % 173.59/173.34 (~P106(f333(f333(f247(a1),f333(f111(a1),x130431)),f2(a1)))), % 173.59/173.34 inference(rename_variables,[],[4700])). % 173.59/173.34 cnf(13044,plain, % 173.59/173.34 (P106(f333(f254(f917(x130441,a905)),x130442))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(13047,plain, % 173.59/173.34 (P106(f333(f254(f917(x130471,a905)),x130472))), % 173.59/173.34 inference(rename_variables,[],[3517])). % 173.59/173.34 cnf(13058,plain, % 173.59/173.34 (~P106(f333(f333(f335(x130581),x130582),f196(f917(x130581,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13059,plain, % 173.59/173.34 (P106(f333(f67(x130591),f196(f917(x130591,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(13068,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),f2(a910)),x130681))), % 173.59/173.34 inference(rename_variables,[],[3477])). % 173.59/173.34 cnf(13071,plain, % 173.59/173.34 (~P106(f333(f333(f335(x130711),x130712),f196(f917(x130711,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13074,plain, % 173.59/173.34 (~P106(f333(f333(f335(x130741),x130742),f196(f917(x130741,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13077,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x130771),x130771))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13085,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x130851),f333(a123,x130851)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(13088,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x130881),x130881))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13093,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x130931),x130931))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13096,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x130961),x130961))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13099,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x130991),x130991))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13102,plain, % 173.59/173.34 (E(f333(f333(f23(f917(x131021,a905)),f196(f917(x131021,a905))),x131022),f196(f917(x131021,a905)))), % 173.59/173.34 inference(rename_variables,[],[3724])). % 173.59/173.34 cnf(13103,plain, % 173.59/173.34 (P106(f333(f67(x131031),f196(f917(x131031,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(13106,plain, % 173.59/173.34 (E(f333(f333(f23(f917(x131061,a905)),f196(f917(x131061,a905))),x131062),f196(f917(x131061,a905)))), % 173.59/173.34 inference(rename_variables,[],[3724])). % 173.59/173.34 cnf(13107,plain, % 173.59/173.34 (P106(f333(f67(x131071),f196(f917(x131071,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(13110,plain, % 173.59/173.34 (E(f333(f333(f23(f917(x131101,a905)),f196(f917(x131101,a905))),x131102),f196(f917(x131101,a905)))), % 173.59/173.34 inference(rename_variables,[],[3724])). % 173.59/173.34 cnf(13111,plain, % 173.59/173.34 (P106(f333(f67(x131111),f196(f917(x131111,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(13114,plain, % 173.59/173.34 (E(f333(f333(f23(f917(x131141,a905)),f196(f917(x131141,a905))),x131142),f196(f917(x131141,a905)))), % 173.59/173.34 inference(rename_variables,[],[3724])). % 173.59/173.34 cnf(13115,plain, % 173.59/173.34 (P106(f333(f67(x131151),f196(f917(x131151,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(13118,plain, % 173.59/173.34 (P106(f333(f333(f335(f911(x131181)),f124(x131181)),f169(x131181,x131182)))), % 173.59/173.34 inference(rename_variables,[],[3650])). % 173.59/173.34 cnf(13119,plain, % 173.59/173.34 (E(f32(x131191,x131192,x131193,x131194,x131195,x131196,x131197,x131198,x131199,a25),x131192)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(13124,plain, % 173.59/173.34 (E(f333(f333(f23(f917(x131241,a905)),f196(f917(x131241,a905))),x131242),f196(f917(x131241,a905)))), % 173.59/173.34 inference(rename_variables,[],[3724])). % 173.59/173.34 cnf(13125,plain, % 173.59/173.34 (P106(f333(f67(x131251),f196(f917(x131251,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(13129,plain, % 173.59/173.34 (P106(f333(f67(x131291),f196(f917(x131291,a905))))), % 173.59/173.34 inference(rename_variables,[],[3532])). % 173.59/173.34 cnf(13132,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x131321),x131321))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13136,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x131361),x131361))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(13149,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x131491),x131491))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13156,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x131561),x131561))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(13165,plain, % 173.59/173.34 (~P106(f333(f333(f335(x131651),x131652),f196(f917(x131651,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13176,plain, % 173.59/173.34 (P106(f333(f333(f335(x131761),x131762),f254(f917(x131761,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(13180,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x131801,a905)),x131802),x131802))), % 173.59/173.34 inference(rename_variables,[],[3752])). % 173.59/173.34 cnf(13186,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x131861),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(13187,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x131871),x131871))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(13191,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x131911),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(13192,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x131921),x131921))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(13201,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x132011),x132011))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13202,plain, % 173.59/173.34 (P106(f333(f67(a910),f309(a910,x132021,x132022)))), % 173.59/173.34 inference(rename_variables,[],[3659])). % 173.59/173.34 cnf(13209,plain, % 173.59/173.34 (E(f333(f333(f16(x132091,x132092),x132093),x132094),x132093)), % 173.59/173.34 inference(rename_variables,[],[3446])). % 173.59/173.34 cnf(13212,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x132121,a905)),f333(f180(x132121),f184(x132121,x132122,x132123))),f333(f180(x132121),x132122)))), % 173.59/173.34 inference(rename_variables,[],[4152])). % 173.59/173.34 cnf(13216,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x132161),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(13217,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x132171),x132171))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(13221,plain, % 173.59/173.34 (~P106(f333(f333(f247(a910),x132211),f2(a910)))), % 173.59/173.34 inference(rename_variables,[],[4687])). % 173.59/173.34 cnf(13222,plain, % 173.59/173.34 (P106(f333(f333(f246(a1),x132221),x132221))), % 173.59/173.34 inference(rename_variables,[],[3458])). % 173.59/173.34 cnf(13227,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x132271),x132271))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13230,plain, % 173.59/173.34 (P106(f333(f333(f246(a910),x132301),x132301))), % 173.59/173.34 inference(rename_variables,[],[3457])). % 173.59/173.34 cnf(13233,plain, % 173.59/173.34 (~P106(f333(f333(f246(a910),f333(a123,x132331)),x132331))), % 173.59/173.34 inference(rename_variables,[],[4693])). % 173.59/173.34 cnf(13239,plain, % 173.59/173.34 (P106(f333(f333(f335(x132391),f333(x132392,x132393)),f333(f316(x132394,x132391,x132392),f254(f917(x132394,a905)))))), % 173.59/173.34 inference(rename_variables,[],[4060])). % 173.59/173.34 cnf(13240,plain, % 173.59/173.34 (P27(x132401,x132401,f5(x132401),x132402)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(13244,plain, % 173.59/173.34 (P106(f333(f333(f335(x132441),x132442),f254(f917(x132441,a905))))), % 173.59/173.34 inference(rename_variables,[],[3609])). % 173.59/173.34 cnf(13245,plain, % 173.59/173.34 (~P106(f333(f333(f335(x132451),x132452),f196(f917(x132451,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13249,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x132491,a905)),x132492),f254(f917(x132491,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(13250,plain, % 173.59/173.34 (P27(x132501,x132501,f5(x132501),x132502)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(13254,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x132541,a905)),x132542),f254(f917(x132541,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(13255,plain, % 173.59/173.34 (P27(x132551,x132551,f5(x132551),x132552)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(13259,plain, % 173.59/173.34 (P27(x132591,x132591,f5(x132591),x132592)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(13262,plain, % 173.59/173.34 (~P106(f333(f333(f247(f917(x132621,a905)),x132622),f196(f917(x132621,a905))))), % 173.59/173.34 inference(rename_variables,[],[4704])). % 173.59/173.34 cnf(13265,plain, % 173.59/173.34 (P27(x132651,x132651,f5(x132651),x132652)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(13268,plain, % 173.59/173.34 (P27(x132681,x132681,f5(x132681),x132682)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(13274,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x132741,a905)),x132742),f254(f917(x132741,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(13279,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x132791,a905)),f196(f917(x132791,a905))),x132792))), % 173.59/173.34 inference(rename_variables,[],[3905])). % 173.59/173.34 cnf(13283,plain, % 173.59/173.34 (E(f32(x132831,x132832,x132833,x132834,x132835,x132836,x132837,x132838,x132839,a25),x132832)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(13287,plain, % 173.59/173.34 (~P106(f333(f333(f335(x132871),x132872),f196(f917(x132871,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13292,plain, % 173.59/173.34 (P27(x132921,x132921,f5(x132921),x132922)), % 173.59/173.34 inference(rename_variables,[],[3690])). % 173.59/173.34 cnf(13295,plain, % 173.59/173.34 (P106(f333(f333(f246(f917(x132951,a905)),x132952),f254(f917(x132951,a905))))), % 173.59/173.34 inference(rename_variables,[],[3839])). % 173.59/173.34 cnf(13303,plain, % 173.59/173.34 (E(f333(f333(f16(x133031,x133032),x133033),x133034),x133033)), % 173.59/173.34 inference(rename_variables,[],[3446])). % 173.59/173.34 cnf(13306,plain, % 173.59/173.34 (~P106(f333(f333(f335(x133061),x133062),f196(f917(x133061,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13309,plain, % 173.59/173.34 (~P106(f333(f333(f335(x133091),x133092),f196(f917(x133091,a905))))), % 173.59/173.34 inference(rename_variables,[],[4696])). % 173.59/173.34 cnf(13316,plain, % 173.59/173.34 (E(f32(x133161,x133162,x133163,x133164,x133165,x133166,x133167,x133168,x133169,a25),x133162)), % 173.59/173.34 inference(rename_variables,[],[4606])). % 173.59/173.34 cnf(13318,plain, % 173.59/173.34 (~E(f333(a123,x133181),x133181)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(13321,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x133211),f333(a123,x133211)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(13322,plain, % 173.59/173.34 (~E(f333(a123,x133221),x133221)), % 173.59/173.34 inference(rename_variables,[],[4622])). % 173.59/173.34 cnf(13325,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x133251),f333(a123,f333(f333(f87(a910),x133252),x133251))))), % 173.59/173.34 inference(rename_variables,[],[3906])). % 173.59/173.34 cnf(13326,plain, % 173.59/173.34 (P106(f333(f333(f247(a910),x133261),f333(a123,x133261)))), % 173.59/173.34 inference(rename_variables,[],[3524])). % 173.59/173.34 cnf(13328,plain, % 173.59/173.34 (~E(f333(f333(f88(a910),f333(a123,f2(a910))),f130(x133281)),f333(f333(f88(a910),f333(a123,f2(a910))),f136(x133281,x133282,x133283)))), % 173.59/173.35 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942,7012,7013,7020,7043,7073,7075,7121,7143,7144,7161,7162,7200,7244,7245,7342,7409,7410,7411,7412,7427,7459,7512,7513,7522,7527,7528,7539,7570,7571,7572,7573,7714,7716,7717,7718,7724,7725,7937,7943,7944,7954,7992,8115,8172,8194,8195,8211,8268,8365,8437,8438,8442,8475,8539,8540,8615,8635,8636,8637,8638,8788,9022,9048,9049,9130,9147,9202,9203,9324,9356,9381,9418,9462,9660,9794,9937,10120,10177,10180,10325,5757,6543,6544,6632])). % 173.59/173.35 cnf(13335,plain, % 173.59/173.35 (P106(f333(f333(f246(a1),f2(a1)),f333(f111(a1),x133351)))), % 173.59/173.35 inference(rename_variables,[],[3556])). % 173.59/173.35 cnf(13338,plain, % 173.59/173.35 (P106(f333(f333(f246(a910),f2(a910)),x133381))), % 173.59/173.35 inference(rename_variables,[],[3477])). % 173.59/173.35 cnf(13342,plain, % 173.59/173.35 (~E(f333(a123,x133421),f2(a910))), % 173.59/173.35 inference(rename_variables,[],[4634])). % 173.59/173.35 cnf(13345,plain, % 173.59/173.35 (P106(f333(f333(f246(a1),x133451),x133451))), % 173.59/173.35 inference(rename_variables,[],[3458])). % 173.59/173.35 cnf(13351,plain, % 173.59/173.35 (~P106(f333(f333(f335(x133511),x133512),f196(f917(x133511,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13354,plain, % 173.59/173.35 (P106(f333(f67(a910),f311(a910,x133541,x133542)))), % 173.59/173.35 inference(rename_variables,[],[3660])). % 173.59/173.35 cnf(13355,plain, % 173.59/173.35 (E(f333(f333(f244(a910),f333(a123,x133551)),f333(a123,x133552)),f333(a123,f333(f333(f244(a910),x133551),x133552)))), % 173.59/173.35 inference(rename_variables,[],[3624])). % 173.59/173.35 cnf(13358,plain, % 173.59/173.35 (P106(f333(f67(a910),f311(a910,x133581,x133582)))), % 173.59/173.35 inference(rename_variables,[],[3660])). % 173.59/173.35 cnf(13359,plain, % 173.59/173.35 (E(f333(f333(f245(a910),f333(a123,x133591)),f333(a123,x133592)),f333(a123,f333(f333(f245(a910),x133591),x133592)))), % 173.59/173.35 inference(rename_variables,[],[3625])). % 173.59/173.35 cnf(13362,plain, % 173.59/173.35 (P106(f333(f67(a910),f311(a910,x133621,x133622)))), % 173.59/173.35 inference(rename_variables,[],[3660])). % 173.59/173.35 cnf(13371,plain, % 173.59/173.35 (~P106(f333(f333(f335(x133711),x133712),f196(f917(x133711,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13372,plain, % 173.59/173.35 (E(f333(f333(f16(x133721,x133722),x133723),x133724),x133723)), % 173.59/173.35 inference(rename_variables,[],[3446])). % 173.59/173.35 cnf(13375,plain, % 173.59/173.35 (P106(f333(f333(f246(f917(x133751,a905)),f333(f180(x133751),f333(f144(x133751,x133752),x133753))),f333(f180(x133751),x133753)))), % 173.59/173.35 inference(rename_variables,[],[4103])). % 173.59/173.35 cnf(13376,plain, % 173.59/173.35 (E(f333(f333(f16(x133761,x133762),x133763),x133764),x133763)), % 173.59/173.35 inference(rename_variables,[],[3446])). % 173.59/173.35 cnf(13379,plain, % 173.59/173.35 (P106(f333(f333(f246(f917(x133791,a905)),f333(f180(x133791),f333(f333(f183(x133791),x133792),x133793))),f333(f180(x133791),x133793)))), % 173.59/173.35 inference(rename_variables,[],[4147])). % 173.59/173.35 cnf(13380,plain, % 173.59/173.35 (E(f333(f333(f16(x133801,x133802),x133803),x133804),x133803)), % 173.59/173.35 inference(rename_variables,[],[3446])). % 173.59/173.35 cnf(13384,plain, % 173.59/173.35 (E(f333(f333(f16(x133841,x133842),x133843),x133844),x133843)), % 173.59/173.35 inference(rename_variables,[],[3446])). % 173.59/173.35 cnf(13397,plain, % 173.59/173.35 (P106(f333(f333(f246(a1),f2(a1)),f333(f111(a1),x133971)))), % 173.59/173.35 inference(rename_variables,[],[3556])). % 173.59/173.35 cnf(13402,plain, % 173.59/173.35 (P27(x134021,x134021,f5(x134021),x134022)), % 173.59/173.35 inference(rename_variables,[],[3690])). % 173.59/173.35 cnf(13405,plain, % 173.59/173.35 (~P106(f333(f333(f335(x134051),x134052),f196(f917(x134051,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13406,plain, % 173.59/173.35 (E(f32(x134061,x134062,x134063,x134064,x134065,x134066,x134067,x134068,x134069,a25),x134062)), % 173.59/173.35 inference(rename_variables,[],[4606])). % 173.59/173.35 cnf(13407,plain, % 173.59/173.35 (P27(x134071,x134071,f5(x134071),x134072)), % 173.59/173.35 inference(rename_variables,[],[3690])). % 173.59/173.35 cnf(13411,plain, % 173.59/173.35 (E(f32(x134111,x134112,x134113,x134114,x134115,x134116,x134117,x134118,x134119,a25),x134112)), % 173.59/173.35 inference(rename_variables,[],[4606])). % 173.59/173.35 cnf(13417,plain, % 173.59/173.35 (E(f32(x134171,x134172,x134173,x134174,x134175,x134176,x134177,x134178,x134179,a25),x134172)), % 173.59/173.35 inference(rename_variables,[],[4606])). % 173.59/173.35 cnf(13418,plain, % 173.59/173.35 (P106(f333(f333(f246(a1),x134181),x134181))), % 173.59/173.35 inference(rename_variables,[],[3458])). % 173.59/173.35 cnf(13421,plain, % 173.59/173.35 (E(f32(x134211,x134212,x134213,x134214,x134215,x134216,x134217,x134218,x134219,a25),x134212)), % 173.59/173.35 inference(rename_variables,[],[4606])). % 173.59/173.35 cnf(13422,plain, % 173.59/173.35 (P106(f333(f333(f246(a1),x134221),x134221))), % 173.59/173.35 inference(rename_variables,[],[3458])). % 173.59/173.35 cnf(13425,plain, % 173.59/173.35 (E(f32(x134251,x134252,x134253,x134254,x134255,x134256,x134257,x134258,x134259,a25),x134252)), % 173.59/173.35 inference(rename_variables,[],[4606])). % 173.59/173.35 cnf(13426,plain, % 173.59/173.35 (P106(f333(f333(f246(a1),x134261),x134261))), % 173.59/173.35 inference(rename_variables,[],[3458])). % 173.59/173.35 cnf(13437,plain, % 173.59/173.35 (P106(f333(f333(f246(a910),f2(a910)),x134371))), % 173.59/173.35 inference(rename_variables,[],[3477])). % 173.59/173.35 cnf(13438,plain, % 173.59/173.35 (P106(f333(f333(f247(a910),f2(a910)),f333(a123,x134381)))), % 173.59/173.35 inference(rename_variables,[],[3536])). % 173.59/173.35 cnf(13439,plain, % 173.59/173.35 (E(f32(x134391,x134392,x134393,x134394,x134395,x134396,x134397,x134398,x134399,a25),x134392)), % 173.59/173.35 inference(rename_variables,[],[4606])). % 173.59/173.35 cnf(13442,plain, % 173.59/173.35 (P106(f333(f54(f32(x134421,f333(f333(f87(a910),f333(f333(f88(a910),f333(f264(a910,a910),f333(f333(f265(a910,a910),f2(a910)),x134422))),f333(a123,f333(f333(f87(a910),x134423),f333(f268(a910,a910),f333(f333(f265(a910,a910),f2(a910)),x134422)))))),f333(f268(a910,a910),f333(f333(f265(a910,a910),f2(a910)),x134422))),x134424,x134425,x134426,x134427,x134428,x134429,x1344210,a25),f333(a123,f333(f333(f87(a910),x134423),f333(f268(a910,a910),f333(f333(f265(a910,a910),f2(a910)),x134422))))),f333(f333(f265(a910,a910),f2(a910)),x134422)))), % 173.59/173.35 inference(scs_inference,[],[4717,4118,12679,12701,12851,12853,12855,3690,11305,12353,12452,12455,12547,12589,12593,12601,12673,12798,12800,13240,13250,13255,13259,13265,13268,13292,13402,13407,3698,12419,12900,12903,3707,3425,12820,12822,12824,3426,12915,3392,12755,4657,4658,11936,4393,12871,3429,12887,3265,3324,12812,3325,12831,3326,3327,3328,12629,12882,4656,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,12010,12327,12523,12733,12783,12785,12807,12816,12818,12826,12841,12843,12845,12859,12869,12880,12901,13119,13283,13316,13406,13411,13417,13421,13425,13439,3754,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,11839,12142,12167,12179,12208,12214,12306,12415,12582,12643,13318,13322,3512,3475,12909,3658,12114,4634,10634,10728,11185,11285,13004,13342,3063,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3096,3097,3100,3101,3102,3104,3105,3107,3108,3111,3117,3120,3129,3136,3139,3140,3150,3151,3152,3154,3157,3161,3163,3166,3169,3190,3199,3205,3213,3217,3218,3219,3220,3228,3229,4617,3247,3323,4618,3794,4021,3437,3497,3413,3387,12614,12618,12622,3402,3508,3915,4222,3370,3523,12108,12676,12758,3288,3289,4007,11627,3511,12787,3355,3315,3773,3310,3418,4126,4015,3837,3297,3273,3277,3927,3334,3513,11033,11155,12416,12633,3386,4091,4647,10474,10631,11494,12574,12615,12619,4654,12586,3446,11959,11962,13209,13303,13372,13376,13380,13384,4050,4694,11211,11310,11538,11541,3856,12796,3441,3560,3779,3552,4672,3527,12849,3350,3351,10541,10852,4681,3612,3342,3268,3401,3372,11617,4236,12604,12745,4094,11231,11366,11425,12558,12564,12690,12693,12723,4712,11133,11377,11488,11511,11546,11552,12502,4713,11264,11380,11491,4714,11383,11436,4715,11443,4716,3371,3650,12458,12499,12585,13118,3821,3602,4507,4508,3634,3671,4645,11610,3798,3756,3800,4092,3972,3724,13102,13106,13110,13114,13124,4017,12449,3636,3898,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,12050,12138,12201,12277,12318,12393,12396,12727,12987,13026,13029,13085,13321,13326,3908,11856,3439,3536,11695,11974,13438,3717,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,12049,12253,12256,12339,12505,12608,12933,12952,12955,12979,13030,13186,13191,13216,4700,11739,11766,11803,11836,13039,13043,3896,3659,13202,3660,12958,12961,12964,12967,12997,13000,13354,13358,13362,3662,4042,3624,13355,3625,13359,3484,3485,3459,4684,3349,4642,3847,4158,3643,4701,4229,11508,3778,3496,11981,11984,12423,12527,12704,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,12046,12607,4198,4157,12131,12473,4103,11030,12312,12483,12632,13375,4147,13379,4152,11234,12350,12422,12482,12526,13212,3822,12141,12284,12360,12406,4122,4186,3839,11237,11315,11398,11462,12305,12374,12638,12700,12720,12730,13249,13254,13274,13295,4704,10980,11388,12486,13262,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,12009,12111,12166,12367,12530,3457,10936,10983,10986,11017,11039,11075,11113,11149,12182,12185,12188,12191,12381,12384,12387,12390,12466,12649,12696,12980,13003,13077,13088,13093,13096,13099,13132,13149,13201,13227,13230,3458,10645,10867,10959,11078,11775,12013,12022,12117,12128,12147,12152,12194,12217,12234,12994,13136,13156,13187,13192,13217,13222,13345,13418,13422,13426,3532,12342,13059,13103,13107,13111,13115,13125,13129,4683,10517,11001,11042,11051,11889,11911,12081,12084,12087,12090,12178,12197,12200,12213,12265,12268,12271,12274,12434,12437,12533,12536,12642,12682,12767,3609,10818,11086,11130,11369,11372,11451,11527,11699,11939,12581,12770,13176,13244,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,11990,12259,12262,12296,12343,12370,12511,12555,12561,12661,12664,12686,12744,12750,12761,12777,13058,13071,13074,13165,13245,13287,13306,13309,13351,13371,13405,3517,10849,10879,10888,10891,11480,11682,12683,12697,13040,13044,13047,3556,13335,3549,3976,3913,10520,11859,11893,13021,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,12040,12069,12072,12075,12078,12338,13233,3477,10882,11036,11106,11863,11894,12039,12239,12442,12467,13068,13338,13437,3937,11987,12974,4277,3665,4690,3948,3983,4675,4678,4679,3432,3436,4677,4676,4444,3768,11852,4371,4706,10751,10754,4711,11220,11223,11413,11535,11572,4060,11569,11914,11918,12592,12600,12689,13239,3903,11146,11152,11172,12163,12289,12373,12657,3752,11290,11416,12399,12508,12518,12597,12652,12660,12774,13180,4234,3905,10885,11253,11422,11456,11467,12309,12596,12646,13279,3720,10801,10804,10894,11062,3719,4709,11853,4705,12942,4710,10757,11401,12461,12470,12514,12714,12717,4333,11023,12479,12494,12517,4240,3936,12780,3882,3883,4707,10493,10496,10843,10846,11736,11919,12726,4708,11833,11924,3906,10807,11068,13325,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509,5510,5511,5541,5542,5543,5551,5552,5553,5554,5595,5600,5602,5638,5640,5641,5643,5644,5646,5647,5649,5658,5663,5664,5666,5667,5668,5669,5670,5671,5680,5690,5693,5704,5720,5721,5724,5734,5736,5737,5738,5763,5773,5788,5789,5798,5799,5801,5803,5808,5843,5848,5850,5908,5942,5943,5948,5954,5957,5958,5959,5960,5978,5981,5982,5990,6011,6039,6058,6061,6062,6064,6073,6088,6092,6095,6096,6097,6115,6126,6127,6158,6159,6163,6184,6187,6190,6212,6213,6239,6242,6250,6260,6268,6272,6279,6280,6281,6282,6312,6329,6380,6418,6420,6441,6442,6448,6452,6453,6456,6470,6485,6506,6507,6510,6513,6523,6538,6559,6566,6568,6583,6584,6587,6588,6590,6592,6593,6594,6596,6598,6600,6605,6606,6608,6609,6615,6617,6622,6659,6664,6680,6682,6683,6684,6719,6724,6726,6731,6732,6740,6744,6757,6780,6781,6783,6784,6795,6800,6818,6821,6839,6869,6870,6871,6877,6891,6910,6912,6914,6916,6921,6927,6929,6943,6948,6949,6984,6985,6986,7000,7001,7003,7004,7023,7025,7042,7067,7089,7100,7102,7104,7106,7107,7141,7142,7145,7146,7153,7154,7156,7158,7180,7189,7190,7201,7211,7250,7260,7264,7271,7282,7287,7289,7296,7304,7305,7318,7335,7356,7358,7376,7428,7429,7430,7432,7434,7438,7443,7507,7536,7551,7556,7567,7599,7602,7625,7647,7665,7668,7669,7679,7699,7701,7703,7705,7706,7707,7732,7758,7759,7790,7792,7793,7794,7799,7822,7840,7845,7851,7853,7861,7873,7874,7876,7899,7906,7929,7995,7996,7997,8045,8051,8052,8076,8077,8094,8095,8096,8159,8160,8189,8219,8229,8240,8251,8283,8287,8293,8305,8323,8328,8351,8397,8427,8441,8460,8463,8489,8514,8580,8581,8584,8585,8659,8693,8694,8695,8696,8722,8754,8785,8792,8793,8834,8855,8899,8915,8961,8964,8979,8986,9029,9075,9076,9096,9097,9113,9238,9244,9248,9268,9279,9302,9304,9307,9313,9316,9317,9327,9328,9347,9353,9363,9371,9417,9434,9494,9495,9501,9540,9563,9569,9608,9618,9621,9622,9624,9625,9638,9662,9678,9692,9693,9697,9699,9729,9851,9852,9900,9901,9941,9977,10093,10151,10295,10311,10316,3,2791,2792,2793,2794,2798,2802,2804,2807,2808,2809,2810,2811,2813,2814,2815,2816,2817,2820,2821,2827,2828,2829,2830,2838,2839,2840,2841,2842,2845,2849,2850,2851,2855,2857,2861,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2883,2884,2885,2886,2890,2893,2894,2895,2914,2915,2917,2922,2923,2927,2929,2933,2935,2937,2942,2943,2945,2946,2953,2954,2966,2968,2969,2998,2999,3000,3022,3023,3024,3025,3026,3031,3032,5431,5469,5611,5612,5613,5691,5787,5817,5851,5867,5869,5875,5936,5937,5938,5939,5946,5980,6110,6147,6157,6181,6216,6251,6397,6402,6439,6440,6461,6463,6465,6472,6473,6474,6475,6476,6477,6478,6479,6561,6629,6630,6718,6751,6752,6792,6793,6928,6942,7012,7013,7020,7043,7073,7075,7121,7143,7144,7161,7162,7200,7244,7245,7342,7409,7410,7411,7412,7427,7459,7512,7513,7522,7527,7528,7539,7570,7571,7572,7573,7714,7716,7717,7718,7724,7725,7937,7943,7944,7954,7992,8115,8172,8194,8195,8211,8268,8365,8437,8438,8442,8475,8539,8540,8615,8635,8636,8637,8638,8788,9022,9048,9049,9130,9147,9202,9203,9324,9356,9381,9418,9462,9660,9794,9937,10120,10177,10180,10325,5757,6543,6544,6632,6652,6653,7064,7280,8424,8708,8955,9158,9159,9229,9230,9414,9512,9513,9514,9515,9732,9998,10012,10369,10370,6614,7508,7754,7755,8531,8532,9011,9030])). % 173.59/173.35 cnf(13446,plain, % 173.59/173.35 (E(f32(x134461,x134462,x134463,x134464,x134465,x134466,x134467,x134468,x134469,a25),x134462)), % 173.59/173.35 inference(rename_variables,[],[4606])). % 173.59/173.35 cnf(13512,plain, % 173.59/173.35 (P106(f333(f333(f247(a1),f2(a1)),f333(f82(a1),f85(a1))))), % 173.59/173.35 inference(scs_inference,[],[4717,4118,12679,12701,12851,12853,12855,3690,11305,12353,12452,12455,12547,12589,12593,12601,12673,12798,12800,13240,13250,13255,13259,13265,13268,13292,13402,13407,3698,12419,12900,12903,3707,3425,12820,12822,12824,3426,12915,3392,12755,4657,4658,11936,4393,12871,3429,12887,3265,3324,12812,3325,12831,3326,3327,3328,12629,12882,4656,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,12010,12327,12523,12733,12783,12785,12807,12816,12818,12826,12841,12843,12845,12859,12869,12880,12901,13119,13283,13316,13406,13411,13417,13421,13425,13439,13446,3754,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,11839,12142,12167,12179,12208,12214,12306,12415,12582,12643,13318,13322,3512,3475,12909,3658,12114,4634,10634,10728,11185,11285,13004,13342,3063,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3096,3097,3100,3101,3102,3104,3105,3107,3108,3109,3111,3113,3117,3120,3129,3136,3139,3140,3150,3151,3152,3154,3157,3161,3163,3166,3169,3190,3199,3205,3213,3217,3218,3219,3220,3228,3229,4617,3247,3323,4618,3794,4021,3437,3497,3413,3387,12614,12618,12622,3402,3508,3915,4222,3370,3523,12108,12676,12758,3288,3289,4007,11627,3511,12787,3355,3315,3773,3310,3418,4126,4015,3837,3297,3273,3277,3927,3334,3513,11033,11155,12416,12633,3386,4091,4647,10474,10631,11494,12574,12615,12619,4654,12586,3446,11959,11962,13209,13303,13372,13376,13380,13384,4050,4694,11211,11310,11538,11541,3856,12796,3441,3560,3779,3552,4672,3527,12849,3350,3351,10541,10852,4681,3612,3342,3268,3401,3372,11617,4236,12604,12745,4094,11231,11366,11425,12558,12564,12690,12693,12723,4712,11133,11377,11488,11511,11546,11552,12502,4713,11264,11380,11491,4714,11383,11436,4715,11443,4716,3371,3650,12458,12499,12585,13118,3821,3602,4507,4508,3634,3671,4645,11610,3798,3756,3800,4092,3972,3724,13102,13106,13110,13114,13124,4017,12449,3636,3898,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,12050,12138,12201,12277,12318,12393,12396,12727,12987,13026,13029,13085,13321,13326,3908,11856,3439,3536,11695,11974,13438,3717,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,12049,12253,12256,12339,12505,12608,12933,12952,12955,12979,13030,13186,13191,13216,13221,4700,11739,11766,11803,11836,13039,13043,3896,3659,13202,3660,12958,12961,12964,12967,12997,13000,13354,13358,13362,3662,4042,3624,13355,3625,13359,3484,3485,3459,4684,3349,4642,3847,4158,3643,4701,4229,11508,3778,3496,11981,11984,12423,12527,12704,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,12046,12607,4198,4157,12131,12473,4103,11030,12312,12483,12632,13375,4147,13379,4152,11234,12350,12422,12482,12526,13212,4153,3822,12141,12284,12360,12406,4122,4186,3839,11237,11315,11398,11462,12305,12374,12638,12700,12720,12730,13249,13254,13274,13295,4704,10980,11388,12486,13262,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,12009,12111,12166,12367,12530,3457,10936,10983,10986,11017,11039,11075,11113,11149,12182,12185,12188,12191,12381,12384,12387,12390,12466,12649,12696,12980,13003,13077,13088,13093,13096,13099,13132,13149,13201,13227,13230,3458,10645,10867,10959,11078,11775,12013,12022,12117,12128,12147,12152,12194,12217,12234,12994,13136,13156,13187,13192,13217,13222,13345,13418,13422,13426,3532,12342,13059,13103,13107,13111,13115,13125,13129,4683,10517,11001,11042,11051,11889,11911,12081,12084,12087,12090,12178,12197,12200,12213,12265,12268,12271,12274,12434,12437,12533,12536,12642,12682,12767,3609,10818,11086,11130,11369,11372,11451,11527,11699,11939,12581,12770,13176,13244,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,11990,12259,12262,12296,12343,12370,12511,12555,12561,12661,12664,12686,12744,12750,12761,12777,13058,13071,13074,13165,13245,13287,13306,13309,13351,13371,13405,3517,10849,10879,10888,10891,11480,11682,12683,12697,13040,13044,13047,3556,13335,13397,3549,3976,3913,10520,11859,11893,13021,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,12040,12069,12072,12075,12078,12338,13233,3477,10882,11036,11106,11863,11894,12039,12239,12442,12467,13068,13338,13437,3937,11987,12974,4277,3665,4690,3948,3983,4675,4678,4679,3432,3436,4677,4676,4444,3768,11852,4371,4706,10751,10754,4711,11220,11223,11413,11535,11572,4060,11569,11914,11918,12592,12600,12689,13239,3903,11146,11152,11172,12163,12289,12373,12657,3752,11290,11416,12399,12508,12518,12597,12652,12660,12774,13180,4234,3905,10885,11253,11422,11456,11467,12309,12596,12646,13279,3720,10801,10804,10894,11062,3719,4709,11853,4705,12942,4710,10757,11401,12461,12470,12514,12714,12717,4333,11023,12479,12494,12517,4240,3936,12780,3882,3883,4707,10493,10496,10843,10846,11736,11919,12726,4708,11833,11924,3906,10807,11068,13325,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509,5510,5511,5541,5542,5543,5551,5552,5553,5554,5595,5600,5602,5638,5640,5641,5643,5644,5646,5647,5649,5658,5663,5664,5666,5667,5668,5669,5670,5671,5680,5690,5693,5704,5720,5721,5724,5734,5736,5737,5738,5763,5773,5788,5789,5798,5799,5801,5803,5808,5843,5848,5850,5908,5942,5943,5948,5954,5957,5958,5959,5960,5978,5981,5982,5990,6011,6039,6058,6061,6062,6064,6073,6088,6092,6095,6096,6097,6115,6126,6127,6158,6159,6163,6184,6187,6190,6212,6213,6239,6242,6250,6260,6268,6272,6279,6280,6281,6282,6312,6329,6380,6418,6420,6441,6442,6448,6452,6453,6456,6470,6485,6506,6507,6510,6513,6523,6538,6559,6566,6568,6583,6584,6587,6588,6590,6592,6593,6594,6596,6598,6600,6605,6606,6608,6609,6615,6617,6622,6659,6664,6680,6682,6683,6684,6719,6724,6726,6731,6732,6740,6744,6757,6780,6781,6783,6784,6795,6800,6818,6821,6839,6869,6870,6871,6877,6891,6910,6912,6914,6916,6921,6927,6929,6943,6948,6949,6984,6985,6986,7000,7001,7003,7004,7023,7025,7042,7067,7089,7100,7102,7104,7106,7107,7141,7142,7145,7146,7153,7154,7156,7158,7180,7189,7190,7201,7211,7250,7260,7264,7271,7282,7287,7289,7296,7304,7305,7318,7335,7356,7358,7376,7428,7429,7430,7432,7434,7438,7443,7507,7536,7551,7556,7567,7599,7602,7625,7647,7665,7668,7669,7679,7699,7701,7703,7705,7706,7707,7732,7758,7759,7790,7792,7793,7794,7799,7822,7840,7845,7851,7853,7861,7873,7874,7876,7899,7906,7929,7995,7996,7997,8045,8051,8052,8076,8077,8094,8095,8096,8159,8160,8189,8219,8229,8240,8251,8283,8287,8293,8305,8323,8328,8351,8397,8427,8441,8460,8463,8489,8514,8580,8581,8584,8585,8659,8693,8694,8695,8696,8722,8754,8785,8792,8793,8834,8855,8899,8915,8961,8964,8979,8986,9029,9075,9076,9096,9097,9113,9238,9244,9248,9268,9279,9302,9304,9307,9313,9316,9317,9327,9328,9347,9353,9363,9371,9417,9434,9494,9495,9501,9540,9563,9569,9608,9618,9621,9622,9624,9625,9638,9662,9678,9692,9693,9697,9699,9729,9851,9852,9900,9901,9941,9977,10093,10151,10295,10311,10316,3,2791,2792,2793,2794,2798,2802,2804,2807,2808,2809,2810,2811,2813,2814,2815,2816,2817,2820,2821,2827,2828,2829,2830,2838,2839,2840,2841,2842,2845,2849,2850,2851,2855,2857,2861,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2883,2884,2885,2886,2890,2893,2894,2895,2914,2915,2917,2922,2923,2927,2929,2933,2935,2937,2942,2943,2945,2946,2953,2954,2966,2968,2969,2998,2999,3000,3022,3023,3024,3025,3026,3031,3032,5431,5469,5611,5612,5613,5691,5787,5817,5851,5867,5869,5875,5936,5937,5938,5939,5946,5980,6110,6147,6157,6181,6216,6251,6397,6402,6439,6440,6461,6463,6465,6472,6473,6474,6475,6476,6477,6478,6479,6561,6629,6630,6718,6751,6752,6792,6793,6928,6942,7012,7013,7020,7043,7073,7075,7121,7143,7144,7161,7162,7200,7244,7245,7342,7409,7410,7411,7412,7427,7459,7512,7513,7522,7527,7528,7539,7570,7571,7572,7573,7714,7716,7717,7718,7724,7725,7937,7943,7944,7954,7992,8115,8172,8194,8195,8211,8268,8365,8437,8438,8442,8475,8539,8540,8615,8635,8636,8637,8638,8788,9022,9048,9049,9130,9147,9202,9203,9324,9356,9381,9418,9462,9660,9794,9937,10120,10177,10180,10325,5757,6543,6544,6632,6652,6653,7064,7280,8424,8708,8955,9158,9159,9229,9230,9414,9512,9513,9514,9515,9732,9998,10012,10369,10370,6614,7508,7754,7755,8531,8532,9011,9030,9999,10368,4800,4801,4802,4852,4856,4861,5000,5047,5048,5079,5137,5198,5258,5310,5330,5369,5371,5378,5379,5403,5447,5477,5497,5627,5696,5697,5698,5813,5814])). % 173.59/173.35 cnf(13526,plain, % 173.59/173.35 (~P106(f333(f333(f247(a910),f333(a123,f333(f333(f87(a910),x135261),x135262))),f333(a123,x135261)))), % 173.59/173.35 inference(scs_inference,[],[4717,4118,12679,12701,12851,12853,12855,3690,11305,12353,12452,12455,12547,12589,12593,12601,12673,12798,12800,13240,13250,13255,13259,13265,13268,13292,13402,13407,3698,12419,12900,12903,3707,3425,12820,12822,12824,3426,12915,3392,12755,4657,4658,11936,4393,12871,3429,12887,3265,3324,12812,3325,12831,3326,3327,3328,12629,12882,4656,4606,10410,10427,10483,10486,10576,10579,10876,10899,11158,11161,11578,11581,11596,11599,11637,11644,11647,11650,11653,11663,11707,11723,11758,11763,11769,11864,11867,11870,11873,11876,11880,11890,11978,12010,12327,12523,12733,12783,12785,12807,12816,12818,12826,12841,12843,12845,12859,12869,12880,12901,13119,13283,13316,13406,13411,13417,13421,13425,13439,13446,3754,4622,10413,10420,10434,10445,10448,10549,10552,10555,10650,10773,11081,11275,11278,11297,11300,11497,11584,11591,11605,11656,11659,11696,11712,11772,11823,11839,12142,12167,12179,12208,12214,12306,12415,12582,12643,13318,13322,3512,3475,12909,3658,12114,4634,10634,10728,11185,11285,13004,13342,3063,3064,3068,3069,3071,3072,3076,3082,3083,3085,3093,3094,3096,3097,3100,3101,3102,3104,3105,3107,3108,3109,3111,3113,3117,3120,3129,3136,3139,3140,3150,3151,3152,3154,3157,3161,3163,3166,3169,3190,3199,3205,3213,3217,3218,3219,3220,3228,3229,4617,3247,3323,4618,3794,4021,3437,3497,3413,3387,12614,12618,12622,3402,3508,3915,4222,3370,3523,12108,12676,12758,3288,3289,4007,11627,3511,12787,3355,3315,3773,3310,3418,4126,4015,3837,3297,3273,3277,3927,3334,3513,11033,11155,12416,12633,3386,4091,4647,10474,10631,11494,12574,12615,12619,4654,12586,3446,11959,11962,13209,13303,13372,13376,13380,13384,4050,4694,11211,11310,11538,11541,3856,12796,3441,3560,3779,3552,4672,3527,12849,3350,3351,10541,10852,4681,3612,3342,3268,3401,3372,11617,4236,12604,12745,4094,11231,11366,11425,12558,12564,12690,12693,12723,4712,11133,11377,11488,11511,11546,11552,12502,4713,11264,11380,11491,4714,11383,11436,4715,11443,4716,3371,3650,12458,12499,12585,13118,3821,3602,4507,4508,3634,3671,4645,11610,3798,3756,3800,4092,3972,3724,13102,13106,13110,13114,13124,4017,12449,3636,3898,3524,10560,10670,10742,10812,10815,10855,10956,11201,11807,12050,12138,12201,12277,12318,12393,12396,12727,12987,13026,13029,13085,13321,13326,3908,11856,3439,3536,11695,11974,13438,3717,4687,10451,10454,10480,10964,10977,11091,11530,11620,11806,12025,12030,12049,12253,12256,12339,12505,12608,12933,12952,12955,12979,13030,13186,13191,13216,13221,4700,11739,11766,11803,11836,13039,13043,3896,3659,13202,3660,12958,12961,12964,12967,12997,13000,13354,13358,13362,3662,4042,3624,13355,3625,13359,3484,3485,3459,4684,3349,4642,3847,4158,3643,4701,4229,11508,3778,3496,11981,11984,12423,12527,12704,4692,10439,10442,10602,10691,10710,10717,10737,10745,10748,10762,10947,11188,11689,11782,11927,12043,12046,12607,4198,4157,12131,12473,4103,11030,12312,12483,12632,13375,4147,13379,4152,11234,12350,12422,12482,12526,13212,4153,3822,12141,12284,12360,12406,4122,4186,3839,11237,11315,11398,11462,12305,12374,12638,12700,12720,12730,13249,13254,13274,13295,4704,10980,11388,12486,13262,3456,10569,10657,10798,10862,11715,11722,11930,11943,11977,12009,12111,12166,12367,12530,3457,10936,10983,10986,11017,11039,11075,11113,11149,12182,12185,12188,12191,12381,12384,12387,12390,12466,12649,12696,12980,13003,13077,13088,13093,13096,13099,13132,13149,13201,13227,13230,3458,10645,10867,10959,11078,11775,12013,12022,12117,12128,12147,12152,12194,12217,12234,12994,13136,13156,13187,13192,13217,13222,13345,13418,13422,13426,3532,12342,13059,13103,13107,13111,13115,13125,13129,4683,10517,11001,11042,11051,11889,11911,12081,12084,12087,12090,12178,12197,12200,12213,12265,12268,12271,12274,12434,12437,12533,12536,12642,12682,12767,3609,10818,11086,11130,11369,11372,11451,11527,11699,11939,12581,12770,13176,13244,4696,11010,11020,11122,11140,11143,11214,11217,11228,11331,11339,11353,11391,11410,11419,11459,11500,11505,11521,11524,11555,11558,11563,11566,11956,11990,12259,12262,12296,12343,12370,12511,12555,12561,12661,12664,12686,12744,12750,12761,12777,13058,13071,13074,13165,13245,13287,13306,13309,13351,13371,13405,3517,10849,10879,10888,10891,11480,11682,12683,12697,13040,13044,13047,3556,13335,13397,3549,3976,3913,10520,11859,11893,13021,4693,10471,10837,10840,11334,11350,11822,11879,11915,11940,12040,12069,12072,12075,12078,12338,13233,3477,10882,11036,11106,11863,11894,12039,12239,12442,12467,13068,13338,13437,3937,11987,12974,4277,3665,4690,3948,3983,4675,4678,4679,3432,3436,4677,4676,4444,3768,11852,4371,4706,10751,10754,4711,11220,11223,11413,11535,11572,4060,11569,11914,11918,12592,12600,12689,13239,3903,11146,11152,11172,12163,12289,12373,12657,3752,11290,11416,12399,12508,12518,12597,12652,12660,12774,13180,4234,3905,10885,11253,11422,11456,11467,12309,12596,12646,13279,3720,10801,10804,10894,11062,3719,4709,11853,4705,12942,4710,10757,11401,12461,12470,12514,12714,12717,4333,11023,12479,12494,12517,4240,3936,12780,3882,3883,4707,10493,10496,10843,10846,11736,11919,12726,4708,11833,11924,3906,10807,11068,13325,4171,4726,4752,4806,4836,4851,4858,4860,4896,4901,4930,4936,5023,5049,5050,5065,5087,5115,5116,5138,5139,5152,5155,5180,5186,5202,5205,5206,5207,5212,5213,5236,5262,5263,5273,5278,5284,5322,5323,5331,5339,5343,5345,5360,5362,5368,5372,5373,5386,5392,5395,5396,5400,5434,5448,5456,5458,5459,5462,5463,5464,5474,5476,5480,5481,5482,5488,5492,5493,5494,5502,5506,5507,5512,5525,5533,5545,5547,5555,5559,5563,5589,5603,5604,5619,5631,5653,5659,5678,5679,5682,5701,5709,5710,5715,5716,5726,5728,5740,5744,5753,5754,5756,5771,5776,5785,5786,5797,5804,5818,5822,5825,5831,5832,5833,5836,5841,5877,5878,5881,5883,5886,5887,5888,5890,5892,5894,5899,5906,5921,5935,5940,5941,5944,5955,5956,5962,5965,5968,5973,6014,6026,6035,6038,6047,6051,6052,6053,6054,6055,6063,6074,6080,6098,6101,6113,6142,6156,6182,6199,6200,6203,6218,6220,6222,6224,6237,6238,6241,6243,6246,6247,6261,6269,6270,6271,6273,6275,6309,6310,6315,6318,6324,6328,6362,6364,6366,6368,6377,6379,6381,6387,6389,6395,6398,6406,6414,6416,6417,6423,6444,6445,6446,6447,6449,6455,6460,6493,6494,6497,6498,6499,6501,6502,6503,6504,6512,6545,6546,6547,6556,6578,6579,6599,6601,6612,6613,6619,6649,6651,6665,6669,6706,6708,6709,6762,6785,6826,6845,6854,6855,6856,6857,6875,6876,6883,6895,6898,6900,6902,6903,6904,6906,6920,6931,6932,6933,6946,6998,7009,7011,7015,7033,7034,7069,7081,7111,7198,7226,7281,7302,7311,7314,7373,7383,7442,7444,7458,7467,7468,7469,7488,7492,7494,7540,7550,7553,7568,7617,7619,7622,7663,7664,7682,7750,7768,7791,7816,7828,7843,7854,7865,7866,7894,7896,7898,7908,7946,7957,7982,8042,8074,8107,8152,8168,8170,8186,8187,8261,8327,8352,8357,8372,8399,8400,8439,8440,8457,8496,8498,8500,8506,8524,8528,8543,8566,8577,8579,8592,8597,8601,8602,8603,8604,8605,8606,8628,8642,8643,8661,8662,8667,8668,8669,8670,8671,8689,8690,8691,8700,8713,8716,8727,8732,8734,8736,8737,8738,8745,8751,8761,8764,8781,8782,8790,8791,8799,8818,8831,8835,8856,8877,8878,8881,8882,8888,8897,8898,8921,8932,8942,8943,8944,8947,8970,8971,8982,9032,9038,9044,9046,9064,9068,9079,9080,9081,9168,9199,9200,9201,9216,9233,9241,9242,9270,9271,9315,9340,9372,9386,9387,9388,9403,9430,9446,9453,9457,9481,9482,9509,9572,9577,9580,9612,9613,9614,9639,9640,9657,9680,9686,9705,9730,9752,9761,9762,9763,9764,9780,9782,9787,9817,9818,9824,9825,9869,9870,9880,9905,9925,9927,9928,9936,9947,9971,10004,10006,10010,10065,10108,10109,10111,10121,10122,10142,10147,10178,10241,10319,10320,10382,10396,2,8,9,4739,4740,4758,4795,4796,4798,4821,4829,4830,4840,4885,4887,4935,5066,5067,5080,5104,5158,5159,5165,5166,5168,5170,5179,5182,5183,5191,5203,5204,5210,5231,5232,5249,5254,5255,5256,5257,5261,5269,5272,5279,5309,5336,5341,5342,5347,5354,5383,5393,5398,5414,5432,5433,5440,5441,5442,5452,5470,5472,5473,5478,5485,5486,5498,5499,5500,5501,5508,5509,5510,5511,5541,5542,5543,5551,5552,5553,5554,5595,5600,5602,5638,5640,5641,5643,5644,5646,5647,5649,5658,5663,5664,5666,5667,5668,5669,5670,5671,5680,5690,5693,5704,5720,5721,5724,5734,5736,5737,5738,5763,5773,5788,5789,5798,5799,5801,5803,5808,5843,5848,5850,5908,5942,5943,5948,5954,5957,5958,5959,5960,5978,5981,5982,5990,6011,6039,6058,6061,6062,6064,6073,6088,6092,6095,6096,6097,6115,6126,6127,6158,6159,6163,6184,6187,6190,6212,6213,6239,6242,6250,6260,6268,6272,6279,6280,6281,6282,6312,6329,6380,6418,6420,6441,6442,6448,6452,6453,6456,6470,6485,6506,6507,6510,6513,6523,6538,6559,6566,6568,6583,6584,6587,6588,6590,6592,6593,6594,6596,6598,6600,6605,6606,6608,6609,6615,6617,6622,6659,6664,6680,6682,6683,6684,6719,6724,6726,6731,6732,6740,6744,6757,6780,6781,6783,6784,6795,6800,6818,6821,6839,6869,6870,6871,6877,6891,6910,6912,6914,6916,6921,6927,6929,6943,6948,6949,6984,6985,6986,7000,7001,7003,7004,7023,7025,7042,7067,7089,7100,7102,7104,7106,7107,7141,7142,7145,7146,7153,7154,7156,7158,7180,7189,7190,7201,7211,7250,7260,7264,7271,7282,7287,7289,7296,7304,7305,7318,7335,7356,7358,7376,7428,7429,7430,7432,7434,7438,7443,7507,7536,7551,7556,7567,7599,7602,7625,7647,7665,7668,7669,7679,7699,7701,7703,7705,7706,7707,7732,7758,7759,7790,7792,7793,7794,7799,7822,7840,7845,7851,7853,7861,7873,7874,7876,7899,7906,7929,7995,7996,7997,8045,8051,8052,8076,8077,8094,8095,8096,8159,8160,8189,8219,8229,8240,8251,8283,8287,8293,8305,8323,8328,8351,8397,8427,8441,8460,8463,8489,8514,8580,8581,8584,8585,8659,8693,8694,8695,8696,8722,8754,8785,8792,8793,8834,8855,8899,8915,8961,8964,8979,8986,9029,9075,9076,9096,9097,9113,9238,9244,9248,9268,9279,9302,9304,9307,9313,9316,9317,9327,9328,9347,9353,9363,9371,9417,9434,9494,9495,9501,9540,9563,9569,9608,9618,9621,9622,9624,9625,9638,9662,9678,9692,9693,9697,9699,9729,9851,9852,9900,9901,9941,9977,10093,10151,10295,10311,10316,3,2791,2792,2793,2794,2798,2802,2804,2807,2808,2809,2810,2811,2813,2814,2815,2816,2817,2820,2821,2827,2828,2829,2830,2838,2839,2840,2841,2842,2845,2849,2850,2851,2855,2857,2861,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2883,2884,2885,2886,2890,2893,2894,2895,2914,2915,2917,2922,2923,2927,2929,2933,2935,2937,2942,2943,2945,2946,2953,2954,2966,2968,2969,2998,2999,3000,3022,3023,3024,3025,3026,3031,3032,5431,5469,5611,5612,5613,5691,5787,5817,5851,5867,5869,5875,5936,5937,5938,5939,5946,5980,6110,6147,6157,6181,6216,6251,6397,6402,6439,6440,6461,6463,6465,6472,6473,6474,6475,6476,6477,6478,6479,6561,6629,6630,6718,6751,6752,6792,6793,6928,6942,7012,7013,7020,7043,7073,7075,7121,7143,7144,7161,7162,7200,7244,7245,7342,7409,7410,7411,7412,7427,7459,7512,7513,7522,7527,7528,7539,7570,7571,7572,7573,7714,7716,7717,7718,7724,7725,7937,7943,7944,7954,7992,8115,8172,8194,8195,8211,8268,8365,8437,8438,8442,8475,8539,8540,8615,8635,8636,8637,8638,8788,9022,9048,9049,9130,9147,9202,9203,9324,9356,9381,9418,9462,9660,9794,9937,10120,10177,10180,10325,5757,6543,6544,6632,6652,6653,7064,7280,8424,8708,8955,9158,9159,9229,9230,9414,9512,9513,9514,9515,9732,9998,10012,10369,10370,6614,7508,7754,7755,8531,8532,9011,9030,9999,10368,4800,4801,4802,4852,4856,4861,5000,5047,5048,5079,5137,5198,5258,5310,5330,5369,5371,5378,5379,5403,5447,5477,5497,5627,5696,5697,5698,5813,5814,5840,5844,5902,5904,5913,5919,5993])). % 173.59/173.35 cnf(13686,plain, % 173.59/173.35 (P106(f333(f333(f246(a910),f2(a910)),x136861))), % 173.59/173.35 inference(rename_variables,[],[3477])). % 173.59/173.35 cnf(13695,plain, % 173.59/173.35 (~E(f333(f333(f159(x136951),x136952),x136953),x136953)), % 173.59/173.35 inference(rename_variables,[],[4647])). % 173.59/173.35 cnf(13704,plain, % 173.59/173.35 (~E(f333(f333(f159(x137041),x137042),x137043),f124(x137041))), % 173.59/173.35 inference(rename_variables,[],[4654])). % 173.59/173.35 cnf(13707,plain, % 173.59/173.35 (~E(f333(f333(f159(x137071),x137072),x137073),x137073)), % 173.59/173.35 inference(rename_variables,[],[4647])). % 173.59/173.35 cnf(13729,plain, % 173.59/173.35 (P106(f333(f333(f246(f917(x137291,a905)),f333(f180(x137291),f184(x137291,x137292,x137293))),f333(f180(x137291),x137292)))), % 173.59/173.35 inference(rename_variables,[],[4152])). % 173.59/173.35 cnf(13735,plain, % 173.59/173.35 (P106(f333(f333(f246(f917(x137351,a905)),x137352),x137352))), % 173.59/173.35 inference(rename_variables,[],[3752])). % 173.59/173.35 cnf(13741,plain, % 173.59/173.35 (E(f333(x137411,f860(x137411,x137412,f333(x137411,x137413))),f333(x137411,x137413))), % 173.59/173.35 inference(rename_variables,[],[11169])). % 173.59/173.35 cnf(13744,plain, % 173.59/173.35 (E(f333(x137441,f860(x137441,x137442,f333(x137441,x137443))),f333(x137441,x137443))), % 173.59/173.35 inference(rename_variables,[],[11169])). % 173.59/173.35 cnf(13754,plain, % 173.59/173.35 (~P106(f333(f333(f247(a910),x137541),x137541))), % 173.59/173.35 inference(rename_variables,[],[4683])). % 173.59/173.35 cnf(13767,plain, % 173.59/173.35 (~P106(f333(f333(f335(a910),x137671),f333(f289(a910),f2(a910))))), % 173.59/173.35 inference(rename_variables,[],[12006])). % 173.59/173.35 cnf(13775,plain, % 173.59/173.35 (~P106(f333(f333(f335(x137751),x137752),f196(f917(x137751,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13780,plain, % 173.59/173.35 (P106(f333(f333(f246(f917(x137801,a905)),f333(f180(x137801),f184(x137801,x137802,x137803))),f333(f180(x137801),x137802)))), % 173.59/173.35 inference(rename_variables,[],[4152])). % 173.59/173.35 cnf(13783,plain, % 173.59/173.35 (~P106(f333(f333(f335(f916(x137831,x137831)),x137832),f253(x137831,f196(f917(x137831,a905)))))), % 173.59/173.35 inference(rename_variables,[],[11139])). % 173.59/173.35 cnf(13789,plain, % 173.59/173.35 (~P106(f333(f333(f335(x137891),x137892),f196(f917(x137891,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13792,plain, % 173.59/173.35 (~P106(f333(f333(f335(a910),x137921),f333(f289(a910),f2(a910))))), % 173.59/173.35 inference(rename_variables,[],[12006])). % 173.59/173.35 cnf(13795,plain, % 173.59/173.35 (~P106(f333(f333(f335(x137951),x137952),f196(f917(x137951,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13798,plain, % 173.59/173.35 (~E(f333(f333(f159(x137981),x137982),x137983),x137983)), % 173.59/173.35 inference(rename_variables,[],[4647])). % 173.59/173.35 cnf(13820,plain, % 173.59/173.35 (P106(f333(f333(f246(a910),x138201),f333(f333(f88(a910),x138201),x138201)))), % 173.59/173.35 inference(rename_variables,[],[3720])). % 173.59/173.35 cnf(13830,plain, % 173.59/173.35 (~P106(f333(f333(f335(x138301),x138302),f196(f917(x138301,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13835,plain, % 173.59/173.35 (~P106(f333(f333(f247(a910),x138351),x138351))), % 173.59/173.35 inference(rename_variables,[],[4683])). % 173.59/173.35 cnf(13838,plain, % 173.59/173.35 (~P106(f333(f333(f335(x138381),x138382),f196(f917(x138381,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13843,plain, % 173.59/173.35 (~E(f333(f333(f159(x138431),x138432),x138433),x138433)), % 173.59/173.35 inference(rename_variables,[],[4647])). % 173.59/173.35 cnf(13875,plain, % 173.59/173.35 (~P106(f333(f333(f335(f916(x138751,x138751)),x138752),f253(x138751,f196(f917(x138751,a905)))))), % 173.59/173.35 inference(rename_variables,[],[11139])). % 173.59/173.35 cnf(13883,plain, % 173.59/173.35 (~P106(f333(f333(f335(f916(x138831,x138831)),x138832),f253(x138831,f196(f917(x138831,a905)))))), % 173.59/173.35 inference(rename_variables,[],[11139])). % 173.59/173.35 cnf(13892,plain, % 173.59/173.35 (~E(f333(f333(f159(x138921),x138922),x138923),x138923)), % 173.59/173.35 inference(rename_variables,[],[4647])). % 173.59/173.35 cnf(13910,plain, % 173.59/173.35 (P106(f333(f333(f247(a1),f333(f333(f23(a1),x139101),f85(a1))),x139101))), % 173.59/173.35 inference(rename_variables,[],[10958])). % 173.59/173.35 cnf(13918,plain, % 173.59/173.35 (~P106(f333(f333(f335(f916(f911(x139181),f911(x139181))),f333(f333(f265(f911(x139181),f911(x139181)),x139182),f124(x139181))),f153(x139181,x139183)))), % 173.59/173.35 inference(rename_variables,[],[4712])). % 173.59/173.35 cnf(13923,plain, % 173.59/173.35 (~P106(f333(f333(f335(x139231),x139232),f196(f917(x139231,a905))))), % 173.59/173.35 inference(rename_variables,[],[4696])). % 173.59/173.35 cnf(13942,plain, % 173.59/173.35 (P106(f333(f333(f246(f917(x139421,a905)),f333(f180(x139421),f184(x139421,x139422,x139423))),f333(f180(x139421),x139422)))), % 173.59/173.35 inference(rename_variables,[],[4152])). % 173.59/173.35 cnf(13997,plain, % 173.59/173.35 ($false), % 173.59/173.35 inference(scs_inference,[],[4717,4198,4236,3459,4709,3457,4684,4094,3532,4712,13918,3549,3908,4060,4696,13775,13789,13795,13830,13838,13923,4152,13729,13780,13942,4647,13695,13707,13798,13843,13892,4654,13704,3536,4103,3913,3477,13686,3903,3752,13735,3905,3720,13820,3906,4606,3401,4714,4716,4683,13754,13835,4706,4705,4710,11751,13328,12066,11976,13512,10734,10791,11397,13442,10958,13910,12769,11085,11124,11421,11169,13741,13744,11574,11543,10898,3514,13526,10903,12401,12507,12004,12006,13767,13792,10911,11139,13783,13875,13883,11142,11469,10893,11000,12267,11157,3115,4008,9,5603,6377,6416,7617,8439,8791,6270,6902,5840,5716,6142,5682,5137,7492,5480,10010,6055,7982,7663,8643,5797,9705,10108,4801,4856,5448,5589,7033,5563,9686,7034,7130,9572,6946,6074,6998,8700,6222,8970,9032,8579,9612,9880,10122,5463,6038,6379,6512,9446,8691,5474,5497,5547,5825,6895,5902,7302,5323,6875,7311,7619,9818,5079,5756,6364,5940,6273,8170,5679,6200,7750,7894,8897,5678,5322,5906,6933,8601,8661,10241,9680,6883,6876,4936,6708,9817,6856,8261,9386,5458,5754,7816,9403,10147,6854,5116,5310,6398,6904,6460,8496,6328,8642,8971,7009,9081,7866,5631,5888,8732,5482,7442,8736,8877,9905,6445,5904,5395,5477,5935,6063,9869,6920,9201,5330,4836]), % 173.59/173.35 ['proof']). % 173.59/173.35 % SZS output end Proof % 173.59/173.35 % Total time :159.030000s %------------------------------------------------------------------------------